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 ${}^1{S}_0^{\text{e}}$ states of the He atom, to the $1{}^1{S}_0^{\text{e}}$ state of the Li${}^{+}$ and Be${}^{2+}$ ions, and to the $X{}^1{\Sigma }_{\text{g}}^{+}$ ground state of the H${}_2$ 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 wave equation. The no-pair Dirac-Coulomb-Breit energies are converged within a sub-parts-per-billion relative precision using an explicitly correlated Gaussian basis optimized to the non-relativistic energies. The $\alpha$ fine-structure constant dependence of the triplet sector contribution to the variational energy is ${\alpha }^4{E}_{\text{h}}$ at leading order, in agreement with the formal perturbation theory result available from the literature.

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Cited by in corpus (8)

• The Bethe-Salpeter QED wave equation for bound-state computations of atoms and molecules
• Bound-state relativistic quantum electrodynamics: a perspective for precision physics with atoms and molecules
• Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians
• Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems
• QED corrections to the correlated relativistic energy: one-photon processes
• One-particle operator representation over two-particle basis sets for relativistic QED computations
• Rovibrational computations for the He${}_2$ a ${}^3{\Sigma }_{\mathrm{u}}^{+}$ state including non-adiabatic, relativistic, and QED corrections
• Double-pair Coulomb and Breit photon correction to the correlated relativistic energy