Model core potentials for studies of scalar-relativistic effects and spin-orbit coupling at Douglas–Kroll level. I. Theory and applications to Pb and Bi

A theory of model core potentials that can treat spin-orbit-coupling (SOC) effects at the level of Douglas-Kroll formalism has been developed. By storing the damping effect of kinematic operator in the Douglas-Kroll spin-orbit operator into an additional set of basis set contraction coefficients, the Breit-Pauli spin-orbit code in the GAMESS-US program was successfully used to perform Douglas-Kroll spin-orbit calculations. It was found that minute errors in the radial functions of valence orbitals lead to large errors in the spin-orbit energy levels and thus fitting the radial part of the spin-orbit matrix elements is necessary in model core potential parametrization. The first model core potentials that include the new formalism were developed for two 6p-block elements, Pb and Bi. The valence space of the 5p, 5d, 6s, and 6p orbitals was used because of the large SOC between the 5p and 6p orbitals. The model core potentials were validated in the calculations of atomic properties as well as spectroscopic constants of diatomic metal hydrides. The agreement between results of the model core potential and all-electron calculations was excellent, with energy errors of hundreds of cm(-1) and hundredths of eV, r(e) errors of thousandths of A, and omega(e) errors under 20 cm(-1). Two kinds of interplay between SOC effect and bonding process (antibonding and bonding SOC) were demonstrated using spin-free term potential curves of PbH and BiH. The present study is the first extension of the model core potential method beyond Breit-Pauli to Douglas-Kroll SOC calculations.