A one-electron variant of direct perturbation theory for the treatment of scalar-relativistic effects

Abstract

ABSTRACTThe different importance of scalar-relativistic two-electron contributions in second-order direct perturbation theory (DPT2) and the spin-free one-electron variant of exact two-component theory (SFX2C-1e) is analysed. The apparent discrepancy is traced back to the fact that SFX2C-1e is not ignoring the total DPT2 two-electron contribution rather just a so-called commutator term which originates from a rewrite of the small-component density (matrix) in terms of the related, though different kinetic-energy density (matrix). This commutator term is shown to be significantly smaller (10% and less) and to have, unlike the total DPT2 two-electron contribution, a negative sign. Based on our findings, we propose a one-electron variant of direct perturbation theory, referred to as DPT-1e, and report on its implementation for the computation of energies and first-order properties at the second-order level, i.e. DPT2-1e. Numerical results are presented for the hydrogen halide series HX, X=F, Cl, Br, I, and At, as well CuF and CuCl in order to investigate its performance in comparison to DPT2 and SFX2C-1e.