Relativistic corrections to the ground state of H_2 calculated without using the Born-Oppenheimer approximation

摘要

The Schr?dinger equation for the ground state of the hydrogen molecule H_2 is solved by applying the Rayleigh-Ritz variational method in Hylleraas coordinates without using the Born-Oppenheimer approximation. The nonrelativistic energy eigenvalue is converged to ?1.164 025 030 880(7) atomic units. The leading-order relativistic corrections, including the mass-velocity, Darwin, orbit-orbit, spin-spin, and relativistic recoil terms, are evaluated perturbatively. Together with the higher-order relativistic and quantum electrodynamic corrections obtained by Puchalski et al. [Phys. Rev. Lett. 117, 263002 (2016)], we determine the dissociation energy of the hydrogen molecule, D_0 = 36 118.069 71(33) cm~(?1), which agrees with the two recent experimental results of Liu et al. [J. Chem. Phys. 130, 174306 (2009)], 36 118.069 62(37) cm~(?1), and Altmann et al. [Phys. Rev. Lett. 120, 043204 (2018)], 36 118.069 45(31) cm~(?1).