Optimized multiple quantum MAS lineshape simulations in solid state NMR

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 produces anisotropic line broadening in spectra for distinct chemical species in polycrystalline solids. In Multiple Quantum Magic Angle Spinning (MQMAS) experiments, a second frequency dimension is created, devoid of quadrupolar anisotropy. As a result, the bary centers 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 optimal simulation of the MQMAS spectrum, generated by random variates from model distributions of isotropic chemical and quadrupole shifts. In this manner, local chemical environments for disordered materials may be characterized and via a re-sampling approach, error estimates for parameters produced.