Accurate Born-Oppenheimer potentials for excited $\Sigma^{+}$ states of the hydrogen molecule

TL;DR

This paper presents highly accurate Born-Oppenheimer potential calculations for excited states of the hydrogen molecule, achieving unprecedented precision up to 10^{-10} and significantly surpassing previous results.

Contribution

The authors provide the most precise Born-Oppenheimer potentials for excited hydrogen molecule states, using advanced variational methods and explicit correlation techniques.

Findings

Achieved relative accuracy of 10^{-10} for all states and distances.

Improved accuracy by at least 6 orders of magnitude over previous results.

Applied efficient integral evaluation with explicitly correlated exponential basis.

Abstract

We report on highly accurate calculations of Born-Oppenheimer potentials for excited $n\,\Sigma^{+}$ states of the hydrogen molecule for all possible combinations of singlet/triplet and gerade/ungerade symmetries up to $n=7$. A relative accuracy of $10^{-10}$ (0.00002 cm$^{-1}$) or better is achieved for all the internuclear distances and all the excited states under consideration -- an improvement with respect to the best results available in the literature by at least 6 orders of magnitude. Presented variational calculations rely on efficient evaluation of molecular integrals with the explicitly correlated exponential basis in arbitrary precision arithmetics.