This is an initial library of BibTex references for the gaussian_step plug-in for SEAMM,
generated automatically by the cookiecutter. You may wish to edit the first entry to correct some
of the information.

Add other references to the end of the file and add code in the plug-in to cite the references as
appropriate. This is done with code like this:

        self.references.cite(
            raw=self._bibliography['doi:10.1002/jcc.21224'],
            alias='packmol',
            module='packmol_step',
            level=1,
            note='The principle PACKMOL citation.'
        )

which is typically in the run() method of the plug-in.

The base node class in SEAMM automatically reads this list of references into a dictionary in
self._bibliography with the key being the key of the BibTex entry -- usually the name on the
first line of the entry after the 'article' or 'misc' (for software) keyword.

See the documentation for the Reference Handler for the other arguments to cite().

# End of initial comments #

# This is the citation for this plug-in, generated and used automatically.
# You might need to edit the author, address, etc. The month, year and version fields
# are automatically filled in with information about current version of the plug-in.
# This is handled in seamm/nody.py, the run() method.

@Misc{gaussian_step,
	author = {Paul Saxe},
	title = {Gaussian plug-in for SEAMM},
	month = {$month},
	year = {$year},
	organization = {The Molecular Sciences Software Institute (MolSSI)},
	url = {https://github.com/molssi-seamm/gaussian_step },
	address = {USA},
	version = {$version}
}
@Misc{G09,
    key = {G09},
    author = {M. J. Frisch and G. W. Trucks and H. B. Schlegel and G. E. Scuseria
	      and M. A. Robb and J. R. Cheeseman and G. Scalmani and V. Barone and
	      B. Mennucci and G. A. Petersson and H. Nakatsuji and M. Caricato and
	      X. Li and H. P. Hratchian and A. F. Izmaylov and J. Bloino and
	      G. Zheng and J. L. Sonnenberg and M. Hada and M. Ehara and K. Toyota
	      and R. Fukuda and J. Hasegawa and M. Ishida and T. Nakajima and
	      Y. Honda and O. Kitao and H. Nakai and T. Vreven and J. A. Montgomery
	      Jr. and J. E. Peralta and F. Ogliaro and M. Bearpark and
	      J. J. Heyd and E. Brothers and K. N. Kudin and V. N. Staroverov and
	      T. Keith and R. Kobayashi and J. Normand and K. Raghavachari and
	      A. Rendell and J. C. Burant and S. S. Iyengar and J. Tomasi and
	      M. Cossi and N. Rega and J. M. Millam and M. Klene and J. E. Knox and
	      J. B. Cross and V. Bakken and C. Adamo and J. Jaramillo and
	      R. Gomperts and R. E. Stratmann and O. Yazyev and A. J. Austin and
	      R. Cammi and C. Pomelli and J. W. Ochterski and R. L. Martin and
	      K. Morokuma and V. G. Zakrzewski and G. A. Voth and P. Salvador and
	      J. J. Dannenberg and S. Dapprich and A. D. Daniels and O. Farkas and
	      J. B. Foresman and J. V. Ortiz and J. Cioslowski and D. J. Fox},
    title = {Gaussian 09},
    month = {$month},
    year = {$year},
    organization = {Gaussian, Inc.},
    url = {https://gaussian.com},
    address = {340 Quinnipiac St., Bldg. 40, Wallingford CT 06492},
    version = {$version},
}
@Misc{G16,
    key = {G16},
    author={M. J. Frisch and G. W. Trucks and H. B. Schlegel and G. E. Scuseria and
	      M. A. Robb and J. R. Cheeseman and G. Scalmani and V. Barone and
	      G. A. Petersson and H. Nakatsuji and X. Li and M. Caricato and
	      A. V. Marenich and J. Bloino and B. G. Janesko and R. Gomperts and
	      B. Mennucci and H. P. Hratchian and J. V. Ortiz and A. F. Izmaylov and
	      J. L. Sonnenberg and D. Williams-Young and F. Ding and F. Lipparini
	      and F. Egidi and J. Goings and B. Peng and A. Petrone and T. Henderson
	      and D. Ranasinghe and V. G. Zakrzewski and J. Gao and N. Rega and
	      G. Zheng and W. Liang and M. Hada and M. Ehara and K. Toyota and
	      R. Fukuda and J. Hasegawa and M. Ishida and T. Nakajima and Y. Honda
	      and O. Kitao and H. Nakai and T. Vreven and K. Throssell and
	      Montgomery, {Jr.}, J. A. and J. E. Peralta and F. Ogliaro and
	      M. J. Bearpark and J. J. Heyd and E. N. Brothers and K. N. Kudin and
	      V. N. Staroverov and T. A. Keith and R. Kobayashi and J. Normand and
	      K. Raghavachari and A. P. Rendell and J. C. Burant and S. S. Iyengar
	      and J. Tomasi and M. Cossi and J. M. Millam and M. Klene and C. Adamo
	      and R. Cammi and J. W. Ochterski and R. L. Martin and K. Morokuma and
	      O. Farkas and J. B. Foresman and D. J. Fox},
    title = {Gaussian 16},
    month = {$month},
    year = {$year},
    organization = {Gaussian, Inc.},
    url = {https://gaussian.com},
    address = {340 Quinnipiac St., Bldg. 40, Wallingford CT 06492},
    version = {$version},
note={Gaussian Inc. Wallingford CT}
}

@article{10.1063/1.1760074,
    author = {Heyd, Jochen and Scuseria, Gustavo E.},
    title = {Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional},
    journal = {The Journal of Chemical Physics},
    volume = {121},
    number = {3},
    pages = {1187-1192},
    year = {2004},
    month = {07},
    abstract = {The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree–Fock (HF) exchange used in the Heyd–Scuseria–Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50\% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2–4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.},
    issn = {0021-9606},
    doi = {10.1063/1.1760074},
    url = {https://doi.org/10.1063/1.1760074},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/121/3/1187/19171502/1187\_1\_online.pdf},
}

@article{10.1063/1.1668634,
    author = {Heyd, Jochen and Scuseria, Gustavo E.},
    title = {Assessment and validation of a screened Coulomb hybrid density functional},
    journal = {The Journal of Chemical Physics},
    volume = {120},
    number = {16},
    pages = {7274-7280},
    year = {2004},
    month = {04},
    abstract = {This paper presents a revised and improved version of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional. The performance of this functional is assessed on a variety of molecules for the prediction of enthalpies of formation, geometries, and vibrational frequencies, yielding results as good as or better than the successful PBE0 hybrid functional. Results for ionization potentials and electron affinities are of slightly lower quality but are still acceptable. The comprehensive test results presented here validate our assumption that the screened, short-range Hartree–Fock (HF) exchange exhibits all physically relevant properties of the full HF exchange. Thus, hybrids can be constructed which neglect the computationally demanding long-range part of HF exchange while still retaining the superior accuracy of hybrid functionals, compared to pure density functionals.},
    issn = {0021-9606},
    doi = {10.1063/1.1668634},
    url = {https://doi.org/10.1063/1.1668634},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/120/16/7274/19162606/7274\_1\_online.pdf},
}

