Interpolation by fast Wigner transform for rapid calculations of magnetic resonance spectra from powders

Automatic fitting of multiple-field solid-state NMR spectra

The NMR lineshapes produced by half-integer quadrupolar nuclei are sensitive to 11 distinct fit parameters per inequivalent site. To date, automatic fitting routines have failed to replace manual parameter insertion and evaluation due to the importance of local minima and the need for fitting multiple-field magic-angle spinning (MAS) and static spectra simultaneously. Herein we introduce a new tool, AMES-Fit (Automatic Multiple Experiment Simulation and Fitting), to automatically find the global best-fit simulation parameters for a series of multiple-field NMR lineshapes. AMES-Fit uses an adaptive step size random search algorithm to dynamically probe parameter space and requires minimal human input. The best fits are obtained in a few minutes of computation time that would otherwise have required several person-hours of work. The program is freely available and open-source.

Numerical recipes for faster MAS-DNP simulations

Numerical simulations of Magic Angle Spinning Dynamic Nuclear Polarization (MAS-DNP) have transformed the way the DNP process is understood in rotating samples. In 2012, two methods were concomitantly developed to simulate small spin systems (< 4 spin-1/2). The development of new polarizing agents, including those containing metal centers with S > 1/2, makes it necessary to further expand the numerical tools with minimal approximations that will help rationalize the experimental observations and build approximate models. In this paper, three strategies developed in the past five years are presented: an adaptive integration scheme, a hybrid Hilbert/Liouville formalism, and a method to truncate the Liouville space basis for periodic Hamiltonian. Each of these methods enable time savings ranging from a factor of 3 to > 100. We illustrate the code performance by reporting for the first time the MAS-DNP field profiles for "AMUPol", in which the couplings to the nitrogen nuclei are explicitly considered, as well as Cross-Effect MAS-DNP field profiles with two electrons spin 5/2 interacting with a nuclear spin 1/2.

Assessment of new symmetry-based dipolar recoupling schemes for homonuclear magnetization exchange between quadrupolar nuclei in two-dimensional correlation MAS NMR

We provide an extensive experimental and numerical evaluation of MQ-phase (S)M supercycles with M={3,4} of three groups of symmetry-based homonuclear dipolar recoupling rf-pulse sequences, [Formula: see text] , for establishing proximities among half-integer spin quadrupolar nuclei under moderately fast magic-angle-spinning (MAS) conditions in single-quantum-single-quantum (1Q-1Q) correlation NMR experiments. The relative merits of the (S)M schemes for variations in resonance offsets and rf-amplitude errors were assessed by numerically simulated magnetization transfers in spin-3/2 pairs with variable isotropic chemical shifts and quadrupolar coupling constants. Experimental demonstrations of ²³Na (spin-3/2) NMR on Na₂MoO₄·2H₂O and ²⁷Al (spin-5/2) NMR on AlPO-CJ19 [(NH₄)₂Al₄(PO₄)₄HPO₄·H₂O] are presented at 14.1 T and 24 kHz MAS. We recommend using the (SR2₂¹)3 or (SR2₂¹)4 supercycles for samples that exhibit small chemical-shift dispersions (<3 kHz), and any (SRN_N^N/2)3 scheme with N⩾10 for larger spreads of isotropic chemical shifts. However, because the (SRN_N^N/2)3 sequences recouple heteronuclear dipolar interactions, their application to proton-bearing samples requires high-power proton decoupling during the mixing period. Alternatively, the (SR2₄¹)3 and (SR2₄¹)4 schemes may be employed in the absence of proton decoupling, but with poorer compensation to resonance-offsets and rf-amplitude errors.

Improved Magnetization Transfers among Quadrupolar Nuclei in Two-Dimensional Homonuclear Correlation NMR Experiments Applied to Inorganic Network Structures

We demonstrate that supercycles of previously introduced two-fold symmetry dipolar recoupling schemes may be utilized successfully in homonuclear correlation nuclear magnetic resonance (NMR) spectroscopy for probing proximities among half-integer spin quadrupolar nuclei in network materials undergoing magic-angle-spinning (MAS). These (SR221)M, (SR241)M, and (SR281)M recoupling sequences with M=3 and M=4 offer comparably efficient magnetization transfers in single-quantum–single-quantum (1Q–1Q) correlation NMR experiments under moderately fast MAS conditions, as demonstrated at 14.1 T and 24 kHz MAS in the contexts of 11B NMR on a Na2O–CaO–B2O3–SiO2 glass and 27Al NMR on the open framework aluminophosphate AlPO-CJ19 [(NH4)2Al4(PO4)4HPO4·H2O]. Numerically simulated magnetization transfers in spin–3/2 pairs revealed a progressively enhanced tolerance to resonance offsets and rf-amplitude errors of the recoupling pulses along the series (SR221)M< (SR241)M< (SR281)M for increasing differences in chemical shifts between the two nuclei. Nonetheless, for scenarios of a relatively minor chemical-shift dispersions (≲3 kHz), the (SR221)M supercycles perform best both experimentally and in simulations.

Computer-intensive simulation of solid-state NMR experiments using SIMPSON

Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations.