Variational calculations on the hydrogen molecular ion

We present high-precision non-relativistic variational calculations of boun d 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 S igma and Pi states but without using the Born-Oppenheimer or any adiabatic approximation. Convergence studies are presented which indicate that the re sulting energies for low-lying levels are accurate to about 10(-13). Our pr ocedure accounts naturally for the lambda-doubling of the Pi(u) state.