Computing nuclear magnetic resonance chemical shielding in large systems via multipole shielding polarizabilities

Whereas ab initio methods are feasible for computational evaluation of chemical shielding parameters in small molecules or molecular fragments, a simpler method is demonstrated for the evaluation of the relative effects of shielding due to electrostatic interactions, such as those which may arise from both inter- and intra-residue interactions in proteins and other biomolecules. The shielding of a small molecule or molecular fragment is expanded in a multipole power series, and the terms of the series may be evaluated by contemporary ab initio methods. The convergence behavior of this expansion using fluorobenzene is shown as a prototypical molecule, and we conclude that the first three multipole polarizability terms are important, but that hyperpolarizability shielding corrections are negligible.