Second-order dipolar order in magic-angle spinning nuclear magnetic resonance

Sensitivity Enhancement of Ultra-Wideline NMR by Progressive Saturation of the Proton Reservoir Under Magic-Angle Spinning

Solid-state NMR of low-γ nuclides is often characterized by low sensitivity and by significant spectral broadenings induced by the quadrupolar and the chemical-shift anisotropy interactions. Herein, we introduce an indirect acquisition method, termed PROgressive Saturation of the Proton Reservoir Under Spinning (PROSPRUS), which could facilitate the acquisition of ultra-wideline NMR spectra under magic-angle spinning (MAS), in systems with a sufficiently long dipolar relaxation time, T1D. PROSPRUS NMR relies on the generation of so-called second-order dipolar order among abundant protons undergoing MAS, and on the subsequent depletion of this dipolar order by a series of looped cross-polarization events, transferring the proton order into polarization of the low-γ I-nuclei as a function of the latter's offsets. While the spin dynamics of the ensuing experiment is complex, particularly when dealing with narrow I spectral lines, it is shown that PROSPRUS can lead to faithful lineshapes for ultra-wideline spin-1/2 and spin-1 species, providing high sensitivity with extremely low RF power requirements. It is also shown that the ensuing 1H-detected PROSPRUS experiments can efficiently characterize I-spin lineshapes in excess of 1 MHz without having to retune electronics, while providing improvements in sensitivity per unit time over current broadband direct-detection methods by up to a factor of four.

Continuous Floquet theory in solid-state NMR

This article presents the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR). Continuous Floquet theory extends the traditional Floquet theory to non-continuous Hamiltonians, enabling the description of observable effects not fully captured by the traditional Floquet theory due to its requirement for a periodic Hamiltonian. We present closed-form expressions for computing first- and second-order effective Hamiltonians, streamlining integration with the traditional Floquet theory and facilitating application in NMR experiments featuring multiple modulation frequencies. Subsequently, we show examples of the practical application of continuous Floquet theory by investigating several solid-state NMR experiments. These examples illustrate the importance of the duration of the pulse scheme regarding the width of the resonance conditions and the near-resonance behavior.

Sensitivity Enhancement by Progressive Saturation of the Proton Reservoir: A Solid-State NMR Analogue of Chemical Exchange Saturation Transfer

Chemical exchange saturation transfer (CEST) enhances solution-state NMR signals of labile and otherwise invisible chemical sites, by indirectly detecting their signatures as a highly magnified saturation of an abundant resonance─for instance, the 1H resonance of water. Stimulated by this sensitivity magnification, this study presents PROgressive Saturation of the Proton Reservoir (PROSPR), a method for enhancing the NMR sensitivity of dilute heteronuclei in static solids. PROSPR aims at using these heteronuclei to progressively deplete the abundant 1H polarization found in most organic and several inorganic solids, and implements this 1H signal depletion in a manner that reflects the spectral intensities of the heteronuclei as a function of their chemical shifts or quadrupolar offsets. To achieve this, PROSPR uses a looped cross-polarization scheme that repeatedly depletes 1H-1H local dipolar order and then relays this saturation throughout the full 1H reservoir via spin-diffusion processes that act as analogues of chemical exchanges in the CEST experiment. Repeating this cross-polarization/spin-diffusion procedure multiple times results in an effective magnification of each heteronucleus's response that, when repeated in a frequency-stepped fashion, indirectly maps their NMR spectrum as sizable attenuations of the abundant 1H NMR signal. Experimental PROSPR examples demonstrate that, in this fashion, faithful wideline NMR spectra can be obtained. These 1H-detected heteronuclear NMR spectra can have their sensitivity enhanced by orders of magnitude in comparison to optimized direct-detect experiments targeting unreceptive nuclei at low natural abundance, using modest hardware requirements and conventional NMR equipment at room temperature.

