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Nuclear magnetic relaxation is widely used to probe protein dynamics. For decades, most analyses of relaxation in proteins have relied successfully on the model-free approach, forgoing mechanistic descriptions of motion. Model-free types of correlation functions cannot describe a large carbon-13 relaxation dataset in protein side chains. Here, we use molecular dynamics simulations to design explicit models of motion and solve Fokker-Planck diffusion equations. These models of motion provide better agreement with relaxation data, mechanistic insight, and a direct link to configuration entropy.

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Dipolar or quadrupolar echoes allow one to observe undistorted powder patterns, in contrast to simple Fourier transformations of free induction decays (FIDs). In this work, the buildup of proton polarization due to dynamic nuclear polarization (DNP) is monitored by observing echoes rather than FIDs. When the microwave irradiation is interrupted during the buildup of DNP, the electrons relax back to their Boltzmann distribution at high fields (B0 = 6.7 T) and low temperatures 1.2 < Tsample < 4.0 K, so that dipolar flip-flop-flip terms involving two electrons and one proton become largely ineffective as a mechanism of proton decoherence. This leads to a prolongation of the nuclear coherence lifetime T2'(1H). The increase in T2'(1H) leads to transient surges of the amplitudes of spin echoes. Conversely, transient slumps of spin echoes are observed when the microwave irradiation is switched back on, due to a shortening of nuclear coherence lifetimes.

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The 17O resonances of zirconium-oxo clusters that can be found in porous Zr carboxylate metal-organic frameworks (MOFs) have been investigated by magic-angle spinning (MAS) NMR spectroscopy enhanced by dynamic nuclear polarization (DNP). High-resolution 17O spectra at 0.037% natural abundance could be obtained in 48 hours, thanks to DNP enhancement of the 1H polarization by factors ε(1H) = Swith/Swithout = 28, followed by 1H → 17O cross-polarization, allowing a saving in experimental time by a factor of ca. 800. The distinct 17O sites from the oxo-clusters can be resolved at 18.8 T. Their assignment is supported by density functional theory (DFT) calculations of chemical shifts and quadrupolar parameters. Protonation of 17O sites seems to be leading to large characteristic shifts. Hence, natural abundance 17O NMR spectra of diamagnetic MOFs can thus be used to probe and characterize the local environment of different 17O sites on an atomic scale.

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Dynamic nuclear polarization of samples at low temperatures, typically between 1.2 and 4.2 K, allows one to achieve spin temperatures of as low as 2 mK so that for many nuclear isotopes the high-temperature approximation is violated for the nuclear Zeeman interaction. This leads to characteristic asymmetries in powder spectra. We show that the line shapes due to the quadrupolar couplings of deuterium spins present in virtually all solvents used for such experiments (DNP juice) allow the quick yet accurate determination of the deuterium spin temperature or, equivalently, the deuterium polarization. The observation of quadrupolar echoes excited by small flip-angle pulses allows one to monitor the build-up and decay of the positive or negative deuterium polarization.

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The isotopic enrichment of nucleic acids with nitrogen-15 is often carried out by solid-phase synthesis of oligonucleotides using phosphoramidite precursors that are synthetically demanding and expensive. These synthetic challenges, combined with the overlap of chemical shifts, explain the lag of nitrogen-15 NMR studies of nucleic acids behind those of proteins. For the structural characterization of DNA and RNA-related systems, new NMR methods that exploit the naturally occurring 99.9 % abundant nitrogen-14 isotope are therefore highly desirable. In this study, we have investigated nitrogen-14 spectra of self-assembled quartets based on the nucleobase guanine in the solid state by means of magic-angle spinning NMR spectroscopy. The network of dipolar proton-nitrogen couplings between neighboring stacked purine units is probed by 2D spectra based on 1 H→14 N→1 H double cross-polarization. Interplane dipolar contacts are identified between the stacked G quartets. The assignment is supported by density functional theory (DFT) calculations of the anisotropic chemical shifts and quadrupolar parameters. The experimental spectra are fully consistent with internuclear distances obtained in silico. Averaging of chemical shifts due to internal motions can be interpreted by semiempirical calculations. This method can easily be extended to synthetic G quartets based on nucleobase or nucleoside analogs and potentially to oligonucleotides.

