Imaging the long-range dipolar field in structured liquid state samples

We describe imaging experiments in which the pattern of the dipolar field generated by spatially modulated nuclear magnetization is directly visualized in simply structured phantoms. Two types of experiment have been carried out at 11.7 T using (1)H NMR signals. In the first, the field from a single spin species is imaged via its own NMR signal. In the second, the NMR signal from one spin species is used to image the field generated by a second species. The field patterns measured in these experiments correspond well with those calculated using simple theoretical expressions for the dipolar field. The results also directly demonstrate the spatial sensitivity of the signal generated using dipolar field effects, indicating that the range of the field depends upon the inverse of the spatial frequency with which the magnetization is modulated.     

Numerical simulation of one- and two-dimensional ESEEM experiments

Numerical simulation has become an indispensable tool for the interpretation of pulse EPR experiments. In this work it is shown how automatic orientation selection, grouping of operator factors, and direct selection and elimination of coherences can be used to improve the efficiency of time-domain simulations of one- and two-dimensional electron spin echo envelope modulation (ESEEM) spectra. The program allows for the computation of magnetic interactions of any symmetry and can be used to simulate spin systems with an arbitrary number of nuclei with any spin quantum number. Experimental restrictions due to finite microwave pulse lengths are addressed and the enhancement of forbidden coherences by microwave pulse matching is illustrated. A comparison of simulated and experimental HYSCORE (hyperfine sublevel correlation) spectra of ordered and disordered systems with varying complexity shows good qualitative agreement.     

Sequential HNCACB and CBCANH protein NMR pulse sequences

The pulse sequences HNCACB and CBCANH correlating side chain C(beta) resonances with amide resonances in the protein backbone do not distinguish between inter- and intraresidue correlations. The new pulse sequences sequential HNCACB and sequential CBCANH make this distinction by suppressing coherence transfer between 13C(alpha) and 15N via the one-bond J(NC(alpha)) coupling so that only the sequential correlations are observed in the spectrum. The experimental results of applying sequential HNCACB in a clean-TROSY-adapted implementation to the protein Chymotrypsin Inhibitor 2 at 800 MHz are presented.     

Achievement of a 920-MHz high resolution NMR

We have developed a 920-MHz NMR system and performed the proton NMR measurement of H(2)O and ethylbenzene using the superconducting magnet operating at 21.6 T (920 MHz for proton), which is the highest field produced by a superconducting NMR magnet in the persistent mode. From the NMR measurements, it is verified that both homogeneity and stability of the magnet have a specification sufficient for a high resolution NMR.     

Millimeter-Wave Spectroscopy, High-Resolution Infrared Spectrum, ab Initio Calculations, and Molecular Geometry of FPS

The transient thiophosphenous fluoride FPS was produced by pyrolysis of 2.5% F₂PSPF₂ in Ar at 1300–1800°C. High-resolution (≥0.004 cm⁻¹) Fourier transform infrared spectra of the a-type ν₁ and b-type ν₂ bands, centered respectively at 803.249 and 726.268 cm⁻¹, were measured and fitted to rotational and quartic centrifugal distortion parameters. The millimeter-wave spectrum, essentially b-type, was measured between 300 and 370 GHz in the ground state and in the ν₃ excited state for FP³²S and in the ground state for FP³⁴S. The frequencies were fitted to a Watson-type A-reduced Hamiltonian up to sextic distortion terms. High level ab initio calculations with large basis sets were performed on FPS and supported the first identification of its infrared and millimeter wave spectra. The calculated anharmonic force field provided precise ab initio rovibrational α constants which were combined with the experimental molecular parameters to determine an accurate equilibrium structure of the molecule: r_e(PS)=188.86 pm, r_e(PF)=158.70 pm, θ(FPS)=109.28°. The collision-controlled 1/e lifetime measured in a 10-Pa (1 : 20) F₂PSPF₂/Ar mixture was 2 s, more than two orders of magnitude larger than that of FPO under the same experimental conditions.     

