Study of the dependence of spin-orbit matrix elements on AO basis set composition for inner and valence shells: Results for the multiplet splitting of X 3Σ− and C 3Π of SO and X 2Π in SO+

Abstract

Abstract The zero-field splitting for the X 3 Σ − ground state of SO is calculated in various AO basis sets employing MRD CI wavefunctions and second-order perturbation theory. It is found that the spin-orbit matrix elements which couple various excited states with X 3 Σ − are relatively stable as long as AO basis sets of roughly double-zeta quality are employed: considerable deviations appear if smaller AO basis sets are used. An analysis of the various contributions to the matrix element on the MO level demonstrates that the quality of the spin-orbit element is essentially governed by the flexibility with which the valence-shell MOs are described. Since little dependence on inner shells is noted, the concept of frozen-core CI calculations as normally used in electronic structure calculations can be carried over to the determination of spin-dependent properties. An analysis with respect to the convergence of the second-order perturbation sum as well as comparisons between MRD CI wavefunctions and single-configuration states in evaluating spin-orbit properties is also made. Calculations for spin-spin splitting in X 3 Σ − , the zero-field splitting of the C 3 Π states and the X 2 Π ground state of SO + substantiate the conclusions drawn from the X 3 Σ − state treatment. All calculated values are in excellent agreement with measured data, whenever these are available.