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The homonuclear dipolar coupling is the internal spin interaction that contributes the most to the line shapes in magic-angle-spinning (MAS) H-1 NMR spectra of solids, and linewidths typically extend over several hundred Hertz, limiting the H-1 resolution. Understanding and reducing this contribution could provide rich structural information for organic solids. Here, we use average Hamiltonian theory to study two- and three-spin systems in the fast MAS regime. Specifically, we develop analytical expressions to third order in the case of two and three inequivalent spins (I = 1/2). The results show that the full third-order expression of the Hamiltonian, without secular approximations or truncation to second order, is the description that agrees the best, by far, with full numerical calculations. We determine the effect on the NMR spectrum of the different Hamiltonian terms, which are shown to produce both residual shifts and splittings in the three-spin systems. Both the shifts and splittings have a fairly complex dependence on the spinning rate with the eigenstates having a polynomial.r dependence. The effect on powder line shapes is also shown, and we find that the anisotropic residual shift does not have zero average so that the powder line shape is broadened and shifted from the isotropic position. This suggests that in H-1 MAS spectra, even at the fastest MAS rates attainable today, the positions observed are not exactly the isotropic shifts. (c) 2021 Author(s).

The work presented here aims at understanding the performance of phase modulated heteronuclear decoupling sequences such as Cosine Modulation or Two Pulse Phase Modulation. To that end we provide an analytical description of the intrinsic behavior of Cosine Modulation decoupling with respect to radio-frequency-inhomogeneity and the proton-proton dipolar coupling network. We discover through a Modulation Frame average Hamiltonian analysis that best decoupling is obtained under conditions where the heteronuclear interactions are removed but notably where homonuclear couplings are recoupled at a homonuclear Rotary Resonance (HORROR) condition in the Modulation Frame. These conclusions are supported by extensive experimental investigations, and notably through the introduction of proton nutation experiments to characterize spin dynamics in solids under decoupling conditions. The theoretical framework presented in this paper allows the prediction of the optimum parameters for a given set of experimental conditions. (C) 2004 American Institute of Physics.

The theory describing nuclear cross-polarization from a spin-1 to spin-1/2 is generalized to sweeps of the radio-frequency field amplitude. This allows efficient cross-polarization over the entire width of the deuterium NMR spectrum of partially oriented systems, such as liquid crystals. Such experiments permit the assignment and measurement of the deuterium quadrupolar couplings, and hence the quantification of the order parameters which characterize the dynamics of such systems. The evolution of the spin system can be understood in terms of individual quasiadiabatic population exchanges, allowing the prediction of the effects of the various experimental parameters on the efficiency of cross-polarization. (C) 1998 American Institute of Physics.

The accuracy of determination of tensor parameters measured using solid-state nuclear magnetic resonance is investigated. In particular, the reliability of the determination of the anisotropy and the asymmetry parameter of the chemical shift is calculated using the Cramer-Rao lower bounds. Minimizing this measure of the error as a function of an experimental parameter (in this case the spinning speed of the sample) enables the optimization of any given experiment. Hence, an optimum number of sidebands is found for which the determination of the anisotropy is most reliable. Comparision to the static limit shows that the reliability of the determination of the anisotropy is always greater in spinning experiments than in static experiments. An analogous analysis for the asymmetry parameter shows it to be consistently more reliably determined from a static spectrum. The sensitivity of the fitting to the simulation algorithm is found to become pronounced with slower speeds and static spectra, and a discussion of such systematic errors is provided. The reliability of the determination of dipolar or first-order quadrupolar tensors is also calculated, and we find that this presents a surprisingly different situation to that of the chemical shift. (C) 1997 American Institute of Physics.

