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 sy stems under the assumption of thermal equilibration of the emitting electro nic state. A recent elaboration of the theory by Sawicki and Knox (SK) [Phy s. Rev. A, 1996 54, 4837] introduces a spectral temperature that is a sensi tive indicator of the failure of the relation. Studies using the SK formali sm, which have been limited almost exclusively to experimental cases, revea l various failures that may be due to incomplete equilibration, inhomogenei ty, or both. Using the Brownian oscillator model for nuclear dynamics, we i nvestigate the KS relation theoretically with the aid of the SK spectral te mperature. The spectral temperature is again found to be a sensitive indica tor, this time of the accuracy of the numerical methods necessary for the m ultiple integrations. The original KS relation appears to hold regardless o f the memory effects of the bath, a result which is not totally unexpected considering the assumptions of excited-state equilibrium implicit in the th eory. We extend the theory to the nonequilibrated case of time-resolved flu orescence, where a time-dependent temperature can, be defined.