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

TL;DR

This paper derives a new formula for paramagnetic NMR chemical shifts in molecules with zero-field splitting, clarifying the temperature dependence of shifts in specific spin states and correcting previous theories.

Contribution

It introduces a general formula for paramagnetic NMR shielding in molecules with zero-field splitting, addressing limitations of earlier models.

Findings

Correctly predicts temperature-independent shifts in certain spin states

Contradicts previous models predicting Curie dependence

Provides a simple application to triplet ground states

Abstract

We derive a general formula for the paramagnetic NMR nuclear shielding tensor of an open-shell molecule in a pure spin state, subject to a zero-field splitting (ZFS). Our findings are in contradiction with a previous proposal. We present a simple application of the newly derived formula to the case of a triplet ground state split by an easy-plane ZFS spin Hamiltonian. When $kT$ is much smaller than the ZFS gap, thus a single non-degenerate level is thermally populated, our approach correctly predicts a temperature-independent paramagnetic shift, while the previous theory leads to a Curie temperature dependence.