Correlations of the Number of Dewar Resonance Structures and Matching Polynomials for the Linear and Zigzag Polyacene Series

Jerry Ray Dias

doi:10.5562/cca2292

Abstract

Linear and zigzag polyacene series have been the subject of numerous studies because of their contrasting electronic and stability characteristics. The correlation of the properties of these series is examined in regard to their number of Dewar resonance structures (DS). Since resonance-theoretic methods require algorithms for determining the number of Dewar resonance structures (DS), recursion equations for calculating DS for these series are presented for the first time. Excellent correlations between DS and the absorption p-band, ionization energies, Huckel HOMO, Aihara's reduced HOMO- LUMO gap, topological resonance energy (TRE), aromatic stabilization energy (ASE), and the Klein and Randic innate degree of freedom are presented and rationalized. (doi: 10.5562/cca2292)

Highlights

The matching polynomial is useful for determining topological resonance energy[1,2] (TRE), the number of Kekulé resonance structures, and the number of Dewar resonance structures[3] (DS) of polycyclic conjugated hydrocarbons (PAH)
While the coefficients of the characteristic polynomial can be computed by summing all the Sachs graphs, the coefficients of the matching polynomial are computed by summing all the Sachs graphs not having cyclic components
It was shown by Linus Pauling that when essentially single bonds are present in a conjugated system, one must employ Dewar resonance structures in addition to Kekulé resonance structures to determine bond lengths of essentially single bonds.[6]

Summary

Introduction

The matching polynomial (called acyclic polynomial) is useful for determining topological resonance energy[1,2] (TRE), the number of Kekulé resonance structures, and the number of Dewar resonance structures[3] (DS) of polycyclic conjugated hydrocarbons (PAH). Since the number of Dewar resonance structures is a measure of its triplet state energy and it is known that the electronic transition from the HOMO to the LUMO corresponds to the p-band in the UV spectrum, we plot DS versus λp in Figures 2 and 3 for the linear acenes and the phenacenes, respectively.[21] The p-band in the UV spectrum arises from polarization along the short axis of these molecules.

Results

Conclusion