Separation of intra- and extramyocellular lipid signals in proton MR spectra by determination of their magnetic field distribution

In skeletal musculature intramyocellular (IMCL) and extramyocellular lipids (EMCL) are stored in compartments of different geometry and experience different magnetic field strengths due to geometrical susceptibility effects. The effect is strong enough to---at least partly---separate IMCL and EMCL contributions in (1)H MR spectroscopy, despite IMCL and EMCL consisting of the same substances. The assessment of intramyocellular lipid stores in skeletal musculature by (1)H MR spectroscopy plays an important role for studying physiological and pathological aspects of lipid metabolism. Therefore, a method using mathematical tools of Fourier analysis is developed to obtain the magnetic field distribution (MFD) from the measured spectra by deconvolution. A reference lipid spectrum is required which was recorded in tibial yellow bone marrow. It is shown that the separation of IMCL contributions can be performed more precisely---compared to other methods---based on the MFD. Examples of deconvolution in model systems elucidate the principle. Applications of the proposed approach on in vivo examinations in m. soleus and m. tibialis anterior are presented. Fitting the IMCL part of the MFD by a Gaussian lineshape with a linewidth kept fixed with respect to the linewidth of creatine and with the assumption of a smooth but not necessarily symmetrical shape for the EMCL part, the only free fit parameter, the amplitude of the IMCL part, is definite and subtraction leads to the EMCL part in the MFD. This procedure is especially justified for the soleus muscle showing a severely asymmetrical distribution which might lead to a marked overestimation of IMCL using common line fitting procedures.     

Development of NMR instrumentation to achieve excitation of large bandwidths in high-resolution spectra at high field

A prototype 2.5-mm (1)H high-resolution probe for an 18.8-T (800 MHz) nuclear magnetic resonance spectrometer has been designed, together with a dedicated amplifier capable of delivering up to 1 kW of power. This probe permits a 90 degrees pulse length of 2 mus to be achieved at 300 W, corresponding to an excitation bandwidth of +/-125 kHz. Probe performances were tested on samples commonly used for this purpose as well as on protein and paramagnetic model compound samples. It is shown that this probe is useful for a wide range of applications at high magnetic field, especially in the study of systems characterized by very broad and far-shifted resonances and in experiments that require high-power radiofrequency irradiation.     

PELDOR at S- and X-band frequencies and the separation of exchange coupling from dipolar coupling

A pulsed electron double resonance (PELDOR) setup working at S-band frequencies is introduced and its performance compared with an X-band setup. Furthermore, to verify experimentally that it is possible to disentangle the dipolar coupling nu(Dip) from the exchange coupling J by PELDOR we synthesized and investigated four bisnitroxide radicals. They exhibit in pairs the same distances r(AB) between the nitroxide moieties but only one of each pair possesses a non-zero J. The experimental values for r(AB) match the ones from molecular modeling very well for the molecules without exchange coupling. For one bisnitroxide it was possible to separate nu(Dip) from J and to ascertain the magnitude and sign of J to +11 MHz (antiferromagnetic spin-spin coupling).     

Divergence- and Curl-Preserving Prolongation and Restriction Formulas

We present new second-order prolongation and restriction formulas which preserve the divergence and, in some cases, the curl of a discretized vector field. The formulas are suitable for adaptive and hierarchical mesh algorithms with a factor-of-2 linear resolution change. We examine both staggered and collocated discretizations for the vector field on two- and three-dimensional Cartesian grids. The new formulas can be used in combination with numerical schemes that require a divergence-free solution in some discrete sense, such as the constrained transport schemes of computational magnetohydrodynamics. We also obtain divergence-preserving interpolation functions which may be used for streamline or field line tracing.     

The Lattice Solid Model to Simulate the Physics of Rocks and Earthquakes: Incorporation of Friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity–Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick–slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics.     

IR Spectrum of C8H2: Integrated Band Intensities and Some Observational Implications

Polyynes are of astrophysical interest since they appear to be involved in organic chemistry in very different mediums. In Titan's atmosphere, the lightest polyyne, C₄H₂, was detected by Voyager. Recently C₄H₂ and C₆H₂ have been discovered in a protoplanetary nebula, suggesting polyynes as a possible chemical pathway to PAH (polycyclic aromatic hydrocarbons). Moreover, several experimental simulations and modeling imply their production from the photochemistry of methane and their involvement in the formation of organic aerosols. After the study of C₄H₂ and C₆H₂ spectra in the UV and IR wavelength range, we report here the first spectrum of gaseous C₈H₂ in the range 400–4000 cm⁻¹ at room temperature and low resolution. The task was hardly achieved because of the high instability of this molecule with temperature and pressure. To avoid exothermic polymerization, the compound as mixed with a solvent. We have performed a separate spectroscopic study of the solvent to determine C₈H₂ partial pressure within the mixture. This allowed us to calculate C₈H₂ integrated band intensities. In the studied wavelength range, C₈H₂ presents three main bands similar to those of C₆H₂ in terms of vibrational type, position, and relative intensity. To study the possible identification of these polyynes by spatial observatories (Cassini–Huygens, ISO), we have also measured the C₆H₂ and C₈H₂ infrared spectra in the range 400–1500 cm⁻¹ at 0.35 cm⁻¹ resolution.     

