Molecular Networks in Position, Momentum, and Phase Space:  A Case Study on Simple Hydrocarbons

Abstract

The notion of a molecular network as a system of local density maxima, connected by gradient paths, is extended from position space and the underlying charge density to momentum and phase space, and the momentum density and Husimi distribution, respectively. Local maxima and gradient paths are identified in a series of nine small hydrocarbonic molecules, and the resulting "molecular graphs" are interpreted in terms of symmetry and topology. For the example of a symmetric SN 2 reaction, it is shown that the topology of the Husimi function based graphs can be useful for the classification of chemical species and their change.In an appendix, a few relationships among elements of the gradient and the Hessian of the Husimi distribution are derived and briefly discussed.

Shannon entropy of chemical changes:SN2 displacement reactions

“…Abrupt changes in the information entropies then could signify the formation of new species such as the intermediates and the products as well as the termination of the reactants. The utility of properties in position space 27, momentum space 28, phase space 29 and nuclear configuration space 30 for the definition of such regions that correspond to specific species, has long been a subject of interest in the literature. The results here suggest that information entropies are suitable candidates for similar studies.…”