A complete product operator theory for IS (I = ½, S = 1) spin system and application to DEPT–HMQC NMR experiment

Abstract

There exist a variety of multi-pulse NMR experiments for spectral assignment of complex molecules in solution. The DEPT−HMQC NMR experiment is a combination of DEPT and HMQC experiments. The product operator theory is widely used for analytical description of multi-pulse NMR experiment for weakly coupled spin systems. In this study, a complete product operator theory for the IS (I = ½, S = 1) spin system is presented by obtaining the evolutions of some product operators under the spin–spin coupling Hamiltonian and the evolutions of some angular momentum operators under the chemical shift and radio frequency (r.f.) pulse Hamiltonians. As an application, product operator theory has been used for the analytical description of DEPT−HMQC NMR experiment for CD_n groups. Theoretical discussions and experimental suggestions for the sub-spectral editing of CD_n groups are presented for this experiment.