The topology of energy hypersurfaces III. The fundamental group of reaction mechanisms on potential energy hypersurfaces

Abstract

The family of all possible reaction mechanisms on a potential surface has an algebraic structure with potential applications in quantum chemical molecular design and synthesis planning.

Transformation properties and equivalence relations of reaction paths on potential energy hypersurfaces lead to a topological definition of reaction mechanisms. The family of all fundamental reaction mechanisms on the hypersurface has a group structure,the fundamental group of an appropriately defined topological space. Isomorphism and homomorphism relations between fundamental groups of reaction mechanisms are used to characterize the chemically important topological properties of various subsets of a hypersurface, or those of different excited state hypersurfaces.