Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of $H2$

The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the $H2$ using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the internuclear distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.