13C- and 1H-NMR Relaxation Investigation of a Polyciclic Nitrogen Compound: 3,3-Dimethyl-1,5-diphenyl-9-hydroxy-bispidinium Iodide

The rigid polycyclic nitrogen compound was considered as a test for the reliability of internuclear distances calculated by ¹H-NMR spin-lattice relaxation rates. The ‘isotropic’ motional correlation time was calculated from ¹³C relaxation rates (τ_C = 0.11 ns at 298 K). Dipolar cross-relaxation rates were calculated by measuring non-, mono- and double-selective proton spin-lattice relaxation rates. All the experimental relaxation rates were thoroughly accounted for by dipolar pairwise interactions. Only at high temperatures a certain contribution from the spin rotational mechanism was apparent.     

Direct Determination of Motional Correlation Times by 1D MAS and 2D Exchange NMR Techniques

One- and two-dimensional static and magic-angle spinning (MAS) exchange NMR experiments for quantifying slow (τ_c> 1 ms) molecular reorientation dynamics are analyzed, emphasizing the extent to which motional correlation times can be extracteddirectlyfrom the experimental data. The static two-dimensional (2D) exchange NMR experiment provides geometric information, as well as exchange time scales via straightforward and model-free application of Legendre-type orientational autocorrelation functions, particularly for axially symmetric interaction tensors, as often encountered in solid-state²H and¹³C NMR. Under conditions of MAS, increased sensitivity yields higher signal-to-noise spectra, with concomitant improvement in the precision and speed of correlation time measurements, although at the expense of reduced angular (geometric) resolution. For random jump motions, one-dimensional (1D)exchange-inducedsidebands (EIS)¹³C NMR and the recently developed ODESSA and time-reverse ODESSA experiments complement the static and MAS two-dimensional exchange NMR experiments by providing faster means of obtaining motional correlation times. For each of these experiments, the correlation time of a dynamic process may be obtained from a simple exponential fit to the integrated peak intensities measured as a function of mixing time. This is demonstrated on polycrystalline dimethylsulfone, where the reorientation rates from EIS, ODESSA, time-reverse ODESSA, and 2D exchange are shown to be equivalent and consistent with literature values. In the analysis, the advantages and limitations of the different methods are compared and discussed.     

Oxygen ion dynamics in yttria-stabilized zirconia as evaluated by solid-state 17O NMR spectroscopy

Solid-state ¹⁷O NMR measurements between room temperature and 973 K were performed for the first time on ¹⁷O-enriched yttria-stabilized zirconia samples. Spin–lattice relaxation is found to exhibit a strong temperature dependence which can be traced back to motional displacements of the oxygen ions and which is almost unaffected by the actual sample constitution. Analysis of the spin–lattice relaxation data provides the motional correlation times. The derived activation energies are relatively low with values of about 30 kJ/mol. In addition, large temperature effects are observed for the ¹⁷O NMR line widths, and thus for spin–spin relaxation, which are again attributed to the oxygen ion mobility. In this case, the underlying oxygen motions, however, occur on a length-scale which is different from that probed by spin–lattice relaxation.     

Fluorine dynamics in BaF2 crystal lattice as an example of complex motion in a simple system

Fluorine relaxation profiles for a BaF₂ single crystal collected at several temperatures have been analyzed in terms of essentially different motional models: free rotational and free translational diffusion. The analysis has been performed to critically review the sensitivity of field dependent relaxation studies to mechanisms of molecular motions. The tested motional models do not realistically describe the fluorine dynamics within the crystal lattice. They have been chosen to attempt to answer quite fundamental questions regarding the feasibility of the field dependent nuclear spin relaxation studies to provide unique information on dynamic processes: 1. Is it possible to get information about the motional mechanisms by analyzing relaxation profiles collected in a broad frequency range? 2. To what extent is it possible to reasonably reproduce relaxation profiles in terms of unrealistic motional models?It has been concluded from the analysis that the rotational model leading to a single exponential correlation function explains the experimental data much better than the translational one. Validity regimes of the second order perturbation theory have been discussed in the context of the investigated system and the applied models.     

