Quantifying Energetics of Topological Frustration in Carbon Nanostructures

Abstract

We develop a graph theoretical formalism to account for the fact that sp2 carbon can become spin ordered or generate free radicals for purely topological reasons. The graph theory method is combined with open-density-functional theory calculations to establish the existence of a universal energy of frustration term that is shown to greatly improve the description of carbon nanostructure energetics using classical force-fields. The methodology is illustrated for a number of systems and, owing to the small computational overhead associated, is shown to be easily integratable into any modeling approach based on an adjacency matrix.