@article{A.Manz2019,
  title = {New Scaling Relations to Compute Atom-in-Material Polarizabilities and Dispersion Coefficients: Part 1. {{Theory}} and Accuracy},
  shorttitle = {New Scaling Relations to Compute Atom-in-Material Polarizabilities and Dispersion Coefficients},
  author = {A.~Manz, Thomas and Chen, Taoyi and J.~Cole, Daniel and Gabaldon~Limas, Nidia and Fiszbein, Benjamin},
  year = {2019},
  journal = {RSC Adv.},
  volume = {9},
  number = {34},
  pages = {19297--19324},
  publisher = {Royal Society of Chemistry},
  doi = {10.1039/C9RA03003D},
  urldate = {2024-06-06},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/A2RS83GT/A. Manz et al_2019_New scaling relations to compute atom-in-material polarizabilities and.pdf}
}

@article{Allehabi2022,
  title = {High-Accuracy Optical Clocks Based on Group-16-like Highly Charged Ions},
  author = {Allehabi, Saleh O. and Brewer, S. M. and Dzuba, V. A. and Flambaum, V. V. and Beloy, K.},
  year = {2022},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {106},
  number = {4},
  pages = {043101},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.106.043101},
  urldate = {2024-06-10},
  abstract = {We identify laser-accessible transitions in group-16-like highly charged ions as candidates for high-accuracy optical clocks, including S-, Se-, and Te-like systems. For this class of ions, the ground 3{$PJ$} fine-structure manifold exhibits irregular (nonmonotonic in {$J$}) energy ordering for large enough ionization degree. We consider the {\textbar}3{$P$}2{$\rangle\longleftrightarrow\vert$}⁢3{$P$}0{$\rangle$} (ground to first-excited state) electric quadrupole transition, performing relativistic many-body calculations of several atomic properties important for optical clock development. All ions discussed are suitable for production in small-scale ion sources and lend themselves to sympathetic cooling and quantum-logic readout with singly charged ions.},
  file = {/Users/yingxing/Zotero/storage/KV5ZE6AI/Allehabi et al_2022_High-accuracy optical clocks based on group-16-like highly charged ions.pdf}
}

@article{Alpher1959,
  title = {Optical {{Refractivity}} of {{High-Temperature Gases}}. {{I}}. {{Effects Resulting}} from {{Dissociation}} of {{Diatomic Gases}}},
  author = {Alpher, Ralph A. and White, Donald R.},
  year = {1959},
  journal = {Phys. Fluids},
  volume = {2},
  number = {2},
  pages = {153},
  issn = {00319171},
  doi = {10.1063/1.1705906},
  abstract = {Shock-tube and discharge techniques make it possible to generate in the laboratory significant volumes of dissociated and/or ionized gases. This paper describes some studies of the optical index of refraction {$\mu$} of dissociated diatomic gases. The physical interpretation of specific refractivity K = ({$\mu$} - 1)/{$\rho$} is discussed and related to polarizability, and various methods of computing such quantities are reviewed briefly. Shock-tube experiments are described in which optical interferometry has been utilized to measure the polarizability of atomic oxygen and nitrogen with the result {$\alpha$}-(O I) = 0.77 {\textpm} 0.06 A3 and {$\alpha$}-(N I) = 1.13 {\textpm} 0.06 A3. The use of optical interferometry for determination of gas density has been justified for experiments involving air at temperatures to at least 5000{$^\circ$}K.},
  file = {/Users/yingxing/Zotero/storage/ZMCGCHXH/Alpher_White_1959_Optical Refractivity of High‐Temperature Gases.pdf}
}

@article{Amini2003,
  title = {High {{Precision Measurement}} of the {{Static Dipole Polarizability}} of {{Cesium}}},
  author = {Amini, Jason M. and Gould, Harvey},
  year = {2003},
  month = oct,
  journal = {Phys. Rev. Lett.},
  volume = {91},
  number = {15},
  pages = {153001},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.91.153001},
  urldate = {2024-06-05},
  abstract = {The cesium 62⁢{$S$}1/2 scalar dipole polarizability {$A$}0 has been determined from the time-of-flight of laser cooled and launched cesium atoms traveling through an electric field. We find {$A$}0=6.611{\textpm}0.009{\texttimes}10-39 C m2/V=59.42{\textpm}0.08{\texttimes}10-24 c⁢m3=401.0{\textpm}0.6⁢{$a$}30. The 0.14\% uncertainty is a factor of 14 improvement over the previous measurement. Values for the 62⁢{$P$}1/2 and 62⁢{$P$}3/2 lifetimes and the 62⁢{$S$}1/2 cesium-cesium dispersion coefficient {$C$}6 are determined from {$A$}0 using the procedure of Derevianko and Porsev [Phys. Rev. A 65, 053403 (2002)].},
  file = {/Users/yingxing/Zotero/storage/CNQSFGD7/Amini_Gould_2003_High Precision Measurement of the Static Dipole Polarizability of Cesium.pdf}
}

@article{Andersson1992,
  title = {Electric Dipole Polarizabilities of Atomic Valence States},
  author = {Andersson, Kerstin and Sadlej, Andrzej J.},
  year = {1992},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {46},
  number = {5},
  pages = {2356--2362},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.46.2356},
  urldate = {2024-06-12},
  abstract = {The second-order perturbation method for single-state multireference wave functions generated in complete-active-space self-consistent-field (CASSCF) calculations has been employed for computing electric dipole polarizabilities of different valence-electronic states of the first- (C,N,O,F) and second-row (Si,P,S,Cl) atoms. The results of calculations with polarized basis functions provide a uniform set of accurate polarizability data for those systems. Also, atomic quadrupole moment values obtained by using the CASSCF method are presented.},
  file = {/Users/yingxing/Zotero/storage/PPZREMTU/Andersson_Sadlej_1992_Electric dipole polarizabilities of atomic valence states.pdf}
}

@article{Aoki2021,
  title = {Quantum Sensing of the Electron Electric Dipole Moment Using Ultracold Entangled {{Fr}} Atoms},
  author = {Aoki, T. and Sreekantham, R. and Sahoo, B. K. and Arora, Bindiya and Kastberg, A. and Sato, T. and Ikeda, H. and Okamoto, N. and Torii, Y. and Hayamizu, T. and Nakamura, K. and Nagase, S. and Ohtsuka, M. and Nagahama, H. and Ozawa, N. and Sato, M. and Nakashita, T. and Yamane, K. and Tanaka, K. S. and Harada, K. and Kawamura, H. and Inoue, T. and Uchiyama, A. and Hatakeyama, A. and Takamine, A. and Ueno, H. and Ichikawa, Y. and Matsuda, Y. and Haba, H. and Sakemi, Y.},
  year = {2021},
  month = sep,
  journal = {Quantum Sci. Technol.},
  volume = {6},
  number = {4},
  pages = {044008},
  publisher = {IOP Publishing},
  issn = {2058-9565},
  doi = {10.1088/2058-9565/ac1b6a},
  urldate = {2024-06-11},
  abstract = {We propose a method to measure the electron electric dipole moment (eEDM) using ultracold entangled francium (Fr) atoms trapped in an optical lattice, yielding an uncertainty below the standard quantum limit. Among the alkali atoms, Fr offers the largest enhancement factor to the eEDM. With a Fr based experiment, quantum sensing using quantum entangled states could enable a search for the eEDM at a level below 10-30 ecm. We estimate statistical and systematic errors attached to the proposed measurement scheme based on this quantum sensing technique. A successful quantum sensing of the eEDM could enable the exploration of new physics beyond the standard model of particle physics.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/TH9S6AY2/Aoki et al_2021_Quantum sensing of the electron electric dipole moment using ultracold.pdf}
}

@article{Archibong1991,
  title = {Finite-Field Many-Body-Perturbation-Theory Calculation of the Static Hyperpolarizabilities and Polarizabilities of {{Mg}}, \$\{{\textbackslash}mathrm\{\vphantom{\}\}}{{Al}}\vphantom\{\}\vphantom\{\}{\textasciicircum}\{+\}\$, and {{Ca}}},
  author = {Archibong, Edet F. and Thakkar, Ajit J.},
  year = {1991},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {44},
  number = {9},
  pages = {5478--5484},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.44.5478},
  urldate = {2023-03-20},
  abstract = {The dipole-dipole-quadrupole (B) and second dipole ({$\gamma$}) hyperpolarizabilities and the dipole ({$\alpha$}1) and quadrupole ({$\alpha$}2) polarizabilities are calculated for the ground states of the magnesium and calcium atoms and the aluminum cation. The results are based on finite-field fourth-order many-body perturbation theory using a finite-field self-consistent-field wave function as the zeroth-order wave function. Our fourth-order results are {$\alpha$}1=71.7e2a20E-1H, {$\alpha$}2=809e2a40E-1H, B=(-7.75{\texttimes}103)e3a40E-2H, and {$\gamma$} =(1.02{\texttimes}105)e4a40E-3H for Mg; {$\alpha$}1=24.2e2a20E-1H, {$\alpha$}2=124e2a40E-1H, B=-642e3a40E-2H, and {$\gamma$}=(2.37 {\texttimes}103)e4a40E-3H for Al+; and {$\alpha$}1=157e2a20E-1H, {$\alpha$}2=(3.02{\texttimes}103)e2a40E-1H, B=(-3.29{\texttimes}104)e3a40E-2H, and {$\gamma$}=(3.83{\texttimes}105)e4a40E-3H for Ca.},
  file = {/Users/yingxing/Zotero/storage/73BCRDWJ/Finite-field many-body-perturbation-theory calculation of the static hyperpolarizabilities and polarizabilities of Mg, Al, and Ca_1991.pdf}
}

@article{Assadollahzadeh2009,
  title = {{Electronic properties for small tin clusters Snn (n {$\leq$} 20) from density functional theory and the convergence toward the solid state}},
  author = {Assadollahzadeh, Behnam and Sch{\"a}fer, Sascha and Schwerdtfeger, Peter},
  year = {2010},
  journal = {J. Comput. Chem.},
  volume = {31},
  number = {5},
  pages = {929--937},
  issn = {1096-987X},
  doi = {10.1002/jcc.21381},
  urldate = {2024-06-12},
  abstract = {Global minimum structures of neutral tin clusters with up to 20 atoms obtained recently from genetic algorithm simulations within a density-functional approach (Sch{\"a}fer et al., J Phys Chem A 2008, 112, 12312) were used to evaluate the corresponding electronic properties. The evolution of these properties with increasing cluster size is discussed in detail and compared with the lighter silicon and germanium clusters. We also discuss the extrapolation of these properties to the bulk limit. {\copyright} 2009 Wiley Periodicals, Inc. J Comput Chem, 2010},
  copyright = {Copyright {\copyright} 2009 Wiley Periodicals, Inc.},
  langid = {ngerman},
  keywords = {density functional theory,electronic properties,polarizability,solid state,tin cluster},
  file = {/Users/yingxing/Zotero/storage/WGFZRQ8B/Assadollahzadeh et al_2010_Electronic properties for small tin clusters Snn (n ≤ 20) from density.pdf}
}

@article{Badhan2022,
  title = {Assessing Slowdown Times Due to Blackbody Friction Forces for High-Precision Experiments},
  author = {Badhan, Vipul and Kaur, Simranpreet and Arora, Bindiya and Sahoo, B. K.},
  year = {2022},
  month = dec,
  journal = {Eur. Phys. J. D},
  volume = {76},
  number = {12},
  pages = {252},
  issn = {1434-6079},
  doi = {10.1140/epjd/s10053-022-00585-2},
  urldate = {2024-06-10},
  abstract = {We probe roles of blackbody friction forces (BBFFs) in slowing down alkali atoms, from Li through Fr, for high-precision measurements. An atom can encounter BBFF caused by the blackbody. We probe roles of blackbody friction radiations of the stray electromagnetic fields present in experimental set-up and other metallic shielding during measurements. Strengths of BBFFs on the alkali atoms are estimated by integrating complex parts of dynamic polarizabilities of atoms over a wide range of frequency. Slowdown times of moving atoms due to these friction forces are analysed as a function of temperature. The results are determined by both including and excluding nonresonant contributions in the polarizabilities of atomic states. This shows that inclusion of nonresonant contributions affects the slowdown time of atoms significantly at low temperatures. Our study will be useful in accounting for these slowdown times in the ongoing and future high-precision experiments involving alkali atoms.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/6LBZZBBX/Badhan et al_2022_Assessing slowdown times due to blackbody friction forces for high-precision.pdf}
}

@article{Bala2019,
  title = {Ab Initio Calculations of Permanent Dipole Moments and Dipole Polarizabilities of Alkaline-Earth Monofluorides},
  author = {Bala, Renu and Nataraj, H. S. and Nayak, Malaya K.},
  year = {2019},
  month = mar,
  journal = {J. Phys. B: At. Mol. Opt. Phys.},
  volume = {52},
  number = {8},
  pages = {085101},
  publisher = {IOP Publishing},
  issn = {0953-4075},
  doi = {10.1088/1361-6455/ab0e26},
  urldate = {2024-06-06},
  abstract = {The ground-state permanent dipole moments (PDMs) and molecular dipole polarizabilities (DPs) of open-shell alkaline-earth monofluorides, and atomic DPs of alkaline-earth- and fluorine atoms are reported at the Kramers-restricted configuration interaction level of theory limited to single and double excitations (KRCISD), using the finite-field approach. Sufficiently large basis sets such as quadrupole-zeta (QZ) and augmented-QZ basis sets together with the generalized active space technique is employed to carry out the field-dependent energy calculations at the KRCISD level. The PDMs and the components of DPs are extracted from the linear- and quadratic fit of energies against perturbative electric field, respectively. Accuracy of the present calculations for the electronic properties is examined by comparison with the measurements and calculations where ever available.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/7JN6ZI5D/Bala et al_2019_Ab initio calculations of permanent dipole moments and dipole polarizabilities.pdf}
}

@article{Bardon1984,
  title = {{{THE POLARISABILITY OF IRIDIUM NEUTRAL ATOMS AND THEIR VAN DER WAALS INTERACTION WITH A TUNGSTEN SURFACE MEASURED BY F}}.{{I}}.{{M}}},
  author = {Bardon, J. and Audiffren, M.},
  year = {1984},
  month = dec,
  journal = {J. Phys. Colloques},
  volume = {45},
  number = {C9},
  pages = {C9-249},
  publisher = {EDP Sciences},
  issn = {0449-1947, 2777-3418},
  doi = {10.1051/jphyscol:1984941},
  urldate = {2024-06-12},
  abstract = {Suppl{\'e}ment au Journal de Physique Colloques, Journal de Physique Archives repr{\'e}sente une mine dinformations facile {\`a} consulter sur la mani{\`e}re dont la physique a {\'e}t{\'e} publi{\'e}e depuis 1872.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/8D9IE8JQ/Bardon_Audiffren_1984_THE POLARISABILITY OF IRIDIUM NEUTRAL ATOMS AND THEIR VAN DER WAALS INTERACTION.pdf}
}

@article{Bast2008,
  title = {Static and Frequency-dependent Dipole--Dipole Polarizabilities of All Closed-shell Atoms up to Radium: A Four-component Relativistic {{DFT}} Study},
  author = {Bast, Radovan and He{\ss}elmann, Andreas and Sa{\l}ek, Pawe{\l} and Helgaker, Trygve and Saue, Trond},
  year = {2008},
  month = feb,
  journal = {ChemPhysChem},
  volume = {9},
  number = {3},
  pages = {445--453},
  publisher = {Wiley},
  issn = {1439-7641},
  doi = {10.1002/cphc.200700504}
}

@article{Becher2018,
  title = {Anisotropic Polarizability of Erbium Atoms},
  author = {Becher, J. H. and Baier, S. and Aikawa, K. and Lepers, M. and Wyart, J.-F. and Dulieu, O. and Ferlaino, F.},
  year = {2018},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {97},
  number = {1},
  pages = {012509},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.97.012509},
  urldate = {2024-06-12},
  abstract = {We report on the determination of the dynamical polarizability of ultracold erbium atoms in the ground and in one excited state at three different wavelengths, which are particularly relevant for optical trapping. Our study combines experimental measurements of the light shift and theoretical calculations. In particular, our experimental approach allows us to isolate the different contributions to the polarizability, namely, the isotropic scalar and anisotropic tensor part. For the latter contribution, we observe a clear dependence of the atomic polarizability on the angle between the laser-field-polarization axis and the quantization axis, set by the external magnetic field. Such an angle dependence is particularly pronounced in the excited-state polarizability. We compare our experimental findings with the theoretical values, based on semiempirical electronic structure calculations, and we observe a very good overall agreement. Our results pave the way to exploit the anisotropy of the tensor polarizability for spin-selective preparation and manipulation.},
  file = {/Users/yingxing/Zotero/storage/3A4DCFCF/Becher et al_2018_Anisotropic polarizability of erbium atoms.pdf}
}

@article{Beloy2012,
  title = {Experimental Constraints on the Polarizabilities of the \$6\{s\}{\textasciicircum}\{2\}\$ \$\{\}{\textasciicircum}\{1\}{\textbackslash}phantom\{{\textbackslash}rule\{-0.16em\}\{0ex\}\}\{\vphantom\}{{S}}\vphantom\{\}\_\{0\}\$ and \$6s6p\$ \$\{\}{\textasciicircum}\{3\}{\textbackslash}phantom\{{\textbackslash}rule\{-0.16em\}\{0ex\}\}\{\vphantom\}{{P}}\vphantom\{\}\_\{0\}{\textasciicircum}\{o\}\$ States of {{Yb}}},
  author = {Beloy, K.},
  year = {2012},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {86},
  number = {2},
  pages = {022521},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.86.022521},
  urldate = {2024-06-12},
  abstract = {We utilize accurate experimental data available in the literature to yield bounds on the polarizabilities of the ground and first-excited states of atomic Yb. For the 6⁢{$s$}2⁢1{$S$}0 ground state, we find the polarizability to be constrained to in atomic units while for the excited state, we find . The uncertainty in each of these values is 1.0. These constraints provide a valuable check for ab initio and semiempirical methods used to compute polarizabilities and other related properties in Yb.},
  file = {/Users/yingxing/Zotero/storage/6JNAFMMD/Beloy_2012_Experimental constraints on the polarizabilities of the $6 s ^ 2 $.pdf}
}

@article{Bendazzoli2004,
  title = {A {{Davidson}} Technique for the Computation of Dispersion Constants: {{Full CI}} Results for {{Be}} and {{LiH}}},
  shorttitle = {A {{Davidson}} Technique for the Computation of Dispersion Constants},
  author = {Bendazzoli, Gian Luigi and Monari, Antonio},
  year = {2004},
  month = nov,
  journal = {Chem. Phys.},
  volume = {306},
  number = {1},
  pages = {153--161},
  issn = {0301-0104},
  doi = {10.1016/j.chemphys.2004.07.023},
  urldate = {2023-03-20},
  abstract = {We describe a method to expand the London formula for dispersion constants in pseudostates obtained from an iterative subspace recursively generated by a procedure inspired by Davidson's algorithm for eigenvectors. The technique proved to be successful and, in the cases we have examined, computationally advantageous over numerical integration of the Casimir Polder formula. We present Full CI results for Be and LiH in extended AO bases.},
  langid = {english},
  keywords = {Ab initio calculations,Be,Direct full CI,Dispersion constants,LiH},
  file = {/Users/yingxing/Zotero/storage/GXZJ9YW5/A Davidson technique for the computation of dispersion constants Full CI results for Be and LiH_2004.pdf}
}

@article{Bezchastnov2010,
  title = {Nonadditivity and Anisotropy of the Polarizability of Clusters: {{Relativistic}} Finite-Field Calculations for the {{Xe}} Dimer},
  shorttitle = {Nonadditivity and Anisotropy of the Polarizability of Clusters},
  author = {Bezchastnov, Victor G. and Pernpointner, Markus and Schmelcher, Peter and Cederbaum, Lorenz S.},
  year = {2010},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {81},
  number = {6},
  pages = {062507},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.81.062507},
  urldate = {2024-06-06},
  abstract = {We present all-electron relativistic studies of the polarizability properties of the Xe dimer. The studies rely on finite-field calculations of the dimer energies obtained by ab initio methods including electron correlations. An extended set of basis functions is designed in order to ensure a high accuracy of the calculations. Particular attention is paid to the analysis of the nonadditivity and anisotropy of the polarizability of the dimer. It is found that the polarizability of the dimer relative to that of the atoms can be accurately described analytically, at least for internuclear distances around and larger than the equilibrium distance of the dimer.},
  file = {/Users/yingxing/Zotero/storage/QVG2999G/Bezchastnov et al_2010_Nonadditivity and anisotropy of the polarizability of clusters.pdf}
}

@article{Borschevsky2012,
  title = {Precision of Calculated Static Polarizabilities: {{Ga}}, {{In}} and {{Tl}} Atoms},
  shorttitle = {Precision of Calculated Static Polarizabilities},
  author = {Borschevsky, Anastasia and Zelovich, Tamar and Eliav, Ephraim and Kaldor, Uzi},
  year = {2012},
  month = feb,
  journal = {Chem. Phys.},
  series = {Recent {{Advances}} and {{Applications}} of {{Relativistic Quantum Chemistry}}},
  volume = {395},
  pages = {104--107},
  issn = {0301-0104},
  doi = {10.1016/j.chemphys.2011.05.011},
  urldate = {2023-03-21},
  abstract = {The static dipole polarizabilities of the group 13 elements Ga, In and Tl in the three 2PJMJ substates are calculated by the Fock space coupled cluster method. The ground 2P1/2 states are also studied by the single reference coupled cluster approach, with triple excitations included perturbatively. Very large basis sets are employed and extended to convergence. The effects of different parameters in the calculation (2- vs.4-component Hamiltonian, basis sets, coupled cluster expansion) are explored. The effect of the Gaunt interaction, which approximates the lowest order relativistic correction to the two-electron interaction, is also studied. Error bounds are estimated at 3\% for the ground states and 5\% for the J=3/2 states. The final recommended values for the ground states are {$\alpha$}(Ga)=51.1(1.5) a.u., {$\alpha$}(In)=62.0(1.9) a.u., and {$\alpha$}(Tl)=52.1(1.6) a.u. The last two are in agreement with the experimental {$\alpha$}(In)=69(8) a.u. and {$\alpha$}(Tl)=51(7) a.u., and have error bars 4 times smaller. No experimental value is available for Ga, and the present calculations provide the first error bars for this element.},
  langid = {english},
  keywords = {Coupled cluster methods,Ga,In,Polarizabilities,Tl},
  file = {/Users/yingxing/Zotero/storage/ISFBC2BK/Precision of calculated static polarizabilities Ga, in and Tl atoms_2012.pdf}
}

@article{Borschevsky2013,
  title = {Ab Initio Studies of Atomic Properties and Experimental Behavior of Element 119 and Its Lighter Homologs},
  author = {Borschevsky, A. and Pershina, V. and Eliav, E. and Kaldor, U.},
  year = {2013},
  month = mar,
  journal = {The Journal of Chemical Physics},
  volume = {138},
  number = {12},
  pages = {124302},
  issn = {0021-9606},
  doi = {10.1063/1.4795433},
  urldate = {2024-06-12},
  abstract = {Static dipole polarizabilities of element 119 and its singly charged cation are calculated, along with those of its lighter homologs, Cs and Fr. Relativity is treated within the 4-component Dirac-Coulomb formalism and electron correlation is included by the single reference coupled cluster approach with single, double, and perturbative triple excitations (CCSD(T)). Very good agreement with available experimental values is obtained for Cs, lending credence to the predictions for Fr and element 119. The atomic properties in group-1 are largely determined by the valence ns orbital, which experiences relativistic stabilization and contraction in the heavier elements. As a result, element 119 is predicted to have a relatively low polarizability (169.7 a.u.), comparable to that of Na. The adsorption enthalpy of element 119 on Teflon, which is important for possible future experimental studies of this element, is estimated as 17.6 kJ/mol, the lowest among the atoms considered here.},
  file = {/Users/yingxing/Zotero/storage/BFSF338E/Borschevsky et al_2013_Ab initio studies of atomic properties and experimental behavior of element 119.pdf}
}

@article{Borschevsky2013a,
  title = {Ab Initio Predictions of Atomic Properties of Element 120 and Its Lighter Group-2 Homologues},
  author = {Borschevsky, A. and Pershina, V. and Eliav, E. and Kaldor, U.},
  year = {2013},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {87},
  number = {2},
  pages = {022502},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.87.022502},
  urldate = {2024-06-12},
  abstract = {The ionization potentials, excitation energies, and electron affinity of superheavy element 120 and the polarizabilities of its neutral and ionized states are calculated. Relativity is treated within the four-component Dirac-Coulomb formalism; Breit or Gaunt terms are added in some cases. Electron correlation is included via the intermediate Hamiltonian Fock-space coupled cluster method for the spectra and ionization potentials and via the single reference coupled cluster singles and doubles with perturbative triples [CCSD(T)] approach for the electron affinities and polarizabilities. To assess the accuracy of the results, the atomic properties of the lighter homologues, Ba and Ra, are also calculated. Very good agreement with available experimental values is obtained, lending credence to the predictions for element 120. The atomic properties in group 2 are largely determined by the valence orbital, which experiences relativistic stabilization and contraction in the heavier group-2 elements. As a result, element 120 is predicted to have a relatively high ionization potential (5.851 eV), similar to that of Sr, and rather low electron affinity (0.021 eV) and polarizability (163 a.u.), comparable to those of Ca. The adsorption enthalphy of element 120 on Teflon, which is important for possible future experiments on this atom, is estimated as 35.4 kJ/mol, the lowest among the elements considered here.},
  file = {/Users/yingxing/Zotero/storage/CJ33APIV/Borschevsky et al_2013_Ab initio predictions of atomic properties of element 120 and its lighter.pdf}
}

@article{Borschevsky2015,
  title = {High-Accuracy Coupled Cluster Calculations of Atomic Properties},
  author = {Borschevsky, A. and Yakobi, H. and Eliav, E. and Kaldor, U.},
  year = {2015},
  month = jan,
  journal = {AIP Conference Proceedings},
  volume = {1642},
  number = {1},
  pages = {209--212},
  issn = {0094-243X},
  doi = {10.1063/1.4906654},
  urldate = {2024-06-11},
  abstract = {The four-component Fock-space coupled cluster and intermediate Hamiltonian methods are implemented to evaluate atomic properties. The latter include the spectra of nobelium and lawrencium (elements 102 and 103) in the range 20000-30000 cm-1, the polarizabilities of elements 112-114 and 118, required for estimating their adsorption enthalpies on surfaces used to separate them in accelerators, and the nuclear quadrupole moments of some heavy atoms. The calculations on superheavy elements are supported by the very good agreement with experiment obtained for the lighter homologues.}
}

@article{Brinck1993,
  title = {Polarizability and Volume},
  author = {Brinck, Tore and Murray, Jane S. and Politzer, Peter},
  year = {1993},
  month = mar,
  journal = {The Journal of Chemical Physics},
  volume = {98},
  number = {5},
  pages = {4305--4306},
  issn = {0021-9606},
  doi = {10.1063/1.465038},
  urldate = {2024-06-12},
  file = {/Users/yingxing/Zotero/storage/WF9AX5D9/Brinck et al_1993_Polarizability and volume.pdf}
}

@article{Bromley2002,
  title = {Configuration-Interaction Calculations of Positron Binding to Group-{{II}} Elements},
  author = {Bromley, M. W. J. and Mitroy, J.},
  year = {2002},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {65},
  number = {6},
  pages = {062505},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.65.062505},
  urldate = {2023-03-20},
  abstract = {The configuration-interaction (CI) method is applied to the study of positronic magnesium (e+Mg), positronic calcium (e+Ca), and positronic strontium (e+Sr). The CI expansion was seen to converge slowly with respect to Lmax, the maximum angular momentum of any orbital used to construct the CI basis. Despite doing explicit calculations with Lmax=10, extrapolation corrections to the binding energies for the Lmax{$\rightarrow\infty$} limit were substantial in the case of e+Ca (25\%) and e+Sr (50\%). The extrapolated binding energies were 0.0162 hartree for e+Mg, 0.0165 hartree for e+Ca, and 0.0101 hartree for e+Sr. The static-dipole polarizabilities for the neutral parent atoms were computed as a by-product, giving 71.7a30, 162a30, and 204a30 for Mg, Ca, and Sr, respectively.}
}

@article{Bromley2002a,
  title = {Configuration-Interaction Calculations of Positron Binding to Zinc and Cadmium},
  author = {Bromley, M. W. J. and Mitroy, J.},
  year = {2002},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {65},
  number = {6},
  pages = {062506},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.65.062506},
  urldate = {2024-06-12},
  abstract = {The configuration-interaction method is applied to the study of positronic zinc ({$e$}+⁢Zn) and positronic cadmium ({$e$}+⁢Cd). The estimated binding energies and annihilation rates were 0.003 73 hartree and 0.42{\texttimes}109 sec-1 for {$e$}+⁢Zn and 0.006 10 hartree and 0.56{\texttimes}109 sec-1 for {$e$}+⁢Cd. The low-energy elastic cross section and {$Z$}eff were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive for Zn and for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.},
  file = {/Users/yingxing/Zotero/storage/LBIB7N45/Bromley_Mitroy_2002_Configuration-interaction calculations of positron binding to zinc and cadmium.pdf}
}

@article{Bromley2002b,
  title = {Positron and Positronium Interactions with {{Cu}}},
  author = {Bromley, M. W. J. and Mitroy, J.},
  year = {2002},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {66},
  number = {6},
  pages = {062504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.66.062504},
  urldate = {2024-06-10},
  abstract = {The configuration-interaction (CI) method is used to investigate the interactions of positrons and positronium with copper at low energies. The calculations were performed within the framework of the fixed-core approximation with semiempirical polarization potentials used to model dynamical interactions between the active particles and the core. Initially, calculations upon the system were used to refine the numerical procedures and highlighted the extreme difficulties of using an orthodox CI calculation to describe the Li system. The positron binding energy of derived from a CI calculation which included electron and positron orbitals with was 0.005 12 hartree while the spin-averaged annihilation rate was The configuration basis used for the bound-state calculation was also used as a part of the trial wave function for a Kohn variational calculation of positron-copper scattering. The positron-copper system has a scattering length of about and the annihilation parameter at threshold was 72.9. The dipole polarizability of the neutral copper ground state was computed and found to be The structure of CuPs was also studied with the CI method and it was found to have a binding energy of 0.0143 hartree and an annihilation rate of},
  file = {/Users/yingxing/Zotero/storage/RBX8DRQR/Bromley_Mitroy_2002_Positron and positronium interactions with Cu.pdf}
}

@article{Buchachenko2006,
  title = {Van Der {{Waals}} Interactions and Dipole Polarizabilities of Lanthanides: {{Tm}}({{F2}})--{{He}} and {{Yb}}({{S1}})--{{He}} Potentials},
  shorttitle = {Van Der {{Waals}} Interactions and Dipole Polarizabilities of Lanthanides},
  author = {Buchachenko, Alexei A. and Szcz{\c e}{\'s}niak, Ma{\l}gorzata M. and Cha{\l}asi{\'n}ski, Grzegorz},
  year = {2006},
  month = mar,
  journal = {J. Chem. Phys.},
  volume = {124},
  number = {11},
  pages = {114301},
  publisher = {American Institute of Physics},
  issn = {0021-9606},
  doi = {10.1063/1.2176602},
  urldate = {2023-03-21},
  file = {/Users/yingxing/Zotero/storage/76ENEHJI/Van der Waals interactions and dipole polarizabilities of lanthanides Tm( 2F)-He and Yb( 1S)-He potentials_2006.pdf}
}

@article{Buchachenko2007,
  title = {Diffuse Basis Functions for Small-Core Relativistic Pseudopotential Basis Sets and Static Dipole Polarizabilities of Selected Lanthanides {{La}}, {{Sm}}, {{Eu}}, {{Tm}} and {{Yb}}},
  author = {Buchachenko, Alexei A. and Cha{\l}asi{\'n}ski, Grzegorz and Szcz{\c e}{\'s}niak, Ma{\l}gorzata M.},
  year = {2007},
  month = dec,
  journal = {Struct Chem},
  volume = {18},
  number = {6},
  pages = {769--772},
  issn = {1572-9001},
  doi = {10.1007/s11224-007-9243-1},
  urldate = {2024-06-12},
  abstract = {The compact sets of the diffuse functions are suggested for better description of the polarization properties of the lanthanide atoms using the small-core effective core potentials and the corresponding basis sets. The pd and 2pdfg augmentations with exponents 0.028 and 0.015 (p), 0.032 (d) and 0.05 (f,g) are recommended for all lanthanides. Scalar and tensor dipole polarizabilities calculated using the multireference averaged quadratic coupled cluster method agree well with the literature data.},
  langid = {english},
  keywords = {Atomic lanthanides,Dipole polarizability,Interaction potential},
  file = {/Users/yingxing/Zotero/storage/ZV7D7MRQ/Buchachenko et al_2007_Diffuse basis functions for small-core relativistic pseudopotential basis sets.pdf}
}

@article{Buchachenko2010,
  title = {Anisotropy of the Static Dipole Polarizability Induced by the Spin--Orbit Interaction: The {{S-state}} Atoms {{N}}--{{Bi}}, {{Cr}}, {{Mo}} and {{Re}}},
  shorttitle = {Anisotropy of the Static Dipole Polarizability Induced by the Spin--Orbit Interaction},
  author = {Buchachenko, Alexei A.},
  year = {2010},
  month = nov,
  journal = {Proc. R. Soc. Math. Phys. Eng. Sci.},
  volume = {467},
  number = {2129},
  pages = {1310--1328},
  publisher = {Royal Society},
  doi = {10.1098/rspa.2010.0440},
  urldate = {2023-03-20},
  abstract = {A systematic ab initio study is performed on the ground state static dipole polarizabilities of the 2S+1S, S{$>$}1/2, atoms from N to Bi, Cr, Mo, Mn, Tc and Re. The benchmark scalar-relativistic values of the scalar polarizability components are obtained using the coupled cluster method. The spin--orbit configuration interaction calculations are carried out for the anisotropic (tensor) polarizability components of these atoms (except Mn and Tc) that arise from the second-order spin--orbit interaction. The tensor polarizabilities are calculated for the first time and found to increase from 10-5 (N) to 3.8 atomic units (Bi) approximately as the fourth power of the nuclear charge. The simple correlations and implication to magnetic trapping of cold atoms are discussed.},
  keywords = {interaction anisotropy,Interaction anisotropy,spin-orbit interaction,Spin-orbit interaction,static dipole polarizabilities,Static dipole polarizabilities},
  file = {/Users/yingxing/Zotero/storage/8B2UH4KH/Anisotropy of the static dipole polarizability induced by the spin-orbit interaction The S-state atoms N-Bi, Cr, Mo and Re_2011.pdf;/Users/yingxing/Zotero/storage/RPZU7CP7/Buchachenko_2010_Anisotropy of the static dipole polarizability induced by the spin–orbit.pdf}
}

@article{Buchachenko2010c,
  title = {State-Interacting Spin-Orbit Configuration Interaction Method for {{J-resolved}} Anisotropic Static Dipole Polarizabilities: {{Application}} to {{Al}}, {{Ga}}, {{In}}, and {{Tl}} Atoms},
  shorttitle = {State-Interacting Spin-Orbit Configuration Interaction Method for {{J-resolved}} Anisotropic Static Dipole Polarizabilities},
  author = {Buchachenko, A. A.},
  year = {2010},
  month = jan,
  journal = {Russ. J. Phys. Chem.},
  volume = {84},
  number = {13},
  pages = {2325--2333},
  issn = {1531-863X},
  doi = {10.1134/S0036024410130200},
  urldate = {2024-06-12},
  abstract = {The state-interacting spin-orbit (SO) configuration interaction (CI) method, which uses the non-relativistic CI wave functions as the basis of the total SO Hamiltonian matrix, is combined with the finite-field approach and applied to J-resolved anisotropic static dipole polarizabilities of the third-group atoms from Al to Tl. Comparison with available data reveals excellent performance of the method for atoms up to the fifth period (In), especially if the scalar relativitic and the high-level correlation corrections are included. The method performs worse for 6s26p Tl atom, most likely due to growing effect of the second-order SO coupling. Refined values of all the scalar and the tensor ground-state non-relativistic and J-resolved polarizabilities and, whenever possible, excited-state polarizabilities, are recommended based on the calculations performed and thorough analysis of the literature data.},
  langid = {english},
  keywords = {Atomic Natural Orbital,Complete Active Space Self Consistent Field,Configuration Interaction,Spin Orbit,Static Dipole Polarizability},
  file = {/Users/yingxing/Zotero/storage/8PWFPJK3/Buchachenko_2010_State-interacting spin-orbit configuration interaction method for J-resolved.pdf}
}

@article{Buchachenko2010d,
  title = {Ab~Initio Dipole Polarizabilities and Quadrupole Moments of the Lowest Excited States of Atomic {{Yb}}},
  author = {Buchachenko, A. A.},
  year = {2011},
  month = jan,
  journal = {Eur. Phys. J. D},
  volume = {61},
  number = {2},
  pages = {291--296},
  issn = {1434-6079},
  doi = {10.1140/epjd/e2010-10413-7},
  urldate = {2024-06-12},
  abstract = {The finite-field scalar relativistic coupled cluster and configurationinteraction, as well as the spin-orbit configuration interaction,methods are employed to calculate the static dipole polarizabilities for thelowest (6s2) 1S, (6s6p) \${\textasciicircum}\{1,3\}\$Po and (6s5d) \${\textasciicircum}\{1,3\}\$D excitedstates of atomic ytterbium. The results agree very well with existingexperimental and besttheoretical data and refine the set of ytterbium polarizabilities known sofar. Similar techniques are used to calculate the electric quadrupole momentsfor the \${\textasciicircum}\{1,3\}\$Po and \${\textasciicircum}\{1,3\}\$D states.},
  langid = {english},
  keywords = {Dipole Polarizability,Polarizability Calculation,Quadrupole Moment,Tensor Polarizability,Ytterbium},
  file = {/Users/yingxing/Zotero/storage/CW76N782/Buchachenko_2011_Ab initio dipole polarizabilities and quadrupole moments of the lowest excited.pdf}
}

@article{Buchachenko2018,
  title = {Interaction Potentials and Transport Properties of {{Ba}}, {{Ba}}+, and {{Ba2}}+ in Rare Gases from {{He}} to {{Xe}}},
  author = {Buchachenko, Alexei A. and Viehland, Larry A.},
  year = {2018},
  month = apr,
  journal = {The Journal of Chemical Physics},
  volume = {148},
  number = {15},
  pages = {154304},
  issn = {0021-9606},
  doi = {10.1063/1.5025861},
  urldate = {2024-06-06},
  abstract = {A highly accurate, consistent set of ab initio interaction potentials is obtained for the title systems at the coupled cluster with singles, doubles, and non-iterative triples level of theory with extrapolation to the complete basis set limit. These potentials are shown to be more reliable than the previous potentials based on their long-range behavior, equilibrium properties, collision cross sections, and transport properties.},
  file = {/Users/yingxing/Zotero/storage/MQ9EME9A/Buchachenko_Viehland_2018_Interaction potentials and transport properties of Ba, Ba+, and Ba2+ in rare.pdf}
}

@article{Calaminici2004,
  title = {Polarizability of {{Fen}} ({\emph{N}}{$\leq$}4) Clusters: An All-Electron Density Functional Study},
  shorttitle = {Polarizability of {{Fen}} ({\emph{N}}{$\leq$}4) Clusters},
  author = {Calaminici, Patrizia},
  year = {2004},
  month = apr,
  journal = {Chemical Physics Letters},
  volume = {387},
  number = {4},
  pages = {253--257},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2004.02.008},
  urldate = {2024-06-12},
  abstract = {The first study of static polarizability and polarizability anisotropy of small iron clusters up to four atoms calculated in the framework of density functional theory is presented. The calculations were of all-electron type and performed using a finite field approach implemented in the density functional program AllChem. A newly developed first-order field induced iron basis set for density functional calculations was employed. The calculated polarizability of iron clusters shows that the size dependency of the static polarizability per atom of iron clusters follows the same trend as that observed for sodium and copper clusters.},
  file = {/Users/yingxing/Zotero/storage/ENDYG2MZ/Calaminici_2004_Polarizability of Fen (in-i⩽4) clusters.pdf}
}

@article{CanalNeto2021,
  title = {All-Electron Triple Zeta Basis Sets for {{ZORA}} Calculations: {{Application}} in Studies of Atoms and Molecules},
  shorttitle = {All-Electron Triple Zeta Basis Sets for {{ZORA}} Calculations},
  author = {Canal Neto, A. and Ferreira, I. B. and Jorge, F. E. and {de Oliveira}, A. Z.},
  year = {2021},
  month = may,
  journal = {Chemical Physics Letters},
  volume = {771},
  pages = {138548},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2021.138548},
  urldate = {2024-06-06},
  abstract = {Segmented all-electron basis set of triple zeta valence quality plus polarization functions for the elements from H to Xe to be used together with the ZORA Hamiltonian is developed. This set was augmented with diffuse functions in order to properly describe electrons distant from the nuclei. At the ZORA-CCSD(T) level of theory, ionization energies and mean dipole polarizabilities of some atoms as well as bond lengths, dissociation energies, and harmonic vibrational frequencies of a set of molecules are calculated. Scalar relativistic effects are estimated for all properties. The performances of the ZORA and DKH2 Hamiltonians are also assessed.},
  keywords = {Atomic and molecular properties,Estimates of scalar relativistic effects,Performance evaluation of the ZORA and DKH2 Hamiltonians,TZP-ZORA and ATZP-ZORA basis sets,ZORA-CCSD(T) method},
  file = {/Users/yingxing/Zotero/storage/NKHP2VX8/Canal Neto et al_2021_All-electron triple zeta basis sets for ZORA calculations.pdf}
}

@article{Centoducatte2022,
  title = {{{ZORA}} Double Zeta Basis Sets for Fifth Row Elements: {{Application}} in Studies of Electronic Structures of Atoms and Molecules},
  shorttitle = {{{ZORA}} Double Zeta Basis Sets for Fifth Row Elements},
  author = {Centoducatte, R. and {de Oliveira}, A. Z. and Jorge, F. E. and Camiletti, G. G.},
  year = {2022},
  month = jan,
  journal = {Computational and Theoretical Chemistry},
  volume = {1207},
  pages = {113511},
  issn = {2210-271X},
  doi = {10.1016/j.comptc.2021.113511},
  urldate = {2024-06-06},
  abstract = {Segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) to be used with the zero-order regular approximation (ZORA) scalar relativistic Hamiltonian was developed for the elements Cs, Ba, La, and from Hf to Rn. This set was augmented with diffuse functions for the purpose of describing electrons distant from atomic nuclei. Using the ZORA-B3LYP method, some atomic and molecular properties are computed. Benchmark theoretical results and experimental data were used to evaluate the performance of the DZP-ZORA and ADZP-ZORA basis sets. Despite their small sizes, these sets have proven to be accurate and reliable and can also be used in property calculations involving electrons not only from the outer shells, but also from the inner shells. Comparison of second order Douglas-Kroll-Hess and ZORA results was made.},
  keywords = {Atomic and molecular property calculations,DZP-ZORA and ADZP-ZORA basis sets,Fifth row elements,ZORA and DKH2 Hamiltonians performance,ZORA-B3LYP method}
}

@article{Cernusak2003,
  title = {Standardized {{Medium-Size Basis Sets}} for {{Calculations}} of {{Molecular Electric Properties}}: {{Group IIIA}}},
  shorttitle = {Standardized {{Medium-Size Basis Sets}} for {{Calculations}} of {{Molecular Electric Properties}}},
  author = {{\v C}ernu{\v s}{\'a}k, Ivan and Kell{\"o}, Vladimir and Sadlej, Andrzej J.},
  year = {2003},
  journal = {Collect. Czech. Chem. Commun.},
  volume = {68},
  number = {2},
  pages = {211--239},
  publisher = {{Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.}},
  issn = {1212-6950, 0010-0765},
  doi = {10.1135/cccc20030211},
  urldate = {2023-03-21},
  langid = {english},
  keywords = {Ab initio calculations,Atomic polarizabilities,Dipole moments,Fluorides,Gallium,Group IIIA elements,Indium,Main group metals,Molecular electric properties,Polarized basis sets,ROHF CCSD(T),Thallium},
  file = {/Users/yingxing/Zotero/storage/C6HPSV5Y/Černušák et al_2003_Standardized Medium-Size Basis Sets for Calculations of Molecular Electric.pdf;/Users/yingxing/Zotero/storage/NIIGDG32/Standardized medium-size basis sets for calculations of molecular electric properties Group IIIA_2003.pdf}
}

@article{Chakraborty2022,
  title = {Relativistic Normal Coupled-Cluster Theory Analysis of Second- and Third-Order Electric Polarizabilities of {{Zn}} \${{I}}\$},
  author = {Chakraborty, A. and Rithvik, S. K. and Sahoo, B. K.},
  year = {2022},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {105},
  number = {6},
  pages = {062815},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.105.062815},
  urldate = {2024-06-10},
  abstract = {We present precise values of electric polarizabilities for the ground state of Zn due to second-order dipole and quadrupole interactions, and due to third-order dipole-quadrupole interactions. These quantities are evaluated in the linear response theory framework by employing a relativistic version of the normal coupled-cluster (NCC) method. The calculated dipole polarizability value is compared with available experimental and other theoretical results, including those obtained using the ordinary coupled-cluster (CC) methods in both finite-field and expectation value evaluation approaches. We also give a term-by-term comparison of contributions from our CC and NCC calculations in order to show differences in the results from these two methods. Moreover, we present results from other lower-order methods to understand the role of electron correlation effects in the determination of the above quantities. A machine-learning-based scheme to generate optimized basis functions for atomic calculations is developed and applied here. From the analysis of the dipole polarizability result, the accuracy of the calculated quadrupole and third-order polarizability values is ascertained, for which no experimental values are currently available.},
  file = {/Users/yingxing/Zotero/storage/UQ6FLNQU/Chakraborty et al. - 2022 - Relativistic normal coupled-cluster theory analysi.pdf}
}

@article{Chandler1987,
  title = {Evaluation of Atomic Polarisabilities Using the Variational Perturbation Approach: The First Transition Series},
  shorttitle = {Evaluation of Atomic Polarisabilities Using the Variational Perturbation Approach},
  author = {Chandler, G. S. and Glass, R.},
  year = {1987},
  month = jan,
  journal = {J. Phys. B: Atom. Mol. Phys.},
  volume = {20},
  number = {1},
  pages = {1},
  issn = {0022-3700},
  doi = {10.1088/0022-3700/20/1/006},
  urldate = {2024-06-12},
  abstract = {Using the variational perturbation approach, mean static dipole polarisabilities for the first transition series, resulting from the contribution to the total polarisability of the polarisation of the 4s shell, are calculated. Two different sets of calculations are performed. With the exception of zinc, the polarisabilities calculated using a 4p polarising function, determined by minimising the second-order energy functional and representing the zero-order wavefunction by the Hartree-Fock configuration 3dn(2S+1L)4s2 and each component of the perturbed function by the configurational function 3dn(2S+1L)4s(2SL)4p, are within 2\% of that obtained from the theoretically more correct calculation, consisting of a 4p correlating function, determined to describe the important near-degeneracy effect 4s2 to 4p2, and a 5p polarising function, determined by optimising the second-order functional. In the latter optimisation the unperturbed wavefunction is represented by the Hartree-Fock single configuration 3dn4s2, augmented by the near-degenerate configuration 3dn4p2, and each component of the perturbed function consists of the most important polarising and configurational functions. In addition, it is shown that the configurations 3dn-14s24p and 3dn-14p3, from the 3d to 4p replacement, can be eliminated from the perturbed-states expansion, as their inclusion in the configuration interaction expansion of the perturbed states causes less than a 1\% change in the polarisability.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/DZ4GT698/Chandler_Glass_1987_Evaluation of atomic polarisabilities using the variational perturbation.pdf}
}

@article{Chattopadhyay2012,
  title = {Perturbed Coupled-Cluster Theory to Calculate Dipole Polarizabilities of Closed-Shell Systems: {{Application}} to {{Ar}}, {{Kr}}, {{Xe}}, and {{Rn}}},
  shorttitle = {Perturbed Coupled-Cluster Theory to Calculate Dipole Polarizabilities of Closed-Shell Systems},
  author = {Chattopadhyay, S. and Mani, B. K. and Angom, D.},
  year = {2012},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {86},
  number = {6},
  pages = {062508},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.86.062508},
  urldate = {2024-06-12},
  abstract = {We use perturbed relativistic coupled-cluster (PRCC) theory to calculate the electric dipole polarizability of the noble-gas atoms Ar, Kr, Xe, and Rn. We also provide a detailed description of the nonlinear terms in the PRCC theory and consider the Dirac-Coulomb-Breit atomic Hamiltonian for the calculations. We find that the largest contribution from the Breit interaction to the electric dipole polarizability is 0.1, in the case of Rn. As we go from Ar to Rn, based on the pattern in the random-phase-approximation effects, the contraction of the outermost orbitals due to relativistic corrections is discernible without any ambiguity.},
  file = {/Users/yingxing/Zotero/storage/6347IUVQ/Chattopadhyay et al_2012_Perturbed coupled-cluster theory to calculate dipole polarizabilities of.pdf}
}

@article{Chattopadhyay2012a,
  title = {Electric Dipole Polarizability from Perturbed Relativistic Coupled-Cluster Theory: {{Application}} to Neon},
  shorttitle = {Electric Dipole Polarizability from Perturbed Relativistic Coupled-Cluster Theory},
  author = {Chattopadhyay, S. and Mani, B. K. and Angom, D.},
  year = {2012},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {86},
  number = {2},
  pages = {022522},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.86.022522},
  urldate = {2024-06-12},
  abstract = {We develop a method based on the relativistic coupled-cluster theory to incorporate a perturbative interaction to the no-pair Dirac-Coulomb atomic Hamiltonian. The method is general and suitable to incorporate any perturbation Hamiltonian in a many-electron atom or ion. Using this perturbed relativistic coupled-cluster (PRCC) theory, we calculate the electric-dipole polarizability of neon. The linearized PRCC results are in very good agreement with the experimental value. However, the results of the nonlinear PRCC theory show larger uncertainty, but they are consistent with the observations from earlier works.},
  file = {/Users/yingxing/Zotero/storage/R2TMX5QN/Chattopadhyay et al_2012_Electric dipole polarizability from perturbed relativistic coupled-cluster.pdf}
}