@article{10.1063/1.2085170,
    author = {Heyd, Jochen and Peralta, Juan E. and Scuseria, Gustavo E. and Martin, Richard L.},
    title = {Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional},
    journal = {The Journal of Chemical Physics},
    volume = {123},
    number = {17},
    pages = {174101},
    year = {2005},
    month = {10},
    abstract = { This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 Å for HSE vs 0.047 Å for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0–1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations. },
    issn = {0021-9606},
    doi = {10.1063/1.2085170},
    url = {https://doi.org/10.1063/1.2085170},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2085170/16716890/174101\_1\_online.pdf},
}

@article{10.1063/1.2204597,
    author = {Heyd, Jochen and Scuseria, Gustavo E. and Ernzerhof, Matthias},
    title = {Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)]},
    journal = {The Journal of Chemical Physics},
    volume = {124},
    number = {21},
    pages = {219906},
    year = {2006},
    month = {06},
    abstract = {Optimization of a single value of ω for a functional of the type reported in this paper will be presented elsewhere. We thank Oleg Vydrov and Artur Izmaylov for finding this error.This erratum applies to all of our ωPBEh and HSE calculations published to date. We emphasize, however, that all our results obtained with this functional are reproducible using the two ω values quoted above. The validity of all our published HSE values is not affected.},
    issn = {0021-9606},
    doi = {10.1063/1.2204597},
    url = {https://doi.org/10.1063/1.2204597},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2204597/15387022/219906\_1\_online.pdf},
}

@article{10.1063/1.3185673,
    author = {Henderson, Thomas M. and Izmaylov, Artur F. and Scalmani, Giovanni and Scuseria, Gustavo E.},
    title = {Can short-range hybrids describe long-range-dependent properties?},
    journal = {The Journal of Chemical Physics},
    volume = {131},
    number = {4},
    pages = {044108},
    year = {2009},
    month = {07},
    abstract = {Long-range-corrected hybrids, which incorporate all of the long-range exact exchange interaction, improve performance for a host of molecular properties. The long-range portion of exact exchange is both computationally and formally problematic in solids, and screened hybrids therefore eliminate it. While screened hybrids give similar results to their parent global hybrids for many molecular properties, one may worry that they perform poorly for those properties that are improved by the long-range-correction procedure. In this paper, we show that at least for the Heyd–Scuseria–Ernzerhof (HSE) screened hybrid, this is not the case; for many properties improved by long-range-correction, screened hybrids and global hybrids deliver essentially the same results. We suggest that this is because screened hybrids and global hybrids have fundamentally the same many-electron self-interaction error. We also introduce some small revisions to our computational implementation of the HSE screened hybrid, and we recommend these revisions for future applications of HSE.},
    issn = {0021-9606},
    doi = {10.1063/1.3185673},
    url = {https://doi.org/10.1063/1.3185673},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.3185673/15635537/044108\_1\_online.pdf},
}

@article{10.1063/1.2347713,
    author = {Izmaylov, Artur F. and Scuseria, Gustavo E. and Frisch, Michael J.},
    title = {Efficient evaluation of short-range Hartree-Fock exchange in large molecules and periodic systems},
    journal = {The Journal of Chemical Physics},
    volume = {125},
    number = {10},
    pages = {104103},
    year = {2006},
    month = {09},
    abstract = {We present an efficient algorithm for the evaluation of short-range Hartree-Fock exchange energies and geometry gradients in Gaussian basis sets. Our method uses a hierarchy of screening levels to eliminate negligible two-electron integrals whose evaluation is the fundamental computational bottleneck of the procedure. By applying our screening technique to the Heyd-Scuseria-Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] short-range Coulomb hybrid density functional, we achieve a computational efficiency comparable with that of standard nonhybrid density functional calculations.},
    issn = {0021-9606},
    doi = {10.1063/1.2347713},
    url = {https://doi.org/10.1063/1.2347713},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2347713/15387883/104103\_1\_online.pdf},
}

@article{10.1063/1.2404663,
    author = {Krukau, Aliaksandr V. and Vydrov, Oleg A. and Izmaylov, Artur F. and Scuseria, Gustavo E.},
    title = {Influence of the exchange screening parameter on the performance of screened hybrid functionals},
    journal = {The Journal of Chemical Physics},
    volume = {125},
    number = {22},
    pages = {224106},
    year = {2006},
    month = {12},
    abstract = {This work reexamines the effect of the exchange screening parameter ω on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional. We show that variation of the screening parameter influences solid band gaps the most. Other properties such as molecular thermochemistry or lattice constants of solids change little with ω. We recommend a new version of HSE with the screening parameter ω=0.11bohr−1 for further use. Compared to the original implementation, the new parametrization yields better thermochemical results and preserves the good accuracy for band gaps and lattice constants in solids.},
    issn = {0021-9606},
    doi = {10.1063/1.2404663},
    url = {https://doi.org/10.1063/1.2404663},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2404663/13263224/224106\_1\_online.pdf},
}

@article{10.1063/1.478522,
    author = {Adamo, Carlo and Barone, Vincenzo},
    title = {Toward reliable density functional methods without adjustable parameters: The PBE0 model},
    journal = {The Journal of Chemical Physics},
    volume = {110},
    number = {13},
    pages = {6158-6170},
    year = {1999},
    month = {04},
    abstract = {We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.},
    issn = {0021-9606},
    doi = {10.1063/1.478522},
    url = {https://doi.org/10.1063/1.478522},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/110/13/6158/19068890/6158\_1\_online.pdf},
}

@article{10.1063/1.476928,
    author = {Ernzerhof, Matthias and Perdew, John P.},
    title = {Generalized gradient approximation to the angle- and system-averaged exchange hole},
    journal = {The Journal of Chemical Physics},
    volume = {109},
    number = {9},
    pages = {3313-3320},
    year = {1998},
    month = {09},
    abstract = {A simple analytic model is proposed for the angle- and system-averaged exchange hole of a many-electron system. The model hole depends on the local density and density gradient. It recovers a nonoscillatory local-spin density (LSD) approximation to the exchange hole for a vanishing density gradient. The model hole reproduces the exchange energy density of the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) for exchange, and facilitates a detailed understanding of the PBE GGA. The hole model is applied to atoms and molecules, and a comparison is made to exact and LSD angle- and system-averaged exchange holes. We find that the GGA hole model significantly improves upon the LSD model. Furthermore, the GGA hole model accurately describes the change in the exchange hole upon the formation of single bonds, but is less accurate for the formation of multiple bonds, where it misses the appearance of a long-range tail.},
    issn = {0021-9606},
    doi = {10.1063/1.476928},
    url = {https://doi.org/10.1063/1.476928},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/109/9/3313/19115007/3313\_1\_online.pdf},
}

