1H line width dependence on MAS speed in solid state NMR - Comparison of experiment and simulation

High-Field Dynamic Nuclear Polarization

Dynamic nuclear polarization (DNP) is one of the most prominent methods of sensitivity enhancement in nuclear magnetic resonance (NMR). Even though solid-state DNP under magic-angle spinning (MAS) has left the proof-of-concept phase and has become an important tool for structural investigations of biomolecules as well as materials, it is still far from mainstream applicability because of the potentially overwhelming combination of unique instrumentation, complex sample preparation, and a multitude of different mechanisms and methods available. In this review, I introduce the diverse field and history of DNP, combining aspects of NMR and electron paramagnetic resonance. I then explain the general concepts and detailed mechanisms relevant at high magnetic field, including solution-state methods based on Overhauser DNP but with a greater focus on the more established MAS DNP methods. Finally, I review practical considerations and fields of application and discuss future developments.

The origin of negative cross-peaks in proton-spin diffusion spectrum of fully protonated solids at fast MAS: Coherent or incoherent effect?

Spin-diffusion (SD) is amongst the first methods proposed to spatially transfer polarization between dipolar-coupled nuclear spins. Lab-frame SD has proved particularly useful in structural characterization of a large variety of molecules. During SD, the rate of magnetization transfer between the two nuclei depends on the square of the dipolar coupling and the zero-quantum lineshape of the two spins. The relative sign of the diagonal and cross-peaks is determined by the spin part of the dipolar Hamiltonian. Practically, SD experiments are used in two ways: (a) SD transfer amongst only the protons (known as proton spin-diffusion or PSD) and b) SD amongst rare nuclei, coupled to a strong proton bath, known as proton driven spin-diffusion (PDSD). It is well established that the diagonal and cross-peaks have the same sign during SD based polarization transfer. 2D PSD experiments recorded on Histidine.HCl.H₂O sample at fast magic angle spinning (MAS) show that some of the cross-peaks in the 2D spectrum are negative with respect to the diagonal peaks. Cross-relaxation due to stochastic motion is generally believed to give rise to such negative peaks. Herein, we use theoretical calculations, numerical simulations and experiments to show that the origin of the negative cross-peaks in PSD spectrum is due to coherent interactions. The origin of negative peaks can be specifically ascribed to a four spin, double-flip-double flop term, in the third-order Hamiltonian. These terms become the dominant terms at fast spinning when additional - conditions are satisfied.

Conjugated porous polymers: incredibly versatile materials with far-reaching applications

This review discusses conjugated porous polymers and focuses on relating design principles and synthetic methods to key properties and applications such as (photo)catalysis, gas storage, chemical sensing, energy storage and environmental remediation.

High-resolution 1H NMR of powdered solids by homonuclear dipolar decoupling

The development of homonuclear dipolar decoupling sequences to obtain high-resolution ¹H NMR spectra from solids has recently celebrated its 50th birthday. Over the years, a series of different decoupling schemes have been developed, starting with the pioneering Lee-Goldburg and WAHUHA sequences up to the most recent generation of experimentally optimized phase-modulated schemes such as eDUMBO-1₂₂ and LG4. These schemes can all yield over an order of magnitude reduction in ¹H NMR linewidths in solids. Here we provide an overview and a broad experimental comparison of the performance of the main sequences, which has so far been absent in the literature, especially between the newest and the oldest decoupling schemes. We compare experimental results obtained using eight different decoupling schemes (LG, WHH-4, MREV-8, BR-24, FSLG/PMLG, DUMBO-1, eDUMBO-1₂₂ and LG4) on three different microcrystalline powdered samples (alanine, glycine and β-AspAla) and at three different MAS rates (3.0, 12.5 and 22.0 kHz). Finally, since these sequences can be technically demanding, we describe the experimental protocol we have used to optimize these schemes with the aim to provide simple guidelines for the optimization of CRAMPS experiments for all NMR users.

H-MAS

We characterize a new generation of MAS probes, designed for 1H detection in solid and viscous structures. High top speed (currently 170 kHz), existence of a wide speed range and quick acceleration enable numerous new experiment categories. Most notably, massive biomolecular structures become amenable to a detailed structural and dynamics studies.

