The underdamped Brownian oscillator model with Ohmic dissipation: Applicability to low-temperature optical spectra

The multimode Brownian oscillator (MBO) model with Ohmic dissipation has frequently been used to interpret photon echo and spectral data on solvation dynamics of chromophores in liquids at room temperature. We report on the applicability of this model to high-resolution linear electronic absorption spectra of chromophores in solid hosts at low temperatures, where the zero-phonon line (ZPL) is resolved from phonon sideband structure. The results are also relevant to frequency and time domain nonlinear spectra. In the MBO model, active BOs (phonons) are linearly coupled to bath modes. This coupling endows the bath modes with absorption intensity which, with Ohmic dissipation (white light spectrum for the bath modes), results in the bath modes contributing to absorption in the region of the ZPL. Experimental results for a multitude of molecular systems indicate that the ZPL profile is determined by electronic dephasing, which is not accounted for in the MBO model. Thus, it is important to assess the contribution of the MBO bath modes to the ZPL profile. To this end, closed-form, finite temperature expressions for the underdamped MBO (UMBO) model are derived for the linear response function, linear absorption spectrum, and width and Franck-Condon factor of the ZPL. It is proven formally that the UMBO ZPL width is zero at T=0 K. Results of calculations for model systems whose parameter values (BO damping constant, frequency and Huang-Rhys factor) are typical of real systems are presented. It is concluded that Ohmic dissipation leads to unphysically large ZPL widths as well as asymmetric ZPL profiles that appear not to have been observed. Moreover, the ZPL width adds to those of the multi-BO (phonon) transitions. Thus, use of the UMBO model with Ohmic dissipation to interpret data on relaxation dynamics of nuclear modes may result in erroneous conclusions. It is shown that Franck-Condon factors of the ZPL obtained with the UMBO model can differ significantly from those calculated with the conventional formula. (C) 2002 American Institute of Physics.