Near omni-conductors and insulators: Alternant hydrocarbons in the SSP model of ballistic conduction

Patrick W. Fowler, Irene Sciriha, Martha Borg, Victoria E. Seville, Barry T. Pickup
2017 Journal of Chemical Physics  
Within the SSP (source-and-sink-potential) model, a complete characterisation is obtained for the conduction behaviour of alternant π-conjugated hydrocarbons (conjugated hydrocarbons without odd cycles). In this model, an omni-conductor has a molecular graph that conducts at the Fermi level irrespective of the choice of connection vertices. Likewise, an omni-insulator is a molecular graph that fails to conduct for any choice of connections. We give a comprehensive classification of possible
more » ... ion of possible combinations of omni-conducting and omni-insulating behaviour for molecular graphs, ranked by nullity (number of non-bonding orbitals). Alternant hydrocarbons are those that have bipartite molecular graphs; they cannot be full omni-conductors or full omni-insulators, but may conduct or insulate within well-defined subsets of vertices (unsaturated carbon centres). This leads to definition of 'near omni-conductors' and 'near omni-insulators'. Of 81 conceivable classes of conduction behaviour for alternants, only 14 are realisable. Of these, nine are realised by more than one chemical graph. For example, conduction of all Kekulean benzenoids (nanographenes) is described by just two classes. In particular, the catafused benzenoids (benzenoids in which no carbon atom belongs to three hexagons) conduct when connected to leads via one starred and one unstarred atom, and otherwise insulate, corresponding to conduction type CII in the near-omni classification scheme.
doi:10.1063/1.4995544 pmid:29096467 fatcat:pkr2to7h2ng53acxbdkfnxiqmy