To date, both the intermolecular multiple-quantum coherence (MQC) and demagnetizing field models have led to fully quantitative predictions of NMR signals in a highly polarized system using the CRAZED and similar sequences. In this paper, measurements of apparent MQC diffusion rates, Dn app, for a specific apparent coherence order, n, were used to investigate the equivalent between the intermolecular MQC and demagnetizing field treatments. A number of physical effects were analyzed both theoretically and experimentally. These effects include molecular diffusion, variation in dipolar correlation distance, radiation damping, inhomogeneous broadening, and spin relaxation, all of which may alter the NMR signal. Two variations of a two-pulse CRAZED sequence, where the signal attenuation is almost entirely caused by the diffusion weighting, were designed to accurately measure and characterize Dn app during the evolution period. Apparent diffusion rates were extracted from a least-squares fitting of a series of 1H spectra, measured with varying diffusion weighting factors. Complete theoretical formations were explicitly derived from both the intermolecular MQC and demagnetizing field treatments. Numerical simulations based on the demagnetizing field treatment were performed and it was found that the model can be used to predict the apparent diffusion rates. A novel diffusion model for intermolecular MQC is proposed in which the phase shift of each individual spin on different molecules is considered to be uncorrelated. This model successfully predicts the unconventional diffusion behaviors of intermolecular MQCs, specifically for differences of apparent diffusion rates between inter-and intramolecular MQCs. Our theoretical predictions and experimental confirmation demonstrate, for the first time, that Dn app for intermolecular MQCs of order n are characterized by Dn app5nDT for n>2 and D0 app52DT for n50, where DT is the translational molecular diffusion rate of the single quantum coherences. These results do not coincide with Dn5n2DT for n>0 which is a general relationship for an intramolecular n-quantum coherence. These works about the apparent diffusion rates during the evolution period of the CRAZED sequences provide additional evidence to support the argument of the equivalence between the intermolecular MQC and demagnetizing field models. The general results derived from both intermolecular MQC and demagnetizing field treatments in this report can reasonably explain new observations of diffusion phenomena in nonlinear spin echoes by Kimmich and co-workers. Even though the theoretical prediction about intermolecular MQC diffusion is verified only with specific experiments using tailor-made pulse sequences, it is demonstrated that the function dependence of diffusion rate on coherence order is general. These results provide independent evidence to support the intermolecular MQC theory proposed by Warren and co-workers.

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.

Although the theories and potential applications of intermolecular multiple-quantum coherences iMQCs have been under active investigations for over a decade, discussion of iMQC NMR signal formation was mainly confined in the time domain. In this paper, a full line-shape theory was developed to describe iMQC signals in the frequency domain. Relevant features of the line shape, such as peak height, linewidth, and phase, were investigated in detail. Predictions based on the theory agree well with experimental and simulated results. Since radiation-damping effects always couple with iMQCs in highly polarized liquid-state NMR systems, and strongly radiation-damped signals have many spectral characteristics similar to those of iMQCs, a detailed comparison was also made between them from different spectral aspects. With detailed comparison of peak height, linewidth, and phase, this work demonstrates that the iMQC and radiation-damping phenomena result from two completely different physical mechanisms despite that both present similar signal features and coexist in highly polarized liquid-state NMR systems.

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.

Residual intermolecular dipolar interactions may result in undesired spectral features on highly concentrated samples in liquid NMR. Although homonuclear decoupling can be employed to suppress the interactions, it may cause a strong irradiation peak, which obscures the nearby peaks. In order to overcome this shortcoming, a modified CRAZED sequence with three radio-frequency pulses was proposed. The analytical expression derived from the dipolar field treatment was employed to select proper flip angles and phase cycling. Theoretical predictions, experimental observations, and computer simulations demonstrated that the new method effectively suppresses the undesired peaks due to residual dipolar effects.