Accurate non-Born-Oppenheimer calculations of the lowest vibrational energies of D₂ and T₂ with including relativistic corrections

In this work we report very accurate variational calculations of the two lowest vibrational states of the D₂ and T₂ 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 α² calculated as expectation values of the operators representing these effects. The ν=0→1 transition energy of D₂ 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.