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

The triplet contribution is computed to the 1 and 2 S0e1 states of the He atom, to the 1S0e1 state of the Li and Be ions, and to the XΣ ground state of the H 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 αE at leading order, in agreement with the formal perturbation theory result available from the literature.