A full topological analysis of unstable and metastable bond critical points

Researchers are developing conceptually based models linking the structure and dynamics of molecular charge density to certain properties. Here we report on our efforts to identify features within the charge density that are indicative of instability and metastability. Towards this, we use our extensions to the quantum theory of atoms in molecules that capitalize on a molecule's ridges to define a natural simplex over the charge density. The resulting simplicial complex can be represented at various levels by its 0-, 1-, and 2-skeleton (dependent sets of points, lines, and surfaces). We show that the geometry of these n-skeletons retains critical information regarding the structure and stability of molecular systems while greatly simplifying charge density analysis. As an example, we use our methods to uncover the fingerprints of instability and metastability in two much-discussed systems, that is, the di-benzene complex and the He and adamantane inclusion complex.