Properties of atoms in molecules: nuclear magnetic shielding

Abstract

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 [Formula: see text] resulting from an element of the induced current density at a distance [Formula: see text] is proportional to [Formula: see text] which defines the shielding density [Formula: see text] 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 [Formula: see text] over the individual atomic basins relates the shielding tensor [Formula: see text] to a sum of atomic contributions. The shielding of nucleus ** is primarily determined by the flow of current within the basin of atom [Formula: see text], 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 flows 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. [Formula: see text]. 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 [Formula: see text] of a nucleus external to it through a series of molecules, the more remarkable result that the whole of the variation in [Formula: see text] can have its origin in the basin of atom [Formula: see text], the contribution from external groups remaining constant. For example, the external contribution to [Formula: see text] for a carbon nucleus in a normal hydrocarbon is independent of chain length and position of [Formula: see text] 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. Key words: NMR, magnetic shielding, current density, magnetic shielding density.