Theory and Computation of Non-RRKM Lifetime Distributions and Rates in Chemical Systems with Three or More Degrees of Freedom

The computation, starting from basic principles, of chemical reaction rates in realistic systems (with three or more degrees of freedom) has been a longstanding goal of the chemistry community. Our current work, which merges tube dynamics with Monte Carlo methods provides some key theoretical and computational tools for achieving this goal. We use basic tools of dynamical systems theory, merging the ideas of Koon et al. [Chaos 10, 427 (2000)] and De Leon et al. [J. Chem. Phys. 94, 8310 (1991)], particularly the use of invariant manifold tubes that mediate the reaction, into the start of a comprehensive theory of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. Previously, the main problem with the application of tube dynamics has been with the analytical evaluation of volumes in phase spaces of arbitrary dimension. The present work overcomes this hurdle with some new ideas and implements them numerically. Specifically, an efficient algorithm that uses tube dynamics to provide the initial bounding box for a Monte Carlo volume determination is used. The combination of a fine scale method for understanding the phase space structure (invariant manifold theory) with statistical methods for practical computations (Monte Carlo) is the main novel contribution of this paper. The methodology, applied here to a three degree of freedom model problem, is not restricted by dimension, and is useful for higher degree of freedom systems as well. ∗Present address: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain.