Notes about the Jensen basis sets
=================================

admm basis sets
------------------------
The most widely used approach to approximate the Coulomb and exchange integrals is density fitting, also known as the resolution-of-the-identity (RI) approximation.
In this, the products of two one-electron basis functions are expanded in one-center auxiliary functions. RI significantly improves performance with a limited impact on
the accuracy and has therfore been applied to HF/KS theory as well as correlated methods. ADMM has been developed specifically for the exchange contribution. The exchange
energy is split into two parts. On consisting of the exact HF exchange and the second is a first-order correction term, evaluated as the difference between the generalized
gradient approximation exchange in the full and auxiliary basis sets.


aug-pc-n and  pc-n basis sets (where n indicates the level of polarization beyond the atomic system)
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For the basis sets pc-0 through pc-4, the exponents were optimized by a pseudo-Newton-Raphson approach. Molecular geometries were either taken from experimental work
or MP2/cc-pVTZ optimized.
The pc-n basis sets have been designed to systematically improve the representation of the wave function, which is the primary contributor to energetic quantities.
It is also expected that the addition of diffuse functions (aug-pc-n basis sets) will improve the performance of the excitation energies.

The Diamagnetic Spin-Orbit Contribution is insensitive to the addiion of tight functions, as their influence is only indirect by changes in the density.
The Paramagnetic Spin-Orbit Contribution provides the largest contribution to the coupling constant
The Spin Dipole Contribution provides the second largest contribution to the coupling constant

Below are the DSO PSO and SD contributions (Hz) to the spin-spin coupling in F2 (which was used as a representative case)
                      DSO                                                     PSO                                                          SD
BASIS       NONE    +s      +p     +d     +f             BASIS       NONE    +s        +p       +d       +f           BASIS       NONE    +s      +p      +d      +f
pc-0        3.41    3.41    3.04                         pc-0        7032    7033    9497                             pc-0        3733    3774    5172
pc-1        2.53    2.53    2.39   2.36                  pc-1        8542    8542    9569    9565                     pc-1        4805    4805    5406    5691
pc-2        2.20    2.20    2.17   2.14   2.13           pc-2        9245    9245    9418    9416     9409            pc-2        5426    5426    5527    5800    5926
pc-3        2.12    2.12    2.12   2.11   2.11           pc-3        9399    9399    9417    9417     9416            pc-3        5728    5738    5749    5873    5927
pc-4        2.11    2.11    2.11   2.11   2.11           pc-4        9409    9409    9414    9414     9414            pc-4        5865    5865    5867    5873    5911
aug-pc-0    3.30    3.30    2.99                         aug-pc-0    7745    7746    10483                            aug-pc-0    4341    4341    5969
aug-pc-1    2.49    2.49    2.36   2.33                  aug-pc-1    8623    8623    9611    9658                     aug-pc-1    4870    4870    5481    5770
aug-pc-2    2.20    2.20    2.17   2.14   2.13           aug-pc-2    9245    9245    9419    9416     9409            aug-pc-2    5428    5428    5530    5803    5929
aug-pc-3    2.12    2.12    2.12   2.11   2.11           aug-pc-3    9395    9295    9414    9413     9413            aug-pc-3    5737    5737    5748    5872    5926


pcJ-n basis sets
-------------------------
Optimized for calculating indirect nuclear spin-spin coupling constants
using density functional methods. The calculation of nuclear magnetic spin-spin constats are a challenging task because the results largely depend on the quality of
the wave function. There are two limiting types of basis set contraction, denoted segmented and general. In a segmented contraction, each primitive basis function is
only allowed to contribute to one contracted function, while in a general contraction, all primitive functions are allowed to contribute to all contracted functions.
The contraction coefficients for a general contraction are normally obtained from SCF coefficients.
Jensen2010a performed a systematic search for the optimum contraction schemes for the pcJ-n sets and permformed extensive analysis on the s and p functions of atoms and
documented the results. The work provides guidelines for searching for optimum contraction schemes at theoretical levels, like CCSD, where a systematic search is impractical.

