A general microscopic theory of bulk second-harmonic generation from molecular crystals

Expressions are derived for bulk second-harmonic generation from molecular crystals including electric dipole, electric quadrupole, magnetic dipole, electric field, electric field gradient and magnetic field contributions. Terms bilinear in the electric field and the electric field gradient or magnetic field depend on differences of molecular response coefficients at different frequencies. The results can be written in terms of non-local hyperpolarizabilities that are significantly generalized through self-consistent and indirect responses, modified by three local field tensors or by two local field tensors and one local field gradient tensor. A previous result for linear optical activity is extended by incorporating the quadrupole field gradient polarizability. Overall, the treatment provides a rigorous basis for numerical calculations of SHG from insulating molecular crystals.