@article{Chattopadhyay2014,
  title = {Electric Dipole Polarizability of Alkaline-Earth-Metal Atoms from Perturbed Relativistic Coupled-Cluster Theory with Triples},
  author = {Chattopadhyay, S. and Mani, B. K. and Angom, D.},
  year = {2014},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {89},
  number = {2},
  pages = {022506},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.89.022506},
  urldate = {2024-06-12},
  abstract = {The perturbed relativistic coupled-cluster (PRCC) theory is applied to calculate the electric dipole polarizabilities of alkaline-earth-metal atoms. The Dirac-Coulomb-Breit atomic Hamiltonian is used and we include the triple excitations in the relativistic coupled-cluster theory. The theoretical issues related to the triple excitation cluster operators are described in detail and we also provide details on the computational implementation. The PRCC theory results are in good agreement with the experimental and previous theoretical results. We, then, highlight the importance of considering the Breit interaction for alkaline-earth-metal atoms.},
  file = {/Users/yingxing/Zotero/storage/4WFGDXE4/Chattopadhyay et al_2014_Electric dipole polarizability of alkaline-earth-metal atoms from perturbed.pdf}
}

@article{Chattopadhyay2015,
  title = {Triple Excitations in Perturbed Relativistic Coupled-Cluster Theory and Electric Dipole Polarizability of Group-{{IIB}} Elements},
  author = {Chattopadhyay, S. and Mani, B. K. and Angom, D.},
  year = {2015},
  month = may,
  journal = {Phys. Rev. A},
  volume = {91},
  number = {5},
  pages = {052504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.91.052504},
  urldate = {2024-06-12},
  abstract = {We use the perturbed relativistic coupled-cluster (PRCC) theory to compute the electric dipole polarizabilities of Zn, Cd, and Hg. The computations are done using the Dirac-Coulomb-Breit Hamiltonian with the Uehling potential to incorporate vacuum polarization corrections. To assimilate the self-energy corrections we use the model self-energy operator of Shabaev et al. [Phys. Rev. A 88, 012513 (2013)]. The triple excitations are included perturbatively in the PRCC theory and nonperturbatively in the unperturbed sector. Our results for for all three elements are in excellent agreement with the experimental data. The other highlight of the results is the orbital energy corrections from Breit interactions. In the literature we could only get the data of Hg [E. Lindroth et al., J. Phys. B 22, 2447 (1989)], which are a near perfect match with our results. We also present the linearized equations of the cluster amplitudes, including the triple excitations, with the angular factors.},
  file = {/Users/yingxing/Zotero/storage/Q8BHNW8Z/Chattopadhyay et al_2015_Triple excitations in perturbed relativistic coupled-cluster theory and.pdf}
}

@article{Chen2010,
  title = {Quantum Phases of the {{Bose-Hubbard}} Model in Optical Superlattices},
  author = {Chen, Bo-Lun and Kou, Su-Peng and Zhang, Yunbo and Chen, Shu},
  year = {2010},
  month = may,
  journal = {Phys. Rev. A},
  volume = {81},
  number = {5},
  pages = {053608},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.81.053608},
  urldate = {2024-06-05},
  abstract = {We analyze the quantum phases of multicomponent Bose-Hubbard models in optical superlattices based on a mean-field method, that is, the decoupling approximation. The global phase diagrams exhibit complex patterns with various charge-density-wave orders for both one- and two-component cases. We further calculate the effective spin excitations for the two-component case in the strong-coupling region at unit filling, and show the existence of a spin-density-wave order. The results of our study can be tested straightforwardly with current cold-atom experimental techniques.},
  file = {/Users/yingxing/Zotero/storage/4HFBSNCJ/Chen et al_2010_Quantum phases of the Bose-Hubbard model in optical superlattices.pdf}
}

@article{Chen2022a,
  title = {Measurement of Dynamic Atomic Polarizabilities of {{Al}} at 19 Wavelengths from 420\>Nm to 680\>Nm in Electrical Exploding Wire Experiments},
  author = {Chen, Ziwei and Wu, Jian and Lu, Yihan and Jiang, Zhiyuan and Zhang, Cheng and Wang, Zhenyu and Shi, Huantong and Li, Xingwen and Zhou, Lin},
  year = {2022},
  month = jul,
  journal = {Opt. Express, OE},
  volume = {30},
  number = {15},
  pages = {26102--26110},
  publisher = {Optica Publishing Group},
  issn = {1094-4087},
  doi = {10.1364/OE.461423},
  urldate = {2024-06-10},
  abstract = {The dynamic polarizabilities of Al atom at 19 wavelengths from 420 nm to 680 nm are measured experimentally for the first time. A 15 \&\#x00B5;m diameter Al wire is heated to the gas/ microdrop stage using a 3 kA, 25 ns pulsed current, and the energy deposition when the resistive voltage reaches its peak is 4.7 eV\&\#x00B7;atom\&\#x2212;1, which is higher than the atomization enthalpy of Al but much lower than its first ionization potential. Two laser interferometric images of the Al gas are obtained simultaneously using a 532 nm laser and an optical parametric oscillator laser. Then an integrated phase method is used to reconstruct the Al atomic linear density distribution based on the known atomic polarizability at 532 nm, which acts as a bridge between the two interferograms to obtain the relative atomic polarizability value at a specific wavelength with respect to the value at 532 nm. The measured dynamic polarizability of Al atom decreases from 13.5\&\#x00D7;10\&\#x2212;24 cm3 to 9.4\&\#x00D7;10\&\#x2212;24 cm3 as the wavelength increases from 420 nm to 680 nm with a measurement error of approximately \&\#x00B1;10\&\#x0025;. The experimental result fits well with an uncoupled Hartree-Fock approximation, and the reconstructed static polarizability of 8.13\&\#x2009;\&\#x00B1;\&\#x2009;0.79\&\#x00D7;10\&\#x2212;24 cm3 is well matched with reference measurement results.},
  copyright = {{\copyright} 2022 Optica Publishing Group},
  langid = {english},
  keywords = {Aperture synthesis,Laser beam propagation,Laser beams,Laser imaging,Nonlinear optical crystals,Phase shift},
  file = {/Users/yingxing/Zotero/storage/ZHA4C53J/Chen et al. - 2022 - Measurement of dynamic atomic polarizabilities of .pdf}
}

@article{Cheng2013,
  title = {Tune-out Wavelengths for the Alkaline-Earth-Metal Atoms},
  author = {Cheng, Yongjun and Jiang, Jun and Mitroy, J.},
  year = {2013},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {88},
  number = {2},
  pages = {022511},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.88.022511},
  urldate = {2024-06-10},
  abstract = {The lowest three tune-out wavelengths of the four alkaline-earth-metal atoms Be, Mg, Ca, and Sr are determined from tabulations of matrix elements produced from large first-principles calculations. The tune-out wavelengths are located near the wavelengths for the 3⁢{$Po$}1 and 1⁢{$Po$}1 excitations. The measurement of the tune-out wavelengths could be used to establish a quantitative relationship between the oscillator strength of the transition leading to existence of the tune-out wavelength and the dynamic polarizability of the atom at the tune-out frequency. The longest tune-out wavelengths for Be, Mg, Ca, Sr, Ba, and Yb are 454.9813, 457.2372, 657.446, 689.200, 788.875, and 553.00 nm, respectively.},
  file = {/Users/yingxing/Zotero/storage/GIAKQLH6/Cheng et al_2013_Tune-out wavelengths for the alkaline-earth-metal atoms.pdf}
}

@article{Chu2004,
  title = {Linear Response Time-Dependent Density Functional Theory for van Der {{Waals}} Coefficients},
  author = {Chu, X. and Dalgarno, A.},
  year = {2004},
  month = sep,
  journal = {The Journal of Chemical Physics},
  volume = {121},
  number = {9},
  pages = {4083--4088},
  issn = {0021-9606},
  doi = {10.1063/1.1779576},
  urldate = {2024-06-12},
  abstract = {A linear response time-dependent density functional theory is described and used to calculate the dynamic polarizabilities and van der Waals C6 coefficients of complex atom pairs. We present values of C6 for dimers of main group atoms and the first row of transition metal atoms.},
  file = {/Users/yingxing/Zotero/storage/MBASRZ6R/Chu_Dalgarno_2004_Linear response time-dependent density functional theory for van der Waals.pdf}
}

@article{Chu2005,
  title = {Polarizabilities of {{Sc}} and {{Ti}} Atoms and Dispersion Coefficients for Their Interaction with Helium Atoms},
  author = {Chu, Xi and Dalgarno, Alexander and Groenenboom, Gerrit C.},
  year = {2005},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {72},
  number = {3},
  pages = {032703},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.72.032703},
  urldate = {2024-06-12},
  abstract = {The dynamic scalar and tensor polarizabilities of Sc and Ti are computed with time-dependent density functional theory. These polarizabilities are used to compute the isotropic and anisotropic dispersion interactions in ScHe and TiHe. We find {$C$}6,0⁡(ScHe)=30.00, {$C$}6,2⁡(ScHe)=-1.63, {$C$}6,0⁡(TiHe)=28.40, and {$C$}6,2⁡(TiHe)=-0.90 ({$E$}ℎ⁢{$a$}60). We show that an estimate of the dispersion anisotropy based on static polarizabilities results in an overestimation by a factor of 2.},
  file = {/Users/yingxing/Zotero/storage/QG2XZMZS/Chu et al_2005_Polarizabilities of Sc and Ti atoms and dispersion coefficients for their.pdf}
}

@article{Chu2007,
  title = {Dynamic Polarizabilities of Rare-Earth-Metal Atoms and Dispersion Coefficients for Their Interaction with Helium Atoms},
  author = {Chu, Xi and Dalgarno, Alexander and Groenenboom, Gerrit C.},
  year = {2007},
  month = mar,
  journal = {Phys. Rev. A},
  volume = {75},
  number = {3},
  pages = {032723},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.75.032723},
  urldate = {2024-06-12},
  abstract = {The dynamic scalar and tensor polarizabilities of the rare-earth-metal atoms are calculated with time-dependent density functional theory. The frequency-dependent polarizabilities at imaginary frequencies are used to determine the isotropic and orientation-dependent van der Waals coefficients for the interactions of the rare-earth-metal atoms with helium atoms. The static polarizabilities are compared with other theoretical values and with experimental results. The agreement is satisfactory in most cases but there are some exceptions where the discrepancy between theory and experiment is significant. The derived isotropic van der Waals coefficients range between 37 and 50 and the orientation-dependent coefficients between 2 and . Thus the ratio of elastic to inelastic scattering cross sections is expected to be substantial and any one of the rare-earth-metal atoms is an excellent candidate for trapping and cooling in a He gas.},
  file = {/Users/yingxing/Zotero/storage/DQL3I42J/Chu et al_2007_Dynamic polarizabilities of rare-earth-metal atoms and dispersion coefficients.pdf}
}

@article{Cole1986,
  title = {Van Der {{Waals}} Interaction between a Tungsten Surface and Iridium and Tantalum Atoms},
  author = {Cole, Milton W. and Bardon, Jacques},
  year = {1986},
  month = feb,
  journal = {Phys. Rev. B},
  volume = {33},
  number = {4},
  pages = {2812--2813},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.33.2812},
  urldate = {2024-06-05},
  abstract = {Calculations are presented of the coefficient {$C$}3 of the {$z-$}3 dispersion interaction between Ir and Ta atoms and a W surface. The results depend sensitively on the assumed value of the atomic polarizability. If experimental values are used, the results for {$C$}3 are consistent with determinations based on the atomic deflection by a field-emission tip.},
  file = {/Users/yingxing/Zotero/storage/757JKWBY/Cole_Bardon_1986_van der Waals interaction between a tungsten surface and iridium and tantalum.pdf}
}

@article{Cuthbertson1997,
  title = {On the Dispersion of Gaseous Mercury, Sulphur, Phosphorous, and Helium},
  author = {Cuthbertson, Clive and Metcalfe, E. Parr and Trouton, Frederick Thomas},
  year = {1997},
  month = jan,
  journal = {Proc. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character},
  volume = {80},
  number = {540},
  pages = {411--419},
  publisher = {Royal Society},
  doi = {10.1098/rspa.1908.0036},
  urldate = {2024-06-07},
  abstract = {In continuation of previous work on the refractive indices of certain elements in the gaseous state, we have measured the dispersion of the elements named above within the limits of the visible spectrum. Jamin's refractometer was used, and the arrangement of the instrument was that described in our previous paper. But, as different wave-lengths had to be employed for the determination of the dispersion, the method of illumination was improved. Light from a Nernst filament was focussed on the slit of one of Messrs. Hilger and Co.'s fixed-deviation spectroscopes, and, in the focal plane of the resulting spectrum, a slit was placed capable of motion in that plane. The adjustment was calibrated by comparing the wave-length of the light passing through the slit with the reading of the drum of the spectroscope. By rotating the drum, light of any required wave-length could be obtained, and, by narrowing the slits, the spectrum was of sufficient purity to admit of two hundred bands being counted to one-fifth of their breadth.},
  file = {/Users/yingxing/Zotero/storage/EBXYCFZH/Cuthbertson et al_1997_On the dispersion of gaseous mercury, sulphur, phosphorous, and helium.pdf}
}

@article{Dalgarno1962,
  title = {Atomic Polarizabilities and Shielding Factors},
  author = {Dalgarno, A.},
  year = {1962},
  month = oct,
  journal = {Adv. Phys.},
  volume = {11},
  number = {44},
  pages = {281--315},
  publisher = {Taylor \& Francis},
  issn = {0001-8732},
  doi = {10.1080/00018736200101302},
  urldate = {2023-03-20},
  abstract = {A detailed discussion is given of the methods of calculating atomic polarizabilities and shielding factors and the relationships between them are demonstrated. The formulation of the uncoupled Hartree-Fock approximation is presented and it is shown that the methods are all approximate versions of it. A more accurate procedure, the coupled Hartree-Fock approximation, is described. Comprehensive tables of dipole and quadrupole polarizabilities and of quadrupole shielding factors are included together with an assessment of the probable accuracy.},
  file = {/Users/yingxing/Zotero/storage/4SQZQFN7/Dalgarno_1962_Atomic polarizabilities and shielding factors.pdf;/Users/yingxing/Zotero/storage/IRU4YRT6/Advances in Physics Atomic polarizabilities and shielding factors_2006.pdf}
}

@article{Dalgarno1997b,
  title = {The Refractive Indices and {{Verdet}} Constants of the Inert Gases},
  author = {Dalgarno, A. and Kingston, A. E. and Bates, David Robert},
  year = {1997},
  month = jan,
  journal = {Proc. R. Soc. Lond. Ser. Math. Phys. Sci.},
  volume = {259},
  number = {1298},
  pages = {424--431},
  publisher = {Royal Society},
  doi = {10.1098/rspa.1960.0237},
  urldate = {2024-06-05},
  abstract = {A method is suggested by which the refractive index and Verdet constant of an atomic system may be derived theoretically. It is applied to atomic hydrogen and to the inert gases and a comparison is made with experimental data. The Verdet constant of neon is not anomalous. The origin of the suggestion appears to be an underestimate of the experimental error. The analysis yields values of th e polarizabilities of th e inert gases which are respectively He, 1-384; Ne, 2-663; Ar, 11-080; K r, 16-734; X e, 27-292 in units of {$\alpha$}30},
  file = {/Users/yingxing/Zotero/storage/QEF7UDRR/Dalgarno et al_1997_The refractive indices and Verdet constants of the inert gases.pdf}
}

@article{Dammalapati2011,
  title = {Light Shifts and Magic Wavelengths for Heavy Alkaline Earth Elements: {{Ba}} and {{Ra}}},
  shorttitle = {Light Shifts and Magic Wavelengths for Heavy Alkaline Earth Elements},
  author = {Dammalapati, U. and Santra, B. and Willmann, L.},
  year = {2011},
  month = dec,
  journal = {J. Phys. B: At. Mol. Opt. Phys.},
  volume = {45},
  number = {2},
  pages = {025001},
  issn = {0953-4075},
  doi = {10.1088/0953-4075/45/2/025001},
  urldate = {2024-06-12},
  abstract = {In this paper, we investigate light shifts of heavy alkaline earth elements barium (Ba) and radium (Ra), which are interesting for optical lattice clocks and for permanent electric dipole moment searches. Detailed knowledge is required in the design of efficient loading of atoms from a magneto-optical trap into an optical dipole trap, to facilitate Doppler cooling while trapping and to achieve longer lifetimes of the trapped atoms with reduced heating rates. The wavelength dependence of light shifts of the ns2 1S0 ground state, the nsnp 3P1 and ns(n - 1)d 1D2 excited states in barium (n = 6) and the n s2 1S0 ground state, the nsnp 3P1 and ns(n - 1)d 3D2 excited states in radium (n = 7) are calculated. Several magic wavelengths in the visible and infrared regions accessible with commercial lasers for optical dipole trapping of Ba and Ra are identified.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/F24V8DKS/Dammalapati et al_2011_Light shifts and magic wavelengths for heavy alkaline earth elements.pdf}
}

@article{Das1998,
  title = {Static Response Properties of Second-Period Atoms: Coupled Cluster Calculations},
  shorttitle = {Static Response Properties of Second-Period Atoms},
  author = {Das, A. K. and Thakkar, Ajit J.},
  year = {1998},
  month = may,
  journal = {J. Phys. B At. Mol. Opt. Phys.},
  volume = {31},
  number = {10},
  pages = {2215},
  issn = {0953-4075},
  doi = {10.1088/0953-4075/31/10/011},
  urldate = {2023-03-21},
  abstract = {Accurate static dipole polarizabilities and hyperpolarizabilities are calculated for the ground states of the boron, carbon, nitrogen, oxygen and fluorine atoms. Anisotropies are reported for the P-state atoms. The computations are based on a finite-field procedure using energies computed with basis sets of contracted Gaussian-type functions and the CCSD(T) method, that is the coupled cluster method in the space of single and double substitutions corrected non-iteratively for the effects of triple substitutions. These are the first electron-correlated hyperpolarizabilities reported to date for all but one of these atoms.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/RYA748W9/Static response properties of second-period atoms Coupled cluster calculations_1998.pdf}
}

@article{deFarias2017,
  title = {Estimation of Some Physical Properties for Tennessine and Tennessine Hydride ({{TsH}})},
  author = {{de Farias}, Robson Fernandes},
  year = {2017},
  month = jan,
  journal = {Chem. Phys. Lett.},
  volume = {667},
  pages = {1--3},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2016.11.023},
  urldate = {2023-03-20},
  abstract = {In the present work, experimental values of several physical properties for hydrogen halides (including At) are used to obtain, by extrapolation, values of physical properties for tennessine (element 117, Ts) and tennessine hydride (TsH). Using experimental data of Cl, Br, I and At halides, two empirical equations are obtained, allowed us to calculate the ionic and covalent contribution to the bond energy, respectively: Eionic=[{$\mu$}2h/d3]c210-12 and Ecovalent=[-22.78P+400.09]+{$\nu$}(HX). Using both equations, as well some empirical trends in the Cl, Br, I and At halides, the values of some physical properties of Ts and TsH are estimated. The frequency energy of the TsH vibration, {$\nu$}(TsH), value is calculated as 20.24kJmol-1. For the same bond: {$\mu$}=0.24D; bond distance=196.76pm; bond energy=163.03kJmol-1. The polarizability and covalent radius for Ts are estimated as 11.31/10-24cm3 and 159.76pm, respectively.},
  langid = {english},
  keywords = {Element 117,Extrapolation,Physical properties,Tennessine,Tennessine hydride},
  file = {/Users/yingxing/Zotero/storage/87ILPZWW/de Farias_2017_Estimation of some physical properties for tennessine and tennessine hydride.pdf}
}

@article{Delone1999,
  title = {{{AC Stark}} Shift of Atomic Energy Levels},
  author = {Delone, N. B. and Krainov, Vladimir P.},
  year = {1999},
  month = jul,
  journal = {Phys.-Usp.},
  volume = {42},
  number = {7},
  pages = {669},
  publisher = {IOP Publishing},
  issn = {1063-7869},
  doi = {10.1070/PU1999v042n07ABEH000557},
  urldate = {2024-06-05},
  abstract = {AC Stark shift of atomic energy levels, N B Delone, Vladimir P Krainov},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/5DUG68MF/Delone_Krainov_1999_AC Stark shift of atomic energy levels.pdf}
}

@article{Derevianko1999,
  title = {High-{{Precision Calculations}} of {{Dispersion Coefficients}}, {{Static Dipole Polarizabilities}}, and {{Atom-Wall Interaction Constants}} for {{Alkali-Metal Atoms}}},
  author = {Derevianko, A. and Johnson, W. R. and Safronova, M. S. and Babb, J. F.},
  year = {1999},
  month = may,
  journal = {Phys. Rev. Lett.},
  volume = {82},
  number = {18},
  pages = {3589--3592},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.82.3589},
  urldate = {2023-03-20},
  abstract = {The van der Waals coefficients for the alkali-metal atoms from Na to Fr interacting in their ground states are calculated using relativistic ab initio methods. The accuracy of the calculations is estimated by also evaluating atomic static electric-dipole polarizabilities and coefficients for the interaction of the atoms with a perfectly conducting wall. The results are in excellent agreement with the latest data from studies of magnetic field induced Feshbach resonances in ultracold collisions of Na and of Rb atoms. For Cs we provide critically needed data for ultracold collision studies.},
  file = {/Users/yingxing/Zotero/storage/4S32U8S3/High-precision calculations of dispersion coefficients, static dipole polarizabilities, and atom-wall interaction constants for alkali-m.pdf;/Users/yingxing/Zotero/storage/QI83C6D8/Derevianko et al. - 1999 - High-Precision Calculations of Dispersion Coeffici.pdf}
}

@article{Desclaux1973,
  title = {Relativistic {{Dirac-Fock}} Expectation Values for Atoms with {{{\emph{Z}}}} = 1 to {{{\emph{Z}}}} = 120},
  author = {Desclaux, J. P.},
  year = {1973},
  month = jan,
  journal = {Atomic Data and Nuclear Data Tables},
  volume = {12},
  number = {4},
  pages = {311--406},
  issn = {0092-640X},
  doi = {10.1016/0092-640X(73)90020-X},
  urldate = {2024-06-12},
  abstract = {Numerical relativistic Dirac-Fock calculations for the average energy of the LS ground-state configuration of neutral atoms with Z = 1 to Z = 120 are presented. For open-shell systems a simple method is used to average over all the jj subconfigurations arising from the single LS configuration. The procedure of minimizing the average energy of the LS configuration allows a detailed comparison with nonrelativistic results and gives values slightly different from most of those previously published and obtained by considering only the lowest energy subconfiguration in jj coupling. Tabulations of total atom energies, orbital binding energies, one-electron integrals, expectation values of rn for n = 6, 4, 2, 1, -1, -2, -3, and the radius at which the orbital density has its maximum value are presented. A comparison with nonrelativistic Hartree-Fock results is given for elements with Z = 1 to Z = 100.}
}

@article{Dong2021,
  title = {Calculations of Atomic Polarizability for Beryllium Using {{MCDHF}} Method*},
  author = {Dong, Hui and Jiang, Jun and Wu, Zhongwen and Dong, Chenzhong and Gaigalas, Gediminas},
  year = {2021},
  month = apr,
  journal = {Chinese Phys. B},
  volume = {30},
  number = {4},
  pages = {043103},
  publisher = {{Chinese Physical Society and IOP Publishing Ltd}},
  issn = {1674-1056},
  doi = {10.1088/1674-1056/abd92d},
  urldate = {2024-06-10},
  abstract = {Based on the fully relativistic multiconfiguration Dirac--Hartree--Fock (MCDHF) method and the corresponding program package GRASP2018, a new program for calculating the polarizabilities is developed. As the first application, the static electric-dipole polarizabilities of the ground state 2s2 1 S 0 and excited state 2s2p 3 P 0 of beryllium are calculated. By means of these polarizabilities, the blackbody radiation (BBR) shift of the 2s2p 3 P 0 {$\rightarrow$} 2s2 1 S 0 clock transition is determined. The present results agree very well with other available theoretical results.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/H4R83ZJ2/Dong et al_2021_Calculations of atomic polarizability for beryllium using MCDHF method.pdf}
}

@article{Doolen1987,
  title = {Calculations of Photoabsorption by Atoms Using a Linear Response Method},
  author = {Doolen, Gary and Liberman, David A.},
  year = {1987},
  month = jul,
  journal = {Phys. Scr.},
  volume = {36},
  number = {1},
  pages = {77},
  issn = {1402-4896},
  doi = {10.1088/0031-8949/36/1/012},
  urldate = {2024-06-08},
  abstract = {We have made extensive calculations of photoabsorption by all neutral atoms from hydrogen to lawrencium for photon energies up to one kilovolt. Our method was the relativistic time-dependent local density approximation with the usual configuration average for open shells. The most important collective effects are included through an induced field. Expected features such as resonant photoemission and autionization are seen. Examples of the calculations will be shown. The computer program used is available from the Computer Physics Communications Program Library.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/T6ZP79WM/Doolen_Liberman_1987_Calculations of photoabsorption by atoms using a linear response method.pdf}
}

@article{Dutta2020,
  title = {Trend of {{Gaunt}} Interaction Contributions to the Electric Dipole Polarizabilities of Noble Gas, Alkaline-Earth, and a Few Group-12 Atoms},
  author = {Dutta, Narendra Nath},
  year = {2020},
  month = nov,
  journal = {Chemical Physics Letters},
  volume = {758},
  pages = {137911},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2020.137911},
  urldate = {2024-06-06},
  abstract = {In this work, we calculate unretarded Breit or Gaunt interaction contributions to the electric dipole or E1 polarizabilities of the noble gas, alkaline-earth, and a few group-12 atoms. The dipole polarizabilities of these atoms are calculated using third-order many-body perturbation theory. The strength of the Gaunt interaction contribution increases rapidly in moving down the periodic group toward heavier atoms. However, our work reveals that the trend of this increasing strength is different between the noble gas and alkaline-earth groups.},
  keywords = {Breit interaction,Electric dipole polarizability,Perturbation theory},
  file = {/Users/yingxing/Zotero/storage/JW3WRVKY/Dutta_2020_Trend of Gaunt interaction contributions to the electric dipole.pdf}
}

@article{Dyugaev2016,
  title = {New Qualitative Results of the Atomic Theory},
  author = {Dyugaev, A. M. and Lebedeva, E. V.},
  year = {2016},
  month = nov,
  journal = {Jetp Lett.},
  volume = {104},
  number = {9},
  pages = {639--644},
  issn = {1090-6487},
  doi = {10.1134/S0021364016210098},
  urldate = {2024-06-12},
  abstract = {The polarizability {$\alpha$} of many atoms and positive ions is related to their energy gap {$\Delta$} and valence m by the expression {$\alpha\Delta$}2 {$\cong$} m (in atomic units). The parameter {$\Delta$} corresponds to a dipolar transition from the ground state to the first excited P state without a change in the principal quantum number n. This relation holds for univalent (m = 1) Na, K, Rb, Cs, Fr and bivalent (m = 2) Mg, Ca, Zn, Sr, Cd, Ba, Yb, Hg atoms. The above relation agrees with the experiment for positive ions Mg+ and Ca+ (m = 1) and Al+ and Ga+ (m = 2). The polarizability has been found for atoms and ions of the type Zn+, In+, Tl+, for which experimental data are unavailable. A method of calculating {$\alpha$} for ions of the types C++, Al++, Si++ and Si+++, P+++, As+++ has been suggested based on the approximate relation {$\alpha$} {$\cong$}(2/3{\textlangle}r2{\textrangle}0)2/m with the parameter {\textlangle}r2{\textrangle}0 expressed in terms of the valence m, the charge number q of the atomic or ionic residue, and the ionization potential \$\$\{J\_q\} = {\textbackslash}frac\{\{\{q{\textasciicircum}2\}\}\}\{\{2v\_s{\textasciicircum}2\}\}\$\$as \$\$\{{\textbackslash}left{\textbackslash}langle \{\{r{\textasciicircum}2\}\} {\textbackslash}right{\textbackslash}rangle \_0\} = {\textbackslash}frac\{m\}\{\{2\{q{\textasciicircum}2\}\}\}{\textbackslash}nu \_s{\textasciicircum}2{\textbackslash}left( \{1 + 5{\textbackslash}nu \_s{\textasciicircum}2\} {\textbackslash}right)\$\$. The hydrogen dependence of {\textlangle}r2{\textrangle}0 on the parameter {$\nu$}s has been derived by analytical continuation from the integer values {$\nu$}s = 1 and 2. A variational estimate of the van der Waals constant characterizing the interaction of two spherically symmetric atoms at large distances has been given.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/64S6NTNW/Dyugaev_Lebedeva_2016_New qualitative results of the atomic theory.pdf}
}

@article{Dzuba2009,
  title = {Calculation of the \$({{T}},{{P}})\$-Odd Electric Dipole Moment of Thallium and Cesium},
  author = {Dzuba, V. A. and Flambaum, V. V.},
  year = {2009},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {80},
  number = {6},
  pages = {062509},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.80.062509},
  urldate = {2024-06-12},
  abstract = {Parity and time invariance violating electric dipole moment of 205T⁢l is calculated using the relativistic Hartree-Fock and configuration interaction methods and the many-body perturbation theory. Contributions from the interaction of the electron electric dipole moments with internal electric field and scalar-pseudoscalar electron-nucleon -odd interaction are considered. The results are or . Interpretation of the measurements are discussed. The results of similar calculations for are or .},
  file = {/Users/yingxing/Zotero/storage/J6SD9SRV/Dzuba_Flambaum_2009_Calculation of the $(T,P)$-odd electric dipole moment of thallium and cesium.pdf}
}

@article{Dzuba2014,
  title = {Scalar Static Polarizabilities of Lanthanides and Actinides},
  author = {Dzuba, V. A. and Kozlov, A. and Flambaum, V. V.},
  year = {2014},
  month = apr,
  journal = {Phys. Rev. A},
  volume = {89},
  number = {4},
  pages = {042507},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.89.042507},
  urldate = {2023-03-21},
  abstract = {We calculate scalar static polarizabilities for lanthanides and actinides, the atoms with open 4f or 5f subshells. We show that polarizabilities of the low states are approximately the same for all states of a given configuration, and we present a way of calculating them reducing valence space to just two or three valence electrons occupying 6s and 5d states for lanthanides or 7s and 6d states for actinides, while 4f and 5f states are considered to be in the core. The configuration interaction technique is used to calculate polarizabilities of lanthanides and actinides for all states of the 4fn6s2 and 4fn-16s25d configurations of lanthanides and all states of the 5fn7s2 and 5fn-17s26d configurations of actinides. Polarizability of the electron core (including f orbitals) has been calculated in the random-phase approximation.},
  file = {/Users/yingxing/Zotero/storage/SYBJ4R78/ref_174.pdf_Unknown.pdf;/Users/yingxing/Zotero/storage/XKSEZA9E/Dzuba et al. - 2014 - Scalar static polarizabilities of lanthanides and .pdf}
}

@article{Dzuba2014a,
  title = {Atomic Properties of Superheavy Elements {{No}}, {{Lr}}, and {{Rf}}},
  author = {Dzuba, V. A. and Safronova, M. S. and Safronova, U. I.},
  year = {2014},
  month = jul,
  journal = {Phys. Rev. A},
  volume = {90},
  number = {1},
  pages = {012504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.90.012504},
  urldate = {2024-06-12},
  abstract = {The combination of the configuration interaction method and all-order single-double coupled-cluster technique is used to calculate excitation energies, ionization potentials, and static dipole polarizabilities of superheavy elements nobelium, lawrencium, and rutherfordium. Breit and quantum electrodynamic corrections are also included. The results for the superheavy elements are compared with earlier calculations where available. Similar calculations for lighter analogs, ytterbium, lutetium, and hafnium, are used to study the accuracy of the calculations. The estimated uncertainties of the final results are discussed.},
  file = {/Users/yingxing/Zotero/storage/JXSMUQXM/Dzuba et al_2014_Atomic properties of superheavy elements No, Lr, and Rf.pdf}
}

@article{Dzuba2016,
  title = {Electron Structure of Superheavy Elements {{Uut}}, {{Fl}} and {{Uup}} ({{Z}}=113 to 115)},
  author = {Dzuba, V. A. and Flambaum, V. V.},
  year = {2016},
  month = nov,
  journal = {Hyperfine Interact.},
  volume = {237},
  number = {1},
  pages = {160},
  issn = {1572-9540},
  doi = {10.1007/s10751-016-1365-7},
  urldate = {2023-03-20},
  abstract = {We use recently developed method of accurate atomic calculations which combines linearized single-double coupled cluster method with the configuration interaction technique to calculate ionisation potentials, excitation energies, static polarizabilities and valence electron densities for superheavy elements Uut, Fl and Uup (Z=113 to 115) and their ions. The accuracy of the calculations is controlled by comparing similar calculations for lighter analogs of the superheavy elements, Tl, Pb and Bi with experiment. The role of relativistic effects and correlations is discussed and comparison with earlier calculations is presented.},
  langid = {english},
  keywords = {,E114,E115,Element flerovium,Elements E113,Elements E113 E114 E115,Relativistic and correlation effects in atoms,Superheavy elements},
  file = {/Users/yingxing/Zotero/storage/8V9N962W/Dzuba and Flambaum - 2016 - Electron structure of superheavy elements Uut, Fl .pdf}
}

@article{Dzuba2016b,
  title = {Ionization Potentials and Polarizabilities of Superheavy Elements from {{Db}} to {{Cn}} \$({{Z}}=105--112)\$},
  author = {Dzuba, V. A.},
  year = {2016},
  month = mar,
  journal = {Phys. Rev. A},
  volume = {93},
  number = {3},
  pages = {032519},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.93.032519},
  urldate = {2024-06-12},
  abstract = {Relativistic Hartree-Fock and random-phase approximation methods for open shells are used to calculate ionization potentials and static scalar polarizabilities of eight superheavy elements with open shells, which include Db, Sg, Bh, Hs, Mt, Ds, Rg, and Cn ( to 112). Interelectron correlations are taken into account with the use of the semiempirical polarization potential. Its parameters are chosen to fit the known ionization potentials of lighter atoms. Calculations for lighter atoms are also used to illustrate the accuracy of the approach.},
  file = {/Users/yingxing/Zotero/storage/ZGABAJU3/Dzuba_2016_Ionization potentials and polarizabilities of superheavy elements from Db to Cn.pdf}
}

@article{Dzuba2018,
  title = {Testing Physics beyond the Standard Model through Additional Clock Transitions in Neutral Ytterbium},
  author = {Dzuba, V. A. and Flambaum, V. V. and Schiller, S.},
  year = {2018},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {98},
  number = {2},
  pages = {022501},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.98.022501},
  urldate = {2024-06-06},
  abstract = {We study the prospects of using transitions from the ytterbium ground state to metastable states at and at as clock transitions in an optical lattice clock. Having more than one clock transition in Yb could benefit the search for new physics beyond the Standard Model via studying the nonlinearity of King's plot or the time variation of the ratio of the frequencies of two clock transitions. We calculate the lifetime of the states, relevant transition amplitudes, systematic shifts, and the sensitivities of the clock transitions to a variation of the fine-structure constant and to the gravitational potential. We find that both transitions can probably support high accuracy, approaching what is already achieved for the clock transition.},
  file = {/Users/yingxing/Zotero/storage/BFQ8YL4N/Dzuba et al_2018_Testing physics beyond the standard model through additional clock transitions.pdf}
}

@article{Dzuba2018a,
  title = {Screening of an Oscillating External Electric Field in Atoms},
  author = {Dzuba, V. A. and Berengut, J. C. and Ginges, J. S. M. and Flambaum, V. V.},
  year = {2018},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {98},
  number = {4},
  pages = {043411},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.98.043411},
  urldate = {2024-06-11},
  abstract = {We study the screening of a homogeneous oscillating external electric field {$E$}0 in noble-gas atoms using atomic many-body calculations. At zero frequency of the oscillations ({$\omega$}=0) the screened field {$E$}⁡({$r$}) vanishes at the nucleus, {$E$}⁡(0)=0. However, the profile of the field {$E$}⁡({$r$}) is complicated, with the magnitude of the field exceeding the external field {$E$}0 at certain points. For the field strongly depends on and at some points may exceed the external field many times. The field at the nucleus is not totally screened and grows with faster than . It can even be enhanced when comes close to resonance with a frequency of an atomic transition. This field interacts with CP-violating nuclear electric dipole moments creating new opportunities for studying them. The screening of the external field by atomic electrons may strongly suppress (or enhance near an atomic resonance) the low energy nuclear electric dipole transitions.},
  file = {/Users/yingxing/Zotero/storage/77IHMCXZ/Dzuba et al_2018_Screening of an oscillating external electric field in atoms.pdf}
}

@article{Dzuba2020,
  title = {Calculation of {{Polarizabilities}} for {{Atoms}} with {{Open Shells}}},
  author = {Dzuba, Vladimir},
  year = {2020},
  month = dec,
  journal = {Symmetry},
  volume = {12},
  number = {12},
  pages = {1950},
  publisher = {Multidisciplinary Digital Publishing Institute},
  issn = {2073-8994},
  doi = {10.3390/sym12121950},
  urldate = {2024-06-06},
  abstract = {A version of the configuration interaction method for atoms with open shells (the Configuration Interaction with Perturbation Theory---CIPT method, PRA 95, 012503 (2017)) is extended for calculation of static and dynamic polarizabilities. Its use is demonstrated by calculation of the polarizabilities for the ground and excited states of Er, Tm and Yb. It is proved to be an useful tool in designing a new generation of optical atomic clocks sensitive to new physics.},
  copyright = {http://creativecommons.org/licenses/by/3.0/},
  langid = {english},
  keywords = {atomic polarizability,atomic theory,electronic correlations,tests of new physics},
  file = {/Users/yingxing/Zotero/storage/GTVJB9Q9/Dzuba_2020_Calculation of Polarizabilities for Atoms with Open Shells.pdf}
}

@article{Dzuba2021,
  title = {Time Keeping and Searching for New Physics Using Metastable States of {{Cu}}, {{Ag}}, and {{Au}}},
  author = {Dzuba, V. A. and Allehabi, Saleh O. and Flambaum, V. V. and Li, Jiguang and Schiller, S.},
  year = {2021},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {103},
  number = {2},
  pages = {022822},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.103.022822},
  urldate = {2024-06-10},
  abstract = {We study the prospects of using the electric quadrupole transitions from the ground states of Cu, Ag, and Au to the metastable states as clock transitions in optical lattice clocks. We calculate lifetimes, transition rates, and systematic shifts and find that they are very suitable for this purpose. In particular, the elements are found to have a blackbody radiation shift that is one to two orders smaller than that of Sr. The Au clock is found to have strong sensitivities to a variation of the fine-structure constant, to effects of scalar dark matter, and to a violation of local Lorentz invariance (LLI). Cu and Ag are also suitable for tests of LLI. We identify two more metastable states (), one in Cu and another in Au, which can serve as additional clock transitions. The -sensitivity coefficients of the two Au clock transitions are large and have opposite sign. This doubles the overall sensitivity to variation of and opens the possibility of a -variation test with a single neutral atomic species. We also present more accurate or additional values of the sensitivity to local position invariance violation for several established or proposed clock transitions. These values are important for properly evaluating the effectiveness of clock-clock comparisons.},
  file = {/Users/yingxing/Zotero/storage/8ZDPTAZE/Dzuba et al. - 2021 - Time keeping and searching for new physics using m.pdf}
}

@article{Ehn2021,
  title = {Atomic and Ionic Polarizabilities of {{B}}, {{C}}, {{N}}, {{O}}, and {{F}}},
  author = {{\'E}hn, Ladislav and {\v C}ernu{\v s}{\'a}k, Ivan},
  year = {2021},
  journal = {Int. J. Quantum Chem.},
  volume = {121},
  number = {4},
  pages = {e26467},
  issn = {1097-461X},
  doi = {10.1002/qua.26467},
  urldate = {2024-06-06},
  abstract = {Accurate polarizabilities of atoms and molecules are critical in the treatment of optical and dielectric properties, in the modeling and interpretation of intermolecular interactions, in scattering processes, and in chemical reactivity. In this work we provide a systematic study of the atomic/ionic static dipole polarizabilities of the first-row elements: B+, B, B-, C2+, C+, C, C-, N2+, N+, N, O2+, O+, O, O-, F2+, F+, F, and F-. We used the CCSD(T) method with a range of large correlation-consistent basis sets augmented with a series of diffusion functions (x-aug-cc-pVXZ). We discuss the trends in the dependence of dipole polarizability from the basis set size and/or number of diffuse functions and report the recommended values of average dipole polarizabilities for this series. The systematic survey of dipole polarizabilities for ions from boron to fluorine, including the extrapolation to complete basis set limit, is presented for the first time.},
  copyright = {{\copyright} 2020 Wiley Periodicals LLC.},
  langid = {english},
  keywords = {CBS limit,correlation energy,dipole polarizability,electron affinity,first-row atoms,ions},
  file = {/Users/yingxing/Zotero/storage/SXE8UT7S/Éhn_Černušák_2021_Atomic and ionic polarizabilities of B, C, N, O, and F.pdf}
}

@article{Ekstrom1995,
  title = {Measurement of the Electric Polarizability of Sodium with an Atom Interferometer},
  author = {Ekstrom, Christopher R. and Schmiedmayer, J{\"o}rg and Chapman, Michael S. and Hammond, Troy D. and Pritchard, David E.},
  year = {1995},
  month = may,
  journal = {Phys. Rev. A},
  volume = {51},
  number = {5},
  pages = {3883--3888},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.51.3883},
  urldate = {2023-03-20},
  abstract = {We have constructed an atom interferometer with interfering beams that are physically isolated by a metal foil. By applying an interaction to one of the two interfering beams, we can measure ground-state energy shifts with a spectroscopic precision of 6.6{\texttimes}10-14 eV/{\textsurd}min , or 16 Hz/{\textsurd}min . Applying an electric field to one beam of the interferometer, we have measured the phase shift induced from the quadratic Stark effect. By analyzing these phase shifts, we have determined the ground-state polarizability of sodium, with much improved accuracy, to be 24.11(6)statistical(6)systematic{\texttimes}10-24 cm3.},
  file = {/Users/yingxing/Zotero/storage/9QMXPEWR/Ekstrom et al_1995_Measurement of the electric polarizability of sodium with an atom interferometer.pdf}
}

@article{Ellingsen2001,
  title = {Dynamic Dipole Polarizabilities for the Ground 4 {{1S}} and the Low-Lying 4 1,{{3P}} and 5 1,{{3S}} Excited States of {{Zn}}. {{Calculation}} of Long-Range Coefficients of {{Zn2}}},
  author = {Ellingsen, K. and M{\'e}rawa, M. and R{\'e}rat, M. and Pouchan, C. and Gropen, O.},
  year = {2001},
  month = jun,
  journal = {J. Phys. B At. Mol. Opt. Phys.},
  volume = {34},
  number = {12},
  pages = {2313},
  issn = {0953-4075},
  doi = {10.1088/0953-4075/34/12/302},
  urldate = {2023-03-20},
  abstract = {Dynamic dipole polarizabilities for the ground 4 1S and the low-lying 4 1,3P and 5 1,3S excited states of Zn are calculated by the time-dependent gauge-invariant method and compared with other experimental and theoretical results. The wavefunctions are obtained from multi-reference configuration-interaction calculations using a two-electron relativistic pseudopotential. Core-valence polarization is accounted for by the use of a semi-empirical core-valence potential. Core-polarization effects are also considered when calculating the oscillator strengths using a modified dipole transition operator. Long-range coefficients for the molecular states of Zn2 dissociating into: 4 1S + 4 1S; 4 1S + 4 3P; 4 1S + 4 1P; 4 1S + 5 1S and 4 1S + 5 3S are presented.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/6ILJ836M/Dynamic dipole polarizabilities for the ground 4 1S and the low-lying 4 1,3P and 5 1,3S excited states of Zn. Calculation of long-range.pdf}
}

@article{Ernst2016,
  title = {Optical Properties of Metal--Organic Networks from Distributed Atomic Polarizabilities},
  author = {Ernst, Michelle and Santos, Leonardo H. R. Dos and Macchi, Piero},
  year = {2016},
  month = sep,
  journal = {CrystEngComm},
  volume = {18},
  number = {38},
  pages = {7339--7346},
  publisher = {The Royal Society of Chemistry},
  issn = {1466-8033},
  doi = {10.1039/C6CE00918B},
  urldate = {2024-06-12},
  abstract = {Metal--organic networks have become very popular materials in view of various chemical and physico-chemical applications. Much attention is normally focused on porous compounds (metal--organic frameworks), although densely packed polymers may also find applications. In this paper, we propose a rather simplified method to estimate the dielectric constants and the optical indicatrices of metal--organic networks, which could be useful for rapid selection of materials with specific optical properties. The method adopts the distributed atomic polarizabilities calculated for secondary building units of metal--organic networks. With the atomic quantities, one can evaluate the crystal susceptibility, assuming an oriented gas model corrected for the polarization induced by the crystal medium. A simple oriented gas model enables a rapid evaluation of the anisotropy of the optical indicatrix of a crystal, as confirmed by calculations under periodic boundary conditions. The correction for polarization induced by the crystalline environment provides, in addition, more accurate estimation of the refractive indices, at least in the regime of low frequencies. The computational costs are smaller than those for fully periodic calculations and could be significantly smaller if a set of precomputed, transferable atomic polarizabilities would be used.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/878D8ENQ/Ernst et al_2016_Optical properties of metal–organic networks from distributed atomic.pdf;/Users/yingxing/Zotero/storage/8QJQ77BQ/Ernst et al. - 2016 - Optical properties of metal–organic networks from .pdf}
}

@article{Eustice2023,
  title = {Optical Telecommunications-Band Clock Based on Neutral Titanium Atoms},
  author = {Eustice, Scott and Filin, Dmytro and Schrott, Jackson and Porsev, Sergey and Cheung, Charles and Novoa, Diego and {Stamper-Kurn}, Dan M. and Safronova, Marianna S.},
  year = {2023},
  month = may,
  journal = {Phys. Rev. A},
  volume = {107},
  number = {5},
  pages = {L051102},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.107.L051102},
  urldate = {2024-06-10},
  abstract = {We propose an optical clock based on ultranarrow transitions in neutral titanium, which exhibit small blackbody radiation and quadratic Zeeman shifts and have wavelengths in the S-, C-, and L-telecommunications fiber bands, allowing for integration with robust laser technology. We calculate relevant properties using a high-precision relativistic hybrid method that combines configuration interaction and coupled-cluster approaches. To identify magic wavelengths, we have completed the largest-to-date direct dynamical polarizability calculations. Finally, we identify challenges that arise from magnetic dipole-dipole interactions and describe an approach to overcome them. A telecommunications-band atomic frequency standard will aid the deployment of optical clock networks and clock comparisons over long distances.},
  file = {/Users/yingxing/Zotero/storage/NVY4YMPI/Eustice et al. - 2023 - Optical telecommunications-band clock based on neu.pdf}
}

@article{Ferreira2020,
  title = {All-Electron Basis Sets Augmented with Diffuse Functions for {{He}}, {{Ca}}, {{Sr}}, {{Ba}}, and Lanthanides: Application in Calculations of Atomic and Molecular Properties},
  shorttitle = {All-Electron Basis Sets Augmented with Diffuse Functions for {{He}}, {{Ca}}, {{Sr}}, {{Ba}}, and Lanthanides},
  author = {Ferreira, I. B. and Campos, C. T. and Jorge, F. E.},
  year = {2020},
  month = apr,
  journal = {J Mol Model},
  volume = {26},
  number = {5},
  pages = {95},
  issn = {0948-5023},
  doi = {10.1007/s00894-020-04365-w},
  urldate = {2024-06-06},
  abstract = {Non-relativistic and Douglas-Kroll-Hess (DKH) basis sets augmented with diffuse functions for He, Ca, Sr, Ba, and lanthanides are generated. These sets are appropriated to describe electrons away from the nuclei. Using the DKH augmented sets along with the B3LYP functional, bond lengths, dissociation energies, harmonic vibrational frequencies, adiabatic ionization potentials, adiabatic~electron affinities, and~dipole moments for CaH, SrH, and BaH are computed. These results agree well with the most recent experimental and benchmark theoretical data published in the literature. The DKH mean dipole polarizabilities reported in this work for some elements are close to the recommended values. Scalar relativistic effects are also estimated.},
  langid = {english},
  keywords = {Atomic and molecular properties,DFT calculations,He Ca Sr Ba and lanthanides,Non-relativistic and DKH basis sets},
  file = {/Users/yingxing/Zotero/storage/TM2CUD5J/Ferreira et al_2020_All-electron basis sets augmented with diffuse functions for He, Ca, Sr, Ba,.pdf}
}

@article{Filippin2014,
  title = {Relativistic Polarizabilities with the {{Lagrange-mesh}} Method},
  author = {Filippin, Livio and Godefroid, Michel and Baye, Daniel},
  year = {2014},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {90},
  number = {5},
  pages = {052520},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.90.052520},
  urldate = {2023-03-21},
  abstract = {Relativistic dipolar to hexadecapolar polarizabilities of the ground state and some excited states of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the Lagrange-mesh method. This approach is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. The partial polarizabilities conserving the absolute value of the quantum number {$\kappa$} are also numerically exact with small numbers of mesh points. The ones where {\textbar}{$\kappa\vert$} changes are very accurate when using three different meshes for the initial and final wave functions and for the calculation of matrix elements. The polarizabilities of the n=2 excited states of hydrogenic atoms are also studied with a separate treatment of the final states that are degenerate at the nonrelativistic approximation. The method provides high accuracies for polarizabilities of a particle in a Yukawa potential and is applied to a hydrogen atom embedded in a Debye plasma.},
  file = {/Users/yingxing/Zotero/storage/LCP3DFRX/Relativistic polarizabilities with the Lagrange-mesh method_2014.pdf;/Users/yingxing/Zotero/storage/W94QJE38/Filippin et al. - 2014 - Relativistic polarizabilities with the Lagrange-me.pdf}
}

