Ab initio ro-vibrational levels of H3+ beyond the Born-Oppenheimer approximation

The value of the adiabatic correction to the Born-Oppenheimer electronic energy is calculated as a function of geometry for H3+ using SCF wavefunctions. A mass-dependent adiabatic function is combined with the near-Born-Oppenheimer electronic structure calculations of Rِhs, Kutzelnigg, Jaquet and Klopper and the rotation-vibration energy levels of H3+ and D3+ are calculated. The levels for H3+ are significantly better than any previous ab initio estimates but are less accurate than those obtained by recent spectroscopically determined effective H3+ potentials. The adiabatic correction is less important for the heavier D3+. For both ions rotational levels are obtained to near experimental accuracy. Small, systematic shifts in the vibrational bands may be attributable to residual errors in the Born-Oppenheimer potential.