A product operator matrix is proposed to describe scalar couplings in liquid NMR. Combination of the product operator matrix and non-linear Bloch equations is employed to describe effects of chemical shift, translational diffusion, dipolar field, radiation damping, and relaxation in multiple spin systems with both scalar and dipolar couplings. A new simulation algorithm based on this approach is used to simulate NMR signals from dipolar field effects in the presence of scalar couplings. Several typical coupled spin systems with both intra-molecular scalar couplings and inter-molecular dipolar couplings are simulated. Monte Carlo methods are incorporated into simulations as well to analyze diffusion process in these complicated spin systems. The simulated results of diffusion and relaxation parameters and 2D NMR spectra are coincident with the experimental measurements, and agree with theoretical predictions as well. The simulation algorithm presented herein therefore provides a convenient means for designing pulse sequences and quantifying experimental results in complex coupled spin systems.

A novel propagator approach for NMR signal attenuation due to anisotropic diffusion is proposed, with consid-eration of the loss of spin phase memory during random motion. This method is applied to explicitly investigate free diffusion, restricted diffusion between two parallel plates, and diffusions under different nonlinear gradients, including an n-order nonlinear field and gradient with a cosine distribution. The method provides an intuitive physical picture and simplifies the treatment with the effects of finite-width gradient pulses in restricted diffusion and with nonlinear gra-dients. Theoretical results are in good agreement with those of previous reports.

A selective 2D intermolecular zero-quantum coherences pulse sequence, SEL-HOMOGENIZED sequence, was developed for high-resolution NMR spectra in inhomogeneous fields. The sequence designed to effectively suppress strong solvent signals and other trivial signals can greatly decrease the t1 noise artifacts. In the homogeneous-like 1D spectrum extracted from the 2D data, chemical shifts, coupling constants, multiplicity patterns, and relative peak areas are almost independent of the magnetic field inhomogeneity. Compared to the HOMOGENIZED sequence, the new sequence provides a total sensitivity enhancement of two times. It was also demonstrated that the theoretical predictions were in excellent agreement with the experimental results.

An NMR pulse sequence was designed to accurately measure the diffusion rates of intermolecular zero-quantum coherences (ZQCs) and double-quantum coherences (DQCs) in two-component spin systems. The Gaussian phase distribution approximation was employed to describe the behavior of intermolecular ZQCs and DQCs as they underwent unrestricted isotropic diffusion. Our experimental and theoretical results demonstrate that intermolecular ZQCs and DQCs evolve with the same diffusion rates. Uncorrelated phases between individual spins on different olecules in intermolecular ZQCs and DQCs are suggested as the cause for their unconventional diffusion behavior. The differences in diffusion rates between inter- and intramolecular ZQCs or DQCs are explained.

Optimal RF flip angles of the NMR CRAZED pulse sequence for multiple spin-echoes (MSEs) and intermolecular multiple quantum coherences (iMQCs) of different orders were investigated theoretically and experimentally. An an-alytical expression for the dependence of signal intensities on RF pulse flip angles was derived for the cases when higher-order expansion terms of Bessel functions can be neglected from a combination of dipolar demagnetizing field treatment and product operator formalism. Theoretical predictions for both the relative signal intensities and the optimal flip angles at which the signal intensities are maximized are found to be in excellent agreement with experimental re-sults.

A general analytical expression for intermolecular dipolar effects in liquids under the influence of magnetic field gradients of varying magnitudes, directions, and durations was explicitly derived with the density matrix formalism. We demonstrate that the time-averaged, not instantaneous, orientation of the applied gradients determines the contributions of long-range intermolecular dipole effects to multiple-quantum coherences. Theoretical and experimental results demonstrate, for the first time, that when the time-averaged orientation of a series of gradient pulses during the evolution period is at the magic angle, intermolecular dipolar effects are suppressed. The experimental evidence presented herein strongly supports our theoretical predictions.

Longitudinal relaxation related to intermolecular dipolar interactions was investigated by solution NMR. A novel pulse sequence with selective pre-saturation and selective excitation was designed for a highly polarized two-component spin system. A general analytical expression for the longitudinal relaxation was derived from a combination of the demagnetizing field theory and product operator formalism. The analytical expression suggests that the longitudinal relaxation is not a mono-exponential process. The predicted relaxation relationship is in excellent agreement with the experimental recovery curves.

A novel diperoxovanadate complex NH4[OV(O2)2{2-(2'-pyridyl)-imidazole}]

The 19F NMR chemical shieldings of solid-state alkaline-earth-metal fluorides MF2 (M) Be, Mg, Ca, Sr, Ba) and alkali-metal fluorides MF (M) Li, Na, K, Rb, Cs) were systematically studied by the gaugeindependent atomic orbital (GIAO) method at the level of density functional theory (DFT). The 6-311+G(d) basis set was used for the inspected fluoride ion. The performance of the effective core potentials (ECP) of LanL2DZ and CRENBL basis sets for metal atoms were compared to 3-21G all-electron basis set. The role of d polarization functions for metal atoms is investigated. The results show that the clusters [FMg3F9]4-, [FM4F6]+ (M) Ca, Sr, Ba), and [FM6]5+ (M) Li, Na, K, Rb, Cs) used to model the bulk solids are reasonable. The electrons in the next outermost shell of metal atoms have significant influence on the 19F NMR calculations and should be treated as valence electrons together with the electrons in the outermost shell, while the remaining electrons can be represented by the ECP of CRENBL basis set. When the CRENBL basis set (with ECP for core electrons) supplemented with two sets of d polarization functions was used for the metal atoms, the approach of locally dense basis sets can be used to successfully reproduce the 19F shielding values. Since only the inspected resonant fluorine atom needs a high-grade all-electron basis set, it is a relatively inexpensive means of obtaining reliable shielding properties for the inspected species. In addition, the different exchangecorrelation functional implemented in hybrid DFT method has a minor influence on the calculated shielding. Although all the calculated results are somewhat overestimated, the correlation coefficients and the slopes of the fitting lines between the theoretical predictions and experimental observations are close to unity, indicating the good agreement of the theoretical results to the experimental values.

The behaviors of molecular self-diffusion were simulated in complex spin systems with both intra-molecular scalar couplings and inter-molecular dipolar couplings in liquid nuclear magnetic resonance (NMR). The simulation algorithm was based on a combination of the non-linear Bloch equations, product operator matrix, and finite difference method. The simulated results reveal different diffusion behaviors of inter-and intra-molecular multiple-quantum coherences, coincident with theoretical predictions and experimental measurements. Compared with the Monte Carlo method, the finite difference method is more precise and efficient for simulating diffusion behaviors of multiple-quantum coherences.