Proton Spin−Spin Coupling and Electron Delocalization

Abstract

The spin−spin coupling of protons measured by the constant JHH‘ in NMR experiments is dominated by a term proportional to the product of the electron spin densities at the two nuclei, the Fermi contact term. The probability of β electrons being in excess over α electrons at the position of nucleus n‘, given that there is an α electron at n, is proportional to the negative of the exchange density, the total Fermi correlation between n and n‘. Thus the delocalization of the Fermi hole between n and n‘ is the mechanism whereby the spin perturbation caused by the magnetic interaction of an electron with nucleus n is transmitted to n‘. The density and exchange density within the basin of a hydrogen atom are described primarily in terms of s-type basis functions, and one may approximate the exchange density between two protons at n and n‘ by the exchange between the two associated atomic basins determined by the delocalization index δ(A,B) within the quantum theory of atoms in molecules. It is shown that this m...