Temperature effects in the time-correlator theory of resonance Raman scattering

Abstract

Within well-defined ‘‘standard’’ assumptions and the time-correlator theory’s separation of resonance Raman (RR) scattering into orders, previously discussed exact relations allow one to calculate mth-order RR profile line shapes directly from optical absorption data at T≠0 K. At T=0 K, the mth-order profiles are identical with the full m-phonon profiles, which are the experimentally measured quantities, while for T≠0 K, the m-phonon profiles include higher-order corrections due to processes which freeze out at T=0 K and which involve virtual phonon excitation–deexcitation in all Franck–Condon active modes. In this paper we show that for one-phonon scattering from a large class of multimode systems, the correction due to a thermally populated mode is small if (1) the mode’s frequency is small compared with the smallest resolvable width in the optical absorption and/or (2) the mode’s electron–phonon coupling is weak. For the multimode system β-carotene in isopentane at T=123 and 298 K, the sum of corrections due to all thermally populated Franck–Condon active modes is found to be negligible, so that even at room temperature, the first-order and one-phonon profiles are essentially identical. Our first-order profile line shapes calculated from optical absorption data for T=123 and T=298 K account well for the observed thermal broadening and are in good overall agreement with the measured one-phonon profiles. A short-time approximation is developed and is shown to give insight into our numerical results—in particular, in the limit of a large number of thermally populated low-frequency modes of comparable electron–phonon coupling strengths, the sum of these modes’ higher-order corrections to the one-phonon profiles is shown to vanish. The negligibility of the higher-order corrections leads to efficient T≠0 K multimode numerical modeling procedures which allow one to conveniently obtain both the optical absorption and RR profiles from a single one-dimensional fast Fourier transform of the absorption time-correlator. Generalizations to mth-order scattering are briefly discussed.