Complete 2 relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of HeH+

Abstract

We report the implementation of the complete set of the lowest-order relativistic corrections of the order of 2 where 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