In this paper, we have constructed a WKB approximation for graphene having Y-shaped Kekulé lattice distortion and special folding of the K K′ valleys, which leads to very specific linear energy dispersions with two non-equivalent pairs subbands. These obtained semi-classical results, include action, electron momentum wave functions, are utilized analyze dynamics tunneling through non-square pot...

An explicit combinatorial expression is obtained for the Zhang-Zhang polynomial (also known as “Clar cover polynomial”) of a large class of pericondensed benzenoid systems, the multiple linear hexagonal chains Mn,m. By means of this result, various problems encountered in the Clar theory of Mn,m are also resolved: counting of Clar and Kekulé structures, determining the Clar number, and calculat...

In this work, two different classes of polyaromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekulé triangular structures phenalenyl, triangulene and a π-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimet...

We make use of the classical correspondence between Kekulé structures and lattice paths to obtain explicit formulas for the Pauling bond order of edges in benzenoid parallelograms. These formulas are further used to establish the average π-electron content of hexagonal rings in such benzenoids. We then compare this quantity with the atom-based π-electron content of rings, and study the local an...

The general Randić index Rα(G) is the sum of the weights (dG(u)dG(v)) over all edges uv of a (molecular) graph G, where α is a real number and dG(u) is the degree of the vertex u of G. In this paper, for any real number α ≤ −1, the minimum general Randić index Rα(T ) among all the conjugated trees (trees with a Kekulé structure) is determined and the corresponding extremal conjugated trees are ...

Possible dimerization patterns and electronic structures in fullerene tubules as the one-dimensional π-conjugated systems are studied with the extended Su-Schrieffer-Heeger model. We assume various lattice geometries, including chiral and achiral tubules. The model is solved for the half-filling case of πelectrons. (1) When the undimerized systems do not have a gap, the Kekulé structures prone ...

In a Perspective accompanying Abad-Franch and colleagues, Lorenz von Seidlein, Alexander Kekulé, and Daniel Strickman discuss the importance of developing effective strategies to minimize mosquito-borne transmission of human diseases.

Carbon nanotubes are composed of cylindrical graphite sheets. Both nanotubes and graphite sheets are benzenoid derivatives composed of sp2 carbon atoms arranged in a hexagonal pattern. Therefore both systems are aromatic. The extent of the aromatic character of a molecule G (here benzenoids) can be explained in terms of the number of possible Kekulé structures in G. In this work the Kekulé stru...