@article{Flambaum2020,
  title = {Electric Dipole Moments of Atoms and Molecules Produced by Enhanced Nuclear {{Schiff}} Moments},
  author = {Flambaum, V. V. and Dzuba, V. A.},
  year = {2020},
  month = apr,
  journal = {Phys. Rev. A},
  volume = {101},
  number = {4},
  pages = {042504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.101.042504},
  urldate = {2024-06-10},
  abstract = {We perform calculations of the {$C$}⁢{$P$}-violating atomic and molecular electric dipole moments (EDMs) induced by the interaction of the nuclear Schiff moments with electrons. EDMs of atoms Eu, Dy, Gd, Ac, Th, Pa, U, Np, and Pu are of special interest since they have isotopes with strongly enhanced nuclear Schiff moments caused by the octupole nuclear deformation or soft octupole vibration mode. These atoms have open or shells making the calculations complicated. We use our special version of the configuration-interaction method combined with the many-body perturbation theory method adopted for an open -shell case. To validate the method we perform similar calculations for simpler atoms (Xe, Hg, , Pb, , Rn, Ra), where some earlier results are available. In addition, we present the estimates of the -violating nuclear spin--molecular axis interaction constants for molecules which may be of experimental interest, including AcF, AcN, , EuN, , ThO, PbO, and TlF. We also present updated values of the nuclear Schiff moments and atomic and molecular EDMs expressed in terms of the -violating -meson--nucleon interaction constants , , , QCD parameter , and quark chromo-EDMs. The results may be used to test -violation theories and search for axion dark matter in atomic, molecular, and solid-state experiments.},
  file = {/Users/yingxing/Zotero/storage/PGL9FAPG/Flambaum_Dzuba_2020_Electric dipole moments of atoms and molecules produced by enhanced nuclear.pdf}
}

@article{Fleig2002,
  title = {Electric Dipole Polarizabilities of the Halogen Atoms in \$\{\}{\textasciicircum}\{2\}\{\vphantom\}{{P}}\vphantom\{\}\_\{1/2\}\$ and \$\{\}{\textasciicircum}\{2\}\{\vphantom\}{{P}}\vphantom\{\}\_\{3/2\}\$ States: {{Scalar}} Relativistic and Two-Component Configuration-Interaction Calculations},
  shorttitle = {Electric Dipole Polarizabilities of the Halogen Atoms in \$\{\}{\textasciicircum}\{2\}\{\vphantom\}{{P}}\vphantom\{\}\_\{1/2\}\$ and \$\{\}{\textasciicircum}\{2\}\{\vphantom\}{{P}}\vphantom\{\}\_\{3/2\}\$ States},
  author = {Fleig, Timo and Sadlej, Andrzej J.},
  year = {2002},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {65},
  number = {3},
  pages = {032506},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.65.032506},
  urldate = {2023-03-20},
  abstract = {A study of the influence of spin-orbit coupling and dynamical electron correlation on the polarizabilities of the halogen atoms in a variational treatment is presented. It is shown that for the heavier homologs it is necessary to replace the averaged values by individual component polarizabilities for the J=32 and J=12 atomic states due to the large spin-orbit coupling. A high level of correlation treatment by large-scale direct configuration interaction with up to quadruple excitations is maintained throughout. We, furthermore, put our relativistic two-component approach to the test by evaluating the change of picture effect on the polarizability values of the astatine atom arising from the neglect of a unitary transformation of the property operator to an approximate relativistic theory.},
  file = {/Users/yingxing/Zotero/storage/JCUFMGXX/Fleig and Sadlej - 2002 - Electric dipole polarizabilities of the halogen at.pdf}
}

@article{Fleig2005,
  title = {Spin-Orbit-Resolved Static Polarizabilities of Group-13 Atoms: {{Four-component}} Relativistic Configuration Interaction and Coupled Cluster Calculations},
  shorttitle = {Spin-Orbit-Resolved Static Polarizabilities of Group-13 Atoms},
  author = {Fleig, Timo},
  year = {2005},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {72},
  number = {5},
  pages = {052506},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.72.052506},
  urldate = {2023-03-21},
  abstract = {This study reports static electric dipole polarizabilities of the group 13 atoms in their lowest J=12,32 states including resolution of the property in the corresponding MJ components. The polarizabilities are obtained by a numerical finite-field technique applying weak external electric fields. Special relativity is accounted for in the four-component Dirac framework. Two large-scale configuration interaction programs which can be applied either including or neglecting spin-dependent terms in the Dirac Hamiltonian, respectively, are used for the treatment of dynamic electron correlation. Coupled cluster calculations are performed for obtaining highly accurate J=12 ground-state polarizabilities and for calibrating the configuration interaction calculations. The heavier atoms show large differences in the properties for different J states, and the effect of spin-orbit coupling is elucidated by separating it off from scalar relativistic contributions. The impact of spin-orbit interaction is also demonstrated for polarizability anisotropy components.},
  file = {/Users/yingxing/Zotero/storage/MZUV5AF7/Fleig - 2005 - Spin-orbit-resolved static polarizabilities of gro.pdf}
}

@article{Fleig2007,
  title = {A Relativistic 4-Component General-Order Multi-Reference Coupled Cluster Method: Initial Implementation and Application to {{HBr}}},
  shorttitle = {A Relativistic 4-Component General-Order Multi-Reference Coupled Cluster Method},
  author = {Fleig, Timo and S{\o}rensen, Lasse K. and Olsen, Jeppe},
  year = {2007},
  month = aug,
  journal = {Theor. Chem. Acc.},
  volume = {118},
  number = {2},
  pages = {347--356},
  issn = {1432-2234},
  doi = {10.1007/s00214-007-0265-y},
  urldate = {2023-03-20},
  abstract = {We present the initial implementation of a determinant-based general-order coupled cluster method which fully accounts for relativistic effects within the four-component framework. The method opens the way for the treatment of multi-reference problems through a state-selective expansion of the model space. The evaluation of the coupled cluster vector function is carried out via relativistic configuration interaction expansions. The implementation is based on a large-scale configuration interaction technique, which may efficiently treat long determinant expansions of more than 108 terms. We demonstrate the capabilities of the new method in calculations of complete potential energy curves of the HBr molecule. The inclusion of spin--orbit interaction and higher excitations than coupled cluster double excitations, either by multi-reference model spaces or the inclusion of full iterative triple excitations, lead to highly accurate results for spectral constants of HBr.},
  langid = {english},
  keywords = {Coupled cluster,Multi-reference,Relativistic 4-component,Spectroscopic properties},
  file = {/Users/yingxing/Zotero/storage/Y3EK7PJU/Fleig et al. - 2007 - A relativistic 4-component general-order multi-ref.pdf}
}

@article{Fleig2012,
  title = {Invited Review: {{Relativistic}} Wave-Function Based Electron Correlation Methods},
  shorttitle = {Invited Review},
  author = {Fleig, Timo},
  year = {2012},
  month = feb,
  journal = {Chem. Phys.},
  series = {Recent {{Advances}} and {{Applications}} of {{Relativistic Quantum Chemistry}}},
  volume = {395},
  pages = {2--15},
  issn = {0301-0104},
  doi = {10.1016/j.chemphys.2011.06.032},
  urldate = {2023-03-20},
  abstract = {Recent developments in molecular relativistic electronic-structure theory are reviewed, with a particular emphasis on post-Hartree--Fock electron correlation methodology. The approaches discussed encompass methods devised for the treatment of small molecules, such as four-component coupled cluster of general excitation rank, ranging to two-component methods based on perturbation theory which are applicable to larger molecules. A critique of the merits and shortcomings of the available methodology is put forward, including a comparison where appropriate.},
  langid = {english},
  keywords = {Electron correlation,Relativistic electronic-structure theory,Wave-function theory},
  file = {/Users/yingxing/Zotero/storage/HR6QM4YP/Fleig - 2012 - Invited review Relativistic wave-function based e.pdf}
}

@article{Fraga_1973,
  title = {Hartree-Fock Values of Coupling Constants, Polarizabilities, Susceptibilities, and {{radII}} for the Neutral Atoms, Helium to Nobelium},
  author = {Fraga, S. and Karwowski, J. and Saxena, K.M.S.},
  year = {1973},
  journal = {At. Data Nucl. Data Tables},
  volume = {12},
  number = {5},
  pages = {467--477},
  publisher = {Elsevier BV},
  issn = {0092-640X},
  doi = {10.1016/0092-640x(73)90003-x}
}

@article{Fuentealba2004,
  title = {The Static Dipole Polarizability of Aluminium Atom: Discrepancy between Theory and Experiment},
  shorttitle = {The Static Dipole Polarizability of Aluminium Atom},
  author = {Fuentealba, P.},
  year = {2004},
  month = oct,
  journal = {Chem. Phys. Lett.},
  volume = {397},
  number = {4},
  pages = {459--461},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2004.09.013},
  urldate = {2023-03-21},
  abstract = {A serious discrepancy of almost 20\% has been found between the experimentally measured static dipole polarizability of aluminium atom and very exhaustive theoretical calculations. This fact is important because in some experimental works the dipole polarizability of atomic clusters is measured with respect to the one of aluminium atom.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/UXBGGTXA/The static dipole polarizability of aluminium atom Discrepancy between theory and experiment_2004.pdf}
}

@article{Gaiser2010,
  title = {Experimental Benchmark Value for the Molar Polarizability of Neon},
  author = {Gaiser, C. and Fellmuth, B.},
  year = {2010},
  month = jul,
  journal = {Europhys. Lett.},
  volume = {90},
  number = {6},
  pages = {63002},
  issn = {0295-5075},
  doi = {10.1209/0295-5075/90/63002},
  urldate = {2023-03-20},
  abstract = {With dielectric-constant gas thermometry (DCGT), the molar polarizability of neon has been determined with a relative standard uncertainty of about 11 parts in 106 (11 ppm). A series of isotherms using helium and neon as measuring gas have been taken and the ab initio value for the polarizability of helium has been used to achieve this unprecedented level of uncertainty. The result of A{$\epsilon$}DCGTNe=9.94727{\texttimes}10-7 m3/mol agrees with the latest theoretical calculation on the level of a few parts in 104, but shows a relative deviation from the existing (experimental) reference value of several parts in 103.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/ISL5ZX6D/Gaiser_Fellmuth_2010_Experimental benchmark value for the molar polarizability of neon.pdf}
}

@article{Gaiser2018,
  title = {Polarizability of {{Helium}}, {{Neon}}, and {{Argon}}: {{New Perspectives}} for {{Gas Metrology}}},
  shorttitle = {Polarizability of {{Helium}}, {{Neon}}, and {{Argon}}},
  author = {Gaiser, Christof and Fellmuth, Bernd},
  year = {2018},
  month = mar,
  journal = {Phys. Rev. Lett.},
  volume = {120},
  number = {12},
  pages = {123203},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.120.123203},
  urldate = {2024-06-10},
  abstract = {With dielectric-constant gas thermometry, the molar polarizability of helium, neon, and argon has been determined with relative standard uncertainties of about 2 parts per million. A series of isotherms measured with the three noble gases and two different experimental setups led to this unprecedented level of uncertainty. These data are crucial for scientists in the field of gas metrology, working on pressure and temperature standards. Furthermore, with the new benchmark values for neon and argon, theoretical calculations, today about 3 orders of magnitude larger in uncertainty, can be checked and improved.},
  file = {/Users/yingxing/Zotero/storage/J5SWANX7/Gaiser and Fellmuth - 2018 - Polarizability of Helium, Neon, and Argon New Per.pdf}
}

@article{Glass1983,
  title = {The Mean Static Dipole Polarisability of Scandium},
  author = {Glass, R. and Chandler, G. S.},
  year = {1983},
  month = aug,
  journal = {J. Phys. B: Atom. Mol. Phys.},
  volume = {16},
  number = {16},
  pages = {2931},
  issn = {0022-3700},
  doi = {10.1088/0022-3700/16/16/013},
  urldate = {2024-06-12},
  abstract = {The mean static dipole polarisability of scandium is calculated. Perturbation theory was used so that the polarisability is expressed in terms of the second-order energy correction. The ground-state and necessary first-order correction to the wavefunction were determined variationally as a superposition of configurations. The importance of the various polarising orbitals and the length of the configuration expansion are examined.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/3F7DL8WB/Glass_Chandler_1983_The mean static dipole polarisability of scandium.pdf}
}

@article{Glass1987,
  title = {The Average Static Dipole Polarisability and Polarised Pseudostates for Scandium},
  author = {Glass, R.},
  year = {1987},
  month = mar,
  journal = {J. Phys. B: Atom. Mol. Phys.},
  volume = {20},
  number = {6},
  pages = {1379},
  issn = {0022-3700},
  doi = {10.1088/0022-3700/20/6/021},
  urldate = {2024-06-10},
  abstract = {The average static dipole polarisability of the ground state of scandium is calculated. The polarisability is expressed in terms of the first-order correction in the wavefunction, due to the static electric dipole perturbation, which is determined variationally as a configuration interaction expansion. The present investigation illustrates the importance of including the configurations 3d4p5p and 3d4d5p in the wavefunction expansions. The importance of including pseudo-orbitals specifically determined to describe the polarisation of 3d is also discussed. It is also shown that it is possible to obtain a value for the average static dipole polarisability of scandium using quite simple wavefunctions.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/6TSLVKIY/Glass - 1987 - The average static dipole polarisability and polar.pdf}
}

@book{gobre2016efficient,
  title = {Efficient {{Modelling}} of {{Linear Electronic Polarization}} in {{Materials Using Atomic Response Functions}}},
  author = {Gobre, Vivekanand V},
  year = {2016},
  publisher = {Technische Universitaet Berlin (Germany)}
}

@article{Godefroid1996,
  title = {Multiconfiguration {{Hartree}}--{{Fock}} Calculations of Atomic Properties in Light Atoms},
  author = {Godefroid, Michel R. and Fischer, Charlotte Froese and J{\"o}nsson, Per},
  year = {1996},
  month = jan,
  journal = {Phys. Scr.},
  volume = {1996},
  number = {T65},
  pages = {70},
  issn = {1402-4896},
  doi = {10.1088/0031-8949/1996/T65/010},
  urldate = {2024-06-12},
  abstract = {The progress achieved over the last few years in variational Multiconfiguration Hartree-Fock and Configuration Interaction calculations is reviewed. The high level of accuracy which can be reached in the ab initio calculation of atomic properties of light systems is illustrated through the results of calculations of isotope shifts, hyperfine structures and transition probabilities. The active space method and associated restricted active space methods allowing systematic calculations from which the accuracy of the studied property can be estimated will be discussed. We exemplify quality checks through results in small systems for which spectroscopic accuracy is often required. For transition probabilities, recent progress derived from new algorithm developments allowing independent optimization of the states is emphasized.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/9IYAABMJ/Godefroid et al_1996_Multiconfiguration Hartree–Fock calculations of atomic properties in light atoms.pdf}
}

@article{Goebel1995,
  title = {Dispersion of the Refractive Index of Cadmium Vapor and the Dipole Polarizability of the Atomic Cadmium \${\textasciicircum}\{1\}\$\$\{{\textbackslash}mathit\{\vphantom{\}\}}{{S}}\vphantom\{\}\vphantom\{\}\_\{0\}\$ State},
  author = {Goebel, Dirk and Hohm, Uwe},
  year = {1995},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {52},
  number = {5},
  pages = {3691--3694},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.52.3691},
  urldate = {2024-06-05},
  abstract = {We report measurements of the frequency dependence of the refractive index and polarizability of cadmium vapor in the frequency range between {$\omega$}=0.045 and 0.091 a.u. The quasicontinuous refractive index spectra have been measured at T≊1050 K with a high-temperature Michelson interferometer using the technique of dispersive Fourier-transform spectroscopy. The dispersion of the dipole polarizability {$\alpha$}({$\omega$}) of Cd obtained in our experiments can be represented as {$\alpha$}({$\omega$})={$\alpha$}(0){$\omega$}20/({$\omega$}20-{$\omega$}2), with a static polarizability of {$\alpha$}(0)=(49.65{\textpm}1.46{\textpm}0.16) a.u. and an effective transition frequency of {$\omega$}0=(0.250 61{\textpm}0.000 23) a.u. In addition, these measurements yield approximations for the dispersion interaction energy constant {$C$}6=466 a.u. and the second hyperpolarizability {$\gamma$}(0)=1.1{\texttimes}105 a.u.},
  file = {/Users/yingxing/Zotero/storage/XMT6QGIH/Goebel_Hohm_1995_Dispersion of the refractive index of cadmium vapor and the dipole.pdf}
}

@article{Goebel1995a,
  title = {Dispersive {{Fourier}} Transform Spectroscopy in the Visible of Absorbing Gases and Vapours},
  author = {Goebel, D. and Hohm, U. and Kerl, K.},
  year = {1995},
  month = apr,
  journal = {Journal of Molecular Structure},
  series = {Molecular {{Spectroscopy}} and {{Molecular Structure}} 1994},
  volume = {349},
  pages = {253--256},
  issn = {0022-2860},
  doi = {10.1016/0022-2860(95)08757-M},
  urldate = {2024-06-12},
  abstract = {Dispersive Fourier transform spectroscopy in the visible (DFTS-VIS) is used to study the complex refractive index {\^n}({$\sigma$}, T, {$\rho$}) of equilibrium mixtures of NO2N2O4 near room temperature, as well as the dispersion of {\^n}({$\sigma$}, T, {$\rho$}) of cadmium vapour up to temperatures of 1052K. In addition, the dispersion of the complex mean dipole polarizability {\^{\textbackslash}}ga({$\sigma$}) is obtained from these measurements.},
  file = {/Users/yingxing/Zotero/storage/LXTU5PAJ/Goebel et al_1995_Dispersive Fourier transform spectroscopy in the visible of absorbing gases and.pdf}
}

@article{Goebel1996,
  title = {Theoretical and Experimental Determination of the Polarizabilities of the Zinc \${\textasciicircum}\{1\}\$\$\{{\textbackslash}mathit\{\vphantom{\}\}}{{S}}\vphantom\{\}\vphantom\{\}\_\{0\}\$ State},
  author = {Goebel, Dirk and Hohm, Uwe and Maroulis, George},
  year = {1996},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {54},
  number = {3},
  pages = {1973--1978},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.54.1973},
  urldate = {2024-06-05},
  abstract = {A combined experimental and theoretical study of the polarizabilities of the ground-state zinc atom is presented. In our interferometric measurements we have obtained the frequency dependence of the linear dipole polarizability {$\alpha$}({$\omega$}) between {$\omega$}=0.05{$EH\hbar-$}1 and 0.14{$EH\hbar-$}1 (here {$EH$} is the Hartree energy). A detailed theoretical CCSD(T) study (coupled-cluster with single and double excitations and perturbational treatment of triple excitations) gives the static (zero-frequency) values of the linear dipole polarizability {$\alpha$}, the second dipole hyperpolarizability {$\gamma$}, the quadrupole-quadrupole polarizability {$\alpha$}2, and the dipole-dipole-quadrupole polarizability B. From these studies we conclude with the static values of {$\alpha$}=38.8(8){$e$}2{$a$}20{$E-$}1{$H$} (from experiment), {$\alpha$}=39.2(8){$e$}2{$a$}20{$E-$}1{$H$} (from theory), {$\gamma$}=31(6){\texttimes}103{$e$}4{$a$}40{$E-$}3{$H$}, {$\alpha$}2=324.8(16.2){$e$}2{$a$}40{$E-$}1{$H$}, and B=-2.37(24){\texttimes}103{$e$}3{$a$}40{$E-$}2{$H$}. {\copyright} 1996 The American Physical Society.},
  file = {/Users/yingxing/Zotero/storage/BHCJMITH/Goebel et al_1996_Theoretical and experimental determination of the polarizabilities of the zinc.pdf}
}

@article{Goebel1996a,
  title = {Dipole {{Polarizability}}, {{Cauchy Moments}}, and {{Related Properties}} of {{Hg}}},
  author = {Goebel, Dirk and Hohm, Uwe},
  year = {1996},
  month = jan,
  journal = {J. Phys. Chem.},
  volume = {100},
  number = {18},
  pages = {7710--7712},
  publisher = {American Chemical Society},
  issn = {0022-3654},
  doi = {10.1021/jp960231l},
  urldate = {2024-06-05},
  abstract = {We report interferometric measurements of the frequency dependence of the refractive index n and the dipole polarizability {$\alpha$} of Hg vapor. From the measured dispersion of the dipole polarizability the Cauchy moments S(-2) = 33.91(34), S(-4) = 279.8(8.4), and S(-6) = 14\,100(2810) have been obtained. The static limit S(-2) is in good accordance with ab initio calculations and results obtained from dielectric constant measurements. The Cauchy moments are used to predict approximations of the dispersion interaction energy constant C6 = 255 au and the second hyperpolarizability {$\gamma$}(0) = 2.2 {\texttimes} 104 au.},
  file = {/Users/yingxing/Zotero/storage/C5KRGDL2/Goebel_Hohm_1996_Dipole Polarizability, Cauchy Moments, and Related Properties of Hg.pdf}
}

@article{Goldman1989,
  title = {Gauge-Invariance Method for Accurate Atomic-Physics Calculations: {{Application}} to Relativistic Polarizabilities},
  shorttitle = {Gauge-Invariance Method for Accurate Atomic-Physics Calculations},
  author = {Goldman, S. P.},
  year = {1989},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {39},
  number = {3},
  pages = {976--980},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.39.976},
  urldate = {2024-06-12},
  abstract = {An accurate method for variational calculations of atomic properties is constructed using the principle that the results must be invariant under gauge transformations. The technique is used with multiexponential basis sets and provides very fast convergence. The method is applied to the relativistic calculation of the dipole polarizability in hydrogenic ions. The results obtained with 21 relativistic Slater-type basis functions are accurate to 13 digits for nuclear charges from Z=1 to Z=115, therefore overcoming the large loss of accuracy for large values of Z, which is typical of single-exponential basis sets. The results are compared with previous calculations and the coefficients of a relativistic expansion of the polarizability in powers of ( up to ( are obtained, where is the fine-structure constant.},
  file = {/Users/yingxing/Zotero/storage/3BMR25PS/Goldman_1989_Gauge-invariance method for accurate atomic-physics calculations.pdf}
}

@incollection{Gould2005,
  title = {Recent {{Developments}} in the {{Measurement}} of {{Static Electric Dipole Polarizabilities}}},
  booktitle = {Advances {{In Atomic}}, {{Molecular}}, and {{Optical Physics}}},
  author = {Gould, Harvey and Miller, Thomas M.},
  editor = {Stroke, H. H.},
  year = {2005},
  month = jan,
  volume = {51},
  pages = {343--361},
  publisher = {Academic Press},
  doi = {10.1016/S1049-250X(05)51019-X},
  urldate = {2024-06-05},
  abstract = {Recent advances in the measurement of static electric dipole polarizabilities are discussed. A brief history of atomic beam methods is given, with an emphasis on the work from Benjamin Bederson's laboratory at New York University. The latest measurements are described, including electric deflection experiments with cluster beams, the light-force method, atom-beam interferometry, electric-field induced velocity change of laser-cooled atoms, beam--foil spectroscopy, and microwave spectroscopy of Rydberg atoms and ions. Atomic-beam interferometry, laser-cooled atoms, and microwave spectroscopy of Rydberg atoms have yielded polarizabilities with unprecedented accuracy.},
  file = {/Users/yingxing/Zotero/storage/W83XRJ68/Gould_Miller_2005_Recent Developments in the Measurement of Static Electric Dipole.pdf}
}

@article{Gould2016a,
  title = {C6 {{Coefficients}} and {{Dipole Polarizabilities}} for {{All Atoms}} and {{Many Ions}} in {{Rows}} 1--6 of the {{Periodic Table}}},
  author = {Gould, Tim and Bu{\v c}ko, Tom{\'a}{\v s}},
  year = {2016},
  month = aug,
  journal = {J. Chem. Theory Comput.},
  volume = {12},
  number = {8},
  pages = {3603--3613},
  publisher = {American Chemical Society},
  issn = {1549-9618},
  doi = {10.1021/acs.jctc.6b00361},
  urldate = {2023-03-20},
  abstract = {Using time-dependent density functional theory (TDDFT) with exchange kernels, we calculate and test imaginary frequency-dependent dipole polarizabilities for all atoms and many ions in rows 1--6 of the periodic table. These are then integrated over frequency to produce C6 coefficients. Results are presented under different models: straight TDDFT calculations using two different kernels; ``benchmark'' TDDFT calculations corrected by more accurate quantum chemical and experimental data; and ``benchmark'' TDDFT with frozen orbital anions. Parametrizations are presented for 411+ atoms and ions, allowing results to be easily used by other researchers. A curious relationship, C6,XY {$\propto$} [{$\alpha$}X(0){$\alpha$}Y(0)]0.73, is found between C6 coefficients and static polarizabilities {$\alpha$}(0). The relationship C6,XY = 2C6,XC6,Y/[({$\alpha$}X/{$\alpha$}Y)C6,Y + ({$\alpha$}Y/{$\alpha$}X)C6,X] is tested and found to work well ({$<$}5\% errors) in {$\sim$}80\% of the cases, but can break down badly ({$>$}30\% errors) in a small fraction of cases.},
  file = {/Users/yingxing/Zotero/storage/37P9ZAP8/Gould and Bučko - 2016 - C6 Coefficients and Dipole Polarizabilities for Al.pdf;/Users/yingxing/Zotero/storage/CL49PGYL/C6 Coefficients and Dipole Polarizabilities for All Atoms and Many Ions in Rows 1–6 of the Periodic Table - 2016.pdf}
}

@article{Gould2016b,
  title = {How Polarizabilities and {{C6}} Coefficients Actually Vary with Atomic Volume},
  author = {Gould, Tim},
  year = {2016},
  month = aug,
  journal = {The Journal of Chemical Physics},
  volume = {145},
  number = {8},
  pages = {084308},
  issn = {0021-9606},
  doi = {10.1063/1.4961643},
  urldate = {2024-06-12},
  abstract = {In this work, we investigate how atomic C6 coefficients and static dipole polarizabilities {$\alpha$} scale with effective volume. We show, using confined atoms covering rows 1-5 of the periodic table, that    C   6   /   C   6   R   {$\approx$}    ( V /   V   R   )      p   Z      and  {$\alpha$} /   {$\alpha$}   R   {$\approx$}    ( V /   V   R   )      p   Z   {$\prime$}      (for volume  V = {$\int$} d r   4 {$\pi$}   3     r   3   n  ( r )  ), where    C   6   R   , {$\alpha$}R, and VR are the reference values and effective volume of the free atom. The scaling exponents pZ and    p   Z   {$\prime$}    vary substantially as a function of element number Z = N, in contrast to the standard ``rule of thumb'' that pZ = 2 and    p   Z   {$\prime$}   = 1 . Remarkably, we find that the polarizability and C6 exponents p{$\prime$} and p are related by p{$\prime$} {$\approx$} p - 0.615 rather than the expected p{$\prime$} {$\approx$} p/2. Results are largely independent of the form of the confining potential (harmonic, cubic, and quartic potentials are considered) and kernel approximation, justifying this analysis.},
  file = {/Users/yingxing/Zotero/storage/GY6FR49U/Gould_2016_How polarizabilities and C6 coefficients actually vary with atomic volume.pdf}
}

@article{Granatier2011,
  title = {The {{Nature}} of the {{Binding}} of {{Au}}, {{Ag}}, and {{Pd}} to {{Benzene}}, {{Coronene}}, and {{Graphene}}: {{From Benchmark CCSD}}({{T}}) {{Calculations}} to {{Plane-Wave DFT Calculations}}},
  shorttitle = {The {{Nature}} of the {{Binding}} of {{Au}}, {{Ag}}, and {{Pd}} to {{Benzene}}, {{Coronene}}, and {{Graphene}}},
  author = {Granatier, Jaroslav and Lazar, Petr and Otyepka, Michal and Hobza, Pavel},
  year = {2011},
  month = nov,
  journal = {J. Chem. Theory Comput.},
  volume = {7},
  number = {11},
  pages = {3743--3755},
  publisher = {American Chemical Society},
  issn = {1549-9618},
  doi = {10.1021/ct200625h},
  urldate = {2024-06-12},
  abstract = {The adsorption of Ag, Au, and Pd atoms on benzene, coronene, and graphene has been studied using post Hartree--Fock wave function theory (CCSD(T), MP2) and density functional theory (M06-2X, DFT-D3, PBE, vdW-DF) methods. The CCSD(T) benchmark binding energies for benzene--M (M = Pd, Au, Ag) complexes are 19.7, 4.2, and 2.3 kcal/mol, respectively. We found that the nature of binding of the three metals is different: While silver binds predominantly through dispersion interactions, the binding of palladium has a covalent character, and the binding of gold involves a subtle combination of charge transfer and dispersion interactions as well as relativistic effects. We demonstrate that the CCSD(T) benchmark binding energies for benzene--M complexes can be reproduced in plane-wave density functional theory calculations by including a fraction of the exact exchange and a nonempirical van der Waals correction (EE+vdW). Applying the EE+vdW method, we obtained binding energies for the graphene--M (M = Pd, Au, Ag) complexes of 17.4, 5.6, and 4.3 kcal/mol, respectively. The trends in binding energies found for the benzene--M complexes correspond to those in coronene and graphene complexes. DFT methods that use empirical corrections to account for the effects of vdW interactions significantly overestimate binding energies in some of the studied systems.},
  file = {/Users/yingxing/Zotero/storage/LMNE8NX8/Granatier et al_2011_The Nature of the Binding of Au, Ag, and Pd to Benzene, Coronene, and Graphene.pdf}
}

@article{Gregoire2015,
  title = {Measurements of the Ground-State Polarizabilities of {{Cs}}, {{Rb}}, and {{K}} Using Atom Interferometry},
  author = {Gregoire, Maxwell D. and Hromada, Ivan and Holmgren, William F. and Trubko, Raisa and Cronin, Alexander D.},
  year = {2015},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {92},
  number = {5},
  pages = {052513},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.92.052513},
  urldate = {2023-03-20},
  abstract = {We measured the ground-state static electric-dipole polarizabilities of Cs, Rb, and K atoms using a three-nanograting Mach-Zehnder atom beam interferometer. Our measurements provide benchmark tests for atomic structure calculations and thus test the underlying theory used to interpret atomic parity-nonconservation experiments. We measured {$\alpha$}Cs=4{$\pi\varepsilon$}0{\texttimes}59.39(9){\AA}3,{$\alpha$}Rb=4{$\pi\varepsilon$}0{\texttimes}47.39(8){\AA}3, and {$\alpha$}K=4{$\pi\varepsilon$}0{\texttimes}42.93(7){\AA}3. In atomic units, these measurements are {$\alpha$}Cs=401.2(7),{$\alpha$}Rb=320.1(6), and {$\alpha$}K=290.0(5). We report ratios of polarizabilities {$\alpha$}Cs/{$\alpha$}Rb=1.2532(10),{$\alpha$}Cs/{$\alpha$}K=1.3834(9), and {$\alpha$}Rb/{$\alpha$}K=1.1040(9) with smaller fractional uncertainty because the systematic errors for individual measurements are largely correlated. Since Cs atom beams have short de Broglie wavelengths, we developed measurement methods that do not require resolved atom diffraction. Specifically, we used phase choppers to measure atomic beam velocity distributions, and we used electric field gradients to give the atom interference pattern a phase shift that depends on atomic polarizability.},
  file = {/Users/yingxing/Zotero/storage/JC2D97BE/Gregoire et al. - 2015 - Measurements of the ground-state polarizabilities .pdf}
}

@article{Gregoire2016,
  title = {Analysis of {{Polarizability Measurements Made}} with {{Atom Interferometry}}},
  author = {Gregoire, Maxwell D. and Brooks, Nathan and Trubko, Raisa and Cronin, Alexander D.},
  year = {2016},
  month = sep,
  journal = {Atoms},
  volume = {4},
  number = {3},
  pages = {21},
  publisher = {Multidisciplinary Digital Publishing Institute},
  issn = {2218-2004},
  doi = {10.3390/atoms4030021},
  urldate = {2023-03-20},
  abstract = {We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then, we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths fik, Einstein coefficients Aik, state lifetimes {$\tau$}k, transition dipole matrix elements Dik, line strengths Sik, and van der Waals C6 coefficients. Finally, we combine atom interferometer measurements of polarizabilities with independent measurements of lifetimes and C6 values in order to quantify the residual contribution to polarizability due to all atomic transitions other than the principal ns-npJ transitions for alkali metal atoms.},
  copyright = {http://creativecommons.org/licenses/by/3.0/},
  langid = {english},
  keywords = {atom interferometry,Atom interferometry,dipole matrix elements,Dipole matrix elements,line strength,Line strength,oscillator strengths,Oscillator strengths,polarizability,Polarizability,state lifetimes,State lifetimes,van der Waals interactions,Van der Waals interactions},
  file = {/Users/yingxing/Zotero/storage/LJA9CPJU/Gregoire et al. - 2016 - Analysis of Polarizability Measurements Made with .pdf}
}

@article{Guella1984,
  title = {Polarizability of \$5\{s\}{\textasciicircum}\{2\}5p({\textasciicircum}\{2\}{{P}}\_\{{\textbackslash}frac\{1\}\{2\}\})\$ Atomic Indium},
  author = {Guella, T. P. and Miller, Thomas M. and Bederson, B. and Stockdale, J. A. D. and Jaduszliwer, B.},
  year = {1984},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {29},
  number = {6},
  pages = {2977--2980},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.29.2977},
  urldate = {2024-06-05},
  abstract = {We have measured the static electric dipole polarizability of ground state 115 49In⁢5⁢{$s$}2⁢5⁢{$p$}⁡(2{$P$}12) with a small ({$\sim$}9\%) admixture of metastable 5⁢{$s$}2⁢5⁢{$p$}⁡(2{$P$}32). Three different methods were used: (a) {$E-H$} gradient balance, (b) comparison of deflection in an inhomogeneous electric field with an alkalimetal-atom "standard," and (c) a deflection analysis using a computer program with no adjustable parameters except the polarizability itself. All methods agree to within 11\%. Our weighted final result is (10.18{\textpm}1.20){\texttimes}10-24 cm3. This is in very close agreement to a recent computation by Liberman and Zangwill, using fully relativistic wave functions and including electron correlation.},
  file = {/Users/yingxing/Zotero/storage/BPDVUIZ6/Guella et al_1984_Polarizability of $5 s ^ 2 5p(^ 2 P_ -frac 1 2 )$ atomic indium.pdf}
}

@article{Guo2021,
  title = {Electric Dipole and Quadrupole Properties of the {{Cd}} Atom for Atomic-Clock Applications},
  author = {Guo, X. T. and Yu, Y. M. and Liu, Y. and Suo, B. B. and Sahoo, B. K.},
  year = {2021},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {103},
  number = {1},
  pages = {013109},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.103.013109},
  urldate = {2024-06-06},
  abstract = {We present accurate values of the atomic properties that are sensitive to an external electric field in an experiment, such as static electric dipole and quadrupole polarizabilities, hyperpolarizabilities, and quadrupole moments of the low-lying 5⁢{$s$}21{$S$}0, 5⁢{$s$}⁢5⁢{$p$}3{$P$}0,1,2, and 5⁢{$s$}⁢5⁢{$p$}1{$P$}1 states of the Cd atom. The four-component relativistic coupled-cluster theory is employed to determine the atomic wave functions and energies. The finite-field approach is adopted to estimate the above quantities from the evaluated energies. The roles of electron correlation effects in the calculations are demonstrated by giving results that are obtained with different approximations. Precise knowledge of the above spectroscopic properties is useful for estimating typical systematics of the optical clocks built using the Cd atoms.},
  file = {/Users/yingxing/Zotero/storage/YJ2W39IZ/Guo et al_2021_Electric dipole and quadrupole properties of the Cd atom for atomic-clock.pdf}
}

@article{Hald2003,
  title = {Calculation of Frequency-Dependent Polarizabilities Using the Approximate Coupled-Cluster Triples Model {{CC3}}},
  author = {Hald, Kasper and Paw{\l}owski, Filip and J{\o}rgensen, Poul and H{\"a}ttig, Christof},
  year = {2003},
  month = jan,
  journal = {The Journal of Chemical Physics},
  volume = {118},
  number = {3},
  pages = {1292--1300},
  issn = {0021-9606},
  doi = {10.1063/1.1523905},
  urldate = {2024-06-12},
  abstract = {The calculation of frequency-dependent polarizabilities is discussed for the iterative approximate coupled-cluster singles, doubles and triples model CC3. A new implementation of the linear response functions is reported, which has the same computational O(N7) scaling as CC3 ground state calculations and uses an explicitly spin-coupled excitation space. Sample calculations are presented for the static and frequency-dependent polarizabilities of Ne and ethylene, as well as for the static polarizabilities of HF. The largest calculation employs the t-aug-cc-pVTZ basis set for ethylene giving a total of 328 basis functions. The results obtained agree well with the experimental data.},
  file = {/Users/yingxing/Zotero/storage/JR46KBI5/Hald et al_2003_Calculation of frequency-dependent polarizabilities using the approximate.pdf}
}

@article{Hamilton2023,
  title = {Experimental and {{Theoretical Study}} of {{Dynamic Polarizabilities}} in the \$5\{\vphantom\}{{S}}\vphantom\{\}\_\{1/2\}\$--\$5\{\vphantom\}{{D}}\vphantom\{\}\_\{5/2\}\$ {{Clock Transition}} in {{Rubidium-87}} and {{Determination}} of {{Electric Dipole Matrix Elements}}},
  author = {Hamilton, Rhona and Roberts, Benjamin M. and Scholten, Sarah K. and Locke, Clayton and Luiten, Andre N. and Ginges, Jacinda S.M. and Perrella, Christopher},
  year = {2023},
  month = may,
  journal = {Phys. Rev. Appl.},
  volume = {19},
  number = {5},
  pages = {054059},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevApplied.19.054059},
  urldate = {2024-06-10},
  abstract = {The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the -- transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the -- transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the -- resonance, and the corresponding reduced E1 matrix element (experimental) and (theoretical). These values resolve a previous discrepancy between theory and experiment.},
  file = {/Users/yingxing/Zotero/storage/MCR4N6XH/Hamilton et al. - 2023 - Experimental and Theoretical Study of Dynamic Pola.pdf}
}

@article{Hellmann2022,
  title = {\${{Ab}}{\textbackslash}phantom\{{\textbackslash}rule\{4pt\}\{0ex\}\}initio\$ Determination of the Polarizability of Neon},
  author = {Hellmann, Robert},
  year = {2022},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {105},
  number = {2},
  pages = {022809},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.105.022809},
  urldate = {2024-06-06},
  abstract = {The static electric-dipole polarizability {$A$} of the neon atom was determined with a relative uncertainty of only about 0.003\% using state-of-the-art ab initio approaches. The new value, {$A$}=2.661067⁢(77)⁢a.u., is almost five times more accurate than the previous ab initio estimate, {$A$}=2.66080⁢(36)⁢a.u., by Lesiuk et al. [Phys. Rev. A 102, 052816 (2020)]. Similar to their work, we calculated {$A$} using ab initio methods up to full configuration interaction and added corrections for finite nuclear mass and size, relativistic, and quantum electrodynamics (QED) effects. The uncertainty reduction of this work was achieved in particular by employing extremely large basis sets, including newly developed ones of 11Z, 12Z, and 13Z quality. Moreover, the finite nuclear mass effects and most of the relativistic contributions were calculated at much higher levels of theory than in the work of Lesiuk et al. However, we adopted their values for the orbit-orbit part of the relativistic correction and for the Bethe logarithm needed to compute the QED correction. The uncertainty of our final value is still an order of magnitude larger than that of the experimental value recently measured by Gaiser and Fellmuth [Phys. Rev. Lett. 120, 123203 (2018)] with an uncertainty of only a few parts per million using dielectric-constant gas thermometry. Yet, our ab initio value agrees with their value, {$A$}exp=2.661057⁢(7)⁢a.u., almost within the experimental uncertainty. This could indicate that the higher-order relativistic corrections and QED contributions, which dominate our uncertainty budget, are more accurate than expected considering the uncontrolled approximations involved in their calculation.},
  file = {/Users/yingxing/Zotero/storage/CPKWZB3A/Hellmann_2022_$Ab-phantom -rule 4pt 0ex initio$ determination of the polarizability of neon.pdf}
}

@article{Henderson1997,
  title = {Lifetime Measurements in {{Tl III}} and the Determination of the Ground-State Dipole Polarizabilities for {{Au I--Bi V}}},
  author = {Henderson, M. and Curtis, L. J. and Matulioniene, R. and Ellis, D. G. and Theodosiou, C. E.},
  year = {1997},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {56},
  number = {3},
  pages = {1872--1878},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.56.1872},
  urldate = {2024-06-12},
  abstract = {Measurements are reported for the lifetimes of the 6⁢{$p$}⁢2⁢{$P$}1/2,3/2, 6⁢{$d$}⁢2⁢{$D$}3/2,5/2, 7⁢{$s$}⁢2⁢{$S$}1/2, 7⁢{$p$}⁢2⁢{$P$}1/2,3/2, 7⁢{$d$}⁢2⁢{$D$}5/2, and 5⁢{$f$}⁢2⁢{$F$}5/2,7/2 levels in Tl III, made using beam-foil excitation. Theoretical calculations are also presented to elucidate conditions of configuration interaction exhibited by the measurements. In addition, values for the measured 6⁢{$p$} lifetimes in the Au sequence are combined with theoretical calculations of resonance transitions to higher levels to specify the ground-state dipole polarizabilities for Au I, Hg II, Tl III, Pb IV, and Bi V.},
  file = {/Users/yingxing/Zotero/storage/HU4XVPPJ/Henderson et al_1997_Lifetime measurements in Tl III and the determination of the ground-state.pdf}
}

@article{Hibbert1980,
  title = {Atomic Polarisabilities and Polarised Pseudostates in the Multiconfigurational Approach. {{III}}. {{Second-row}} Atoms and Ions},
  author = {Hibbert, A.},
  year = {1980},
  month = oct,
  journal = {J. Phys. B At. Mol. Phys.},
  volume = {13},
  number = {19},
  pages = {3725},
  issn = {0022-3700},
  doi = {10.1088/0022-3700/13/19/009},
  urldate = {2023-03-20},
  abstract = {For pt.II see ibid., vol.10, no.6, p.1015 (1977). Mean static dipole polarisabilities are calculated for the ground states of neutral atoms from Al to Cl and for singly ionised Si+ to Ar+. The polarisability is expressed in terms of the first-order correction in the wavefunction (due to the static electric dipole perturbation) which is determined variationally as a configuration interaction expansion. Near-degeneracy effects are included. The results are comparable with those obtained from the coupled Hartree-Fock scheme. The first-order wavefunctions may be used as target pseudostates in electron-atom scattering.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/4JA6XLR9/Atomic polarisabilities and polarised pseudostates in the multiconfigurational approach. III. Second-row atoms and ions_1980.pdf}
}

@article{Hohm1990,
  title = {Interferometric Measurements of the Dipole Polarizability {$\alpha$} of Molecules between 300 {{K}} and 1100 {{K}}},
  author = {Hohm, Uwe and Kerl, Klaus},
  year = {1990},
  month = apr,
  journal = {Mol. Phys.},
  volume = {69},
  number = {5},
  pages = {803--817},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268979000100611},
  urldate = {2023-03-20},
  abstract = {The temperature dependence of the dipole polarizability {$\alpha$}({$\lambda$}, T) of free atoms and molecules is determined by precise measurements of the refractive index n of gases in the extended temperature range between 300 K and 1100 K for wavelength {$\lambda$} = 632{$\cdot$}99 nm, using a specially constructed Michelson twin interferometer. {$\alpha$} of the noble gases is observed to be independent of T. {$\alpha$} of the molecular gases H2, N2, O2, and CH4 increases with increasing temperature by an amount of approximately 1 per cent per 1000 K. These results are in excellent agreement with theoretical predictions. They will be compared to previously measured temperature dependent polarizabilities.},
  file = {/Users/yingxing/Zotero/storage/3B39J9JP/Interferometric measurements of the dipole polarizability α of molecules between 300K and 1100K I. Monochromatic measurements at λ = 6.pdf;/Users/yingxing/Zotero/storage/G6GU9C55/Hohm_Kerl_1990_Interferometric measurements of the dipole polarizability α of molecules.pdf}
}

@article{Hohm2012,
  title = {New {{Relationships Connecting}} the {{Dipole Polarizability}}, {{Radius}}, and {{Second Ionization Potential}} for {{Atoms}}},
  author = {Hohm, Uwe and Thakkar, Ajit J.},
  year = {2012},
  month = jan,
  journal = {J. Phys. Chem. A},
  volume = {116},
  number = {1},
  pages = {697--703},
  publisher = {American Chemical Society},
  issn = {1089-5639},
  doi = {10.1021/jp2094438},
  urldate = {2024-06-12},
  abstract = {The atomic dipole polarizability {$\alpha$} of the 101 elements from He to No is related to the second ionization potential I2 and the Waber--Cromer radius rWC. Our recommended model is the function {$\alpha$} = P1{$\cdot$}I2--4 + P2{$\cdot$}r3WCI2y. With the parameters P1 = 2.26, P2 = 3.912, and y = 0.439, it reproduces the polarizabilities of all 101 elements with a mean absolute deviation of 7.5 au.},
  file = {/Users/yingxing/Zotero/storage/QEESAGBW/Hohm_Thakkar_2012_New Relationships Connecting the Dipole Polarizability, Radius, and Second.pdf}
}

@article{Hohm2022a,
  title = {Dipole--{{Dipole Polarizability}} of the {{Cadmium 1S0 State Revisited}}},
  author = {Hohm, Uwe},
  year = {2022},
  month = apr,
  journal = {Opt. Spectrosc.},
  volume = {130},
  number = {4},
  pages = {290--294},
  issn = {1562-6911},
  doi = {10.1134/S0030400X22040105},
  urldate = {2024-06-10},
  abstract = {Experimental results and high-level quantum chemical ab initio calculations of the static polarizability {$\alpha$}0 = {$\alpha$}({$\omega$} = 0) of the cadmium 1S0 state are still in marked disagreement. Here we analyze this discrepancy by using experimentally determined dipole oscillator strength distributions (DOSD). It will be shown that within this procedure the experimentally determined static polarizability {$\alpha$}0 will shift from 49.7 {\textpm} 1.6 au to considerably lower values. We now conclude an experimentally determined polarizability of {$\alpha$}0 = 47.5 {\textpm} 2.0 au in much better agreement with the latest calculations of {$\alpha$}0 {$\approx$} 46 au.},
  langid = {english},
  keywords = {cadmium,DOSD,polarizability},
  file = {/Users/yingxing/Zotero/storage/RWLX7MKN/Hohm_2022_Dipole–Dipole Polarizability of the Cadmium 1S0 State Revisited.pdf}
}

@article{Huot1991,
  title = {Experimental Determination of the Dielectric Virial Coefficients of Atomic Gases as a Function of Temperature},
  author = {Huot, J. and Bose, T. K.},
  year = {1991},
  month = aug,
  journal = {The Journal of Chemical Physics},
  volume = {95},
  number = {4},
  pages = {2683--2687},
  issn = {0021-9606},
  doi = {10.1063/1.461801},
  urldate = {2024-06-05},
  abstract = {The second dielectric virial coefficient of atomic gases has been measured precisely as a function of temperature in the range 77 to 407 K. The experimental values are compared with the ab\hphantom{,}initio calculations and the collision-induced polarized scattered spectra (CIS). Except for helium, the B{$\varepsilon$} values derived from ab\hphantom{,}initio calculations and CIS parameters do not agree with the experimental values.},
  file = {/Users/yingxing/Zotero/storage/XWYMTZLN/Huot_Bose_1991_Experimental determination of the dielectric virial coefficients of atomic.pdf}
}

@article{Hylleraas1930,
  title = {{{\"U}ber den Grundterm der Zweielektronenprobleme von H-, He, Li+, Be++ usw.}},
  author = {Hylleraas, Egil A.},
  year = {1930},
  month = mar,
  journal = {Z. Physik},
  volume = {65},
  number = {3},
  pages = {209--225},
  issn = {0044-3328},
  doi = {10.1007/BF01397032},
  urldate = {2024-06-07},
  abstract = {Es wird die Ionisierungsenergie des normalen Heliums und der mit ihm analogen Atomkonfigurationen berechnet. Diese Probleme werden in ein einheitliches Problem zusammengefa{\ss}t, in dem die reziproke Kernladung als kontinuierlicher St{\"o}rungsparameter aufgefa{\ss}t wird. F{\"u}r die Gesamtenergie ergibt sich:\$\$E = Rh{\textbackslash}left( \{ - 2Z{\textasciicircum}2  + {\textbackslash}frac\{5\}\{4\}Z - 0,31488 + 0,01752{\textbackslash}frac\{1\}\{Z\} - 0,00548{\textbackslash}frac\{1\}\{\{Z{\textasciicircum}2 \}\}\} {\textbackslash}right)\$\$. Daserste Glied in dieser Entwicklung nach 1/Z ist die bekannte ungest{\"o}rte Energie, daszweite Glied erh{\"a}lt man durch eine gew{\"o}hnliche St{\"o}rungsrechnung. Die Bestimmung der beiden Glieder fordert nur die Kenntnis der Eigenfunktionnullter N{\"a}herung, d. h. daserste Glied in der entsprechenden Entwicklung der Eigenfunktion. --- Dasdritte Glied l{\"a}{\ss}t sich nach einem schnell konvergierenden Rechenverfahren beliebig genau berechnen. Dies Verfahren liefert auch die Eigenfunktionerster N{\"a}herung, die aber viel langsamer konvergiert. Das vierte Glied, das man auch theoretisch mit Hilfe der letztgenannten Funktion berechnen kann, konvergiert infolgedessen auch sehr langsam. Praktisch lohnt sich daher nur die theoretische Bestimmung des dritten Gliedes. Die zwei noch hinzugef{\"u}gten Glieder sind daher nur rechnerisch bestimmte Korrektionsglieder, d. h. sie sind so gew{\"a}hlt, da{\ss} die Formel mit den beiZ=1 undZ=2, also bei H- und He, direkt berechneten Energiewerten {\"u}bereinstimmt. --- Bei He, Li+ und Be++ stimmt die Formel vorz{\"u}glich mit den genauen spektroskopischen Bestimmungen der Energie. Bei H- liegen nur unsichere thermochemische Daten vor, die dem theoretischen Wert jedenfalls nicht widersprechen. In diesem letzten Falle wollen wir daher auch das Resultat als die richtige Bestimmung der Energie und somit auch der Elektronenaffinit{\"a}t des Wasserstoffatoms ansehen.},
  langid = {ngerman},
  file = {/Users/yingxing/Zotero/storage/WIVPYL85/Hylleraas_1930_Über den Grundterm der Zweielektronenprobleme von H−, He, Li+, Be++ usw.pdf}
}

