Isotropic hyperfine coupling constants equation

This property of the — SiMes group has also been quite clearly demonstrated in an extremely elegant manner by Bedford et al. (77). It has been amply demonstrated that in an electron spin resonance spectrum the isotropic hyperfine coupling constant, an, of a hydrogen atom attached to an sp2 hybridised carbon atom having an unpaired electron in the 2p—orbital is given approximately by an Equation (3) due to McConnel (18)... 

The large isotropic component is due to the unpaired electron spin density in the carbon 2s orbital, and this value (544MHz) can be used to derive an estimate of the carbon 2 s orbital contribution to the molecular orbital. Since the theoretical isotropic coupling constant for is 3777MHz, then C2s = 544/3777 = 0.144. The anisotropic dipolar part of the hyperfine arises from unpaired spin density in the 2p orbital. However because the dipolar contribution in Equation 1.52 cannot be reduced to zero, this implies that a fraction of the spin density is allocated to the 2p orbital perpendicular to the molecular plane. Therefore, the dipolar component of Equation 1.52 must be further decomposed into two symmetrical tensors oriented along the z and x axes ... 

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