Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling

Abstract

Development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) together with pilot applications are reported. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. To demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO+ is reported.