Calculation of Chemical Shifts. I. General Formulation and the <i>Z</i> Dependence

Explicit expressions for the paramagnetic contribution σ(2) to the nuclear magnetic shielding are derived in the valence bond and the LCAO—MO framework including d as well as p orbitals on the atom in question. A survey of published experimental data reveals a periodic dependence of the range of chemical shifts on atomic number, which is explained in terms of the paramagnetic contribution to the chemical shift and its dependence on 〈1/r3〉 for the bonding electrons. A brief discussion is given of related but more complex periodicities in the electron coupling of nuclear spins, using the M—H coupling in Group IV hydrides as an example. It is suggested that the anisotropy in the nuclear shielding and internuclear coupling tensors may combine to give observable linewidth differences in the high-resolution NMR spectra of directly bonded nuclei of large Z.