Protonation tuned dipolar order mediated 1H→13C cross-polarization for dissolution-dynamic nuclear polarization experiments

A strategy of dipolar order mediated nuclear spin polarization transfer has recently been combined with dissolution-dynamic nuclear polarization (dDNP) and improved by employing optimized shaped radiofrequency pulses and suitable molecular modifications. In the context of dDNP experiments, this offers a promising means of transferring polarization from high-gamma ¹H spins to insensitive ¹³C spins with lower peak power and lower energy compared with state-of-the-art cross-polarization schemes. The role of local molecular groups and the glassing matrix protonation level are both postulated to play a key role in the polarization transfer pathway via an intermediary reservoir of dipolar spin order. To gain appreciation of the mechanisms involved in the dipolar order mediated polarization transfer under dDNP conditions, we investigate herein the influence of the pivotal characteristics of the sample makeup: (i) revising the protonation level for the constituents of the DNP glass; and (ii) utilizing deuterated molecular derivatives. Experimental demonstrations are presented for the case of [1-¹³C]sodium acetate. We find that the proton sample molarity has a large impact on both the optimal parameters and the performance of the dipolar order mediated cross-polarization sequence, with the ¹³C signal build-up time drastically shortened in the case of high solvent protonation levels. In the case of a deuterated molecular derivative, we observe that the nearby ²H substituted methyl group is deleterious to the ¹H→¹³C transfer phenomenon (particularly at low levels of sample protonation). Overall, increased solvent protonation makes the dipolar order governed polarization transfer significantly faster and more efficient. This study sheds light on the influential sample formulation traits which govern the dipolar order-controlled transfer of polarization and indicates that the polarization transfer efficiencies of deuterated molecules can be boosted and reach high performances simply by adequate solvent protonation.

Floquet theory in magnetic resonance: Formalism and applications

Floquet theory is an elegant mathematical formalism originally developed to solve time-dependent differential equations. Besides other fields, it has found applications in optical spectroscopy and nuclear magnetic resonance (NMR). This review attempts to give a perspective of the Floquet formalism as applied in NMR and shows how it allows one to solve various problems with a focus on solid-state NMR. We include both matrix- and operator-based approaches. We discuss different problems where the Hamiltonian changes with time in a periodic way. Such situations occur, for example, in solid-state NMR experiments where the time dependence of the Hamiltonian originates either from magic-angle spinning or from the application of amplitude- or phase-modulated radiofrequency fields, or from both. Specific cases include multiple-quantum and multiple-frequency excitation schemes. In all these cases, Floquet analysis allows one to define an effective Hamiltonian and, moreover, to treat cases that cannot be described by the more popularly used and simpler-looking average Hamiltonian theory based on the Magnus expansion. An important example is given by spin dynamics originating from multiple-quantum phenomena (level crossings). We show that the Floquet formalism is a very general approach for solving diverse problems in spectroscopy.

Quantum irreversible decoherence behaviour in open quantum systems with few degrees of freedom: application to 1H NMR reversion experiments in nematic liquid crystals

An experimental study of NMR spin decoherence in nematic liquid crystals is presented. Decoherence dynamics can be put in evidence by means of refocusing experiments of the dipolar interactions. The experimental technique used in this work is based on the MREV8 pulse sequence. The aim of the work is to detect the main features of the irreversible quantum decoherence in liquid crystals, on the basis of the theory presented by the authors recently. The focus is laid on experimentally probing the eigen-selection process in the intermediate time scale, between quantum interference of a closed system and thermalization, as a signature of the quantum spin decoherence of the open quantum system, as well as on quantifying the effects of non-idealities as possible sources of signal decays which could mask the intrinsic decoherence. In order to contrast experiment and theory, the theory was adapted to obtain the decoherence function corresponding to the MREV8 reversion experiments. Non-idealities of the experimental setting, like external field inhomogeneity, pulse misadjustments, and the presence of non-reverted spin interaction terms are analysed in detail within this framework, and their effects on the observed signal decay are numerically estimated. It is found that though all these non-idealities could in principle affect the evolution of the spin dynamics, their influence can be mitigated and they do not present the characteristic behaviour of the irreversible spin decoherence. As unique characteristic of decoherence, the experimental results clearly show the occurrence of eigen-selectivity in the intermediate timescale, in complete agreement with the theoretical predictions. We conclude that the eigen-selection effect is the fingerprint of decoherence associated with a quantum open spin system in liquid crystals. Besides, these features of the results account for the quasi-equilibrium states of the spin system, which were observed previously in these mesophases, and lead to conclude that the quasi-equilibrium is a definite stage of the spin dynamics during its evolution towards equilibrium.