Revisiting the Concept of Equivalence in Solid-State NMR

Abstract

The concepts of chemical and magnetic equivalence have profound impacts on the understanding and interpretation of NMR phenomena. In solution, magnetic equivalence between spin-1/2 nuclei is generally associated with the lack of an observable spectral J-splitting. We examine here the concept of equivalence between quadrupolar nuclei with an emphasis on solid powdered samples. In this context, magnetic equivalence means that the coupled nuclei have identical NMR interaction tensor magnitudes and orientations. Contrary to the spin-1/2 case, J-couplings between magnetically equivalent quadrupolar nuclei are manifested as spectral splittings in solids and in aligned media. Following an overview of the relevant theory, examples employing double-rotation NMR, MQMAS NMR, ultrahigh-field NMR, and two-dimensional J-resolved experiments under both spinning and stationary conditions are discussed. The dependence of the observed splittings on the type of equivalence shared by the coupled nuclei (none, chemical, or magnetic) provides a unique experimental handle on crystallographic symmetry, which is of value for structure elucidation. Keywords: magnetic equivalence; chemical equivalence; quadrupolar nuclei; J-coupling; chemical shifts; J-resolved spectroscopy