Department of Chemistry, University of Sheffield, Sheffield S3 7HF, United Kingdom.
Department of Mathematics, University of Malta, Msida MSD 2080, Malta.
J Chem Phys. 2017 Oct 28;147(16):164115. doi: 10.1063/1.4995544.
Within the 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 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 the 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.
在源-汇势模型中，交替π共轭烃（没有奇数环的共轭烃）的传导行为得到了完整的描述。在这个模型中，全导体的分子图在费米能级上导电，而与连接顶点的选择无关。同样，全绝缘体是一种分子图，对于任何连接选择都无法导电。我们给出了分子图中可能的全导体和全绝缘体行为的组合的全面分类，按零化子（非键轨道数）排序。交替烃是具有二部分子图的烃；它们不可能是全导体或全绝缘体，但可能在顶点的定义明确的子集（不饱和碳原子中心）中导电或绝缘。这导致了“近全导体”和“近全绝缘体”的定义。在交替烃的 81 种可能的传导行为类别中，只有 14 种是可实现的。其中，有九个是由多个化学图实现的。例如，所有 Kekule 苯并（纳米石墨烯）的传导仅由两类描述。特别是，catafused benzenoids（没有碳原子属于三个六边形的苯并）通过一个带星号和一个不带星号的原子与引线连接时导电，否则绝缘，对应于近全分类方案中的传导类型 CII。
