SPECTRAL-LINE SHAPES OF DAMPED QUANTUM OSCILLATORS - APPLICATIONS TO BIOMOLECULES

We present a full quantum mechanical treatment, using the quantum fluc tuation-dissipation theorem, which is useful in describing the absorpt ion line shpae of a system composed of damped vibrational (harmonic) o scillators that are linearly coupled to an electronic excitation. The closed from expressions obtained from the model predict optical line s hapes that are identical to standard treatments at high temperature of in the absence of damping. However, at low temperature, quantum corre ctions become important and the model predicts a skewed optical line s hape taht reflects the condition of detailed balance and differs signi ficantly from the ''Brownian oscillator'' model of Yan and Mukamel [J. Chem. Phys. 89, 5160 (1988)]. We also find that quantum effects becom e observable in the line shape of the overdamped oscillator only when k(B)T/($) over bar omega(0)<to>omega 0/gamma <1, which effectively dep resses the temperature for crossover into the quantum regime. In Appen dix D we discuss how the time correlator expressions derived for the l ine shape analyisis can also be used to describe chemical reactions in the presence of quantum damping. The fact that the transition tempera ture for quantum bahaviour is dperessed int he presence of strong damp ing may explain why the ''classical'' Arrhenius expression is often fo und to hold, even at temperatures where k(B)T<($) over bar h omega(0). Finally we exploare the consequences of introducing a classical contr ol variable (corresponding to slow conformational motions of a biomole cule), which is coupled to the optically active vibrational mode(s) of the embedded chromophore. This leads to a modulation of the Stokes sh ift and optical coupling in the system and results in a type of inhomo geneous broadening that has both a Guassian and non-Guassian component . The non-Guassian broadening is found to be consistent with the highl y skewed inhomogeneous line shape of deoxymyoglobin.