Omni-conducting fullerenes

Pickup

Todorova

et al. 2014

The source and sink potential model is used to predict the existence of omni-conductors (and omniinsulators): molecular conjugated π systems that respectively support ballistic conduction or show insulation at the Fermi level, irrespective of the centres chosen as connections. Distinct, ipso, and strong omni-conductors/omni-insulators show Fermi-level conduction/insulation for all distinct pairs of connections, for all connections via a single centre, and for both, respectively. The class of conduction behaviour depends critically on the number of non-bonding orbitals (NBO) of the molecular system (corresponding to the nullity of the graph). Distinct omni-conductors have at most one NBO; distinct omni-insulators have at least two NBO; strong omni-insulators do not exist for any number of NBO. Distinct omni-conductors with a single NBO are all also strong and correspond exactly to the class of graphs known as nut graphs. Families of conjugated hydrocarbons corresponding to chemical graphs with predicted omni-conducting/insulating behaviour are identified. For example, most fullerenes are predicted to be strong omni-conductors. © 2014 AIP Publishing LLC.

Section: Theorem 61 (I) No Tree Is An Ipso Omni-conductor;mentioning

confidence: 99%

Section: Insulatorsmentioning

confidence: 99%

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Omni-conducting and omni-insulating molecules

Pickup

Todorova

et al. 2014

“…[28][29][30][31][32][33][34][35] In our approach, the solutions for an incoming beam of electrons with energy E are written in terms of five molecular structural polynomials, which comprise the real characteristic polynomials, 28 s = det (E1 − A) ,…”

Section: Introductionmentioning

confidence: 99%

A new approach to the method of source-sink potentials for molecular conduction

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Borg

et al. 2015

Articles you may be interested in PHYSICS 143, 194105 (2015) A new approach to the method of source-sink potentials for molecular conduction We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells. We make explicit the behaviour of the total current and individual MO and shell currents at molecular eigenvalues. A rich variety of behaviour is found. A SSP device has specific insulation or conduction at an eigenvalue of the molecular graph (a root of the characteristic polynomial) according to the multiplicities of that value in the spectra of four defined device polynomials. Conduction near eigenvalues is dominated by the transmission curves of nearby shells. A shell may be inert or active. An inert shell does not conduct at any energy, not even at its own eigenvalue. Conduction may occur at the eigenvalue of an inert shell, but is then carried entirely by other shells. If a shell is active, it carries all conduction at its own eigenvalue. For bipartite molecular graphs (alternant molecules), orbital conduction properties are governed by a pairing theorem. Inertness of shells for families such as chains and rings is predicted by selection rules based on node counting and degeneracy. C 2015 AIP Publishing LLC. [http://dx

“…36,37 It has the significant advantage that it can be framed in purely graph-theoretical terms. [38][39][40][41][42][43][44][45][46][47] In chemical graph theory, vertices of the molecular graph of a π system are unsaturated C atoms, and edges are σ bonds between them. Models based on graph theory have the advantage of leading to global solutions for whole classes of molecules and giving a systematic typology 41, 45 of conduction behaviour of devices.…”

Section: Introductionmentioning

confidence: 99%

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

Sciriha

Borg

et al. 2017

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 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.