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The longitudinal spin-lattice relaxation properties of water molecules trapped in a static powdered polycrystalline sample of barium chlorate monohydrate are investigated by means of solid-state 1H NMR spectroscopy. Different portions of the inhomogeneous Pake pattern that are associated with crystallites at different orientations with respect to the external magnetic field show either a mono- or a biexponential recovery. At high field (9.4 T), the chemical shift anisotropy is the main interaction that is responsible for the inhomogeneity of the relaxation rates. A theoretical description of rapid two-site hopping about the H-O-H bisector in the framework of Liouville space agrees very well with the experimental evidence. Numerical simulations predict a distribution of monoexponential time constants associated with individual single-crystal orientations. Overlapping signals give rise to biexponential recovery. This is confirmed experimentally by 1H NMR spectra of static single crystals.

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Water molecules trapped in crystals of barium chlorate monohydrate have been investigated by magic-angle spinning (MAS) proton NMR spectroscopy in the temperature range 110-300 K. At high temperatures, a single spinning sideband pattern is observed. Below 150 K, however, two interleaved spinning sideband manifolds appear, with distinct centerbands that do not coincide with the average isotropic chemical shift seen at high temperatures. This hitherto unknown "cross-term splitting" results from the interplay of the homonuclear dipole-dipole coupling and two anisotropic proton shielding tensors that have identical principal components but nonequivalent orientations. The resulting cross terms cannot be averaged out by rotation about the magic angle. The analysis of the exchange-induced broadening, coalescence, and narrowing of the cross-term splitting in MAS spectra allows one to estimate the rate of exchange of the two protons between 140 and 190 K. The experimental data is compared with 2H and 1H NMR studies of the same sample reported in the literature. Density functional theory methods are utilized to estimate the thermal activation energy for a 2-fold hopping process of proton exchange about the H-O-H bisector. The Bell-Limbach model allows one to take into account contributions due to incoherent quantum tunneling in the low-temperature regime.

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Nitrogen-14 NMR spectra at fast magic-angle spinning rates can be acquired indirectly by means of two-dimensional techniques based on double cross polarization transfer 1H → 14N →1H. Experimental evidence is given for polycrystalline samples of glycine, l-histidine, and the dipeptide Ala-Gly. Either one-bond or long-range correlations can be favored by choosing the length of the cross polarization contact pulses. Longer contact pulses allow the detection of unprotonated nitrogen sites. In contrast to earlier methods that exploited second-order quadrupolar/dipolar cross-terms, cross polarization operates in the manner of the method of Hartmann and Hahn, even for 14N quadrupolar couplings up to 4 MHz. Simulations explain why amorphous samples tend to give rise to featureless spectra because the 14N quadrupolar interactions may vary dramatically with the lattice environment. The experiments are straightforward to set up and are shown to be effective for different nitrogen environments and robust with respect to the rf-field strengths and to the 14N carrier frequency during cross polarization. The efficiency of indirect detection of 14N nuclei by double cross polarization is shown to be similar to that of isotopically enriched 13C nuclei.

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The columnar self-assembly resulting from units of N,N',N''-trihexylbenzene-1,3,5-tricarboxamide is investigated in solution and the solid state by means of NMR spectroscopy. A parallel computational study utilizing both semiempirical and DFT methods allows comparison between experimental results and calculated data for self-assembled and non-assembled structural hypotheses. The hybrid functional B3LYP is compared with the B3LYP-D and B97D functionals to assess contributions due to dispersion interactions. Interatomic distances are studied utilizing ROE experiments on proton spins in solution. Isotropic shifts as measured experimentally are shown to offer a method to assess the self-assemblies 'on-the-fly'. The anisotropic part of the shift interaction for carbon nuclei is probed in the solid state with specific magic-angle spinning experiments. The sensitivity of the NMR parameters for various carbon environments with respect to the orientation of the substituents and packing effects is investigated computationally. We show that all the utilized experimental techniques, in both solution and the solid state, and in combination with DFT calculations, are capable of discerning between assembled and non-assembled systems and offer a robust set of independent tools to highlight atomic details in self-organized structures.

