Inclusion of Nuclear Motion in Calculations of Optical Properties of Diatomic Molecules

An explicit expression is derived which permits the exact inclusion of nuclear motion in calculations of second-order optical and magnetic molecular properties within the Born-Oppenheimer approximation. Explicit calculations are carried out on the model problem of the hydrogen molecular ion for the exact zz component of the Rayleigh and vibrational Raman scattering tensors and for several approximations to these tensors. The result is somewhat sensitive to the approximate expression employed but the semiclassical approximation is accurate to within a percent in both cases.