Methods for analyzing spectroscopic line shapes. NMR solid powder patterns

A new method is described for numerically computing theoretical NMR powder patterns which achieves a many‐fold increase in speed and accuracy over previous techniques. The method incorporates a simple and efficient technique for selecting the set of crystal orientations over which the spectral frequencies are calculated. The orientation selection technique is then integrated with an interpolation scheme which transfers the intensities at these frequencies to the computed spectrum. The method will be useful whenever an average over a sphere is computed numerically. The new efficiency of the method makes practical least squares fitting of theoretical spectra to experimental NMR data. The fits provide unbiased estimates of the NMR parameters and their errors. The technique is illustrated by extracting chemical shift tensors from a proton decoupled carbon‐13 NMR spectrum.