@article{doi:10.1021/j100096a001,
    author = {Stephens, P. J. and Devlin, F. J. and Chabalowski, C. F. and Frisch, M. J.},
    title = {Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields},
    journal = {The Journal of Physical Chemistry},
    volume = {98},
    number = {45},
    pages = {11623-11627},
    year = {1994},
    doi = {10.1021/j100096a001},
    URL = {https://doi.org/10.1021/j100096a001},
    eprint = {https://doi.org/10.1021/j100096a001}
}

@article{10.1063/1.464913,
    author = {Becke, Axel D.},
    title = {Density‐functional thermochemistry. III. The role of exact exchange},
    journal = {The Journal of Chemical Physics},
    volume = {98},
    number = {7},
    pages = {5648-5652},
    year = {1993},
    month = {04},
    abstract = {Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.},
    issn = {0021-9606},
    doi = {10.1063/1.464913},
    url = {https://doi.org/10.1063/1.464913},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/98/7/5648/19277469/5648\_1\_online.pdf},
}

@article{PhysRevLett.77.3865,
  title = {Generalized Gradient Approximation Made Simple},
  author = {Perdew, John P. and Burke, Kieron and Ernzerhof, Matthias},
  journal = {Phys. Rev. Lett.},
  volume = {77},
  issue = {18},
  pages = {3865--3868},
  numpages = {0},
  year = {1996},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.77.3865},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.77.3865}
}

@article{PhysRevLett.78.1396,
  title = {Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]},
  author = {Perdew, John P. and Burke, Kieron and Ernzerhof, Matthias},
  journal = {Phys. Rev. Lett.},
  volume = {78},
  issue = {7},
  pages = {1396--1396},
  numpages = {0},
  year = {1997},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.78.1396},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.78.1396}
}

@article{PhysRev.136.B864,
  title = {Inhomogeneous Electron Gas},
  author = {Hohenberg, P. and Kohn, W.},
  journal = {Phys. Rev.},
  volume = {136},
  issue = {3B},
  pages = {B864--B871},
  numpages = {0},
  year = {1964},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.136.B864},
  url = {https://link.aps.org/doi/10.1103/PhysRev.136.B864}
}

@article{PhysRev.140.A1133,
  title = {Self-Consistent Equations Including Exchange and Correlation Effects},
  author = {Kohn, W. and Sham, L. J.},
  journal = {Phys. Rev.},
  volume = {140},
  issue = {4A},
  pages = {A1133--A1138},
  numpages = {0},
  year = {1965},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.140.A1133},
  url = {https://link.aps.org/doi/10.1103/PhysRev.140.A1133}
}

@article{RevModPhys.23.69,
  title = {New Developments in Molecular Orbital Theory},
  author = {Roothaan, C. C. J.},
  journal = {Rev. Mod. Phys.},
  volume = {23},
  issue = {2},
  pages = {69--89},
  numpages = {0},
  year = {1951},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/RevModPhys.23.69},
  url = {https://link.aps.org/doi/10.1103/RevModPhys.23.69}
}

@article{berthier1954extension,
  title={Extension de la methode du champ moleculaire self-consistent a letude des etats a couches incompletes},
  author={Berthier, Gaston},
  journal={COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES},
  volume={238},
  number={1},
  pages={91--93},
  year={1954},
  publisher={GAUTHIER-VILLARS/EDITIONS ELSEVIER 23 RUE LINOIS, 75015 PARIS, FRANCE}
}

@article{10.1063/1.1740120,
    author = {Pople, J. A. and Nesbet, R. K.},
    title = {Self‐Consistent Orbitals for Radicals},
    journal = {The Journal of Chemical Physics},
    volume = {22},
    number = {3},
    pages = {571-572},
    year = {1954},
    month = {03},
    issn = {0021-9606},
    doi = {10.1063/1.1740120},
    url = {https://doi.org/10.1063/1.1740120},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/22/3/571/18804555/571\_1\_online.pdf},
}

@article{PhysRev.46.618,
  title = {Note on an Approximation Treatment for Many-Electron Systems},
  author = {M\o{}ller, Chr. and Plesset, M. S.},
  journal = {Phys. Rev.},
  volume = {46},
  issue = {7},
  pages = {618--622},
  numpages = {0},
  year = {1934},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.46.618},
  url = {https://link.aps.org/doi/10.1103/PhysRev.46.618}
}

@article{FRISCH1990275,
title = {A direct MP2 gradient method},
journal = {Chemical Physics Letters},
volume = {166},
number = {3},
pages = {275-280},
year = {1990},
issn = {0009-2614},
doi = {https://doi.org/10.1016/0009-2614(90)80029-D},
url = {https://www.sciencedirect.com/science/article/pii/000926149080029D},
author = {Michael J. Frisch and Martin Head-Gordon and John A. Pople},
abstract = {We present a direct method for evaluating the gradient of the second-order Møller-Plesset (MP2) energy without storing any quartic quantities, such as two-electron repulsion integrals (ERIs), double substitution amplitudes or the two-particle density matrix. For an N-basis-function calculation, N3 memory is required, and the ERIs and their first derivatives are computed up to O (number of occupied orbitals) times, plus additional ERI evaluations to obtain the Hartree-Fock (HF) orbitals and solve the coupled perturbed HF equation. Larger amounts of memory are used to reduce the O evaluations in the MP2 step. The floating point operation count is still proportional to ON4, as in conventional MP2 gradient codes since ERI evaluation is just an N4 step. Illustrative calculations are reported to assess the performance of the algorithm.}
}

@article{https://doi.org/10.1002/qua.560100802,
author = {Pople, John A. and Binkley, J. Stephen and Seeger, Rolf},
title = {Theoretical models incorporating electron correlation},
journal = {International Journal of Quantum Chemistry},
volume = {10},
number = {S10},
pages = {1-19},
doi = {https://doi.org/10.1002/qua.560100802},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.560100802},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560100802},
abstract = {Abstract Some methods of describing electron correlation are compared from the point of view of requirements for theoretical chemical models. The perturbation approach originally introduced by Møller and Plesset, terminated at finite order, is found to satisfy most of these requirements. It is size consistent, that is, applicable to an ensemble of isolated systems in an additive manner. On the other hand, it does not provide an upper bound for the electronic energy. The independent electron-pair approximation is accurate to second order in a Møller-Plesset expansion, but inaccurate in third order. A series of variational methods is discussed which gives upper bounds for the energy, but which lacks size consistency. Finally, calculations on some small molecules using a moderately large Gaussian basis are presented to illustrate these points. Equilibrium geometries, dissociation energies, and energy separations between electronic states of different spin multiplicities are described substantially better by Moller-Plesset theory to second or third order than by Hartree-Fock theory.},
year = {1976}
}