Applications of 95Mo NMR Spectroscopy. X1. 95Mo 97Mo,and 17O relaxation times,quadrupole coupling constants,and the molybdenum relaxation mechanism in Mo(CO)6

Spin-lattice relaxation times (T₁'s) of ⁹⁵Mo ⁹⁷Mo, ¹⁷O, and ¹³C for Mo(CO)₆ in CDCl₃ are reported. The rotational correlation time of the molecule is obtained from the chemical-shift anisotropy relaxation of ¹³C. Quadrupole coupling constants are calculated for ⁹⁵Mo ⁹⁷Mo, and ¹⁷O. The results indicate that ⁹⁵Mo and ⁹⁷Mo, relaxation is entirely quadrupolar and is caused by rotational reorientation of a permanent quadrupole coupling constant rather than from solvent molecule collisions and vibrationally induced momentary electric field gradients.     

A new approach to visualizing spectral density functions and deriving motional correlation time distributions: applications to an alpha-helix-forming peptide and to a well-folded protein

A new approach to visualizing spectral densities and analyzing NMR relaxation data has been developed. By plotting the spectral density function, J(omega), as F(omega)=2 omega J(omega) on the log-log scale, the distribution of motional correlation times can be easily visualized. F(omega) is calculated from experimental data using a multi-Lorentzian expansion that is insensitive to the number of Lorentzians used and allows contributions from overall tumbling and internal motions to be separated without explicitly determining values for correlation times and their weighting coefficients. To demonstrate the approach, (15)N and (13)C NMR relaxation data have been analyzed for backbone NH and C(alpha)H groups in an alpha-helix-forming peptide 17mer and in a well-folded 138-residue protein, and the functions F(omega) have been calculated and deconvoluted for contributions from overall tumbling and internal motions. Overall tumbling correlation time distribution maxima yield essentially the same overall correlation times obtained using the Lipari-Szabo model and other standard NMR relaxation data analyses. Internal motional correlational times for NH and C(alpha)H bond motions fall in the range from 100 ps to about 1 ns. Slower overall molecular tumbling leads to better separation of internal motional correlation time distributions from those of overall tumbling. The usefulness of the approach rests in its ability to visualize spectral densities and to define and separate frequency distributions for molecular motions.     

Ion and polymer chain motion in a superionic sodium-poly (ethylene oxide) complex

Magnetic resonance measurements have been performed on the ion conducting complex poly(ethylene oxide)_4.5NaClO. Low temperature²³Na NMR spectra suggest a highly symmetric environment for the Na-ions as evidenced by the absence of quadrupole broadening. Proton spin-lattice relaxation measurements provide an estimate of ~4×10^?10 sec for the polymer chain motional correlation time at T = 69C. Correlation times of tumbling paramagnetic probe molecule have been extracted from EPR spectra of¹⁵N-enriched TANOL-doped complex. Changes in polymer chain mobility above T = 120C are inferred from the results and may be consistent with previous scanning calorimetry measurements.     

13C spin-lattice relaxation in rotationally disordered solids

¹³C spin-lattice relaxation times and ¹⁴N linewidths at selected temperatures in liquid and solid I (plastic) succinonitrile are reported. Effective rotational correlation times are derived from these and the results for solid I are discussed in terms of a model which assumes that the main contributions to the rotational disorder come from gauche?trans isomerization and the jumping of the central C-C bond of the trans species between the 3-fold axes of the b.c.c. lattice. The general applicability of the ¹³C technique is emphasized and the results are compared with those of other experiments reported in the literature.     

Improvement of duty-cycle heating compensation in NMR spin relaxation experiments

To reliably measure NMR relaxation properties of macromolecules is a prerequisite for precise experiments that identify subtle variations in relaxation rates, as required for the determination of rotational diffusion anisotropy, CSA tensor determination, advanced motional modeling or entropy difference estimations. An underlying problem with current NMR relaxation measurement protocols is maintaining constant sample temperature throughout the execution of the relaxation series especially when rapid data acquisition is required. Here, it is proposed to use a combination of a heating compensation and a proton saturation sequence at the beginning of the NMR relaxation pulse scheme. This simple extension allows reproducible, robust and rapid acquisition of NMR spin relaxation data sets. The method is verified with (15)N spin relaxation measurements for human ubiquitin.     

Investigation of H+ motion in the 21-hydrates of 12-tungstophosphoric and 12-molybdophosphoric acids by ac conductivity and pulsed 1H NMR measurements

AC conductivity and ¹H NMR relaxation time measurements are reported for the heteropolyacids H₃PM₁₂O₄₀. 21H₂O (M = W, Mo) over a range of tempereatures.Ambient temperature proton conductivites are ? 1 S m^-1, with conductivity activation energies E ? 40 kJ mol^-1.The NMR results are interpreted in terms of a range of motional processes leading to distributions of translational correlation times. The behaviour is compared to motions in zeolites and of water sorbed by charcoal.     

