Methods of enumerating Kekulé structures, exemplified by applications to rectangle-shaped benzenoids

Aromaticity of Polycyclic Conjugated Hydrocarbons

“…Gutman, Cyvin, and co-workers 79,451 have considered, in a number of publications, enumeration of the Kekule ´valence structures for numerous benzenoids that belongs to different classes, characterized by an overall identical shape. We direct the reader to the book by Cyvin and Gutman, Kekule ´Structures in Benzenoid Hydrocarbons, 79 where the results of such enumerations are collected for many classes of different benzenoids.…”

“…455 A brief review of various methods used for enumeration of Kekule ´structures for rectangle-shaped benzenoids has appeared in Topics in Current Chemistry, volume 153. 451 Enumeration of Kekule ´valence structures has also been extended to a class of generalized benzenoid hydrocarbons, the so-called coronoid hydrocarbons, which are built from fused benzene rings, but permitting in the interior one or more larger "holes". For some coronoids it was possible to get an adequate mathematical formulation, 456 or a practical and relatively simple algorithm.…”

Aromaticity of Carbon Nanotubes

“…9 Methods of enumerating Kekulé structures of rectangle-shaped benzenoids were discussed by Rongsi et al 10 General explicit formulas were obtained by Klein et al 11 for benzenoid polymers with armchair edges. An efficient algorithm for determining K in cata-condensed benzenoids was devised by Gordon and Davison.…”

An Alternative Strategy for Count and Storage of Kekulé and Longer Range Resonance Valence Bond Structures

“…Aside from the systematic search method of Kekulé valence structures suggested by Pauling, people have also found analytical formulas for specific kinds of systems − or derived recursion relations between smaller fragments and larger systems. − There were also particular techniques developed to work on this problem, − which made it possible to enumerate Kekulé valence structures for systems with hundreds of atoms, such as nanotubes. Readers may refer to several review articles for the detailed description of the enumeration techniques. − …”

“…Readers may refer to several review articles for the detailed description of the enumeration techniques. [26][27][28] Despite the impressive achievements they have made, topological indices 28 built on the basis of the Kekule ´valence structure count have unreasonably implied the equal contributions from different Kekule ´valence structures. 29 Such differences were partly taken into considerations in Clar's aromatic sextet 30 and Randic ´'s conjugated circuits 31 theories, while the full consideration of it is reflected in the Kekule valence structure based Valence Bond theory (KVB) 29,[32][33][34] performed on the space spanned by the Kekule ´structures.…”