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.