Institute for Theoretical Chemistry, University of Cologne

Pseudopotentials, ECPs

Pseudopotentials of the Stuttgart/Cologne group
(Revision: August 19, 2014)

The energy-consistent pseudopotentials of the Stuttgart/Cologne group are semi-
local pseudopotentials adjusted to reproduce atomic valence-energy spectra.
The adjustment of the pseudopotential parameters has been done in fully nume-
rical calculations, valence basis sets have been generated a-posteriori via
energy optimization. The complete set of potentials includes one-component
(non-relativistic and scalar-relativistic) effective-core potentials (ECP),
spin-orbit (SO) and core-polarization potentials (CPP); only the one-component
ECPs are listed in full, in the present file. The energy-consistent pseudo-
potentials are under continuous development and extension, for information
Michael Dolg (
Kirk A. Peterson (
Peter Schwerdtfeger (
Hermann Stoll (

Library keywords are of the form ECPnXY; n is the number of core electrons
which are replaced by the pseudopotential, X denotes the reference system
used for generating the pseudopotential (X=S: single-valence-electron ion;
X=M: neutral atom), and Y stands for the theoretical level of the reference
data (Y=HF: Hartree-Fock; Y=WB: quasi-relativistic; Y=DF: relativistic).
For one- or two-valence electron atoms SDF is a good choice, while other-
wise MWB or MDF is recommended. (For light atoms, or for the discussion
of relativistic effects, the corresponding SHF, MHF pseudopotentials may
be useful.) The same keyword applies to the set of pseudopotential para-
meters and the corresponding optimized valence basis sets.

For each pseudopotential, the keyword is immediately followed by 4 parameters:
the number of core electrons, the number of l-projectors (lmax) in the one-
component (non-relativistic or scalar-relativistic) ECP, the number of l-
projectors (lmax') of the SO potential (if given; lmax'=0 otherwise), and
the total number of parameters listed below the commentary line. The latter
parameters provide information on V(lmax) first, and then for the semi-local
one-component and SO potentials, V(l) and V'(l') respectively, in the order
l=0, 1, 2, ..., lmax-1; l'=1, 2, ..., lmax'. For each V(l) or V'(l'), the
number of terms of the form A(i)*r**(n(i)-2)*exp(-a(i)*r**2) is given first,
and then the parameters specifying the individual terms in the sequence
n(1),a(1),A(1);n(2),a(2),A(2);..... Note that the V'(l') are defined as
radial prefactors of l*s terms, i.e., the difference of l+1/2 and l-1/2
potentials, for a given l, is multiplied by 2/(2l+1).

CPP parameters (if given) are included in the commentary line of the ECPs.
The parameters are the core dipole polarizability, alpha, and the exponents,
delta and ncut, of the cut-off function (1-exp(-delta*r**2)**ncut multiplying
the operators of the polarizing field.

For each valence basis set of a specified symmetry (s, p, d, ...),
the number of exponents is specified first, then the number of recom-
mended contractions and the contraction patterns (n.m defines the range
of primitives to be contracted). On the following lines, the exponents
of the primitives are given first, and afterwards the sets of contraction


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