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

Abstract

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.

Performance of dynamically weighted multiconfiguration self-consistent field and spin-orbit coupling calculations of diatomic molecules of Group 14 elements

“…Using both SA-and DW-MCSCF orbitals at the correlation level of MCQDPT should bring about similar results, as Table I and Fig. Our experience with the SOC calculations 10,14,17 indicates that the inclusion of dynamic correlation is necessary to reproduce experimental data and to predict experimentally unknown data accurately. Our experience with the SOC calculations 10,14,17 indicates that the inclusion of dynamic correlation is necessary to reproduce experimental data and to predict experimentally unknown data accurately.…”

“…One should recall that the use of BP-SOC for the twoelectron terms underestimates the SOC splittings because the kinematic damping operators andK are missing and the two-electron SOC integrals (and the subsequent shielding for the one-electron SOC effect) are overestimated, 17 and this partly induced the lower values of our SOC compared to experiment. Completely neglecting the two-electron SOC interactions produced the values of 904 and 2146 cm −1 for the SOC of GeH and SnH, almost identical to the experimental values due to some error cancellation.…”

“…Using the two-electron BP-SOC operator leads to an underestimation of SOC splitting because the damping effect of the kinematic operators is missing in the BP-SOC operator 17 and the SOC shielding effect 2, 57-59 is overestimated. We should emphasize that we approximated only the one-electron SOC operator at the DK level, because the two-electron SOC operator is more difficult to transform.…”

Model core potentials of p-block elements generated considering the Douglas–Kroll relativistic effects, suitable for accurate spin-orbit coupling calculations

“…The nonrelativistic kinetic operator plus parametrized potential functions is used, replacing the integrals of the complicated relativistic operators by those of simple functions, e.g., Gaussian type functions, leading to extra saving of computational resources. 16 In this algorithm, we employed the local atomic nature of the SOC operator to incorporate the differences between the DK-SOC and Breit-Pauli ͑BP͒-SOC into an additional set of basis contraction coefficients. 11,12 Because the MCP can retain the inner nodal structure of the valence orbitals, which is salient for the evaluation of SOC integrals, the MCP method is a perfect candidate to carry out efficient and accurate SOC calculations.…”

Excitation energies from relativistic coupled-cluster theory of general excitation rank: Initial implementation and application to the silicon atom and to the moleculesXH (X= As, Sb, Bi)

“…We have chosen an atomic case (Si) featuring excited states of two different kinds: excited states due to the first-order spin-orbit splitting within a spectroscopic term, and states corresponding to a different spectroscopic term. As a second and molecular example we apply our approach to the second-order spinorbit splitting of the 3 ground state of heavier pnictogen hydrides, a notoriously difficult problem [17,18] requiring the treatment of static and dynamic electron correlation as well as spin-dependent magnetic interactions accurately. In the final section (Sec.…”