The two-component calculation of KPACK relies on the use of SOREP. There are two types of SOREPs in use by KPACK: shape-consistent and energy-adjusted SOREP. The former has been developed by the groups of Christiansen and Ermler and their co-workers (EMSL lists their potentials as CRENBL and CRENBS), while the latter by the groups of Dolg and Stoll and their co-workers is often called as the Stuttgart pseudopotential.

Most quantum chemistry programs employ the spin-free scalar-relativistic part of the SOREP known as averaged relativistic effective core potential (AREP) since the formalism is then compatible with nonrelativistic ECP calculation.

In the publications of shape-consistent SOREPs, the given spin-orbit potentials are different from the one that is used in KPACK by some factor. Also, the energy-adjusted SOREPs are published in their original format that are not compatible with KPACK. However, KPACK library contains those SOREPs in the converted format. To minimize the confusion in the use of SOREP, especially with spin-orbit potential, the following naming, which is somewhat based on the nomenclature of Stuttgart pseudopotential,Dolg13 has been proposed.Park13


A  Authors initials
    CE for Christiansen, Ermler and their co-workers, i.e. shape-consisntent
    DS for Dolg, Stoll and their co-workers, i.e. energy-adjusted

N  Number of core electrons

X  The reference system used for generating the SOREP (Energy-adjusted SOREP only)
  M for neutral atom
  S for single valence electron ion

Y  The theoretical level of the reference data (Energy-adjusted SOREP only) 
  DF for relativistic Dirac-Fock
  WB for quasi-relativistic Wood-Boring
  HF for nonrelativistic Hartree-Fock

Z  Additional information (Energy-adjusted SOREP only) 
  B = low-frequency Breit term included
  Q = QED effect included

S  Spin-free or spin-dependent potential
  SF for AREP
  SO for SOREP

The format of spin-orbit potential follows the Pitzer convention first used in ARGOS program.Pitzer88 For instance, in case of shape-consistent SOREPs a factor of (2/l) has been multiplied to the published parameters.

Generally, ECPs with A=DS and Y=HF do not come with spin-orbit potentials (hence, S=SF), and Y=WB potentials sometimes provide the spin-orbit potentials but care must be taken before use. Since KPACK assumes the jj-coupling in the SCF stage and thus, the employed SOREPs must qualify a variational usage. Some Y=WB SOREPs are fitted after the construction of ECP and may cause problems within variational treatment. The CE SOREPs and the DS SOREPs with XY=MDF are possible with KPACK in this sense, and the usage is strongly recommended.

The SOREPs can be downloaded from following websites:

 NameCore configurationCoverage 
ECPCE2SO [He] 2s: 3Li, 4Be
2p: 5B - 10Ne
3s: 11Na, 12Mg
ECPCE10SO[Ne] 3p: 13Al - 18Ar
4s: 19K, 20Ca
3d: 21Sc - 30Zn
ECPCE18SO[Ar] 3d: 21Sc - 30Zn
4p: 31Ga - 36Kr
ECPCE28SO[Ar]3d103p: 31Ga - 36Kr
5s: 37Rb, 38Sr
4d: 39Y - 48Cd
ECPCE36SO[Kr] 4d: 39Y - 48Cd
5p: 49In - 54Xe
ECPCE46SO [Kr]4d10 4p: 49In - 54Xe
6s: 55Cs, 56Ba
4f: 57La
ECPCE54SO [Xe] 4f: 57La - 71Lu
ECPCE60SO [Kr]4d104f14 5d: 72Hf - 80Hg
ECPCE68SO [Xe]4f14 5d: 72Hf - 80Hg
6p: 81Tl - 86Rn
ECPCE78SO [Xe]4f145d10 6p: 81Tl - 86Rn
7s: 87Fr, 88Ra
5f: 89Ac - 103Lr
6d: 104Rf - 112Cn
7p: 113E113 - 118E118
ECPCE92SO [Xe]4f145d105f14 6d: 104Rf - 112Cn
7p: 113E113 - 118E118

 NameCore configurationCoverage 
ECPDS10MDFSO[Ne] 4s: 19K, 20Ca
3d: 29Cu, 30Zn
4p: 31Ga - 36Kr
ECPDS28MDFSO[Ar]3d105s: 37Rb, 38Sr
4d: 39Y - 48Cd
5p: 49In - 54Xe
ECPDS46MDFSO [Kr]4d10 6s: 55Cs, 56Ba
ECPDS60MDFSO [Kr]4d104f14 5d: 72Hf - 80Hg
6p: 81Tl - 86Rn
5f: 89Ac - 92U
ECPDS78MDFSO [Xe]4f145d10 7s: 87Fr, 88Ra
ECPDS92MDF(B,Q)SO [Xe]4f145d105f14 6d: 104Rf - 112Cn
7p: 113E113 - 118E118
8s: 119E119 - 120E120


Dolg13    M. Dolg, K. A. Peterson, P. Schwerdtfeger, and H. Stoll, See here.
Park13    Y. C. Park and Y. S. Lee, See here.
Pitzer88    R. M. Pitzer and N. W. Winter, J. Phys. Chem. 92, 3061 (1988)