Study of the franck-condon and herzberg-teller approximations

Using the Born-Oppenheimer parameter lambda = (m/M)(1/4) as a perturbation parameter, we find that for allowed transitions, the zeroth order approximation of the spectral intensity gives rise to the Condon approximation, the first order vibronic coupling and anharmonic effect appear in the first order approximation of the spectral intensity, which gives us the non-Condon scheme, and only the intensity of the transitions of totally-symmetric modes with nonvanishing normal coordinate displacements is affected by the inclusion of the first order vibronic coupling and anharmonic effect. For symmetry-forbidden but vibronic-allowed transitions, the first nonvanishing term of the spectral intensity is second order with respect to lambda and the B-O couplings do not appear in the calculation of the spectral intensity until the fourth order approximation with respect to lambda; in this case, other high order vibronic couplings and anharmonic effect are competing with the B-O couplings.