Abstract:
We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational
states of diatomic molecular systems with electrons within the framework that does not assume
the Born-Oppenheimer BO approximation. The correction is calculated as the expectation value of
the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly
correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we
can now calculate the complete relativistic correction of the order of 2 where =1/c . The new
algorithm is applied to determine the full set of the rotationless vibrational levels and the
corresponding transition frequencies of the H2 molecule. The results are compared with the previous
calculations, as well as with the frequencies obtained from the experimental spectra. The
comparison shows the need to include corrections higher than second order in to further improve
the agreement between the theory and the experiment