Additivity of resonance energy in benzenoid hydrocarbons

A simple method is described for the calculation of resonance energies (RE ) of linear acenes based on their number of Kekulé structures. The values obtained for the first five linear acenes are used to graph–theoretically calculate RES of a wide variety of benzenoid hydrocarbons. Excellent linear relationships are found between RES and each of A-II, graph-theoretical (GT ), Hess–Schaad (HS ), and Dewar resonance energies (SCF ). These relations apply to 42 hydrocarbons and lead to the following equations: A-II = 0.084RE + 0.080 (0.9999); GT = 0.072RE + 0. 135 (0.9832); HS = 0. 106RE + 0. 169 (0.9889); and SCF = 0.316RE + 0. 166 (0.9899). Correlation coefficients are shown in parentheses. A linear relation also exists between RES and the square roots of the wavelengths of the UV spectra of hydrocarbons of the linear acenes and phene series. Least-squares analysis of the data leads to the following equation: RE = 0.412(λ)^½ ?15.479, with a correlation coefficient equal to 0.9903, in which λ is the wavelength of the β band of the UV spectra of these hydrocarbons. The method predicts no resonance energies for both open chain polyenes and the radialenes.