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Complex overlapping multiplets due to scalar couplings (n)J((13)C, (13)C) in fully (13)C-enriched molecules can be simplified by polychromatic irradiation of selected spins. The signal intensities of the remaining non-irradiated signals are proportional to the concentrations, as shown in this work for the anomeric (13)C signals of the α- and ß-conformers of glucose. Homonuclear decoupling can therefore be useful for quantitative NMR studies. The resulting decoupled lineshapes show residual fine structures that have been investigated by means of numerical simulations. Simulations also show that homonuclear decoupling schemes remain effective despite inhomogeneous static fields that tend to hamper in cellulo and in vivo studies. Homonuclear decoupling schemes can be combined with dissolution DNP to obtain signal enhancements of more than four orders of magnitude. Polychromatic irradiation of selected spins does not cause significant losses of hyperpolarization of the remaining non-irradiated spins.

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The hydrogen-bonded arene ruthenium metalla-rectangle, [(p-cymene)2Ru2(OO∩OO)(UPy)2]2(4+), obtained from 1-(4-oxo-6-undecyl-1,4-dihydropyrimidin-2-yl)-3-(pyridin-4-ylmethyl)urea (UPy) and the dinuclear arene ruthenium clip (p-cymene)2Ru2(OO∩OO)Cl2 (OO∩OO = 2,5-dioxido-1,4-benzoquinonato), is investigated by means of solution-phase NMR spectroscopy. Rotating frame nuclear Overhauser effect measurements are used to probe the H-bond network that drives the UPy self-assembly as well as the full rectangular supramolecular system. An effective distance that takes into account both intra- and intermolecular polarization-transfer pathways is utilised for data analysis. The experimental findings are corroborated by DFT calculations of NMR parameters and internuclear distances, thus confirming the formation of a very stable tetranuclear metalla-assembly.

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Para-water is an analogue of para-hydrogen, where the two proton spins are in a quantum state that is antisymmetric under permutation, also known as singlet state. The populations of the nuclear spin states in para-water are believed to have long lifetimes just like other Long-Lived States (LLSs). This hypothesis can be verified by measuring the relaxation of an excess or a deficiency of para-water, also known as a "Triplet-Singlet Imbalance" (TSI), i.e., a difference between the average population of the three triplet states T (that are symmetric under permutation) and the population of the singlet state S. In analogy with our recent findings on ethanol and fumarate, we propose to adapt the procedure for Dissolution Dynamic Nuclear Polarization (D-DNP) to prepare such a TSI in frozen water at very low temperatures in the vicinity of 1.2 K. After rapid heating and dissolution using an aprotic solvent, the TSI should be largely preserved. To assess this hypothesis, we studied the lifetime of water as a molecular entity when diluted in various solvents. In neat liquid H2O, proton exchange rates have been characterized by spin-echo experiments on oxygen-17 in natural abundance, with and without proton decoupling. One-dimensional exchange spectroscopy (EXSY) has been used to study proton exchange rates in H2O, HDO and D2O mixtures diluted in various aprotic solvents. In the case of 50 mM H2O in dioxane-d8, the proton exchange lifetime is about 20 s. After dissolving, one can observe this TSI by monitoring intensities in oxygen-17 spectra of H2O (if necessary using isotopically enriched samples) where the AX2 system comprising a "spy" oxygen A and two protons X2 gives rise to binomial multiplets only if the TSI vanishes. Alternatively, fast chemical addition to a suitable substrate (such as an activated aldehyde or ketone) can provide AX2 systems where a carbon-13 acts as a spy nucleus. Proton signals that relax to equilibrium with two distinct time constants can be considered as a hallmark of a TSI. We optimized several experimental procedures designed to preserve and reveal dilute para-water in bulk.

