Magnetic multipoles and the ‘pseudo-contact’ chemical shift

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 (Formula presented) where K_n is a coefficient measuring the anisotropy in the group’s 2ⁿ-pole susceptibility and the P_n(cos θ) are Legendre polynomials. Sector rules for shift reagents are developed.