NMR relaxation in binary aqueous mixtures of acetone and tetrahydrofurane

NMR proton relaxation rates of normal and ¹⁷O-enriched water and deuteron relaxation rates of heavy water were measured in mixtures with acetone and tetrahydrofurane at different compositions. The ¹⁷O-induced proton relaxation rate was extracted and from this the rotational correlation time of water was determined. Using these correlation times the composition-dependence of the deuteron quadrupole coupling constant of water was derived. A strong variation was found for the system acetone-water, whereas little variation was observed for tetrahydrofurane-water.     

NMR proton relaxation and chemical exchange in the system H16 2O/H17 2O-[2H6]dimethylsulphoxide

NMR proton relaxation rates of normal and ¹⁷O enriched water in a mixture of 68 mol% water and 32 mol% [²H₆]dimethylsulphoxide were measured for temperatures between 298 K and 183 K. In the range between 240 K and 204 K the limit of fast proton-proton exchange between H¹⁶ ₂O and H¹⁷ ₂O is not obeyed, and relaxation curves deviate from mono-exponential behaviour. By fitting the relaxation curves to a model of NMR two-phase relaxation the proton-proton exchange rate within the aqueous component could be obtained. With decreasing temperature, proton-proton exchange slows down and a residence time of about 125 ms at 215 K is found, but it becomes faster again for still lower temperatures. From the phase-averaged relaxation rates of water in the ¹⁷O enriched mixtures, the ¹⁷O induced proton relaxation rate was derived as a function of temperature. This yields the rotational correlation times of the water molecule in the mixture and the dipolar spin-lattice coupling parameter. The latter is considerably lower than the one predicted from the geometry of water.     

Solid-State NMR Studies on the Guest Ordering and Dynamics in α,ω-Dibromoalkane/Urea Inclusion Compounds

Solid-state nuclear magnetic resonance (NMR) spectroscopy is utilized to study the molecular behavior of 1,10-dibromodecane and 1,11-dibromoundecane in their urea inclusion compounds. The guest dynamics and conformational order are explored by ¹³C cross polarization magic-angle spinning (CP/MAS) and ¹H MAS NMR spectroscopy which confirm an all-trans conformation of the guest chains. Dynamic ²H NMR experiments are carried out on two guest molecules selectively deuterated at both end groups. A quantitative analysis of the experimental data, obtained from variable-temperature line shape, spin–spin and spin–lattice relaxation measurements, shows that both guest molecules undergo similar motions within the investigated temperature range between 100 and 298 K. The combination of nondegenerate 6-site (or 3-site) rotational jumps and small-angle overall chain wobbling provides an appropriate motional model for the guest motions in these compounds. It is found that the populations of the jump sites exhibit a characteristic temperature dependence, although a discontinuity is missing at the solid–solid phase transition. The same holds for the guest motions which also remain unaffected by the change of the urea lattice structure. Rather, a discontinuity of the guest dynamics at about 30 and 10 degrees above the corresponding solid–solid phase transition is observed for 1,10-dibromodecane and 1,11-dibromoundecane in urea, respectively. Likewise, there is no clear evidence for an odd–even effect due to the change of the guest chain length on the molecular properties of the present inclusion compounds. As a general result, it is concluded that the intermolecular interactions in the present materials are stronger than in n-alkane/urea inclusion compounds. Authors' address: Klaus Müller, Institut für Physikalische Chemie, Universit?t Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany     

1H relaxation and dynamics of triphenylbismuth in deuterated solvents

ABSTRACT

¹H spin–lattice relaxation experiments have been performed for triphenylbismuth dissolved in fully deuterated glycerol and tetrahydrofuran. The experiments have been carried out in a broad frequency range, from 10?kHz to 40?MHz, versus temperature. The data have been analysed in terms of a relaxation model including two relaxation pathways: ¹H-¹H dipole–dipole interactions between intrinsic protons of triphenylbismuth molecule and ¹H-²H dipole–dipole interactions between the solvent and solute molecules. As a result of the analysis, rotational correlation times of triphenylbismuth molecules in the solutions and relative translational diffusion coefficient between the solvent and solute molecules have been determined. Moreover, the role of the intramolecular ¹H-¹H relaxation contribution has been revealed, depending on the motional parameters, as a result of decomposing the overall relaxation dispersion profile into contributions associated with the ¹H-¹H and ¹H-²H relaxation pathways. The possibility of accessing the contribution of the relaxation of the intrinsic protons is important from the perspective of exploiting Quadrupole Relaxation Enhancement effects as possible contrast mechanisms for Magnetic Resonance Imaging.     

