Spectral line shapes of damped quantum oscillators: Applications to biomolecules

Gu, Yuangang; Widom, Allan; Champion, Paul M.
February 1994
Journal of Chemical Physics;2/15/1994, Vol. 100 Issue 4, p2547
Academic Journal
We present a full quantum mechanical treatment, using the quantum fluctuation–dissipation theorem, which is useful in describing the absorption line shape of a system composed of damped vibrational (harmonic) oscillators that are linearly coupled to an electronic excitation. The closed form expressions obtained from the model predict optical line shapes that are identical to standard treatments at high temperature or in the absence of damping. However, at low temperature, quantum corrections become important and the model predicts a skewed optical line shape that reflects the condition of detailed balance and differs significantly from the ‘‘Brownian oscillator’’ model of Yan and Mukamel [J. Chem. Phys. 89, 5160 (1988)]. We also find that quantum effects become observable in the line shape of the overdamped oscillator only when kBT/hω0≲ω0 /γ <1, which effectively depresses the temperature for crossover into the quantum regime. In Appendix D we discuss how the time correlator expressions derived for the line shape analysis can also be used to describe chemical reactions in the presence of quantum damping. The fact that the transition temperature for quantum behavior is depressed in the presence of strong damping may explain why the ‘‘classical’’ Arrhenius expression is often found to hold, even at temperatures where kBT


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