The vibrational energy flow transition in organic molecules: theory meets experiment

Abstract

Most large dynamical systems are thought to have ergodic dynamics, whereas small systems may not have free interchange of energy between degrees of freedom. This assumption is made in many areas of chemistry and physics, ranging from nuclei to reacting molecules and on to quantum dots. We examine the transition to facile vibrational energy flow in a large set of organic molecules as molecular size is increased. Both analytical and computational results based on local random matrix models describe the transition to unrestricted vibrational energy flow in these molecules. In particular, the models connect the number of states participating in intramolecular energy flow to simple molecular properties such as the molecular size and the distribution of vibrational frequencies. The transition itself is governed by a local anharmonic coupling strength and a local state density. The theoretical results for the transition characteristics compare well with those implied by experimental measurements using IR fluorescence spectroscopy of dilution factors reported by Stewart and McDonald [Stewart, G. M. & McDonald, J. D. (1983) J. Chem. Phys. 78, 3907-3915].

Figure 1

Experimental dilution factors σ correlated with different molecular quantities. (A) Plotted vs. the total density of states. (B) plotted vs. T, an analytical local coupling strength. (C) plotted vs. N_loc, a computational local number of coupled states. (D) Correlation between N_loc and T. Because T and σ extend over several orders of magnitude, all plots are shown on log–log scales.

Figure 2

Distribution P(σ) of dilution factors for four different values of the locally coupled number of states. (Left) Experimental distribution obtained by binning the data in Fig. 1C into the N_loc ranges shown. (Center) Analytical P(t) (normalized to 1) from Eq. 8 for four values of T. (Right) Numerical BSTR P(t) (normalized so ∫dσP(σ) = 1) for different coupling strengths.