Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule

Abstract

We report on accurate variational calculations of the Born–Oppenheimer potential for excited states of the hydrogen molecule with $\mathrm{\Pi },\mathrm{\Delta }$, and Φ 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 the recursive evaluation of two-centre 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.

GRAPHICAL ABSTRACT

Keywords:

• Born–Oppenheimer
• hydrogen molecule
• excited state
• Kolos–Wolniewicz

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors acknowledge support from the National Science Center (Poland) [grant number 2017/27/B/ST2/02459], and M.S. acknowledges additional support [grant number 2020/36/T/ST2/00605] (Doctoral scholarship ETIUDA).