Abstract
An alternative time-frame approach, which is canonically conjugate to the energy-frame approach, for implementing the transform relations for calculating Raman excitation profiles directly from the optical absorption spectrum is presented. Practical and efficient fast Fourier transformation in the time frame replaces the widely used Chan and Page algorithm for evaluating the Hilbert transform in the energy frame. The time-frame approach is applied to: (a) a two-mode model which illustrates the missing mode effect in both absorption and Raman excitation profiles, (b) carotene, in which both the absorption spectrum and the Raman excitation profile show vibrational structure and (c) hexamethylbenzene: TCNE electron donor—acceptor complex where the same spectra are structureless and the Raman excitation profile for the 168 cm −1 mode poses a problem for the energy-frame approach. A similar time-frame approach can be used for the inverse transform from the Raman excitation profile to the optical absorption spectrum.
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