Reflection properties of reaction paths in the reduced nuclear configuration space

Abstract

Chemical reactions and conformational changes of N-atom systems can be described as displacements in a (3N-6)-dimensional metric configuration space M provided with a global metric. Although space M has a metric, it is not in general a vector space; it is a topological space. In contrast to the commonly used internal configuration spaces based on bond length/bond angle internal coordinates, and having no global metrics, within space M each internal configuration of the nuclei of the molecule corresponds to one and only one point of the space. This property of M is advantageous when analyzing chemical reactions. The global metric of M ensures that differences between any two internal configurations can be interpreted as a distance in this space that allows one to provide M with coordinate systems by turning M into a manifold with boundary. Certain formal reaction paths show some counterintuitive behavior within this space: they may undergo a formal reflection at some points of M. A condition, the tangent criterion, is used for the diagnosis of such reaction paths and for the determination of special nuclear configurations where such reflections occur.