Classification of sp²-bonded carbon allotropes in two dimensions

A taxonomy for sp² carbon allotropes in two dimensions (2D) is proposed where single-layer structures are assigned a unique symbol associated with the geometry of each allotrope. The naming scheme is demonstrated for structures described in the literature and is further illustrated for a number of other topology-allowed sp² carbon systems. The symbol is easy to use and gives a direct access to geometrical features such as the number of polygons and their arrangement. It facilitates the classification of structures reported in the literature, where many such structures are found to have been assigned a name based on each author's somewhat arbitrary choice. This naming scheme will help rationalize future studies on this class of systems. A comparative study of the energetics of the structures is also performed, using a consistent set of numerical parameters. The naming scheme can be expanded to carbon systems with mixed hybridizations and to other non-carbon 2D systems.