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Heteronuclear spin decoupling is a highly important component of solid-state NMR experiments to remove undesired coupling interactions between unlike spins for spectral resolution. Recently, experiments using a unification strategy of standard decoupling schemes were presented for high radio-frequency (RF) amplitudes and slow-intermediate magic-angle-spinning (MAS) frequencies, in the pursuit of deeper understanding of spin decoupling under phase-modulated RF irradiation [A. Equbal et al., J. Chem. Phys. 142, 184201 (2015)]. The approach, unified two-pulse heteronuclear decoupling (UTPD), incorporates the simultaneous time- and phase-modulation strategies, commonly used in solid-state NMR. Here, the UTPD based decoupling scheme is extended to the experimentally increasingly important regime of low RF amplitudes and fast MAS frequencies. The unified decoupling approach becomes increasingly effective in identifying the deleterious dipole-dipole and, in particular, J recoupling conditions which become critical for the low-amplitude RF regime. This is because J coupling is isotropic and therefore not averaged out by sample spinning unlike the anisotropic dipole-dipole coupling. Numerical simulations and analytic theory are used to understand the effects of various nuclear spin interactions on the decoupling performance of UTPD, in particular, the crucial difference between the low-phase and high-phase UTPD conditions with respect to J coupling. In the UTPD scheme, when the cycle-frequency of the pulse-sequence is comparable to the RF nutation frequency, the existence of a non-zero effective rotation in the basic two-pulse scheme becomes an essential feature for the efficient and robust averaging out of the scalar J coupling. This broad viewpoint is expected to bring different optimum low-power decoupling pulse schemes under a common footing. [ABSTRACT FROM AUTHOR]

Rotational-Echo DOuble Resonance, REDOR, is an experimentally robust and a well-established dipolar-recoupling technique to measure dipolar couplings between isolated pairs of spin-1/2 heteronuclei in solid-state nuclear magnetic resonance. REDOR can also be used to estimate motional order parameters when the bond distance is known, for example, in the case of directly bound nuclei. However, the relatively fast dipolar dephasing for strongly coupled spin-1/2 pairs, such as 13C–1H, makes the stroboscopic measurement required in this experiment challenging, even at fast Magic-Angle-Spinning (MAS) frequencies. In such cases, modified REDOR-based methods like Shifted-REDOR (S-REDOR) are used to scale the dipolar coupling compared to REDOR. This is achieved by changing the position of one of the two recoupling π-pulses in a rotor period. This feature, however, comes at the cost of mixing multiple Fourier components of the dipolar coupling and can, additionally, require high radio-frequency amplitudes to realise small scaling factors. We introduce here a general pulse scheme which involves shifting both the π pulses in the REDOR scheme to achieve arbitrary scaling factors whilst retaining the robustness and simplicity of REDOR recoupling and avoiding the disadvantages of S-REDOR. The classical REDOR is a specific case of this scheme with a scaling factor of one. We demonstrate the results on isolated 13C–15N and 1H–13C spin pairs at 20 and 62.5 kHz MAS, respectively. [ABSTRACT FROM AUTHOR]

Pulse imperfections like pulse transients and radio-frequency field maladjustment or inhomogeneity are the main sources of performance degradation and limited reproducibility in solid-state nuclear magnetic resonance experiments.We quantitatively analyze the influence of such imperfections on the performance of symmetry-based pulse sequences and describe how they can be compensated. Based on a triple-mode Floquet analysis, we develop a theoretical description of symmetry-based dipolar recoupling sequences, in particular, R2611 4 , calculating first and second-order effective Hamiltonians using real pulse shapes. We discuss the various origins of effective fields, namely, pulse transients, deviation from the ideal flip angle, and fictitious fields, and develop strategies to counteract them for the restoration of full transfer efficiency. We compare experimental applications of transientcompensated pulses and an asynchronous implementation of the sequence to a supercycle, SR26, which is known to be efficient in compensating higher-order error terms. We are able to show the superiority of R26 compared to the supercycle, SR26, given the ability to reduce experimental error on the pulse sequence by pulse-transient compensation and a complete theoretical understanding of the sequence. [ABSTRACT FROM AUTHOR]

Rotational-Echo DOuble-Resonance (REDOR) is a versatile experiment for measuring internuclear distance between two heteronuclear spins in solid-state NMR. At slow to intermediate magic-angle spinning (MAS) frequencies, the measurement of distances between strongly coupled spins is challenging due to rapid dephasing of magnetisation. This problem can be remedied by employing the pulse-shifted version of REDOR known as Shifted-REDOR (S-REDOR) that scales down the recoupled dipolar coupling. In this study, we propose a new variant of the REDOR sequence where the positions of the Л pulses are determined by a sine-squared function. This new variant has scaling properties similar to S-REDOR. We use theory, numerical simulations and experiments to compare the dipolar recoupling efficiencies and the experimental robustness of the three REDOR schemes. The proposed variant has advantages in terms of radiofrequency field requirements at fast MAS frequencies. [ABSTRACT FROM AUTHOR]

We present a general theoretical description that allows us to describe the influence of isotropic chemical shift in homonuclear and heteronuclear dipolar recoupling experiments in magic-angle-spinning solid-state NMR. Through a transformation of the Hamiltonian into an interaction frame with the combined radio-frequency irradiation and the isotropic chemical shift, we determine an effective Hamiltonian to first order with respect to the relevant internal nuclear spin interactions. This unravels the essential resonance conditions for efficient dipolar recoupling. Furthermore, we propose how to handle situations where the resonance conditions are not exactly fulfilled. To verify the general theoretical description, we compare numerical simulations using a time-sliced time-dependent Hamiltonian with simulations using the calculated effective Hamiltonian for propagation. The comparisons are exemplified for the homonuclear dipolar recoupling experiments C72¹ and POST-C72¹. [ABSTRACT FROM AUTHOR]

Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient 1H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the ¹H-¹H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of ¹H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme. [ABSTRACT FROM AUTHOR]

A unified strategy of two-pulse based heteronuclear decoupling for solid-state magic-angle spinning nuclear magnetic resonance is presented. The analysis presented here shows that different decoupling sequences like two-pulse phase-modulation (TPPM), X-inverse-X (XiX), and finite pulse refocused continuous wave (rCWA) are basically specific solutions of a more generalized decoupling scheme which incorporates the concept of time-modulation along with phase-modulation. A plethora of other good decoupling conditions apart from the standard, TPPM, XiX, and rCWA decoupling conditions are available from the unified decoupling approach. The importance of combined time- and phasemodulation in order to achieve the best decoupling conditions is delineated. The consequences of different indirect dipolar interactions arising from cross terms comprising of heteronuclear and homonuclear dipolar coupling terms and also those between heteronuclear dipolar coupling and chemicalshift anisotropy terms are presented in order to unfold the effects of anisotropic interactions under different decoupling conditions. Extensive numerical simulation results are corroborated with experiments on standard amino acids. [ABSTRACT FROM AUTHOR]

We here revisit expansion schemes used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators, namely, Magnus, Floquet, and Fer expansions. While all the expansion schemes are powerful methods there are subtle differences among them. To understand the differences, weperformed explicit calculation for heteronuclear dipolar decoupling, cross-polarization, and rotary-resonance experiments in solid-state NMR. As the propagator from the Fer expansion takes the form of a product of sub-propagators, it enables us to appreciate effects of time-evolution under Hamiltonians with different orders separately. While 0th-order average Hamiltonian is the same for the three expansion schemes with the three cases examined, there is a case that the 2nd-order term for the Magnus/Floquet expansion is different from that obtained with the Fer expansion. The difference arises due to the separation of the 0th-order term in the Fer expansion. The separation enables us to appreciate time-evolution under the 0th-order average Hamiltonian, however, for that purpose, we use a so-called left-running Fer expansion. Comparison between the left-running Fer expansion and the Magnus expansion indicates that the sign of the odd orders in Magnus may better be reversed if one would like to consider its effect in order. [ABSTRACT FROM AUTHOR]

We show a theoretical framework, based on triple-mode Floquet theory, to analyze recoupling sequences derived from symmetry-based pulse sequences, which have a non-vanishing effective field and are not rotor synchronized. We analyze the properties of one such sequence, a homonuclear double-quantum recoupling sequence derived from the C7¹2 sequence. The new asynchronous sequence outperforms the rotor-synchronized version for spin pairs with small dipolar couplings in the presence of large chemical-shift anisotropy. The resonance condition of the new sequence is analyzed using triple-mode Floquet theory. Analytical calculations of second-order effective Hamiltonian are performed to compare the efficiency in suppressing second-order cross terms. Experiments and numerical simulations are shown to corroborate the results of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Although the range of photocatalysts with controllable size, shape and morphology has developed in recent years with a large number of silica‐supported TiO2 catalysts, the details of photocatalytic interfaces between nanosilica and TiO2 them and the mechanisms of TiO2 functionalization of silica surfaces are not yet well understood. It is worth mentioning that the understanding of a mechanism from a molecular point of view has always been a challenge in the field of materials science. Here, we probe interfaces in (dendritic fibrous nano‐silica (DFNS) supported TiO2 photocatalysts as well as propose and prove the formation mechanism of the photocatalyst, DFNS/TiO2, by ammonia‐assisted functionalization of DFNS by titanium butoxide (TBOT). The proposed formation mechanism includes the following steps: i) the deprotonation of silica surface (silanols) by ammonia and the hydrolysis of TBOT to titanium hydroxide [Ti(OH)4], ii) the donation of electron lone pair from ammonia to the Ti4+ ion of Ti(OH)4, iii) the release of hydroxide ions, followed by hetero‐condensation of dehydroxylated titanium ions with the deprotonated silanols, generating Si−O−Ti oxobridges, iv) the formation of oxy‐anion of titanols and its reaction with another molecule of ammonia‐activated titanium hydroxide to generate Ti−O−Ti oxobridges, and v) the continuation of the above cycle of steps until the titanium hydroxide precursor is consumed to produce silica supported titanium hydroxide. During thermal treatment, the titanols condense, yielding DFNS/TiO2 photocatalysts. To prove this mechanism, detailed solid‐state 1H, 29Si, 47,49Ti NMR and in situ FTIR studies were carried out, based on which different surface species formed during TiO2 growth on DFNS were identified. This has led to fundamental insights into the reaction of TBOT with DFNS silica surface and interfaces between DFNS and TiO2. The interfaces and formation mechanism of TiO2 photocatalysts supported by dendritic fibrous nanosilica (DFNS) are explored by using detailed solid‐state 1H, 29Si, 47,49Ti NMR and in situ FTIR studies. Different surface species formed during TiO2 growth on DFSN were identified, along with fundamental insights into the reaction of titanium butoxide with the DFNS silica surface and interfaces between DFNS and TiO2. [ABSTRACT FROM AUTHOR]