Nonlinear least‐squares fitting procedure for solid‐state NMR powder patterns

A fitting procedure for the extraction of the characteristic NMR parameters from solid‐state NMR powder patterns is described at an introductory level. The Levenberg‐Marquardt nonlinear least‐squares algorithm is recoded in Matlab, a vector‐oriented programming language, so that the NMR simulation programs are more condensed than are those in traditional programming languages. Three examples of line‐shape fitting are shown: the deuterium powder pattern for the bridging deuterium site in [Et4N] [2HCr2(CO)10], the proton‐coupled 13C powder pattern for the bridging methylene site in cis‐(μ‐CH2)(μ‐CO)[FeCp(CO)]2, and the (14N, 195Pt)‐coupled 13C powder pattern for the Pt‐CN system in K2Pt(CN)4 · 3H2O. The results provide information about quadrupolar, dipolar, and chemical‐shielding tensors. In each case, the line‐shape is calculated from the spin Hamiltonian expressed in a simple, uncoupled basis set. The variables in each case are a small set of NMR parameters: the quadruple‐coupling constant and the asymmetry parameter. The effects of finite pulse‐lengths or anisotropic cross‐polarization are not included in the line‐shape simulations. The line‐shapes are powder patterns; averaging over the Euler angles, θ and x, is done either with constant angle step size or by the Conroy‐Wolfsberg tiling scheme.