Coherent Raman and Infrared Studies of Sulfur Trioxide

High-resolution (0.001 cm⁻¹) coherent anti-Stokes Raman scattering (CARS) was used to observe the Q-branch structure of the IR-inactive ν₁ symmetric stretching mode of ³²S¹⁶O₃ and its various ¹⁸O isotopomers. The ν₁ spectrum of ³²S¹⁶O₃ reveals two intense Q-branches in the region 1065–1067 cm⁻¹, with surprisingly complex vibrational–rotational structure not resolved in earlier studies. Efforts to simulate this with a simple Fermi-resonance model involving ν₁ and 2ν₄ states do not reproduce the spectral detail, nor do they yield reasonable spectroscopic parameters. A more subtle combination of Fermi resonance and indirect Coriolis interactions with nearby states, 2ν₄(1=0, ±2), ν₂+ν₄(1=±1), 2ν₂(1=0), is suspected and a determination of the location of these coupled states by high-resolution infrared measurements is under way. At medium resolution (0.125 cm⁻¹), the infrared spectra reveal Q-branch features from which approximate band origins are estimated for the ν₂, ν₃, and ν₄ fundamental modes of ³²S¹⁸O₃, ³²S¹⁸O₂¹⁶O, and ³²S¹⁸O¹⁶O₂. These and literature data for ³²S¹⁶O₃ are used to calculate force constants for SO₃ and a comparison is made with similar values for SO₂ and SO. The frequencies and force constants are in excellent agreement with those obtained by Martin in a recent ab initio calculation.     

A General Deterministic Treatment of Derivatives in Particle Methods

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using “one-sided” integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.     

H Spectroscopy without Solvent Suppression: Characterization of Signal Modulations at Short Echo Times

While most proton (¹H) spectra acquired in vivo utilize selective suppression of the solvent signal for more sensitive detection of signals from the dilute metabolites, recent reports have demonstrated the feasibility and advantages of collecting in vivo data without solvent attenuation. When these acquisitions are performed at short echo times, the presence of frequency modulations of the water resonance may become an obstacle to the identification and quantitation of metabolite resonances. The present report addresses the characteristics, origin, and elimination of these sidebands. Sideband amplitudes were measured as a function of delay time between gradient pulse and data collection, as a function of gradient pulse amplitude, and as a function of spatial location of the sample for each of the three orthogonal gradient sets. Acoustic acquisitions were performed to demonstrate the correlation between mechanical vibration resonances and the frequencies of MR sidebands. A mathematical framework is developed and compared with the experimental results. This derivation is based on the theory that these frequency modulations are induced by magnetic field fluctuations generated by the transient oscillations of gradient coils.     

Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method

In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non-slip wall is assumed to be at the boundary nodes. Moreover, for a specific inclination angle of 45 degrees, the scheme is found to be second-order accurate when the location of the non-slip velocity is fitted halfway between the last fluid nodes and the first solid nodes. The error as a function of the relaxation parameter is in that case qualitatively similar to that of flat walls. Next, a comparison of simulations of fluid flow by means of pressure boundaries and by means of body force is presented. A good agreement between these two boundary conditions has been found in the creeping-flow regime. For higher Reynolds numbers differences have been found that are probably caused by problems associated with the pressure boundaries. Furthermore, two widely used 3D models, namelyD₃Q₁₅andD₃Q₁₉, are analysed. It is shown that theD₃Q₁₅model may induce artificial checkerboard invariants due to the connectivity of the lattice. Finally, a new iterative method, which significantly reduces the saturation time, is presented and validated on different benchmark problems.     

