Born-Oppenheimer potentials for $\Pi$, $\Delta$, and $\Phi$ 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 $\Pi$, $\Delta$, 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.