Comparison of simplified sum-over-state expressions to calculate resonance Raman intensities including Franck-Condon and Herzberg-Teller effects

Sum-over-state (SOS) expressions to simulate absorption spectroscopy and resonance Raman (RR) scattering including Franck-Condon (FC) and Herzberg-Teller (HT) effects are described. Starting from the general SOS method, several simplified SOS formulae are derived. In particular, within the so-called independent mode displaced harmonic oscillator model, it is shown that including the vibronic structure in the absorption and RR spectra only requires the calculation of FC overlap integrals of the type , where g, e, and v stand for the electronic ground state, excited state, and vibrational quantum number, respectively. Additionally, an approximation of the latter approach is introduced, referred as the simplified Phi(e) method, in which the FC factors are neglected. This method is advantageous from the computational point of view and it is demonstrated that it reproduces the main characteristics of the more involved approaches. The merits and drawbacks of the different methods are discussed by applying them to the prototypical compound of Rhodamine 6G. Overall, this work intends to unravel and clarify some differences in the SOS theories of RR scattering. (C) 2016 AIP Publishing LLC.