Hyperconjugation in the electron resonance spectra of free radicals

The electron resonance hyperfine splitting a H produced by protons of a methyl group attached to one of the aromatic carbon atoms of a π-electron radical is calculated by the valence bond theory, treating the exchange inter-action between the odd electron and the methyl group as a perturbation. The formula a H = Q ρ which relates a H for a ring proton with the spin density ρ on the aromatic carbon atom also holds for methyl protons. Q is predicted to be positive with a theoretical value of about 28 gauss in the ethyl radical. Experimental data for several radicals indicate that Q is about 25 gauss. It is suggested that the CH3 and CH2 protons appear to be equivalent in the spectrunl of the ethyl radical because Q has the same magnitude for both. The spectra of some Wurster's blue ions are interpreted on the assumption that hyperconjugation takes place between methyl groups and the nitrogen atoms.