Nonadiabatic effects in the ground state of the hydrogen molecule

A sum-over-states procedure is used in the ab initio evaluation of the matrix elements needed for a nonadiabatic treatment of the ground electronic state of H₂. Bunker's (J. Mol. Spectrosc.42, 478 (1972)) semiempirical value for the nonadiabatic parameter l₁ = 0.130 ± 0.006 is in agreement with the present calculation, which therefore supports the interpretation of the difference between theoretical adiabatic and experimental vibrational energies as being due to nonadiabatic effects. The same techniques are used to evaluate the expectation value of $\text{?}{}^2\text{?R}{}^2$ in the H₂ ground electronic state. Finally, it is pointed out that an average energy denominator used in several recent treatments of nonadiabatic effects in H₂ is in error by roughly a factor of two. The correct average energy denominator reflects that the sums have large contributions from states in the electronic continuum.