The theory of the second moments of ESR spectra of π-electron radicals in polycrystalline environments is discussed and extended. Expressions for the effects of finite linewidth, satellite lines, carbon-13 in natural abundance, g-value anisotropy, and σ-electron spin density are developed. Second moments of a series of aromatic monopositive ion radicals of known spin density distribution are measured and compared with calculated values. The second moment theory is applied to a radical of unknown spin distribution, the benzyl radical. This radical is prepared photochemically and the experimental second moment, 127±6 G2, is compared with values calculated on the basis of a number of valence-theoretical approximations. Closest agreement is obtained for an alternant MO wavefunction [J. Chem. Phys. 32, 176 (1960)] with b/a=0.1. In the course of this investigation the ESR component shape of radicals in single crystals is determined experimentally to be very closely Gaussian. The radical product of the ultraviolet illumination of an aromatic hydrocarbon in a rigid boric acid glass is unambiguously identified by ESR as the aromatic monopositive ion.
Molecular orbital calculations of the unpaired electron density in a number of semiquinone ions have been made as a function of a range of values of the Coulomb integral αO for the oxygen atom and the resonance integral βCO between the oxygen atom and the carbon atom. The unpaired electron densities ρi were compared with the experimental hyperfine splitting constants ai arising from the proton bonded to carbon atom i by the use of McConnell's relation ai=Qρi. Excellent agreement is obtained for the proper choice of αO and βCO. In contrast to most experimental tests of molecular orbital theory, the agreement depends rather critically on the choice of these two parameters. The best values found for the parasemiquinone ions are in the neighborhood of αO≅αC+1.2 βCC and βCO≅1.56 βCC. The values of | Q | are close to 22.5 gauss. A different set of parameters is needed for the ortho-semiquinones. The molecular orbital calculation also fits the experimental splitting constants of the ring protons in the positions meta and para to the methyl group of the tolusemiquinone ion, but there is a large discrepancy at the position ortho to the methyl group. The results of detailed examination of a number of spectra of semiquinone ions are also reported.
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