Quantifying proton NMR coherent linewidth in proteins under fast MAS conditions: a second moment approach

Proton detected solid-state NMR under fast magic-angle-spinning (MAS) conditions is currently redefining the applications of solid-state NMR, in particular in structural biology. Understanding the contributions to the spectral linewidth is thereby of paramount importance. When disregarding the sample-dependent inhomogeneous contributions, the NMR proton linewidth is defined by homogeneous broadening, which has incoherent and coherent contributions. Understanding and disentangling these different contributions in multi-spin systems like proteins is still an open issue. The coherent contribution is mainly caused by the dipolar interaction under MAS and is determined by the molecular structure and the proton chemical shifts. Numerical simulation approaches based on numerically exact direct integration of the Liouville-von Neumann equation can give valuable information about the lineshape, but are limited to small spin systems (<12 spins). We present an alternative simulation method for the coherent contributions based on the rapid and partially analytic calculation of the second moments of large spin systems. We first validate the method on a simple system by predicting the ¹⁹F linewidth in CaF₂ under MAS. We compare simulation results to experimental data for microcrystalline ubiquitin (deuterated 100% back-exchanged at 110 kHz and fully-protonated at 125 kHz). Our results quantitatively explain the observed linewidth per-residue basis for the vast majority of residues.

Line narrowing in 1H NMR of powdered organic solids with TOP-CT-MAS experiments at ultra-fast MAS

The residual broadening observed in ¹H spectra of rigid organic solids at natural abundance under 111 kHz magic angle spinning (MAS) is typically a few hundred Hertz. Here we show that refocusable and non-refocusable interactions contribute roughly equally to this residual at high-fields (21.14 T), and suggest that the removal of the non-refocusable part will produce significant increase in spectral resolution. To this end, we demonstrate an experiment for the indirect acquisition of constant-time experiments at ultra-fast MAS (CT-MAS) which verifies this hypothesis. The combination of this experiment with the two-dimensional one pulse (TOP) transformation reduces the experimental time to a fraction of the original cost while retaining the narrowing effects. Results obtained with TOP-CT-MAS at 111 kHz MAS on a sample of β-AspAla yield up to 30% higher resolution spectra than the equivalent one-pulse experiment, in less than 10 min.

A suite of solid-state NMR experiments to utilize orphaned magnetization for assignment of proteins using parallel high and low gamma detection

We present a suite of two-receiver solid-state NMR experiments for backbone and side chain resonance assignment. The experiments rely on either dipolar coupling or scalar coupling for polarization transfer and are devised to acquire a ¹H-detected 3D experiment AND a nested ¹³C-detected 2D from a shared excitation pulse. In order to compensate for the lower sensitivity of detection on ¹³C nucleus, 2D rows are signal averaged during 3D planes. The 3D dual receiver experiments do not suffer from any appreciable signal loss compared to their single receiver versions and require no extra optimization. The resulting data is higher in information content with no additional experiment time. The approach is expected to become widespread as multiple receivers become standard for new NMR spectrometers.

Linear-scaling ab initio simulations of spin diffusion in rotating solids

We investigated the utility of locally restricting the basis sets involved in low-order correlations in Liouville space (LCL) calculations of spin diffusion. Using well-known classical models of spin diffusion, we describe a rationale for selecting the optimal basis set for such calculations. We then show that the use of these locally restricted basis sets provides the same computational accuracy as the full LCL set while reducing the computational time by several orders of magnitude. Speeding up the calculations also enables us to use higher maximum spin orders and increase the computational accuracy. Furthermore, unlike exact and full LCL calculations, locally restricted LCL calculations scale linearly with the system size and should thus enable the ab initio study of spin diffusion in spin systems containing several thousand spins.

Resolution enhancement and proton proximity probed by 3D TQ/DQ/SQ proton NMR spectroscopy under ultrafast magic-angle-spinning beyond 70 kHz

