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.

[M6F]5+ clusters were chosen to calculate the F NMR chemical shielding for solid state alkali-metal fluorides MF MsLi, Na, K, Rb.using gauge-independent atomic orbitals (GIAO) at Hartree–Fock (HF) and density functional theory DFT.levels, respectively. The results agree with those measured experimentally, in particular when the relative deviations within the same series are considered. Our results reveal that the variation of chemical shielding from LiF to RbF correlates well with a combined effect from the lattice factor Ry2 and the valency factor Q+Q-

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.

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.

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.