Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory

TL;DR

This paper provides highly accurate theoretical calculations of rovibrational energy levels of hydrogen molecules, incorporating all significant corrections beyond the Born-Oppenheimer approximation, including nonadiabatic, relativistic, QED, and finite nuclear size effects.

Contribution

It introduces a comprehensive nonadiabatic perturbation theory approach to accurately determine rovibrational levels of hydrogen molecules, including relativistic and QED effects, with results accessible via simple computer code.

Findings

Achieved transition wavelength accuracy of 10^{-3} to 10^{-7} cm^{-1}

Included all significant corrections beyond Born-Oppenheimer approximation

Provided computational tools for practical use

Abstract

We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading $\alpha^5\,m$ and the next-to-leading $\alpha^6\,m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of $10^{-3}$--$10^{-7}$ cm$^{-1}$, and are provided by simple to use computer code.