D. W. Alderman

Methods for analyzing spectroscopic line shapes. NMR solid powder patterns

A new method is described for numerically computing theoretical NMR powder patterns which achieves a many‐fold increase in speed and accuracy over previous techniques. The method incorporates a simple and efficient technique for selecting the set of crystal orientations over which the spectral frequencies are calculated. The orientation selection technique is then integrated with an interpolation scheme which transfers the intensities at these frequencies to the computed spectrum. The method will be useful whenever an average over a sphere is computed numerically. The new efficiency of the method makes practical least squares fitting of theoretical spectra to experimental NMR data. The fits provide unbiased estimates of the NMR parameters and their errors. The technique is illustrated by extracting chemical shift tensors from a proton decoupled carbon‐13 NMR spectrum.

A sensitive, high resolution magic angle turning experiment for measuring chemical shift tensor principal values

A sensitive, high-resolution ‘FIREMAT’ two-dimensional (2D) magic-angle-turning experiment is described that measures chemical shift tensor principal values in powdered solids. The spectra display spinning-sideband patterns separated by their isotropic shifts. The new methods sensitivity and high resolution in the isotropic-shift dimension result from combining the 5π magic-angle-turning pulse sequence, an extension of the pseudo-2D sideband-suppression data rearrangement, and the TIGER protocol for processing 2D data. TPPM decoupling is used to enhance resolution. The method requires precise synchronization of the pulses and sampling to the rotor position. It is shown that the technique obtains 35 natural-abundance 13C tensors from erythromycin in 19 hours, and high quality natural-abundance 15N tensors from eight sites in potassium penicillin V in three days on a 400 MHz spectrometer.

Director dynamics and NMR applications of nematic liquid crystals spinning at various angles from the magnetic field

The dynamics of the director of a nematic liquid crystal spinning in a magnetic field are studied. A simple average potential theory which gives a qualitative understanding of the director behavior is presented along with an exact quantitative treatment of situations in which the director is stationary in the laboratory frame. NMR spectra of an A2 spin system, 19F in CF2CBr2, are used to verify the theory. For nematic liquid crystals in which the magnetic susceptibility anisotropy Δχ = (χ∥−χ⊥) is positive, the director aligns along the spinning axis when the sample is spun at a rate much greater than that characteristic of director reorientation and the angle between the spinning axis and the magnetic field is less than the magic angle ϑm = 54.74°. Past the magic angle the director distributes in the plane perpendicular to the spinning axis. For liquid crystals in which Δχ is negative, alignment parallel to the spinning axis occurs for angles greater than ϑm and distribution in the plane occurs for angles...

Nuclear relaxation in coupled spin systems. A heteronuclear two pulse experiment and a general numerical method for analyzing spin dynamics

A convenient new heteronuclear two pulse nuclear spin relaxation experiment is described. When combined with relaxation experiments already in the literature, each of the interlevel transition probabilities for a system of weakly coupled nuclear spins may be determined. Previous work in coupled spin relaxation has yielded only certain linear combinations of these transition probabilities. The well understood AX spin system was selected to illustrate the method, and sodium formate in D2O solution is used as the specific case. Values for all four interlevel transition probabilities characterizing the spin lattice relaxation of the 1H–13C spin system of the formate ion are obtained. These data yield the first experimental verification of the extreme narrowing condition commonly assumed for small molecules in nonviscous liquids. A general numerical method is described for estimating the relaxation parameters from measurements of the time evolution of nonequilibrium magnetization. The method involves numerical...

NMR spectra from powdered solids spinning at any angle and speed: simulations and experiments

A new method is described for calculating NMR spectra of powdered solids spinning at any speed and at any angle relative to the magnetic field. The algorithm provides the intensities and shapes of the centreband and all sidebands through a computation involving the solution of homogeneous linear equations. The method is also applicable to cases where two or more interactions simultaneously affect the spectral response. A simple extension of the algorithm treats cases where an analytical expression for the resonance frequency is not available. The method is demonstrated with simulations and experimental examples of anisotropic chemical-shift spectra obtained by spinning samples at various low speeds and angles. The technique is also applied to a spin-½ nucleus with both an anisotropic chemical shift and a dipolar coupling either to a heteronuclear spin-½ nucleus or to a spin-1 nucleus experiencing a strong quadrupole interaction.

