Q-shear transformation for MQMAS and STMAS NMR spectra

The multiple-quantum magic-angle spinning (MQMAS) and satellite-transition magic-angle spinning (STMAS) experiments refocus second-order quadrupolar broadening of half-integer quadrupolar spins in the form of two-dimensional experiments. Isotropic shearing is usually applied along the indirect dimension of the 2D spectra such that an isotropic projection free of anisotropic quadrupolar broadening can be obtained. An alternative shear transformation by a factor equal to the coherence level (quantum number) selected during the evolution period is proposed. Such a transformation eliminates chemical shift along the indirect dimension leaving only the second-order quadrupolar-induced shift and anisotropic broadening, and is expected to be particularly useful for disordered systems. This transformation, dubbed Q-shearing, can help avoid aliasing problems due to large chemical shift ranges and spinning sidebands. It can also be used as an intermediate step to the isotropic representation for expanding the spectral window of rotor-synchronized experiments.     

Local structure in perovskite relaxor ferroelectrics: high-resolution Nb 3QMAS NMR

Solid solutions of (1'-x)Pb(Mg(1/3)Nb(2/3))O3xPb(Sc(1/2)Nb(1/2))O3 (PMN/PSN) have been investigated using high-resolution 93Nb 3-quantum magic-angle spinning nuclear magnetic resonance experiments (3QMAS NMR). In previous MAS NMR investigations, the local B-cation ordering in these relaxor ferroelectric solid solutions was quantitatively determined. However, in conventional one-dimensional MAS spectra the effects of chemical shifts and quadrupole interaction are convoluted; this, in addition to the insufficient resolution, precludes reliable extraction of the values of isotropic chemical shift and quadrupole coupling product. In the current 3QMAS investigation, 93Nb spectra are presented for concentrations x=0, 0.1, 0.2, 0.6, 0.7, and 0.9 at high magnetic field (19.6 T) and fast sample spinning speed (35.7 kHz). Seven narrow peaks and two broad components are observed. The unique high-resolution of the two-dimensional 3QMAS spectra enables unambiguous and consistent assignments of spectral intensities to the specific 28 nearest B-site neighbor (nBn) configurations, (NMg, NSc, NNb) where each number ranges from 0 to 6 and their sum is 6. It is now possible to isolate the isotropic chemical shift and quadrupole coupling product and separately determine their values for most of the 28 nBn configurations. The isotropic chemical shift depends linearly on the number of Mg2+ cations in the configuration; delta iso CS=(13.7 +/- 0.1)NMg-970 +/- 0.4 ppm, regardless of the ratio NSc/NNb. For the seven Nb5+-deficient configurations (NMg, 6-NMg, 0) and the pure niobium configuration (0, 0, 6), the quadrupole coupling products (and hence the electric field gradients) are small (PQ approximately 6-12 MHz) and for the remaining configurations containing small, ferroelectric active Nb5+ ions, the quadrupole coupling products are significantly larger (PQ approximately 40 MHz), indicating larger electric field gradients.     

Molecular recognition in cyclodextrin complexes of amino acid derivatives: the effects of kinetic energy on the molecular recognition of a pseudopeptide in a nonconstraining host environment as revealed by a temperature-dependent crystallographic study

The crystal structure of a triclinic 2:2 inclusion complex of beta-cyclodextrin with N-acetyl-L-phenylalanine methyl ester has been determined at several temperatures between 298 and 20 K to further study molecular recognition using solid-state supramolecular beta-cyclodextrin complexes. The study reveals kinetic energy dependent changes in guest molecule conformations, orientations, and positions in the binding pocket presented by the crystal lattice. Accompanying these changes are observable differences in guest-guest interactions and hydrogen-bonding interactions in the binding pocket that involve guest molecules, water of hydration molecules, and beta-cyclodextrin molecules. On the basis of the differences observed in the crystal structures, we present a solid-state example of a system that displays the properties of both classical and quantum chemical models. At higher temperatures, the structure conforms to a classical mechanical model with dynamic disorder. At lower temperatures, the observations conform to examples in which there is static disorder representative of models in which quantum states differing in conformation, position, and orientation of components in the crystal structure are occupied. Ab initio theoretical calculations on the different guest molecule conformations have been carried out. Superpositions of theoretical electrostatic surface potential diagrams on the observed molecular positions in the complexes provide confidence that the deconvolution of the guest molecule disorder is acceptable. Temperature-dependent solid-state magic angle spinning deuteron NMR measurements provide evidence for large-amplitude, diffusive motion on a microsecond time scale in the complex.     