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Thurber and Tycko recently described a 'bleaching effect' that occurs in magnetic resonance when solid samples that are doped with paramagnetic agents are subjected to rotation by magic angle spinning (MAS) in a static magnetic field with a rotation period comparable to the longitudinal relaxation time T1e of the electron spins. The bleaching effect has been investigated by Thurber and Tycko in samples spinning at temperatures near 20 K in a field of 9.4 T and by Corzilius et al. near 80 K in a field of 4.9 T. In our experience, the bleaching effect is not very severe at temperatures near 100 K in a field of 9.4 T at spinning frequencies up to 12 kHz. Bleaching can partly cancel DNP enhancements that are normally evaluated by comparing signal intensities with and without microwave irradiation. The signal attenuation due to doping and sample rotation is usually not taken into consideration when defining enhancement factors. In this paper, we describe a novel observation that the rotation of glassy samples doped with lanthanides spinning at frequencies as low as 0.1 kHz can lead to a significant reduction of the spin-lattice relaxation times T1((1)H) of protons. This effect, which bears similarities with the so-called spin refrigerators, may contribute to the success of 'brute force polarization' at sample temperatures in the mK range. The acceleration of longitudinal proton relaxation also allows one to improve the signal-to-noise ratio per unit time.

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Fibrous nanosilica (KCC-1) oxynitrides are promising solid-base catalysts. Paradoxically, when their nitrogen content increases, their catalytic activity decreases. This counterintuitive observation is explained here for the first time using (15) N-solid-state NMR spectroscopy enhanced by dynamic nuclear polarization.

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We report applications of dynamic nuclear polarization to enhance proton and vanadium-51 polarization of vanadyl sulfate samples doped with TOTAPOL under magic angle spinning conditions. The electron paramagnetic resonance response stemming from the paramagnetic (51)V species was monitored as a function of pH, which can be adjusted to improve the enhancement of the proton polarization. By means of cross-polarization from the proton bath, (51)V spins could be hyperpolarized. Enhancement factors, build-up times, and longitudinal relaxation times T1((1)H) and T1((51)V) were investigated as a function of pH.

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The ruthenium-containing sensitizing dye N719 grafted on TiO2 nanoparticles was investigated by solid-state NMR. The carbon resonances are assigned by means of (13)C cross-polarized dipolar dephasing experiments. DFT calculations of the carbon magnetic shielding tensors accurately describe the changes in chemical shifts observed upon grafting onto a titania surface via one or two carboxylic functions in the plane defined by the two isothiocyanate groups.

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We show how (27)Al-(13)C proximities in the microporous metal-organic framework MIL-100(Al) can be probed using advanced (27)Al-(13)C NMR methods boosted by Dynamic Nuclear Polarization.