@article{Irikura2021,
  title = {Polarizability of Atomic {{Pt}}, {{Pt}}+, and {{Pt}}-},
  author = {Irikura, Karl K.},
  year = {2021},
  month = may,
  journal = {The Journal of Chemical Physics},
  volume = {154},
  number = {17},
  pages = {174302},
  issn = {0021-9606},
  doi = {10.1063/5.0044996},
  urldate = {2024-06-06},
  abstract = {Electrostatic properties are important for understanding and modeling many phenomena, such as the adsorption of a catalytic metal upon an oxide support. The charge transfer between the metal and the support can lead to positive or negative charges on the metal. Here, the static dipole polarizability is computed for atomic platinum in charge states 0, +1, and -1 in several low-lying electronic terms and levels. Core pseudopotentials are used along with coupled-cluster theory. The best results are estimates for the coupled-cluster CCSDTQ/q-aug-cc-pwCV{$\infty$}Z-PP values for atomic terms, combined with compositional data from spin--orbit configuration interaction. The polarizability of the anion Pt- is especially challenging for the theory with wildly varying results from different coupled-cluster perturbative approximations such as CCSD(T). For atomic mercury (Hg), selected as a nearby experimental value, our polarizability volume is larger than experiment by 0.8 bohrs3 (or 0.12 {\texttimes} 10-30 m3). For the ground level of neutral platinum, Pt(3D3), we find {$\alpha$}0 = (41.2 {\textpm} 1.1) bohrs3 or (6.10 {\textpm} 0.16) {\texttimes} 10-30 m3. A handful of density functional theory methods are tested and found generally within 10\% of our best values.},
  file = {/Users/yingxing/Zotero/storage/SJMXJ7QN/Irikura_2021_Polarizability of atomic Pt, Pt+, and Pt−.pdf}
}

@article{Iskrenova-Tchoukova2008a,
  title = {High-Precision Study of {{Cs}} Polarizabilities},
  author = {{Iskrenova-Tchoukova}, E. and Safronova, M. S. and Safronova, U. I.},
  year = {2007},
  month = jan,
  journal = {J. Comput. Methods Sci. Eng.},
  volume = {7},
  number = {5-6},
  pages = {521--540},
  publisher = {IOS Press},
  issn = {1472-7978},
  doi = {10.3233/JCM-2007-75-616},
  urldate = {2024-06-12},
  abstract = {We present results of the first-principles calculation of Cs dipole static polarizabilities for the N s (N =6--12), N p j (N =6--10), and N d j (N =5--10) states using the relativistic all-order method. In our implementation of the all-order method, sin},
  langid = {english}
}

@article{Jerabek2018,
  title = {Electron and {{Nucleon Localization Functions}} of {{Oganesson}}: {{Approaching}} the {{Thomas-Fermi Limit}}},
  shorttitle = {Electron and {{Nucleon Localization Functions}} of {{Oganesson}}},
  author = {Jerabek, Paul and Schuetrumpf, Bastian and Schwerdtfeger, Peter and Nazarewicz, Witold},
  year = {2018},
  month = jan,
  journal = {Phys. Rev. Lett.},
  volume = {120},
  number = {5},
  pages = {053001},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.120.053001},
  urldate = {2023-03-20},
  abstract = {Fermion localization functions are used to discuss electronic and nucleonic shell structure effects in the superheavy element oganesson, the heaviest element discovered to date. Spin-orbit splitting in the 7p electronic shell becomes so large ({$\sim$}10 eV) that Og is expected to show uniform-gas-like behavior in the valence region with a rather large dipole polarizability compared to the lighter rare gas elements. The nucleon localization in Og is also predicted to undergo a transition to the Thomas-Fermi gas behavior in the valence region. This effect, particularly strong for neutrons, is due to the high density of single-particle orbitals.},
  keywords = {,doi:10.1103/PhysRevLett.120.053001 url:https://doi},
  file = {/Users/yingxing/Zotero/storage/2R54LGQM/Jerabek et al_2018_Electron and Nucleon Localization Functions of Oganesson.pdf;/Users/yingxing/Zotero/storage/JFY2FXDP/Jerabek et al. - 2018 - Electron and Nucleon Localization Functions of Oga.pdf}
}

@article{Jerabek2018b,
  title = {Static Dipole Polarizability of Palladium from Relativistic Coupled-Cluster Theory},
  author = {Jerabek, Paul and Schwerdtfeger, Peter and Nagle, Jeffrey K.},
  year = {2018},
  month = jul,
  journal = {Phys. Rev. A},
  volume = {98},
  number = {1},
  pages = {012508},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.98.012508},
  urldate = {2024-06-12},
  abstract = {Nonrelativistic and relativistic coupled-cluster calculations extrapolated to the complete basis set limit including excitations up to the quintuple level were carried out to accurately determine the static electric dipole polarizability of the closed-shell palladium atom. The resulting value of {$A$} = 26.14(10) a.u. implies that palladium has the smallest dipole polarizability of all known elemental metal atoms due to its unique configuration. Relativistic effects are found to be already sizable ( = +1.86 a.u.) compared to electron correlation ( = +5.06 a.u.) and need to be included for the accurate determination of the dipole polarizability. We also report a value of the second hyperpolarizability to be 40 000 a.u., but here the coupled-cluster contributions are not yet converged with respect to higher than quintuple excitations.},
  file = {/Users/yingxing/Zotero/storage/RS8BA3H3/Jerabek et al_2018_Static dipole polarizability of palladium from relativistic coupled-cluster.pdf}
}

@article{Jiang2013,
  title = {Hyperfine Effects on Potassium Tune-out Wavelengths and Polarizabilities},
  author = {Jiang, Jun and Mitroy, J.},
  year = {2013},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {88},
  number = {3},
  pages = {032505},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.88.032505},
  urldate = {2024-06-12},
  abstract = {The influence of hyperfine interactions on the tune-out wavelengths of the 39K, 40K, and 41K isotopes of the potassium atom was investigated. The hyperfine interaction of the 4⁢{$s$}1/2 ground state results in a shift and splitting of the primary tune-out wavelength near 769 nm. The 4⁢{$s$}1/2 state hyperfine splittings of the primary tune-out wavelength were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0009, 0.0026, and 0.0005 nm for K, K, and K, respectively. The hyperfine splitting of the levels leads to the creation of additional tune-out wavelengths. The additional tune-out wavelengths could be difficult to detect due to very small differences from the transition wavelengths to the states. The hyperfine Stark shift for the ground states of all three isotopes was also computed, and the value for K was found to be compatible with the previous experiments and the most recent calculation using relativistic many-body perturbation theory.},
  file = {/Users/yingxing/Zotero/storage/9XPNPBWW/Jiang_Mitroy_2013_Hyperfine effects on potassium tune-out wavelengths and polarizabilities.pdf}
}

@article{Jiang2015a,
  title = {Effective Oscillator Strength Distributions of Spherically Symmetric Atoms for Calculating Polarizabilities and Long-Range Atom--Atom Interactions},
  author = {Jiang, Jun and Mitroy, J. and Cheng, Yongjun and Bromley, M. W. J.},
  year = {2015},
  month = jan,
  journal = {Atomic Data and Nuclear Data Tables},
  volume = {101},
  pages = {158--186},
  issn = {0092-640X},
  doi = {10.1016/j.adt.2014.10.001},
  urldate = {2024-06-10},
  abstract = {Effective oscillator strength distributions are systematically generated and tabulated for the alkali atoms, the alkaline-earth atoms, the alkaline-earth ions, the rare gases and some miscellaneous atoms. These effective distributions are used to compute the dipole, quadrupole and octupole static polarizabilities, and are then applied to the calculation of the dynamic polarizabilities at imaginary frequencies. These polarizabilities can be used to determine the long-range C6, C8 and C10 atom--atom interactions for the dimers formed from any of these atoms and ions, and we present tables covering all of these combinations.},
  keywords = {Dispersion coefficient,Dynamic polarizability,Effective oscillator strength distribution,Long-range interaction,Oscillator strength sum- rule},
  file = {/Users/yingxing/Zotero/storage/ITPZ7VWZ/Jiang et al_2015_Effective oscillator strength distributions of spherically symmetric atoms for.pdf}
}

@article{Johnson2008,
  title = {Relativistic Many-Body Calculation of Energies, Lifetimes, Hyperfine Constants, and Polarizabilities in \${\textasciicircum}\{7\}{\textbackslash}text\{\vphantom\}{{L}}\vphantom\{\}{\textbackslash}text\{i\}\$},
  author = {Johnson, W. R. and Safronova, U. I. and Derevianko, A. and Safronova, M. S.},
  year = {2008},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {77},
  number = {2},
  pages = {022510},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.77.022510},
  urldate = {2024-06-05},
  abstract = {The excitation energies of {$n$}⁢{$s$}, {$n$}⁢{$p$}, {$n$}⁢{$d$}, and {$n$}⁢{$f$} ({$n\leq$}6) states in neutral lithium are evaluated within the framework of relativistic many-body theory. First-, second-, third-, and all-order Coulomb energies and first- and second-order Breit corrections to energies are calculated. All-order calculations of reduced matrix elements, oscillator strengths, transition rates, and lifetimes are given for levels up to {$n$}=4. Electric-dipole (2⁢{$s-n$}⁢{$p$}), electric-quadrupole (2⁢{$s-n$}⁢{$d$}), and electric-octupole (2⁢{$s-n$}⁢{$f$}), matrix elements are evaluated to obtain the corresponding ground-state multipole polarizabilities using the sum-over-states approach. Scalar and tensor polarizabilities for the 2⁢{$p$}1/2 and 2⁢{$p$}3/2 states are also calculated. Magnetic-dipole hyperfine constants {$A$} are determined for low-lying levels up to {$n$}=4. The quadratic Stark shift for the ({$F$}=2 {$M$}=0){$\leftrightarrow$}({$F$}=1 {$M$}=0) ground-state hyperfine transition is found to be -0.0582 Hz/(kV/cm)2, in slight disagreement with the experimental value -0.061{\textpm}0.002 Hz/(kV/cm)2. Matrix elements used in evaluating polarizabilities, hyperfine constants, and the quadratic Stark shift are obtained using the all-order method.},
  file = {/Users/yingxing/Zotero/storage/EN7UAVLW/Johnson et al_2008_Relativistic many-body calculation of energies, lifetimes, hyperfine constants,.pdf}
}

@article{Johnston1960,
  title = {Dielectric {{Constants}} of {{Imperfect Gases}}. {{I}}. {{Helium}}, {{Argon}}, {{Nitrogen}}, and {{Methane}}},
  author = {Johnston, D. R. and Oudemans, G. J. and Cole, R. H.},
  year = {1960},
  month = nov,
  journal = {The Journal of Chemical Physics},
  volume = {33},
  number = {5},
  pages = {1310--1317},
  issn = {0021-9606},
  doi = {10.1063/1.1731405},
  urldate = {2024-06-05},
  abstract = {Measurements from 1 to 100 atm have been made at one or more temperatures between ---30{$^\circ$} and 70{$^\circ$}C by a special transformer ratio arm bridge operating at 10 kc; derived values of the Clausius-Mossotti function are of sufficient precision (0.1\%) to justify comparison with theoretical pair fluctuation, polarizability and multipole moment interaction effects at higher densities. Helium shows a decrease of 0.3\% and argon an increase of 0.1\% in C-M at 100 atm, while nitrogen and methane show somewhat larger positive effects, especially at lower temperatures. A decreased effective polarizability of atom pairs at small distances is discussed as a possible explanation of the data for helium and argon, while the effect in nitrogen is consistent with quadrupole-induced dipole moments of pairs. A theory of octupole-induced dipole interactions is shown to be capable of explaining the methane results with plausible estimated values of the octupole moment.},
  file = {/Users/yingxing/Zotero/storage/AC8FQ5IM/Johnston et al_1960_Dielectric Constants of Imperfect Gases.pdf}
}

@article{Joshipura2013,
  title = {Atoms --- {{How}} Small, and How Large!},
  author = {Joshipura, K. N.},
  year = {2013},
  month = sep,
  journal = {Reson},
  volume = {18},
  number = {9},
  pages = {799--809},
  issn = {0973-712X},
  doi = {10.1007/s12045-013-0104-5},
  urldate = {2024-06-12},
  abstract = {The spatial extent of a free or an isolated atom can be gauged by defining its radius, and there are several different ways in which this quantity can be defined. Four of them are considered in this article. Quantum mechanical wave functions are employed to estimate the most probable and the average radii of atoms. Atomic polarizability radius and van der Waals radius are also considered, and all the four radii are examined across the periodic table. Atomic ions are then briefly dwelt upon, and a big contrast is noted in the sizes of (free) Li+ ion and the exotic H- ion, both iso-electronic with helium atom. Brief mention is also made of large exotic species like the metastable atoms and Rydberg atoms. The article seeks to provide a quantitative glimpse of how small or large the atomic systems can be.},
  langid = {english},
  keywords = {Atomic radius,metastable atoms,periodic table,polarizability,quantum mechanical expectation,van der Waals radii},
  file = {/Users/yingxing/Zotero/storage/Q3CEAZRW/Joshipura_2013_Atoms — How small, and how large.pdf}
}

@article{Kadar-Kallen1994,
  title = {Uranium Polarizability Measured by Light-Force Technique},
  author = {{Kadar-Kallen}, Michael A. and Bonin, Keith D.},
  year = {1994},
  month = feb,
  journal = {Phys. Rev. Lett.},
  volume = {72},
  number = {6},
  pages = {828--831},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.72.828},
  urldate = {2024-06-05},
  abstract = {We report the measurement of the scalar {$\alpha$}0 and tensor {$\alpha$}2 polarizabilities of uranium using a light-force technique, the first accurate measurement of the polarizabilities of a refractory element. At the fundamental wavelength of a Nd:YAG laser (1.064 {$\mu$}m) we measure {$\alpha$}0=24.9{\textpm}1.5 {\AA}3 and {$\alpha$}2=0.7{\textpm}1.7 {\AA}3. From these values we determine the dc polarizabilities to be {$\alpha$}0=20.3{\textpm}1.4 {\AA}3 and {$\alpha$}2=0.7{\textpm}1.8 {\AA}3. Calculations of {$\alpha$}0(dc) are within 30\% of this measurement.},
  file = {/Users/yingxing/Zotero/storage/5YYDBJF3/Kadar-Kallen_Bonin_1994_Uranium polarizability measured by light-force technique.pdf}
}

@article{Kannemann2012,
  title = {Atomic Volumes and Polarizabilities in Density-Functional Theory},
  author = {Kannemann, Felix O. and Becke, Axel D.},
  year = {2012},
  month = jan,
  journal = {The Journal of Chemical Physics},
  volume = {136},
  number = {3},
  pages = {034109},
  issn = {0021-9606},
  doi = {10.1063/1.3676064},
  urldate = {2024-06-12},
  abstract = {Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys.\hphantom{,}124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H--Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.},
  file = {/Users/yingxing/Zotero/storage/W38Y9HKN/Kannemann_Becke_2012_Atomic volumes and polarizabilities in density-functional theory.pdf}
}

@misc{Kaur2022,
  title = {Roles of {{Blackbody Friction Forces}} in the {{Rb}} and {{Cs Atom Interferometers}}},
  author = {Kaur, Simranpreet and Arora, Bindiya and Sahoo, B. K.},
  year = {2022},
  month = jun,
  number = {arXiv:2012.07362},
  eprint = {2012.07362},
  primaryclass = {physics},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2012.07362},
  urldate = {2024-06-10},
  abstract = {Atom interferometry is amongst the most advanced technologies that provides very high-precision measurements. There can exist a number of obscure forces that can interfere with the atoms used in this instrument. In the present work, we are probing possible roles of one such important forces, known as ``blackbody friction force (BBFF)'', that may affect the precisions in the measurements made using atom interferometers based on the Rb and Cs atoms. The BBFF can be generated on atoms due to the black-body radiations emitted by the stray electromagnetic fields present in the experimental set-up and other metallic shielding. The strength of the BBFF can be calculated by integrating the complex parts of the dynamic polarizabilities of atoms, which show varying behaviour at the resonant and non-resonant transitions in the above atoms. Our analyses suggest that the off-resonant atomic transitions make significant contributions to the BBFF at low temperatures in the Rb and Cs atom interferometers. Present study also advocates that it is imperative to carry out the integration over a wide spectrum of frequencies for correct evaluation of the BBFF; specially at higher temperatures.},
  archiveprefix = {arxiv},
  keywords = {Physics - Atomic Physics}
}

@article{Kaur2022a,
  title = {Determination of Quadrupolar Dispersion Coefficients of the Alkali-Metal Atoms Interacting with Different Material Media},
  author = {Kaur, Harpreet and Badhan, Vipul and Arora, Bindiya and Sahoo, B. K.},
  year = {2022},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {106},
  number = {4},
  pages = {042813},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.106.042813},
  urldate = {2024-06-11},
  abstract = {In the present work, we determine the {$C$}5 coefficients along with their uncertainties due to quadrupole polarization effects of all the alkali atoms interacting with a metal (Au), a semiconductor (Si), and four dielectric materials (SiO2, SiN{$x$}, yttrium aluminum garnet, and sapphire). The required dynamic electric quadrupole () polarizabilities are evaluated by calculating matrix elements of a large number of transitions in the alkali atoms by employing a relativistic coupled-cluster method. A significant contribution towards the long-range van der Waals potential is made by the quadrupole polarization effects. Our finding shows that contributions from the coefficients to the atom-wall interaction potentials are pronounced at short distances (1--10 nm). The coefficients of a Fr atom interacting with the above material media are also reported. These results could be useful in understanding the interactions of alkali atoms trapped in different material bodies during high-precision measurements.},
  file = {/Users/yingxing/Zotero/storage/ZQD9RTRL/Kaur et al_2022_Determination of quadrupolar dispersion coefficients of the alkali-metal atoms.pdf}
}

@article{Kellö1992,
  title = {Medium-Size Polarized Basis Sets for High-Level-Correlated Calculations of Molecular Electric Properties},
  author = {Kell{\"o}, Vladimir and Sadlej, Andrzej J.},
  year = {1992},
  month = sep,
  journal = {Theoret. Chim. Acta},
  volume = {83},
  number = {5},
  pages = {351--366},
  issn = {1432-2234},
  doi = {10.1007/BF01113061},
  urldate = {2024-06-12},
  abstract = {The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH3 (-0.499 a.u.), PoH2 (-0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to ---0.230 a.u., -0.177 a.u., and -0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.},
  langid = {english},
  keywords = {AtH,Atomic dipole polarizabilities of Pb Bi Po and At,BiH3,Dipole moments and polarizabilities of the fifth-row hydrides,Molecular electric properties,PbH4,PoH2,Polarized basis sets,Relativistic contributions to atomic and molecular properties},
  file = {/Users/yingxing/Zotero/storage/ZDTSB2JG/Kellö_Sadlej_1992_Medium-size polarized basis sets for high-level-correlated calculations of.pdf}
}

@article{Kellö1995,
  title = {Polarized Basis Sets for High-Level-Correlated Calculations of Molecular Electric Properties},
  author = {Kell{\"o}, Vladimir and Sadlej, Andrzej J.},
  year = {1995},
  month = jun,
  journal = {Theoret. Chim. Acta},
  volume = {91},
  number = {5},
  pages = {353--371},
  issn = {1432-2234},
  doi = {10.1007/BF01133080},
  urldate = {2024-06-12},
  abstract = {The first-order polarized basis sets are generated for Zn, Cd, and Hg and their performance is tested in high-level-correlated calculations of electric dipole polarizabilities of these atoms. The present results calculated at the level of the non-relativistic CCSD(T) approximation with 12 explicitly correlated electrons are: 40.4 a.u. for Zn, 56.3 a.u. for Cd, and 58.0 a.u. for Hg. Upon including the relativistic and electron correlation-relativistic corrections within the quasirelativistic scheme based on the mass-velocity and Darwin terms these values are reduced to 37.9 a.u., 47.6 and 31.8 a.u., respectively. The derived polarized basis sets have been also used for the evaluation of the dipole polarizability of singly and doubly positive ions of the group IIb elements and are recommended for calculations of interaction energies and interaction-induced electric properties in both neutral and charged systems.},
  langid = {english},
  keywords = {Electric dipole polarizabilities of Zn Cd Hg and their positive ions,Electron correlation effects on atomic properties,Polarized basis sets,Relativistic effects on atomic properties},
  file = {/Users/yingxing/Zotero/storage/CC6BYRWD/Kellö_Sadlej_1995_Polarized basis sets for high-level-correlated calculations of molecular.pdf}
}

@article{Kellö1996,
  title = {Standardized Basis Sets for High-Level-Correlated Relativistic Calculations of Atomic and Molecular Electric Properties in the Spin-Averaged {{Douglas-Kroll}} (No-Pair) Approximation {{I}}. {{Groups Ib}} and {{IIb}}},
  author = {Kell{\"o}, Vladimir and Sadlej, Andrzej J.},
  year = {1996},
  month = aug,
  journal = {Theoret. Chim. Acta},
  volume = {94},
  number = {2},
  pages = {93--104},
  issn = {1432-2234},
  doi = {10.1007/BF00194934},
  urldate = {2024-06-12},
  abstract = {The technique developed earlier for the generation of the so-called first-order polarized basis sets for accurate non-relativistic calculations of molecular electric properties is used to obtain similar basis sets suitable for calculations in the Douglas-Kroll no-pair approximation. The corresponding (relativistic) basis sets are devised for atoms of the Groups Ib and IIb of the periodic table and tested in calculations of atomic polarizabilities and dipole moments of the coinage metal hydrides. Excellent performance of these basis sets has been found in the case of molecular calculations.},
  langid = {english},
  keywords = {Dipole polarizabilities of Zn Cd Hg - Dipole moments of CuH AgH and AuH,Douglas-Kroll no-pair approximation,Polarizabilities of atomic ions: Cu+ Ag+ Zn2+ Cd2+ Hg2+,Polarized basis sets,Relativistic effects},
  file = {/Users/yingxing/Zotero/storage/RXDZMHT3/Kellö_Sadlej_1996_Standardized basis sets for high-level-correlated relativistic calculations of.pdf}
}

@article{Kłos2005a,
  title = {Anisotropic Dipole Polarizability of Transition Metal Atoms: {{Sc}}({{D2}}), {{Ti}}({{F3}},{{P3}}), {{V}}({{F4}},{{P4}},{{D6}}), {{Ni}}({{F3}}) and Ions: {{Sc2}}+({{D2}}), {{Ti2}}+({{F3}},{{P3}})},
  shorttitle = {Anisotropic Dipole Polarizability of Transition Metal Atoms},
  author = {K{\l}os, J.},
  year = {2005},
  month = jul,
  journal = {The Journal of Chemical Physics},
  volume = {123},
  number = {2},
  pages = {024308},
  issn = {0021-9606},
  doi = {10.1063/1.1953447},
  urldate = {2024-06-12},
  abstract = {Dipole polarizability tensor components and quadrupole moments of transition-metal atoms Sc, Ti, V, Ni, and Cu and ions Sc2+ and Ti2+ are computed using finite field complete active space self-consistent field and multireference configuration interaction ab initio methods. Perpendicular components of the dipole polarizability tensor are calculated from equations involving only parallel components of the polarizability tensor and its average value. Mean polarizability and polarizability anisotropy decrease in the Sc--Ni series. Relativistic effects are accounted for with the Douglas-Kroll Hamiltonian. The consequences of the anisotropic properties of these atoms to their interactions with spherically symmetric rare gases are also discussed.},
  file = {/Users/yingxing/Zotero/storage/64MR9L4V/Kłos_2005_Anisotropic dipole polarizability of transition metal atoms.pdf}
}

@article{Komasa2001,
  title = {Dipole and Quadrupole Polarizabilities and Shielding Factors of Beryllium from Exponentially Correlated {{Gaussian}} Functions},
  author = {Komasa, Jacek},
  year = {2001},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {65},
  number = {1},
  pages = {012506},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.65.012506},
  urldate = {2024-06-05},
  abstract = {Dynamic dipole and quadrupole polarizabilities as well as shielding factors of the beryllium atom in the ground state were computed at real frequencies by using the variation-perturbation method. The zeroth- and the first-order wave functions were expanded in many-electron basis of exponentially correlated Gaussian functions. The 1600-term expansion of the unperturbed wave function yielded the ground-state energy accurate to 1 cm-1. The first-order wave functions were expanded in very large bases (4800 and 4400 terms). The nonlinear parameters of the first-order correction functions were optimized with respect to both the static and dynamic polarizabilities, and with respect to the excited-state energies. The procedure employed ensures a high accuracy of determination of dynamic properties in a wide range of frequencies and correct positions of the transition poles. Test calculations, performed on He and Li, confirmed the ability of this method to obtain the atomic properties with very high accuracy. The final values of the static properties of Be were 3⁢7.7⁢5⁢5⁢{$e$}2⁢{$a$}20⁢{$E-$}1{$H$} and 3⁢0⁢0.9⁢6⁢{$e$}2⁢{$a$}40⁢{$E-$}1{$H$} for the dipole and quadrupole polarizabilities, respectively, and 1.4769 for the quadrupole shielding factor. The convergence of the atomic properties with the size of the expansion of both the zeroth- and first-order functions was checked. Thanks to very high accuracy of the unperturbed wave function and the efficient method of construction of the first-order wave functions, the dynamic polarizability results presented in this work are of benchmark quality. As a by-product of this project, a set of the most accurate upper bounds to the energies of 1⁢{$P$} and 1⁢{$D$} states of Be was obtained.},
  file = {/Users/yingxing/Zotero/storage/4WYWBYNH/Komasa_2001_Dipole and quadrupole polarizabilities and shielding factors of beryllium from.pdf}
}

@article{Kozlov2001,
  title = {Parity Nonconservation in Thallium},
  author = {Kozlov, M. G. and Porsev, S. G. and Johnson, W. R.},
  year = {2001},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {64},
  number = {5},
  pages = {052107},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.64.052107},
  urldate = {2024-06-12},
  abstract = {We report a calculation of the parity nonconserving (PNC) {$E$}⁢1 amplitude for the 6⁢{$p$}1/2{$\rightarrow$}6⁢{$p$}3/2 transition in 205⁢Tl. Our result for the reduced matrix element is ({$E$}⁢1)PNC=-(66.7{\textpm}1.7){\texttimes}i⁢10-11⁢(-{$QW$}/{$N$}) a.u. Comparison with the experiment of Vetter et al. [Phys. Rev. Lett. 74, 2658 (1995)] gives the following result for the weak charge of 205⁢Tl: {$QW$}⁢/{$Q$}SM{$W$}=0.97({\textpm}0.0⁢1)expt({\textpm}0.0⁢3)theor, where {$Q$}SM{$W$}=-116.7{\textpm}0.1 is the standard-model prediction. This result confirms an earlier conclusion based on the analysis of a Cs experiment that atomic PNC experiments are in agreement with the standard model.},
  file = {/Users/yingxing/Zotero/storage/E3MK5P7K/Kozlov et al_2001_Parity nonconservation in thallium.pdf}
}

@article{Kumar2021,
  title = {Relativistic Coupled-Cluster Calculation of the Electric Dipole Polarizability and Correlation Energy of {{Cn}}, \$\{{\textbackslash}mathrm\{\vphantom{\}\}}{{Nh}}\vphantom\{\}\vphantom\{\}{\textasciicircum}\{+\}\$, and {{Og}}: {{Correlation}} Effects from Lighter to Superheavy Elements},
  shorttitle = {Relativistic Coupled-Cluster Calculation of the Electric Dipole Polarizability and Correlation Energy of {{Cn}}, \$\{{\textbackslash}mathrm\{\vphantom{\}\}}{{Nh}}\vphantom\{\}\vphantom\{\}{\textasciicircum}\{+\}\$, and {{Og}}},
  author = {Kumar, Ravi and Chattopadhyay, S. and Angom, D. and Mani, B. K.},
  year = {2021},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {103},
  number = {6},
  pages = {062803},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.103.062803},
  urldate = {2024-06-11},
  abstract = {We employ a relativistic coupled-cluster theory to compute the ground-state electric dipole polarizability {$A$} and the electron correlation energy of the superheavy elements Cn, Nh+, and Og. To assess the electron correlation trends with , we also compute the correlation energies of the three lighter homologs for each of the elements. In the computations, we use the Dirac-Coulomb-Breit Hamiltonian and incorporate the quantum electrodynamical corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the theory. Our recommended values of are in good agreement with previous theoretical results. As expected, the dominant contribution is from the valence electrons. Except for Cn and Og, the contribution from the Breit interaction decreases with . For the vacuum polarization and self-energy corrections, the contributions increase with . To understand the correlation energy trends better, we also compute the correlation energy with the relativistic many-body perturbation theory.},
  file = {/Users/yingxing/Zotero/storage/TB4C2LGT/Kumar et al_2021_Relativistic coupled-cluster calculation of the electric dipole polarizability.pdf}
}

@article{Kumar2022,
  title = {Fock-Space Perturbed Relativistic Coupled-Cluster Theory for Electric Dipole Polarizability of One-Valence Atomic Systems: {{Application}} to {{Al}} and {{In}}},
  shorttitle = {Fock-Space Perturbed Relativistic Coupled-Cluster Theory for Electric Dipole Polarizability of One-Valence Atomic Systems},
  author = {Kumar, Ravi and Angom, D. and Mani, B. K.},
  year = {2022},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {106},
  number = {3},
  pages = {032801},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.106.032801},
  urldate = {2024-06-06},
  abstract = {We have developed a Fock-space relativistic coupled-cluster theory-based method for the calculation of electric dipole polarizability of one-valence atoms and ions. We employ this method to compute the ground-state and spin-orbit coupled excited state electric dipole polarizability of Al and In. To check the quality of many-electron wave functions, we also compute the excitation energies of some low-lying states of Al and In. The effects of the Breit interaction and QED corrections from the Uehling potential and the self-energy are included to improve the accuracy of {$A$} further. Our recommended values of the ground-state {$A$} for both atoms are in good agreement with the previous theoretical results. From our computations, we find that more than 65\% of contributions come from the dipolar mixing of 3⁢{$p$}(5⁢{$p$}) with 3⁢{$d$}(5⁢{$d$}) and 4⁢{$s$}(6⁢{$s$}) electrons for Al(In). The largest Breit and QED contributions are found to be 1.3\% and 0.6\%, respectively.},
  file = {/Users/yingxing/Zotero/storage/6W5XVGWI/Kumar et al_2022_Fock-space perturbed relativistic coupled-cluster theory for electric dipole.pdf}
}

@article{Labello2005,
  title = {{An augmented effective core potential basis set for the calculation of molecular polarizabilities}},
  author = {Labello, Nicholas P. and Ferreira, Antonio M. and Kurtz, Henry A.},
  year = {2005},
  journal = {J. Comput. Chem.},
  volume = {26},
  number = {14},
  pages = {1464--1471},
  issn = {1096-987X},
  doi = {10.1002/jcc.20282},
  urldate = {2024-06-12},
  abstract = {Calculations of molecular polarizabilities require basis sets capable of accurately describing the responses of the electrons to an external perturbation. Unfortunately, basis sets that yield suitable quantitative results have traditionally been all-electron sets with large numbers of primitives, making their use computationally intractable even for moderately sized systems. We present a systematic augmentation of the effective core potential basis set of Stevens et al. [J Chem Phys 81, 12 (1984), Can J Chem 70, 612 (1992)] for 39 main group elements based on the procedure used to construct diffuse and polarization functions in the well-known Sadlej basis sets [Collec Czech Chem Comm 53, 1995 (1988)]. Representative calculations have been performed and we have shown that results to within 1\% of all-electron calculations using the Sadlej basis set can be obtained for {$<$}1--35\% of the computational cost using this new basis set. {\copyright} 2005 Wiley Periodicals, Inc. J Comput Chem 26: 1464--1471, 2005},
  copyright = {Copyright {\copyright} 2005 Wiley Periodicals, Inc.},
  langid = {french},
  keywords = {core potential basis set,molecular polarizabilities},
  file = {/Users/yingxing/Zotero/storage/M8U695VF/Labello et al_2005_An augmented effective core potential basis set for the calculation of.pdf}
}

@article{Lach2004b,
  title = {Radiative {{Corrections}} to the {{Polarizability}} of {{Helium}}},
  author = {{\L}ach, Grzegorz and Jeziorski, Bogumi{\l} and Szalewicz, Krzysztof},
  year = {2004},
  month = jun,
  journal = {Phys. Rev. Lett.},
  volume = {92},
  number = {23},
  pages = {233001},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.92.233001},
  urldate = {2023-03-21},
  abstract = {The complete {$\alpha$}3 QED correction to the helium atom polarizability is computed assuming an infinite nuclear mass and found to be equal to 0.000 030 666(3) a.u., with the contribution from the electric-field dependence of the Bethe logarithm amounting to 0.000 000 193(2) a.u. After including the {$\alpha$}2 and {$\alpha$}3 corrections for the nuclear recoil and the leading part of the {$\alpha$}4 QED correction, we find that the molar polarizability of 4He is 0.517 254 19(9)(4) cm3/mol. The first of the two error bounds is dominated by the uncertainty of {$\alpha$}4 and higher-order QED corrections and the second reflects the uncertainty of the Avogadro constant.},
  file = {/Users/yingxing/Zotero/storage/KKIUHWM5/Radiative corrections to the polarizability of helium_2004.pdf}
}

@article{Langhoff1969,
  title = {Pad{\'e} {{Summation}} of the {{Cauchy Dispersion Equation}}*},
  author = {Langhoff, P. W. and Karplus, M.},
  year = {1969},
  month = jul,
  journal = {J. Opt. Soc. Am., JOSA},
  volume = {59},
  number = {7},
  pages = {863--871},
  publisher = {Optica Publishing Group},
  doi = {10.1364/JOSA.59.000863},
  urldate = {2024-06-12},
  abstract = {A method is presented, based on recognition of the Cauchy dispersion equation as a series of Stieltjes, for the bounded extrapolation of long-wavelength refractivity data into the far ultraviolet. The extrapolation is performed with the [n, n-1] and [n,n] Pad{\'e} approximants, which improve the convergence of the Cauchy equation and provide upper and lower bounds to its exact sum. Illustrative applications are given for atomic hydrogen, the inert gases, and molecular hydrogen, oxygen, and nitrogen. Comparison with the exact dispersion curve for atomic hydrogen and with available theoretical and experimental ultraviolet-dispersion data for the inert and diatomic gases indicates that the Pad{\'e} approximants converge rapidly to accurate refractivity values. In addition, recognition of the Cauchy equation as a series of Stieltjes provides nontrivial constraints on the Cauchy coefficients; these afford a test of their accuracy and allow estimates of higher-order coefficients from measured refractivity data.},
  copyright = {{\copyright} 1969 Optical Society of America},
  langid = {english},
  keywords = {Augmented reality,Curvature,Dispersion,Hydrogen,Rayleigh scattering},
  file = {/Users/yingxing/Zotero/storage/LHY6FQF5/Langhoff_Karplus_1969_Padé Summation of the Cauchy Dispersion Equation.pdf}
}

@article{Larsen1999,
  title = {Polarizabilities and First Hyperpolarizabilities of {{HF}}, {{Ne}}, and {{BH}} from Full Configuration Interaction and Coupled Cluster Calculations},
  author = {Larsen, Helena and Olsen, Jeppe and H{\"a}ttig, Christof and Jo/rgensen, Poul and Christiansen, Ove and Gauss, J{\"u}rgen},
  year = {1999},
  month = aug,
  journal = {The Journal of Chemical Physics},
  volume = {111},
  number = {5},
  pages = {1917--1925},
  issn = {0021-9606},
  doi = {10.1063/1.479460},
  urldate = {2024-06-12},
  abstract = {Static and frequency-dependent polarizabilities and first hyperpolarizabilities have been calculated for HF and Ne using full configuration interaction (FCI) and a hierarchy of coupled cluster models: coupled cluster singles (CCS), an approximate coupled cluster singles and doubles model (CC2), coupled cluster singles and doubles (CCSD), an approximate coupled cluster singles, doubles, and triples model (CC3), and coupled cluster singles, doubles, and triples (CCSDT). A previous study of BH concerning FCI benchmarking has been extended to include CC3 and static CCSDT values. Systematic improvements of the polarizabilities and the hyperpolarizabilities are found going from CCS to CCSD and from CCSD to CC3 or CCSDT. Little or no improvement of the polarizabilities and no improvement of the hyperpolarizabilities are seen when going from CCS to CC2. The CCSD results represent a significant improvement over CCS and CC2 but are again surpassed by the CC3 results which agree very well with the FCI values. The relative error for the static polarizability at the CC3 level is 0.11\% for Ne and, respectively, 0.16\% and 0.20\% for {$\alpha$}xx and {$\alpha$}zz of HF. For {$\beta$}zzz and {$\beta$}zxx the errors are 0.50\% and 1.7\%, respectively. Only in the challenging case of BH does CCSDT improve the CC3 values. The dispersion for the polarizabilities and hyperpolarizabilities is predicted with increasing accuracy in the CCS--CC2--CCSD--CC3 sequence as expected from the increasing accuracy of the electronic excitation energies. For all molecules the effect of orbital relaxation has been investigated for the static properties. The inclusion of orbital relaxation gives results that are somewhat different from the unrelaxed results but are in general no improvement.},
  file = {/Users/yingxing/Zotero/storage/IVUTAJCI/Larsen et al_1999_Polarizabilities and first hyperpolarizabilities of HF, Ne, and BH from full.pdf}
}

@article{Lepers2014,
  title = {Anisotropic Optical Trapping of Ultracold Erbium Atoms},
  author = {Lepers, M. and Wyart, J.-F. and Dulieu, O.},
  year = {2014},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {89},
  number = {2},
  pages = {022505},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.89.022505},
  urldate = {2024-06-12},
  abstract = {Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and transition dipole moments from ground-state erbium, which are computed using the Racah-Slater least-squares fitting procedure provided by the cowan codes. This allows us to predict nine unobserved odd-parity energy levels of total angular momentum , 6, and 7, in the range 25 000--31 000 cm above the ground state. Regarding the trapping potential, we find that ground-state erbium essentially behaves like a spherically symmetric atom, in spite of its large electronic angular momentum. We also find a mostly isotropic van der Waals interaction between two ground-state erbium atoms, characterized by a coefficient a.u. To the contrary, the photon-scattering rate shows a pronounced anisotropy since it strongly depends on the polarization of the trapping light.},
  file = {/Users/yingxing/Zotero/storage/3QPXFWBG/Lepers et al_2014_Anisotropic optical trapping of ultracold erbium atoms.pdf}
}

@article{Lesiuk2020,
  title = {Theoretical Determination of Polarizability and Magnetic Susceptibility of Neon},
  author = {Lesiuk, Micha{\l} and Przybytek, Micha{\l} and Jeziorski, Bogumi{\l}},
  year = {2020},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {102},
  number = {5},
  pages = {052816},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.102.052816},
  urldate = {2024-06-10},
  abstract = {We report theoretical determination of the dipole polarizability of the neon atom, including its frequency dependence. Corrections for the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size effects are taken into account. We obtain the value {$A$}0=2.66080⁢(36) for the static polarizability, and {$A$}2=2.850⁢(7) and {$A$}4=4.932⁢(14) for the first two polarizability dispersion coefficients (Cauchy moments); all values are in atomic units (a.u.). In the case of static polarizability, our result agrees with the best experimental determination, Gaiser et al. [Phys. Rev. Lett. 120, 123203 (2018)], but our estimated uncertainty is significantly larger. For the dispersion coefficients, the results obtained in this work appear to be the most accurate to date overall compared to published theoretical and experimental data. We also calculated the static magnetic susceptibility of the neon atom, needed to obtain the refractive index of gaseous neon. Our result, a.u., is about 9\% larger in absolute value than the recommended experimental value, Rumble et al. [CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 2019)].},
  file = {/Users/yingxing/Zotero/storage/IMUPE2N2/Lesiuk et al. - 2020 - Theoretical determination of polarizability and ma.pdf}
}

@article{Lesiuk2023,
  title = {First-Principles Calculation of the Frequency-Dependent Dipole Polarizability of Argon},
  author = {Lesiuk, Micha{\l} and Jeziorski, Bogumi{\l}},
  year = {2023},
  month = apr,
  journal = {Phys. Rev. A},
  volume = {107},
  number = {4},
  pages = {042805},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.107.042805},
  urldate = {2024-06-10},
  abstract = {In this work we report state-of-the-art theoretical calculations of the dipole polarizability of the argon atom. Frequency dependence of the polarizability is taken into account by means of the dispersion coefficients (Cauchy coefficients), which is sufficient for experimentally relevant wavelengths below the first resonant frequency. In the proposed theoretical framework, all known physical effects including the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size corrections are accounted for. We obtained {$A$}0=11.0775⁢(19) for the static polarizability and {$A$}2=27.976⁢(15) and {$A$}4=95.02⁢(11) for the second and fourth dispersion coefficients, respectively. The result obtained for the static polarizability agrees (within the estimated uncertainty) with the most recent experimental data [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)] but is less accurate. The dispersion coefficients determined in this work appear to be the most accurate in the literature, improving by more than an order of magnitude upon previous estimates. By combining the experimentally determined value of the static polarizability with the dispersion coefficients from our calculations, the polarizability of argon can be calculated with accuracy of around 10ppm for wavelengths above roughly 450nm. This result is important from the point of view of quantum metrology, especially for a new pressure standard based on thermophysical properties of gaseous argon. Additionally, in this work we calculate the static magnetic susceptibility of argon, which relates the refractive index of dilute argon gas with its pressure. While our results for this quantity are less accurate than in the case of the polarizability, they can provide, via the Lorenz-Lorentz formula, the best available theoretical estimate of the refractive index of argon.},
  file = {/Users/yingxing/Zotero/storage/NZJCTTZ8/Lesiuk and Jeziorski - 2023 - First-principles calculation of the frequency-depe.pdf}
}

@article{Li2009,
  title = {Correlations of the {{Stability}}, {{Static Dipole Polarizabilities}}, and {{Electronic Properties}} of {{Yttrium Clusters}}},
  author = {Li, Xi-Bo and Wang, Hong-Yan and Lv, Ran and Wu, Wei-Dong and Luo, Jiang-Shan and Tang, Yong-Jian},
  year = {2009},
  month = sep,
  journal = {J. Phys. Chem. A},
  volume = {113},
  number = {38},
  pages = {10335--10342},
  publisher = {American Chemical Society},
  issn = {1089-5639},
  doi = {10.1021/jp904420z},
  urldate = {2023-03-20},
  abstract = {Static dipole polarizabilities for the ground-state geometries of yttrium clusters (Yn, n {$\leq$} 15) are investigated by using the numerically finite field method in the framework of density functional theory. The structural size dependence of electronic properties, such as the highest occupied molecular orbital-lowest occupied molecular orbital (HOMO-LUMO) gap, ionization energy, electron affinity, chemical hardness and softness, etc., has been determined for yttrium clusters. The energetic analysis, minimum polarizability principle, and principle of maximum hardness are used to characterize the stability of yttrium clusters. The correlations of stability, static dipole polarizabilities, and electronic properties are analyzed especially. The results show that static polarizability and electronic structure can reflect obviously the stability of yttrium clusters. The static polarizability per atom decreases slowly with an increase in the cluster size and exhibits a local minimum at the magic number cluster. The ratio of the mean static polarizability to the HOMO-LUMO gap has a much lower value for the most stable clusters. The static dipole polarizabilities of yttrium clusters are highly dependent on their electronic properties and are also partly related to their geometrical characteristics. A large HOMO-LUMO gap of an yttrium cluster usually corresponds to a large dipole moment. Strong correlative relationships of the ionization potential, softness, and static dipole polarizability are observed for yttrium clusters.},
  file = {/Users/yingxing/Zotero/storage/GJ7TL2VV/Correlations of the stability, static dipole polarizabilities, and electronic properties of yttrium clusters_2009.pdf}
}

@article{Li2016,
  title = {Optical Trapping of Ultracold Dysprosium Atoms: Transition Probabilities, Dynamic Dipole Polarizabilities and van Der {{Waals C6}} Coefficients},
  shorttitle = {Optical Trapping of Ultracold Dysprosium Atoms},
  author = {Li, H. and Wyart, J.-F. and Dulieu, O. and Nascimb{\`e}ne, S. and Lepers, M.},
  year = {2016},
  month = dec,
  journal = {J. Phys. B: At. Mol. Opt. Phys.},
  volume = {50},
  number = {1},
  pages = {014005},
  publisher = {IOP Publishing},
  issn = {0953-4075},
  doi = {10.1088/1361-6455/50/1/014005},
  urldate = {2024-06-12},
  abstract = {The efficiency of the optical trapping of ultracold atoms depends on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited levels. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the C6 coefficients characterizing the van der Waals interaction between two dysprosium atoms in the two lowest levels. We have computed the energies of excited states and the transition probabilities appearing in the sums, using a combination of ab initio and least-square-fitting techniques provided by the Cowan codes and extended in our group. Regarding the real part of the polarizability, for field frequencies far from atomic resonances, the vector and tensor contributions are two-orders-of-magnitude smaller than the scalar contribution, whereas for the imaginary part, the vector and tensor contributions represent a noticeable fraction of the scalar contribution. Finally, our anisotropic C6 coefficients are much smaller than those published in the literature.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/ALCKYFCP/Li et al_2016_Optical trapping of ultracold dysprosium atoms.pdf}
}

@article{Li2024,
  title = {Electric {{Polarization}} from a {{Many-Body Neural Network Ansatz}}},
  author = {Li, Xiang and Qian, Yubing and Chen, Ji},
  year = {2024},
  month = apr,
  journal = {Phys. Rev. Lett.},
  volume = {132},
  number = {17},
  pages = {176401},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.132.176401},
  urldate = {2024-06-10},
  abstract = {Ab initio calculation of dielectric response with high-accuracy electronic structure methods is a long-standing problem, for which mean-field approaches are widely used and electron correlations are mostly treated via approximated functionals. Here we employ a neural network wave function ansatz combined with quantum Monte Carlo method to incorporate correlations into polarization calculations. On a variety of systems, including isolated atoms, one-dimensional chains, two-dimensional slabs, and three-dimensional cubes, the calculated results outperform conventional density functional theory and are consistent with the most accurate calculations and experimental data. Furthermore, we have studied the out-of-plane dielectric constant of bilayer graphene using our method and reestablished its thickness dependence. Overall, this approach provides a powerful tool to accurately describe electron correlation in the modern theory of polarization.},
  file = {/Users/yingxing/Zotero/storage/F6DTLXI4/Li et al_2024_Electric Polarization from a Many-Body Neural Network Ansatz.pdf}
}

@book{Lide2004,
  title = {{{CRC}} Handbook of Chemistry and Physics},
  author = {Lide, David R},
  year = {2004},
  volume = {85},
  publisher = {CRC press}
}

@article{Liepack1956,
  title = {{Messung der Polarisierbarkeiten von Metallatomen mit dem Feldelektronenmikroskop}},
  author = {Liepack, H. and Drechsler, M.},
  year = {1956},
  month = jan,
  journal = {Naturwissenschaften},
  volume = {43},
  number = {3},
  pages = {52--53},
  issn = {1432-1904},
  doi = {10.1007/BF00628607},
  urldate = {2024-06-12},
  langid = {ngerman},
  file = {/Users/yingxing/Zotero/storage/XXQJ8ZM3/Liepack_Drechsler_1956_Messung der Polarisierbarkeiten von Metallatomen mit dem Feldelektronenmikroskop.pdf}
}

@article{Lim1999,
  title = {Relativistic Coupled-Cluster Static Dipole Polarizabilities of the Alkali Metals from {{Li}} to Element 119},
  author = {Lim, Ivan S. and Pernpointner, Markus and Seth, Michael and Laerdahl, Jon K. and Schwerdtfeger, Peter and Neogrady, Pavel and Urban, Miroslav},
  year = {1999},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {60},
  number = {4},
  pages = {2822--2828},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.60.2822},
  urldate = {2023-03-21},
  abstract = {Static dipole polarizabilities {$\alpha$}D of the first main group elements from Li down to superheavy element 119 were calculated using a relativistic Douglas-Kroll Hamiltonian within an open-shell coupled-cluster theory. Spin-orbit effects were investigated using a fully relativistic four-component Dirac-Hartree-Fock scheme. Our final recommended values for the dipole polarizabilities from Li to Cs should be more accurate than currently available experimental data. Relativistic effects in {$\alpha$}D are roughly {$\sim$}Z2 and we establish a clear relationship for relativistic and electron correlation effects between the dipole polarizability and the ionization potential of the neutral atom. Spin-orbit effects become non-negligible for Fr and element 119. For the latter, relativistic effects clearly dominate over electron correlation resulting in a very small {$\alpha$}D value comparable to that of sodium.},
  file = {/Users/yingxing/Zotero/storage/UKU6UUDD/Lim et al_1999_Relativistic coupled-cluster static dipole polarizabilities of the alkali.pdf}
}

@article{Lim2004,
  title = {Four-Component and Scalar Relativistic {{Douglas-Kroll}} Calculations for Static Dipole Polarizabilities of the Alkaline-Earth-Metal Elements and Their Ions from \$\{{\textbackslash}mathrm\{\vphantom{\}\}}{{Ca}}\vphantom\{\}\vphantom\{\}{\textasciicircum}\{n\}\$ to \$\{{\textbackslash}mathrm\{\vphantom{\}\}}{{Ra}}\vphantom\{\}\vphantom\{\}{\textasciicircum}\{n\}\$ (\$n=0\$,+1,+2)},
  author = {Lim, Ivan S. and Schwerdtfeger, Peter},
  year = {2004},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {70},
  number = {6},
  pages = {062501},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.70.062501},
  urldate = {2023-03-20},
  abstract = {Static dipole polarizabilities for the neutral and ionized M, M+, and M2+ group 2 elements from M=Ca to Ra are predicted from relativistic coupled-cluster calculations using finite field techniques together with carefully optimized Gaussian-type basis sets. Useful relations between the dipole polarizability and the ionization potential are established.},
  file = {/Users/yingxing/Zotero/storage/5VXZ3VM9/Four-component and scalar relativistic Douglas-Kroll calculations for static dipole polarizabilities of the alkaline-earth-metal element.pdf}
}

