Is the adiabatic approximation sufficient to account for the post-Born-Oppenheimer effects on molecular electric dipole moments?

We estimated the post-Born-Oppenheimer (post-BO) contribution to electric dipole moments by finite-field derivatives of the diagonal Born-Oppenheimer correction computed with correlated electronic wave functions. The new method is used to examine the effect of isotopic substitution on the dipole moments of the HD, LiH, LiD, and (H2O)-O-16 molecules. The non-zero dipole moment of HD is solely due to the post-BO effect and is predicted within a few percent of the best experimental and theoretical results. The post-BO contribution to the dipole moment in LiH and LiD is comparable in magnitude to that in HD, but the difference in total adiabatic dipole moments of LiH and LiD is dominated by the vibrationally averaged BO contribution, and the post-BO contribution is relatively unimportant. However, the post-BO contribution to the dipole moment in H2O is much larger than the vibrationally averaged BO contribution determined by Lodi et al. [J. Chem. Phys. 128, 044304 (2008)] and is twice as large as the discrepancy between their best theoretical BO estimate and the most recent experimental result. Our findings suggest that for species that are well behaved in the BO sense, the post-BO contribution to molecular electric dipole moments can be described within the adiabatic approximation to a few percent accuracy.