Extremal non-bonding orbitals

Abstract

A graph G is singular of nullity η if the nullspace of its adjacency matrix G has dimension η. In the Huckel model, a molecular graph of nullity η has η non-bonding orbitals (NBOs). By considering the properties of vertices playing different roles in a singular graph, we give a geometrical significance to the maximal induced subgraphs that have lower rank. We determine lower and upper sharp bounds for the order of the substructures where the spin of the NBO electrons is concentrated. In the case of degeneracy of the NBOs, lack of stability points towards a "first order" Jahn-Teller distortion, resulting in a combined effect of the NBOs.