Variational calculations on the hydrogen molecular ion

Abstract

We present high-precision non-relativistic variational calculations of bound vibrational-rotational state energies for the $H_2^+$ and $D_2^+$ molecular ions in each of the lowest electronic states of $Σ_g$, $Σ_u$, and $Π_u$ symmetry. The calculations are carried out including coupling between $Σ$ and $Π$ states but without using the Born-Oppenheimer or any adiabatic approximation. Convergence studies are presented which indicate that the resulting energies for low-lying levels are accurate to about $10^{-13}$. Our procedure accounts naturally for the lambda-doubling of the $Π_u$ state.