Simulation of dynamics in NMR spectra of rotating solids

Abstract

A general formalism, suitable for the simulation of dynamically modulated nuclear magnetic resonance lineshapes, is presented. The relaxation function containing all the observable components of transverse magnetization is generated by successive multiplication by a complex propagator matrix. Its elements are determined by the spin Hamiltonians at each site visited by the spins, and by the conditional probability function which describes the motion of the spins between these sites. Chemical exchange, diffusion and sample rotation are accounted for by employing appropriate discretization schemes in each case. Frequency spectra are calculated by Fourier transformation of the relaxation function, evaluated at intervals of Δ, where Δ is equal to the inverse sweep width. The method is entirely general but is particularly efficient in the slow motional regime. It is applied to evaluate ²H magic angle spinning (MAS) NMR lineshapes for deuterons undergoing 180° flip motion and ³¹P MAS lineshapes for phospholipids undergoing lateral diffusion across curved membrane surfaces.