31P spectral spin diffusion in crystalline solids

Hybrid quantum-classical simulations of magic angle spinning dynamic nuclear polarization in very large spin systems

Solid-state nuclear magnetic resonance can be enhanced using unpaired electron spins with a method known as dynamic nuclear polarization (DNP). Fundamentally, DNP involves ensembles of thousands of spins, a scale that is difficult to match computationally. This scale prevents us from gaining a complete understanding of the spin dynamics and applying simulations to design sample formulations. We recently developed an ab initio model capable of calculating DNP enhancements in systems of up to ∼1000 nuclei; however, this scale is insufficient to accurately simulate the dependence of DNP enhancements on radical concentration or magic angle spinning (MAS) frequency. We build on this work by using ab initio simulations to train a hybrid model that makes use of a rate matrix to treat nuclear spin diffusion. We show that this model can reproduce the MAS rate and concentration dependence of DNP enhancements and build-up time constants. We then apply it to predict the DNP enhancements in core–shell metal-organic-framework nanoparticles and reveal new insights into the composition of the particles’ shells.

Structural Analyses of Alanine Trimer and Tetramer Crystals with Antiparallel and Parallel β-Sheet Structures Using Solid-State 1H Spin-Diffusion 2D Correlation NMR Spectroscopy

Poly-l-alanine (PLA) sequences are key elements of the crystalline domains of spider dragline and wild silkworm silks. In the present work, ¹H spin-diffusion two-dimensional (2D) correlation NMR spectra were observed for selectively deuterated (Ala)₃ and (Ala)₄ crystals to develop the analytical method for the structure of PLA sequences. The build-up curves of the cross peaks for three kinds of ¹H pairs in selectively deuterated (Ala)₃ and (Ala)₄ crystals were observed to obtain spin-diffusion rate constant k _{j, k} from relaxation master equations P _{i, j}(τ_m). The k _{j, k} values subsequently lead to effective interproton distance r _{j, k}^eff (obs) values for individual proton-proton pairs, which include intra- and intermolecular contributions. The r _{j, k}^eff (obs) values were compared to r _{j, k}^eff (calc) values obtained from the experimentally determined atomic coordinates of antiparallel (AP) β-sheet (Ala)₃ and (Ala)₄ and parallel (P) β-sheet of (Ala)₃ and (Ala)₄ crystals. The agreement between the r _{j, k}^eff (obs) and r _{j, k}^eff (calc) values was good for AP β-sheet (Ala)₃ and (Ala)₄ crystals but poor for P β-sheet (Ala)₃ and (Ala)₄ crystals. These deviations were obtained from the interproton distances of the interchain contributions due to different packing arrangements. The packing arrangements of the PLA region are important when considering the relevant structure and the mechanical properties of silks.

Quantitative Analysis of Solid-State Homonuclear Correlation Spectra of Antiparallel β-Sheet Alanine Tetramers

Poly-l-alanine (PLA) sequences are a key element in the structure of the crystalline domains of spider dragline silks, wild silkworm silks, antifreeze proteins, and amyloids. To date, no atomic-level structures of antiparallel (AP)-PLA longer than Ala₄ have been reported using the single-crystal X-ray diffraction analysis. In this work, dipolar-assisted rotational resonance solid-state NMR spectra were observed to determine the effective internuclear distances of ¹³C uniformly labeled alanine tetramer with antiparallel (AP) β-sheet structure whose atomic coordinates are determined from the X-ray crystallographic analysis. Initial build-up rates, R _{j, k}, were obtained from the build-up curves of the cross peaks by considering the internuclear distances arising in the master equation. Subsequently, experimentally obtained effective internuclear distances, r^eff_{j, k}(obs), were compared with the calculated r^eff_{j, k}(calc) values obtained from the X-ray crystallographic data. Fairly good correlation between r^eff_{j, k}(obs) and r^eff_{j, k}(calc) was obtained in the range of 1.0-6.0 Å, with the standard deviation of 0.244 Å, without considering the zero-quantum line-shape functions. It was further noted that the internuclear distances of intermolecular contributions provide details relating to the molecular packing in solid-state samples. Thus, the present data agree well with AP-β-sheet packing but do not agree with P-β-sheet packing.

Packing arrangement of 13C selectively labeled sequence model peptides of Samia cynthia ricini silk fibroin fibers studied by solid-state NMR

Samia cynthia ricini silk fibroin fiber was proposed to take anti-parallel β-sheet structure with staggered arrangement.

Macroscopic nuclear spin diffusion constants of rotating polycrystalline solids from first-principles simulation

A method for quantitatively calculating nuclear spin diffusion constants directly from crystal structures is introduced. This approach uses the first-principles low-order correlations in Liouville space (LCL) method to simulate spin diffusion in a box, starting from atomic geometry and including both magic-angle spinning (MAS) and powder averaging. The LCL simulations are fit to the 3D diffusion equation to extract quantitative nuclear spin diffusion constants. We demonstrate this method for the case of (1)H spin diffusion in ice and L-histidine, obtaining diffusion constants that are consistent with literature values for (1)H spin diffusion in polymers and that follow the expected trends with respect to magic-angle spinning rate and the density of nuclear spins. In addition, we show that this method can be used to model (13)C spin diffusion in diamond and therefore has the potential to provide insight into applications such as the transport of polarization in non-protonated systems.

Fluoride solid electrolytes: investigation of the tysonite-type solid solutions La1−xBaxF3−x (x < 0.15)

La_1−xBa_xF_3−x solid solutions for x < 0.15 were prepared by solid state synthesis in a platinum tube under an nitrogen atmosphere with subsequent quenching for 0.07 ≤ x < 0.15.

