Relativistic corrections to the ground states of HD and D calculated without using the Born-Oppenheimer approximation.

The Schrödinger equation for the ground states of the hydrogen molecules HD and D is solved variationally by treating the constituent particles of HD or D on the same footing without assuming the Born-Oppenheimer approximation. The variational basis sets are constructed using Hylleraas coordinates that are traditionally adopted for few-electron atomic systems. The nonrelativistic energy eigenvalues are converged to the level of 10 cm. The leading-order relativistic corrections, including relativistic recoil terms, are calculated rigorously. Together with the higher-order relativistic and quantum electrodynamic corrections obtained by the Pachucki's group [Phys. Rev. A., 2017, 95, 052506; Phys. Rev. Lett., 2018, 120, 153001], we determine the dissociation energy of D to be 36748.36240(28) cm, which agrees with the recent experimental result of Liu et al. [J. Chem. Phys., 2010, 132, 154301] 36748.36286(68) cm. For HD, the dissociation energy determined by us is 36405.78252(27) cm, which deviates from the most accurate experimental result of Sprecher et al. [J. Chem. Phys., 2010, 133, 111102] 36405.78366(36) cm by about 2σ.