Ring-Current Maps for Benzenoids: Comparisons, Contradictions, and a Versatile Combinatorial Model.

As a key diagnostic property of benzenoids and other polycyclic hydrocarbons, induced ring current has inspired diverse approaches for calculation, modeling, and interpretation. Grid-based methods include the ipsocentric calculation of current maps, and its surrogate, the pseudo-π model. Graph-based models include a family of conjugated-circuit (CC) models and the molecular-orbital Hückel-London (HL) model.

Perimeter ring currents in benzenoids from Pauling bond orders.

It is shown that the ring currents in perimeter hexagonal rings of Kekulean benzenoids, as estimated within the Randić conjugated-circuit model, can be calculated directly without tedious pairwise comparison of Kekulé structures or Kekulé counting for cycle-deleted subgraphs. Required are only the Pauling bond orders of perimeter bonds and the number of Kekulé structures of the benzenoid, both readily available from the adjacency matrix of the carbon skeleton. This approach provides easy calculation of complete current maps for benzenoids in which every face has at least one bond on the perimeter (as in the example of cata-condensed benzenoids), and allows qualitative evaluation of the main ring-current contributions to (1)H chemical shifts in general benzenoids.

Distributed curvature and stability of fullerenes.

Energies of non-planar conjugated π systems are typically described qualitatively in terms of the balance of π stabilisation and the steric strain associated with geometric curvature. Curvature also has a purely graph-theoretical description: combinatorial curvature at a vertex of a polyhedral graph is defined as one minus half the vertex degree plus the sum of reciprocal sizes of the faces meeting at that vertex. Prisms and antiprisms have positive combinatorial vertex curvature at every vertex.

The "anthracene problem": closed-form conjugated-circuit models of ring currents in linear polyacenes.

Conjugated-circuit models for induced π ring currents differ in the types of circuit that they include and the weights attached to them. Choice of circuits for general π systems can be expressed compactly in terms of matchings of the circuit-deleted molecular graph. Variants of the conjugated-circuit model for induced π currents are shown to have simple closed-form solutions for linear polyacenes.

Non-IPR fullerenes with properly closed shells.

Fullerenes with properly closed shells (having exactly half their adjacency eigenvalues strictly positive) are rare. All reported examples obey the isolated-pentagon rule (IPR), usually considered a necessary condition of overall stability, and fall into three series (leapfrogs, carbon cylinders and sporadic closed shells). It is shown here that there also exist fullerenes with properly closed shells that violate the IPR ('super-sporadic' fullerenes).

Vertex spirals in fullerenes and their implications for nomenclature of fullerene derivatives.

The IUPAC nomenclature of fullerene derivatives is based on the vertex spiral, but not all fullerenes possess one. There are 1495 isomers with View Article and Find Full Text PDF