Experimental and theoretical aspects of carbon-13 line shapes in static solids are described for on-resonance spin decoupling conditions. A relatively simple theoretical approach is provided for describing line shapes in static solids based on an operator representation of static second-order perturbation theory and theoretical line shapes in I2S and InS systems are calculated. The line shapes are predicted to comprise a single center line and `'decoupling sidebands'' on each side of the center line which move outward and diminish in amplitude as the decoupling field is increased. The predicted behavior is confirmed by experiments on an isolated seven spin system, where the decoupling sidebands are observed directly, and some organic solids in which the decoupling sidebands are not observed directly but in which their presence can be deduced from the behavior of the center line. A comparison is made between the theoretical predictions based on a complete quantum mechanical treatment and the predictions made using classical approximations in the model for the line shape. We conclude, based on our experimental results, that the line shape has a character which reflects the quantum nature of the spin system, even it? organic solids, and that on-resonance terms appear to dominate experimental line shapes. (C) 1996 American Institute of Physics.

Slow, large-amplitude chain motions play an important role in determining the macroscopic mechanical properties of polymers. Although such motions have been studied quantitatively by two-dimensional (2D) nuclear: magnetic resonance (NMR) exchange experiments, overlapping anisotropic patterns hamper spectral analysis, and limit applications. Variable angle correlation spectroscopy (VACSY) has proven useful in resolving such problems for rapidly spinning samples by separating anisotropic spectral patterns according to isotropic chemical shifts. In a previous study [J. Am. Chem. Sec. 115, 4825 (1993)], we described a three-dimensional (3D) NMR experiment that incorporates; the VACSY method and a hop of the rotor axis to correlate the isotropic chemical shifts to 2D anisotropic exchange patterns. The hop of the rotor axis, however, presents experimental difficulties and limits the range of motional rates that may be studied. We present in this paper a new 3D VACSY exchange experiment that obtains the same correlations without the need for the rotor axis hop. A series of 2D exchange spectra are recorded with the sample spinning at different rotation axis angles.' Then using the scaling of the anisotropic frequency at the different angles, we construct the data onto a 3D matrix so that a Fourier transformation directly yields the desired correlations. The technique is applied to C-13 exchange NMR to study the slow molecular motion of ordered isotactic polypropylene.

We explain how and under which conditions it is possible to obtain an efficient inversion of an entire sideband family of several hundred kHz using low-power, sideband-selective adiabatic pulses, and we illustrate with some experimental results how this framework opens new avenues in solid-state NMR for manipulating spin systems with wide spinning-sideband (SSB) manifolds. This is achieved through the definition of the criteria of phase and amplitude modulation for designing an adiabatic inversion pulse for rotating solids. In turn, this is based on a framework for representing the Hamiltonian of the spin system in an NMR experiment under magic angle spinning (MAS). Following earlier ideas from Caravatti et al. [J. Magn. Reson. 55, 88 (1983)], the so-called ``jolting frame'' is used, which is the interaction frame of the anisotropic interaction giving rise to the SSB manifold. In the jolting frame, the shift modulation affecting the nuclear spin is removed, while the Hamiltonian corresponding to the RF field is frequency modulated and acquires a spinning-sideband pattern, specific for each crystallite orientation. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3521491]

Adiabaticity plays a central role in modern magnetic resonance experiments, as excitations with adiabatic Hamiltonians allow precise control of the dynamics of the spin states during the course of an experiment. Surprisingly, many commonly used adiabatic processes in magnetic resonance perform well even though the adiabatic approximation does not appear to hold throughout the process. Here we show that this discrepancy can now be explained through the use of Berry's superadiabatic formalism, which provides a framework for including the finite duration of the process in the theoretical and numerical treatments. In this approach, a slow, but finite time-dependent Hamiltonian is iteratively transformed into time-dependent diagonal frames until the most accurate adiabatic approximation is obtained. In the case of magnetic resonance, the magnetization during an adiabatic process of finite duration is not locked to the effective Hamiltonian in the conventional adiabatic frame, but rather to an effective Hamiltonian in a superadiabatic frame. Only in the superadiabatic frame can the true validity of the adiabatic approximation be evaluated, as the inertial forces acting in this frame are the true cause for deviation from adiabaticity and loss of control during the process. Here we present a brief theoretical background of superadiabaticity and illustrate the concept in the context of magnetic resonance with commonly used shaped radio-frequency pulses.