Relaxation Behavior of Laser-Polarized Xe Gas: Size Dependency and Wall Effect of the T1 Relaxation Time in Glass and Gelatin Bulbs

Size dependency of the relaxation time T₁ was measured for laser-polarized ¹²⁹Xe gas encapsulated in different sized cavities made by glass bulbs or gelatin capsules. The use of laser-polarized gas enhances the sensitivity a great deal, making it possible to measure the longer ¹²⁹Xe relaxation time in quite a short time. The size dependency is analyzed on the basis of the kinetic theory of gases and a relationship is derived in which the relaxation rate is connected with the square inverse of the diameter of the cavity. Such an analysis provides a novel parameter which denotes the wall effect on the relaxation rate when a gas molecule collides with the surface once in a second. The relaxation time of ¹²⁹Xe gas is also dependent on the material which forms the cavity. This dependency is large and the relaxation study using polarized ¹²⁹Xe gas is expected to offer important information about the state of the matter of the cavity wall.     

14N chemical shifts and quadrupole coupling constants of inorganic nitrates

The isotropic chemical shift and the nuclear quadrupole coupling constant for (14)N were obtained for 14 inorganic nitrates by solid-state MAS NMR measurements at two different field strengths, 9.4 and 11.7 T. The compounds studied were polycrystalline powders of AgNO(3), Al(NO(3))(3), Ba(NO(3))(2), Ca(NO(3))(2), CsNO(3), KNO(3), LiNO(3), Mg(NO(3))(2), NaNO(3), Pb(NO(3))(2), RbNO(3), Sr(NO(3))(2), Th(NO(3))(4)center dot4H(2)O, and UO(2)(NO(3))(2)center dot3H(2)O. Even though the spectra show broadening due to (14)N quadrupole interactions, linewidths of a few hundred hertz and a good signal-to-noise ratio were achieved. From the position of the central peaks at the two fields, the chemical shifts and the nuclear quadrupole coupling constants were calculated. The chemical shifts for all compounds studied range from 282 to 342 ppm with respect to NH(4)Cl. The nuclear quadrupole coupling constants range from 429 kHz for AgNO(3) to 993 kHz for LiNO(3). These data are compared with those available in the literature.     

Through-Bond Correlation of Sugar and Base Protons in Unlabeled Nucleic Acids

This work presents two methods for through-bond correlation between sugar and base protons in view of model-independent assignment in unlabeled or slightly enriched nucleic acids. Each method uses a combination of multiple-bond and one-bond heteronuclear J-couplings to the aromatic carbon C6 for pyrimidines ((3)J(H1',C6) and (1)J(H6,C6)) or C8 for purines ((3)J(H1',C8) and (1)J(H8,C8)). The techniques are demonstrated in the duplex [d(CGCGAATTCGCG)](2) and the dimeric G-quadruplex [d(GGGTTCAGG)](2) at natural abundance.     

High-Resolution H NMR Spectroscopy in the Solid State: Very Fast Sample Rotation and Multiple-Quantum Coherences

In the past few years, solid-state ¹H NMR spectroscopy under fast magic-angle spinning (MAS) has developed into a versatile tool for elucidating structure and dynamics. Dipolar multiple-quantum (MQ), in particular double-quantum (DQ), MAS spectroscopy has been applied to a variety of materials and provided unique insight, e.g., into the structure of hydrogen-bonded systems. This review intends to present solid-state ¹H DQ and MQ MAS spectroscopy in a systematic fashion with a particular emphasis on methodological aspects, followed by an overview of applications.     

The effects of dissolved oxygen upon amide proton relaxation and chemical shift in a perdeuterated protein

The effects of dissolved molecular oxygen upon amide proton ((1)H(N)) longitudinal and transverse relaxation rates and chemical shifts were studied for a small protein domain, the second type 2 module of fibronectin ((2)F2)-isotopically enriched to 99% (2)H, 98% (15)N. Longitudinal relaxation rate enhancements, R(O(2))((1)H(N)), of individual backbone (1)H(N) nuclei varied up to 14 fold between a degassed and oxygenated (1 bar) solution, indicating that the oxygen distribution within the protein is inhomogeneous. On average, smaller relaxation rate enhancements were observed for (1)H(N) nuclei associated with the core of the protein compared to (1)H(N) nuclei closer to the surface, suggesting restricted oxygen accessibility to some regions. In agreement with an O(2)-(1)H(N) hyperfine interaction in the extreme narrowing limit, the (1)H(N) transverse relaxation rates showed no significant change, up to an oxygen pressure of 9.5 bar (the maximum pressure used in this study). For most (1)H(N) resonances, small deltadelta(O(2))((1)H(N)) hyperfine chemical shifts could be detected between oxygen pressures of 1 bar and 9.5 bar.