Abstract
Proton hyperfine interactions in aromatic radicals and aromatic ions are calculated by the MO (molecular orbital) method, and the basis of the semi-empirical equation, aN = Qρ, is clarified; here aN is the splitting constant referred to proton N, ρ is the unpaired electron density at the carbon atom adjacent to proton N, and Q is the semi-empirical constant assumed to be the same for all CH bonds. Two essential approximations in this treatment are: a) the singlet-triplet excitation energies in σ orbitals are replaced by an averaged value ΔEAV, b) all σ orbitals containing CH bonds are transformed into σ̅ orbitals which are strongly localized to each CH bond, and are approximated to be CH bond orbitals between the 1s hydrogen atomic orbitals and the carbon sp2 hybrid orbitals. Then it is shown that the calculation of proton hyperfine splittings in the hypothetical CH fragment leads to the same results as in the case of the entire set of the aromatic system. The above two approximations are shown to be reasonable for aromatic systems. The cauculated value of Q in the present paper is -22.2 gauss, which is quite close to the semi-empirical value -22.5 gauss.