Local aromaticity and aromatic sextet theory beyond Clar

Abstract

Recently assigned numerical expressions to qualitative benzenoid formulas of Clar have transformed Clar's theory into a quantitative model that allowed a structural characterization of aromaticity in benzenoid polycyclic hydrocarbons and construction of aromaticity maps for benzenoid polycyclic hydrocarbons. The key structural elements of the novel quantitative aromatic sextet theory of Clar are (1) Kekul e valence structures, (2) Pauling bond orders, and (3) Clar's aromatic sextet benzenoid rings. In the present contribution we go beyond Clar and consider local aromaticities of benzenoid rings in benzenoid polycyclic hydrocarbons. We have characterized each benzenoid ring by two descriptors: (1) their content of C 5 C bonds in the set of Kekul e valence structures, which is reflected in the ring bond orders, and by (2) the variations of CC bond orders within rings, which are zero for benzene. This allows us to introduce for any set of benzenoid hydrocarbons local aromaticity map, which allows one to graphically view similarities and dissimilarities of local aromaticity of different benzenoid rings. For such map, one can calculate the "distance" of each ring from the benzene, with coordinates (3.00, 0) for benzene RBO and variations in CC bonds, respectively. We show that the central ring in peropyrene is visibly less aromatic that the terminal sextets, as has been claimed by Gutman and Agranat, and similarly we show that the central ring of anthracene is unexpectedly more aromatic than the terminal rings, in having greater similarity in bond lengths to benzene ring than the terminal rings. This suggests limitations of the assumption of the Clar model that migrating sextets have equal local aromaticities.Finally, we examined a pair of non benzenoid hydrocarbons related to peropyrene, built from terminal benzenoid rings and naphthalene fragments. Surprisingly, we have found the terminal benzene rings in the two non benzenoid compounds to have unusually high ring bond orders, approaching that of benzene.

The chemical space of B, N-substituted polycyclic aromatic hydrocarbons: Combinatorial enumeration and high-throughput first-principles modeling

“…Another such descriptor is Wiener index 77,78 , which is a topological score mapping the molecular structure to various chemical properties. Algebraic representations of CSs have indeed been shown to capture more chemical information than a single KS 79,80 . Multiple Clar diagrams, where the π-sextets are located in adjacent rings, can be collectively represented by a single migrating CS 76 .…”

Cyclic Aromaticity within Huckel and Quasi-Correlated Huckel-like Models

“…This elegant relation was analyzed and used in many papers. It is also suitable to be applied when discussing local aromaticity in the spirit of the recent works [43,57,58]. However, there is one unpleasant disadvantage with R -P…”

“…Whilst this paper was in preparation a new analysis of -electron aromaticity was reported [43], and one of the Referees kindly informed the author about this work. The cited paper motivated us to provide in Appendix B a supplementary example which elucidates peculiarities of using bond orders in -theories.…”

“…We see that using Pauling bond orders is not generally wholly satisfactory procedure, and it warns us to be cautious when analyzing local aromaticity by the technique from Refs. [43].…”

A novel numerical model for protein sequences analysis based on spherical coordinates and multiple physicochemical properties of amino acids

“…Sequence analysis is fundamentally important in the omics era. In particular, how to represent protein or DNA sequences mathematically to capture their intrinsic features is an active area of research, with statistical methods and graphical representations as two main approaches . Compared to statistical methods, graphical representations are more intuitive and simpler to calculate.…”