``Forbidden'' Character in Allowed Electronic Transitions

A theory for calculating the intensity of ``forbidden'' character in allowed electronic transitions is given based upon the early work of Herzberg and Teller. It is seen how both symmetric and nontotally symmetric vibrations may be active in the perturbation, and the temperature dependence of ``forbidden'' intensity is explicitly obtained for harmonic oscillator wave functions. As an example the case of certain p-disubstituted benzenes is discussed in detail. A model derivative normal coordinate analysis is used to calculate perturbation energies in terms of electronic wave function parameters. It is seen how the magnitude of ``forbidden'' character is very sensitive to the detailed nature of the mixing electronic wave functions. Several trial functions are introduced to calculate the ratio of ``forbidden'' to allowed character in the near ultraviolet band. Comparison is made with recent observations of mixed polarization in two benzene derivatives. Finally, the possible significance of ``forbidden'' character with respect to radiationless transitions is briefly discussed.