Quadrupole interactions: NMR, NQR, and in between from a single viewpoint.

Nuclear spins with quantum numbers >1/2 can interact with a static magnetic field, or a local electric field gradient, to produce quantized energy levels. If the magnetic field interaction dominates, we are doing nuclear magnetic resonance (NMR). If the interaction of the nuclear electric quadrupole with electric field gradients is much stronger, this is nuclear quadrupole resonance (NQR).

Evolution of magnetization due to asymmetric dimerization: theoretical considerations and application to aberrant oligomers formed by apoSOD1(2SH).

A set of coupled differential equations is presented describing the evolution of magnetization due to an exchange reaction whereby a pair of identical monomers form an asymmetric dimer. In their most general form the equations describe a three-site exchange process that reduces to two-site exchange under certain limiting conditions that are discussed. An application to the study of sparsely populated, transiently formed sets of aberrant dimers, symmetric and asymmetric, of superoxide dismutase is presented.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus. The magic-angle spinning case.

For a nucleus with a half-integral spin and a strong quadrupole coupling, the central transition (from magnetic quantum number -1/2 to +1/2) in the spectrum shows a characteristic lineshape. By strong coupling, we mean an interaction strong enough so that second-order perturbation theory is needed, yet still sufficient. The spectrum of a static sample is well-known and the magic-angle-spinning (MAS spectrum) is different, but still can be calculated.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting.

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory.

Complete description of the interactions of a quadrupolar nucleus with a radiofrequency field. Implications for data fitting.

We present a theory, with experimental tests, that treats exactly the effect of radiofrequency (RF) fields on quadrupolar nuclei, yet retains the symbolic expressions as much as possible. This provides a mathematical model of these interactions that can be easily connected to state-of-the-art optimization methods, so that chemically-important parameters can be extracted from fits to experimental data. Nuclei with spins >1/2 typically experience a Zeeman interaction with the (possibly anisotropic) local static field, a quadrupole interaction and are manipulated with RF fields.

Dynamical theory of spin relaxation.

The dynamics of a spin system is usually calculated using the density matrix. However, the usual formulation in terms of the density matrix predicts that the signal will decay to zero, and does not address the issue of individual spin dynamics. Using stochastic calculus, we develop a dynamical theory of spin relaxation, the origins of which lie in the component spin fluctuations.

The garuganin and garugamblin diarylether heptanoids: total synthesis and determination of chiral properties using dynamic NMR.

The synthesis of the garuganin and garugamblin diarylether heptanoids using an intramolecular Ullmann coupling is reported. Alkene stereoisomers, vinylogous ester regioisomers, and β-diketone congeners are also synthesized. The chiral properties and free energies of activation for racemization of the garuganin and garugamblin diarylether heptanoids and congeners are determined using dynamic NMR methods.

Spin-lattice relaxation in aluminum-doped semiconducting 4H and 6H polytypes of silicon carbide.

NMR spin-lattice relaxation efficiency is similar at all carbon and silicon sites in aluminum-doped 4H- and 6H-polytype silicon carbide samples, indicating that the valence band edge (the top of the valence band), where the holes are located in p-doped materials, has similar charge densities at all atomic sites. This is in marked contrast to nitrogen-doped samples of the same polytypes where huge site-specific differences in relaxation efficiency indicate that the conduction band edge (the bottom of the conduction band), where the mobile electrons are located in n-doped materials, has very different charge densities at the different sites. An attempt was made to observe (27)Al NMR signals directly, but they are too broad, due to paramagnetic line broadening, to provide useful information about aluminum doping.

Designing optimal universal pulses using second-order, large-scale, non-linear optimization.

Recently, RF pulse design using first-order and quasi-second-order pulses has been actively investigated. We present a full second-order design method capable of incorporating relaxation, inhomogeneity in B(0) and B(1). Our model is formulated as a generic optimization problem making it easy to incorporate diverse pulse sequence features.

Interconversion study in 1,4-substituted six-membered cyclohexane-type rings. Structure and dynamics of trans-1,4-dibromo-1,4-dicyanocyclohexane.

Cyclohexane is an extremely flexible molecule that oscillates, at room temperature, between two clearly distinct and extreme conformations that cannot be distinguished at room temperature; so much so that the NMR spectrum is a single line that includes all 12 protons be they axial or equatorial. This raises the interesting question as to what happens when there are equal substituents at the 1 and 4 carbon atoms of the ring. Therefore substitution in the 1,4-positions in the cyclohexane ring has been the subject of considerable interest because some form of interconversion between extreme conformations could lead to the existence of a rather unusual behavior.

Definitive solid-state 185/187Re NMR spectral evidence for and analysis of the origin of high-order quadrupole-induced effects for I=5/2.

Rhenium-185/187 solid-state nuclear magnetic resonance (SSNMR) experiments using NaReO(4) and NH(4)ReO(4) powders provide unambiguous evidence for the existence of high-order quadrupole-induced effects (HOQIE) in SSNMR spectra. Fine structure, not predicted by second-order perturbation theory, has been observed in the (185/187)Re SSNMR spectrum of NaReO(4) at 11.75 T, where the ratio of the Larmor frequency (ν(0)) to the quadrupole frequency (ν(Q)) is ∼2.

Solvent effects on chemical exchange in a push-pull ethylene as studied by NMR and electronic structure calculations.

NMR measurements of chemical exchange in a push-pull ethylene, dissolved in a number of different solvents, are presented. These are complemented by high-level electronic structure calculations, using both gas-phase conditions and those which simulate solvents. The results show that it is essential to include entropy effects in order to understand the observed trends.

