Intramolecular vibrational energy redistribution and the time evolution of molecular fluorescence

Abstract

We note the presence of contradictory estimates of intramolecular vibrational relaxation rates in the literature where large molecules in high energy states, corresponding to huge densities of vibrational levels, have been ascribed relaxation rates orders of magnitude smaller than those assigned to smaller molecules with much smaller densities of vibrational levels. This unphysical disparity is explained as arising from vague (or undefined) definitions of intramolecular vibrational relaxation and/or from a consideration of quantities which are not directly measured or measurable. A resolution of a portion of the problem is already well known for electronic relaxation, but the application of those results to a description of the time evolution of the molecular fluorescence, produced during the intramolecular vibrational relaxation of the electronically excited molecules, requires a generalization of the electronic relaxation theory to separate and describe the ’’unrelaxed’’ and ’’relaxed’’ emission spectra. We provide this general theory of the time variation of the emission spectrum for molecules conforming to both the intermediate and statistical limits of intramolecular vibrational relaxation with emphasis placed upon the distinguishability between these two cases. The intermediate case analysis utilizes egalitarian and random coupling type models with essentially identical conclusions from both. The time evolution and relative yields associated with the emission spectra are described for both continuous and short pulse excitation, and reasons are provided for the absence of observation of time varying emission spectra in the experiments of Smalley and co‐workers. Quantum beats are possible in principle in the sparse intermediate case. Their observability depends, however, on the detection method. When the emission spectrum can be resolved, beats are expected only in the frequency integrated intensity.