Angular dependence of the β-proton isotropic hyperfine coupling constant

Abstract

The angular dependence of the β‐proton isotropic hyperfine coupling in alkyl or π radicals is investigated using a limited CI approach. Values of B₀ and B₂ for the equation $A_{\beta }{\mathrm{=B}}_0{\mathrm{+B}}_2\hspace{0.17em}{\cos }^2\theta$ are found to be 2.71 and 50.14 G, respectively. The dominant contribution is found to arise from an electron exchange mechanism. Approximate treatment of this term by a simple charge transfer model leads to an expression for the β‐proton coupling constant, $A_{\beta }\text{=413.2\hspace{0.17em}{1+}\mathrm{sgn}{\text{F(θ)[1+F(θ)}}^{\text{−2}}{]}^{\text{−1/2}}\}$ , where F(θ) is a simple function of the angular variable cosθ and sgn F(θ) indicates its sign. The CI study also shows that the cos⁴θ factor in a power series expansion of A_β makes a negligible contribution to the hyperfine coupling.