An atom–dipole interaction theory of the hyperpolarizability contribution to the optical activity of molecules

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Abstract
The atom–dipole interaction model formulation of the polarizability theory of optical activity is generalized to include hyperpolarizability effects. This is done by considering the response of the optical rotation of a high frequency light signal to the intensity and orientation of the electric vector of another low frequency but intense light signal. The molecular polarizabilities are written in terms of the two‐, three‐, and four‐atom relay tensors and the electric vector of the low frequency field. Expressions are derived for the electric displacement and magnetic induction vectors, and values for the refractive indices of two different elliptically polarized light waves are extracted from Maxwell’s equations. Lastly, expressions for the optical rotation rate and the ellipticity rate are derived, and a sample calculation is performed on the halomethane CHFClBr.