The Nature of the Chemical Bond. V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals

The secular equations corresponding to the five canonical structures for benzene and the forty-two for naphthalene, considered as six and ten-electron systems, respectively, are set up and solved with certain simplifying assumptions, leading to energy values differing by 1.1055α and 2.0153α, respectively, from those corresponding to unexcited (Kekulé-type) structures, α being a single exchange integral involving neighboring carbon atoms. Equating these values to the empirical values of the resonance energy, α is found to be about — 1.5 v.e. It is pointed out that the dissociation of certain substituted ethanes into free radicals is due not to weakness of the carbon-carbon bond in the ethane but to the stabilization of the free radicals resulting from resonance among the structures in which the unpaired electron is located on the methyl carbon and those in which it is on other atoms (ortho, para, etc., to the methyl carbon). The secular equations for a number of such radicals have been solved, neglecting excited structures. The experimentally determined heat of formation of hexaphenylethane from triphenylmethyl, 0.5 v.e., when equated to the calculated value C–C+2.2156α, with C–C = 3.65 v.e., leads to α = — 1.4 v.e. The calculated tendencies towards dissociation are in satisfactory agreement with observation, such features as the smaller dissociating power of β-naphthyl than of α-naphthyl and of biphenylene than of diphenyl being accounted for, so that resonance among the structures considered may be accepted as the principal effect causing the stability of the hydrocarbon free radicals.