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 ${\Sigma }_g$, ${\Sigma }_u$, and ${\Pi }_u$ symmetry. The calculations are carried out including coupling between $\Sigma$ and $\Pi$ 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 ${\Pi }_u$ state.

23 pp., RevTeX, epsf.sty, 5 figs. Enhanced data in Table II, dropped 3 figs. from previous version