Calculation of resonance Raman excitation profiles

The present work describes a novel mathematical scheme for the evaluation of multidimensional time domain integrals that arise in the calculation of resonance Raman excitation profiles and the optical absorption spectra when the electronic transitions take place between displaced, distorted, and rotated harmonic potential energy surfaces. A recipe is provided for formulating the time domain integrals in terms of a tractable summation of products involving hermite polynomials. Expressions for the special cases (displaced and/or distorted oscillators) are written in terms of mathematical special functions which are computationally easier to deal with. Relations with the socalled transform theory are discussed. Resonance Raman excitation profiles and the optical absorption spectrum for a 7-mode system are calculated as an illustration of our expressions