Omni-conducting and omni-insulating molecules

Abstract

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.

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

“…A molecular graph with nullity ≤ 1 may be a distinct omni-conductor; if it has nullity ≥ 2, it may be a distinct omni-insulator. 45 This dichotomy ultimately derives from the mathematics of the interlacing theorem, 48 as deletion of two vertices of a graph can change its nullity by at most two.…”

“…It follows, for example, that significant classes of conjugated hydrocarbons, such as the Kekulean benzenoids, cannot be distinct omni-conductors. 45 Hence, it is natural to ask how closely an alternant hydrocarbon can approach omni-conductor or omni-insulator status. The present paper gives a systematic answer to this question by defining near omniconduction and insulation and showing that there are only a very few possible cases needed to describe real π systems.…”

“…It turns out that the transmission of a model device as a function of electron energy can be expressed in closed form in terms of four characteristic polynomials, those of the molecular graph and the three graphs formed by deletion of one or both of the vertices that are in contact with the external leads. 38 This simple 'empty-molecule' version of the SSP approach, in which the ballistic electron has no interaction with the molecular electrons, has already given rise to useful generalisations such as derivations of classes of equi-conductors, 39 omni-conductors and omniinsulators, 45 and the construction of selection rules for conduction/insulation at the Fermi level that depend on counting zero roots of the structural polynomials. 41,42 Omni-conductors are molecular graphs that conduct at the Fermi level, in the SSP model, no matter which connection vertices are chosen to make the distinct (respectively, ipso) device.…”

“…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.…”

“…[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. (A device is defined in this context by a molecular graph in which vertices L and R (in the molecule) are respectively connected to source and sink vertices L and R (outside the molecule) to represent the effect of two semi-infinite leads.…”