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

ABSTRACT

The 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.

GRAPHICAL ABSTRACT

KEYWORDS:

• Relativistic quantum chemistry
• direct perturbation theory
• exact-two-component theory
• scalar-relativistic two-electron contributions

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported in Mainz by the Deutsche Forschungsgemeinschaft via projects GA 370/5, GA 370/6-1, and GA 370/6-2.