Accurate Born-Oppenheimer potential for HeH+

TL;DR

This paper presents highly accurate calculations of the HeH$^+$ molecule's Born-Oppenheimer potential using new analytic formulas, achieving near-spectroscopic precision across a broad range of internuclear distances.

Contribution

Introduction of novel analytic formulas for two-center two-electron integrals enabling highly precise Born-Oppenheimer potential calculations for HeH$^+$.

Findings

Potential calculated with $10^{-12}$ au precision

Potential at equilibrium distance specified with high accuracy

Results enable spectroscopic-level theoretical predictions

Abstract

We demonstrate high accuracy calculations for the HeH$^+$ molecule using newly developed analytic formulas for two-center two-electron integrals with exponential functions. The Born-Oppenheimer potential for the ground electronic $^1\Sigma^+$ state is obtained in the range of 0.1 -- 60 au with precision of about $10^{-12}$ au. As an example at the equilibrium distance $r=1.463\,283$ au the Born-Oppenheimer potential amounts to $-2.978\,708\,310\,771(1)$. Obtained results lay the ground for theoretical predictions in HeH$^+$ with spectroscopic precision.