Assessment of minimal active space CASSCF-SO methods for calculation of atomic Slater–Condon and spin–orbit coupling parameters in d- and f-block ions

Abstract

Slater–Condon parameters and the spin–orbit (SO) coupling constants for various oxidation states of transition metal ions (3d/4d/5d) and trivalent f-block ions were calculated using minimal active space complete active space self-consistent field (CASSCF)-SO methods in OpenMolcas. The SO coupling constants have a quadratic relationship to atomic number Z for a fixed dⁿ configuration, as do those for the trivalent lanthanides where configuration also changes as a function of Z. Compared to experimentally-derived values, minimal active space CASSCF-SO approximates SO coupling constants within ca. 200 cm⁻¹, which is usually <10% error for 4dⁿ, 5dⁿ and 4fⁿ configurations, but up to 30% error for 3dⁿ configurations. Slater–Condon parameters are usually overestimated on the order of 10–50%, arising from a lack of dynamic correlation in the method, and thus we do not recommend minimal active space CASSCF-SO methods where accurate term excitation energies are required. However, the error in the Slater–Condon parameters appears to be systematic for divalent 4d and trivalent 4f ions such that scaling may be a useful approach where computational resources are limited, but this is not the case for 3d ions. Hence, caution is advised when using CASSCF-SO methods for comparisons with spectroscopic data, wherein only qualitative results can be expected, and methods accounting for dynamic correlation effects (such as CASPT2 or NEVPT2) should be employed if more quantitative results are required.