Dynamics of the biopolymers in articular cartilage studied by magic angle spinning NMR

To understand the viscoelastic properties of cartilage tissue and for the development of tissue-engineered cartilage, we have studied the physicochemical properties of bovine nasal and pig articular cartilage by¹³C nuclear magnetic resonance (NMR) methods. The major macromolecular components of cartilage can be investigated individually by applying¹³C high-resolution (HR) NMR with scalar decoupling (for the polysaccharide component) and solid-state NMR with dipolar decoupling (for the collagen component). Partially resolved NMR spectra of the cartilage polysaccharides can be obtained by HR¹³C NMR indicating that these polysaccharides are highly mobile. Resonance lines have been assigned to chondroitin sulfate, the most mobile component of cartilage. To characterize time scales of molecular motions, we have measuredT ₁ andT ₂ relaxation times as a function of temperature and analyzed these data by means of a broad distribution of molecular correlation times. Typical correlation times for the large amplitude motions of chondroitin sulfate are of the order of 0.1–10 ns. For the detection and dynamical characterization of the cartilage collagen cross-polarization magic angle spinning (CP MAS) and high-power decoupling are indispensable.¹³C CP MAS spectra of cartilage are dominated by resonances from rigid collagen, while only low-intensity signals from the polysaccharides are observed. The good sensitivity at a magnetic field strength of 17.6 T allows the site-specific investigation of cartilage collagen dynamics by two-dimensional NMR methods. The cartilage collagen is essentially rigid with low-amplitude segmental motions on the fast time scale. Considering the high water content of cartilage and the almost isotropic mobility of the chondroitin sulfate molecules it is remarkable how little this affects the collagen dynamics. The dynamics of cartilage macromolecules is broadly distributed from almost completely rigid to highly mobile, which lends cartilage its mechanical strength and shock-absorbing properties.     

A theoretical perspective on the accuracy of rotational resonance (R 2)-based distance measurements in solid-state NMR

The application of solid-state NMR methodology for bio-molecular structure determination requires the measurement of constraints in the form of ¹³C–¹³C and ¹³C–¹⁵N distances, torsion angles and, in some cases, correlation of the anisotropic interactions. Since the availability of structurally important constraints in the solid state is limited due to lack of sufficient spectral resolution, the accuracy of the measured constraints become vital in studies relating the three-dimensional structure of proteins to its biological functions. Consequently, the theoretical methods employed to quantify the experimental data become important. To accentuate this aspect, we re-examine analytical two-spin models currently employed in the estimation of ¹³C–¹³C distances based on the rotational resonance (R ²) phenomenon. Although the error bars for the estimated distances tend to be in the range 0.5–1.0 Å, R ² experiments are routinely employed in a variety of systems ranging from simple peptides to more complex amyloidogenic proteins. In this article we address this aspect by highlighting the systematic errors introduced by analytical models employing phenomenological damping terms to describe multi-spin effects. Specifically, the spin dynamics in R ² experiments is described using Floquet theory employing two different operator formalisms. The systematic errors introduced by the phenomenological damping terms and their limitations are elucidated in two analytical models and analysed by comparing the results with rigorous numerical simulations.     

Detection of correlated dynamics on multiple timescales by measurement of the differential relaxation of zero- and double-quantum coherences involving sidechain methyl groups in proteins

Multiple effects may lead to significant differences between the relaxation rates of zero-quantum coherences (ZQC) and double-quantum coherences (DQC) generated between a pair of nuclei in solution. These include the interference between the anisotropic chemical shifts of the two nuclei participating in formation of the ZQC or DQC, the individual dipolar interactions of each of the two nuclei with the same proton, and the slow modulation of the isotropic chemical shifts of the two nuclei due to conformational exchange. Motional events that occur on a timescale much faster than the rotational correlation time (ps-ns) influence the first two effects, while the third results from processes that occur on a far slower timescale (mus-ms). An analysis of the differential relaxation of ZQC and DQC is thus informative about dynamics on the fast as well as the slow timescales. We present here an experiment that probes the differential relaxation of ZQC and DQC involving methyl groups in protein sidechains as an extension to our recently proposed experiments for the protein backbone. We have applied the methodology to (15)N, (13)C-labeled ubiquitin and used a detailed analysis of the measured relaxation rates using a simple single-axis diffusion model to probe the motional restriction of the C(next)H(next) bond vector where C(next) is the carbon that is directly bonded to a sidechain methyl carbon (C(methyl)). Comparison of the present results with the motional restriction of the C(next)C(methyl) bond (S(axis)(2)) reveals that the single-axis diffusion model, while valid in the fringes of the protein and for shorter chain amino acids, proves inadequate in the central protein core for long chain, asymmetrically branched amino acids where more complex motional models are necessary, as is the inclusion of the possibility of correlation between multiple motional modes. In addition, the present measurements report on the modulation of isotropic chemical shifts due to motion on the mus-ms timescale. Three Leu residues (8, 50, and 56) are found to display these effects. These residues lie in regions where chemical shift modulation had been detected previously both in the backbone and sidechain regions of ubiquitin.     