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We analyze the direct excitation of wide one-dimensional spectra of nuclei with spin I=1/2 or 1 in rotating solids submitted to pulse trains in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE), either with one short rotor-synchronized pulse of duration τp in each of K rotor periods (D1(K)) or with N interleaved equally spaced pulses τp in each rotor period, globally also extending over K rotor periods (D(N)(K)). The excitation profile of D(N)(K) scheme is a comb of rf-spikelets with Nν(R)=N/T(R) spacing from the carrier frequency, and a width of each spikelet inversely proportional to the length, KT(R), of D(N)(K) scheme. Since the individual pulse lengths, τp, are typically of a few hundreds of ns, D(N)(K) scheme can readily excite spinning sidebands families covering several MHz, provided the rf carrier frequency is close enough to the resonance frequency of one the spinning sidebands. If the difference of isotropic chemical shifts between distinct chemical sites is less than about 1.35/(KT(R)), D(N)(K) scheme can excite the spinning sidebands families of several sites. For nuclei with I=1/2, if the homogeneous and inhomogeneous decays of coherences during the DANTE sequence are neglected, the K pulses of a D1(K) train have a linearly cumulative effect, so that the total nutation angle is θ(tot)=K2πν1τp, where ν1 is the rf-field amplitude. This allows obtaining nearly ideal 90° pulses for excitation or 180° rotations for inversion and refocusing across wide MAS spectra comprising many spinning sidebands. If one uses interleaved DANTE trains D(N)(K) with N>1, only spinning sidebands separated by intervals of Nν(R) with respect to the carrier frequency are observed as if the effective spinning speed was Nν(R). The other sidebands have vanishing intensities because of the cancellation of the N contributions with opposite signs. However, the intensities of the remaining sidebands obey the same rules as in spectra obtained with νR. With increasing N, the intensities of the non-vanishing sidebands increase, but the total intensity integrated over all sidebands decreases. Furthermore, the NK pulses in a D(N)(K) train do not have a simple cumulative effect and the optimal cumulated flip angle for optimal excitation, θ(tot)(opt)=NK2πν1τp, exceeds 90°. Such D(N)(K) pulse trains allow achieving efficient broadband excitation, but they are not recommended for broadband inversion or refocusing as they cannot provide proper 180° rotations. Since D(N)(K) pulse trains with N>1 are shorter than basic D1(K) sequences, they are useful for broadband excitation in samples with rapid homogeneous or inhomogeneous decay. For nuclei with I=1 (e.g., for (14)N), the response to basic D1(K) pulse train is moreover affected by inhomogeneous decay due to 2nd-order quadrupole interactions, since these are not of rank 2 and therefore cannot be eliminated by spinning about the magic angle. For large quadrupole interactions, the signal decay produced by second-order quadrupole interaction can be minimized by (i) reducing the length of D(N)(K) pulse trains using N>1, (ii) fast spinning, (iii) large rf-field, and (iv) using high magnetic fields to reduce the 2nd-order quadrupole interaction.

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The impact of Nuclear Magnetic Resonance (NMR) on studies of large macromolecular complexes hinges on improvements in sensitivity and resolution. Dynamic nuclear polarization (DNP) in the solid state can offer improved sensitivity, provided sample preparation is optimized to preserve spectral resolution. For a few nanomoles of intact ribosomes and an 800 kDa ribosomal complex we demonstrate that the combination of DNP and magic-angle spinning NMR (MAS-NMR) allows one to overcome current sensitivity limitations so that homo- and heteronuclear (13)C and (15)N NMR correlation spectra can be recorded. Ribosome particles, directly pelleted and frozen into an NMR rotor, yield DNP signal enhancements on the order of ~25-fold and spectra that exhibit narrow linewidths, suitable for obtaining site-specific information. We anticipate that the same approach is applicable to other high molecular weight complexes.

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We systematically studied the enhancement factor (per scan) and the sensitivity enhancement (per unit time) in (13)C and (29)Si cross-polarization magic angle spinning (CP-MAS) NMR boosted by dynamic nuclear polarization (DNP) of functionalized mesoporous silica nanoparticles (MSNs). Specifically, we separated contributions due to: (i) microwave irradiation, (ii) quenching by paramagnetic effects, (iii) the presence of frozen solvent, (iv) the temperature, as well as changes in (v) relaxation and (vi) cross-polarization behaviour. No line-broadening effects were observed for MSNs when lowering the temperature from 300 to 100 K. Notwithstanding a significant signal reduction due to quenching by TOTAPOL radicals, DNP-CP-MAS at 100 K provided global sensitivity enhancements of 23 and 45 for (13)C and (29)Si, respectively, relative to standard CP-MAS measurements at room temperature. The effects of DNP were also ascertained by comparing with state-of-the-art two-dimensional heteronuclear (1)H{(13)C} and (29)Si{(1)H} correlation spectra, using, respectively, indirect detection or Carr-Purcell-Meiboom-Gill (CPMG) refocusing to boost signal acquisition. This study highlights opportunities for further improvements through the development of high-field DNP, better polarizing agents, and improved capabilities for low-temperature MAS.