A Brownian oscillator approach to the Kennard-Stepanov relation

The Kennard-Stepanov (KS) relation, also known as the reciprocity relation, connects the absorption and fluorescence spectra of homogeneous complex systems under the assumption of thermal equilibration of the emitting electronic state. A recent elaboration of the theory by Sawicki and Knox (SK) [Phys. Rev. A, 1996 54, 4837] introduces a spectral temperature that is a sensitive indicator of the failure of the relation. Studies using the SK formalism, which have been limited almost exclusively to experimental cases, reveal various failures that may be due to incomplete equilibration, inhomogeneity, or both. Using the Brownian oscillator model for nuclear dynamics, we investigate the KS relation theoretically with the aid of the SK spectral temperature. The spectral temperature is again found to be a sensitive indicator, this time of the accuracy of the numerical methods necessary for the multiple integrations. The original KS relation appears to hold regardless of the memory effects of the bath, a result which is not totally unexpected considering the assumptions of excited-state equilibrium implicit in the theory. We extend the theory to the nonequilibrated case of time-resolved fluorescence, where a time-dependent temperature can, be defined.