Accurate non-Born–Oppenheimer calculations of the lowest vibrational energies of and with including relativistic corrections

In this work we report very accurate variational calculations of the two lowest vibrational states of the D 2 and T 2 molecules within the framework that does not assume the Born–Oppenheimer approximation. The non-relativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α 2 calculated as expectation values of the operators representing these effects. The v = 0 → 1 transition energy of D 2 obtained in the calculations is compared with the transition frequency obtained from the experimental spectra. The comparison shows the need to include corrections higher than second-order in α to further improve the agreement between the theory and the experiment.