A method to calculate the NMR spectra of paramagnetic species using thermalized electronic relaxation

For paramagnetic species, it has been long understood that the hyperfine interaction between the unpaired electrons and the nucleus results in a nuclear magnetic resonance (NMR) peak that is shifted by a paramagnetic shift, rather than split by the coupling, due to an averaging of the electronic magnetic moment caused by electronic relaxation that is fast in comparison to the hyperfine coupling constant. However, although this feature of paramagnetic NMR has formed the basis of all theories of the param-agnetic shift, the precise theory and mechanism of the electronic relaxation required to predict this result has never been discussed, nor has the assertion been tested. In this paper, we show that the standard semi-classical Redfield theory of relaxation fails to predict a paramagnetic shift, as does any attempt to correct for the semi-classical theory using modifications such as the inhomogeneous master equation or Levitt-di Bari thermalization. In fact, only the recently-introduced Lindbladian theory of relaxation in magnetic resonance [J. Magn. Reson., 310, 106645 (2019)] is able to correctly predict the paramagnetic shift tensor and relaxation-induced linewidth in pNMR. Furthermore, this new formalism is able to pre-dict the NMR spectra of paramagnetic species outside the high-temperature and weak-order limits, and is therefore also applicable to dynamic nuclear polarization. The formalism is tested by simulations of five case studies, which include Fermi-contact and spin-dipolar hyperfine couplings, g-anisotropy, zero-field splitting, high and low temperatures, and fast and slow electronic relaxation. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper discusses the paramagnetic shift in nuclear magnetic resonance (NMR) and shows that traditional Redfield theory fails to predict it, while the recently-introduced Lindbladian theory can accurately do so, applicable to dynamic nuclear polarization and beyond. The formalism is tested through simulations of various case studies, proving its effectiveness in predicting paramagnetic shifts and relaxation-induced linewidths in pNMR.