Leading-order relativistic corrections to the rovibrational spectrum of H2 + and HD+ molecular ions

High-precision variational calculations of the operators for the relativistic corrections in the leading mα4 order are presented. The rovibrational states in the range of the total orbital angular momentum L=0-4 and vibrational quantum number v=0-10 for the H2+ and HD+ molecular ions are considered. We estimate that about 10 significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of 10-12 relative uncertainty. © 2019 American Physical Society.