Properties of atoms in molecules: Nuclear magnetic shielding

This paper analyzes the nuclear magnetic shielding tensors underlying the chemical shift in NMR spectroscopy in terms of the field generated at the nucleus by the current J((1))(r) induced by an external magnetic field. The magnetic field at nucleus N resulting from an element of the induced current density at a distance r(N) is proportional to r(N) x J((1))(r)/r(N)(3) which defines the shielding density sigma(N)(r). The magnetic shielding of a nucleus is fundamentally an atomic property, a feature brought to the fore by using the theory of atoms in molecules, and the integration of sigma(N)(r) over the individual atomic basins relates the shielding tensor sigma(N) to a sum of atomic contributions. The shielding of nucleus N is primarily determined by the flow of current within the basin of atom N, a contribution that varies from the approximate diamagnetic limit, given by the atomic Lamb value for the atom in the molecule, to values that are greatly reduced by the presence of paramagnetic current hows associated with particular bonding effects. Whether the contribution of a neighbouring atom is shielding or deshielding is readily understood by relating the form of the current flow within its basin to the magnetization density r(N) x J((1))(r). A study of the currents induced in benzene shows that the extent to which a proton, bonded to a ring of atoms, is deshielded by the field exerted by its bonded neighbour provides a direct diagnostic test for a ring current and an accurate relative measure of its strength. The theory of atoms in molecules isolates transferable atomic properties, and because of this ability one finds, in addition to the anticipated result that a given functional group contributes identical amounts to the isotropic shielding <(sigma)over bar>(N) of a nucleus external to it through a series of molecules, the more remarkable result that the whole of the variation in <(sigma)over bar>(N) can have its origin in the basin of atom N, the contribution from external groups remaining constant. For example; the external contribution to <(sigma)over bar>(N) for a carbon nucleus in a normal hydrocarbon is independent of chain length and position of N within the chain, the methyl group in ethane contributing the same shielding to a methyl carbon as does the butyl group in pentane. This constancy in external contributions to the shielding is also found for N, O, and F nuclei in substituted, saturated hydrocarbons.