Structure and dynamics of methylene iodide in solution from nuclear spin–lattice relaxation studies

The nuclear spin–lattice relaxation of carbon‐13 enriched methylene iodide (diiodomethane) dissolved in benzene‐d6 has been studied both with and without proton decoupling and using various pulse techniques to perturb the AX2(13CH2) spin system from thermal equilibrium. The return of the spin system to steady state was monitored using carbon‐13 Fourier transform nuclear magnetic resonance techniques. It is shown that the equation of motion of the spin density matrix reduces in general to the master equation for populations in terms of interlevel transition rates, and that a linear transformation based on the complete set of irreducible spherical tensor operators which span the spin space further simplifies the equation of motion. The relaxation was modeled as intramolecular dipole–dipole interactions modulated by rotational reorientation of the molecule plus other mechanisms which can be treated collectively as external random magnetic fields interacting with the nuclear spins of interest. Extreme narrowi...

Measurement of 13C chemical shift tensor principal values with a magic-angle turning experiment

The magic-angle turning (MAT) experiment introduced by Gan is developed into a powerful and routine method for measuring the principal values of 13C chemical shift tensors in powdered solids. A large-volume MAT probe with stable rotation frequencies down to 22 Hz is described. A triple-echo MAT pulse sequence is introduced to improve the quality of the two-dimensional baseplane. It is shown that measurements of the principal values of chemical shift tensors in complex compounds can be enhanced by using either short contact times or dipolar dephasing pulse sequences to isolate the powder patterns from protonated or non-protonated carbons, respectively. A model compound, 1,2,3-trimethoxybenzene, is used to demonstrate these techniques, and the 13C principal values in 2,3-dimethylnaphthalene and Pocahontas coal are reported as typical examples.

Relationship of 13C NMR chemical shift tensors to diffraction structures.

13C chemical shift tensor measurements on single crystals provide a powerful method to study changes in the electron environment of nuclei with changes in molecular structure. Thus, diffraction structures are critical to an understanding of chemical shift tensors. This work explores the general reliability of using structural data to predict components of the symmetrical chemical shift tensor. Imprecision in the hydrogen positions introduces considerable scatter in the simulated 13C shift tensors, and optimized C-H bond distances in methyl-beta-D-glucopyranoside used with the X-ray positions of the heavier C and O atoms greatly improve the simulated chemical shifts. Acenaphthene, with two crystallographically different molecules per unit cell, offers an excellent example for comparing and contrasting structural differences in the two molecules. A recently improved X-ray structure of naphthalene obtained at low temperature provides chemical shift simulations which are comparable to those from neutron diffraction methods and appear to reflect breaks in the D2h symmetry measured in the NMR chemical shift tensors. These data illustrate the close relationship between NMR and diffraction structures.

Cylindrical spinner and speed controller for magic angle spinning nuclear magnetic resonance

A new design for a cylindrical spinner suitable for magic angle spinning nuclear magnetic resonance (NMR) is described. The rotor has a large sample volume (0.66 cm3) and is capable of spinning speeds from 500 Hz to 5 kHz at drive gas pressures below 50 lb/in.2. The rotor is completely supported by gas bearings. Axial positioning is provided by the rotor’s T shape, leaving the bottom surface available for a photoelectric tachometer. The coil is wrapped on a form machined into the outer surface of the stator, producing a high filling factor. Also described is an instrument which controls the spinning speed of such a rotor to ±0.6 Hz around a set speed in the range of 3–4 kHz. The rotor’s speed is determined by means of a photoelectric tachometer. The instrument then compares this measured speed to the desired value and adjusts the gas flow to the rotor to correct any difference.

Carbon-13 chemical-shift tensors in single-crystal methoxybenzenes

Using a two-dimensional NMR orientational correlation technique, carbon-13 chemical-shift tensors have been measured in single crystals of 1,4-dimethoxybenzene, 1,3,5-trimethoxybenzene and 1,2,3-trimethoxybenzene. The two-dimensional technique greatly extends the single-crystal method to materials with a much larger number of different carbon-13 resonance lines. The manner of dealing with chemically identical, but magnetically inequivalent carbons in the unit cell is discussed. The X-ray structure of 1,2,3-trimethoxybenzene is reported for the first time, and a redetermination of the X-ray structure for 1,4-dimethoxybenzene is given. The principal values of all carbon-13 chemical-shift tensors in the three molecules and the orientation of their principal axes have been obtained. Using multiple regressional analysis the principal values of the tensors have been discussed in terms of additive substituent effects. Ab initio calculations of the shielding tensors in anisole (methoxybenzene) and benzene were used to calculate substituent effects which agree closely with the parameters obtained from the regressional analysis.