Abstract: The majority of nuclei available for study in solid state Nuclear Magnetic Resonance have half-integer spin I > 1/2, with corresponding electric quadrupole moment. As such, they may couple with a surrounding electric field gradient. This effect introduces anisotropic line broadening to spectra, arising from distinct chemical species within polycrystalline solids. In Multiple Quantum Magic Angle Spinning (MQMAS) experiments, a second frequency dimension is created, devoid of quadrupolar anisotropy. As a result, the center of gravity of peaks in the high resolution dimension are functions of isotropic quadrupole and chemical shifts alone. However, for complex materials, these parameters take on a stochastic nature due in turn to structural and chemical disorder. Lineshapes may still overlap in the isotropic dimension, complicating the task of assignment and interpretation. A distributed computational approach is presented here which permits simulation of the MQMAS spectrum, generated by random variates from model distributions of isotropic chemical and quadrupole shifts. Owing to the non-convex nature of the least squared cost function between experimental and simulated spectra, simulated annealing is used to optimize the simulation parameters. In this manner, local chemical environments for disordered materials may be characterized, and via a re-sampling approach, error estimates for parameters produced.
Key words: Nuclear Magnetic Resonance, Multiple Quantum Magic Angle Spinning, OpenMP, Sobol sequence, quasi-random numbers, simulated annealing, distribution functions, quadrupole interaction.