Nuclear Magnetic Resonance Chemical Shift in an Arbitrary Electronic Spin State

Abstract

We present a general and systematic electronic structure theory of the nuclear magnetic resonance shielding tensor and the associated chemical shift for paramagnetic atoms, molecules, and nonmetallic solids. The approach is for the first time rigorous for an arbitrary spin state as well as arbitrary spatial symmetry and is formulated without reference to spin susceptibility. The leading-order magnetic-field dependence of shielding is derived. The theory is demonstrated by first principles calculations of organometallic molecules.

DFT investigation of the effect of spin-orbit coupling on the NMR shifts in paramagnetic solids

“…As discussed in Ref. 20, by retaining only the terms that contain at most one leading-order spin-orbit coupling term in the product g · A, the resulting contributions can be separated based on the nature of the involved hyperfine term. This corresponds to retaining terms up to fourth order in the fine-structure constant.…”

“…[35] In the presence of a single paramagnetic centre, the specific form of σ s is derived to be [17,19,20] …”

“…Substantial progress has been made in the theoretical description of various contributions to the NMR shift of molecular systems with a single paramagnetic centre. After the pioneering work of Kurland and McGarvey [16], Moon and Patchkovski derived a formalism to describe the entire shift tensor including the effects of spin-orbit coupling [19], later ex-tended to the presence of zero-field splitting by Vaara et al [20,21] and Soncini and Van den Heuvel [22], with the consequent extensive study of the NMR shift of paramagnetic molecules [23][24][25][26][27][28]. The shift mechanisms in paramagnetic transition metal-containing extended solids have been studied by Carlier, Grey and co-workers and the effects of multiple paramagnetic centres on the isotropic Fermi contact shift and its relation to the bulk magnetic properties of the solid have been qualitatively [13], and subsequently more quantitatively [29], rationalised.…”

Communication: Paramagnetic NMR chemical shift in a spin state subject to zero-field splitting

“…Despite the increasingly central role played by paramagnetic NMR in the elucidation of the structure of metallo-proteins, 1 and in the investigation of the spin dynamics in novel magnetic materials, 2 only quite recently rigorous theories have been developed for the ab initio calculation of the paramagnetic NMR chemical shift. [3][4][5][6] Of particular relevance in this respect is the work of Moon and Patchkovskii, 3 that of Pennanen and Vaara, 4 and that of Van den Heuvel and Soncini. 5,6 Moon and Patchkovskii 3 derived an expression for the paramagnetic shielding tensor of a spin doublet state in terms of its gand A-tensors.…”

“…5,6 Moon and Patchkovskii 3 derived an expression for the paramagnetic shielding tensor of a spin doublet state in terms of its gand A-tensors. This treatment was extended by Pennanen and Vaara 4 to arbitrary spin states, in the limit of weak spinorbit coupling, and later generalised by us to a theory that is valid for arbitrary strength of spin-orbit coupling, and arbitrary size of the degenerate manifold. 5,6 In Ref.…”