@article{https://doi.org/10.1002/qua.560120820,
author = {Pople, J. A. and Seeger, R. and Krishnan, R.},
title = {Variational configuration interaction methods and comparison with perturbation theory},
journal = {International Journal of Quantum Chemistry},
volume = {12},
number = {S11},
pages = {149-163},
doi = {https://doi.org/10.1002/qua.560120820},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.560120820},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560120820},
abstract = {Abstract A configuration interaction (Cl) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Møller-Plesset perturbation results to second and third order are obtained in the first Cl iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final Cl energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these Cl methods with perturbation theory.},
year = {1977}
}

@article{https://doi.org/10.1002/qua.560140109,
author = {Krishnan, R. and Pople, J. A.},
title = {Approximate fourth-order perturbation theory of the electron correlation energy},
journal = {International Journal of Quantum Chemistry},
volume = {14},
number = {1},
pages = {91-100},
doi = {https://doi.org/10.1002/qua.560140109},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.560140109},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560140109},
abstract = {Abstract An approximate fourth-order expression for the electron correlation energy in the Møller–Plesset perturbation scheme is proposed. It takes into account all the contributions to the fourthorder energy neglecting only those of the triple-substituted determinants. It is size consistent and correct to fourth order for an assembly of isolated two-electron systems. Illustrative calculations are reported for a series of small molecules.},
year = {1978}
}

@article{10.1063/1.439657,
    author = {Krishnan, R. and Frisch, M. J. and Pople, J. A.},
    title = {Contribution of triple substitutions to the electron correlation energy in fourth order perturbation theory},
    journal = {The Journal of Chemical Physics},
    volume = {72},
    number = {7},
    pages = {4244-4245},
    year = {1980},
    month = {04},
    issn = {0021-9606},
    doi = {10.1063/1.439657},
    url = {https://doi.org/10.1063/1.439657},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/72/7/4244/18921599/4244\_1\_online.pdf},
}

@article{doi:10.1021/j100377a033,
    author = {Raghavachari, Krishnan. and Pople, John A. and Replogle, Eric S. and Head-Gordon, Martin.},
    title = {Fifth order Moeller-Plesset perturbation theory:  comparison of existing correlation methods and implementation of new methods correct to fifth order},
    journal = {The Journal of Physical Chemistry},
    volume = {94},
    number = {14},
    pages = {5579-5586},
    year = {1990},
    doi = {10.1021/j100377a033},
    URL = {https://doi.org/10.1021/j100377a033},
    eprint = {https://doi.org/10.1021/j100377a033}
}

@article{10.1063/1.453520,
    author = {Pople, John A. and Head‐Gordon, Martin and Raghavachari, Krishnan},
    title = {Quadratic configuration interaction. A general technique for determining electron correlation energies},
    journal = {The Journal of Chemical Physics},
    volume = {87},
    number = {10},
    pages = {5968-5975},
    year = {1987},
    month = {11},
    abstract = {A general procedure is introduced for calculation of the electron correlation energy, starting from a single Hartree–Fock determinant. The normal equations of (linear) configuration interaction theory are modified by introducing new terms which are quadratic in the configuration coefficients and which ensure size consistency in the resulting total energy. When used in the truncated configuration space of single and double substitutions, the method, termed QCISD, leads to a tractable set of quadratic equations. The relation of this method to coupled‐cluster (CCSD) theory is discussed. A simplified method of adding corrections for triple substitutions is outlined, leading to a method termed QCISD(T). Both of these new procedures are tested (and compared with other procedures) by application to some small systems for which full configuration interaction results are available.},
    issn = {0021-9606},
    doi = {10.1063/1.453520},
    url = {https://doi.org/10.1063/1.453520},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/87/10/5968/18967386/5968\_1\_online.pdf},
}

@article{https://doi.org/10.1002/qua.560140504,
author = {Bartlett, Rodney J. and Purvis, George D.},
title = {Many-body perturbation theory, coupled-pair many-electron theory, and the importance of quadruple excitations for the correlation problem},
journal = {International Journal of Quantum Chemistry},
volume = {14},
number = {5},
pages = {561-581},
doi = {https://doi.org/10.1002/qua.560140504},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.560140504},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560140504},
abstract = {Abstract Many-body (diagrammatic) perturbation theory (MBPT), coupled-pair many-electron theory (CPMET), and configuration interaction (CI) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO2, HCN, N2, CO, BH3, and NH3. It is demonstrated that the sum of double and quadruple excitation diagrams through fourth-order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the 1∑ potential curve of Be2. This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R. This is resolved once the quadruple excitation terms are fully included by CPMET.},
year = {1978}
}

@article{https://doi.org/10.1002/qua.560140503,
author = {Pople, J. A. and Krishnan, R. and Schlegel, H. B. and Binkley, J. S.},
title = {Electron correlation theories and their application to the study of simple reaction potential surfaces},
journal = {International Journal of Quantum Chemistry},
volume = {14},
number = {5},
pages = {545-560},
doi = {https://doi.org/10.1002/qua.560140503},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.560140503},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560140503},
abstract = {Abstract This paper serves two purposes. The first is to describe an implementation of the coupled cluster theory with double substitutions (CCD) previously developed by Cizek. The second is to apply this method and closely related fourth-order perturbation methods to some simple molecules and reaction potential surfaces. These studies show that CCD theory gives results close to those of a Møller-Plesset perturbation treatment to fourth order in the space of double and quadruple substitutions MP4(DQ). Addition of contributions from single substitutions at fourth order makes little change in predicted relative energies. Preliminary results on the potential surfaces for 1,2-hydrogen shifts in C2H2, HCN, CH2O, and N2H2 are discussed and compared with previous studies.},
year = {1978}
}

@inbook{doi:https://doi.org/10.1002/9780470143599.ch2,
author = {Čížek, Jiří},
publisher = {John Wiley & Sons, Ltd},
isbn = {9780470143599},
title = {On the Use of the Cluster Expansion and the Technique of Diagrams in Calculations of Correlation Effects in Atoms and Molecules},
booktitle = {Advances in Chemical Physics},
chapter = {},
pages = {35-89},
doi = {https://doi.org/10.1002/9780470143599.ch2},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/9780470143599.ch2},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470143599.ch2},
year = {1969},
keywords = {cluster expansion, hole-particle formalism, graphology suppliments, Wick's theorem, Schrödinger equation transformation},
abstract = {Summary This chapter contains sections titled: Introduction Basic Terms and Definitions Introduction to “Graphology“ Equations for Matrix Elements of the Operator T̂ The Evaluation of the Mean Values of One- and Two-Particle Operators Final Remarks}
}

