Magic-angle spinning nuclear magnetic resonance spectra of second-order two-spin systems in the solid state

Abstract

Magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectra of second-order two-spin (AB) systems are investigated. Using average Hamiltonian theory (AHT), general expressions for the positions and relative intensities of the four allowed transitions are derived. In principle, correction terms to any order of the average Hamiltonian may be applied; however, terms up to and including third order appear to be adequate in reproducing the most important experimental features. In general, both the positions and relative intensities of the peaks are sensitive to the sample spinning frequency. Only at the high MAS frequency extreme do the MAS NMR spectra of two-spin (AB) systems in solids correspond to those predicted using formulas derived for solution samples. Under slow MAS conditions, MAS NMR spectra of AB spin systems deviate considerably from the corresponding AB spectra in solution NMR studies. Three general types of MAS NMR spectra are identified and their characteristic features are discussed. The theoretical expressions derived here are applied to reproduce the observed 31P MAS NMR spectra of a phosphole tetramer and cis-1,2-bis(diphenylphosphino)ethylene. It is shown that correction terms higher than first order must be considered in order to reproduce the anomalous spinning-frequency dependencies in MAS NMR spectra. The importance of carrying out measurements at two different applied fields is also demonstrated in the case of the phosphole tetramer.