Born-Oppenheimer potentials for $\Pi$, $\Delta$, and $\Phi$ states of the hydrogen molecule

TL;DR

This paper presents highly precise variational calculations of the Born-Oppenheimer potentials for excited states of the hydrogen molecule with various symmetries, significantly improving accuracy and providing first-ever results for many states.

Contribution

The study introduces a novel recursive integral evaluation method achieving unprecedented precision in potential energy curves for excited hydrogen molecule states.

Findings

Potential energy curves with $10^{-9}$ accuracy

First-ever calculations for many excited states

Significant improvement over previous results

Abstract

We report on accurate variational calculations of the Born-Oppenheimer potential for excited states of the hydrogen molecule with $\Pi$, $\Delta$, and $\Phi$ symmetries. The obtained potential energy curves reach the relative precision of $10^{-9}$ or better along internuclear distances of 0.01 -- 20 au. Calculations rely on recursive evaluation of two-center two-electron molecular integrals with exponential functions in arbitrary precision arithmetics. Our results for most of the states are the first ever reported, and for the previously calculated states constitute an improvement by several orders of magnitude.