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

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.

References in corpus (2)

• Analytical two-center integrals over Slater geminal functions
• Photolysis production and spectroscopic investigation of the highest vibrational states in H${}_2$ (X${}^1{\Sigma }_g^{+}$ $v=13,14$)

Cited by in corpus (9)

• Improved Ionization and Dissociation Energies of the Deuterium Molecule
• Born-Oppenheimer potentials for $\Pi$, $\Delta$, and $\Phi$ states of the hydrogen molecule
• Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ ${}^1{\Sigma }_{\text{g}}^{+}$ manifold of molecular hydrogen
• Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen
• Precision measurement of quasi-bound resonances in H${}_2$ and the H + H scattering length
• Shape resonances in H${}_2$ as photolysis reaction intermediates
• Spectroscopic study of the F${}^1{\Sigma }_g^{+}$ outer well state in H${}_2$, HD and D${}_2$
• Indirect probing of light-induced nonadiabatic dynamics in lossy nanocavities
• The Stark effect in molecular Rydberg states: Calculation of Rydberg-Stark manifolds of H${}_2$ and D${}_2$ including fine and hyperfine structures