Sublinear scaling quantum chemical methods for magnetic shieldings in large molecules

It is shown that quantum chemical calculations of the nuclear magnetic shieldings of a group of vicinal nuclei in a large molecule can be made sublinear scaling [i.e., $O(1)$] with respect to the molecular size. This is achieved by making both the diamagnetic and paramagnetic terms translation invariant [following the work of Ochsenfeld et al. J. Chem. Phys. 134, 074102 (2011)] and by making use of a local representation that is independent of the molecular size. Although only Hartree-Fock results are reported here, the idea can readily be extended to correlated wave function methods as well as the relativistic domain.