@article{10.1063/1.443164,
    author = {Purvis, George D., III and Bartlett, Rodney J.},
    title = {A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples},
    journal = {The Journal of Chemical Physics},
    volume = {76},
    number = {4},
    pages = {1910-1918},
    year = {1982},
    month = {02},
    abstract = {The coupled‐cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher‐order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98\% of the full CI correlation energy. For H2O, CCSD plus the fourth‐order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low‐order models provide estimates of the effect of the higher‐order terms T1T2, T21T2, T31, and T41 on the correlation energy.},
    issn = {0021-9606},
    doi = {10.1063/1.443164},
    url = {https://doi.org/10.1063/1.443164},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/76/4/1910/18935003/1910\_1\_online.pdf},
}

@article{10.1063/1.477924,
    author = {Montgomery, J. A., Jr. and Frisch, M. J. and Ochterski, J. W. and Petersson, G. A.},
    title = {A complete basis set model chemistry. VI. Use of density functional geometries and frequencies},
    journal = {The Journal of Chemical Physics},
    volume = {110},
    number = {6},
    pages = {2822-2827},
    year = {1999},
    month = {02},
    abstract = {The recently introduced complete basis set, CBS-Q, model chemistry is modified to use B3LYP hybrid density functional geometries and frequencies, which give both improved reliability (maximum error for the G2 test set reduced from 3.9 to 2.8 kcal/mol) and increased accuracy (mean absolute error reduced from 0.98 to 0.87 kcal/mol), with little penalty in computational speed. The use of a common method for geometries and frequencies makes the modified model applicable to transition states for chemical reactions.},
    issn = {0021-9606},
    doi = {10.1063/1.477924},
    url = {https://doi.org/10.1063/1.477924},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/110/6/2822/19050678/2822\_1\_online.pdf},
}

@article{10.1063/1.481224,
    author = {Montgomery, J. A., Jr. and Frisch, M. J. and Ochterski, J. W. and Petersson, G. A.},
    title = {A complete basis set model chemistry. VII. Use of the minimum population localization method},
    journal = {The Journal of Chemical Physics},
    volume = {112},
    number = {15},
    pages = {6532-6542},
    year = {2000},
    month = {04},
    abstract = {It is shown that localization is necessary to preserve size consistency in nonlinear extrapolations of molecular energies. We demonstrate that the unphysical behavior of Mulliken populations obtained from extended basis set wave functions can lead to incomplete localization of orbitals by the Pipek–Mezey population localization method, and introduce a modification to correct this problem. The new localization procedure, called minimum population localization, is incorporated into the CBS-QB3 and the new CBS-4M model chemistries, and their performance is assessed on the G2/97 test set. The errors found for CBS-QB3 are comparable with those for the G3 and G3(MP2) (mean absolute deviation of 1.10, 0.94, and 1.21 kcal/mol, respectively, on the G2/97 test set). The CBS-4M is less accurate than the other models (mean absolute deviation of 3.26 kcal/mol on the G2/97 test set), but can be applied to much larger systems. The modified localization method resolves several problem cases found with CBS-4 and improves the reliability of CBS-QB3.},
    issn = {0021-9606},
    doi = {10.1063/1.481224},
    url = {https://doi.org/10.1063/1.481224},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/112/15/6532/19237155/6532\_1\_online.pdf},
}

@article{10.1063/1.470985,
    author = {Ochterski, Joseph W. and Petersson, G. A. and Montgomery, J. A., Jr.},
    title = {A complete basis set model chemistry. V. Extensions to six or more heavy atoms},
    journal = {The Journal of Chemical Physics},
    volume = {104},
    number = {7},
    pages = {2598-2619},
    year = {1996},
    month = {02},
    abstract = {The major source of error in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. Extrapolation to the complete basis set second‐order (CBS2) limit using the N−1 asymptotic convergence of N‐configuration pair natural orbital (PNO) expansions can be combined with the use of relatively small basis sets for the higher‐order (i.e., MP3, MP4, and QCI) correlation energy to develop cost effective computational models. Following this strategy, three new computational models denoted CBS‐4, CBS‐q, and CBS‐Q, are introduced. The mean absolute deviations (MAD) from experiment for the 125 energies of the G2 test set are 2.0, 1.7, and 1.0 kcal/mol, respectively. These results compare favorably with the MAD for the more costly G2(MP2), G2, and CBS‐QCI/APNO models (1.6, 1.2, and 0.5 kcal/mol, respectively). The error distributions over the G2 test set are indistinguishable from Gaussian distribution functions for all six models, indicating that the rms errors can be interpreted in the same way that experimental uncertainties are used to assess reliability.However, a broader range of examples reveals special difficulties presented by spin contamination, high molecular symmetry, and localization problems in molecules with multiple lone pairs on the same atom. These characteristics can occasionally result in errors several times the size expected from the Gaussian distributions. Each of the CBS models has a range of molecular size for which it is the most accurate computational model currently available. The largest calculations reported for these models include: The CBS‐4 heat of formation of tetranitrohydrazine (91.5±5 kcal/mol), the CBS‐4 and CBS‐q isomerization energies for the conversion of azulene to naphthalene (ΔHcalc=−35.2±1.0 kcal/mol, ΔHexp=−35.3±2.2 kcal/mol), and the CBS‐Q heat of formation of SF6 (ΔHcalc=−286.6±1.3 kcal/mol, ΔHexp=−288.3±0.2 kcal/mol). The CBS‐Q value for the dissociation energy of a C–H bond in benzene (113.1±1.3 kcal/mol) is also in agreement with the most recent experimental result (112.0±0.6 kcal/mol). The CBS‐QCI/APNO model is applicable to the prediction of the C–H bond dissociation energies for the primary (100.7±0.7 kcal/mol calc.) and secondary (97.7±0.7 kcal/mol calc., 97.1±0.4 kcal/mol exp.) hydrogens of propane.},
    issn = {0021-9606},
    doi = {10.1063/1.470985},
    url = {https://doi.org/10.1063/1.470985},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/104/7/2598/19069701/2598\_1\_online.pdf},
}

@article{10.1063/1.456415,
    author = {Pople, John A. and Head‐Gordon, Martin and Fox, Douglas J. and Raghavachari, Krishnan and Curtiss, Larry A.},
    title = {Gaussian‐1 theory: A general procedure for prediction of molecular energies},
    journal = {The Journal of Chemical Physics},
    volume = {90},
    number = {10},
    pages = {5622-5629},
    year = {1989},
    month = {05},
    abstract = {A general procedure is developed for the computation of the total energies of molecules at their equilibrium geometries. Ab initio molecular orbital theory is used to calculate electronic energies by a composite method, utilizing large basis sets (including diffuse‐sp, double‐d and f‐polarization functions) and treating electron correlation by Mo/ller–Plesset perturbation theory and by quadratic configuration interaction. The theory is also used to compute zero‐point vibrational energy corrections. Total atomization energies for a set of 31 molecules are found to agree with experimental thermochemical data to an accuracy greater than 2 kcal mol−1 in most cases. Similar agreement is achieved for ionization energies, electron and proton affinities. Residual errors are assessed for the total energies of neutral atoms.},
    issn = {0021-9606},
    doi = {10.1063/1.456415},
    url = {https://doi.org/10.1063/1.456415},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/90/10/5622/18976621/5622\_1\_online.pdf},
}

