Nuclear magnetic resonance of J-coupled quadrupolar nuclei: Use of the tensor operator product basis

Abstract

In nuclear magnetic resonance (NMR) of I=1/2 nuclei that are scalar coupled to quadrupolar spins, a tensor operator product (TOP) basis set provides a convenient description of the time evolution of the density operator. Expressions for the evolution of equivalent I=1/2 spins, coupled to an arbitrary spin S>1/2, were obtained by explicit algebraic density operator calculations in Mathematica, and specific examples are given for S=1 and S=3/2. Tensor operators are described by the convenient quantum numbers rank and order and this imparts to the TOP basis features that enable an intuitive understanding of NMR behavior of these spin systems. It is shown that evolution as a result of J coupling alone changes the rank of tensors for the coupling partner, generating higher-rank tensors, which allow efficient excitation of S-spin multiple-quantum coherences. Theoretical predictions obtained using the TOP formalism were confirmed using multiple-quantum filtered heteronuclear spin-echo experiments and were further employed to demonstrate polarization transfer directly to multiple-quantum transitions using the insensitive nucleus enhancement by polarization transfer pulse sequence. This latter experiment is the basis of two-dimensional heteronuclear correlation experiments and direct generation of multiple-quantum S-spin coherences can therefore be exploited to yield greater spectral resolution in such experiments. Simulated spectra and experimental results are presented.