Our group proposed a generalization of the "shape-consistent" Effective Core Potential (ECP) method (which is widely used in the electronic structure calculations of molecules with heavy atoms) both for nonrelativistic [1,2] and for relativistic cases [3,4]. In these papers, the widespread conception about necessity of the "shape-consistent" ECP generation for the nodeless pseudoorbitals (to avoid the singularities when inverting the Hartree-Fock equations) was overcome, and the outermost core pseudoorbitals together with the valence pseudoorbitals which may have nodes were included in the ECP generation scheme for the use in precise calculations.
It was shown that the difference between the valence and outer core effective potentials with the same angular (l) and total (j) electronic momenta should be taken into account to perform precise Relativistic ECP (RECP) calculations, and a new (Generalized RECP or GRECP) operator including non-local terms with the projectors on the outer core spinors additionally to the conventional semi-local RECP operator was proposed. These correcting terms are especially important for accurate simulation of interactions with the valence electrons [3,4].
Such a modification of the original semi-local RECP operator permited to increase the accuracy of simulation of an atomic Hamiltonian about 10 times in valence region when reducing 2-3 times the radii of the atomic core regions where orbitals are smoothed by any manner.
Our group suggested a development of the RECP method for the case of transition and rare earth elements . New terms with projectors on the occupation numbers of outermost d-shells (which can be determined in SCF iterations) were added to the conventional RECP operator. These terms correcting the interaction of inner-core electrons (excluded from the RECP calculations) with explicitly treated d-electrons of transition metals (which are slightly relaxed when forming the chemical bonds) can improve significantly the quality of the model Hamiltonian in the outer core region of a heavy atom if excitations from the outer core d-shell are important for studied properties. Significant improvement (2-8 times) was achieved in reproduction of atomic excitation energies as compared with the conventional "shape-consistent" RECP calculation (without increasing the number of electrons explicitly included in calculations with RECP).
We have generated the GRECPs for following atoms (.zip file ~ 5K) :
Ba, Yb, Hg,
Tl, Pb, Bi,
Po, At, Rn,
Th, U, E112,
Here you can find a file with all the above potentials (~25K).
The constructed GRECPs were used for calculation of parameters of P,T-odd
spin-rotational hamiltonian for YbF molecule . Now these potentials
are used in precise molecular calculations implemented by us with German
and Israel groups.
[ 1 ] A.V.Titov, A.O.Mitrushenkov, and I.I.Tupitsyn,
Chem.Phys.Lett. 185, 330 (1991).
[ 2 ] N.S.Mosyagin, A.V.Titov, and A.V.Tulub, Phys.Rev.A 50, 2239 (1994).
[ 3 ] I.I.Tupitsyn, N.S.Mosyagin, and A.V.Titov, J.Chem.Phys. 103, 6548 (1995).
[ 4 ] N.S.Mosyagin, A.V.Titov, and Z.Latajka, Preprint 2050 (Petersburg Nuclear Physics Institute, Gatchina, St.-Petersburg, 1995), 42p;.
[ 5 ] A.V.Titov and N.S.Mosyagin, Struct.Chem. 6, 317 (1995).
[ 6 ] A.V.Titov, N.S.Mosyagin, and V.F.Ezhov, Phys.Rev.Lett. 77, 5346 (1996).