Non-linear least squares procedure for the extraction of NMR parameters from multi-tensor solid state line shapes

Abstract

A suite of nuclear magnetic resonance (NMR) line shape programs, that simulate five common interactions in solids, has been written. Non-linear least squares routines based on the SIMPLEX and Levenberg-Marquardt algorithms have been implemented to extract physical parameters from solid state NMR powder line shapes. Both optimization strategies produce error estimates for the parameters extracted. As an example to illustrate the difficulties of applying least squares in NMR, the system of mono- and dilabeled 13C ethylene on silver, supported on γ-alumina was studied. The experimental line shapes produced were analyzed by non-linear least squares fitting to extract the principal components of the chemical shift (CS) tensor, the bond distance, and the orientation of the components of the chemical shift tensor in the molecular frame of ethylene. To evaluate the techniques performance, the reliability of the error estimates produced by the optimization has been investigated.