Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen

TL;DR

This paper calculates highly precise energies for excited states of molecular hydrogen, including relativistic and QED corrections, achieving excellent agreement with experimental data.

Contribution

It provides the first highly accurate pre-Born-Oppenheimer energies for multiple excited states of hydrogen, incorporating relativistic and QED effects.

Findings

Achieved 1-3 ppb precision for non-relativistic energies.

Included leading-order relativistic and QED corrections.

Results agree well with experimental measurements.

Abstract

For rovibronic states corresponding to the $B$ and $B'\ ^1\Sigma_\text{u}^+$ electronic states of the hydrogen molecule, the pre-Born--Oppenheimer (four-particle) non-relativistic energy is converged to a 1-3 parts-per-billion relative precision. The four-particle non-relativistic energy is appended with leading-order relativistic, leading- and estimated higher-order quantum-electrodynamics corrections. The resulting term values referenced to the rovibronic ground state are obtained in an excellent agreement with the experimental results. Further results are reported and discussed for other rovibronic states assignable to the $C\ ^1\Pi_\text{u}$ and the $EF,GK,$ and $HH\ ^1\Sigma_\text{g}^+$ electronic states.