Conjugated Molecules Described by a One-Dimensional Dirac Equation

The eigenvalue problem of one-dimensional Dirac operator

The properties of the eigenvalue problem of the one-dimensional Dirac operator are discussed in terms of the mutual relations between vector, scalar and pseudo-scalar contributions to the potential. Relations to the exact solubility are analyzed.

Molecular graphs and molecular conduction: the d-omni-conductors

Graph–theoretical distance gives a complete classification of conduction behaviour of alternant and non-alternant molecular devices within the source-sink-potential model.

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

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.

Simple orbital theory for the molecular electrician

Theories of molecular electronic devices (MEDs) are quite involved in general. However, various prominent features of MEDs can be understood drawing only on elementary quantum theory. To support this point of view, we provide a two component orbital theory that enables one to reproduce various important features of MEDs. In this theory, the device orbitals are divided into two components, each of which is obtained from simple rules. To illustrate our two-component model, we apply it to explain, among other things, the conductance suppression in cross-conjugated systems and the dependence of the conductance on the contact position in aromatic systems.