In this paper, signals originating from a pure specific coherence of intermolecular three-spin orders were separated and characterized experimentally in highly polarized two-component spin systems. A modified CRAZED sequence with selective radio-frequency excitation was designed to separate the small signals from the strong conventional single-spin single-quantum signals. General theoretical expressions of the pulse sequence with arbitrary flip angle pulses were derived using dipolar field treatment. The expressions were used to predict the relaxation and diffusion properties and optimal xperimental parameters such as flip angles. For the first time, relaxation and diffusion properties of pure intermolecular single-quantum, double-quantum, and triple-quantum coherences of three-spin orders were characterized and analyzed in one-dimensional experiments. All experimental observations are in excellent agreement with the theoretical predictions. The theoretical results show that the quantum-mechanical treatment leads to exactly the same predictions as the dipolar field treatment. The quantitative study of intermolecular multiple-quantum coherences of three-spin orders presented herein provides a better nderstanding of their mechanisms.

Intermolecular zero-quantum and double-quantum coherences (iZQCs and iDQCs) are frequently discussed in literature since they may provide novel contrast mechanisms in magnetic resonance imaging and possibilities for high-resolution spectra in an inhomogeneous and unstable magnetic field. In a previous paper [J. Chem. Phys. 115, 10769 (2001)], we have studied both theoretically and experimentally the properties of iZQC and iDQC nuclear magnetic resonance (NMR) Signals related to intermolecular dipolar interactions in two-component systems. In this paper, the investigation is extended to homonuclear intermolecular single-quantum coherences (iSQCs) from the second-order spin interactions, which have not been observed and studied previously. Selective excitation was used to suppress the strong conventional single-spin single-quantum signals. A combination of dipolar field treatment and Torrey equation was used to derive a general theoretical expression for the time evolution of spins with arbitrary flip angles of rf pulses. The expression was used to predict the optimal conditions for iSQCs among highly polarized spins in liquid. Dependence of the iSQC signals on the experimental parameters was measured and analyzed to verify the theoretical predictions. For the first time, signals from pure homonuclear two-spin iSQCs free of much larger conventional single-spin single-quantum signals, and intermolecular iSQC cross peaks in homonuclear pulsed-field gradient COSY experiments were observed and characterized, in one-and two-dimensional (1D and 2D) experiments, respectively. The use of coherence-selection gradients tilted at the magic angle results in the suppression of iSQC cross peaks. It provides strong evidence that the observed signals originate from distant dipolar interactions. Relaxation and diffusion properties of iSQCs in multiple-component samples were characterized and analyzed as well as the optimal rf flip angles. Theoretical and experimental results presented herein demonstrate that the signals from the homonuclear second-order iSQCs not only have a similar signal intensity as iZQCs or iDQCs, all of which are much stronger than that from three-spin iSQCs reported previously, but also provide spatial information related to dipolar correlation scales similar to iZQCs and iDQCs, which is not present in conventional SQC experiments. All 1D and 2D NMR experimental observations based on single- and multiple-component samples are in excellent agreement with the theoretical predictions. The quantitative study of iSQCs provides a better understanding of their unique mechanisms, and may find useful applications in NMR analyses such as sample purification and/or preparation of metabolites, biofluids, and natural compounds dissolved in nondeuterated solvents.

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.

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.

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.