HYPERPOLARIZABILITY AND FORBIDDEN RAMAN LINES

Abstract

The familiar selection rules for the Raman spectra of gases are based upon the symmetry properties of the first term in a power series expansion of the induced electric moment as a function of the local electric field. This theory is extended to include the second term in such a power series, i.e.\begin{equation} \mu = \alpha F +\frac{\beta} {2}F^{2} \end {equation} where $\mu$ is the induced moment and F is the local field. By considering the transformation properties of $\beta$ for various molecular symmetries and by assessing the relative importance of the terms in F due respectively to the exciting illumination or to neighboring molecules in the condensed state, a large variety of forbidden transitions can be predicted. Depolarization factors Lave been evaluated and related to previous experimental studies of $CO_{2}$, $CS_{2}$, $C_{6}H_{6}$, etc.