Topological Tools for the Study of Families of Reaction Mechanisms: The Fundamental Groups of Potential Surfaces in the Universal Molecule Context

Abstract

Two types of the main topological properties of potential energy surfaces are compared, where the first types are related to the chemical processes, conformational changes and chemical reactions along the potential energy surface, and where the second types are describing the presence, interrelations, structural variability, and shape variations of identifiable chemical species associated with the potential surface. Some new relations are obtained when the families of topologically equivalent reaction paths representing reaction mechanisms at some energy bound, and the algebraic structure of the fundamental group of reaction mechanisms for a given collection of atoms (that is, for a given stoichiometry) are constrained by the collection of “catchment regions” of the potential surface, representing chemical species. These relations, providing additional detail when they are compared to the more traditional, unconstrained cases, are phrased in terms of potential energy surface level set relations and the originally integer, but “unquantized” continuous variables of the Universal Molecule model.