Efficient Spectral Simulations in NMR of Rotating Solids. The γ-COMPUTE Algorithm

Abstract

We explore the time-translational relation between one of the powder angles (γ) and the sample rotation angle (ωrt) in NMR spectroscopy of rotating solids. Averaging over the γ powder angle is shown to be generally equivalent to a cross correlation of two periodic functions. This leads to a fundamental relation concerning the phases of NMR spectra of rotating solids as well as improved strategies for efficient simulation of experimental spectra. Using these results in combination with the frequency-domain simulation procedure COMPUTE (M. Edénet al., J. Magn. Reson. A120, 56 (1996)), it proves possible to reduce the computation time for spectral simulations by typically a factor 10–30 relative to the state-of-the-art calculations using the original COMPUTE algorithm. The advantage and the general applicability of the new simulation procedure, referred to as γ-COMPUTE, are demonstrated by simulation of single- and multiple-pulse MAS NMR spectra of31P–31P and1H–1H spin pairs influenced by anisotropic chemical shielding and homonuclear dipolar interactions.