@article{10.1063/1.458892,
    author = {Curtiss, Larry A. and Jones, Christopher and Trucks, Gary W. and Raghavachari, Krishnan and Pople, John A.},
    title = {Gaussian‐1 theory of molecular energies for second‐row compounds},
    journal = {The Journal of Chemical Physics},
    volume = {93},
    number = {4},
    pages = {2537-2545},
    year = {1990},
    month = {08},
    abstract = {The Gaussian‐1 theoretical procedure is extended and tested on compounds containing second‐row atoms (Na–Cl). This is a composite procedure based on ab initio molecular orbital theory, utilizing large basis sets (including diffuse‐sp, double‐d, and f‐polarization functions) and treating electron correlation by Mo/ller–Plesset perturbation theory and by quadratic configuration interaction. Total atomization energies for a set of 24 species agree with accurate experimental data to an accuracy of better than 3 kcal/mol in most cases, SO2 being the notable exception. Similar agreement is achieved for ionization energies, electron affinities, and proton affinities. The method is used to assess experimental data for a number of other compounds having less accurate atomization energies.},
    issn = {0021-9606},
    doi = {10.1063/1.458892},
    url = {https://doi.org/10.1063/1.458892},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/93/4/2537/18987374/2537\_1\_online.pdf},
}

@article{10.1063/1.460205,
    author = {Curtiss, Larry A. and Raghavachari, Krishnan and Trucks, Gary W. and Pople, John A.},
    title = {Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds},
    journal = {The Journal of Chemical Physics},
    volume = {94},
    number = {11},
    pages = {7221-7230},
    year = {1991},
    month = {06},
    abstract = {The Gaussian‐2 theoretical procedure (G2 theory), based on ab initio molecular orbital theory, for calculation of molecular energies (atomization energies, ionization potentials, electron affinities, and proton affinities) of compounds containing first‐ (Li–F) and second‐row atoms (Na–Cl) is presented. This new theoretical procedure adds three features to G1 theory [J. Chem. Phys. 90, 5622 (1989)] including a correction for nonadditivity of diffuse‐sp and 2df basis set extensions, a basis set extension containing a third d function on nonhydrogen and a second p function on hydrogen atoms, and a modification of the higher level correction. G2 theory is a significant improvement over G1 theory because it eliminates a number of deficiencies present in G1 theory. Of particular importance is the improvement in atomization energies of ionic molecules such as LiF and hydrides such as C2H6, NH3, N2H4, H2O2, and CH3SH. The average absolute deviation from experiment of atomization energies of 39 first‐row compounds is reduced from 1.42 to 0.92 kcal/mol. In addition, G2 theory gives improved performance for hypervalent species and electron affinities of second‐row species (the average deviation from experiment of electron affinities of second‐row species is reduced from 1.94 to 1.08 kcal/mol). Finally, G2 atomization energies for another 43 molecules, not previously studied with G1 theory, many of which have uncertain experimental data, are presented and differences with experiment are assessed.},
    issn = {0021-9606},
    doi = {10.1063/1.460205},
    url = {https://doi.org/10.1063/1.460205},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/94/11/7221/18992981/7221\_1\_online.pdf},
}

@article{10.1063/1.477422,
    author = {Curtiss, Larry A. and Raghavachari, Krishnan and Redfern, Paul C. and Rassolov, Vitaly and Pople, John A.},
    title = {Gaussian-3 (G3) theory for molecules containing first and second-row atoms},
    journal = {The Journal of Chemical Physics},
    volume = {109},
    number = {18},
    pages = {7764-7776},
    year = {1998},
    month = {11},
    abstract = {Gaussian-3 theory (G3 theory) for the calculation of molecular energies of compounds containing first (Li–F) and second row (Na–Cl) atoms is presented. This new theoretical procedure, which is based on ab initio molecular-orbital theory, modifies G2 theory [J. Chem. Phys. 94, 7221 (1991)] in several ways including a new sequence of single point energy calculations using different basis sets, a new formulation of the higher level correction, a spin–orbit correction for atoms, and a correction for core correlation. G3 theory is assessed using 299 energies from the G2/97 test set including enthalpies of formation, ionization potentials, electron affinities, and proton affinities. This new procedure corrects many of the deficiencies of G2 theory. There is a large improvement for nonhydrogen systems such as SiF4 and CF4, substituted hydrocarbons, and unsaturated cyclic species. Core-related correlation is found to be a significant factor, especially for species with unsaturated rings. The average absolute deviation from experiment for the 148 calculated enthalpies of formation is reduced to under one kcal/mol, from 1.56 kcal/mol for G2 theory to 0.94 kcal/mol for G3 theory. Significant improvement is also found for ionization potentials and electron affinities. The overall average absolute deviation of G3 theory from experiment for the 299 energies is 1.02 kcal/mol compared to 1.48 kcal/mol for G2 theory.},
    issn = {0021-9606},
    doi = {10.1063/1.477422},
    url = {https://doi.org/10.1063/1.477422},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/109/18/7764/19114603/7764\_1\_online.pdf},
}

@article{10.1063/1.2436888,
    author = {Curtiss, Larry A. and Redfern, Paul C. and Raghavachari, Krishnan},
    title = {Gaussian-4 theory},
    journal = {The Journal of Chemical Physics},
    volume = {126},
    number = {8},
    pages = {084108},
    year = {2007},
    month = {02},
    abstract = {The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li–F), second- (Na–Cl), and third-row main group (K, Ca, and Ga–Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five ways. First, an extrapolation procedure is used to obtain the Hartree-Fock limit for inclusion in the total energy calculation. Second, the d-polarization sets are increased to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the latter. Third, the QCISD(T) method is replaced by the CCSD(T) method for the highest level of correlation treatment. Fourth, optimized geometries and zero-point energies are obtained with the B3LYP density functional. Fifth, two new higher level corrections are added to account for deficiencies in the energy calculations. The new method is assessed on the 454 experimental energies in the G3∕05 test set [L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys. 123, 124107 (2005)], and the average absolute deviation from experiment shows significant improvement from 1.13kcal∕mol (G3 theory) to 0.83kcal∕mol (G4 theory). The largest improvement is found for 79 nonhydrogen systems (2.10kcal∕mol for G3 versus 1.13kcal∕mol for G4). The contributions of the new features to this improvement are analyzed and the performance on different types of energies is discussed.},
    issn = {0021-9606},
    doi = {10.1063/1.2436888},
    url = {https://doi.org/10.1063/1.2436888},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2436888/15395680/084108\_1\_online.pdf},
}

