Complete α2 relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of HeH+

We report the implementation of the complete set of the lowest-order relativistic corrections of the order of alpha(2) (where alpha is the fine structure constant) for calculating vibrational states of diatomic molecular systems within the framework that does not assume the Born-Oppenheimer approximation. To test the accuracy of the approach we have performed calculations for all rotationless vibrational states (also called pure vibrational states or S states) of the HeH+ ion in the ground electronic state. For the lowest transitions, where very precise experimental results are available, an excellent agreement with the experimental values has been achieved.