The use of single-spin operator basis sets in the N.M.R. spectroscopy of scalar-coupled spin systems

Abstract

The use of a complete set comprising products of single-spin angular momentum operators is introduced as a basis for the expansion of the density operators of typical simple nuclear spin systems encountered in double-resonance high-resolution liquid state nuclear magnetic resonance experiments. Some simple rules are presented for calculating the evolution of the density operator due to arbitrary sequences of unselective radio frequency pulses and periods of free precession due to chemical shifts and scalar couplings. The proportions and nature of the zero-, single- and multiple-quantum order excited by such pulse sequences can readily be predicted, as can the form of the N.M.R. signal itself, when all relaxation effects are neglected. The evolution of some of the basic product operators is interpreted in terms of pictorial models.

Some important restrictions on the nature of the states which can be produced by arbitrary pulse sequences are discussed and the possible states of the AX spin system are analysed in detail. As examples the rules mentioned previously are employed to analyse two 2-D N.M.R. pulse sequences, the heteronuclear J-resolved and shift-correlated experiments.