Sum-Over-State Expressions Including Second-Order Herzberg-Teller Effects For The Calculation Of Absorption And Resonance Raman Intensities

The sum-over-state expressions are derived to calculate the second-order Herzberg-Teller (HT) effects in absorption and resonance Raman spectroscopies. These effects depend on the second derivatives of the transition dipole moment with respect to the vibrational coordinates. The method is applied to the molecule of 1,3-butadiene using density functional theory calculations. It is found that the second-order HT effects are significant for both absorption and resonance Raman intensities, and that the calculated spectra are in good agreement with the experimental data. The second-order HT effects originate from diagonal elements of the second derivatives matrix, whereas non-diagonal elements have a negligible impact on the intensities of 1,3-butadiene. Published under an exclusive license by AIP Publishing.