Interval Analysis For Computational Chemistry

Abstract

A problem frequently encountered in all disciplines of science is to obtain all the solutions for a system of non-linear equations. A similar problem exists for reaction systems with many reactants, products, and intermediates. Such systems may have many steady states. Here one would like to have a list of all such steady states. Conventional methods rely on multiple initial start points, which means that they are initialization dependent and also might converge to trivial or unfeasible solutions. Such methods give one or a very limited set of steady states. The objective in thesis is to investigate how useful method of interval analysis is for determining the steady states of reaction systems. In particular, we are interested in solving kinetic equations of reactions involved in transition metal heterogeneous catalysis. The method of interval analysis can yield all steady states of a reaction system with mathematical certainty and are initialization independent. Here we will address how costly these methods are, and up to what size of the systems that one can reasonably handle.