2 1 N ov 1 99 8 Variational calculations on the hydrogen molecular ion

We present high-precision non-relativistic variational calculations of bound vibrational-rotational state energies for the H2 + and D2 + molecular ions in each of the lowest electronic states of Σg, Σu, and Πu 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 Πu state. PACS numbers: 31.15.Ar, 31.15.Pf, 33.15.Fm Typeset using REVTEX