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 magnet ic 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 proper ty, a feature brought to the fore by using the theory of atoms in mole cules, and the integration of sigma(N)(r) over the individual atomic b asins relates the shielding tensor sigma(N) to a sum of atomic contrib utions. The shielding of nucleus N is primarily determined by the flow of current within the basin of atom N, a contribution that varies fro m the approximate diamagnetic limit, given by the atomic Lamb value fo r the atom in the molecule, to values that are greatly reduced by the presence of paramagnetic current hows associated with particular bondi ng effects. Whether the contribution of a neighbouring atom is shieldi ng or deshielding is readily understood by relating the form of the cu rrent 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 fie ld exerted by its bonded neighbour provides a direct diagnostic test f or a ring current and an accurate relative measure of its strength. Th e theory of atoms in molecules isolates transferable atomic properties , and because of this ability one finds, in addition to the anticipate d result that a given functional group contributes identical amounts t o the isotropic shielding <(sigma)over bar>(N) of a nucleus external t o it through a series of molecules, the more remarkable result that th e whole of the variation in <(sigma)over bar>(N) can have its origin i n 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 cha in length and position of N within the chain, the methyl group in etha ne contributing the same shielding to a methyl carbon as does the buty l group in pentane. This constancy in external contributions to the sh ielding is also found for N, O, and F nuclei in substituted, saturated hydrocarbons.