Optimized Multiple Quantum MAS Lineshape Simulations in Solid State NMR

TL;DR

This paper introduces a computational method using simulated annealing to optimize and simulate 2D MQMAS NMR spectra for disordered materials, enabling better characterization of local chemical environments despite spectral overlap.

Contribution

It presents a novel distributed simulation approach combined with optimization techniques to analyze complex MQMAS spectra of disordered solids.

Findings

Effective simulation of 2D MQMAS spectra using stochastic parameter distributions.

Optimization of spectral parameters via simulated annealing improves spectral interpretation.

Method provides error estimates for local chemical environment characterization.

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 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.