@article{Lim2005,
  title = {All-Electron and Relativistic Pseudopotential Studies for the Group 1 Element Polarizabilities from {{K}} to Element 119},
  author = {Lim, Ivan S. and Schwerdtfeger, Peter and Metz, Bernhard and Stoll, Hermann},
  year = {2005},
  month = mar,
  journal = {The Journal of Chemical Physics},
  volume = {122},
  number = {10},
  pages = {104103},
  issn = {0021-9606},
  doi = {10.1063/1.1856451},
  urldate = {2024-06-12},
  abstract = {Two-component and scalar relativistic energy-consistent pseudopotentials for the group 1 elements from K to element 119 are presented using nine electrons for the valence space definition. The accuracy of such an approximation is discussed for dipole polarizabilities and ionization potentials obtained at the coupled-cluster level as compared to experimental and all-electron Douglas--Kroll results.},
  file = {/Users/yingxing/Zotero/storage/G4Z83PKU/Lim et al_2005_All-electron and relativistic pseudopotential studies for the group 1 element.pdf}
}

@article{Liu2010,
  title = {Ideas of Relativistic Quantum Chemistry},
  author = {Liu, Wenjian},
  year = {2010},
  month = jul,
  journal = {Mol. Phys.},
  volume = {108},
  number = {13},
  pages = {1679--1706},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268971003781571},
  urldate = {2023-03-20},
  abstract = {The basic ideas of relativistic quantum chemistry are highlighted, with the most important ingredients summarised as follows. (1) The restricted kinetic balance (RKB) condition, being both necessary and sufficient, serves as the cornerstone for the matrix representation of the Dirac-based Hamiltonian. (2) The concept of matrix transformation plays the key role in formulating two-component relativistic theories. Some popular ones, albeit presented as operators, are de facto matrix formulations in terms implicitly of the RKB condition. They merely make simple things complicated as a one-step block-diagonalization of the matrix Dirac equation can do the whole job. (3) The computational efficiency for both four- and two-component relativistic theories can be gained by means of the simple chemical idea of `from atoms to molecule' without recourse to mathematical tricks. The two branches of relativistic theories have thus been made fully equivalent in all the aspects of simplicity, accuracy, and efficiency. It is concluded that the best relativistic electrons-only Hamiltonian has been found, which can be combined with any know-how correlation methods for electronic structure calculations of all the atoms in the Periodic Table. Most amazingly, the new quantum mechanical equation serves as a seamless bridge between the Schr{\"o}dinger and Dirac equations. In short, the `relativity problem' in chemistry has been solved.},
  keywords = {'from atoms to molecule',exact two-component Hamiltonian,kinetic balance,matrix transformation,relativistic quantum chemistry},
  file = {/Users/yingxing/Zotero/storage/QWUGRYRC/Ideas of relativistic quantum chemistry_2010.pdf}
}

@article{Lundin1973,
  title = {Lifetime {{Measurements}} in {{Mg I-Mg IV}}},
  author = {Lundin, L. and Engman, B. and Hilke, J. and Martinson, I.},
  year = {1973},
  month = dec,
  journal = {Phys. Scr.},
  volume = {8},
  number = {6},
  pages = {274},
  issn = {1402-4896},
  doi = {10.1088/0031-8949/8/6/009},
  urldate = {2023-03-20},
  abstract = {We have investigated the beam-foil spectra of Mg (100-500 {\AA}, 2 000-5 000 {\AA}) using 100-360 keV Mg+ ions from a heavy ion accelerator. Transitions belonging to MgI-MgIV were observed and evidence was found for non-autoionizing doubly-excited states in MgII. Lifetimes were determined for several excited levels in MgI-MgIV. The results are compared with previous experimental data and accurate theoretical calculations.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/3IWPG4EJ/Lundin et al_1973_Lifetime Measurements in Mg I-Mg IV.pdf}
}

@article{Lupinetti2005,
  title = {Polarizabilities and Hyperpolarizabilities for the Atoms {{Al}}, {{Si}}, {{P}}, {{S}}, {{Cl}}, and {{Ar}}: {{Coupled}} Cluster Calculations},
  shorttitle = {Polarizabilities and Hyperpolarizabilities for the Atoms {{Al}}, {{Si}}, {{P}}, {{S}}, {{Cl}}, and {{Ar}}},
  author = {Lupinetti, Concetta and Thakkar, Ajit J.},
  year = {2005},
  month = jan,
  journal = {The Journal of Chemical Physics},
  volume = {122},
  number = {4},
  pages = {044301},
  issn = {0021-9606},
  doi = {10.1063/1.1834512},
  urldate = {2024-06-12},
  abstract = {Accurate static dipole polarizabilities and hyperpolarizabilities are calculated for the ground states of the Al, Si, P, S, Cl, and Ar atoms. The finite-field computations use energies obtained with various ab initio methods including M{\o}ller--Plesset perturbation theory and the coupled cluster approach. Excellent agreement with experiment is found for argon. The experimental {\=undefined} for Al is likely to be in error. Only limited comparisons are possible for the other atoms because hyperpolarizabilities have not been reported previously for most of these atoms. Our recommended values of the mean dipole polarizability (in the order Al--Ar) are {\=undefined}/e2a02Eh-1=57.74, 37.17, 24.93, 19.37, 14.57, and 11.085 with an error estimate of {\textpm}0.5\%. The recommended values of the mean second dipole hyperpolarizability (in the order Al--Ar) are {\=undefined}/e4a04Eh-3=2.02{\texttimes}105,\hphantom{,}4.31{\texttimes}104,\hphantom{,}1.14{\texttimes}104,\hphantom{,}6.51{\texttimes}103,\hphantom{,}2.73{\texttimes}103, and 1.18{\texttimes}103 with an error estimate of {\textpm}2\%. Our recommended polarizability anisotropy values are {$\Delta\alpha$}/e2a02Eh-1=-25.60, 8.41, -3.63, and 1.71 for Al, Si, S, and Cl respectively, with an error estimate of {\textpm}1\%. The recommended hyperpolarizability anisotropies are {$\Delta\gamma$}/e4a04Eh-3=-3.88{\texttimes}105,\hphantom{,}4.16{\texttimes}104,\hphantom{,}-7.00{\texttimes}103, and 1.65{\texttimes}103 for Al, Si, S, and Cl, respectively, with an error estimate of {\textpm}4\%.},
  file = {/Users/yingxing/Zotero/storage/I3ZLIJB2/Lupinetti_Thakkar_2005_Polarizabilities and hyperpolarizabilities for the atoms Al, Si, P, S, Cl, and.pdf}
}

@article{Ma2015,
  title = {Measured Atomic Ground-State Polarizabilities of 35 Metallic Elements},
  author = {Ma, Lei and Indergaard, John and Zhang, Baiqian and Larkin, Ilia and Moro, Ramiro and {de Heer}, Walt A.},
  year = {2015},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {91},
  number = {1},
  pages = {010501},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.91.010501},
  urldate = {2023-03-20},
  abstract = {Advanced pulsed cryogenic molecular-beam electric deflection methods involving position-sensitive mass spectrometry and 7.87-eV ionizing radiation were used to measure the polarizabilities of more than half of the metallic elements in the Periodic Table. Concurrent Stern-Gerlach deflection measurements verified the ground-state condition of the measured atoms. Comparison with state-of-the-art calculations exposes significant systematic and isolated discrepancies throughout the Periodic Table.},
  file = {/Users/yingxing/Zotero/storage/Z5PIGRJ7/Ma et al. - 2015 - Measured atomic ground-state polarizabilities of 3.pdf;/Users/yingxing/Zotero/storage/ZWCT9EYZ/Ma et al_2015_Measured atomic ground-state polarizabilities of 35 metallic elements.pdf}
}

@article{Maeder1979,
  title = {Natural States of Interacting Systems and Their Use for the Calculation of Intermolecular Forces: {{IV}}. {{Calculation}} of van Der {{Waals}} Coefficients between One- and Two-Valence-Electron Atoms in Their Ground States, as Well as of Polarizabilities, Oscillator Strength Sums and Related Quantities, Including Correlation Effects},
  shorttitle = {Natural States of Interacting Systems and Their Use for the Calculation of Intermolecular Forces},
  author = {Maeder, F. and Kutzelnigg, W.},
  year = {1979},
  month = sep,
  journal = {Chemical Physics},
  volume = {42},
  number = {1},
  pages = {95--112},
  issn = {0301-0104},
  doi = {10.1016/0301-0104(79)85171-X},
  urldate = {2024-06-12},
  abstract = {The constants C6, C8, C10, {$\alpha$}1, {$\alpha$}2, {$\alpha$}3, and the ``effective oscillator strengths'' for H, Li, Na, K. Rb, Cs, He, Be, Mg, Ca, Hg are computed in an ab-initio frozen-core and a pseudopotential approach including electron correlation.},
  file = {/Users/yingxing/Zotero/storage/BD2VHGS8/Maeder_Kutzelnigg_1979_Natural states of interacting systems and their use for the calculation of.pdf}
}

@article{Malmqvist2002,
  title = {The Restricted Active Space ({{RAS}}) State Interaction Approach with Spin--Orbit Coupling},
  author = {Malmqvist, Per {\AA}ke and Roos, Bj{\"o}rn O. and Schimmelpfennig, Bernd},
  year = {2002},
  month = may,
  journal = {Chemical Physics Letters},
  volume = {357},
  number = {3},
  pages = {230--240},
  issn = {0009-2614},
  doi = {10.1016/S0009-2614(02)00498-0},
  urldate = {2024-06-12},
  abstract = {A method to compute spin--orbit coupling between electronic states is presented. An effective one-electron spin--orbit Hamiltonian is used, based on atomic mean field integrals. The basic electronic states are obtained using the restricted active space (RAS) SCF method. The Hamiltonian matrix is obtained by an extension of the restricted active space state interaction (RASSI) method. Several hundred states can be included. Tests for atoms and molecules from the entire periodic system show accurate results. Computed spin--orbit effects on relative energies are normally accurate within a few percent. The method has been included in the MOLCAS-5.0 quantum chemistry software.},
  file = {/Users/yingxing/Zotero/storage/HUB8LGKT/Malmqvist et al_2002_The restricted active space (RAS) state interaction approach with spin–orbit.pdf}
}

@article{Mani2009,
  title = {Relativistic Coupled-Cluster Calculations of \${\textasciicircum}\{20\}{\textbackslash}text\{\vphantom\}{{N}}\vphantom\{\}{\textbackslash}text\{e\}\$, \${\textasciicircum}\{40\}{\textbackslash}text\{\vphantom\}{{A}}\vphantom\{\}{\textbackslash}text\{r\}\$, \${\textasciicircum}\{84\}{\textbackslash}text\{\vphantom\}{{K}}\vphantom\{\}{\textbackslash}text\{r\}\$, and \${\textasciicircum}\{129\}{\textbackslash}text\{\vphantom\}{{X}}\vphantom\{\}{\textbackslash}text\{e\}\$: {{Correlation}} Energies and Dipole Polarizabilities},
  shorttitle = {Relativistic Coupled-Cluster Calculations of \${\textasciicircum}\{20\}{\textbackslash}text\{\vphantom\}{{N}}\vphantom\{\}{\textbackslash}text\{e\}\$, \${\textasciicircum}\{40\}{\textbackslash}text\{\vphantom\}{{A}}\vphantom\{\}{\textbackslash}text\{r\}\$, \${\textasciicircum}\{84\}{\textbackslash}text\{\vphantom\}{{K}}\vphantom\{\}{\textbackslash}text\{r\}\$, and \${\textasciicircum}\{129\}{\textbackslash}text\{\vphantom\}{{X}}\vphantom\{\}{\textbackslash}text\{e\}\$},
  author = {Mani, B. K. and Latha, K. V. P. and Angom, D.},
  year = {2009},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {80},
  number = {6},
  pages = {062505},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.80.062505},
  urldate = {2024-06-11},
  abstract = {We have carried out a detailed and systematic study of the correlation energies of inert gas atoms Ne, Ar, Kr, and Xe using relativistic many-body perturbation theory and relativistic coupled-cluster theory. In the relativistic coupled-cluster calculations, we implement perturbative triples and include these in the correlation energy calculations. We then calculate the dipole polarizability of the ground states using perturbed coupled-cluster theory.},
  file = {/Users/yingxing/Zotero/storage/NWEJ9JNX/Mani et al_2009_Relativistic coupled-cluster calculations of $^ 20 -text N -text e $,.pdf}
}

@article{Margraf2017,
  title = {Single-Reference Coupled Cluster Theory for Multi-Reference Problems},
  author = {Margraf, Johannes T. and Perera, Ajith and Lutz, Jesse J. and Bartlett, Rodney J.},
  year = {2017},
  month = nov,
  journal = {The Journal of Chemical Physics},
  volume = {147},
  number = {18},
  pages = {184101},
  issn = {0021-9606},
  doi = {10.1063/1.5003128},
  urldate = {2024-06-12},
  abstract = {Coupled cluster (CC) theory is widely accepted as the most accurate and generally applicable approach in quantum chemistry. CC calculations are usually performed with single Slater-determinant references, e.g., canonical Hartree-Fock (HF) wavefunctions, though any single determinant can be used. This is an attractive feature because typical CC calculations are straightforward to apply, as there is no potentially ambiguous user input required. On the other hand, there can be concern that CC approximations give unreliable results when the reference determinant provides a poor description of the system of interest, i.e., when the HF or any other single determinant ground state has a relatively low weight in the full CI expansion. However, in many cases, the reported ``failures'' of CC can be attributed to an unfortunate choice of reference determinant, rather than intrinsic shortcomings of CC itself. This is connected to well-known effects like spin-contamination, wavefunction instability, and symmetry-breaking. In this contribution, a particularly difficult singlet/triplet splitting problem in two phenyldinitrene molecules is investigated, where CC with singles, doubles and perturbative triples [CCSD(T)] was reported to give poor results. This is analyzed by using different reference determinants for CCSD(T), as well as performing higher level CCSDT-3 and CCSDT calculations. We show that doubly electron attached and doubly ionized equation-of-motion (DEA/DIP-EOM) approaches are powerful alternatives for treating such systems. These are operationally single-determinant methods that adequately take the multi-reference nature of these molecules into account. Our results indicate that CC remains a powerful tool for describing systems with both static correlation and dynamic correlation, when pitfalls associated with the choice of the reference determinant are avoided.},
  file = {/Users/yingxing/Zotero/storage/DW5XHFR6/Margraf et al_2017_Single-reference coupled cluster theory for multi-reference problems.pdf}
}

@article{Marlow1964,
  title = {Shock-{{Tube Measurement}} of the {{Polarizability}} of {{Atomic Hydrogen}}},
  author = {Marlow, Wayland C. and Bershader, Daniel},
  year = {1964},
  month = feb,
  journal = {Phys. Rev.},
  volume = {133},
  number = {3A},
  pages = {A629-A632},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.133.A629},
  urldate = {2024-06-12},
  abstract = {The electric polarizability of atomic hydrogen has been measured at optical frequencies by shock heating a gaseous mixture of argon and molecular hydrogen to temperatures causing nearly complete dissociation of the latter. Application of Mach-Zehnder interferometry to the shock-heated gas gave measurements of fringe shift across the shock front which were subsequently reduced to obtain the polarizability of the ground state of atomic hydrogen. The resultant value is {$AH$}=(4.61{\textpm}0.0⁢7)⁢{$a$}03, for a wavelength of 5870 {\AA}, where is the first Bohr radius and the error assignment is purely statistical. The shock waves employed were in the Mach number range 10 to 12 in a mixture (by volume) and produced temperatures of the order of 4600{$^\circ$}K at densities high enough to ensure thermal equilibrium. Under these conditions there was negligible ionization or excitation of the argon diluent. In contrast to earlier experiments reported in the literature, the present result is in good agreement with the predictions of the quantum-mechanical time-dependent perturbation theory which gives a value of for the same wavelength as that used in the experimental work.},
  file = {/Users/yingxing/Zotero/storage/4PFFYCMF/Marlow_Bershader_1964_Shock-Tube Measurement of the Polarizability of Atomic Hydrogen.pdf}
}

@article{Maroulis1997,
  title = {Electrooptical {{Properties}} and {{Molecular Polarization}} of {{Iodine}}, {{I2}}},
  author = {Maroulis, George and Makris, Constantinos and Hohm, Uwe and Goebel, Dirk},
  year = {1997},
  month = jan,
  journal = {J. Phys. Chem. A},
  volume = {101},
  number = {5},
  pages = {953--956},
  publisher = {American Chemical Society},
  issn = {1089-5639},
  doi = {10.1021/jp962578u},
  urldate = {2024-06-12},
  abstract = {Experimental and theoretical efforts are combined to determine a reliable value of the static dipole polarizability of I2. The experimental estimate of the mean dipole polarizability is {$\alpha$} = 69.7 {\textpm} 1.8e2a02Eh-1. The polarizability of the iodine atom has also been deduced from experimental measurements and is estimated at 32.9 {\textpm} 1.3e2a02Eh-1. Accurate ab initio calculations predict {$\alpha$} = 70.9 {\textpm} 1.4e2a02Eh-1 and for the anisotropy {$\Delta\alpha$} = 41.2 {\textpm} 0.8e2a02Eh-1. The deformation of the iodine molecule in the presence of general static fields has been studied and analyzed.},
  file = {/Users/yingxing/Zotero/storage/KAIVPS3A/Maroulis et al_1997_Electrooptical Properties and Molecular Polarization of Iodine, I2.pdf}
}

@article{Maroulis2003,
  title = {Static Dipole (Hyper)Polarizability of the Silicon Atom},
  author = {Maroulis, George and Pouchan, Claude},
  year = {2003},
  month = may,
  journal = {J. Phys. B: At. Mol. Opt. Phys.},
  volume = {36},
  number = {10},
  pages = {2011},
  issn = {0953-4075},
  doi = {10.1088/0953-4075/36/10/311},
  urldate = {2024-06-12},
  abstract = {We report static dipole (hyper)polarizability values for silicon. Relying on finite-field M{\o}ller--Plesset perturbation theory and coupled-cluster calculations with large Gaussian-type basis sets of near-Hartree--Fock quality, we find electron correlation effects to be small for both properties. We estimate the mean dipole polarizability at {\=undefined} = 37.4 {\textpm} 0.1e2 a 02 E h-1 and {\=undefined} = (4.3 {\textpm} 0.1) {\texttimes} 104 e4 a 04 E h-3.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/2IH2U289/Maroulis_Pouchan_2003_Static dipole (hyper)polarizability of the silicon atom.pdf}
}

@book{Maroulis2006,
  title = {Atoms, {{Molecules And Clusters In Electric Fields}}: {{Theoretical Approaches To The Calculation Of Electric Polarizability}}},
  shorttitle = {Atoms, {{Molecules And Clusters In Electric Fields}}},
  author = {Maroulis, George},
  year = {2006},
  month = jul,
  publisher = {World Scientific},
  abstract = {With the central importance of electric polarizability and hyperpolarizability for a wide spectrum of activities, this book charts the trends in the accurate theoretical determination of these properties in specialized fields. The contributions include reviews and original papers that extend from methodology to applications in specific areas of primary importance such as cluster science and organic synthesis of molecules with specific properties./a},
  googlebooks = {lWW7CgAAQBAJ},
  isbn = {978-1-908979-74-2},
  langid = {english},
  keywords = {Science / Chemistry / Physical & Theoretical},
  file = {/Users/yingxing/Zotero/storage/X6NDDGIW/Maroulis_2006_Atoms, Molecules And Clusters In Electric Fields.pdf}
}

@article{Maroulis2007,
  title = {Cluster Size Effect on the Electric Polarizability and Hyperpolarizability in Small Antimony Clusters Sbn, N=1,2 and 4},
  author = {Maroulis, George},
  year = {2007},
  month = aug,
  journal = {Chem. Phys. Lett.},
  volume = {444},
  number = {1--3},
  pages = {44--47},
  publisher = {Elsevier BV},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2007.07.015}
}

@article{Martins2016,
  title = {All-Electron {{Gaussian}} Basis Sets of Double Zeta Quality for the Actinides},
  author = {Martins, L. S. C. and Jorge, F. E. and Franco, M. L. and Ferreira, I. B.},
  year = {2016},
  month = dec,
  journal = {The Journal of Chemical Physics},
  volume = {145},
  number = {24},
  pages = {244113},
  issn = {0021-9606},
  doi = {10.1063/1.4973377},
  urldate = {2024-06-12},
  abstract = {For the actinides, two segmented all-electron basis sets of valence double zeta quality plus polarization functions (DZP) are developed. One of them must be used along with the non-relativistic Hamiltonian, whereas the other with the Douglas-Kroll-Hess (DKH) one. Adding diffuse functions of s, p, d, f, and g symmetries to the non-relativistic and relativistic sets, augmented basis sets are developed. These functions are essential to describe correctly electrons far away from the nuclei. For some compounds, geometric parameters, atomic charges and valence orbital populations of the actinides, and bond dissociation energies are calculated using the Becke 3-parameter (exchange) and the Lee, Yang, and Parr (correlation) functional in conjunction with the DZP-DKH basis set. For Am and No, the static electric mean dipole polarizabilities are also reported. Comparison with benchmark theoretical and experimental values found in the literature is carried out. It is verified that the performances of the relativistic compact size basis sets generated in this work are regular, efficient, and reliable. They will be extremely helpful in molecular property calculations that need explicitly to consider the core electrons.},
  file = {/Users/yingxing/Zotero/storage/5WTA6MAT/Martins et al_2016_All-electron Gaussian basis sets of double zeta quality for the actinides.pdf}
}

@article{McNeill2020,
  title = {Polarizabilities of Neutral Atoms and Atomic Ions with a Noble Gas Electron Configuration},
  author = {McNeill, Ashley S. and Peterson, Kirk A. and Dixon, David A.},
  year = {2020},
  month = nov,
  journal = {The Journal of Chemical Physics},
  volume = {153},
  number = {17},
  pages = {174304},
  issn = {0021-9606},
  doi = {10.1063/5.0026876},
  urldate = {2024-06-06},
  abstract = {Atomic polarizabilities play an important role in the development of force fields for molecular simulations, as well as for the development of qualitative concepts of atomic and molecular behavior. Coupled cluster theory at the coupled cluster singles doubles triples level with very large correlation-consistent basis sets with extended diffuse functions has been used to predict the polarizabilities of the atomic neutrals, mono-cations and mono-anions with a noble gas configuration. Additional corrections for scalar relativistic and spin--orbit effects were also included for the electron configurations of Kr, Xe, and Rn. The results are in excellent agreement with experiment or with other high level calculations where available. The current results for most of these species represent the best available values for the polarizabilities. The results show that the polarizability of H- is very difficult to calculate without extremely diffuse functions. The polarizability of H- is the largest value, 34.05 {\AA}3, calculated for all species in the current study. The polarizabilities of the remaining halogen anions are also the best available values. The polarizabilities of the halogen anions (excluding F-) and H- have a linear correlation with the electron affinity of the neutral atom. Spin--orbit effects, even for closed shell species, cannot be ignored for quantitative accuracy, and the inclusion of spin--orbit effects for Fr+, Rn, and At- increases the polarizability by 4\%, 6\%, and 15\%, respectively.},
  file = {/Users/yingxing/Zotero/storage/2AVDKMG5/McNeill et al_2020_Polarizabilities of neutral atoms and atomic ions with a noble gas electron.pdf}
}

@article{MEDVEĎ2000a,
  title = {Anisotropie Dipole Polarizabilities and Quadrupole Moments of Open-Shell Atoms and Ions: {{O}}, {{F}}, {{S}}, {{Cl}}, {{Se}}, {{Br}} and Isoelectronic Systems},
  shorttitle = {Anisotropie Dipole Polarizabilities and Quadrupole Moments of Open-Shell Atoms and Ions},
  author = {MEDVE{\v D}, M. and FOWLER, P. W. and HUTSON, J. M.},
  year = {2000},
  month = apr,
  journal = {Mol. Phys.},
  volume = {98},
  number = {7},
  pages = {453--463},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268970009483311},
  urldate = {2023-03-20},
  abstract = {Quadrupole moment and dipole polarizability tensor components are calculated at the correlated complete-active-space self-consistent-field (CASSCF) and complete-active-space perturbation-theory (CASPT) levels for 2P states of O-, F, Ne+, Na2+, S-, Cl, Ar+, 98, K2+ , Se-, Br, Kr+, Rb2+ and 3P, 1D, 1S states of O-, F+, Ne2+, Na3+, S, Cl+, Ar2+, K3+, Se, Br+, Kr2+, Rb3+. Relativistic corrections are included perturbatively for the 34- and 35-electron systems.}
}

@article{Miffre2006a,
  title = {Measurement of the Electric Polarizability of Lithium by Atom Interferometry},
  author = {Miffre, A. and Jacquey, M. and B{\"u}chner, M. and Tr{\'e}nec, G. and Vigu{\'e}, J.},
  year = {2006},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {73},
  number = {1},
  pages = {011603},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.73.011603},
  urldate = {2024-06-05},
  abstract = {We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium {$A$}=(24.33{\textpm}0.16){\texttimes}10-30m3 with a 0.66\% uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and the interference signals have a large intensity and a high visibility, resulting in accurate phase measurements. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to 4{\texttimes}10-9 for our largest field, is measured with a 10-3 accuracy.},
  file = {/Users/yingxing/Zotero/storage/GSVB2UJ2/Miffre et al_2006_Measurement of the electric polarizability of lithium by atom interferometry.pdf}
}

@article{Milani1990,
  title = {Experimental and Theoretical Electric Dipole Polarizabilities of {{Al}} and \$\{{\textbackslash}mathrm\{\vphantom{\}\}}{{Al}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  author = {Milani, Paolo and Moullet, I. and {de Heer}, Walt A.},
  year = {1990},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {42},
  number = {9},
  pages = {5150--5154},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.42.5150},
  urldate = {2024-06-05},
  abstract = {The static electric dipole polarizabilities of the aluminum atom and dimer have been measured by deflecting a molecular beam in an inhomogeneous electric field. Collimated aluminum-cluster beams are produced by a pulsed laser vaporization source. Deflections are determined by means of a novel position-sensitive time-of-flight mass spectrometer. The measured polarizabilities are 6.8{\textpm}0.3 and 19{\textpm}2 {\AA}3 for the atom and dimer, respectively, in good agreement with the ab initio calculations presented here. The experimental techniques described here allow precise determination of the mean deflections and velocities of the particles in the beam and are generally applicable for beams produced by laser vaporization sources.},
  file = {/Users/yingxing/Zotero/storage/R8GWKHAB/Milani et al_1990_Experimental and theoretical electric dipole polarizabilities of Al and.pdf}
}

@incollection{Miller1978,
  title = {Atomic and {{Molecular Polarizabilities-A Review}} of {{Recent Advances}}},
  booktitle = {Advances in {{Atomic}} and {{Molecular Physics}}},
  author = {Miller, Thomas M. and Bederson, Benjamin},
  editor = {Bates, D. R. and Bederson, Benjamin},
  year = {1978},
  month = jan,
  volume = {13},
  pages = {1--55},
  publisher = {Academic Press},
  doi = {10.1016/S0065-2199(08)60054-8},
  urldate = {2023-03-20},
  abstract = {This chapter focuses on the recent developments in the experimental and theoretical determination of the polarizabilities of simple atoms and molecules. Polarizability values (related to the ``quadratic Stark effect'') are accurately known for the noble gas atoms and for hydrogen, in theory, but the remainder of the periodic table has proven much more difficult to deal with, both theoretically and experimentally. The static electric dipole polarizability of the ground-state hydrogen atom is almost exactly 4.5a30, where a0 is the Bohr radius. Across rows of the periodic table, polarizabilities range from hundreds (of a30 units) for the alkali metal atoms generally monotonically down to a few for noble gas atoms. Excited atoms have much larger polarizabilities; recent polarizability measurements for atoms in Rydberg orbits have yielded values on the order of 1010a30. Further research on molecular polarizabilities can help in the determination of polarizability anisotropies whether through state selection or with beams of different temperatures. Supersonic molecular beams are found to have low internal energies, and the internal energy can be controlled somewhat in ``seeded'' beams.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/BB8RPYAE/Miller and Bederson - 1978 - Atomic and Molecular Polarizabilities-A Review of .pdf}
}

@incollection{Miller1989,
  title = {Electric {{Dipole Polarizability Measurements}}},
  booktitle = {Advances in {{Atomic}} and {{Molecular Physics}}},
  author = {Miller, Thomas M. and Bederson, Benjamin},
  editor = {Bates, David and Bederson, Benjamin},
  year = {1989},
  month = jan,
  volume = {25},
  pages = {37--60},
  publisher = {Academic Press},
  doi = {10.1016/S0065-2199(08)60081-0},
  urldate = {2024-06-05},
  abstract = {This chapter discusses the perturbation and nonperturbation methods of calculating atomic polarizabilities and shielding factors. Shielding factors are of considerable specialized interest because of the role they play in the determination of nuclear properties obtained from atomic spectroscopy experiments. Atomic and molecular polarizabilities, however, are of general interest because they appear as parameters in a large variety of atomic, molecular, and condensed matter properties. The most accurate polarizabilities available currently are determined from bulk measurements of a dielectric constant or refractive index for a gas of atoms or molecules. The determination of a dielectric constant is accomplished by measuring a capacitance change with and without the gas present. The dynamic polarizability corresponding to the frequency of the radiation can be obtained by replacing the molar polarization in the formula with the molar refraction. A permanent electric dipole moment would tend to cancel some of the deflection of the molecular beam that is observed for an induced moment alone, leading to the underestimation of the induced polarizability.},
  file = {/Users/yingxing/Zotero/storage/DW9SG5VX/Miller_Bederson_1989_Electric Dipole Polarizability Measurements.pdf}
}

@article{Mitroy2003,
  title = {Semiempirical Calculation of van Der {{Waals}} Coefficients for Alkali-Metal and Alkaline-Earth-Metal Atoms},
  author = {Mitroy, J. and Bromley, M. W. J.},
  year = {2003},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {68},
  number = {5},
  pages = {052714},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.68.052714},
  urldate = {2023-03-21},
  abstract = {The van der Waals coefficients, C6,C8, and C10 for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, D8 and the three-body coefficient, C9 are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.},
  file = {/Users/yingxing/Zotero/storage/VMGEERJ6/Semiempirical calculation of van der Waals coefficients for alkali-metal and alkaline-earth-metal atoms_2003.pdf}
}

@article{Mitroy2008,
  title = {Properties and Long Range Interactions of the Calcium Atom},
  author = {Mitroy, J. and Zhang, J.-Y.},
  year = {2008},
  month = apr,
  journal = {The Journal of Chemical Physics},
  volume = {128},
  number = {13},
  pages = {134305},
  issn = {0021-9606},
  doi = {10.1063/1.2841470},
  urldate = {2024-06-10},
  abstract = {The properties of a number of states of calcium are determined from a large basis configuration interaction calculation. The main focus is on the polarizabilities of the low lying states (the 4s2Se1, 4s3dDe1,3, 4s4pPo1,3, and 4s5sSe1,3 states) and the dispersion interactions of those states with the calcium ground state, the hydrogen atom, and the rare gases.},
  file = {/Users/yingxing/Zotero/storage/9USC34TY/Mitroy and Zhang - 2008 - Properties and long range interactions of the calc.pdf}
}

@article{Mitroy2010,
  title = {Dispersion and Polarization Interactions of the Strontium Atom},
  author = {Mitroy, J. and Zhang, J.Y.},
  year = {2010},
  month = aug,
  journal = {Mol. Phys.},
  volume = {108},
  number = {15},
  pages = {1999--2006},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268976.2010.501766},
  urldate = {2023-03-20},
  abstract = {Dispersion coefficients involving the 5s 2 1 S e and 5s5p 1,3P o states of strontium are determined from a large basis configuration interaction calculation. Dispersion coefficients are presented for the strontium dimer and also for strontium interactions with hydrogen and the rare gases. Polarizabilities and oscillator strengths from some low lying states are also given. The ground state polarizability and that of the 5s5p 1P o and 5s4d 1D e states are very similar in size.},
  keywords = {dispersion,Dispersion,polarizability,Polarizability,strontium,Strontium,van der Waals,Van der Waals},
  file = {/Users/yingxing/Zotero/storage/DRMKQIHV/Dispersion and polarization interactions of the strontium atom_2010.pdf}
}

@article{Mitroy2010a,
  title = {Theory and Applications of Atomic and Ionic Polarizabilities},
  author = {Mitroy, J. and Safronova, M. S. and Clark, Charles W.},
  year = {2010},
  month = oct,
  journal = {J. Phys. B: At. Mol. Opt. Phys.},
  volume = {43},
  number = {20},
  pages = {202001},
  issn = {0953-4075},
  doi = {10.1088/0953-4075/43/20/202001},
  urldate = {2024-06-05},
  abstract = {Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wavefunctions, interferometry with atom beams and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/49ANCNTX/Mitroy et al_2010_Theory and applications of atomic and ionic polarizabilities.pdf}
}

@book{Mohr2009,
  title = {Gold {{Chemistry}}: {{Applications}} and {{Future Directions}} in the {{Life Sciences}}},
  shorttitle = {Gold {{Chemistry}}},
  author = {Mohr, Fabian},
  year = {2009},
  month = mar,
  publisher = {John Wiley \& Sons},
  abstract = {Written by world-class authors, this most recent major book on the topic highlights new and current trends as well as future directions. It is comprehensive in its scope, covering all aspects of gold chemistry -- from homogeneous to heterogeneous catalysis, from supramolecular assemblies to sensors and medicinal applications. The result is an invaluable work for both organic and inorganic chemists working in universities and industry, as well as material scientists.},
  isbn = {978-3-527-62673-1},
  langid = {english},
  keywords = {Science / Chemistry / General,Science / Chemistry / Organic}
}

@article{Molof1974,
  title = {Measurements of Electric Dipole Polarizabilities of the Alkali-Metal Atoms and the Metastable Noble-Gas Atoms},
  author = {Molof, Robert W. and Schwartz, Henry L. and Miller, Thomas M. and Bederson, Benjamin},
  year = {1974},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {10},
  number = {4},
  pages = {1131--1140},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.10.1131},
  urldate = {2023-03-20},
  abstract = {The E-H-gradient balance technique has been used to measure the static electric dipole polarizabilities of the alkali-metal atoms and the tensor polarizabilities of the 3P2 metastable noble-gas atoms. All of the measurements are normalized to the scalar polarizability of 3S1 metastable helium, a value which has been accurately calculated. The scalar polarizabilities of the alkali atoms, in units of 10-24 cm3, are for lithium, 24.3 {\textpm} 0.5; sodium, 23.6 {\textpm} 0.5; potassium, 43.4 {\textpm} 0.9; rubidium, 47.3 {\textpm} 0.9; cesium, 59.6 {\textpm} 1.2. For the 3P2 metastable noble-gas atoms we measure the zz components of the polarizability tensors for mJ=1 and 2, which completely determines the polarizability tensors for all mJ. For {$\alpha$}zz(mJ) we find, in units of 10-24 cm3, for neon, 28.4 {\textpm} 0.6 (mJ=1) and 26.7 {\textpm} 0.5 (mJ=2); argon, 49.5 {\textpm} 1.0 (mJ=1) and 44.7 {\textpm} 0.9 (mJ=2); krypton, 52.7 {\textpm} 1.0 (mJ=1) and 46.8 {\textpm} 0.9 (mJ=2); xenon, 66.6 {\textpm} 1.3 (mJ=1) and 57.4 {\textpm} 1.1 (mJ=2). The rare-gas results, while more precise, are in good agreement with earlier work. The alkali-metal results are in excellent agreement with recent theory and the experiment of Hall and Zorn.},
  file = {/Users/yingxing/Zotero/storage/PMQS7GMR/Molof et al_1974_Measurements of electric dipole polarizabilities of the alkali-metal atoms and.pdf}
}

@article{Mori2023,
  title = {Convergent Close-Coupling Calculations of Positron Scattering from Atomic Carbon},
  author = {Mori, N. A. and Scarlett, L. H. and Bray, I. and Fursa, D. V.},
  year = {2023},
  month = mar,
  journal = {Phys. Rev. A},
  volume = {107},
  number = {3},
  pages = {032817},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.107.032817},
  urldate = {2024-06-10},
  abstract = {We report on the extension of the single-center convergent close-coupling method to positron scattering on multielectron atoms, along with the development of a technique for separating the direct ionization and positronium-formation channels in single-center calculations. We have performed calculations of positron scattering on carbon and present total elastic, momentum transfer, excitation, direct ionization, total ionization, total inelastic, positronium-formation, stopping power, and total cross sections from threshold to 5000 eV. We also present oscillator strengths, the scattering length, the hidden Ramsauer-Townsend minimum, the energy of the positron-carbon virtual state, and the mean excitation energy. Agreement with electron-scattering experiment and positron-scattering theory for several cross sections has been demonstrated for high energies. However, discrepancies exist between different theoretical methods at lower energies and for the ionization and positronium-formation processes.},
  file = {/Users/yingxing/Zotero/storage/IZLEXK3Q/Mori et al. - 2023 - Convergent close-coupling calculations of positron.pdf}
}

@article{Moszynski2003,
  title = {Long-Range Relativistic Interactions in the {{Cowan-Griffin}} Approximation and Their {{QED}} Retardation: {{Application}} to Helium, Calcium, and Cadmium Dimers},
  shorttitle = {Long-Range Relativistic Interactions in the {{Cowan-Griffin}} Approximation and Their {{QED}} Retardation},
  author = {Moszynski, Robert and {\L}ach, Grzegorz and Jaszu{\'n}ski, Micha{\l} and {Bussery-Honvault}, B{\'e}atrice},
  year = {2003},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {68},
  number = {5},
  pages = {052706},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.68.052706},
  urldate = {2024-06-10},
  abstract = {The theory of long-range relativistic interactions in the Cowan-Griffin approximation is formulated and the expression for the leading-order relativistic correction to the dispersion energy is derived. It is shown that the relativistic dispersion energy for closed-shell atoms behaves as with the interatomic distance R. The relativistic correction to the van der Waals constant is expressed as a Casimir-Polder integral of the product of a nonrelativistic frequency-dependent linear-response function with two dipole operators and a frequency-dependent quadratic-response function, including in addition one relativistic operator. In the Cowan-Griffin approximation, there are two contributions, involving the mass-velocity and the one-electron Darwin operators. The QED retardation effect on the long-range relativistic dispersion energy is also considered, and applications to the helium, calcium, and cadmium dimers are presented.},
  file = {/Users/yingxing/Zotero/storage/5HNULSEN/Moszynski et al. - 2003 - Long-range relativistic interactions in the Cowan-.pdf}
}

@article{Müller1984,
  title = {Treatment of Intershell Correlation Effects in Ab\hphantom{,}Initio Calculations by Use of Core Polarization Potentials. {{Method}} and Application to Alkali and Alkaline Earth Atoms},
  author = {M{\"u}ller, Wolfgang and Flesch, Joachim and Meyer, Wilfried},
  year = {1984},
  month = apr,
  journal = {The Journal of Chemical Physics},
  volume = {80},
  number = {7},
  pages = {3297--3310},
  issn = {0021-9606},
  doi = {10.1063/1.447083},
  urldate = {2024-06-08},
  abstract = {In the present approach the high reliability of ab\hphantom{,}initio techniques is combined with the easily amenable phenomenological core polarization concept for an efficient treatment of intershell correlation effects in all-electron SCF and valence CI calculations. By use of only a single adjustable atomic parameter, which is related to the radius of the core and determines the cutoff at short range, our effective core polarization potential (CPP) accounts quantitatively for dynamical intershell correlation as well as exclusion effects on the correlation energy of the core. The applications refer to alkali and alkaline earth atoms (Li to K and Be to Ca) and a detailed analysis is performed for core polarization effects on ionization energies, electron affinities, oscillator strengths, polarizabilities, van der Waals coefficients, the valence electron density, and spin densities. Very accurate results are obtained for well-known energetic properties and spin densities at the nucleus. With respect to the other applications we consider our results as the most reliable to date with an estimated uncertainty of 1\%--2\%.},
  file = {/Users/yingxing/Zotero/storage/RP3HJT5W/Müller et al_1984_Treatment of intershell correlation effects in ab initio calculations by use of.pdf}
}

@article{Nakajima2001,
  title = {Relativistic {{Effects}} for {{Polarizabilities}} and {{Hyperpolarizabilities}} of {{Rare Gas Atoms}}},
  author = {Nakajima, Takahito and Hirao, Kimihiko},
  year = {2001},
  month = aug,
  journal = {Chem. Lett.},
  volume = {30},
  number = {8},
  pages = {766--767},
  publisher = {The Chemical Society of Japan},
  issn = {0366-7022},
  doi = {10.1246/cl.2001.766},
  urldate = {2023-03-21},
  abstract = {The relativistic effects for static polarizabilities {$\alpha$} and hyperpolarizabilities {$\gamma$} of rare gas atoms (Ne through Rn) are investigated theoretically with the third-order Douglas--Kroll method. The results yield interesting trends of relativity in going from Ne to Rn: The relativistic effect decreases {$\alpha$} values of Ne and Ar and increases the values of Kr, Xe, and Rn, and it decreases {$\gamma$} values of Rn slightly and increases the values of other rare gas atoms, while the electron correlation effect increases {$\alpha$} and {$\gamma$} of all rare gas atoms.},
  file = {/Users/yingxing/Zotero/storage/XHNYSE5Q/Relativistic effects for polarizabilities and hyperpolarizabilities of rare gas atoms_2001.pdf}
}

@article{Nash2005,
  title = {Atomic and {{Molecular Properties}} of {{Elements}} 112, 114, and 118},
  author = {Nash, Clinton S.},
  year = {2005},
  month = apr,
  journal = {J. Phys. Chem. A},
  volume = {109},
  number = {15},
  pages = {3493--3500},
  publisher = {American Chemical Society},
  issn = {1089-5639},
  doi = {10.1021/jp050736o},
  urldate = {2023-03-20},
  abstract = {The results of calculations outlining aspects of the chemistry of element 112, element 114, and element 118 are compared to those for their 6th row analogues Hg, Pb, and Rn, respectively. Element 112 and element 114 are found to be relatively inert as compared to Hg and Pb, while element 118 is much more active than radon. Spin-orbit coupling plays a dominant role in this behavior.},
  file = {/Users/yingxing/Zotero/storage/BIAATGKF/Atomic and molecular properties of elements 112, 114, and 118_2005.pdf}
}

@article{Neogrády1997,
  title = {Ionization Potentials and Electron Affinities of {{Cu}}, {{Ag}}, and {{Au}}: {{Electron}} Correlation and Relativistic Effects},
  shorttitle = {Ionization Potentials and Electron Affinities of {{Cu}}, {{Ag}}, and {{Au}}},
  author = {Neogr{\'a}dy, Pavel and Kell{\"o}, Vladimir and Urban, Miroslav and Sadlej, Andrzej J.},
  year = {1997},
  journal = {Int. J. Quantum Chem.},
  volume = {63},
  number = {2},
  pages = {557--565},
  issn = {1097-461X},
  doi = {10.1002/(SICI)1097-461X(1997)63:2<557::AID-QUA25>3.0.CO;2-3},
  urldate = {2023-09-08},
  abstract = {The electron correlation and relativistic effects on ionization potentials and electron affinities of Cu, Ag, and Au are investigated in the framework of the coupled cluster method and different 1-component approximations to the relativistic Dirac-Coulomb Hamiltonian. The first-order perturbation approach based on the massvelocity and Darwin terms is found to be sufficiently accurate for Cu and Ag while it fails for Au. The spin-averaged Douglas-Kroll no-pair method gives excellent results for the studied atomic properties. The ionization potentials obtained within this method and the coupled cluster scheme for the electron correlation effects are 7.733(7.735) eV for Cu, 7.461(7.575) eV for Ag, and 9.123(9.225) eV for Au (experimental values given in parentheses). The calculated (experimental) electron affinity results for Cu, Ag, and Au are 1.236(1.226), 1.254(1.303), and 2.229(2.309) eV, respectively. There is a marked relativistic effect on both the ionization potential and electron affinity of Ag which sharply increases for Au while Cu exhibits only a little relativistic character. A similar pattern of relativistic effects is also observed for electric dipole polarizabilities of the coinage metal atoms and their ions. The coupled cluster dipole polarizabilities of the coinage metal atoms calculated in this article in the Douglas-Kroll no-pair formalism (Cu: 46.50 au; Ag: 52.46 au; Au: 36.06 au) are compared with our earlier data for their singly positive and singly negative ions. {\copyright} 1997 John Wiley \& Sons, Inc. Int J Quant Chem 63: 557--565, 1997},
  copyright = {Copyright {\copyright} 1997 John Wiley \& Sons, Inc.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/UX84Q7R5/Neogrády et al_1997_Ionization potentials and electron affinities of Cu, Ag, and Au.pdf}
}

@article{Neto2021,
  title = {{{ZORA}} All-Electron Double Zeta Basis Sets for the Elements from {{H}} to {{Xe}}: Application in Atomic and Molecular Property Calculations},
  shorttitle = {{{ZORA}} All-Electron Double Zeta Basis Sets for the Elements from {{H}} to {{Xe}}},
  author = {Neto, Ant{\^o}nio Canal and {de Oliveira}, Amanda Z. and Jorge, Francisco Elias and Camiletti, Giuseppi G.},
  year = {2021},
  month = aug,
  journal = {J Mol Model},
  volume = {27},
  number = {8},
  pages = {1--9},
  publisher = {Springer Berlin Heidelberg},
  issn = {0948-5023},
  doi = {10.1007/s00894-021-04847-5},
  urldate = {2024-06-06},
  abstract = {From the segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) for the elements from H to Xe, the zeroth-order regular approximation (ZORA) is used to generate a DZP-ZORA basis set, i.e., the contraction coefficients of the DZP set are re-optimized using the minimum ZORA energy criterion. To properly describe electrons distant from the nuclei, a diffuse function is added to each atomic symmetry (s, p, d, and f). The later basis set is designated as DZP-ZORA augmented. To test the effectiveness of the basis sets developed in this work, calculations of ionization energies and mean dipole polarizabilities of some elements are performed using the ZORA-CCSD(T) method. At the same level of theory, bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatoms are also reported. Comparison with experimental data and recommended values available in the literature is made. Except for polarizability, scalar relativistic effects are estimated for the other properties. The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated. Graphical abstract},
  copyright = {2021 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/RAJJHBSV/Neto et al_2021_ZORA all-electron double zeta basis sets for the elements from H to Xe.pdf}
}

@article{Neto2023,
  title = {All-Electron {{ZORA}} Triple Zeta Basis Sets for the Elements {{Cs}}--{{La}} and {{Hf}}--{{Rn}}},
  author = {Neto, Ant{\^o}nio Canal and Jorge, Francisco E. and da Cruz, Henrique R. C.},
  year = {2023},
  month = sep,
  journal = {Chinese Phys. B},
  volume = {32},
  number = {9},
  pages = {093101},
  publisher = {{Chinese Physical Society and IOP Publishing Ltd}},
  issn = {1674-1056},
  doi = {10.1088/1674-1056/acbe34},
  urldate = {2024-06-06},
  abstract = {Segmented all-electron basis set of triple zeta valence quality plus polarization functions (TZP) for the elements of the fifth row to be used together with the zero-order regular approximation (ZORA) is carefully constructed. To correctly describe electrons distant from atomic nuclei, the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA. At the ZORA-B3LYP theoretical level, these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms, bond length, dissociation energy, and harmonic vibrational frequency of diatomic molecules. Then, these results are compared with the theoretical and experimental data found in the literature. Even considering that our sets are relatively compact, they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell. The performances of the ZORA and second-order Douglas--Kroll--Hess Hamiltonians are evaluated and the results are also discussed.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/IS5JX4UQ/Neto et al_2023_All-electron ZORA triple zeta basis sets for the elements Cs–La and Hf–Rn.pdf}
}

@article{Newell1965,
  title = {Absolute {{Determination}} of {{Refractive Indices}} of {{Gases}} at 47.7 {{Gigahertz}}},
  author = {Newell, A. C. and Baird, R. C.},
  year = {1965},
  month = dec,
  journal = {Journal of Applied Physics},
  volume = {36},
  number = {12},
  pages = {3751--3759},
  issn = {0021-8979},
  doi = {10.1063/1.1713942},
  urldate = {2024-06-05},
  abstract = {The refractive index of a gas is determined to high accuracy by measuring the change in the resonant frequency when the gas is admitted to a previously evacuated microwave cavity. This measurement was made at a frequency of 47.736 GHz, and is the first such measurement in this frequency range.The resonant frequency of the cavity is detected by means of a hybrid tee bridge circuit. When the cavity is matched to the waveguide the null at resonance is very sharp, and the frequency can be set to {\textpm}5 parts in 108.Two types of resonant structures were used in this measurement, a conventional cylindrical cavity and a Fabry-Perot resonator using one plane and one spherical mirror. Measurements were made with both structures on each of the gases, and the agreement between the two was within the limits of experimental error. Because the Fabry-Perot resonator has no side walls, air could be passed through it much more easily, and it is therefore preferred for use with moist air.The values of (n-1){\texttimes}106 for the gases at 0{$^\circ$}C and 760 Torr are as follows: Dry CO2\,free air288.13{\textpm}0.05,Argon277.48{\textpm}0.05,Carbon dioxide495.16{\textpm}0.08,Helium34.51{\textpm}0.05,Hydrogen135.77{\textpm}0.05,Nitrogen293.81{\textpm}0.07,Oxygen266.95{\textpm}0.05.The primary values of these results lies in their increased accuracy over previous measurements and their confirmation of existing accurate data on these gases. In addition the use of the Fabry-Perot resonator as a refractometer is demonstrated and its advantages under certain conditions discussed.},
  file = {/Users/yingxing/Zotero/storage/VVIZI9GW/Newell and Baird - 1965 - Absolute Determination of Refractive Indices of Ga.pdf}
}