@article{10.1063/1.464297,
    author = {Curtiss, Larry A. and Raghavachari, Krishnan and Pople, John A.},
    title = {Gaussian‐2 theory using reduced Mo/ller–Plesset orders},
    journal = {The Journal of Chemical Physics},
    volume = {98},
    number = {2},
    pages = {1293-1298},
    year = {1993},
    month = {01},
    abstract = {Two variations of Gaussian‐2 (G2) theory are presented. In the first, referred to as G2 (MP2) theory, the basis‐set‐extension energy corrections are obtained at the 2nd order Mo/ller–Plesset (MP2) level and in the second, referred to as G2(MP3) theory, they are obtained at the MP3 level. The methods are tested out on the set of 125 systems used for validation of G2 theory [J. Chem Phys. 94, 7221 (1991)]. The average absolute deviation of the G2(MP2) and G2(MP3) theories from experiment are 1.58 and 1.52 kcal/mol, respectively, compared to 1.21 kcal/mol for G2 theory. The new methods provide significant savings in computational time and disk storage.},
    issn = {0021-9606},
    doi = {10.1063/1.464297},
    url = {https://doi.org/10.1063/1.464297},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/98/2/1293/19125557/1293\_1\_online.pdf},
}

@article{10.1063/1.478385,
    author = {Curtiss, Larry A. and Redfern, Paul C. and Raghavachari, Krishnan and Rassolov, Vitaly and Pople, John A.},
    title = {Gaussian-3 theory using reduced Mo/ller-Plesset order},
    journal = {The Journal of Chemical Physics},
    volume = {110},
    number = {10},
    pages = {4703-4709},
    year = {1999},
    month = {03},
    abstract = {A variation of Gaussian-3 (G3) theory is presented in which the basis set extensions are obtained at the second-order Mo/ller–Plesset level. This method, referred to as G3(MP2) theory, is assessed on 299 energies from the G2/97 test set [J. Chem. Phys. 109, 42 (1998)]. The average absolute deviation from experiment of G3(MP2) theory for the 299 energies is 1.30 kcal/mol and for the subset of 148 neutral enthalpies it is 1.18 kcal/mol. This is a significant improvement over the related G2(MP2) theory [J. Chem. Phys. 98, 1293 (1993)], which has an average absolute deviation of 1.89 kcal/mol for all 299 energies and 2.03 kcal/mol for the 148 neutral enthalpies. The corresponding average absolute deviations for full G3 theory are 1.01 and 0.94 kcal/mol, respectively. The new method provides significant savings in computational time compared to G3 theory and, also, G2(MP2) theory.},
    issn = {0021-9606},
    doi = {10.1063/1.478385},
    url = {https://doi.org/10.1063/1.478385},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/110/10/4703/19302176/4703\_1\_online.pdf},
}

@article{10.1063/1.478676,
    author = {Baboul, Anwar G. and Curtiss, Larry A. and Redfern, Paul C. and Raghavachari, Krishnan},
    title = {Gaussian-3 theory using density functional geometries and zero-point energies},
    journal = {The Journal of Chemical Physics},
    volume = {110},
    number = {16},
    pages = {7650-7657},
    year = {1999},
    month = {04},
    abstract = {A variation of Gaussian-3 (G3) theory is presented in which the geometries and zero-point energies are obtained from B3LYP density functional theory [B3LYP/6-31G(d)] instead of geometries from second-order perturbation theory [MP2(FU)/6-31G(d)] and zero-point energies from Hartree–Fock theory [HF/6-31G(d)]. This variation, referred to as G3//B3LYP, is assessed on 299 energies (enthalpies of formation, ionization potentials, electron affinities, proton affinities) from the G2/97 test set [J. Chem. Phys. 109, 42 (1998)]. The G3//B3LYP average absolute deviation from experiment for the 299 energies is 0.99 kcal/mol compared to 1.01 kcal/mol for G3 theory. Generally, the results from the two methods are similar, with some exceptions. G3//B3LYP theory gives significantly improved results for several cases for which MP2 theory is deficient for optimized geometries, such as CN and O2+. However, G3//B3LYP does poorly for ionization potentials that involve a Jahn–Teller distortion in the cation (CH4+, BF3+, BCl3+) because of the B3LYP/6-31G(d) geometries. The G3(MP2) method is also modified to use B3LYP/6-31G(d) geometries and zero-point energies. This variation, referred to as G3(MP2)//B3LYP, has an average absolute deviation of 1.25 kcal/mol compared to 1.30 kcal/mol for G3(MP2) theory. Thus, use of density functional geometries and zero-point energies in G3 and G3(MP2) theories is a useful alternative to MP2 geometries and HF zero-point energies.},
    issn = {0021-9606},
    doi = {10.1063/1.478676},
    url = {https://doi.org/10.1063/1.478676},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/110/16/7650/19328698/7650\_1\_online.pdf},
}

@article{10.1063/1.2770701,
    author = {Curtiss, Larry A. and Redfern, Paul C. and Raghavachari, Krishnan},
    title = {Gaussian-4 theory using reduced order perturbation theory},
    journal = {The Journal of Chemical Physics},
    volume = {127},
    number = {12},
    pages = {124105},
    year = {2007},
    month = {09},
    abstract = {Two modifications of Gaussian-4 (G4) theory [L. A. Curtiss et al., J. Chem. Phys. 126, 084108 (2007)] are presented in which second- and third-order perturbation theories are used in place of fourth-order perturbation theory. These two new methods are referred to as G4(MP2) and G4(MP3), respectively. Both methods have been assessed on the G3/05 test set of accurate experimental data. The average absolute deviation from experiment for the 454 energies in this test set is 1.04kcal∕mol for G4(MP2) theory and 1.03kcal∕mol for G4(MP3) theory compared to 0.83kcal∕mol for G4 theory. G4(MP2) is slightly more accurate for enthalpies of formation than G4(MP3) (0.99 versus 1.04kcal∕mol), while G4(MP3) is more accurate for ionization potentials and electron affinities. Overall, the G4(MP2) method provides an accurate and economical method for thermochemical predictions. It has an overall accuracy for the G3/05 test set that is much better than G3(MP2) theory (1.04 versus 1.39kcal∕mol) and even better than G3 theory (1.04 versus 1.13kcal∕mol). In addition, G4(MP2) does better for challenging hypervalent systems such as H2SO4 and for nonhydrogen species than G3(MP2) theory.},
    issn = {0021-9606},
    doi = {10.1063/1.2770701},
    url = {https://doi.org/10.1063/1.2770701},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2770701/10925274/124105\_1\_online.pdf},
}

@article{doi:10.1021/ja00299a024,
    author = {Dewar, Michael J. S. and Zoebisch, Eve G. and Healy, Eamonn F. and Stewart, James J. P.},
    title = {Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model},
    journal = {Journal of the American Chemical Society},
    volume = {107},
    number = {13},
    pages = {3902-3909},
    year = {1985},
    doi = {10.1021/ja00299a024},
    URL = {https://doi.org/10.1021/ja00299a024},
    eprint = {https://doi.org/10.1021/ja00299a024}
}

