VIBRONIC SPECTRA IN CONDENSED MATTER - A COMPARISON OF EXACT QUANTUM-MECHANICAL AND VARIOUS SEMICLASSICAL TREATMENTS FOR HARMONIC BATHS

We consider the problem of calculating the vibronic absorption spectru m of a diatomic molecule coupled to a condensed phase environment, whe re all nuclear degrees of freedom are taken in the quadratic approxima tion, and where the two electronic states couple differently to the so lvent. This simple model is used to examine several commonly used semi classical approximations. The method of Kubo-Toyozawa is adapted to en able exact calculation of the real-time dipole autocorrelation functio n for the quantum mechanical treatment. Alternatively, we derive an ex pression for this correlation function in terms of a path-integral inf luence functional, which is not limited to a finite number of bath mod es and could be applied to treat anharmonic solutes in condensed matte r. We then obtain an analytical solution for the classical treatment o f nuclear dynamics, and develop a mixed quantum-classical approach, wh ere the dynamics of the diatomic vibrational mode is treated quantum m echanically and the bath is treated classically. It is shown that the mixed quantum-classical treatment provides better agreement with the e xact quantum treatment than the other approximations for a wide range of parameters. Exact analytical results similar to the pure dephasing theory of Skinner and Hsu are obtained for the asymptotic long time be havior of the dipole autocorrelation functions. (C) 1998 American Inst itute of Physics. [S0021-9606(98)50303-0].