Vibrational Mixing and Energy Flow in Polyatomics: Quantitative Prediction Using Local Random Matrix Theory

Abstract

The theory of local random matrix models has provided a way for understanding many aspects of quantum ergodicity and energy flow in molecules. In this paper quantitative results are presented for a random matrix model that yields analytical expressions for the degree of vibrational mixing and flow rates in polyatomics in terms of a small number of parameters. The results of these generally applicable expressions are compared with large scale computation on energy flow in several organic molecules studied experimentally: formaldehyde, thiophosgene, and propyne. We show these systems are respectively below, at, and significantly above the quantum ergodicity transition. Effects of finite molecular size on the quantum ergodicity transition are also discussed. I. Introduction The central role of intramolecular energy flow in chemical kinetics and photochemistry has long motivated experimental, 1 computational, 2-4 and theoretical studies 5 of vibrational relaxation in polyatomics. Large scale simulations and experimental studies on a number of small molecules have provided a wealth of detailed information about vibrational mixing and energy transfer. However, despite notable successes on rather large molecules, 2-4 detailed analysis of the complete vibrational Hamiltonian of a large polyatomic is still a very demanding undertaking. Fortunately, such large scale computation is apparently not needed for understanding a great deal about the qualitative nature of intramolecular energy flow or, as we shall show here, even to predict the extent and rates of flow to modest accuracy. Alternative approaches 6,7 to large scale computation treat the oscillator energies and local couplings statistically, the distributions of which are parametrized to suit the harmonic vibrational spectrum and anharmonicities of a particular polyatomic. The resulting local random matrix ensemble yields analytical expressions predicting vibrational mixing, rates of energy flow, and the location of the quantum ergodicity transition between localized and extended states. In this article, we compare predictions for vibrational energy flow and localization obtained from local random matrix models with results of computational studies 4,8,9 on several organic molecules. Our results are in some sense meant to serve as an