Sum over Histories Representation for Chemical Kinetics

Abstract

A new representation for chemical kinetics is introduced that is based on a sum over histories formulation that employs chemical pathways defined at a molecular level. The time evolution of a chemically reactive system is described by enumerating the most important pathways followed by a chemical moiety. An explicit formula for the pathway probabilities is derived and takes the form of an integral over a time-ordered product. When evaluating long pathways, the time-ordered product has a simple Monte Carlo representation that is computationally efficient. A small numerical stochastic simulation was used to identify the most important paths to include in the representation. The method was applied to a realistic H₂/O₂ combustion problem and is shown to yield accurate results