@article{Oleynichenko2020,
  title = {Relativistic {{Fock Space Coupled Cluster Method}} for {{Many-Electron Systems}}: {{Non-Perturbative Account}} for {{Connected Triple Excitations}}},
  shorttitle = {Relativistic {{Fock Space Coupled Cluster Method}} for {{Many-Electron Systems}}},
  author = {Oleynichenko, Alexander V. and Zaitsevskii, Andr{\'e}i and Skripnikov, Leonid V. and Eliav, Ephraim},
  year = {2020},
  month = jul,
  journal = {Symmetry},
  volume = {12},
  number = {7},
  pages = {1101},
  publisher = {Multidisciplinary Digital Publishing Institute},
  issn = {2073-8994},
  doi = {10.3390/sym12071101},
  urldate = {2024-06-06},
  abstract = {The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.},
  copyright = {http://creativecommons.org/licenses/by/3.0/},
  langid = {english},
  keywords = {excited states,heavy-element compounds,high-precision electronic structure modeling,relativistic coupled cluster method},
  file = {/Users/yingxing/Zotero/storage/7YGLSRDE/Oleynichenko et al_2020_Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems.pdf}
}

@article{Orcutt1967,
  title = {Dielectric {{Constants}} of {{Imperfect Gases}}. {{III}}. {{Atomic Gases}}, {{Hydrogen}}, and {{Nitrogen}}},
  author = {Orcutt, R. H. and Cole, R. H.},
  year = {1967},
  month = jan,
  journal = {The Journal of Chemical Physics},
  volume = {46},
  number = {2},
  pages = {697--702},
  issn = {0021-9606},
  doi = {10.1063/1.1840728},
  urldate = {2024-06-12},
  abstract = {A modified cyclic-expansion method has been used to determine dielectric constants as a function of relative density with a precision of less than 1 ppm for He, Ne, Ar, Kr, H2, and N2 at 49{$^\circ$}C and pressures below 150 atm, which with data at measured pressures below 7 atm determine the first and second dielectric virial coefficients, and can also be used to determine pressure second virial coefficients.Dielectric second virial coefficients are for all six gases less than values predicted by present theories of fluctuations and pair polarizabilities, an effect believed to result from overlap interactions at short range. The low-density values of the Clausius---Mossotti function are in good agreement with other recent determinations.},
  file = {/Users/yingxing/Zotero/storage/WKBEY3D2/Orcutt_Cole_1967_Dielectric Constants of Imperfect Gases.pdf}
}

@article{Pachucki2000,
  title = {Relativistic and {{QED}} Corrections to the Polarizability of Helium},
  author = {Pachucki, Krzysztof and Sapirstein, Jonathan},
  year = {2000},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {63},
  number = {1},
  pages = {012504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.63.012504},
  urldate = {2023-03-21},
  abstract = {Relativistic and leading QED corrections to the static electric dipole polarizability of helium are calculated. The resulting theoretical uncertainty is estimated to be under 2 ppm.},
  file = {/Users/yingxing/Zotero/storage/TE5NP753/Relativistic and QED corrections to the polarizability of helium_2001.pdf}
}

@article{Pantazis2012,
  title = {All-Electron Scalar Relativistic Basis Sets for the 6p Elements},
  author = {Pantazis, Dimitrios A. and Neese, Frank},
  year = {2012},
  month = oct,
  journal = {Theor Chem Acc},
  volume = {131},
  number = {11},
  pages = {1292},
  issn = {1432-2234},
  doi = {10.1007/s00214-012-1292-x},
  urldate = {2024-06-12},
  abstract = {New segmented all-electron relativistically contracted (SARC) basis sets have been developed for the elements 81Tl--86Rn, thus extending the SARC family of all-electron basis sets to include the 6p block. The SARC basis sets are separately contracted for the second-order Douglas--Kroll--Hess and the zeroth-order regular approximation scalar relativistic Hamiltonians. Their compact size and segmented construction are best suited to the requirements of routine density functional theory (DFT) applications. Evaluation of the basis sets is performed in terms of incompleteness and contraction errors, orbital properties, ionization energies, electron affinities, and atomic polarizabilities. From these atomic metrics and from computed basis set superposition errors for a series of homonuclear dimers, it is shown that the SARC basis sets achieve a good balance between accuracy and size for efficient all-electron scalar relativistic DFT applications.},
  langid = {english},
  keywords = {All-electron basis sets,DKH,SARC,Scalar relativistic calculations,ZORA},
  file = {/Users/yingxing/Zotero/storage/IQR9D78I/Pantazis_Neese_2012_All-electron scalar relativistic basis sets for the 6p elements.pdf}
}

@article{Patil2000,
  title = {A Simple Model Potential Description of the Alkaline Earth Isoelectronic Sequences},
  author = {Patil, S.H.},
  year = {2000},
  month = may,
  journal = {Eur. Phys. J. D},
  volume = {10},
  number = {3},
  pages = {341--347},
  issn = {1434-6079},
  doi = {10.1007/s100530050557},
  urldate = {2024-06-12},
  abstract = {We have developed a simple model potential with a hard core and the correct large-r Coulombic behaviour, to describe the interaction of an electron with a closed shell. One has an exact, analytic ground state wave function for this potential. This potential is used to develop two-electron perturbed and unperturbed wave functions, with the correct asymptotic behaviour and cusp conditions. These wave functions allow us to obtain accurate values for the two-electron energies, polarisabilities, hyperpolarisabilities, and dispersion coefficients of alkaline earth sequences. Many of these results are the only ones available in the literature.},
  langid = {english},
  keywords = {PACS. 31.15.-p Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)},
  file = {/Users/yingxing/Zotero/storage/RBMEUYXF/Patil_2000_A simple model potential description of the alkaline earth isoelectronic.pdf}
}

@article{Pershina2008,
  title = {Adsorption of Inert Gases Including Element 118 on Noble Metal and Inert Surfaces from Ab Initio {{Dirac}}--{{Coulomb}} Atomic Calculations},
  author = {Pershina, V. and Borschevsky, A. and Eliav, E. and Kaldor, U.},
  year = {2008},
  month = oct,
  journal = {The Journal of Chemical Physics},
  volume = {129},
  number = {14},
  pages = {144106},
  issn = {0021-9606},
  doi = {10.1063/1.2988318},
  urldate = {2024-06-12},
  abstract = {The interaction of the inert gases Rn and element 118 with various surfaces has been studied on the basis of fully relativistic ab initio Dirac--Coulomb CCSD(T) calculations of atomic properties. The calculated polarizability of element 118, 46.3 a.u., is the largest in group 18, the ionization potential is the lowest at 8.91 eV, and the estimated atomic radius is the largest, 4.55 a.u. These extreme values reflect, in addition to the general trends in the Periodic Table, the relativistic expansion and destabilization of the outer valence 7p3/2 orbital. Van der Waals coefficients C3 and adsorption enthalpies {$\Delta$}Hads of Ne through element 118 on noble metals and inert surfaces, such as quartz, ice, Teflon, and graphite, were calculated in a physisorption model using the atomic properties obtained. The C3 coefficients were shown to steadily increase in group 18, while the increase in {$\Delta$}Hads from Ne to Rn does not continue to element 118: The large atomic radius of the latter element is responsible for a decrease in the interaction energy. We therefore predict that experimental distinction between Rn and 118 by adsorption on these types of surfaces will not be feasible. A possible candidate for separating the two elements is charcoal; further study is needed to test this possibility.},
  file = {/Users/yingxing/Zotero/storage/CWB3TPTR/Pershina et al_2008_Adsorption of inert gases including element 118 on noble metal and inert.pdf}
}

@article{Pershina2008a,
  title = {Atomic {{Properties}} of {{Element}} 113 and {{Its Adsorption}} on {{Inert Surfaces}} from Ab {{Initio Dirac}}-{{Coulomb Calculations}}},
  author = {Pershina, V. and Borschevsky, A. and Eliav, E. and Kaldor, U.},
  year = {2008},
  month = dec,
  journal = {J. Phys. Chem. A},
  volume = {112},
  number = {51},
  pages = {13712--13716},
  publisher = {American Chemical Society},
  issn = {1089-5639},
  doi = {10.1021/jp8061306},
  urldate = {2023-03-20},
  abstract = {Fully relativistic ab initio Dirac-Coulomb Fock-space coupled cluster calculations were performed on Tl and element 113. The calculated polarizabilty of element 113, 29.85 au, is the smallest in group 13, except for B. The estimated atomic and van der Waals radii of element 113 are also the smallest among these elements. Using the calculated atomic properties and an adsorption model, adsorption enthalpies of elements Al through 113 on inert surfaces, such as Teflon and polyethylene, are predicted. The trends in the atomic properties and {$\Delta$}Hads in group 13 were found to reverse from In to element 113, reflecting the strong relativistic contraction and stabilization of the outer np1/2 orbital, which are largest for element 113. The small values of {$\Delta$}Hads for element 113 on Teflon (14 kJ/mol) and polyethylene (16 kJ/mol) guarantee its transport from the target chamber to the chemistry set up, and the 6 kJ/mol difference relative to Tl values makes possible the separation and identification of the superheavy element on the inert surfaces.},
  file = {/Users/yingxing/Zotero/storage/8N8JRPRJ/Atomic properties of element 113 and its adsorption on inert surfaces from ab initio Dirac-Coulomb calculations_2008.pdf}
}

@article{Pershina2008b,
  title = {Prediction of the Adsorption Behavior of Elements 112 and 114 on Inert Surfaces from Ab Initio {{Dirac-Coulomb}} Atomic Calculations},
  author = {Pershina, V. and Borschevsky, A. and Eliav, E. and Kaldor, U.},
  year = {2008},
  month = jan,
  journal = {The Journal of Chemical Physics},
  volume = {128},
  number = {2},
  pages = {024707},
  issn = {0021-9606},
  doi = {10.1063/1.2814242},
  urldate = {2024-06-12},
  abstract = {The interaction of elements 112 and 114 with inert surfaces has been studied on the basis of fully relativistic ab initio Dirac-Coulomb CCSD(T) calculations of their atomic properties. The calculated polarizabilities of elements 112 and 114 are significantly lower than corresponding Hg and Pb values due to the relativistic contraction of the valence ns and np1/2 orbitals, respectively, in the heavier elements. Due to the same reason, the estimated van der Waals radius of element 114 is smaller than that of Pb. The enthalpies of adsorption of Hg, Pb, and elements 112 and 114 on inert surfaces such as quartz, ice, and Teflon were predicted on the basis of these atomic calculations using a physisorption model. At the present level of accuracy, -{$\Delta$}Hads of element 112 on these surfaces is slightly (about 2kJ/mol) larger than -{$\Delta$}Hads(Hg). The calculated -{$\Delta$}Hads of element 114 on quartz is about 7kJ/mol and on Teflon is about 3kJ/mol smaller than the respective values of -{$\Delta$}Hads(Pb). The trend of increasing -{$\Delta$}Hads in group 14 from C to Sn is thus reversed, giving decreasing values from Sn to Pb to element 114 due to the relativistic stabilization and contraction of the np1/2 atomic orbitals. This is similar to trends shown by other atomic properties of these elements. The small difference in {$\Delta$}Hads of Pb and element 114 on inert surfaces obtained within a picture of physisorption contrasts with the large difference (more than 100kJ/mol) in the chemical reactivity between these elements.},
  file = {/Users/yingxing/Zotero/storage/8R7BRZBF/Pershina et al_2008_Prediction of the adsorption behavior of elements 112 and 114 on inert surfaces.pdf}
}

@incollection{Pershina2014,
  title = {Theoretical {{Chemistry}} of the {{Heaviest Elements}}},
  booktitle = {The {{Chemistry}} of {{Superheavy Elements}}},
  author = {Pershina, Valeria},
  editor = {Sch{\"a}del, Matthias and Shaughnessy, Dawn},
  year = {2014},
  pages = {135--239},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  doi = {10.1007/978-3-642-37466-1_3},
  urldate = {2024-06-11},
  abstract = {Theoretical chemical research in the area of the heaviest elements is extremely important. It deals with predictions of properties of exotic species and their behavior in sophisticated and expensive experiments with single atoms and permits the interpretation of experimental results. Spectacular developments in the relativistic quantum theory and computational algorithms have allowed for accurate calculations of electronic structures of the heaviest elements and their compounds. Due to the experimental restrictions in this area, the theoretical studies are often the only source of useful chemical information. The works on relativistic calculations and predictions of chemical properties of elements with Z~{$\geq~$}104 are overviewed. Preference is given to those related to the experimental research. The increasingly important role of relativistic effects in this part of the Periodic Table is demonstrated.},
  isbn = {978-3-642-37466-1},
  langid = {english}
}

@article{Porsev2002,
  title = {High-Accuracy Relativistic Many-Body Calculations of van Der {{Waals}} Coefficients \$\{\vphantom\}{{C}}\vphantom\{\}\_\{6\}\$ for Alkaline-Earth-Metal Atoms},
  author = {Porsev, Sergey G. and Derevianko, Andrei},
  year = {2002},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {65},
  number = {2},
  pages = {020701},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.65.020701},
  urldate = {2024-06-12},
  abstract = {Relativistic many-body calculations of van der Waals coefficients {$C$}6 for dimers correlating to two ground-state alkaline-earth-metal atoms at large internuclear separations are reported. The following values and uncertainties were determined: for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.},
  file = {/Users/yingxing/Zotero/storage/9GXXD9QN/Porsev_Derevianko_2002_High-accuracy relativistic many-body calculations of van der Waals coefficients.pdf}
}

@article{Porsev2006,
  title = {High-Accuracy Calculations of Dipole, Quadrupole, and Octupole Electric Dynamic Polarizabilities and van Der {{Waals}} Coefficients {{C6}}, {{C8}}, and {{C10}} for Alkaline-Earth Dimers},
  author = {Porsev, S. G. and Derevianko, A.},
  year = {2006},
  month = feb,
  journal = {J. Exp. Theor. Phys.},
  volume = {102},
  number = {2},
  pages = {195--205},
  issn = {1090-6509},
  doi = {10.1134/S1063776106020014},
  urldate = {2023-03-20},
  abstract = {The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C6, C8, and C10 of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.},
  langid = {english},
  keywords = {,31.15.Ar,31.15.Md,32.10.Dk,34.30.+h},
  file = {/Users/yingxing/Zotero/storage/T79QNNG3/Porsev and Derevianko - 2006 - High-accuracy calculations of dipole, quadrupole, .pdf}
}

@article{Porsev2006a,
  title = {Multipolar Theory of Blackbody Radiation Shift of Atomic Energy Levels and Its Implications for Optical Lattice Clocks},
  author = {Porsev, Sergey G. and Derevianko, Andrei},
  year = {2006},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {74},
  number = {2},
  pages = {020502},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.74.020502},
  urldate = {2024-06-12},
  abstract = {Blackbody radiation (BBR) shifts of the clock transition in the divalent atoms Mg, Ca, Sr, and Yb are evaluated. The dominant electric-dipole contributions are computed using accurate relativistic many-body techniques of atomic structure. At room temperatures, the resulting uncertainties in the BBR shifts are large and substantially affect the projected fractional accuracy of the optical-lattice-based clocks. A peculiarity of these clocks is that the characteristic BBR wavelength is comparable to the fine-structure intervals. To evaluate relevant and contributions, a theory of multipolar BBR shifts is developed. The resulting corrections, although presently masked by the uncertainties in the contribution, are required at the accuracy goal.},
  file = {/Users/yingxing/Zotero/storage/H9IB3U52/Porsev_Derevianko_2006_Multipolar theory of blackbody radiation shift of atomic energy levels and its.pdf}
}

@article{Porsev2008,
  title = {Determination of {{Sr}} Properties for a High-Accuracy Optical Clock},
  author = {Porsev, S. G. and Ludlow, Andrew D. and Boyd, Martin M. and Ye, Jun},
  year = {2008},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {78},
  number = {3},
  pages = {032508},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.78.032508},
  urldate = {2024-06-12},
  abstract = {We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to 1{\texttimes}10-17 and below. In particular, we focused on ac polarizabilities of the 5⁢{$s$}2 1{$S$}0 and 5⁢{$s$}⁢5⁢{$p$} 3{$Po$}0 clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the 1{$S$}0-3{$Po$}0 clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the clock state is at the level of 90\%. We show that if the contribution of these states is experimentally known with 0.1\% accuracy, the same accuracy can be achieved for the total polarizability of the state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below . The calculations are confirmed by a number of experimental measurements on various Sr properties.},
  file = {/Users/yingxing/Zotero/storage/H2H7T6XT/Porsev et al_2008_Determination of Sr properties for a high-accuracy optical clock.pdf}
}

@article{Pou-Amérigo1995,
  title = {Density Matrix Averaged Atomic Natural Orbital ({{ANO}}) Basis Sets for Correlated Molecular Wave Functions},
  author = {{Pou-Am{\'e}rigo}, Rosendo and Merch{\'a}n, Manuela and {Nebot-Gil}, Ignacio and Widmark, Per-Olof and Roos, Bj{\"o}rn O.},
  year = {1995},
  month = sep,
  journal = {Theoret. Chim. Acta},
  volume = {92},
  number = {3},
  pages = {149--181},
  issn = {1432-2234},
  doi = {10.1007/BF01114922},
  urldate = {2024-06-12},
  abstract = {Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsdn,dn-1s, anddn-2s2 for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.},
  langid = {english},
  keywords = {Atomic natural orbitals,Basis sets,General contraction},
  file = {/Users/yingxing/Zotero/storage/4LTIIKS6/Pou-Amérigo et al_1995_Density matrix averaged atomic natural orbital (ANO) basis sets for correlated.pdf}
}

@article{Puchalski2011,
  title = {Lithium Electric Dipole Polarizability},
  author = {Puchalski, M. and K{\k e}dziera, D. and Pachucki, K.},
  year = {2011},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {84},
  number = {5},
  pages = {052518},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.84.052518},
  urldate = {2023-03-20},
  abstract = {The electric dipole polarizability of the lithium atom in the ground state is calculated including relativistic and quantum electrodynamics corrections. The obtained result {$\alpha$}E=164.0740(5) a.u. is in good agreement with the less accurate experimental value of 164.19(1.08) a.u. The small uncertainty of about 3 parts per 106 comes from the approximate treatment of quantum electrodynamics corrections. Our theoretical result can be considered as a benchmark for more general atomic structure methods and may serve as a reference value for the relative measurement of polarizabilities of the other alkali-metal atoms.},
  file = {/Users/yingxing/Zotero/storage/4M37P8VW/Puchalski et al_2011_Lithium electric dipole polarizability.pdf}
}

@article{Puchalski2016,
  title = {Theoretical Determination of the Polarizability Dispersion and the Refractive Index of Helium},
  author = {Puchalski, Mariusz and Piszczatowski, Konrad and Komasa, Jacek and Jeziorski, Bogumi{\l} and Szalewicz, Krzysztof},
  year = {2016},
  month = mar,
  journal = {Phys. Rev. A},
  volume = {93},
  number = {3},
  pages = {032515},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.93.032515},
  urldate = {2024-06-05},
  abstract = {The refractive index {$n$} of gaseous helium can be measured by optical interferometry so accurately that it can be used to establish a pressure standard which is expected to be superior to the current standard based on the height of a mercury column. The new standard requires knowledge of the dynamic polarizability of helium atom with accuracy significantly higher than obtainable in the best experiments, but possible to achieve computationally. Calculations of this quantity are presented at relativistic and quantum electrodynamics levels of theory including relativistic nuclear recoil effects. The uncertainties of the results are carefully estimated. Our recommended value of the dynamic polarizability at the He-Ne laser wavelength of 6329.908 {\AA}, equal 1.39181197(14) a.u., has uncertainty at least two orders of magnitude smaller than that of recent measurements and is sufficiently accurate to establish a new pressure standard. Purely ab initio values of the refraction coefficient {$n$} are computed using our polarizability, literature values of magnetic susceptibility, and dielectric virial coefficients. It is shown that {$n-$}1 can be predicted by theory as a function of density and temperature with uncertainty of 1 ppm for pressures up to 3 MPa.},
  file = {/Users/yingxing/Zotero/storage/6XTLQFJV/Puchalski et al_2016_Theoretical determination of the polarizability dispersion and the refractive.pdf}
}

@article{Puchalski2020,
  title = {{{QED}} Calculation of the Dipole Polarizability of Helium Atom},
  author = {Puchalski, Mariusz and Szalewicz, Krzysztof and Lesiuk, Micha{\l} and Jeziorski, Bogumi{\l}},
  year = {2020},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {101},
  number = {2},
  pages = {022505},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.101.022505},
  urldate = {2024-06-10},
  abstract = {The QED contribution to the dipole polarizability of the 4He atom was computed, including the effect of finite nuclear mass. The computationally most challenging contribution of the second electric-field derivative of the Bethe logarithm was obtained using two different methods: the integral representation method of Schwartz and the sum-over-states approach of Goldman and Drake. The results of both calculations are consistent, although the former method turned out to be much more accurate. The obtained value of the electric-field derivative of the Bethe logarithm, equal to 0.048 557 2(14) in atomic units, confirms the small magnitude of this quantity found in the only previous calculation [G. {\L}ach, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 92, 233001 (2004)], but differs from it by about 5\%. The origin of this difference is explained. The total QED correction of the order of in the fine-structure constant amounts to , including the contribution from the electric-field derivative of the Bethe logarithm and the correction for the finite nuclear mass, with all values in atomic units. The resulting theoretical value of the molar polarizability of helium-4 is with the error estimate dominated by the uncertainty of the QED corrections of order and higher. Our value is in agreement with but an order of magnitude more accurate than the result of the most recent experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].},
  file = {/Users/yingxing/Zotero/storage/PLENSMT9/Puchalski et al_2020_QED calculation of the dipole polarizability of helium atom.pdf}
}

@article{Qiao2012,
  title = {Dynamic Polarizabilities of {{Zn}} and {{Cd}} and Dispersion Coefficients Involving Group 12 Atoms},
  author = {Qiao, L. W. and Li, P. and Tang, K. T.},
  year = {2012},
  month = aug,
  journal = {The Journal of Chemical Physics},
  volume = {137},
  number = {8},
  pages = {084309},
  issn = {0021-9606},
  doi = {10.1063/1.4746155},
  urldate = {2024-06-12},
  abstract = {The refractive index data for Zn and Cd measured by Goebel and Hohm are analyzed with a three-term Maxwell-Sellmeier expression which incorporates the experimental oscillator strengths of the first two dipole transitions. These expressions are extended to imaginary frequencies for the determination of the upper and lower bounds of the dynamic polarizabilities {$\alpha$}(i{$\omega$}), from which the van der Waals coefficients of two-body interactions and the non-additive three-body interactions are generated. The determined C6 values for Zn2 (359{\textpm}8\,a.u.) and Cd2 (686{\textpm}10\,a.u.) are much larger than those originally estimated by Goebel and Hohm. This is because their one-term approximation of {$\alpha$}({$\omega$}), which fits the measurements very well in the normal frequency range, greatly underestimates {$\alpha$}(i{$\omega$}) when the frequency is extended into the imaginary domain. On the other hand, the present results of heteronuclear interactions verify once again that Tang's one-term approximation of {$\alpha$}(i{$\omega$}) leads to accurate combining rules. The two- and three-body interaction coefficients between group 12 atoms (Zn, Cd, Hg) and the alkali, alkaline-earth, rare-gas atoms, and some molecules are estimated with these combining rules.},
  file = {/Users/yingxing/Zotero/storage/I6IADUW5/Qiao et al_2012_Dynamic polarizabilities of Zn and Cd and dispersion coefficients involving.pdf}
}

@article{Reiher2006,
  title = {Douglas--{{Kroll}}--{{Hess Theory}}: A Relativistic Electrons-Only Theory for Chemistry},
  shorttitle = {Douglas--{{Kroll}}--{{Hess Theory}}},
  author = {Reiher, Markus},
  year = {2006},
  month = aug,
  journal = {Theor Chem Acc},
  volume = {116},
  number = {1},
  pages = {241--252},
  issn = {1432-2234},
  doi = {10.1007/s00214-005-0003-2},
  urldate = {2024-06-12},
  abstract = {A unitary transformation allows to separate (block-diagonalize) the Dirac Hamiltonian into two parts one part: solely describes electrons, while the other gives rise to negative-energy states, which are the so-called positronic states. The block-diagonal form of the Hamiltonian no longer accounts for the coupling of both kinds of states. The positive-energy (`electrons-only') part can serve as a `fully' relativistic electrons-only theory, which can be understood as a rigorous basis for chemistry. Recent developments of the Douglas--Kroll--Hess (DKH) method allowed to derive a sequence of expressions, which approximate this electrons-only Hamiltonian up to arbitrary-order. While all previous work focused on the numerical stability and accuracy of these arbitrary-order DKH Hamiltonians, conceptual issues and paradoxa of the method were mostly left aside. In this work, the conceptual side of DKH theory is revisited in order to identify essential aspects of the theory to be distinguished from purely computational consideration.},
  langid = {english},
  keywords = {Chem Phys,External Potential Versus,Positronic State,Radial Electron Density,Unitary Transformation},
  file = {/Users/yingxing/Zotero/storage/8WNUUTBU/Reiher_2006_Douglas–Kroll–Hess Theory.pdf}
}

@article{Reiher2011,
  title = {Relativistic {{Douglas}}--{{Kroll}}--{{Hess}} Theory},
  author = {Reiher, Markus},
  year = {2012},
  journal = {WIREs Comput. Mol. Sci.},
  volume = {2},
  number = {1},
  pages = {139--149},
  issn = {1759-0884},
  doi = {10.1002/wcms.67},
  urldate = {2024-06-12},
  abstract = {Relativistic effects on molecular properties and energies are ubiquitous in chemistry. Their consideration in quantum chemical calculations requires Dirac's theory of the electron, whose application is not without obstacles. Douglas--Kroll--Hess theory accomplishes a decoupling of positive- and negative-energy eigenstates of the Dirac one-electron Hamiltonian by an expansion in the external potential. At low orders, this expansion already converges and provides efficient relativistic Hamiltonians to be used in routine quantum chemical calculations. The basic principles of the approach are reviewed, and most recent developments are discussed. {\copyright} 2011 John Wiley \& Sons, Ltd. This article is categorized under: Electronic Structure Theory {$>$} Ab Initio Electronic Structure Methods},
  copyright = {Copyright {\copyright} 2011 John Wiley \& Sons, Ltd.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/ETUZUU3M/Reiher_2012_Relativistic Douglas–Kroll–Hess theory.pdf}
}

@article{Reinsch1976,
  title = {Finite Perturbation Calculation for the Static Dipole Polarizabilities of the Atoms {{Na}} through {{Ca}}},
  author = {Reinsch, Ernst-Albrecht and Meyer, Wilfried},
  year = {1976},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {14},
  number = {3},
  pages = {915--918},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.14.915},
  urldate = {2024-06-12},
  abstract = {Static dipole polarizabilities are calculated from pseudonatural orbital configuration expansion wave functions for the ground states of the atoms Na through Ca with an accuracy estimated to about 2\%. The resulting values are (in the order Na-Ca) 165.02, 71.32, 56.27, 36.32, 24.52, 19.60, 14.71, 11.096, 287.6, and 153.9 a.u. The influence of the electron correlation on the polarizabilities is shown to reflect its influence on the radial distribution of the electrons.},
  file = {/Users/yingxing/Zotero/storage/W9WLVXMS/Reinsch_Meyer_1976_Finite perturbation calculation for the static dipole polarizabilities of the.pdf}
}

@article{Rice1992,
  title = {Connected Triple Excitations in Coupled-Cluster Calculations of Hyperpolarizabilities: Neon},
  shorttitle = {Connected Triple Excitations in Coupled-Cluster Calculations of Hyperpolarizabilities},
  author = {Rice, Julia E. and Scuseria, Gustavo E. and Lee, Timothy J. and Taylor, Peter R. and Alml{\"o}f, Jan},
  year = {1992},
  month = mar,
  journal = {Chem. Phys. Lett.},
  volume = {191},
  number = {1},
  pages = {23--28},
  issn = {0009-2614},
  doi = {10.1016/0009-2614(92)85362-E},
  urldate = {2023-03-20},
  abstract = {We have calculated the second hyperpolarizability {$\gamma$} of neon using the CCSD(T) method. The accuracy of the CCSD(T) approach has been established by explicit comparison with the single, double and triple excitation coupled-cluster (CCSDT) method using extended basis sets that are known to be adequate for the description of {$\gamma$}. Our best estimate for {$\gamma$}0 of 110{\textpm}3 au is in good agreement with other recent theoretical values and with Shelton's recent experimental estimate of 108{\textpm}2 au. Comparison of the MP2 and CCSD(T) hyperpolarizability values indicates that MP2 gives a very good description of the electron correlation contribution to {$\gamma$}0. We have combined MP2 frequency-dependent corrections with the CCSD(T) {$\gamma$}0 value to yield {$\gamma$}(-2{$\omega$}; {$\omega$}, {$\omega$}, 0) and {$\gamma$}K(-{$\omega$}; {$\omega$}, 0, 0).},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/I8HJFR4P/Connected triple excitations in coupled-cluster calculations of hyperpolarizabilities neon_1992.pdf;/Users/yingxing/Zotero/storage/QY33J2PB/Rice et al. - 1992 - Connected triple excitations in coupled-cluster ca.pdf}
}

@incollection{Roos1996,
  title = {Multiconfigurational {{Perturbation Theory}}: {{Applications}} in {{Electronic Spectroscopy}}},
  shorttitle = {Multiconfigurational {{Perturbation Theory}}},
  booktitle = {Advances in {{Chemical Physics}}},
  author = {Roos, Bj{\"o}rn O and Andersson, Kerstin and F{\"u}lscher, Markus P and Malmqvist, Per-{\^a}ke and {Serrano-Andr{\'e}s}, Luis and Pierloot, Kristin and Merch{\'a}n, Manuela},
  year = {1996},
  pages = {219--331},
  publisher = {John Wiley \& Sons, Ltd},
  doi = {10.1002/9780470141526.ch5},
  urldate = {2024-06-12},
  abstract = {This chapter contains sections titled: Introduction Multiconfigurational Perturbation Theory Applications in Spectroscopy Summary},
  copyright = {Copyright {\copyright} 1996 by John Wiley \& Sons, Inc.},
  isbn = {978-0-470-14152-6},
  langid = {english},
  keywords = {carbonyl ligands,Cr2 Molecule,multistate CASPT2,spectroscopy,zeroth-order hamiltonian}
}

@article{Roos2004,
  title = {Main {{Group Atoms}} and {{Dimers Studied}} with a {{New Relativistic ANO Basis Set}}},
  author = {Roos, Bj{\"o}rn O. and Lindh, Roland and Malmqvist, Per-{\AA}ke and Veryazov, Valera and Widmark, Per-Olof},
  year = {2004},
  month = apr,
  journal = {J. Phys. Chem. A},
  volume = {108},
  number = {15},
  pages = {2851--2858},
  publisher = {American Chemical Society},
  issn = {1089-5639},
  doi = {10.1021/jp031064+},
  urldate = {2023-03-20},
  abstract = {New basis sets of the atomic natural orbital (ANO) type have been developed for the main group and rare gas atoms. The ANO's have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the dimer at its equilibrium geometry. Scalar relativistic effects are included through the use of a Douglas-Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and the ground-state potentials for the dimers. These calculations include spin-orbit coupling using the RASSCF State Interaction (RASSI-SO) method. The spin-orbit splitting for the lowest atomic term is reproduced with an accuracy of better than 0.05 eV, except for row 5, where it is 0.15 eV. Ionization energies and electron affinities have an accuracy better than 0.2 eV, and atomic polarizabilities for the spherical atoms are computed with errors smaller than 2.5\%. Computed bond energies for the dimers are accurate to better than 0.15 eV in most cases (the dimers for row 5 excluded).},
  file = {/Users/yingxing/Zotero/storage/YYBFG4EJ/Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set_2004(2).pdf}
}

@article{Roos2004a,
  title = {Relativistic Atomic Natural Orbital Type Basis Sets for the Alkaline and Alkaline-Earth Atoms Applied to the Ground-State Potentials for the Corresponding Dimers},
  author = {Roos, Bj{\"o}rn O. and Veryazov, Valera and Widmark, Per-Olof},
  year = {2004},
  month = mar,
  journal = {Theor. Chem. Acc.},
  volume = {111},
  number = {2},
  pages = {345--351},
  issn = {1432-2234},
  doi = {10.1007/s00214-003-0537-0},
  urldate = {2023-03-21},
  abstract = {New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li--Fr and Be--Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas--Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be2).},
  langid = {english},
  keywords = {Atomic natural orbitals,Complete-active-space self-consistent field/comple,Complete-active-space self-consistent field/complete-active-space second-order perturbation theory,Douglas-kroll,Douglas-Kroll,Relativistic basis sets},
  file = {/Users/yingxing/Zotero/storage/VJYEE8WN/Roos et al. - 2004 - Relativistic atomic natural orbital type basis set.pdf}
}

@article{Roos2005,
  title = {New {{Relativistic ANO Basis Sets}} for {{Transition Metal Atoms}}},
  author = {Roos, Bj{\"o}rn O. and Lindh, Roland and Malmqvist, Per-{\AA}ke {\AA}ke and Veryazov, Valera and Widmark, Per-Olof Olof},
  year = {2005},
  month = jul,
  journal = {J. Phys. Chem. A},
  volume = {109},
  number = {29},
  pages = {6575--6579},
  issn = {1089-5639},
  doi = {10.1021/jp0581126},
  abstract = {New basis sets of the atomic natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically symmetric atoms. These calculations include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the experimental values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals. {\copyright} 2005 American Chemical Society.}
}

@article{Roos2005a,
  title = {New Relativistic {{ANO}} Basis Sets for Actinide Atoms},
  author = {Roos, Bj{\"o}rn O. and Lindh, Roland and Malmqvist, Per-{\AA}ke and Veryazov, Valera and Widmark, Per-Olof},
  year = {2005},
  month = jun,
  journal = {Chem. Phys. Lett.},
  volume = {409},
  number = {4},
  pages = {295--299},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2005.05.011},
  urldate = {2023-03-21},
  abstract = {New basis sets of the atomic natural orbital (ANO) type have been developed for the actinide atoms Ac--Cm. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in a electric field. Scalar relativistic effects are included through the use of a Douglas--Kroll--Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The lowest multiplet levels have been computed. These calculations include spin--orbit coupling using a variation-perturbation approach. The atomic polarizability of the spherically symmetric americium atom has been computed to be 116 au3.},
  langid = {english}
}

@article{Runeberg1998,
  title = {{Relativistic pseudopotential calculations on Xe2, RnXe, and Rn2: The van der Waals properties of radon}},
  shorttitle = {{Relativistic pseudopotential calculations on Xe2, RnXe, and Rn2}},
  author = {Runeberg, Nino and Pyykk{\"o}, Pekka},
  year = {1998},
  journal = {Int. J. Quantum Chem.},
  volume = {66},
  number = {2},
  pages = {131--140},
  issn = {1097-461X},
  doi = {10.1002/(SICI)1097-461X(1998)66:2<131::AID-QUA4>3.0.CO;2-W},
  urldate = {2024-06-12},
  abstract = {Counterpoise-corrected supermolecular calculations on the title molecules at MP2, CCSD, and CCSD(T) levels are used to extract a van der Waals radius of 224 pm for Rn, 6 pm more than for Xe. The spin--orbit effects are found to significantly stabilize Rn2 and RnXe. Van der Waals C6 and C8 coefficients, which are in good agreement with both experiment and TDMP2 calculations, were obtained from calculations at large distances. {\copyright} 1998 John Wiley \& Sons, Inc. Int J Quant Chem 66: 131--140, 1998},
  copyright = {Copyright {\copyright} 1998 John Wiley \& Sons, Inc.},
  langid = {ngerman},
  keywords = {pseudopotentials,radon,relativistic effects,spin-orbit,van der Waals radii},
  file = {/Users/yingxing/Zotero/storage/DDGGPINZ/Runeberg_Pyykkö_1998_Relativistic pseudopotential calculations on Xe2, RnXe, and Rn2.pdf}
}

@article{Sadlej1991,
  title = {Relativistic and Electron-Correlation Contributions to the Dipole Polarizability of the Alkaline-Earth-Metal Atoms {{Ca}}, {{Sr}}, and {{Ba}}},
  author = {Sadlej, Andrzej J. and Urban, Miroslav and Gropen, Odd},
  year = {1991},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {44},
  number = {9},
  pages = {5547--5557},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.44.5547},
  urldate = {2024-06-12},
  abstract = {A series of high-level correlated (many-body-perturbation-theory and coupled-cluster) calculations on the dipole polarizability of Ca, Sr, and Ba has been carried out. The relativistic effects have been incorporated in calculations at both the Hartree-Fock and correlated levels of approximation. Calculated values of the dipole polarizability of Ca, Sr, and Ba are 152, 190, and 273 a.u., respectively, and in agreement with experimental data from electric-deflection measurements. The relativistic effect on the dipole polarizability is very small (-2 a.u.) for Ca, amounts to about -11 a.u. for Sr, and becomes comparable with the electron-correlation contribution for Ba (-37 a.u.). An optimized Gaussian basis set has been generated for Ba, the details of which are included in the paper.},
  file = {/Users/yingxing/Zotero/storage/2FSCJBXU/Sadlej et al_1991_Relativistic and electron-correlation contributions to the dipole.pdf}
}

@article{Sadlej1991a,
  title = {Medium-Size Polarized Basis Sets for High-Level-Correlated Calculations of Molecular Electric Properties: {{III}}. {{Alkali}} ({{Li}}, {{Na}}, {{K}}, {{Rb}}) and Alkaline-Earth ({{Be}}, {{Mg}}, {{Ca}}, {{Sr}}) Atoms},
  shorttitle = {Medium-Size Polarized Basis Sets for High-Level-Correlated Calculations of Molecular Electric Properties},
  author = {Sadlej, Andrzej J. and Urban, Miroslav},
  year = {1991},
  month = sep,
  journal = {Journal of Molecular Structure: THEOCHEM},
  volume = {234},
  pages = {147--171},
  issn = {0166-1280},
  doi = {10.1016/0166-1280(91)89010-X},
  urldate = {2024-06-10},
  abstract = {The basis set polarization method is applied for the generation of medium size polarized basis sets for Li, Na, K, Rb, Be, Mg, Ca, and Sr. The derived basis sets are shown to give satisfactory results in calculations of atomic dipole polarizabilities and in calculations of dipole moments and dipole polarizabilities of diatomic hydrides and hydride ions at both the SCF and highly correlated levels of approximation. The MBPT and CC results for hydrides and hydride ions of the group Ia and IIa metals calculated with polarized basis sets derived in this study indicate the importance of the electron correlation contribution to the electric properties of those systems. The dominant part of this contribution involves excitations from core orbitais of the metal atom and is recognized as the core polarization effect. The valence approximation is found to be completely unsatisfactory for hydrides involving heavier metals of the present series. Details of the basis set data supplement this paper. Some possible applications of those basis sets are surveyed.}
}

@article{Sadlej1992,
  title = {Medium-Size Polarized Basis Sets for High-Level-Correlated Calculations of Molecular Electric Properties},
  author = {Sadlej, Andrzej J.},
  year = {1992},
  month = jul,
  journal = {Theoret. Chim. Acta},
  volume = {81},
  number = {4},
  pages = {339--354},
  issn = {1432-2234},
  doi = {10.1007/BF01118573},
  urldate = {2024-06-12},
  abstract = {The basis set polarization method is used to generate the first-order polarized basis sets for Sn, Sb, Te, and I. The standard (spd) and extended (spdf) versions of those basis sets are derived for the purpose of calculations of dipole moments and dipole polarizabilities for molecules involving the fourth-row atoms. The verification of the performance of the generated polarized basis sets is achieved mainly by a cross-examination of different atomic and molecular results calculated in this paper. The role of the core-polarization and relativistic effects is investigated. It is shown that the relativistic contribution to dipole moments of the fourth-row hydrides is commensurate with the contribution due to electron correlation and must be explicitly considered in accurate calculations. The detailed basis set data for Sn through I are presented in the Appendix.},
  langid = {english},
  keywords = {Core-polarization effects,Dipole moments and polarizabilities of the fourth-row atom hydrides (SnH4 SbH3 H2Te HI),Dipole polarizabilities of Sn Sb Te and I,Molecular electric properties,Polarized basis sets,Relativistic effects on electric properties},
  file = {/Users/yingxing/Zotero/storage/2DTLFK8B/Sadlej_1992_Medium-size polarized basis sets for high-level-correlated calculations of.pdf}
}

@article{Safronova2004,
  title = {Inconsistencies between Lifetime and Polarizability Measurements in \${\textbackslash}text\{\vphantom\}{{Cs}}\vphantom\{\}\$},
  author = {Safronova, M. S. and Clark, Charles W.},
  year = {2004},
  month = apr,
  journal = {Phys. Rev. A},
  volume = {69},
  number = {4},
  pages = {040501},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.69.040501},
  urldate = {2024-06-12},
  abstract = {Electric dipole matrix elements for , , , , transitions in cesium are calculated using a relativistic all-order method. The resulting matrix elements are used to evaluate lifetimes and polarizabilities. The data are compared with experimental lifetime and polarizability measurements made by different groups. Domination of the scalar polarizabilities by dipole matrix elements facilitates an exacting consistency check of lifetime and polarizability data. Values of matrix elements obtained from experimental lifetime data are found to be inconsistent with those inferred from polarizabilities derived from experimental Stark shift data. Our calculated polarizabilities agree well with experimental determinations.},
  file = {/Users/yingxing/Zotero/storage/AANLZUEQ/Safronova_Clark_2004_Inconsistencies between lifetime and polarizability measurements in $-text Cs $.pdf}
}

@article{Safronova2006,
  title = {Relativistic Many-Body Calculations of the {{Stark-induced}} Amplitude of the \$6\{\vphantom\}{{P}}\vphantom\{\}\_\{1/2\}{\textbackslash}text\{{\textbackslash}ensuremath\{-\}\}7\{\vphantom\}{{P}}\vphantom\{\}\_\{1/2\}\$ Transition in Thallium},
  author = {Safronova, M. S. and Johnson, W. R. and Safronova, U. I. and Cowan, T. E.},
  year = {2006},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {74},
  number = {2},
  pages = {022504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.74.022504},
  urldate = {2024-06-11},
  abstract = {Stark-induced amplitudes for the 6⁢{$P$}1/2-7⁢{$P$}1/2 transition in T⁢lI are calculated using the relativistic singles-doubles (SD) approximation in which single and double excitations of Dirac-Hartree-Fock levels are summed to all orders in perturbation theory. Our SD values {$AS$}=368⁢{$a$}30 and {$\midBS\mid$}=298⁢{$a$}30 are in good agreement with the measurements and by D. DeMille, D. Budker, and E. D. Commins [Phys. Rev. A 50, 4657 (1994)]. Calculations of the Stark shifts in the and transitions are also carried out. The Stark shifts predicted by our calculations agree with the most accurate measured values within the experimental uncertainties for both transitions.},
  file = {/Users/yingxing/Zotero/storage/IP4W36TY/Safronova et al_2006_Relativistic many-body calculations of the Stark-induced amplitude of the.pdf}
}

@article{Safronova2007,
  title = {Excitation Energies, Polarizabilities, Multipole Transition Rates, and Lifetimes of Ions along the Francium Isoelectronic Sequence},
  author = {Safronova, U. I. and Johnson, W. R. and Safronova, M. S.},
  year = {2007},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {76},
  number = {4},
  pages = {042504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.76.042504},
  urldate = {2024-06-05},
  abstract = {Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the 7⁢{$s$}, 7⁢{$p$}, 6⁢{$d$}, and 5⁢{$f$} states of Fr-like ions with nuclear charges {$Z$}=87--100 are calculated through third order; reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for 7⁢{$s-$}7⁢{$p$}, 7⁢{$p-$}6⁢{$d$}, and 6⁢{$d-$}5⁢{$f$} electric-dipole transitions; and 7⁢{$s-$}6⁢{$d$}, 7⁢{$s-$}5⁢{$f$}, and 5⁢{$f$}5/2-5⁢{$f$}7/2 multipole matrix elements are evaluated to obtain the lifetimes of low-lying excited states. Moreover, for the ions {$Z$}=87--92 calculations are also carried out using the relativistic all-order single-double method, in which single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. With the aid of the single-double wave functions, we obtain accurate values of energies, transition rates, oscillator strengths, and the lifetimes of these six ions. Ground state scalar polarizabilities in FrI, RaII, AcIII, and ThIV are calculated using relativistic third-order and all-order methods. Ground state scalar polarizabilities for other Fr-like ions are calculated using a relativistic second-order method. These calculations provide a theoretical benchmark for comparison with experiment and theory.},
  file = {/Users/yingxing/Zotero/storage/QXEVJK9R/Safronova et al_2007_Excitation energies, polarizabilities, multipole transition rates, and.pdf}
}

@article{Safronova2012,
  title = {Ytterbium in {{Quantum Gases}} and {{Atomic Clocks}}: Van Der {{Waals Interactions}} and {{Blackbody Shifts}}},
  shorttitle = {Ytterbium in {{Quantum Gases}} and {{Atomic Clocks}}},
  author = {Safronova, M. S. and Porsev, S. G. and Clark, Charles W.},
  year = {2012},
  month = dec,
  journal = {Phys. Rev. Lett.},
  volume = {109},
  number = {23},
  pages = {230802},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.109.230802},
  urldate = {2024-06-12},
  abstract = {We evaluated the {$C$}6 coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2\% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, {$C$}6=1929⁢(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb clock transition with 3.5\% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the level.},
  file = {/Users/yingxing/Zotero/storage/WGKD6BEI/Safronova et al_2012_Ytterbium in Quantum Gases and Atomic Clocks.pdf}
}

@article{Safronova2013,
  title = {Polarizabilities, {{Stark}} Shifts, and Lifetimes of the {{In}} Atom},
  author = {Safronova, M. S. and Safronova, U. I. and Porsev, S. G.},
  year = {2013},
  month = mar,
  journal = {Phys. Rev. A},
  volume = {87},
  number = {3},
  pages = {032513},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.87.032513},
  urldate = {2024-06-12},
  abstract = {We evaluate the polarizabilities of the 5⁢{$p$}1/2, 6⁢{$s$}, 6⁢{$p$}1/2, and 6⁢{$p$}3/2 states of In using two high-precision relativistic methods: the linearized coupled-cluster approach, where single, double, and partial triple excitations of the Dirac-Fock wave function are included to all orders of perturbation theory, and an approach that combines the configuration interaction and the coupled-cluster method. An extensive comparison of the accuracy of these methods is carried out. The uncertainties of all recommended values are evaluated. Our result for the - Stark shift is in excellent agreement with a recent measurement [Ranjit et al., Phys. Rev. A 87, 032506 (2013)]. Combining our calculation with this precision measurement allows us to infer the values of the and lifetimes in In with 0.8 accuracy. Our predictions for the scalar and tensor polarizabilities may be combined with the future measurement of the - Stark shift to accurately determine the - matrix elements.},
  file = {/Users/yingxing/Zotero/storage/TYDF7CC7/Safronova et al_2013_Polarizabilities, Stark shifts, and lifetimes of the In atom.pdf}
}

@article{Safronova2013a,
  title = {Thallium 7\$p\$ Lifetimes Derived from Experimental Data and Ab Initio Calculations of Scalar Polarizabilities},
  author = {Safronova, M. S. and Majumder, P. K.},
  year = {2013},
  month = apr,
  journal = {Phys. Rev. A},
  volume = {87},
  number = {4},
  pages = {042502},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.87.042502},
  urldate = {2024-06-12},
  abstract = {Two different theoretical methods have been used to complete a calculation of polarizability in the thallium 6⁢{$p$}1/2, 7⁢{$s$}, and 7⁢{$p$}1/2 states. The predictions of the two methods agree to within 1\% for the 6⁢{$p$}1/2 and 7⁢{$s$} states and 2\% for the 7⁢{$p$}1/2 state. We find that the theoretical expression for the 6⁢{$p$}1/2-7⁢{$s$} transition polarizability difference is dominated (greater than 90 contribution) by mixing of the state with the and states. By comparing the theoretical expression to an existing measurement of [Doret et al., Phys. Rev. A 66, 052504 (2002)], highly accurate values for the thallium excited-state lifetimes have been extracted. The scalar polarizability of the state is also computed, anticipating an experimental determination of this quantity, which will then enable a high-precision determination of the - transition rates and provide a benchmark test of the two theoretical approaches in the near future.},
  file = {/Users/yingxing/Zotero/storage/XNDDMZYA/Safronova_Majumder_2013_Thallium 7$p$ lifetimes derived from experimental data and ab initio.pdf}
}

@article{Safronova2013b,
  title = {Blackbody-Radiation Shift in the {{Sr}} Optical Atomic Clock},
  author = {Safronova, M. S. and Porsev, S. G. and Safronova, U. I. and Kozlov, M. G. and Clark, Charles W.},
  year = {2013},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {87},
  number = {1},
  pages = {012509},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.87.012509},
  urldate = {2024-06-10},
  abstract = {We evaluated the static and dynamic polarizabilities of the 5⁢{$s$}21⁢{$S$}0 and 5⁢{$s$}⁢5⁢{$p$}3⁢{$Po$}0 states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental dc Stark shift measurement [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1 uncertainty; 0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.},
  file = {/Users/yingxing/Zotero/storage/G8VPGVCN/Safronova et al_2013_Blackbody-radiation shift in the Sr optical atomic clock.pdf}
}

@article{Safronova2015a,
  title = {Atomic Polarizabilities},
  author = {Safronova, M. S. and Mitroy, J. and Clark, Charles W. and Kozlov, M. G.},
  year = {2015},
  month = jan,
  journal = {AIP Conference Proceedings},
  volume = {1642},
  number = {1},
  pages = {81--89},
  issn = {0094-243X},
  doi = {10.1063/1.4906633},
  urldate = {2024-06-12},
  abstract = {The atomic dipole polarizability governs the first-order response of an atom to an applied electric field. Atomic polarization phenomena impinge upon a number of areas and processes in physics and have been the subject of considerable interest and heightened importance in recent years. In this paper, we will summarize some of the recent applications of atomic polarizability studies. A summary of results for polarizabilities of noble gases, monovalent, and divalent atoms is given. The development of the CI+all-order method that combines configuration interaction and linearized coupled-cluster approaches is discussed.}
}

