  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 is a function of isotropic
second order quadrupole and chemical shift 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 two-dimensional MQMAS spectrum, generated by random variates from model
distributions of isotropic chemical and quadrupole shifts. Owing to the
non-convex nature of the residual sum of squares (RSS) 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.
