Coronoids, Patches and Generalised Altans

TL;DR

This paper formalizes the theory of coronoids and perforated patches based on hexagonal grid incidence, introduces a generalized altan operation, and derives formulas for Kekulé structures and bond orders.

Contribution

It provides a mathematical formalization of coronoids and perforated patches, extending the altan operation to multiple holes and deriving related structural formulas.

Findings

Formula for Kekulé structures of generalized altans

Method to derive Pauling Bond Orders for generalized altans

Extension of coronoid theory to perforated patches

Abstract

In this paper we revisit coronoids, in particular multiple coronoids. We consider a mathematical formalisation of the theory of coronoid hydrocarbons that is solely based on incidence between hexagons of the infinite hexagonal grid in the plane. In parallel, we consider perforated patches, which generalise coronoids: in addition to hexagons, other polygons may also be present. Just as coronoids may be considered as benzenoids with holes, perforated patches are patches with holes. Both cases, coronoids and perforated patches, admit a generalisation of the altan operation that can be performed at several holes simultaneously. A formula for the number of Kekul\'e structures of a generalised altan can be derived easily if the number of Kekul\'e structures is known for the original graph. Pauling Bond Orders for generalised altans are also easy to derive from those of the original graph.