Time domain information from resonant Raman excitation profiles: A direct inversion by maximum entropy

A direct method for the inversion of resonant Raman excitation profiles to the time domain is proposed. The inversion procedure is implemented within the maximum entropy (ME) formalism. The constraints used in the ME procedure are the values of the Fourier transform of the Raman excitation profile at a given set of values of times t_r. It is shown that the ME functional form of the Raman cross section can be expressed in terms of a Raman amplitude, depending on the Lagrange multipliers and on the constraints. The Fourier transform of the Raman amplitude yields the time dependent cross correlation function. Another route to direct inversion, using a Fourier series expansion of the dispersion relation, is also considered. The analytical requirements that must be satisfied by the input excitation profile for a successful inversion to be possible are discussed. The optimum values of the times t_r and of the Lagrange multipliers which determine the Raman amplitude are computed using a new algorithm (the min-max algorithm). The proposed ME jumerical procedure is implemented for computed resonant Raman excitation profiles of the B electronic state of the iodobenzene molecule and of a model anharmonic system. In addition, the analytical implications of the ME functional form of the excitation profile are discussed with special reference to the separation of time scales in the dynamics.