Second Moments of Electron Spin Resonance Proton Hyperfine Spectra

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Abstract
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.