Hyperfine coupling constants and their dependence on charge densities

In paramagnetic aromatic systems the relation between the hyperfine coupling constants a _H for the protons and the spin density ρ on the adjacent carbon atom is usually given by the relation a _H = -Qρ (McConnell) in which Q is a constant characteristic for the C-H bond. In the paramagnetic ions of aromatic molecules the carbon atoms have in general besides a non-zero spin density also a non-zero excess charge density.

If one takes into account both the effect of the spin density ρ and the excess charge density ε on the C-H bond, the following formula is obtained for the proton hyperfine coupling constant:

in which Q and K are predicted to be positive constants of the same order of magnitude.

Comparison with experimental data gives Q = 31·2 gauss; K = 17 gauss.