Use of continuous optimization methods to find carbon links in 2D INADEQUATE spectra.

The 2-D INADEQUATE experiment is a useful experiment for determining carbon structures of organic molecules, which is known for having low signal-to-noise ratios. A non-linear optimization method for solving low-signal spectra resulting from this experiment is introduced to compensate. The method relies on the peak locations defined by the INADEQUATE experiment to create boxes around these areas and measure the signal in each.

Exact solution of the CPMG pulse sequence with phase variation down the echo train: application to Râ‚‚ measurements.

An implicit exact algebraic solution of CPMG experiments is presented and applied to fit experiments. Approximate solutions are also employed to explore oscillations and effective decay rates of CPMG experiments. The simplest algebraic approximate solution has illustrated that measured intensities will oscillate in the conventional CPMG experiments and that using even echoes can suppress errors of measurements of Râ‚‚ due to the imperfection of high-power pulses.

NMR spectroscopic evidence for the intermediacy of XeF(3)(-) in XeF(2)/F(-) exchange, attempted syntheses and thermochemistry of XeF(3)(-) salts, and theoretical studies of the XeF(3)(-) anion.

The existence of the trifluoroxenate(II) anion, XeF(3)(-), had been postulated in a prior NMR study of the exchange between fluoride ion and XeF(2) in CH(3)CN solution. The enthalpy of activation for this exchange, ΔH(⧧), has now been determined by use of single selective inversion (19)F NMR spectroscopy to be 74.1 ± 5.

Exact solution to the Bloch equations and application to the Hahn echo.

The exact symbolic solution of the Bloch equations is given in the Lagrange form and illustrated with R2 experiments using a Hahn echo. Two different methods are also applied to approximately solve the Bloch equations, we find that splittings with effective-field interpretations are very substantially better than other approximations by comparing the errors. Estimates of transverse relaxation, R2, from Hahn echos are effected by frequency offset and field inhomogeneity.

Problems, artifacts and solutions in the INADEQUATE NMR experiment.

The INADEQUATE experiment can provide unequalled, detailed information about the carbon skeleton of an organic molecule. However, it also has the reputation of requiring unreasonable amounts of sample. Modern spectrometers and probes have mitigated this problem, and it is now possible to get good structural data on a few milligrams of a typical organic small molecule.

Magnetic resonance tensors in uracil: calculation of 13C, 15N, 17O NMR chemical shifts, 17O and 14N electric field gradients and measurement of 13C and 15N chemical shifts.

The experimental (13)C NMR chemical shift components of uracil in the solid state are reported for the first time (to our knowledge), as well as newer data for the (15)N nuclei. These experimental values are supported by extensive calculated data of the (13)C, (15)N and (17)O chemical shielding and (17)O and (14)N electric field gradient (EFG) tensors. In the crystal, uracil forms a number of strong and weak hydrogen bonds, and the effect of these on the (13)C and (15)N chemical shift tensors is studied.

N-triphenylboryl- and N,N'-bis(triphenylboryl)benzo-2,1,3-telluradiazole.

Being isoelectronic and isostructural analogues of N-alkyl-substituted telluradiazolyl cations, the adducts of triphenylborane with benzo-2,1,3-telluradiazole provide an electrically neutral point of reference with which the properties of the heterocyclic ions can be compared.

Optimized sampling patterns for multidimensional T2 experiments.

Non-uniform sampling in multidimensional NMR shows great promise to significantly decrease experimental acquisition times, especially for relaxation experiments for which peak locations are already known. In this paper we present a method for optimizing the non-uniform sampling points such that the noise amplification and numerical instabilities are minimized. In particular, the minimum singular value of the Moore-Penrose pseudo-inverse is maximized using sequential semi-definite programming, thereby minimizing the worst-case errors.

Molecular self-assembly inhibition leads to basket-shaped cyclophane formation with chiral dynamics.

Planar perylene derivatives form macrocyclic dimers and concatenated dimer-dimer rings under the action of molecular self-assembly. If this underpinning principle is true, highly twisted perylene derivatives should be more frustrated toward formation of multimeric cyclic compounds such as macrocyclic dimers and concatenated dimer-dimers because of perturbation resulting from intermolecular pi-pi stacking. Indeed, 1,6,7,12- tetraphenoxy-substituted perylene is highly twisted and undergoes unimolecular cyclization rather than bimolecular or multimolecular cyclization.

Simulation of steady-state NMR of coupled systems using Liouville space and computer algebra methods.

A series of repeated pulses and delays applied to a spin system generates a steady state. This is relatively easy to calculate for a single spin, but coupled systems present real challenges. We have used Maple, a computer algebra program to calculate one- and two-spin symbolically, and larger systems numerically.

Interconversion of carbon sites in boat-chair-boat cyclodecane; conformations of chlorocyclodecane and cyclodecyl acetate.

Interconversion of carbon sites in boat-chair-boat (BCB) cyclodecane occurs by way of the twist-boat-chair (TBC) conformation, which predicts that C-1 exchanges with C-4, etc. The previously obtained low-temperature 13C spectra could be matched by assuming (1,4) or (1,3) exchange, but not (1,2) exchange. A free-energy barrier of 5.

ApoA-I mimetic peptides with differing ability to inhibit atherosclerosis also exhibit differences in their interactions with membrane bilayers.

Two homologous apoA-I mimetic peptides, 3F-2 and 3F(14), differ in their in vitro antiatherogenic properties (Epand, R. M., Epand, R.