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arXiv · 2211.14180

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

Péter Jeszenszki·Edit Mátyus
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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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Péter Jeszenszki, Edit Mátyus. 2022-11-25. Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states. https://doi.org/10.1063/5.0136360

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