David Bishop approach to vibrational dynamic contributions to molecular properties. Application to Jones and Magnetoelectric birefringences in diatomic molecules

The expressions derived by D. M. Bishop for the pure vibrational contributions to the dynamic electric dipole polarizabilities and hyperpolarizabilities of polyatomic molecules (see Bishop, D. M. Rev Mod Phys, 1990, 62, 343) are generalized to arbitrary linear, quadratic and cubic response functions, and then applied to determine the effect of nuclear motion on two diatomic molecules (N2 and CO) on Jones (and Magnetoelectric) linear birefringences. The influence of nuclear motion on the anisotropy of the refractive index appears to be quite contained: the observable differs from the equilibrium electronic estimate by ≈4% for N2, and by ≈8–9% in CO. As a case study, also the effect of vibrations on the temperature independent contribution to Buckingham birefringence of H2 and D2 is analyzed and discussed.