Calculations of resonance Raman spectra of conjugated molecules

A method for calculations of the complete resonance Raman (RR) spectrum of large conjugated molecules is presented. The method is based on calculations of the Franck–Condon factors and on differentiation of the electronic transition moments with respect to the vibrational normal modes. This approach is more simple and practical than previous treatments which are based on the Herzberg–Teller expansion. It allows one to evaluate quantitatively the contributions of the A and B terms to the RR intensity pattern. This paper gives the detailed derivation of the calculation scheme and examines different possible approximations. The multimode nature of the RR process is considered in detail and the effect of combination levels is taken into account explicitly. It is shown that in cases of resonance with strong electronic transitions the A term is much more important than the B term. The calculations are demonstrated by the evaluation of the Raman spectra of butadiene and 1,3,5-hexatriene in the nonresonance region, and by the evaluation of the RR spectra of β-carotene, β-ionone, and all-trans retinal. A reasonable agreement is obtained between the calculated and observed relative intensities and excitation profiles. Applications of the calculations to cases of weak electronic transitions are also considered.