Below are the recommended contraction schemes for the pcJ-n Basis Sets:
                   Hydrogen                       1st Row                        2nd Row
Basis    Uncontracted    Contracted    Uncontracted     Contracted    Uncontracted    Contracted
pcJ-0    5s              3s            7s4p             4s3p          10s7p           5s4p
pcJ-1    6s2p            4s            9s5p2d           5s4p          13s9p2d         6s5p
pcJ-2    8s3p2d          5s            12s7p3d2f        7s5p          15s11p3d2f      8s6p
pcJ-3    11s5p3d1f       8s            16s10p5d2f1g     10s8p         19s14p5d3f1g    11s10p
pcJ-4    12s7p4d2f1g     10s           19s12p7d3f2g1h   15s10p        22s17p7d4f2g1h  16s12p


pcX-n basis sets
-------------------------
The self-consistent-field method (SCF) includes orbital relaxation effects by separate optimizations of the ground and the core–hole states, and calculates the
CEBE (core-electron binding energy) as the difference between total electronic energies, and this method is widely used. The first SCF calculations were performed using HF
which ignores electron correlation and relativistic effects, but the inclusion of the relaxation energy allowed reproduction of experimental results. The SCF method can
be extended to post HF-methods such as MPn, MCSCF and CCSD methods, but they significantly increase the required computational resources and achieving convergence of the highly
excited hole state using coupled cluster methids can be difficult. PcX-n basis sets can approach the basis set limit for core-excitation processes such as XPS and XAS calculated
by the SCF approach. They are shown to provide lower basis set errors than other basis sets of similar size, and can be used as local basis sets in combination with the energy
optimized pcseg-n basis sets for reducing computational costs when core-excitation processes are only required for a small subset of atoms.


pcseg-n and psSseg-n basis sets
------------------------------------
These segmented basis sets were constructed from polarization consistent basis sets. An energy-optimized uncontracted basis set is augmented with property specific functions
to improve the basis set convergence. It is then general contracted based on the property basis set error relative to the complete basis set limit at each ζ level, and finally
converted into a computational more efficient segmented contraction by removing the redundancy among the primitive functions in the general contracted functions. The pcSseg-n
basis sets are in qualities ranging from double-ζ to pentuple-ζ quality and should be suitable for both routine and benchmark calculations of nuclear magnetic shielding constants.
While these basis sets have been developed for use with DFT methods, they may also be suitable for wave function methods including electron correlation. They can furthermore be
used as locally dense basis sets in combination with the energy-optimized pcseg-n basis sets for large systems, where shielding constants are only required for a small subset
of atoms.


pcH basis sets
--------------
Note that these differ slightly from those given in the SI of jakobsen2019a. The data here contains slight corrections.


Notes from Frank Jensen
-----------------------

pcseg:  the most recent (2014) segmented contracted version of the pc-n basis sets, defined for H-Kr, for n=0,1,2,3,4
apcseg: the most recent (2014) segmented contracted version of the aug-pc-n basis sets, defined for H-Kr, for n=0,1,2,3,4
    These should be used for DFT energetic properties (energies, geometry optimization, vibrational frequencies, ...)
    The apcseg has in addition a full set of diffuse functions, useful for anions, polar systems, and electric properties (dipole moments, polarizabilities, ...)
    NOTE: the old general contracted pc-n should be considered out-dated, as the pcseg have the same (or slightly better) performance and are computationally
        more efficient

pcSseg:  the most recent (2015) segmented contracted version of the pcS-n basis sets, defined for H-Kr, for n=0,1,2,3,4
apcSseg: the most recent (2015) segmented contracted version of the aug-pcS-n basis sets, defined for H-Kr, for n=0,1,2,3,4
    These should be used for NMR shielding constants, and have been shown to be better than other basis sets also for correlated methods (MP2, CC)
    The apcSseg has in addition a full set of diffuse functions, which may improve results for some systems
    NOTE: the old general contracted pcS-n should be considered out-dated, as the pcSseg have the same (or slightly better) performance and are computationally
        more efficient

pcJ:       the most recent contracted version of the pcJ-n basis sets, defined for H-Ar, for n=0,1,2,3,4
apcJ:      the most recent contracted version of the aug-pcJ-n basis sets, defined for H-Ar, for n=0,1,2,3,4
    These should be used for NMR spin-spin coupling constants, and are probably also close to optimum for correlated methods (MP2, CC)
    The apcJ has in addition a full set of diffuse functions, which may improve results for some systems