@article{Sahoo2008,
  title = {Relativistic Coupled-Cluster Studies of Dipole Polarizabilities in Closed-Shell Atoms},
  author = {Sahoo, B. K. and Das, B. P.},
  year = {2008},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {77},
  number = {6},
  pages = {062516},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.77.062516},
  urldate = {2023-03-21},
  abstract = {We investigate the role of electron correlation effects in the electric-dipole polarizabilities of the ground states of the alkaline earth metals, helium, and ytterbium by employing the relativistic coupled-cluster (RCC) theory. These effects are incorporated via the residual Coulomb interaction to all orders in the RCC singles and doubles approximations. The perturbed wave functions used in the calculations of the polarizabilities are obtained by directly solving the first-order perturbed RCC equations, thereby avoiding the sum-over-states approach. Our results are compared with other calculations and available experimental data.},
  file = {/Users/yingxing/Zotero/storage/2J4E3X5K/Sahoo_Das_2008_Relativistic coupled-cluster studies of dipole polarizabilities in closed-shell.pdf}
}

@article{Sahoo2017,
  title = {Significance of Distinct Electron-Correlation Effects in Determining the (\${{P}},{{T}}\$)-Odd Electric Dipole Moment of \${\textasciicircum}\{171\}{\textbackslash}mathrm\{\vphantom\}{{Yb}}\vphantom\{\}\$},
  author = {Sahoo, B. K. and Singh, Yashpal},
  year = {2017},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {95},
  number = {6},
  pages = {062514},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.95.062514},
  urldate = {2024-06-11},
  abstract = {The parity and time-reversal violating electric dipole moment (EDM) of 171Yb is calculated accounting for the electron-correlation effects over the Dirac-Hartree-Fock method in the relativistic Rayleigh-Schr{\"o}dinger many-body perturbation theory, with the second- [MBPT(2) method] and third-order [MBPT(3) method] approximations, and two variants of all-order relativistic many-body approaches, in the random phase approximation (RPA) and coupled-cluster (CC) method with singles and doubles (CCSD method) framework. We consider electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions as the predominant sources that induce EDM in a diamagnetic atomic system. Our results from the CCSD method to EDM () of due to the T-PT and NSM interactions are found to be and , respectively, where is the T-PT coupling constant and is the NSM. These values differ significantly from the earlier calculations. The reason for the same has been attributed to large correlation effects arising through non-RPA type of interactions among the electrons in this atom that are observed by analyzing the differences in the RPA and CCSD results. This has been further scrutinized from the MBPT(2) and MBPT(3) results and their roles have been demonstrated explicitly.},
  file = {/Users/yingxing/Zotero/storage/T4WMSZN2/Sahoo_Singh_2017_Significance of distinct electron-correlation effects in determining the.pdf}
}

@article{Sahoo2018,
  title = {The Role of Relativistic Many-Body Theory in Probing New Physics beyond the Standard Model via the Electric Dipole Moments of Diamagnetic Atoms},
  author = {Sahoo, B. K. and Das, B. P.},
  year = {2018},
  month = jun,
  journal = {J. Phys. Conf. Ser.},
  volume = {1041},
  number = {1},
  pages = {012014},
  publisher = {IOP Publishing},
  issn = {1742-6596},
  doi = {10.1088/1742-6596/1041/1/012014},
  urldate = {2023-03-21},
  abstract = {The observation of electric dipole moments (EDMs) in atomic systems due to parity and time-reversal violating (P,T-odd) interactions can probe new physics beyond the standard model and also provide insights into the matter-antimatter asymmetry in the Universe. The EDMs of open-shell atomic systems are sensitive to the electron EDM and the P,T-odd scalar-pseudoscalar (S-PS) semi-leptonic interaction, but the dominant contributions to the EDMs of diamagnetic atoms come from the hadronic and tensor-pseudotensor (T-PT) semi-leptonic interactions. Several diamagnetic atoms like 129Xe, 171Yb, 199Hg, 223Rn, and 225Ra are candidates for the experimental search for the possible existence of EDMs, and among these 199Hg has yielded the lowest limit till date. The T or CP violating coupling constants of the aforementioned interactions can be extracted by combining the EDM measurements from with atomic and nuclear calculations. In this work, we report the calculations of the EDMs of the above atoms by including both the electromagnetic and P,T-odd violating interactions simultaneously. These calculations are performed by employing relativistic many-body methods based on the random phase approximation (RPA) and the singles and doubles coupled-cluster (CCSD) method starting with the Dirac-Hartree-Fock (DHF) wave function in both cases. The differences in the results from both the methods shed light on the importance of the non-core-polarization electron correlation effects that are accounted for by the CCSD method. We also determine THE electric dipole polarizabilities of these atoms, which have computational similarities with EDMs and compare them with the available experimental and other theoretical results to assess the accuracy of our calculations.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/38G6AYK2/The role of relativistic many-body theory in probing new physics beyond the standard model via the electric dipole moments of diamagneti.pdf}
}

@article{Sahoo2018b,
  title = {Dipole Polarizability Calculation of the {{Cd}} Atom: {{Inconsistency}} with Experiment},
  shorttitle = {Dipole Polarizability Calculation of the {{Cd}} Atom},
  author = {Sahoo, B. K. and Yu, Yan-mei},
  year = {2018},
  month = jul,
  journal = {Phys. Rev. A},
  volume = {98},
  number = {1},
  pages = {012513},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.98.012513},
  urldate = {2024-06-12},
  abstract = {Three earlier relativistic coupled-cluster (RCC) calculations of dipole polarizability ({$Ad$}) of the Cd atom are not in good agreement with the available experimental value of 49.65⁢(1.65)⁢{$e$}⁢{$a$}30. Among these two are finite-field approaches in which the relativistic effects have been included approximately, while the other calculation uses a four-component perturbed RCC method. However, another work adopting an approach similar to the latter perturbed RCC method gives a result very close to that of experiment. The major difference between these two perturbed RCC approaches lies in their implementation. To resolve this ambiguity, we have developed and employed the relativistic normal coupled-cluster (RNCC) theory to evaluate the value of Cd. The distinct features of the RNCC method are that the expression for the expectation value in this approach terminates naturally and that it satisfies the Hellmann-Feynman theorem. In addition, we determine this quantity in the finite-field approach in the framework of a four-component relativistic coupled-cluster theory. Considering the results from both approaches, we arrive at a reliable value of . We also demonstrate that the contribution from the triples excitations in this atom is significant.},
  file = {/Users/yingxing/Zotero/storage/XBRIS9TU/Sahoo_Yu_2018_Dipole polarizability calculation of the Cd atom.pdf}
}

@article{Sahoo2018d,
  title = {Relativistic {{Normal Coupled-Cluster Theory}} for {{Accurate Determination}} of {{Electric Dipole Moments}} of {{Atoms}}: {{First Application}} to the \${\textasciicircum}\{199\}{\textbackslash}mathrm\{\vphantom\}{{Hg}}\vphantom\{\}\$ {{Atom}}},
  shorttitle = {Relativistic {{Normal Coupled-Cluster Theory}} for {{Accurate Determination}} of {{Electric Dipole Moments}} of {{Atoms}}},
  author = {Sahoo, B. K. and Das, B. P.},
  year = {2018},
  month = may,
  journal = {Phys. Rev. Lett.},
  volume = {120},
  number = {20},
  pages = {203001},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.120.203001},
  urldate = {2024-06-12},
  abstract = {Recent relativistic coupled-cluster (RCC) calculations of electric dipole moments (EDMs) of diamagnetic atoms due to parity and time-reversal violating ({$P$},{$T$}-odd) interactions, which are essential ingredients for probing new physics beyond the standard model of particle interactions, differ substantially from the previous theoretical results. It is therefore necessary to perform an independent test of the validity of these results. In view of this, the normal coupled-cluster method has been extended to the relativistic regime [relativistic normal coupled-cluster (RNCC) method] to calculate the EDMs of atoms by simultaneously incorporating the electrostatic and -odd interactions in order to overcome the shortcomings of the ordinary RCC method. This new relativistic method has been applied to , which currently has a lower EDM limit than that of any other system. The results of our RNCC and self-consistent RCC calculations of the EDM of this atom are found to be close. The discrepancies between these two results on the one hand and those of previous calculations on the other are elucidated. Furthermore, the electric dipole polarizability of this atom, which has computational similarities with the EDM, is evaluated and it is in very good agreement with its measured value.},
  file = {/Users/yingxing/Zotero/storage/PKBW7FH9/Sahoo_Das_2018_Relativistic Normal Coupled-Cluster Theory for Accurate Determination of.pdf}
}

@article{Sahoo2023,
  title = {Revisiting Theoretical Analysis of the Electric Dipole Moment of \${\textasciicircum}\{129\}{\textbackslash}mathrm\{\vphantom\}{{Xe}}\vphantom\{\}\$},
  author = {Sahoo, B. K. and Yamanaka, Nodoka and Yanase, Kota},
  year = {2023},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {108},
  number = {4},
  pages = {042811},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.108.042811},
  urldate = {2024-06-10},
  abstract = {The linear response approach to the relativistic coupled-cluster (RCC) theory has been extended to estimate contributions from the parity and time-reversal violating pseudoscalar-scalar (Ps-S) and scalar-pseudoscalar (S-Ps) electron-nucleus interactions along with electric dipole moments (EDMs) of electrons ({$de$}) interacting with internal electric and magnetic fields. The random phase approximation (RPA) is also employed to produce results to compare with the earlier reported values and demonstrate the importance of the non-RPA contributions arising through the RCC method. It shows that contributions from the S-Ps interactions and {$de$} arising through the hyperfine-induced effects are very sensitive to the contributions from the high-lying virtual orbitals. Combining atomic results with the nuclear shell-model calculations, we impose constraints on the pion-nucleon coupling coefficients, and the EDMs of a proton and a neutron. These results are further used to constrain EDMs and chromo-EDMs of the up- and down-quarks by analyzing particle physics models.},
  file = {/Users/yingxing/Zotero/storage/YJEGLUSD/Sahoo et al_2023_Revisiting theoretical analysis of the electric dipole moment of.pdf}
}

@article{Sakurai2018,
  title = {Electric Dipole Polarizability of \${\textasciicircum}\{129\}{\textbackslash}mathrm\{\vphantom\}{{Xe}}\vphantom\{\}\$ Using the Relativistic Coupled-Cluster and the Normal Coupled-Cluster Methods},
  author = {Sakurai, Akitada and Sahoo, B. K. and Das, B. P.},
  year = {2018},
  month = jun,
  journal = {Phys. Rev. A},
  volume = {97},
  number = {6},
  pages = {062510},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.97.062510},
  urldate = {2024-06-06},
  abstract = {is an important candidate for the searches of electric dipole moments due to time-reversal and parity violations in diamagnetic atoms. In view of the similarities between the electric dipole moment and the polarizability from the point of view of many-body theory, we have performed rigorous calculations of the ground-state polarizability of using a self-consistent relativistic coupled-cluster method and the relativistic normal coupled-cluster method. The discrepancy between the results from these two methods is 2\%, but each of them differs from the accurate measurement of the polarizability of the ground state of by 1\%. Our results clearly suggest that the two theoretical methods we have employed in this work can be applied in the future to capture electron correlation effects in the electric dipole moment of to a high degree of accuracy.},
  file = {/Users/yingxing/Zotero/storage/MYCHEGXF/Sakurai et al_2018_Electric dipole polarizability of $^ 129 -mathrm Xe $ using the relativistic.pdf}
}

@article{Sarkisov2006,
  title = {Interferometric Measurements of Dynamic Polarizabilities for Metal Atoms Using Electrically Exploding Wires in Vacuum},
  author = {Sarkisov, G. S. and Beigman, I. L. and Shevelko, V. P. and Struve, K. W.},
  year = {2006},
  month = apr,
  journal = {Phys. Rev. A},
  volume = {73},
  number = {4},
  pages = {042501},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.73.042501},
  urldate = {2024-06-12},
  abstract = {Measurements within 10\% accuracy of the dynamic dipole polarizabilities {$A$}⁡({$\lambda$}) for five nonrefractory metal atoms (Mg, Ag, Al, Cu, and Au) at laser wavelengths of and are presented using electrical explosion of thin wires in vacuum and a novel laser probing integrated-phase technique. The technique is based on single-wavelength interferometry and does not require axial symmetry of the tested object. Theoretical prediction of for wavelengths , 532, and , as well as the static dipole polarizabilities , are also presented. An agreement within 20\% was obtained between calculated data, recommended static polarizabilities , and the measured dynamic polarizabilities and .},
  file = {/Users/yingxing/Zotero/storage/P46HBFFD/Sarkisov et al_2006_Interferometric measurements of dynamic polarizabilities for metal atoms using.pdf}
}

@article{Sarkisov2022,
  title = {Laser Measurements of Static and Dynamic Dipole Polarizability for 11 Metal Atoms Using Fast Exploding Wires in Vacuum and Integrated-Phase Technique},
  author = {Sarkisov, G. S.},
  year = {2022},
  month = jul,
  journal = {Physics of Plasmas},
  volume = {29},
  number = {7},
  pages = {073502},
  issn = {1070-664X},
  doi = {10.1063/5.0084981},
  urldate = {2024-06-10},
  abstract = {The rapid electrical explosion of thin metal wires in a vacuum can completely vaporize the wire and form a fast-expanding gas cylinder of metal atoms. Thin metal wires 12.7\,{$\mu$}m in diameter made of W, Mo, Pt, Pd, Ni, Cu, Au, and Al completely evaporated during the first {$\sim$}10\,ns under the action of a fast-rising current of {$\sim$}1\,kA/ns. Laser interferometry and the integrated phase technique were used to reconstruct the dynamic atomic polarizability for fully vaporized thin metal wires at 532 and 1064\,nm wavelength, calculate the static atomic polarizability, the first dipole-allowed electronic transition energy, and transition wavelengths, and compare our reconstructions with available tabulated values.},
  file = {/Users/yingxing/Zotero/storage/8GDUFDTQ/Sarkisov - 2022 - Laser measurements of static and dynamic dipole po.pdf}
}

@article{Schäfer2007,
  title = {Polarizabilities of {{Ba}} and \$\{{\textbackslash}text\{\vphantom{\}\}}{{Ba}}\vphantom\{\}\vphantom\{\}\_\{2\}\$: {{Comparison}} of Molecular Beam Experiments with Relativistic Quantum Chemistry},
  shorttitle = {Polarizabilities of {{Ba}} and \$\{{\textbackslash}text\{\vphantom{\}\}}{{Ba}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  author = {Sch{\"a}fer, Sascha and Mehring, Max and Sch{\"a}fer, Rolf and Schwerdtfeger, Peter},
  year = {2007},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {76},
  number = {5},
  pages = {052515},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.76.052515},
  urldate = {2024-06-12},
  abstract = {The dielectric response to an inhomogeneous electric field has been investigated for Ba and Ba2 within a molecular beam experiment. The ratio of the polarizabilities per atom of Ba2 and Ba is determined to be . The experimental result is compared to a high level ab initio quantum chemical coupled cluster calculation with an energy-consistent scalar relativistic small-core pseudopotential for Ba. For the barium atom a polarizability of is obtained and the isotropic value of the polarizability calculated for is , which is in good agreement with the experimental results, demonstrating that a quantitative understanding of the interaction between two closed-shell heavy element metal atoms has been achieved.},
  file = {/Users/yingxing/Zotero/storage/MLPE2LJE/Schäfer et al_2007_Polarizabilities of Ba and $ -text Ba _ 2 $.pdf}
}

@article{Schmidt2007,
  title = {Polarizability of {{Helium}} and {{Gas Metrology}}},
  author = {Schmidt, J. W. and Gavioso, R. M. and May, E. F. and Moldover, M. R.},
  year = {2007},
  month = jun,
  journal = {Phys. Rev. Lett.},
  volume = {98},
  number = {25},
  pages = {254504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.98.254504},
  urldate = {2023-03-21},
  abstract = {Using a quasispherical, microwave cavity resonator, we measured the refractive index of helium to deduce its molar polarizability in the limit of zero density. We obtained , where the standard uncertainty (9.1 ppm) is a factor of 3.3 smaller than that of the best previous measurement. If the theoretical value of is accepted, these data determine a value for the Boltzmann constant that is only larger than the accepted value. Our techniques will enable a helium-based pressure standard and measurements of thermodynamic temperatures.},
  file = {/Users/yingxing/Zotero/storage/273DHSYY/Schmidt et al_2007_Polarizability of Helium and Gas Metrology.pdf}
}

@book{Schooley1992,
  title = {Temperature: {{Its}} Measurement and Control in Science and Industry},
  author = {Schooley, James F.},
  year = {1992},
  volume = {1269},
  publisher = {American Institute of Physics},
  address = {New York}
}

@article{Schwartz1974,
  title = {Measurement of the Static Electric Dipole Polarizabilities of Barium and Strontium},
  author = {Schwartz, Henry L. and Miller, Thomas M. and Bederson, Benjamin},
  year = {1974},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {10},
  number = {6},
  pages = {1924--1926},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.10.1924},
  urldate = {2024-06-05},
  abstract = {The static electric dipole polarizabilities of barium and strontium atoms have been measured using an electric deflection technique. The results are normalized to the polarizability of lithium by comparing deflections of the alkaline-earth beams to deflections of a lithium beam passing through an inhomogeneous electrostatic field. The measured polarizabilities are (39.7 {\textpm} 3.2) {\texttimes} 10-24 cm3 for barium and (27.6 {\textpm} 2.2) {\texttimes} 10-24 cm3 for strontium.},
  file = {/Users/yingxing/Zotero/storage/62BYS55T/Schwartz et al_1974_Measurement of the static electric dipole polarizabilities of barium and.pdf}
}

@article{Schwerdtfeger1994,
  title = {Relativistic Effects in Gold Chemistry. {{V}}. {{Group}} 11 Dipole Polarizabilities and Weak Bonding in Monocarbonyl Compounds},
  author = {Schwerdtfeger, Peter and Bowmaker, Graham A.},
  year = {1994},
  month = mar,
  journal = {The Journal of Chemical Physics},
  volume = {100},
  number = {6},
  pages = {4487--4497},
  issn = {0021-9606},
  doi = {10.1063/1.466280},
  urldate = {2024-06-12},
  abstract = {Hartree--Fock and Mo/ller--Plesset second order (MP2) calculations have been carried out in order to study the stability and structure of open-shell group 11 monocarbonyl compounds MCO (M=Cu,Ag,Au). AgCO is calculated to be a very weakly bound molecule with a dissociation energy of less than 1 kJ/mol, and this casts some doubt on the previously reported identification of this species in matrix isolation studies. AuCO is stable only if relativistic effects are included, which explains the recently observed anomaly in the strength of the metal--CO interaction within the group 11 series. The metal--carbonyl interactions in CuCO and AuCO are relatively weak, with dissociation energies of about 30 kJ/mol and may be best described as a combination of dispersion, donor--acceptor (charge-transfer) and repulsive interactions. The MP2 Cu--CO dissociation energy of 32 kJ/mol is in good agreement with the estimated experimental value of 23{\textpm}6 kJ/mol. At the highest level of theory, AuCO possesses a bent geometry with a bond angle of 151{$^\circ$} at the MP2 level, but this arrangement lies only 2 kJ/mol below the linear structure. The basis set superposition error and the role of metal f functions are discussed. Dipole polarizabilities are calculated for the group 11 elements at various levels of electron correlation in order to discuss dispersion interactions. These are found to be very sensitive to relativistic and electron correlation effects. For the neutral gold atom, relativistic effects in the dipole polarizability become comparable to electron correlation contributions. The multielectron adjusted group 11 pseudopotentials give reliable results for the atomic and molecular properties discussed.},
  file = {/Users/yingxing/Zotero/storage/8CQKYYJC/Schwerdtfeger_Bowmaker_1994_Relativistic effects in gold chemistry.pdf}
}

@article{Schwerdtfeger2000,
  title = {The Accuracy of the Pseudopotential Approximation. {{III}}. {{A}} Comparison between Pseudopotential and All-Electron Methods for {{Au}} and {{AuH}}},
  author = {Schwerdtfeger, Peter and Brown, J. Reuben and Laerdahl, Jon K. and Stoll, Hermann},
  year = {2000},
  month = nov,
  journal = {The Journal of Chemical Physics},
  volume = {113},
  number = {17},
  pages = {7110--7118},
  issn = {0021-9606},
  doi = {10.1063/1.1313556},
  urldate = {2024-06-12},
  abstract = {The quality of the pseudopotential approximation has been tested thoroughly by calculating spectroscopic properties of the gold atom and ground state AuH for eight different effective core potentials using Hartree--Fock, second-order Mo/ller--Plesset and coupled cluster methods. The pseudopotential valence basis set \{{$\varphi$}\}v for Au was chosen to be identical for all pseudopotentials, a subset of the all-electron basis set \{{$\varphi$}\}v{$\subset$}\{{$\varphi$}\}AE, and the condition was applied that all sets are of near basis set limit quality. The pseudopotential results are compared with data obtained from nonrelativistic, scalar relativistic Douglas--Kroll and fully relativistic four-component all-electron calculations. The variation between the results obtained for all valence electron small-core pseudopotentials and all electron Douglas--Kroll calculations is found to be small (for the Stuttgart pseudopotential {$\Delta$}re=0.001 {\AA}, {$\Delta$}De=0.03 eV, {$\Delta\omega$}e=9{\enspace}cm-1,\hphantom{,}{$\Delta\mu$}e=0.04 D). Sizable differences to all electron results are only found for the 11 valence electron large-core pseudopotentials. The effects of the basis set superposition error on spectroscopic constants were investigated. Calculated coupled cluster electron affinities and ionization potentials for gold and spectroscopic properties for AuH were found to be in excellent agreement with available experimental data. The variation between the different small-core pseudopotentials for one particular spectroscopic property is shown to be less than the error due to the incompleteness of electron correlation procedure or the basis set and approximately of the same size as the basis set superposition error. The results show that scalar relativistic effects for valence properties are perfectly described by the pseudopotential approximation.},
  file = {/Users/yingxing/Zotero/storage/CZPPDK8W/Schwerdtfeger et al_2000_The accuracy of the pseudopotential approximation.pdf}
}

@article{Schwerdtfeger2019,
  title = {2018 {{Table}} of Static Dipole Polarizabilities of the Neutral Elements in the Periodic Table},
  author = {Schwerdtfeger, Peter and Nagle, Jeffrey K.},
  year = {2019},
  month = jun,
  journal = {Mol. Phys.},
  volume = {117},
  number = {9-12},
  pages = {1200--1225},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268976.2018.1535143},
  urldate = {2023-03-20},
  abstract = {A 2018 update of the most accurate calculated and experimental static dipole polarizabilities of the neutral atoms in the Periodic Table from nuclear charge Z = 1 to 120 is given. Periodic trends are analyzed and discussed.},
  keywords = {,Atomic polarizabilies,Correction,periodic table},
  file = {/Users/yingxing/Zotero/storage/CQ9NBDZV/Schwerdtfeger and Nagle - 2019 - 2018 Table of static dipole polarizabilities of th.pdf}
}

@article{Seth1996,
  title = {Large Relativistic Effects in Molecular Properties of the Hydride of Superheavy Element 111},
  author = {Seth, Michael and Schwerdtfeger, Peter and Dolg, Michael and Faegri, Knut and Hess, Bernd A. and Kaldor, Uzi},
  year = {1996},
  month = mar,
  journal = {Chemical Physics Letters},
  volume = {250},
  number = {5},
  pages = {461--465},
  issn = {0009-2614},
  doi = {10.1016/0009-2614(96)00039-5},
  urldate = {2024-06-12},
  abstract = {Relativistic and electron correlation contributions in the hydride of the recently discovered superheavy element 111 were studied using ab-initio methods within different relativistic approaches. Relativistic effects decrease the (111)H bond distance by 0.42 {\AA}. As a result of this large bond contraction, the bond distance of (111)H (1.51 {\AA}) is comparable to that of the hydride of its lighter congener AuH (1.52 {\AA}), but below that of AgH (1.60 {\AA}). The dissociation energy is relativistically increased by approximately 1.2 eV and the stretching force constant is more than quadrupled from 1.1 mdyn/{\AA} at the nonrelativistic level to 5.0 mdyn/{\AA} at the relativistic level.},
  file = {/Users/yingxing/Zotero/storage/N96NP7AW/Seth et al_1996_Large relativistic effects in molecular properties of the hydride of superheavy.pdf}
}

@article{Seth1997,
  title = {The Chemistry of the Superheavy Elements. {{I}}. {{Pseudopotentials}} for 111 and 112 and Relativistic Coupled Cluster Calculations for (112){{H}}+, (112){{F2}}, and (112){{F4}}},
  author = {Seth, Michael and Schwerdtfeger, Peter and Dolg, Michael},
  year = {1997},
  month = mar,
  journal = {The Journal of Chemical Physics},
  volume = {106},
  number = {9},
  pages = {3623--3632},
  issn = {0021-9606},
  doi = {10.1063/1.473437},
  urldate = {2024-06-12},
  abstract = {One- and two-component (spin--orbit coupled) relativistic and nonrelativistic energy adjusted pseudopotentials and basis sets for the elements 111 and 112 are presented. Calculations on the positively charged monohydride of the recently discovered superheavy element 112 are reported. Electron correlation is treated at the multireference configuration interaction and coupled cluster level and fine structure effects are derived from a single-reference configuration interaction treatment. Relativistic effects decrease the (112)H+ bond distance by 0.41 {\AA}. This bond contraction is similar to the one calculated recently for (111)H [Chem. Phys. Lett. 250, 461 (1996)]. As a result the bond distance of (112)H+ (1.52 {\AA}) is predicted to be smaller compared to those of the hydrides of the lighter congeners HgH+ (1.59 {\AA}), CdH+ (1.60 {\AA}) and similar to that of ZnH+ (1.52 {\AA}). We predict that (112)H+ is the most stable hydride in the Group 12 series due to relativistic effects. As in the case of (111)H the relativistic increase of the stretching force constant is quite large, from 1.5 to 4.3 mdyn/{\AA} at the coupled cluster level. The trend in the dipole polarizabilities of the Group 12 elements is discussed. Relativistic and electron correlation effects are nonadditive and due to the relativistic ns contraction (n=7 for 112), correlation effects out of the (n-1)d core are more important at the relativistic than the nonrelativistic level. We also show evidence that element 112 behaves like a typical transition element, and as a consequence the high oxida-tion state +4 in element 112 might be accessible.},
  file = {/Users/yingxing/Zotero/storage/39ZK7FP6/Seth et al_1997_The chemistry of the superheavy elements.pdf}
}

@article{Shukla2020,
  title = {Two-Dipole and Three-Dipole Dispersion Coefficients for Interaction of Alkaline-Earth-Metal Atoms with Alkaline-Earth-Metal Atoms and Alkaline-Earth-Metal Ions},
  author = {Shukla, Neelam and Arora, Bindiya and Sharma, Lalita and Srivastava, Rajesh},
  year = {2020},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {102},
  number = {2},
  pages = {022817},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.102.022817},
  urldate = {2024-06-10},
  abstract = {Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole and three-dipole dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The and coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e., , and , as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.},
  file = {/Users/yingxing/Zotero/storage/NMAA2WTX/Shukla et al. - 2020 - Two-dipole and three-dipole dispersion coefficient.pdf}
}

@article{Singer1997,
  title = {The Use of {{Gaussian}} (Exponential Quadratic) Wave Functions in Molecular Problems - {{I}}. {{General}} Formulae for the Evaluation of Integrals},
  author = {Singer, K. and Wilkes, Maurice Vincent},
  year = {1997},
  month = jan,
  journal = {Proc. R. Soc. Lond. Ser. Math. Phys. Sci.},
  volume = {258},
  number = {1294},
  pages = {412--420},
  publisher = {Royal Society},
  doi = {10.1098/rspa.1960.0196},
  urldate = {2024-06-07},
  abstract = {It is shown that for wave functions of the form{$\psi$}=⁢{$\sumk$}⁡{$Ck$}⁢exp⁡(-{$Qk$}),{$\psi$}=⁢{$\sum$}k⁡Ck⁢exp⁡(-Qk),, where Qk is any positive definite quadratic form in the Cartesian co-ordinates of n particles and Ck a constant, all integrals required for the calculation of the electronic energy of molecules by the variation method can be readily evaluated. The potential energy integrals are reduced to quadratures and the other integrals are expressed in closed form. In the general case the quadratic forms Qk determine many-electron functions formed from correlated electron orbitals of ellipsoidal symmetry and with variable centres. The results are easily extended to wave functions of the form{$\psi$}=⁢{$\sumk$}⁡{$Pk$}⁢exp⁡(-{$Qk$}),{$\psi$}=⁢{$\sum$}k⁡Pk⁢exp⁡(-Qk),, where Pk is a polynomial.},
  file = {/Users/yingxing/Zotero/storage/H4BMDVFC/Singer_Wilkes_1997_The use of Gaussian (exponential quadratic) wave functions in molecular.pdf}
}

@article{Singh2013,
  title = {Correlation Trends in the Ground-State Static Electric Dipole Polarizabilities of Closed-Shell Atoms and Ions},
  author = {Singh, Yashpal and Sahoo, B. K. and Das, B. P.},
  year = {2013},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {88},
  number = {6},
  pages = {062504},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.88.062504},
  urldate = {2023-03-20},
  abstract = {We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A 77, 062516 (2008)] to evaluate the ground-state static electric dipole polarizabilities ({$\alpha$}s) of several atomic systems. In this work, we have incorporated a class of higher-order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracies of {$\alpha$}s. We also calculate the ground state {$\alpha$}s of the inert gas atoms and several isoelectronic singly and doubly charged ions in order to make a comparative study of the trends of the correlation effects. Furthermore, we have developed a method to construct intermediate diagrams that are required for the computations of the unperturbed single and doubl coupled-cluster amplitudes. Our RCC results are compared with those of many-body perturbation theory at different orders to demonstrate the importance of higher-order correlation effects for the accurate determination of ({$\alpha$}s) of the systems that we have considered.},
  file = {/Users/yingxing/Zotero/storage/U7J2WK5E/Singh et al. - 2013 - Correlation trends in the ground-state static elec.pdf}
}

@article{Singh2014,
  title = {Correlation Trends in the Polarizabilities of Atoms and Ions in the Boron, Carbon, and Zinc Homologous Sequences of Elements},
  author = {Singh, Yashpal and Sahoo, B. K.},
  year = {2014},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {90},
  number = {2},
  pages = {022511},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.90.022511},
  urldate = {2023-03-20},
  abstract = {We investigate the role of electron-correlation effects in calculations of the electric-dipole polarizabilities {$\alpha$} of elements belonging to three different groups (12--14) of the periodic table. To understand the propagation of the electron-correlation effects at different levels of approximations, we employ the relativistic many-body methods developed, based on first principles, at mean-field Dirac--Fock (DF), third-order many-body perturbation theory [MBPT(3)], random-phase approximation (RPA), and singly and doubly approximated coupled-cluster methods at the linearized (LCCSD) and nonlinearized (CCSD) levels. We observe a variance in the trends of the contributions of the correlation effects in a particular group of elements through the many-body method used; however, they resemble a similar tendency among the iso-electronic systems. Our CCSD results are within sub-1\% agreement with the experimental values which are further ameliorated by including the contributions from the important triple excitations (CCSDpT method).}
}

@article{Singh2015,
  title = {Rigorous Limits on the Hadronic and Semileptonic \${\textbackslash}mathit\{\vphantom\}{{CP}}\vphantom\{\}\$-Violating Coupling Constants from the Electric Dipole Moment of \${\textasciicircum}\{199\}{\textbackslash}mathrm\{\vphantom\}{{Hg}}\vphantom\{\}\$},
  author = {Singh, Yashpal and Sahoo, B. K.},
  year = {2015},
  month = mar,
  journal = {Phys. Rev. A},
  volume = {91},
  number = {3},
  pages = {030501},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.91.030501},
  urldate = {2024-06-11},
  abstract = {Electric dipole polarizability and the electric dipole moment (EDM) due to the electron-nucleus tensor-pseudotensor (T-PT) and the nuclear Schiff moment (NSM) interactions are accurately determined for . Relativistic many-body methods at different levels of approximations are employed to gain insights into the passage of the electron correlation effects in the evaluation of these properties. Significant changes in the results compared to previous calculations are observed. We estimate our final EDM results to be within 2\% accuracy, which, in combination with the measured value of EDM, yield limits on the T-PT coupling constant as and on the NSM as . Using these values, together with the latest nuclear structure and quantum chromodynamics calculations, we get limits for the strong CP-violating parameter as and for the combined up- and down-quark chromo-EDMs as .},
  file = {/Users/yingxing/Zotero/storage/YATYNBJ6/Singh_Sahoo_2015_Rigorous limits on the hadronic and semileptonic $-mathit CP $-violating.pdf}
}

@article{Singh2016,
  title = {Comparing Magic Wavelengths for the Transitions of {{Cs}} Using Circularly and Linearly Polarized Light},
  author = {Singh, Sukhjit and Kaur, Kiranpreet and Sahoo, B. K. and Arora, Bindiya},
  year = {2016},
  month = jun,
  journal = {J. Phys. B At. Mol. Opt. Phys.},
  volume = {49},
  number = {14},
  pages = {145005},
  publisher = {IOP Publishing},
  issn = {0953-4075},
  doi = {10.1088/0953-4075/49/14/145005},
  urldate = {2023-03-20},
  abstract = {We demonstrate magic wavelengths, at which an external electric field produces null differential Stark shifts, for the transitions in a Cs atom due to circularly polarized light. In addition, we also obtain magic wavelengths using linearly polarized light in order to verify the previously reported values, and make a comparative study with the values obtained for circularly polarized light. A number of these wavelengths are found to be in the optical region and could be of immense interest to experimentalists for carrying out high precision measurements. To obtain these wavelengths, we have calculated dynamic dipole polarizabilities of the ground, and states of Cs. We use the available precise values of the electric dipole (E1) matrix elements of the transitions that give the dominant contributions from the lifetime measurements of the excited states. Other significantly contributing E1 matrix elements are obtained by employing a relativistic coupled-cluster singles and doubles method. The accuracies of the dynamic polarizabilities are substantiated by comparing the static polarizability values with the corresponding experimental results.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/KB4Q48IY/Singh et al. - 2016 - Comparing magic wavelengths for the transitions of.pdf}
}

@article{Singh2016a,
  title = {Determination of Magic Wavelengths for the \$7s {\textasciicircum}\{2\}{{S}}\_\{1/2\}{\textbackslash}ensuremath\{-\}7p {\textasciicircum}\{2\}{{P}}\_\{3/2,1/2\}\$ Transitions in {{Fr}}},
  author = {Singh, Sukhjit and Sahoo, B. K. and Arora, Bindiya},
  year = {2016},
  month = aug,
  journal = {Phys. Rev. A},
  volume = {94},
  number = {2},
  pages = {023418},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.94.023418},
  urldate = {2024-06-11},
  abstract = {Magic wavelengths ({$\lambda$}magic) for the 7⁢{$S$}1/2-7⁢{$P$}1/2,3/2 transitions (D lines) in Fr were reported by Dammalapati et al. [U. Dammalapati, K. Harada, and Y. Sakemi, Phys. Rev. A 93, 043407 (2016)]. These {$\lambda$}magic were determined by plotting dynamic polarizabilities ({$A$}) of the involved states with the above transitions against a desired range of wavelengths. Electric dipole (E1) matrix elements listed in [J. E. Sansonetti, J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine . However, contributions from core correlation effects and from the E1 matrix elements of the , and transitions to of the states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small values for the states. Owing to this, we find disagreement in reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of will be very useful for guiding experiments to carry out their measurements.},
  file = {/Users/yingxing/Zotero/storage/R8HTI3DY/Singh et al_2016_Determination of magic wavelengths for the $7s ^ 2 S_ 1-2 -ensuremath - 7p.pdf}
}

@article{Smialkowski2021,
  title = {Highly Polar Molecules Consisting of a Copper or Silver Atom Interacting with an Alkali-Metal or Alkaline-Earth-Metal Atom},
  author = {{\'S}mia{\l}kowski, Micha{\l} and Tomza, Micha{\l}},
  year = {2021},
  month = feb,
  journal = {Phys. Rev. A},
  volume = {103},
  number = {2},
  pages = {022802},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.103.022802},
  urldate = {2024-06-10},
  abstract = {We theoretically investigate the properties of highly polar diatomic molecules containing 2{$S$}-state transition-metal atoms. We calculate potential energy curves, permanent electric dipole moments, spectroscopic constants, and leading long-range dispersion-interaction coefficients for molecules consisting of either a Cu or Ag atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones, with large Gaussian basis sets and small-core relativistic-energy-consistent pseudopotentials. We predict that the studied molecules in the ground electronic state are strongly bound with highly polarized covalent or ionic bonds resulting in very large permanent electric dipole moments. We find that highly excited vibrational levels have maximal electric dipole moments, e.g., exceeding 13 D for CsAg and 6 D for BaAg. Results for , and CuAg are also reported. The studied molecules may find application in ultracold dipolar many-body physics, controlled chemistry, or precision measurement experiments.},
  file = {/Users/yingxing/Zotero/storage/7CEQNQEZ/Śmiałkowski_Tomza_2021_Highly polar molecules consisting of a copper or silver atom interacting with.pdf}
}

@article{Smits2018,
  title = {A Hundred-year-old Experiment Re-evaluated: {{Accurate}} Ab\>Initio Monte\>Carlo Simulations of the Melting of Radon},
  author = {Smits, Odile R. and Jerabek, Paul and Pahl, Elke and Schwerdtfeger, Peter},
  year = {2018},
  month = jul,
  journal = {Angew. Chem. Int. Ed.},
  volume = {57},
  number = {31},
  pages = {9961--9964},
  publisher = {Wiley},
  issn = {1521-3773},
  doi = {10.1002/anie.201803353}
}

@article{Soldán2001a,
  title = {Static Dipole Polarizabilities ({$\alpha$}) and Static Second Hyperpolarizabilities ({$\gamma$}) of the Rare Gas Atoms ({{He}}--{{Rn}})},
  author = {Sold{\'a}n, Pavel and Lee, Edmond P. F. and Wright, Timothy G.},
  year = {2001},
  month = oct,
  journal = {Phys. Chem. Chem. Phys.},
  volume = {3},
  number = {21},
  pages = {4661--4666},
  publisher = {The Royal Society of Chemistry},
  issn = {1463-9084},
  doi = {10.1039/B105433N},
  urldate = {2023-03-21},
  abstract = {Static polarizabilities, {$\alpha$}, and static second hyperpolarizabilities, {$\gamma$}, of the rare gas atoms, He--Rn, are investigated employing CCSD(T) calculations and large basis sets. For the lighter atoms, He--Kr, x-aug-cc-pVXZ basis sets were employed in order to test convergence (x = s--5; X = D--6). Further basis sets were employed for He in order to investigate basis set requirements. For the heavier species, effective core potentials (ECPs) are employed, together with a large, flexible valence space. {$\alpha$} and {$\gamma$} were obtained by fitting the energies to standard expressions.},
  langid = {english}
}

@article{Srivastava2016,
  title = {Encapsulation of Lawrencium into {{C60}} Fullerene: {{Lr}}@{{C60}} {\emph{versus}} {{Li}}@{{C60}}},
  shorttitle = {Encapsulation of Lawrencium into {{C60}} Fullerene},
  author = {Srivastava, Ambrish Kumar and Pandey, Sarvesh Kumar and Misra, Neeraj},
  year = {2016},
  month = jul,
  journal = {Materials Chemistry and Physics},
  volume = {177},
  pages = {437--441},
  issn = {0254-0584},
  doi = {10.1016/j.matchemphys.2016.04.050},
  urldate = {2024-06-12},
  abstract = {The position of Lawrencium (Lr) in the periodic table has been debated several times. It has been noticed that some fundamental properties of Lr differ from the other elements of the actinide series and closely resemble those of alkali metal. To be specific, the first ionization energy of Lr 4.96~eV [Nature 520 (2015) 209] lies within the range assigned to alkali metals. Motivated by this fact, we study Lr@C60 for the first time and compared its electronic properties with those of Li@C60. Using density functional theory and its time dependent version, we explore structures, vibrational infrared spectra, molecular orbital surfaces, density of states and electronic absorption spectra of Lr@C60 and Li@C60. We notice that although Lr resides very close to the centre of C60 than Li does, the electronic properties of Lr@C60 closely resemble those of Li@C60. For instance, Lr@C60 is as conducting and polarizable as Li@C60 due to almost equal frontier orbital energy gap and mean polarizability. This study is expected to provide further evidence where Lr atom mimics the alkali metal.},
  keywords = {ab initio calculations,Computer modelling and simulation,Electrical properties,Fullerenes},
  file = {/Users/yingxing/Zotero/storage/RUR7V854/Srivastava et al_2016_Encapsulation of lawrencium into C60 fullerene.pdf}
}

@article{Stiehler1995,
  title = {Calculation of Static Polarizabilities and Hyperpolarizabilities for the Atoms {{He}} through {{Kr}} with a Numerical {{RHF}} Method},
  author = {Stiehler, J. and Hinze, J.},
  year = {1995},
  month = sep,
  journal = {J. Phys. B: At. Mol. Opt. Phys.},
  volume = {28},
  number = {18},
  pages = {4055},
  issn = {0953-4075},
  doi = {10.1088/0953-4075/28/18/010},
  urldate = {2024-06-12},
  abstract = {The static electric dipole polarizabilities and hyperpolarizabilities for different states of the ground configuration of the atoms He through Kr have been calculated at the restricted Hartree-Fock level using a finite perturbation method. The required field-dependent energy and dipole moment data have been computed with a recently developed numerical MCSCP code for atoms in a static electric field.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/54A7W35I/Stiehler_Hinze_1995_Calculation of static polarizabilities and hyperpolarizabilities for the atoms.pdf}
}

@article{Stwalley1971,
  title = {Polarizability and {{Long}}-{{Range Interactions}} of {{Magnesium Atoms}}},
  author = {Stwalley, William C.},
  year = {1971},
  month = may,
  journal = {The Journal of Chemical Physics},
  volume = {54},
  number = {10},
  pages = {4517--4518},
  issn = {0021-9606},
  doi = {10.1063/1.1674711},
  urldate = {2024-06-05},
  file = {/Users/yingxing/Zotero/storage/8T2DSHRT/Stwalley_1971_Polarizability and Long‐Range Interactions of Magnesium Atoms.pdf}
}

@article{Sulzer2012,
  title = {Atomic {{C}} 6 Dispersion Coefficients: A Four-Component Relativistic {{Kohn}}--{{Sham}} Study},
  shorttitle = {Atomic {{C}} 6 Dispersion Coefficients},
  author = {Sulzer, David and Norman, Patrick and Saue, Trond},
  year = {2012},
  month = oct,
  journal = {Mol. Phys.},
  volume = {110},
  number = {19-20},
  pages = {2535--2541},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268976.2012.709283},
  urldate = {2023-03-20},
  abstract = {We present C 6 homo- and heteroatomic dispersion coefficients for all closed-shell atoms of the periodic table based on dipole--dipole polarizabilities at imaginary frequencies calculated using our recent extension of the complex polarization propagator approach to the four-component relativistic Kohn--Sham approach. Lack of proper reference data bars definite conclusions as to which density functional shows the overall best performance, and we therefore call for state-of-the-art wave function-based correlated calculations of dispersion coefficients. Scalar relativistic effects are significant already for elements as light as zinc, whereas spin--orbit effects must be taken into account only for very heavy elements.},
  keywords = {C6 dispersion coefficient,density functional theory,relativistic effects,van der Waals interaction},
  file = {/Users/yingxing/Zotero/storage/F5TA533F/Atomic C 6 dispersion coefficients a four-component relativistic Kohn–Sham study - 2012.pdf}
}

@article{Szarek2019,
  title = {Unconventional {{Look}} at the {{Diameters}} of {{Quantum Systems}}: {{Could}} the {{Characteristic Atomic Radius Be Interpreted}} as a {{Reactivity Measure}}?},
  shorttitle = {Unconventional {{Look}} at the {{Diameters}} of {{Quantum Systems}}},
  author = {Szarek, Pawe{\l} and Witkowski, Marcin and Wo{\'z}niak, Aleksander P.},
  year = {2019},
  month = may,
  journal = {J. Phys. Chem. C},
  volume = {123},
  number = {18},
  pages = {11572--11580},
  publisher = {American Chemical Society},
  issn = {1932-7447},
  doi = {10.1021/acs.jpcc.9b00221},
  urldate = {2024-06-06},
  abstract = {Decoding of atomic and ionic radii of transition metals in terms of energy response against changes in electron number and external potential variation has been considered. Energy as a functional of electron density by means of its derivatives is linked to response density and the electron detachment process. Employing charge sensitivity analysis and the electronegativity equalization principle, we interpret the electronic structure transformations (electron-following/preceding perspectives) into atomic diameters. Additionally, qualitative associations described within hard/soft acid/base theory and the approximate correlations of respective conceptual density functional theory reactivity descriptors were considered to meet postulates of the correspondence principle, giving the characteristic radius the attribute of latent variable related to quantum mechanical observables. By means of local density approximation, an insight from statistical analysis of frontier electron density complements the picture of classical (electrostatic) radii formulations as well as provides a view on the electron correlation effect on the atomic size. The presented radius identifies ground and excited states, as well as spin configurations through measurable properties. Its correspondence with empirical radii is illustrated. The provided mathematical interpretation associated with energy evolution contrasts with the classically understood physical boundary.},
  file = {/Users/yingxing/Zotero/storage/35JHD68S/Szarek et al_2019_Unconventional Look at the Diameters of Quantum Systems.pdf}
}

@article{Tang2008,
  title = {The Dynamical Polarisability and van Der {{Waals}} Dimer Potential of Mercury},
  author = {Tang, K.T. and Toennies, J.P.},
  year = {2008},
  month = jun,
  journal = {Mol. Phys.},
  volume = {106},
  number = {12-13},
  pages = {1645--1653},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268970802270059},
  urldate = {2024-06-12},
  abstract = {Wolfsohn's parameters for the frequency-dependent polarisability {$\alpha$}({$\omega$}) of mercury are modified to fit the recent interferometric measurements of Goebel and Hohm [J. Phys. Chem. 100, 7710 (1996)]. The resulting {$\alpha$}({$\omega$}) are extended to imaginary frequencies {$\alpha$}(i{$\omega$}) and used to calculate the upper and lower bounds of the dipole dispersion coefficient in the long range dimer potential. The new value of C 6 = 392{\textpm}4 a.u. is much greater than the generally accepted value. With the corresponding changes in the dipole--quadrupole and dipole--octopole interactions, new dispersion coefficients C 8 and C 10 are obtained. Together with the experimentally determined D e (well-depth) and R e (equilibrium distance), the Tang--Toennies model is used to predict the shape of the entire dimer potential energy curve. The new potential is found to be in excellent agreement with the ab initio calculations of Munro et al. [J. Chem. Phys. 114, 5545 (2001)] and the parameters {$\omega$}e and {$\chi$}e{$\omega$}e agree with the spectroscopic measurements within the small experimental errors.},
  keywords = {Dispersion coeffecients,dynamic polarisability,mercury,van der Waals dimer potential},
  file = {/Users/yingxing/Zotero/storage/SDGYBTH8/Tang_Toennies_2008_The dynamical polarisability and van der Waals dimer potential of mercury.pdf}
}

@article{Tang2012,
  title = {Computational Investigation of Static Multipole Polarizabilities and Sum Rules for Ground-State Hydrogenlike Ions},
  author = {Tang, Li-Yan and Zhang, Yong-Hui and Zhang, Xian-Zhou and Jiang, Jun and Mitroy, J.},
  year = {2012},
  month = jul,
  journal = {Phys. Rev. A},
  volume = {86},
  number = {1},
  pages = {012505},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.86.012505},
  urldate = {2024-06-12},
  abstract = {High-precision multipole polarizabilities, {$A\ell$} for {$\ell\leq$}4 of the 1⁢{$s$} ground state of the hydrogen isoelectronic series, are obtained from the Dirac equation using the -spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of with a relative accuracy of 10 up to are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules for all multipoles from to . The dispersion coefficients for the long-range H-H and H-He interactions are given.},
  file = {/Users/yingxing/Zotero/storage/RSHIV6RC/Tang et al_2012_Computational investigation of static multipole polarizabilities and sum rules.pdf}
}

@article{Tang2018,
  title = {Determination of Static Dipole Polarizabilities of {{Yb}} Atom*},
  author = {Tang, Zhi-Ming and Yu, Yan-Mei and Dong, Chen-Zhong},
  year = {2018},
  month = jun,
  journal = {Chinese Phys. B},
  volume = {27},
  number = {6},
  pages = {063101},
  publisher = {{Chinese Physical Society and IOP Publishing Ltd}},
  issn = {1674-1056},
  doi = {10.1088/1674-1056/27/6/063101},
  urldate = {2024-06-06},
  abstract = {We determine the static values of the scalar and tensor dipole polarizabilities of the ground, 6s6p , and 6s6p states of the Yb atom. These results can be useful in many experiments undertaken using this atom. We employed a combined configuration interaction (CI) method and a second-order many-body perturbation theory (MBPT) to evaluate energies and electric dipole (E1) matrix elements of many low-lying excited states of the above atom. These values are compared with the other available theoretical calculations and experimental values. By combining these E1 matrix elements with the experimental excitation energies, we estimate the dominant valence correlation contributions to the dipole polarizabilities of the above states. The core contribution is obtained from the finite field approach. We also compare these values with the other theoretical results as there are no precise experimental values that are available for these properties.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/WXXQEXRT/Tang et al_2018_Determination of static dipole polarizabilities of Yb atom.pdf}
}

@article{Tang2018a,
  title = {Relativistic Coupled-Cluster Calculations of the Polarizabilities of Atomic Thallium},
  author = {Tang, Yong-Bo and Gao, Ning-Ning and Lou, Bing-Qiong and Shi, Ting-Yun},
  year = {2018},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {98},
  number = {6},
  pages = {062511},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.98.062511},
  urldate = {2024-06-06},
  abstract = {Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the , , , , , and states and the dynamic dipole polarizabilities of the and states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the , , , and states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the -- and -- transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the -- and -- transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the -- transition, are also evaluated and compared with available theoretical and experimental values.},
  file = {/Users/yingxing/Zotero/storage/4MFG22BX/Tang et al_2018_Relativistic coupled-cluster calculations of the polarizabilities of atomic.pdf}
}

