Relativistic two-electron atomic and molecular energies using LS coupling and double groups: Role of the triplet contributions to singlet states

Abstract

The triplet contribution is computed to the 1 and 2 [Formula: see text] states of the He atom, to the [Formula: see text] state of the Li+ and Be2+ ions, and to the [Formula: see text] ground state of the H2 molecule by extensive use of double-group symmetry (equivalent to LS coupling for the atomic systems) during the course of the variational solution of the no-pair Dirac–Coulomb–Breit (DCB) wave equation. The no-pair DCB energies are converged within sub-parts-per-billion relative precision, using an explicitly correlated Gaussian basis optimized to the non-relativistic energies. The α fine-structure constant dependence of the triplet sector contribution to the variational energy is α4 Eh at leading order, in agreement with the formal perturbation theory result available from the literature.