Excited-State Equilibration and the Fluorescence-Absorption Ratio

Abstract

In any complex system at temperature T the absorption cross-section and fluorescent power at a given photon energy are connected by a simple relation if the system is in thermal equilibrium while occupying one particular electronic excited state. Although this situation is impossible in principle because of finite excited-state lifetimes, it is often approximated to the extent that the simple relation, which is expressed as a linear function of energy with slope —1/kBT, holds in a variety of cases. (The usual symbols for Boltzmann's constant and absolute temperature are used.) Observed deviations are of two principal kinds: a slope characteristic of some temperature T* other than ambient, and departures from a single pure straight line. The latter may include seemingly random variations and in some cases multiple regions of straight-line behavior. We have recently introduced an effective temperature T* (E), derived from the actual local slope of the putative straight line at energy E, which turns out to be a very sensitive detector of deviations from the ideal and, we believe, from equilibrium in the excited state. Plots of T* (E) display a variety of features. An anomaly in the T* (E) spectrum of chlorophyll a can be analyzed on this model, indicating a second weakly fluorescent state about 70 meV below the well-known Qy band. The cases of chlorophyll and many others are included in a selective review of applications of the universal relation to fluorescent systems.