A master-equation approach to the description of proton-driven spin diffusion from crystal geometry using simulated zero-quantum lineshapes

Measurements of proton-driven carbon-13 spin diffusion (PDSD) by NMR spectroscopy are a central component of structural analyses of biomolecules in the solid-state. However, the quantitative link between experimental PDSD data and structural information is difficult to make. Here we observe that a master-equation approach can be used to model full PDSD dynamics accurately in polycrystalline (13)C-labelled L-histidine·HCl·H(2)O under magic-angle spinning. In the master-equation approach, PDSD rates and effective dipolar couplings are related by a function of the carbon-carbon zero-quantum lineshapes; we find that numerical simulations of the zero-quantum lineshapes are sufficiently accurate so as to allow the calculation of PDSD rates that are in good agreement with the measured rates, directly from crystal geometry and with no adjustable parameters. Finally, using carbon-carbon internuclear distances we illustrate the potential of the master-equation approach for structural studies. Generalisation of these results to proton-driven carbon-13 spin diffusion in more complex molecular systems is readily envisaged.

Challenges in numerical simulations of solid-state NMR experiments: spin exchange pulse sequences

While simulations are essential for interpretation of solid-state NMR experiments, large spin systems involved in e.g. spin-diffusion experiments and/or dynamic effects like chemical exchange pose great challenges for the numerical simulations, where we typically want to include effects of finite pulses and other external manipulations in the simulation. In this paper, these topics are reviewed and addressed by simple numerical simulations. The numerical simulations comprise a 2-spin simulation of (2)H two-site jumps and a 332-spin simulation of a CHHC experiment for a small protein.

Powder NMR crystallography of thymol

A protocol for the structure determination of powdered solids at natural abundance by NMR is presented and illustrated for the case of the small drug molecule thymol. The procedure uses proton spin-diffusion data from two-dimensional NMR experiments in combination with periodic DFT refinements incorporating (1)H and (13)C NMR chemical shifts. For thymol, the method yields a crystal structure for the powdered sample, which differs by an atomic root-mean-square-deviation (all atoms except methyl group protons) of only 0.07 A from the single crystal X-ray diffraction structure with DFT-optimized proton positions.

Microscopic Description of the Polyamorphic Phases of Triphenyl Phosphite by Means of Multidimensional Solid-State NMR Spectroscopy

The structural properties of a second, apparently amorphous phase (aII) of the molecular glass former triphenyl phosphite were studied by means of multidimensional solid-state NMR spectroscopy and X-ray diffraction. Phase aII was prepared by annealing the supercooled liquid in the temperature range 210 K <or= T(a) <or= 230 K. In addition to 1D (1)H and (31)P spectra and spin-lattice relaxation data, we used (31)P radio-frequency-driven spin-diffusion exchange spectroscopy to analyze the arrangement of neighboring TPP molecules on both a local and intermediate scale. For the first time, our results give a detailed microscopic description of phase aII. For T(a) > 223 K a nano- or microcrystalline material is formed, whereas for T(a) < 223 K phase aII is homogeneous and disordered. Our data strongly suggest that some of the TPP molecules in phase aII tend toward a parallel alignment. The regions, where the molecules preferentially align appear to be spatially separated and consist of only a few molecules. Whereas the mean cubic expansion of an individual region does not change within the experimental error, the percentage of correlated molecules increases with rising T(a). Based on our results, phase aII can consistently be described as a second liquid, where a part of the molecules exhibit structural correlations. The transformation of the supercooled liquid into phase aII is therefore considered as a liquid-liquid phase transition.

One- and two-dimensional 15N exchange CP/MAS NMR studies of the structure and electronic properties of the intermolecular N-H...N hydrogen bond in imidazole crystal

The hydrogen bond of the type N-H...N in imidazole crystal has been studied by one and two-dimensional 15N exchange CP/MAS NMR measurements as well as the powder NMR spectrum. The chemical shift anisotropies for -N= and -N< were determined from the powder 1D spectrum. In 2D exchange CP/MAS NMR spectrum, the cross peaks between the 15N main resonance peaks for -N= and -N< were observed, implying that magnetization exchange between -N= and -N< takes place. The 1D exchange CP/MAS NMR measurements determined the exchange rate of magnetization at 289 K to be 1.3 and 1.5 s(-1) for -N= and -N<, respectively. The proton-driven spin-diffusion model interprets the experimental values, and the exchange rate depends strongly on the RF power of the proton decoupling field, suggesting that the magnetization transfer between -N= and -N< takes place by the 1H-driven spin-diffusion mechanism.

High-order spin diffusion mechanisms in (19)F 2-D NMR of oxyfluorides

Negative cross-peaks have been observed in the (19)F 2-D magnetization-exchange MAS NMR spectra of Ba(2)MoO(3)F(4) under fast-spinning conditions. The polarization transfer dynamics are studied as a function of the spinning frequency and the frequency separation of the resonances. The results are consistent with a novel mechanism, in which four spins simultaneously exchange Zeeman magnetization with each other, in an energy-conserving process.

Radiofrequency-Driven and Slow-Magic-Angle-Sample-Spinning Polarization-Transfer Techniques: A Comparative Study

The rate constant of radiofrequency-driven (RF-driven) polarization transfer and that of polarization transfer under slow-magic-angle sample spinning (S-MAS) are compared using a model system, polycrystalline alpha-alpha'-13C2-phthalic acid. While the rate constant under RF irradiation in static samples strongly depends on the orientation of the internuclear vector, the rate constant under S-MAS is hardly sensitive to that orientation and, thus, depends almost exclusively on the internuclear distance. Consequently, polarization-transfer rate constants obtained under S-MAS can be interpreted more simply when used to study local order in polycrystalline or amorphous solids. Copyright 1998 Academic Press.