pcX:       basis sets optimized for core-spectroscopy, defined for Li-Ar, for n=1,2,3,4
apcX:      as pcX, with a full set of diffuse functions, defined for Li-Ar, for n=1,2,3,4
    These should be used for X-ray spectroscopy (XPS) in combination with Delta-SCF methods, especially when using DFT, but are probably also suitable for
        correlated methods (MP2, CC)
    The apcX has in addition a full set of diffuse functions, which is important/essential for XAS
    These basis sets are uncontracted, as any contraction destroys the accuracy. The n=1,2 basis sets are generated by exponent interpolation, while the n=3,4
        simply are the uncontracted versions of the original (general contracted) pc-n basis sets, as no improvment was found by exponent interpolation
    NOTE: these basis sets should not be used for XPS/XAS using response methods, as basis set requirements here are different than when using Delta-SCF methods.
        Basis sets suitable for response methods are in progress.

admm:    auxiliary basis sets for representing the exchange energy using the auxiliary-density matrix method (ADMM), defined for Li-Ar, for n=1,2,3
aadmm:    as admm, with a full set of diffuse functions, defined for Li-Ar, for n=1,2,3
    These basis sets are designed to be used in combination with pcseg-n and aug-pcseg-n, with the same n, when using the ADMM method in Dalton

Each of the directories contains the basis sets as files: ATOM-n.fmt, where fmt is a format for specific programs:
    fmt = inp  : Gaussian
    fmt = gms  : Gamess-US
    fmt = mol  : Dalton
    fmt = mol2 : Dalton, old(er) versions

Key references:
pcseg:  Atoms H-Kr:
    F. Jensen "Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent Basis Sets." J. Chem. Theory Comp. 10 (2014) 1074-1085
    These build on previous versions for selected subgroups of atoms using a general contraction:
    F. Jensen "Polarization Consistent Basis Sets. Principles." J. Chem. Phys. 115 (2001) 9113-9125; 116 (2002) 3502.
    F. Jensen "Polarization Consistent Basis Sets III. The Importance of Diffuse Functions." J. Chem. Phys. 117 (2002) 9234-9240.
    F. Jensen, T. Helgaker "Polarization Consistent Basis Sets V. The Elements Si-Cl." J. Chem. Phys. 121 (2004) 3463-3470
    F. Jensen "Polarization Consistent Basis Sets. VI. The Elements He, Li, Be, B, Ne, Na, Mg, Al, Ar." J. Phys. Chem. A 111 (2007) 11198-11204
    F. Jensen "Polarization Consistent Basis Sets. VII. The Elements K, Ca, Ga, Ge, As, Se, Br and Kr." J. Chem. Phys. 136 (2012) 114107
    F. Jensen "Polarization Consistent Basis Sets. VIII. The Transition Metals Sc-Zn." J. Chem. Phys. 138 (2013) 014107

pcSseg: Atoms H-Kr:
    F. Jensen "Segmented Contracted Basis Sets Optimized for Nuclear Magnetic Shielding." J. Chem. Theory Comp. 11 (2015) 132-138
    These build on previous versions for atoms H-Ar using a general contraction:
    F. Jensen "Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods." J. Chem. Theory Comp. 4 (2008) 719-727

pcJ:    Atoms H,He,B-Ne,Al-Ar:
    F. Jensen "The Optimum Contraction of Basis Sets for Calculating Spin-Spin Coupling Constants." Theor. Chem. Acc. 126 (2010) 371-382
    The contractions for the Al-Ar pcJ-0 and pcJ-1 have subsequently been changed from general to segmented based on unpublished work.
    These build on previous versions using a different (less) contraction:
    F. Jensen "The Basis Set Convergence of Spin-Spin Coupling Constants Calculated by Density Functional Methods." J. Chem. Theory Comp. 2 (2006) 1360-1369
        Atoms Li,Be,Na,Mg:
    P. A. Aggelund, S. P. A. Sauer, F. Jensen "Development of polarization consistent basis sets for spin-spin coupling constant calculations for the atoms
        Li, Be, Na and Mg." J. Chem. Phys. 149 (2018) 044117

pcX:    Atoms Li-Ar:
    M. A. Ambroise, F. Jensen "Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Delta-SCF Approach"
        J. Chem. Theory Comp. 14 (2018) 0000

admm:    Atoms
    C. Kumar, H. Fliegl, F. Jensen, A. M. Teale, S. Reine, T. Kjaergaard "Accelerating Kohn-Sham Response Theory using Density Fitting and the
        Auxiliary-Density-Matrix Method." Int. J. Quant. Chem. 118 (2018) e25639