Characterization of molecular motion in the solid state by carbon-13 spin-lattice relaxation times

Relaxation calculations for rapidly spinning samples show that spin-lattice relaxation time (T(1Z)) anisotropy varies with the angle between the rotor spinning axis and the external field. When the rate of molecular motion is in the extreme narrowing limit, the measurement of T(1Z) anisotropies for two different values of the spinning angle allows the determination of two linear combinations of the three static spectral densities, J(0)(0), J(1)(0), and J(2)(0). These functions are sensitive to molecular geometry and the rate and trajectory of motion. The utility of these linear combinations in the investigation of molecular dynamics in solids has been demonstrated with natural abundance (13)C NMR experiments on ferrocene. In an isolated (13)C-(1,2)H group, the dipole-dipole interaction has the same orientational dependence as the quadrupole interaction. Thus, the spectral densities that are responsible for dipolar relaxation of (13)C are the same as those responsible for deuteron quadrupolar relaxation. For ferrocene-d(10), deuteron T(1Z) and T(1Q) anisotropies and the relaxation time of the (13)C magic angle spinning peak provide sufficient information to determine the orientation dependence of all three individual spectral densities.     

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR _em = 〈n _s〉/〈n _ch〉, where 〈n _ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R _em = 1·71 implies an effectiveA-dependence ofR _A =A ^0.18,i.e., a very weak dependence. Predictions ofR _em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.     

High field 207Pb spin-lattice relaxation in solid lead nitrate and lead molybdate

Spin-lattice relaxation rates of lead have been measured at 17.6 T (156.9 MHz) as a function of temperature in polycrystalline lead nitrate and lead molybdate. Comparing the results with relaxation rates measured at lower fields, it is found that at high fields and low temperature, chemical shift anisotropy (CSA) makes small but observable contributions to lead relaxation in both materials. At 17.6 T and 200 K, CSA accounts for about 15% of the observed relaxation rate. Above 300 K, the dominant relaxation mechanism even at 17.6 T is an indirect Raman process involving modulation of the (207)Pb spin-rotation tensor, as first proposed by Grutzner et al. [J. Am. Chem. Soc. 123, 7094 (2001)] and later treated theoretically in more detail by Vega et al. [Phys. Rev. B 74, 214420 (2006)]. The improved signal to noise ratio at high fields makes it possible to quantify relaxation time anisotropy by analyzing saturation-recovery functions for individual frequencies on the powder pattern line shape. No orientation dependence is found for the spin-lattice relaxation rate of either material. It is argued from examination of the appropriate theoretical expressions, derived here for the first time, that the lack of observable relaxation time anisotropy is probably a general feature of this indirect Raman mechanism.     

Investigation of multiaxis molecular motion by off-magic angle spinning deuteron NMR

The relatively new deuteron NMR method of off-axis-magic angle spinning (OMAS) has been extended and used to investigate multiaxis rotational jump motion. Floquet theory is developed for simulating deuteron OMAS spectra with multisite jumps at different rates about noncoincident axes, and efficient procedures are presented for computing the sideband line shapes. It is demonstrated experimentally that reproducible adjustment of the angle between the rotor axis and the static magnetic field is feasible with precision approaching +/- 0.01 degrees. This leads to the reintroduction of a scaled, first-order quadrupole coupling that defines a new kinetic window and makes deuteron OMAS much more sensitive than ordinary magic angle spinning to motion on the kilohertz time scale. Temperature-dependent deuteron OMAS line shapes of octanoic acid/urea-d4 inclusion compound have been recorded and fitted, using least-squares procedures, to provide rates of rotation about both CN and CO bonds. The Arrhenius activation parameters for rotation about CN bonds, Ea = 60.4+/-2.4 kJ/mol and ln(A) = 24.9+/-0.3, agree well with previous values determined by selective inversion experiments. However, OMAS yields Ea = 26.3+/-0.4 kJ/mole and ln(A) = 24.9+/-0.3 for whole-body rotation about the CO bond axis in contrast to previous analysis of static quadrupole echo (QE) line shapes which gave Ea = 22.3+/-0.3 kJ/mole and ln(A) = 24.8+/-0.6 for the same sample. The underlying homogeneous linewidths of OMAS spectra are much smaller than those of QE spectra, and this provides higher precision and less systematic error in the determination of rates.