Proton nuclear magnetic resonance (NMR) in solid state has gained significant attention in recent years due to the remarkable resolution and sensitivity enhancement afforded by ultrafast magic-angle-spinning (MAS). In spite of the substantial suppression of ¹H-¹H dipolar couplings, the proton spectral resolution is still poor compared to that of ¹³C or ¹⁵N NMR, rendering it challenging for the structural and conformational analysis of complex chemicals or biological solids. Herein, by utilizing the benefits of double-quantum (DQ) and triple-quantum (TQ) coherences, we propose a 3D single-channel pulse sequence that correlates proton triple-quantum/double-quantum/single-quantum (TQ/DQ/SQ) chemical shifts. In addition to the two-spin proximity information, this 3D TQ/DQ/SQ pulse sequence enables more reliable extraction of three-spin proximity information compared to the regular 2D TQ/SQ correlation experiment, which could aid in revealing the proton network in solids. Furthermore, the TQ/DQ slice taken at a specific SQ chemical shift only reveals the local correlations to the corresponding SQ chemical shift, and thus it enables accurate assignments of the proton peaks along the TQ and DQ dimensions and simplifies the interpretation of proton spectra especially for dense proton networks. The high performance of this 3D pulse sequence is well demonstrated on small compounds, L-alanine and a tripeptide, N-formyl-L-methionyl-L-leucyl-L-phenylalanine (MLF). We expect that this new methodology can inspire the development of multidimensional solid-state NMR pulse sequences using the merits of TQ and DQ coherences and enable high-throughput investigations of complex solids using abundant protons.

Characterization of H2 -Splitting Products of Frustrated Lewis Pairs: Benefit of Fast Magic-Angle Spinning

Proton spectroscopy in solid-state NMR on catalytic materials offers new opportunities in structural characterization, in particular of reaction products of catalytic reactions such as hydrogenation reactions. Unfortunately, the ¹ H NMR line widths in magic-angle spinning solid-state spectra are often broadened by an incomplete averaging of ¹ H-¹ H dipolar couplings. We herein discuss two model compounds, namely the H₂ -splitting products of two phosphane-borane Frustrated Lewis Pairs (FLPs), to study potentials and limitations of proton solid-state NMR experiments employing magic-angle spinning frequencies larger than 100 kHz at a static magnetic field strength of 20.0 T. The ¹ H lines are homogeneously broadened as illustrated by spin-echo decay experiments. We study two structurally similar materials which however show significant differences in ¹ H line widths which we explain by differences in their ¹ H-¹ H dipolar networks. We discuss the benefit of fast MAS experiments up to 110 kHz to detect the resonances of the H⁺ /H^- pair in the hydrogenation products of FLPs.

Spinning faster: protein NMR at MAS frequencies up to 126 kHz

We report linewidth and proton T₁, T_1ρ and T₂' relaxation data of the model protein ubiquitin acquired at MAS frequencies up to 126 kHz. We find a predominantly linear improvement in linewidths and coherence decay times of protons with increasing spinning frequency in the range from 93 to 126 kHz. We further attempt to gain insight into the different contributions to the linewidth at fast MAS using site-specific analysis of proton relaxation parameters and present bulk relaxation times as a function of the MAS frequency. For microcrystalline fully-protonated ubiquitin, inhomogeneous contributions are only a minor part of the proton linewidth, and at 126 kHz MAS coherent effects are still dominating. We furthermore present site-specific proton relaxation rate constants during a spinlock at 126 kHz MAS, as well as MAS-dependent bulk T_1ρ (¹H^N).

Large-scale ab initio simulations of MAS DNP enhancements using a Monte Carlo optimization strategy

Magic-angle-spinning (MAS) dynamic nuclear polarization (DNP) has recently emerged as a powerful technology enabling otherwise unrealistic solid-state NMR experiments. The simulation of DNP processes which might, for example, aid in refining the experimental conditions or the design of better performing polarizing agents, is, however, plagued with significant challenges, often limiting the system size to only 3 spins. Here, we present the first approach to fully ab initio large-scale simulations of MAS DNP enhancements. The Landau-Zener equation is used to treat all interactions concerning electron spins, and the low-order correlations in the Liouville space method is used to accurately treat the spin diffusion, as well as its MAS speed dependence. As the propagator cannot be stored, a Monte Carlo optimization method is used to determine the steady-state enhancement factors. This new software is employed to investigate the MAS speed dependence of the enhancement factors in large spin systems where spin diffusion is of importance, as well as to investigate the impacts of solvent and polarizing agent deuteration on the performance of MAS DNP.

Preparation of fibril nuclei of beta-amyloid peptides in reverse micelles

Protofibrils of beta-amyloid peptides formed by fibril nuclei incubated in reverse micelles.