Magnetic multipoles and the ‘pseudo-contact’ chemical shift

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Abstract
Formulae are presented for molecular magnetic multipoles in a uniform field and for the corresponding susceptibilities. An explicit expression is given for the magnetic octopole moment of a hydrogenic atom. The well-known dipole formula for the neighbour-anisotropy or ‘pseudo-contact’ contribution to nuclear magnetic shielding is generalized to include higher multipoles. For a nucleus with coordinates (R, ϑ) relative to an origin in an axially symmetric group the shielding is shown to take the form where Kn is a coefficient measuring the anisotropy in the group's 2 n -pole susceptibility and the Pn (cos ϑ) are Legendre polynomials. Sector rules for shift reagents are developed.

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