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

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 SN2 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.