@article{https://doi.org/10.1002/jcc.540100208,
    author = {Stewart, James J. P.},
    title = {Optimization of parameters for semiempirical methods I. Method},
    journal = {Journal of Computational Chemistry},
    volume = {10},
    number = {2},
    pages = {209-220},
    doi = {https://doi.org/10.1002/jcc.540100208},
    url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.540100208},
    eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.540100208},
    abstract = {Abstract A new method for obtaining optimized parameters for semiempirical methods has been developed and applied to the modified neglect of diatomic overlap (MNDO) method. The method uses derivatives of calculated values for properties with respect to adjustable parameters to obtain the optimized values of parameters. The large increase in speed is a result of using a simple series expression for calculated values of properties rather than employing full semiempirical calculations. With this optimization procedure, the rate-determining step for parameterizing elements changes from the mechanics of parameterization to the assembling of experimental reference data.},
    year = {1989}
}

@article{https://doi.org/10.1002/jcc.540100209,
    author = {Stewart, James J. P.},
    title = {Optimization of parameters for semiempirical methods II. Applications},
    journal = {Journal of Computational Chemistry},
    volume = {10},
    number = {2},
    pages = {221-264},
    doi = {https://doi.org/10.1002/jcc.540100209},
    url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.540100209},
    eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.540100209},
    abstract = {Abstract MNDO/AM1-type parameters for twelve elements have been optimized using a newly developed method for optimizing parameters for semiempirical methods. With the new method, MNDO-PM3, the average difference between the predicted heats of formation and experimental values for 657 compounds is 7.8 kcal/mol, and for 106 hypervalent compounds, 13.6 kcal/mol. For MNDO the equivalent differences are 13.9 and 75.8 kcal/mol, while those for AM1, in which MNDO parameters are used for aluminum, phosphorus, and sulfur, are 12.7 and 83.1 kcal/mol, respectively. Average errors for ionization potentials, bond angles, and dipole moments are intermediate between those for MNDO and AM1, while errors in bond lengths are slightly reduced.},
    year = {1989}
}

@article{Stewart_2007,
	doi = {10.1007/s00894-007-0233-4},
	url = {https://doi.org/10.1007%2Fs00894-007-0233-4},
	year = 2007,
	month = {sep},
	publisher = {Springer Science and Business Media {LLC}},
	volume = {13},
	number = {12},
	pages = {1173--1213},
	author = {James J. P. Stewart},
	title = {Optimization of parameters for semiempirical methods V: Modification of {NDDO} approximations and application to 70 elements},
	journal = {Journal of Molecular Modeling}
}

@article{https://doi.org/10.1002/jcc.10162,
    author = {Repasky, Matthew P. and Chandrasekhar, Jayaraman and Jorgensen, William L.},
    title = {PDDG/PM3 and PDDG/MNDO: Improved semiempirical methods},
    journal = {Journal of Computational Chemistry},
    volume = {23},
    number = {16},
    pages = {1601-1622},
    keywords = {semiempirical MO, heats of formation, composite ab initio, PM3, NDDO},
    doi = {https://doi.org/10.1002/jcc.10162},
    url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.10162},
    eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.10162},
    abstract = {Abstract Two new semiempirical methods employing a Pairwise Distance Directed Gaussian modification have been developed: PDDG/PM3 and PDDG/MNDO; they are easily implemented in existing software, and yield heats of formation for compounds containing C, H, N, and O atoms with significantly improved accuracy over the standard NDDO schemes, PM5, PM3, AM1, and MNDO. The PDDG/PM3 results for heats of formation also show substantial improvement over density functional theory with large basis sets. The PDDG modifications consist of a single function, which is added to the existing pairwise core repulsion functions within PM3 and MNDO, a reparameterized semiempirical parameter set, and modified computation of the energy of formation of a gaseous atom. The PDDG addition introduces functional group information via pairwise atomic interactions using only atom-based parameters. For 622 diverse molecules containing C, H, N, and O atoms, mean absolute errors in calculated heats of formation are reduced from 4.4 to 3.2 kcal/mol and from 8.4 to 5.2 kcal/mol using the PDDG modified versions of PM3 and MNDO over the standard versions, respectively. Several specific problems are overcome, including the relative stability of hydrocarbon isomers, and energetics of small rings and molecules containing multiple heteroatoms. The internal consistency of PDDG energies is also significantly improved, enabling more reliable analysis of isomerization energies and trends across series of molecules; PDDG isomerization energies show significant improvement over B3LYP/6-31G* results. Comparison of heats of formation, ionization potentials, dipole moments, isomer, and conformer energetics, intermolecular interaction energies, activation energies, and molecular geometries from the PDDG techniques is made to experimental data and values from other semiempirical and ab initio methods. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1601–1622, 2002},
    year = {2002}
}

@article{doi:10.1021/ct0500287,
    author = {Tubert-Brohman, Ivan and Guimarães, Cristiano Ruch Werneck and Jorgensen, William L.},
    title = {Extension of the PDDG/PM3 Semiempirical Molecular Orbital Method to Sulfur, Silicon, and Phosphorus},
    journal = {Journal of Chemical Theory and Computation},
    volume = {1},
    number = {5},
    pages = {817-823},
    year = {2005},
    doi = {10.1021/ct0500287},
    note ={PMID: 19011692},
    URL = {https://doi.org/10.1021/ct0500287},
    eprint = {https://doi.org/10.1021/ct0500287}
}


@article{Stewart_2012,
	doi = {10.1007/s00894-012-1667-x},
	url = {https://doi.org/10.1007%2Fs00894-012-1667-x},
	year = 2012,
	month = {nov},
	publisher = {Springer Science and Business Media {LLC}},
	volume = {19},
	number = {1},
	pages = {1--32},
	author = {James J. P. Stewart},
	title = {Optimization of parameters for semiempirical methods {VI}: more modifications to the {NDDO} approximations and re-optimization of parameters},
	journal = {Journal of Molecular Modeling}
}

@Article{10.1039/B810189B,
author ="Chai, Jeng-Da and Head-Gordon, Martin",
title  ="Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections",
journal  ="Phys. Chem. Chem. Phys.",
year  ="2008",
volume  ="10",
issue  ="44",
pages  ="6615-6620",
publisher  ="The Royal Society of Chemistry",
doi  ="10.1039/B810189B",
url  ="http://dx.doi.org/10.1039/B810189B"
}

@article{10.1007/s00214-007-0310-x,
  title={The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals},
  author={Zhao, Yan and Truhlar, Donald G},
  journal={Theoretical chemistry accounts},
  volume={120},
  number={1},
  pages={215--241},
  year={2008},
  doi = "10.1007/s00214-007-0310-x",
  publisher={Springer}
}
