An efficient method to calculate resonance Raman amplitudes via polynomial propagation

An accurate and efficient method is suggested for calculating the resonance Raman spectrum. This approach, based on Chebyshev propagation, bears close resemblance to the time-dependent theory of resonance Raman scattering due to Heller and co-workers [S.-Y. Lee, E.J. Heller, J. Chem. Phys. 71 (1979) 4777; D.J. Tannor, E.J. Heller, J. Chem. Phys. 77 (1982) 202; E.J. Heller, R.L. Sundberg, D.J. Tannor, J. Phys. Chem. 86 (1982) 1822]. However, it makes no reference to time and requires no approximation of the propagator. Since Raman amplitudes can be expressed in this method as a discrete Fourier transform of cross-correlation functions, no integration error is introduced. In addition, the propagation of the excited-state wave packet can be restricted to real space, further reducing computational costs. Numerical testing of the method is carried out with a two-dimensional methyl iodide model.