Optimized multiple quantum MAS lineshape simulations in solid state NMR

William J. Brouwer, Michael C. Davis, Karl T. Mueller

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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. Program summary: Program title: mqmasOPT. Catalogue identifier: AEEC_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEC_v1_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html. No. of lines in distributed program, including test data, etc.: 3650. No. of bytes in distributed program, including test data, etc.: 73 853. Distribution format: tar.gz. Programming language: C, OCTAVE. Computer: UNIX/Linux. Operating system: UNIX/Linux. Has the code been vectorised or parallelized?: Yes. RAM: Example: (1597 powder angles) × (200 Samples) × (81 F2 frequency pts) × (31 F1 frequency points) = 3.5M, SMP AMD opteron. Classification: 2.3. External routines: OCTAVE (http://www.gnu.org/software/octave/), GNU Scientific Library (http://www.gnu.org/software/gsl/), OPENMP (http://openmp.org/wp/). Nature of problem: The optimal simulation and modeling of multiple quantum magic angle spinning NMR spectra, for general systems, especially those with mild to significant disorder. The approach outlined and implemented in C and OCTAVE also produces model parameter error estimates. Solution method: A model for each distinct chemical site is first proposed, for the individual contribution of crystallite orientations to the spectrum. This model is averaged over all powder angles [1], as well as the (stochastic) parameters; isotropic chemical shift and quadrupole coupling constant. The latter is accomplished via sampling from a bi-variate Gaussian distribution, using the Box-Muller algorithm to transform Sobol (quasi) random numbers [2]. A simulated annealing optimization is performed, and finally the non-linear jackknife [3] is applied in developing model parameter error estimates. Additional comments: The distribution contains a script, mqmasOpt.m, which runs in the OCTAVE language workspace. Running time: Example: (1597 powder angles) × (200 Samples) × (81 F2 frequency pts) × (31 F1 frequency points) = 58.35 seconds, SMP AMD opteron. References: [1]S.K. Zaremba, Annali di Matematica Pura ed Applicata 73 (1966) 293.[2]H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, 1992.[3]T. Fox, D. Hinkley, K. Larntz, Technometrics 22 (1980) 29.

Original languageEnglish (US)
Pages (from-to)1973-1982
Number of pages10
JournalComputer Physics Communications
Issue number10
StatePublished - Oct 2009

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • General Physics and Astronomy


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