An Efficient Method for Calculating Powder Patterns

A novel approach to the calculation of powder lineshapes is presented. Lineshapes from asymmetric second-rank tensor interactions are produced by summing lineshapes from symmetric tensors. This approach significantly reduces the calculation time, greatly facilitating iterative nonlinear least-squares fitting of experimental spectra. Results are reported for anisotropic 13C NMR lineshapes of glycine, benzoic acid, and octanoic acid in a urea inclusion compound. Lineshapes from nonuniform distributions of crystallite orientations can also be calculated by using distributions of the Euler angles that define the orientation of the principal-axis system of the chemical-shielding tensor with respect to the magnetic field.