Quantum Theory of the Intensities of Molecular Vibrational Spectra

Formulas for the transition probabilities and hence the absolute intensities of molecular vibrational spectra are obtained from a unified quantum field treatment. The theory of infrared, Raman, and hyper-Raman spectroscopy of molecular vibrations is developed by assuming these processes occur as time-ordered steps involving the creation or destruction of one quantum of vibrational energy and changes in the occupation number of one, two, or three photons, respectively. The formulas obtained by this method for ir transitions become equivalent to the earlier treatment of Jones and Simpson if the energy difference of the ground and first excited electronic energy levels are very large relative to that of the vibrational quantum. The formulas obtained for Raman transitions are very similar to those obtained by the method originated by Albrecht and developed further by Savin; we get not only the original terms of Albrecht but also the trace terms obtained by Savin. Furthermore by using third-order time-dependent equations from the start we avoid many of the difficulties of the earlier treatments; our equations predict different conditions for the resonant Raman effect than do the earlier equations, and experiments are suggested for testing the new equations. The formula which we give for the absolute intensity of the hyper-Raman effect appears to be the first ever given.