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

• URL: http://arxiv.org/abs/2211.14180v1
• Date: Fri, 25 Nov 2022 15:37:31 GMT
• Title: Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states
• Authors: P\'eter Jeszenszki and Edit M\'atyus
• Abstract summary: The triplet contribution is computed to the 1 and 2 states of the He atom. The no-pair Dirac-Coulomb-Breit wave equation is converged within a sub-parts-per-billion relative precision. The fine-structure constant dependence of the triplet sector contribution to the variational energy is $alpha4E_texth$ at leading order.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The triplet contribution is computed to the 1 and 2 $^1S^\text{e}_0$ states of the He atom, to the $1\ ^1S^\text{e}_0$ 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 $\alpha^4E_\text{h}$ at leading order, in agreement with the formal perturbation theory result available from the literature.

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