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.

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.

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.

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.