Nuclear spin relaxation and magnetic shielding tensors of atoms constituting cyanogen bromide molecule

The temperature dependence of the correlation time describing reorientation kinetics of cyanogen bromide in CDCl₃ solution has been determined on the basis of the linewidths of the ¹⁴N NMR signal. It has been found that the longitudinal spin relaxation of the ¹⁵N nucleus occurs by shielding anisotropy and spin-rotation mechanisms, whereas for the ¹³C nucleus these mechanisms are of lesser importance. In the latter case the scalar relaxation of the second kind due to carbon-bromine coupling is the predominant relaxation mechanism. The parameter values: ¹ J(¹³C—⁷⁹Br) = 349 ± 10 Hz, T ₁ (⁷⁹Br, 303 K) = 2.31 ± 0.22 × 10^?7 s, Δσ(¹⁵N) = 565 ± 16 ppm and Δσ(¹³C) = 276 ± 120 ppm have been determined from the relaxation data analysis. The shielding anisotropy parameters Δσ(¹⁵N) = 580 ± 50 ppm and Δσ(¹³C) = 274 ± 9 ppm have been independently determined using ¹³C and ¹⁵N NMR in liquid crystalline solvent. The experimentally determined shielding tensors for sp-hybridized atoms in the investigated compound and in a series of bromoacetylenes have been compared with the results of quantum mechanical calculations [GIAO, DFT B3LYP/6-311 + +G(2d,p)]. The ‘heavy atom effect’ shielding bromine-bonded carbons is of the order of — 25 ppm and concerns mainly the σ⊥ component.     

Water-filled MCM-41 characterized by double-quantum-filtered2H NMR spectral analysis

The dynamics of water molecules confined in adsorbed layers of siliceous MCM-41 with a pore diameter of 2.8 nm is investigated at 230 K by deuteron nuclear magnetic resonance (NMR) relaxation studies including line shapes of theT ₁ process and double quantum filtered (DQF) spectral analyses.²H DQF NMR is a particularly sensitive tool for the determination of the adsorbate dynamics resulting from residual quadrupolar interaction due to the local order. The amount of monolayer water is determined. The monolayer water is composed of two different water components characterized by water, with isotropic reorientational motions, exchanging with water displaying a solid-like spectrum with 4 kHz edge splitting. One may expect that the latter water is situated on surface sites in MCM-41. The restricted wobbling motion of the D-O bond is used to describe its dynamics which is one order of magnitude slower than the isotropic reorientational motion. The order parameter, the motional correlation time, and the exchange rate thus determined provide useful information on the structure and the adsorptive properties of the mesoporous system.     

Proton NMR relaxation study of the CsHSO4 solid acid system

At 141 °C the solid acid CsHSO₄ is known to undergo transition to a superprotonic phase that is characterized by dramatic (several-order-of-magnitude) increases in hydrogen ion conductivity. Proton NMR spin-spin relaxation time T₂ measurements reported here for CsHSO₄ also reveal substantial increases (factors of 20-30) in the vicinity of the transition temperature. In the temperature range just below the transition (70-136 °C), T₂ increases by a factor of order 10 relative to the rigid-lattice regime, suggesting motional narrowing of the NMR resonance line. In the regime of motional narrowing, the activation energy barrier to diffusion is 0.40 eV, as determined from the present T₂ results. NMR spin-lattice relaxation T₁ measurements also show behavior consistent with transition to a regime of rapid hydrogen motion. In particular, proton T₁'s decrease with temperature (from 80 to 120 °C), and then drop sharply near the transition temperature. Above the transition temperature, T₁ exhibits a minimum in which the correlation time is found to be ∼2 ns.