Theory of Hyperfine Interactions in Aromatic Radicals

The relation aH=Qρ between the ring proton isotropic hyperfine splitting aH and the unpaired spin density ρ on the carbon atom in an aromatic hydrocarbon radical is derived under even more general conditions than McConnell and Chesnut's.1 There are only three essential assumptions in the new theory: (a) that σ-π exchange interaction is small; (b) that an antisymmetrised product U (π) V (σ), which allows π-π and σ-σ, but not σ-π correlations, is a good first approximation to the ground-state electronic wave function; and (c) that U (π) is formed exclusively of π-orbital configurations, and V (σ) exclusively of σ ones. In the framework of our theory the unpaired spin density in the molecular plane arises entirely from σ-electron excitations. The general relation aN=tr(QNρ) holds for any nucleus N, including C13 and N14, which lies in the molecular plane. Here ρ is the π-electron spin-density matrix, and QN a hyperfine coupling matrix, whose elements depend on σ-π exchange integrals and excited σ triplet states. The diagonal elements of QN for C13 are estimated in a simple way to be +41 gauss for the same carbon atom and —14 gauss for each next neighbor, while experimental data fit the values +41 and —6.9 gauss.