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

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 Rancho innate degree of freedom are presented and rationalized.