@article{Tang2023,
  title = {Simultaneous Magic Trapping Conditions for Three Additional Clock Transitions in {{Yb}} to Search for Variation of the Fine-Structure Constant},
  author = {Tang, Zhi-Ming and Yu, Yan-mei and Sahoo, B. K. and Dong, Chen-Zhong and Yang, Yang and Zou, Yaming},
  year = {2023},
  month = may,
  journal = {Phys. Rev. A},
  volume = {107},
  number = {5},
  pages = {053111},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.107.053111},
  urldate = {2024-06-11},
  abstract = {We demonstrate that the 4⁢{$f$}14⁢6⁢{$s$}⁡6⁢{$p$}⁡(3{$P$}2)-4⁢{$f$}13⁢5⁢{$d$}⁢6⁢{$s$}2⁡(3{$P$}*2) transition in neutral ytterbium (Yb) can serve as an additional clock transition with the highest fine-structure constant ({$Ae$}) varying sensitivity coefficient [{$q$}=-46165⁢(3000)]. We demonstrate a scheme to attain simultaneous magic trapping conditions for this clock transition with other two proposed clock transitions and , which also possess very large values. These conditions can be realized by subjecting Yb atoms to a bias magnetic field with tuning the particular polarization angles of the trapping laser. Upon realization, it can serve as the most potential optical lattice clock to probe variation.},
  file = {/Users/yingxing/Zotero/storage/2GI4HZH4/Tang et al_2023_Simultaneous magic trapping conditions for three additional clock transitions.pdf}
}

@article{Teachout1971,
  title = {The Static Dipole Polarizabilities of All the Neutral Atoms in Their Ground States},
  author = {Teachout, Rodney R. and Pack, Russell T},
  year = {1971},
  month = aug,
  journal = {Atomic Data and Nuclear Data Tables},
  volume = {3},
  pages = {195--214},
  issn = {0092-640X},
  doi = {10.1016/S0092-640X(71)80007-4},
  urldate = {2024-06-05},
  abstract = {Values of the static dipole polarizabilities of all neutral atoms in their ground electronic states have been collected and tabulated. A bibliography for both theoretical and experimental determinations is included.},
  file = {/Users/yingxing/Zotero/storage/6PAEFXTC/Teachout_Pack_1971_The static dipole polarizabilities of all the neutral atoms in their ground.pdf}
}

@article{Thakkar1992,
  title = {Ab\hphantom{,}Initio Dispersion Coefficients for Interactions Involving Rare-gas Atoms},
  author = {Thakkar, Ajit J. and Hettema, Hinne and Wormer, Paul E. S.},
  year = {1992},
  month = sep,
  journal = {The Journal of Chemical Physics},
  volume = {97},
  number = {5},
  pages = {3252--3257},
  issn = {0021-9606},
  doi = {10.1063/1.463012},
  urldate = {2024-06-12},
  abstract = {Calculations of the dynamic dipole, quadrupole, and octopole polarizabilities of Ne, Ar, Kr, and Xe are carried out using both time-dependent coupled Hartree--Fock and many-body perturbation theory methods. Dispersion coefficients are calculated for interactions involving these species. The dynamic polarizabilities are combined with previously published dynamic polarizabilities of H, He, H2, N2, HF, and CO to obtain dispersion coefficients for the interactions involving one of these species and one of Ne, Ar, Kr, or Xe. The dipole--dipole dispersion coefficients agree quite well with the best available semiempirical estimates. The isotropic higher multipole coefficients are in reasonable agreement with previous semiempirical estimates where available, and the anisotropic ones are, in most cases, the first reliable ones to appear in the literature. Nonadditive three-body dispersion coefficients for the Ne3, Ar3, Kr3, and Xe3 interactions are also calculated.},
  file = {/Users/yingxing/Zotero/storage/73XRT9SX/Thakkar et al_1992_Ab initio dispersion coefficients for interactions involving rare‐gas atoms.pdf}
}

@article{Thakkar2005,
  title = {The Polarizability of Sodium: Theory and Experiment Reconciled},
  shorttitle = {The Polarizability of Sodium},
  author = {Thakkar, Ajit J. and Lupinetti, Concetta},
  year = {2005},
  month = jan,
  journal = {Chem. Phys. Lett.},
  volume = {402},
  number = {1},
  pages = {270--273},
  issn = {0009-2614},
  doi = {10.1016/j.cplett.2004.12.046},
  urldate = {2023-03-21},
  abstract = {Coupled cluster computations using large basis sets and the Douglas--Kroll Hamiltonian for relativistic effects are reported for the dipole polarizability, {$\alpha$}, of the sodium atom. Our best value of {$\alpha$}(Na)/e2a02Eh-1=162.88{\textpm}0.6 is in excellent agreement with the value obtained by atomic-beam interferometry, thus resolving a persistent discrepancy between theory and experiment. Combining our {$\alpha$}(Na) with a very accurate value of {$\alpha$}(Li), we find that {$\alpha$}(Li)/{$\alpha$}(Na)=1.0071{\textpm}0.0037 establishing that {$\alpha$}(Li) is greater than {$\alpha$}(Na).},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/9CK7RJ99/The polarizability of sodium Theory and experiment reconciled_2005.pdf}
}

@article{Thierfelder2008,
  title = {Relativistic and Electron Correlation Effects in Static Dipole Polarizabilities for the Group-14 Elements from Carbon to Element \${{Z}}=114\$: {{Theory}} and Experiment},
  shorttitle = {Relativistic and Electron Correlation Effects in Static Dipole Polarizabilities for the Group-14 Elements from Carbon to Element \${{Z}}=114\$},
  author = {Thierfelder, Christian and Assadollahzadeh, Behnam and Schwerdtfeger, Peter and Sch{\"a}fer, Sascha and Sch{\"a}fer, Rolf},
  year = {2008},
  month = nov,
  journal = {Phys. Rev. A},
  volume = {78},
  number = {5},
  pages = {052506},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.78.052506},
  urldate = {2023-03-21},
  abstract = {Static dipole polarizabilities for the 3P0 ground state of the neutral group-14 elements C, Si, Ge, Sn, Pb and element Z=114 were obtained from all-electron relativistic coupled cluster theory, and compared to molecular beam electric field deflection experiments for Sn and Pb. The isotropic and anisotropic components of the polarizability increase monotonically with the nuclear charge Z, except for the spin-orbit coupled J=0 states, which start to decrease from Sn to Pb and even further to element Z=114. Hence, spin-orbit coupling leads to a significant reduction of the polarizability of element Z=114, i.e., from 47.9a.u. at the scalar-relativistic Douglas-Kroll level to 31.5a.u. at the Dirac-Coulomb level of theory, which is below the value of Si (37.3a.u.). The calculations further demonstrate that relativistic and electron correlation effects are nonadditive. The measured dipole polarizabilities of Sn and Pb are in reasonable agreement with the theoretical values.},
  file = {/Users/yingxing/Zotero/storage/83FT6LYG/Thierfelder et al. - 2008 - Relativistic and electron correlation effects in s.pdf}
}

@article{Thierfelder2009,
  title = {Effect of Relativity and Electron Correlation in Static Dipole Polarizabilities of Ytterbium and Nobelium},
  author = {Thierfelder, Christian and Schwerdtfeger, Peter},
  year = {2009},
  month = mar,
  journal = {Phys. Rev. A},
  volume = {79},
  number = {3},
  pages = {032512},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.79.032512},
  urldate = {2023-03-20},
  abstract = {Static dipole polarizabilities for the electronic ground state of neutral Yb and No are investigated by all-electron relativistic coupled cluster theory. We find a significant reduction in the polarizability due to both electron correlation and scalar-relativistic effects. Whereas electron correlation effects are of the same size as relativistic contributions for Yb, for No relativistic effects are dominant and result in smaller polarizability for No compared to Yb. In comparison the contributions from spin-orbit coupling and Gaunt interaction are rather small. Our recommended dipole polarizabilities for Yb and No are 140.7 and 110.8 a.u., respectively.},
  file = {/Users/yingxing/Zotero/storage/7AIYUYKM/Effect of relativity and electron correlation in static dipole polarizabilities of ytterbium and nobelium_2009.pdf}
}

@article{Tomza2021,
  title = {Interaction Potentials, Electric Moments, Polarizabilities, and Chemical Reactions of {{YbCu}}, {{YbAg}}, and {{YbAu}} Molecules},
  author = {Tomza, Micha{\l}},
  year = {2021},
  month = aug,
  journal = {New J. Phys.},
  volume = {23},
  number = {8},
  pages = {085003},
  publisher = {IOP Publishing},
  issn = {1367-2630},
  doi = {10.1088/1367-2630/ac1696},
  urldate = {2024-06-10},
  abstract = {Ultracold YbAg molecules have been recently proposed as promising candidates for electron electric dipole moment searches Verma et al (2020 Phys. Rev. Lett. 125 153201). Here, we calculate potential energy curves, permanent electric dipole and quadrupole moments, and static electric dipole polarizabilities for the YbCu, YbAg, and YbAu molecules in their ground electronic states. We use the coupled cluster method restricted to single, double, and noniterative triple excitations with large Gaussian basis sets, while the scalar relativistic effects are included within the small-core energy-consistent pseudopotentials. We find that the studied molecules are relatively strongly bound with the well depths of 5708 cm-1, 5253 cm-1, and 13349 cm-1 and equilibrium distances of 5.50 bohr, 5.79 bohr, and 5.55 bohr for YbCu, YbAg, and YbAu, respectively. They have large permanent electric dipole moments of 3.2D, 3.3D, and 5.3D at equilibrium distances, respectively. We also calculate equilibrium geometries and energies of corresponding trimers. The studied molecules are chemically reactive unless they are segregated in an optical lattice or shielded with external fields. The investigated molecules may find application in ultracold controlled chemistry, dipolar many-body physics, or precision measurement experiments.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/R2F2JJTJ/Tomza - 2021 - Interaction potentials, electric moments, polariza.pdf}
}

@article{Torrens2002,
  title = {Molecular Polarizability of {{Scn}}, {{Cn}} and Endohedral {{Scn}}@{{Cm}} Clusters},
  author = {Torrens, Francisco},
  year = {2002},
  month = may,
  journal = {Nanotechnology},
  volume = {13},
  number = {3},
  pages = {433},
  issn = {0957-4484},
  doi = {10.1088/0957-4484/13/3/338},
  urldate = {2024-06-12},
  abstract = {The interacting induced dipoles polarization model implemented in the program POLAR is used for the calculation of the molecular dipole-dipole polarizability . The method is tested with Sc1-Sc7, Sc12, Sc17, Sc74, C, C12, C60, C70, C82-fullerene, Sc@C60, Sc@C82, Sc2@C82, Sc3@C82, C1-C6, C10, C13, C16, C19, C22, C24, C42, C54, C84 and C96-graphite clusters. The polarizability is an important quantity for the identification of clusters with different numbers of atoms and even for the separation of isomers. The results for the polarizability are of the same order of magnitude as reference calculations performed with another program based on the same formulation. The bulk limit for the polarizability is estimated from the Clausius-Mossotti relationship. The polarizability trend for these clusters as a function of size is different from what one might have expected. The clusters are more polarizable than one might have inferred from the bulk. Previous theoretical work has yielded the same trend for small Sin, Gen and GanAsm clusters. However, previous experimental work has yielded the opposite trend for larger Sin, GanAsm and GenTem clusters. At present, the origin of this difference is problematic. One might argue that smaller clusters need not behave like those of intermediate size. The high polarizability of small clusters is attributed to dangling bonds at the surface of the cluster, which resembles a metallic cluster.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/DQDPTM5N/Torrens_2002_Molecular polarizability of Scn, Cn and endohedral Scn@Cm clusters.pdf}
}

@article{Tunega1997,
  title = {Basis Set Limit Value for the Static Dipole Polarizability of Beryllium},
  author = {Tunega, Daniel and Noga, Jozef and Klopper, Wim},
  year = {1997},
  month = may,
  journal = {Chem. Phys. Lett.},
  volume = {269},
  number = {5},
  pages = {435--440},
  issn = {0009-2614},
  doi = {10.1016/S0009-2614(97)00301-1},
  urldate = {2023-03-20},
  abstract = {The static dipole polarizability ({$\alpha$}) and the second dipole hyperpolarizability ({$\gamma$}) for the ground state of the beryllium atom are calculated using the recently developed explicitly correlated (electronic cusp corrected) coupled cluster method (CC-R12) and high quality basis sets of Gaussian atomic functions. The CC-R12 convergence with increasing size of the basis set of the polarizability towards the limiting value is significantly faster than for the conventional coupled cluster approach. The predicted values are {$\alpha$} = 37.73 {\textpm} 0.05 au and {$\gamma$} = 32.0 {\textpm} 1.0 {\texttimes} 103 au.},
  langid = {english}
}

@article{Udem2018,
  title = {Quantum Electrodynamics and the Proton Size},
  author = {Udem, Thomas},
  year = {2018},
  month = jun,
  journal = {Nature Phys},
  volume = {14},
  number = {6},
  pages = {632--632},
  publisher = {Nature Publishing Group},
  issn = {1745-2481},
  doi = {10.1038/s41567-018-0166-0},
  urldate = {2024-06-12},
  abstract = {Tests of one of the most fundamental theories in physics reveal an issue with the size of the proton --- or the Rydberg constant. Thomas Udem explains.},
  copyright = {2018 Springer Nature Limited},
  langid = {english},
  keywords = {Atomic and molecular physics,Scientific community and society,Techniques and instrumentation},
  file = {/Users/yingxing/Zotero/storage/JKQDS3UX/Udem_2018_Quantum electrodynamics and the proton size.pdf}
}

@article{vanGisbergen1996,
  title = {Improved Density Functional Theory Results for Frequency-dependent Polarizabilities, by the Use of an Exchange-correlation Potential with Correct Asymptotic Behavior},
  author = {{van Gisbergen}, S. J. A. and Osinga, V. P. and Gritsenko, O. V. and {van Leeuwen}, R. and Snijders, J. G. and Baerends, E. J.},
  year = {1996},
  month = aug,
  journal = {The Journal of Chemical Physics},
  volume = {105},
  number = {8},
  pages = {3142--3151},
  issn = {0021-9606},
  doi = {10.1063/1.472182},
  urldate = {2024-06-12},
  abstract = {The exchange-correlation potentials vxc which are currently fashionable in density functional theory (DFT), such as those obtained from the local density approximation (LDA) or generalized gradient approximations (GGAs), all suffer from incorrect asymptotic behavior. In atomic calculations, this leads to substantial overestimations of both the static polarizability and the frequency dependence of this property. In the present paper, it is shown that the errors in atomic static dipole and quadrupole polarizabilities are reduced by almost an order of magnitude, if a recently proposed model potential with correct Coulombic long-range behavior is used. The frequency dependence is improved similarly. The model potential also removes the overestimation in molecular polarizabilities, leading to slight improvements for average molecular polarizabilities and their frequency dependence. For the polarizability anisotropy we find that the model potential results do not improve over the LDA and GGA results. Our method for calculating frequency-dependent molecular response properties within time-dependent DFT, which we described in more detail elsewhere, is summarized.},
  file = {/Users/yingxing/Zotero/storage/J5YP4SJB/van Gisbergen et al_1996_Improved density functional theory results for frequency‐dependent.pdf}
}

@article{vanWijngaarden1999a,
  title = {Precision Measurements of Atomic Polarizabilities},
  author = {{van Wijngaarden}, William Arie},
  year = {1999},
  month = jun,
  journal = {AIP Conference Proceedings},
  volume = {477},
  number = {1},
  pages = {305--321},
  issn = {0094-243X},
  doi = {10.1063/1.59362},
  urldate = {2024-06-12},
  abstract = {Substantial progress has occurred during the last decade to develop improved methods for determining atomic polarizabilities. We review work that has been done on ground states as well as the study of Stark shifts of transitions to excited states that have been made with a precision of parts in 104. Measurements done on alkali atoms have yielded significantly more accurate data than previously available, stringently testing atomic theory.},
  file = {/Users/yingxing/Zotero/storage/C3VNTBYY/van Wijngaarden_1999_Precision measurements of atomic polarizabilities.pdf}
}

@article{Visentin2019,
  title = {Polarizabilities, Dispersion Coefficients, and Retardation Functions at the Complete Basis Set {{CCSD}} Limit: {{From Be}} to {{Ba}} plus {{Yb}}},
  shorttitle = {Polarizabilities, Dispersion Coefficients, and Retardation Functions at the Complete Basis Set {{CCSD}} Limit},
  author = {Visentin, Giorgio and Buchachenko, Alexei A.},
  year = {2019},
  month = dec,
  journal = {The Journal of Chemical Physics},
  volume = {151},
  number = {21},
  pages = {214302},
  issn = {0021-9606},
  doi = {10.1063/1.5129583},
  urldate = {2024-06-06},
  abstract = {Static and dynamic polarizabilities of alkaline earth metal atoms Be-Ba and of the Yb atom, as well as dispersion coefficients and retardation functions for their long-range interactions, are used as a benchmark for the restricted coupled cluster method with singles and doubles (CCSD) and noniterative triples added [CCSD(T)] and related polarization propagator CCSD(3) methods at the complete basis set limit. The latter is attained through the sequence of the augmented correlation-consistent polarized weighted core valence n-zeta basis sets with the exact 2-component approximation for the scalar relativistic effects and with the small-core effective core potentials (for Ca, Sr, and Ba). At the converged level of core correlation treatment, the finite-field CCSD(T) method reproduces the best available data for the static dipole and quadrupole polarizabilities better than 1\% and 4\%, respectively. Systematic cancelation of the triple contribution in the CCSD(3) calculations of the dynamic polarizabilities of alkaline earth metal atoms makes their dispersion coefficients accurate within 3\%. The retardation functions are computed and used for the analysis of the long-range interactions in the homonuclear dimers. Implications to accurate ab initio calculations of the global interaction potentials are discussed.},
  file = {/Users/yingxing/Zotero/storage/HXV4JR8L/Visentin_Buchachenko_2019_Polarizabilities, dispersion coefficients, and retardation functions at the.pdf}
}

@article{Visentin2020,
  title = {Extended Combination Rule for Like-Atom Dipole Dispersion Coefficients},
  author = {Visentin, Giorgio and Kalinina, Inna S. and Buchachenko, Alexei A.},
  year = {2020},
  month = aug,
  journal = {The Journal of Chemical Physics},
  volume = {153},
  number = {6},
  pages = {064110},
  issn = {0021-9606},
  doi = {10.1063/5.0019010},
  urldate = {2024-06-10},
  abstract = {An extended combination rule is proposed to relate the dipole--dipole dispersion coefficient for the interaction of the like target species to the same coefficients for the interactions between the target and a set of partner species. The rule can be derived either by uniform discretization of the Casimir--Polder integral on a quadrature or by relating the dynamic dipole polarizabilities of the target species and the partner species. Both methods result in the same system of linear equations, whose solution also requires the knowledge of the dispersion coefficients for interaction between the partner species. The test examples indicate a high accuracy of the proposed rule for dispersion coefficients (better than 1\% in the stringent test for the Yb atom interacting with a rare gas and alkaline-earth metal atoms). However, the combination rule does not warrant correct approximation of the dynamic polarizability of the target species.},
  file = {/Users/yingxing/Zotero/storage/F3IMTK59/Visentin et al. - 2020 - Extended combination rule for like-atom dipole dis.pdf}
}

@article{Wang1998,
  title = {Pseudopotential Study of the Ground and Excited States of {{Yb2}}},
  author = {Wang, Yixuan and Dolg, Michael},
  year = {1998},
  month = nov,
  journal = {Theor Chem Acc},
  volume = {100},
  number = {1},
  pages = {124--133},
  issn = {1432-2234},
  doi = {10.1007/s002140050373},
  urldate = {2024-06-12},
  abstract = {The ground state of the van der Waals-type lanthanide dimer Yb2 has been studied by means of relativistic energy-consistent ab initio pseudopotentials using three different core definitions. Electron correlation was treated by coupled-cluster theory, whereby core-valence correlation effects have been accounted for either explicitly by correlating the energetically highest coreorbitals or implicitly by means of an effective core-polarization potential. Results for the first and second atomic ionization potentials, the atomic dipole polarizability, and the spectroscopic constants of the molecular ground state are reported. Low-lying excited states have been investigated with spin-orbit configuration interaction calculations. It is also demonstrated for the whole lanthanide series that correlation effects due to the atomic-like, possibly open 4f-shell in lanthanides can be modeled effectively by adding a core-polarization potential to pseudopotentials attributing the 4f-shell to the core.},
  langid = {english},
  keywords = {Key words: Core-polarization potential,Lanthanides,Pseudopotential,Van der Waals interaction,Ytterbium},
  file = {/Users/yingxing/Zotero/storage/C68A3XKT/Wang_Dolg_1998_Pseudopotential study of the ground and excited states of Yb2.pdf}
}

@article{Wang2021,
  title = {Static Dipole Polarizabilities of Atoms and Ions from {{Z}} = 1 to 20 Calculated within a Single Theoretical Scheme},
  author = {Wang, Kai and Wang, Xiaohan and Fan, Zheng and Zhao, Hong-Yuan and Miao, Lin and Yin, Guang-Jia and Moro, Ramiro and Ma, Lei},
  year = {2021},
  month = feb,
  journal = {Eur. Phys. J. D},
  volume = {75},
  number = {2},
  pages = {1--11},
  publisher = {Springer Berlin Heidelberg},
  issn = {1434-6079},
  doi = {10.1140/epjd/s10053-021-00054-2},
  urldate = {2024-06-06},
  abstract = {Abstract Static dipole polarizabilities for the first 20 atoms and ions of the Periodic Table are calculated within a single theoretical scheme: the coupled-cluster method with a Hartree--Fock reference wavefunction using an augmented-polarization-consistent and polarization-consistent basis set. The values of the atomic polarizabilities of neutral atoms obtained here agree extremely well with the experimentally measured values. For the ions, all the calculations are consistent with experimental values with the highest resolution so far, except for the monovalent calcium ion, probably due to strong relativistic effects. To the best of our knowledge, this is the first time, applying a single theoretical scheme successfully predicts static polarizabilities of all 20 consecutive elements across 8 columns and more than 3 full periods being consistent with the experimentally measured values both for neutrals and ions. The results clearly signal the universality of this theoretical scheme for the atomic polarizability calculation, and should be easy to extend to other elements with weak relativistic effects. Graphic Abstract We adopt the CCSD(T) method with an augmented polarization-consistent and polarization-consistent basis set to calculate the atomic and ionic polarizabilities for the first 20 atoms and ions of the Periodic Table. Our calculation results are in good agreement with the experimental data with the highest accuracy so far and the reported high accuracy calculation results. Semi-logarithm plot of calculated static polarizabilities of neutral atoms (filled circles, black line) and ions (open circles). The colored lines join isoelectronic species.},
  copyright = {2021 The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/GUP8CCIQ/Wang et al_2021_Static dipole polarizabilities of atoms and ions from Z = 1 to 20 calculated.pdf}
}

@article{Wang2023b,
  title = {Reconciliation of the {{Theoretical}} and {{Experimental Value}} of the {{Static Electric Polarizability}} of the {{Aluminum Atom}}},
  author = {Wang, Kai and Fang, Shao-Zheng and Fan, Zheng and Zhao, Hong-Yuan and Miao, Lin and Yin, Guang-Jia and Moro, Ramiro and Ma, Lei},
  year = {2023},
  month = jul,
  journal = {J Clust Sci},
  volume = {34},
  number = {4},
  pages = {2147--2151},
  issn = {1572-8862},
  doi = {10.1007/s10876-022-02377-5},
  urldate = {2024-06-10},
  abstract = {The electric polarizability of the aluminum atom has become a benchmark for calibration in electric polarizability measurements of clusters during the past decades. However, there is a large discrepancy between the experimentally measured value and the theoretically predicted one. It is worth to clarify the argument through systematic modern calculations. Here, we present high-level computation of the static dipole polarizability of the ground-state aluminum atom by applying the PC-4 basis set with various ab initio methods including Unrestricted-Hartree--Fock, M{\o}ller-Plesset perturbation and the coupled cluster. In contrast to the previously calculated values which deviate from the experimentally measured one by 20\%, our recommended value of 47.69 a.u. lies within the experimental one of 46\,{\textpm}\,2 a.u. This reconciliates the theoretical with the experimental value again and reaffirms its reliability as calibration for future experiments.},
  langid = {english},
  keywords = {Aluminum atom,Coupled cluster theory,Electric polarizability,Moller-Plesset perturbation},
  file = {/Users/yingxing/Zotero/storage/MYS7IPTM/Wang et al. - 2023 - Reconciliation of the Theoretical and Experimental.pdf}
}

@article{Weitz1995,
  title = {Precision Measurement of the {{1S}} Ground-State {{Lamb}} Shift in Atomic Hydrogen and Deuterium by Frequency Comparison},
  author = {Weitz, M. and Huber, A. and {Schmidt-Kaler}, F. and Leibfried, D. and Vassen, W. and Zimmermann, C. and Pachucki, K. and H{\"a}nsch, T. W. and Julien, L. and Biraben, F.},
  year = {1995},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {52},
  number = {4},
  pages = {2664--2681},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.52.2664},
  urldate = {2024-06-12},
  abstract = {We have measured the hydrogen and deuterium 1S Lamb shift by direct optical frequency comparison of the 1S-2S and 2S-4S/4D two-photon transitions. Our result of 8172.874(60) MHz for the 1S Lamb shift in hydrogen is in agreement with the theoretical value of 8172.802(40) MHz. For the 1S Lamb shift in deuterium, we obtain a value of 8183.807(78) MHz, from which we derive a deuteron matter radium of 1.945(28) fm. The precision of our value for the 1S Lamb shift has surpassed that of radio frequency measurements of the 2S-2P Lamb shift. By comparison with a recent absolute measurement of the hydrogen 1S-2S transition frequency, we deduce a value for the Rydberg constant =109 737.315 684 9(30) .},
  file = {/Users/yingxing/Zotero/storage/FSSVFA9M/Weitz et al_1995_Precision measurement of the 1S ground-state Lamb shift in atomic hydrogen and.pdf}
}

@article{Werner1976,
  title = {Finite Perturbation Calculations for the Static Dipole Polarizabilities of the First-Row Atoms},
  author = {Werner, Hans-Joachim and Meyer, Wilfried},
  year = {1976},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {13},
  number = {1},
  pages = {13--16},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.13.13},
  urldate = {2024-06-12},
  abstract = {Static dipole polarizabilities are calculated from self-consistent-field and highly correlated wave functions for the ground states of the atoms Li through Ne. The correlation contributions to the polarizabilities are found to vary between -16\% for Be and + 14\% for F. The polarizabilities as obtained from the coupled-electron-pair approximation are expected to be accurate to about 2\%.},
  file = {/Users/yingxing/Zotero/storage/B7XE5GFD/Werner_Meyer_1976_Finite perturbation calculations for the static dipole polarizabilities of the.pdf}
}

@article{Wesendrup2000,
  title = {Extremely {{Strong}} S2 -- S2 {{Closed-Shell Interactions}}},
  author = {Wesendrup, Ralf and Schwerdtfeger, Peter},
  year = {2000},
  journal = {Angew. Chem. Int. Ed.},
  volume = {39},
  number = {5},
  pages = {907--910},
  issn = {1521-3773},
  doi = {10.1002/(SICI)1521-3773(20000303)39:5<907::AID-ANIE907>3.0.CO;2-M},
  urldate = {2023-03-20},
  abstract = {Closed-shell interactions are generally assumed to be weak but relativistic coupled-cluster calculations (see figure) reveal that the s2-s2 system Au-+Ba has an unusually high dissociation energy of 143 kJ mol-1. The main bond contribution is a charge-induced dipole interaction that profits from a relativistically contracted bond length and the high dipole polarizability for barium.},
  keywords = {ab initio calculations,Ab initio calculations,electronic structures,Electronic structures,relativistic effects,Relativistic effects},
  file = {/Users/yingxing/Zotero/storage/PQDUFQTV/Extremely strong s2-s2 closed-shell interactions_2000.pdf}
}

@book{Williams2016,
  title = {Quantifying {{Measurement}}: {{The}} Tyranny of Numbers},
  shorttitle = {Quantifying {{Measurement}}},
  author = {Williams, Jeffrey H.},
  year = {2016},
  month = oct,
  publisher = {Morgan \& Claypool Publishers},
  urldate = {2024-06-04},
  abstract = {{$<$}p{$>$}Measurements and experiments are made each and every day, in fields as disparate as particle physics, chemistry, economics and medicine, but have you ever wondered why it is that a particular experiment has been designed to be the way it is. Indeed, how do you design an experiment to measure something whose value is unknown, and what should your considerations be on deciding whether an experiment has yielded the sought after, or indeed any useful result? These are old questions, and they are the reason behind this volume. We will explore the origins of the methods of data analysis that are today routinely applied to all measurements, but which were unknown before the mid-19th Century. Anyone who is interested in the relationship between the precision and accuracy of measurements will find this volume useful. Whether you are a physicist, a chemist, a social scientist, or a student studying one of these subjects, you will discover that the basis of measurement is the struggle to identify the needle of useful data hidden in the haystack of obscuring background noise.{$<$}/p{$>$}},
  isbn = {978-1-68174-433-9},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/AGNXM84F/quantifying_measurement.pdf}
}

@article{Wu2023,
  title = {Be Optical Lattice Clocks with the Fractional {{Stark}} Shift up to the Level of 10-19},
  author = {Wu, Lei and Wang, Xia and Wang, Ting and Jiang, Jun and Dong, Chenzhong},
  year = {2023},
  month = apr,
  journal = {New J. Phys.},
  volume = {25},
  number = {4},
  pages = {043011},
  publisher = {IOP Publishing},
  issn = {1367-2630},
  doi = {10.1088/1367-2630/acc81e},
  urldate = {2024-06-10},
  abstract = {The energy levels and electric dipole () matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic , magnetic dipole () and electric quadrupole () polarizabilities as well as the hyperpolarizabilities of the and states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity I is in the range of 14.3--15.9 kW cm-2 and the detuning {$\delta$} (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7--40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 {\texttimes} 10-18. While, when I is in the range of 15.01--15.46 kW cm-2 and {$\delta$} is in the range of 40.73--40.76 MHz, the fractional Stark shifts are lower than 1.0 {\texttimes} 10-19.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/J83V9FI3/Wu et al_2023_Be optical lattice clocks with the fractional Stark shift up to the level of.pdf}
}

@article{Xi-Bo2009,
  title = {Static Dipole Polarizabilities of {{Scn}} (n {$\leq$} 15) Clusters},
  author = {{Xi-Bo}, Li and {Hong-Yan}, Wang and {Jiang-Shan}, Luo and {Yun-Dong}, Guo and {Wei-Dong}, Wu and {Yong-Jian}, Tang},
  year = {2009},
  month = aug,
  journal = {Chinese Phys. B},
  volume = {18},
  number = {8},
  pages = {3414},
  issn = {1674-1056},
  doi = {10.1088/1674-1056/18/8/048},
  urldate = {2024-06-12},
  abstract = {The static dipole polarizabilities of scandium clusters with up to 15 atoms are determined by using the numerically finite field method in the framework of density functional theory. The electronic effects on the polarizabilities are investigated for the scandium clusters. We examine a large highest occupied molecular orbital --- the lowest occupied molecular orbital (HOMO--LUMO) gap of a scandium cluster usually corresponds to a large dipole moment. The static polarizability per atom decreases slowly and exhibits local minimum with increasing cluster size. The polarizability anisotropy and the ratio of mean static polarizability to the HOMO--LUMO gap can also reflect the cluster stability. The polarizability of the scandium cluster is partially related to the HOMO--LUMO gap and is also dependent on geometrical characteristics. A strong correlation between the polarizability and ionization energy is observed.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/Y4CBTTP3/Xi-Bo et al_2009_Static dipole polarizabilities of Scn (n ≤ 15) clusters.pdf}
}

@article{Xu2016,
  title = {Is the Chemistry of Lawrencium Peculiar?},
  author = {Xu, Wen-Hua and Pyykk{\"o}, Pekka},
  year = {2016},
  month = jun,
  journal = {Phys. Chem. Chem. Phys.},
  volume = {18},
  number = {26},
  pages = {17351--17355},
  publisher = {The Royal Society of Chemistry},
  issn = {1463-9084},
  doi = {10.1039/C6CP02706G},
  urldate = {2024-06-12},
  abstract = {It is explicitly verified that the atomic 7p1 ground-state configuration of Lr originates from relativistic effects. Without relativity one has 6d1. All three ionization potentials IP1--3 of Lr resemble those of Lu. Simple model studies on mono- and trihydrides, monocarbonyls or trichlorides suggest no major chemical differences between Lr and the lanthanides.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/G9SZPALG/Xu_Pyykkö_2016_Is the chemistry of lawrencium peculiar.pdf;/Users/yingxing/Zotero/storage/MDJHL37I/Xu and Pyykkö - 2016 - Is the chemistry of lawrencium peculiar.pdf}
}

@article{Ye2008,
  title = {Dipole Polarizabilities of \$n\{s\}{\textasciicircum}\{2\}{\textbackslash}text\{ \}\{{\textasciicircum}\{1\}\vphantom\}{{S}}\vphantom\{\}\_\{0\}\$ and \$nsnp{\textbackslash}text\{ \}\{{\textasciicircum}\{3\}\vphantom\}{{P}}\vphantom\{\}\_\{0\}\$ States and Relevant Magic Wavelengths of Group-{{IIB}} Atoms},
  author = {Ye, Anpei and Wang, Guangfu},
  year = {2008},
  month = jul,
  journal = {Phys. Rev. A},
  volume = {78},
  number = {1},
  pages = {014502},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.78.014502},
  urldate = {2024-06-12},
  abstract = {The dipole polarizabilities of the ground state {$n$}⁢{$s$}2 1{$S$}0 and the metastable state {$n$}⁢{$s$}⁢{$n$}⁢{$p$} 3{$P$}0 are crucial for estimating the light shifts and blackbody radiation shifts in the optical frequency standard based on alkaline-earth-metal--like atoms. In this paper, the correlative dipole polarizabilities for group IIB atoms were calculated by the method of the -spline configuration interaction with a semiempirical core-polarization model potential. The results are consistent with the experimental values in a reasonable accuracy and agree with other theoretical results as well. With these results, the magic wavelengths, at which the lowest-order light shift of the clock transition is null, were also obtained. For Zn, Cd, and Hg, they are 413, 420, and 363 nm, respectively.},
  file = {/Users/yingxing/Zotero/storage/BWSXHPXM/Ye_Wang_2008_Dipole polarizabilities of $n s ^ 2 -text ^ 1 S _ 0 $ and $nsnp-text .pdf}
}

@article{Yoshizawa2016,
  title = {Calculations of Electric Dipole Moments and Static Dipole Polarizabilities Based on the Two-Component Normalized Elimination of the Small Component Method},
  author = {Yoshizawa, Terutaka and Zou, Wenli and Cremer, Dieter},
  year = {2016},
  month = nov,
  journal = {The Journal of Chemical Physics},
  volume = {145},
  number = {18},
  pages = {184104},
  issn = {0021-9606},
  doi = {10.1063/1.4964765},
  urldate = {2024-06-12},
  abstract = {The analytical energy gradient and Hessian of the two-component Normalized Elimination of the Small Component (2c-NESC) method with regard to the components of the electric field are derived and used to calculate spin-orbit coupling (SOC) corrected dipole moments and dipole polarizabilities of molecules, which contain elements with high atomic number. Calculated 2c-NESC dipole moments and isotropic polarizabilities agree well with the corresponding four-component-Dirac Hartree--Fock or density functional theory values. SOC corrections for the electrical properties are in general small, but become relevant for the accurate prediction of these properties when the molecules in question contain sixth and/or seventh period elements (e.g., the SO effect for At2 is about 10\% of the 2c-NESC polarizability). The 2c-NESC changes in the electric molecular properties are rationalized in terms of spin-orbit splitting and SOC-induced mixing of frontier orbitals with the same j = l + s quantum numbers.},
  file = {/Users/yingxing/Zotero/storage/R7HAH5CE/Yoshizawa et al_2016_Calculations of electric dipole moments and static dipole polarizabilities.pdf}
}

@article{Zalialiutdinov2016,
  title = {Spin-Statistic Selection Rules for Multiphoton Transitions: {{Application}} to Helium Atoms},
  shorttitle = {Spin-Statistic Selection Rules for Multiphoton Transitions},
  author = {Zalialiutdinov, T. and Solovyev, D. and Labzowsky, L. and Plunien, G.},
  year = {2016},
  month = jan,
  journal = {Phys. Rev. A},
  volume = {93},
  number = {1},
  pages = {012510},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.93.012510},
  urldate = {2024-06-12},
  abstract = {A theoretical investigation of the three-photon transition rates 21⁢{$P$}1{$\rightarrow$}21⁢{$S$}0,11⁢{$S$}0 and 23⁢{$P$}2{$\rightarrow$}21⁢{$S$}0,11⁢{$S$}0 for the helium atom is presented. Photon energy distributions and precise values of the nonrelativistic transition rates are obtained with employment of correlated wave functions of the Hylleraas type. The possible experiments for the tests of the Bose-Einstein statistics for multiphoton systems are discussed.},
  file = {/Users/yingxing/Zotero/storage/P6Q2TIEA/Zalialiutdinov et al_2016_Spin-statistic selection rules for multiphoton transitions.pdf}
}

@article{Zaremba-Kopczyk2021,
  title = {Van Der {{Waals}} Molecules Consisting of a Zinc or Cadmium Atom Interacting with an Alkali-Metal or Alkaline-Earth-Metal Atom},
  author = {{Zaremba-Kopczyk}, Klaudia and Tomza, Micha{\l}},
  year = {2021},
  month = oct,
  journal = {Phys. Rev. A},
  volume = {104},
  number = {4},
  pages = {042816},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.104.042816},
  urldate = {2024-06-10},
  abstract = {Alkaline-earth-like transition-metal atoms such as Zn and Cd are promising candidates for precision measurements and quantum many-body physics experiments. Here, we theoretically investigate the properties of diatomic molecules containing these closed-shell atoms. We calculate potential-energy curves, permanent electric dipole moments, and spectroscopic constants for molecules consisting of either a Zn or Cd atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use the ab initio electronic-structure coupled-cluster method with single, double, and triple excitations combined with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials for heavier atoms. We predict that the studied molecules in the ground electronic state are chemically reactive weakly bound van der Waals complexes with small permanent electric dipole moments. The present results may be useful for spectroscopy and application of the studied molecules in modern ultracold physics and chemistry experiments.},
  file = {/Users/yingxing/Zotero/storage/7T3X3EE7/Zaremba-Kopczyk and Tomza - 2021 - Van der Waals molecules consisting of a zinc or ca.pdf}
}

@article{Zeiss1977,
  title = {Dispersion Energy Constants {{C}} 6({{A}}, {{B}}), Dipole Oscillator Strength Sums and Refractivities for {{Li}}, {{N}}, {{O}}, {{H2}}, {{N2}}, {{O2}}, {{NH3}}, {{H2O}}, {{NO}} and {{N2O}}},
  author = {Zeiss, G.D. and Meath, William J.},
  year = {1977},
  month = apr,
  journal = {Mol. Phys.},
  volume = {33},
  number = {4},
  pages = {1155--1176},
  publisher = {Taylor \& Francis},
  issn = {0026-8976},
  doi = {10.1080/00268977700100991},
  urldate = {2023-03-20},
  abstract = {Accurate values for the orientation-averaged long-range dipole-dipole dispersion energy coefficients, C 6(A, B), have been determined for all possible pair interactions involving ground state H, Li, N, O, H2, N2, O2, NH3, H2O, NO, and N2O. The calculations have been carried out by employing dipole oscillator strength distributions for these species that have been constructed (except in the case of H) by using discrete oscillator strength, photo-absorption, and high energy inelastic scattering data and by requiring the distributions to reproduce the Thomas-Reiche-Kuhn sum rule and, in the case of the molecules, available accurate refractivity and dispersion measurements for the relevant dilute gases. These oscillator strength distributions were also used to evaluate the refractivity R({$\lambda$}), as a function of wavelength {$\lambda$} in the visible and ultra-violet region below the ultra-violet absorption thresholds, and the dipole oscillator strength sums S -2l , l = 1, 2, {\dots}, 7, for each atom and molecule. The calculated values of R({$\lambda$}) provide refractivities for wavelengths, especially in the ultra-violet region, for which accurate experimental data are often not available. The accurate results for C 6(A, B) and for various dipole oscillator strength sums are used to make self-consistent tests of the adequacy of (1) the C 6(A, A) bounds provided by Pad{\'e} approximant methods and (2) various semi-empirical formulae for C 6(A, B). Some problems that can arise in using other procedures to evaluate the S -2l and C 6(A, B) are discussed briefly.},
  file = {/Users/yingxing/Zotero/storage/AW5VHKWM/Dispersion energy constants C6(A, B), dipole oscillator strength sums and refractivities for Li, N, O, H2, N2, 02, NH3, H20, NO and N2O_.pdf;/Users/yingxing/Zotero/storage/ECDXB54W/Zeiss_Meath_1977_Dispersion energy constants C 6(A, B), dipole oscillator strength sums and.pdf}
}

@article{Zhang2007a,
  title = {Dispersion Coefficients of the Excited States of Lithium Atoms},
  author = {Zhang, J.-Y. and Mitroy, J. and Bromley, M. W. J.},
  year = {2007},
  month = apr,
  journal = {Phys. Rev. A},
  volume = {75},
  number = {4},
  pages = {042509},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.75.042509},
  urldate = {2024-06-05},
  abstract = {The dispersion coefficients of a number of the low-lying states of Li are determined for the homonuclear case. The Li wave functions and energies were computed in a frozen core Hamiltonian with a semiempirical polarization potential. Besides computing the dispersion coefficients, the scalar and tensor polarizabilities and oscillator strengths are computed and generally seen to be in good agreement with other accurate calculations.},
  file = {/Users/yingxing/Zotero/storage/ADG8YQT6/Zhang et al_2007_Dispersion coefficients of the excited states of lithium atoms.pdf}
}

@article{Zhang2007b,
  title = {Static Dipole Polarizability of Ytterbium},
  author = {Zhang, Peng and Dalgarno, Alexander},
  year = {2007},
  month = oct,
  journal = {J. Phys. Chem. A},
  volume = {111},
  number = {49},
  pages = {12471--12476},
  publisher = {American Chemical Society (ACS)},
  issn = {1520-5215},
  doi = {10.1021/jp0750856}
}

@article{Zhang2008a,
  title = {Long-Range Interactions of Copper and Silver Atoms with Hydrogen, Helium, and Rare-Gas Atoms},
  author = {Zhang, J. Y. and Mitroy, J. and Sadeghpour, H. R. and Bromley, M. W. J.},
  year = {2008},
  month = dec,
  journal = {Phys. Rev. A},
  volume = {78},
  number = {6},
  pages = {062710},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.78.062710},
  urldate = {2024-06-12},
  abstract = {Dispersion interactions of the ground and resonantly excited states of Cu and Ag with a number of buffer gases are determined. The valence excitation spectrum was calculated by diagonalizing a semiempirical Hamiltonian in a large-dimension single-electron basis. The core made a significant contribution to the and dispersion coefficients for both copper and silver. Oscillator strengths and static scalar and tensor polarizabilities are given for some of the low-lying states.},
  file = {/Users/yingxing/Zotero/storage/NCAP8BY8/Zhang et al_2008_Long-range interactions of copper and silver atoms with hydrogen, helium, and.pdf}
}

@article{Zhang2009,
  title = {Scattering of {{Yb}} and \$\{{\textbackslash}text\{\vphantom{\}\}}{{Yb}}\vphantom\{\}\vphantom\{\}{\textasciicircum}\{+\}\$},
  author = {Zhang, Peng and Dalgarno, Alex and C{\^o}t{\'e}, Robin},
  year = {2009},
  month = sep,
  journal = {Phys. Rev. A},
  volume = {80},
  number = {3},
  pages = {030703},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.80.030703},
  urldate = {2024-06-12},
  abstract = {We calculate the cross sections for scattering of a neutral ytterbium atom with its positive ion at energies up to 30 eV. We identify peaks in the forward direction as arising from elastic collisions and those in the backward direction as from charge transfer. We show that the total cross section follows a semiclassical expression over a large range of energies and that the resonant charge transfer may be characterized by four energy regimes: an -wave regime at ultralow energies, a modified Langevin regime at low energy, a Langevin regime at medium energy, and an ``exchange'' regime at high energy. We find large variations between the different isotopes for the two lowest-energy regimes and very little variation for the two highest-energy regimes. Our results are consistent with recent measurements.},
  file = {/Users/yingxing/Zotero/storage/VLH3NBGC/Zhang et al_2009_Scattering of Yb and $ -text Yb ^ + $.pdf}
}

@article{Zhang2023,
  title = {Magic-Zero and Magic Wavelengths of the {{Ca}} Atom},
  author = {Zhang, Ru-Kui and Jiang, Jun and Dong, Chen-Zhong and Tang, Yong-Bo},
  year = {2023},
  month = jul,
  journal = {Phys. Rev. A},
  volume = {108},
  number = {1},
  pages = {012803},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.108.012803},
  urldate = {2024-06-10},
  abstract = {The relativistic configuration interaction plus many-body perturbation (RCI + MBPT) method is utilized to calculate the wave functions, energy levels, and reduced transition matrix elements of Ca atoms in detail. The static and dynamic polarizabilities of the , and states are determined by the sum-over-states method. A number of magic-zero wavelengths for the ground and states, as well as magic wavelengths for the and transitions, are obtained. We suggest that the measurements of the magic-zero wavelengths of the states can be used to determine oscillator strengths with high precision. In addition, the angle-dependent magic wavelengths of each magnetic sublevel transition of the transition are provided, which are of particular interest for optical frequency measurements, Bose-Einstein condensate generation, and superradiant laser technology.},
  file = {/Users/yingxing/Zotero/storage/A79939YU/Zhang et al. - 2023 - Magic-zero and magic wavelengths of the Ca atom.pdf}
}

@article{Zhou2021a,
  title = {Calculations of Dynamic Multipolar Polarizabilities of the {{Cd}} Clock Transition Levels*},
  author = {Zhou, Mi and Tang, Li-Yan},
  year = {2021},
  month = aug,
  journal = {Chinese Phys. B},
  volume = {30},
  number = {8},
  pages = {083102},
  publisher = {{Chinese Physical Society and IOP Publishing Ltd}},
  issn = {1674-1056},
  doi = {10.1088/1674-1056/abf0fc},
  urldate = {2024-06-10},
  abstract = {The pursuit of a systematic frequency uncertainty beyond 10-18 clock has triggered a multitude of investigations on the multipolar and higher-order lattice light shifts. The Cd atom has been proposed as a new candidate for the development of a lattice clock because of its smaller blackbody radiation shift at room temperature. Here, we apply an improved combined method of the Dirac--Fock plus core polarization and relativistic configuration interaction methods to calculate the dynamic multipolar polarizabilities of the Cd clock states. The effects of the high-order core-polarization potentials on the energies, reduced matrix elements, and multipolar polarizabilities have been evaluated systematically. The detailed comparison with available literature demonstrates that taking into account of the high-order core-polarization potentials is a simple and effective approach to improve the results of atomic properties for heavy atoms.},
  langid = {english},
  file = {/Users/yingxing/Zotero/storage/D7486YTK/Zhou_Tang_2021_Calculations of dynamic multipolar polarizabilities of the Cd clock transition.pdf}
}


@article{Holmgren2010,
	title = {Absolute and ratio measurements of the polarizability of {Na}, {K}, and {Rb} with an atom interferometer},
	volume = {81},
	url = {https://link.aps.org/doi/10.1103/PhysRevA.81.053607},
	doi = {10.1103/PhysRevA.81.053607},
	abstract = {We measured the ground-state electric-dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric-field gradient. We find αNa=24.11(2)stat(18)sys×10−24cm3, αK=43.06(14)(33), and αRb=47.24(12)(42). Since these measurements were all performed in the same apparatus and subject to the same systematic errors, we can present polarizability ratios with 0.3\% uncertainty. We find αRb/αNa=1.959(5), αK/αNa=1.786(6), and αRb/αK=1.097(5). We combine our ratio measurements with the higher-precision measurement of sodium polarizability by Ekstrom et al. [Phys. Rev. A 51, 3883 (1995)] to find αK=43.06(21) and αRb=47.24(21).},
	number = {5},
	urldate = {2023-03-20},
	journal = {Physical Review A},
	author = {Holmgren, William F. and Revelle, Melissa C. and Lonij, Vincent P. A. and Cronin, Alexander D.},
	month = may,
	year = {2010},
	note = {Publisher: American Physical Society},
	pages = {053607},
	file = {Submitted Version:/Users/yingxing/Zotero/storage/3LY2USZL/Holmgren et al. - 2010 - Absolute and ratio measurements of the polarizabil.pdf:application/pdf},
}


@misc{Schwerdtfeger2023,
	title = {2023 {Table} of static dipole polarizabilities of the neutral elements in the periodic table},
	url = {https://ctcp.massey.ac.nz/2023Tablepol.pdf},
	language = {en},
	urldate = {2024-06-06},
	journal = {2023 Table of Polarizabilities},
	author = {Schwerdtfeger, Peter and Nagle, Jeffrey K.},
	year = {2023},
}


@article{Derevianko2010,
	title = {Electric dipole polarizabilities at imaginary frequencies for hydrogen, the alkali–metal, alkaline–earth, and noble gas atoms},
	volume = {96},
	issn = {0092-640X},
	url = {https://www.sciencedirect.com/science/article/pii/S0092640X09000874},
	doi = {10.1016/j.adt.2009.12.002},
	language = {en},
	number = {3},
	urldate = {2023-03-20},
	journal = {Atomic Data and Nuclear Data Tables},
	author = {Derevianko, Andrei and Porsev, Sergey G. and Babb, James F.},
	month = may,
	year = {2010},
	pages = {323--331},
}
