Variational calculations on the hydrogen molecular ion

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.