Photochemical pump and NMR probe : Chemically created NMR coherence on a microsecond time scale

We report pump-probe experiments employing laser-synchronized reactions of para-hydrogen (para-H2) with transition metal dihydride complexes in conjunction with nuclear magnetic resonance (NMR) detection. The pump-probe experiment consists of a single nanosecond laser pump pulse followed, after a precisely defined delay, by a single radio frequency (rf) probe pulse. Laser irradiation eliminates H2 from either Ru(PPh3) 3(CO)(H)2 1 or cis-Ru(dppe)2(H)2 2 in C6D6 solution. Reaction with para-H2 then regenerates 1 and 2 in a well-defined nuclear spin state. The rf probe pulse produces a high-resolution, single-scan 1H NMR spectrum that can be recorded after a pump-probe delay of just 10 μs. The evolution of the spectra can be followed as the pump-probe delay is increased by micro- or millisecond increments. Due to the sensitivity of this para-H2 experiment, the resulting NMR spectra can have hydride signal-to-noise ratios exceeding 750:1. The spectra of 1 oscillate in amplitude with frequency 1101 ± 3 Hz, the chemical shift difference between the chemically inequivalent hydrides. The corresponding hydride signals of 2 oscillate with frequency 83 ± 5 Hz, which matches the difference between couplings of the hydrides to the equatorial 31P nuclei. We use the product operator formalism to show that this oscillatory behavior arises from a magnetic coherence in the plane orthogonal to the magnetic field that is generated by use of the laser pulse without rf initialization. In addition, we demonstrate how chemical shift imaging can differentiate the region of laser irradiation thereby distinguishing between thermal and photochemical reactivity within the NMR tube

Coherent evolution of parahydrogen induced polarisation using laser pump, NMR probe spectroscopy : Theoretical framework and experimental observation

We recently reported a pump-probe method that uses a single laser pulse to introduce parahydrogen (p-H2) into a metal dihydride complex and then follows the time-evolution of the p-H2-derived nuclear spin states by NMR. We present here a theoretical framework to describe the oscillatory behaviour of the resultant hyperpolarised NMR signals using a product operator formalism. We consider the cases where the p-H2-derived protons form part of an AX, AXY, AXYZ or AA′XX′ spin system in the product molecule. We use this framework to predict the patterns for 2D pump-probe NMR spectra, where the indirect dimension represents the evolution during the pump-probe delay and the positions of the cross-peaks depend on the difference in chemical shift of the p-H2-derived protons and the difference in their couplings to other nuclei. The evolution of the NMR signals of the p-H2-derived protons, as well as the transfer of hyperpolarisation to other NMR-active nuclei in the product, is described. The theoretical framework is tested experimentally for a set of ruthenium dihydride complexes representing the different spin systems. Theoretical predictions and experimental results agree to within experimental error for all features of the hyperpolarised 1H and 31P pump-probe NMR spectra. Thus we establish the laser pump, NMR probe approach as a robust way to directly observe and quantitatively analyse the coherent evolution of p-H2-derived spin order over micro-to-millisecond timescales

Improved Phase-Modulated Homonuclear Dipolar Decoupling for Solid-State NMR Spectroscopy from Symmetry Considerations

We explore the effects of symmetry on the performance of phase-modulated homonuclear dipolar decoupling in H-1 solid-state NMR. We demonstrate that the symmetry of the DUMBO family of decoupling sequences is the result of two well-defined symmetry expansions. The first is an antipalindromic expansion that arises from the symmetrization step that was built into the original architecture of the DUMBO sequence. The second is a mirror-pair expansion that inverts the sign of the phase modulation in the second half of the pulse sequence relative to the first. The combination of these two symmetry expansions generates a sequence of four Lee-Goldburg-type rotations in the rotating frame. The axes of rotation, oriented at the magic angle, are separated in the transverse plane by 2 alpha, where alpha is chosen to minimize the sensitivity of the sequence to instrument imperfections such as rf inhomogeneity. The efficiency of the DUMBO symmetry for decoupling is demonstrated experimentally, and the effect of the alpha-phase-shift parameter is investigated. A new decoupling sequence (LG4) that combines the DUMBO symmetry with alpha = 55 degrees is introduced and is shown to produce very efficient decoupling as well as a nearly 2-fold increase in coherence lifetimes when compared to standard PMLG/FSLG decoupling

A common theory for phase-modulated homonuclear decoupling in solid-state NMR

We propose a new framework for homonuclear dipolar decoupling in solid-state NMR that provides a theoretical link between the FSLG, PMLG and DUMBO families. We show that through the use of a Legendre polynomial basis, the phase modulation of these decoupling schemes can be described by the same set of parameters, permitting for the first time a direct theoretical comparison between these methods. Use of this common basis reveals that the central decoupling mechanism is the same for DUMBO and FSLG/PMLG and that a similar vector picture can be used to describe both methods. In addition to the common root of decoupling efficiency, this new analysis highlights two major points of difference between the methods. First, the DUMBO phase modulation consists not only of a linear change in phase with time a la PMLG but also smaller high-order oscillations, which act to improve line-narrowing performance. Second, we show how the DUMBO phase waveforms are generated from a four-step permutation of a single asymmetric unit, in contrast to the two-step permutation of PMLG. Numerical simulations and experimental results suggest that this latter point of difference is responsible for the superior performance of DUMBO in the presence of significant RF inhomogeneity

High-Resolution H-1 Solid-State NMR Spectroscopy Using Windowed LG4 Homonuclear Dipolar Decoupling

We investigate the optimal implementation of windowed LG4 decoupling for the direct acquisition of high-resolution H-1 solid-state NMR spectra in the moderate magic-angle spinning regime ((r)<2 x 35kHz). We determine how the optimal value of the azimuth of the LG rotation axis, , is affected by the choice of windowing parameters. We find that for both the windowless and windowed implementation of LG4, the optimal value of is that for which the chemical-shift scaling factor is approximately 0.43. We then provide an analytical expression for estimating the chemical-shift scaling factor as a function of both and the windowed decoupling parameters, which allows the optimal value of to be easily determined for any implementation of LG4. We also introduce a simple and general method for improving the performance of any phase-modulated homonuclear dipolar decoupling sequence by compensating for pulse imperfection errors that accumulate in windowed spectra due to the repeated switching of the RF irradiation. This method involves the introduction of short (<0.5 mu s) compensation pulses at the start and end of each decoupling pulse, the duration and phase of which are chosen to cancel the effects of the amplitude and phase transients that arise as a result of the RF switching. We demonstrate how this method can be implemented for homonuclear dipolar decoupling sequences such as wPMLG and wLG4 to reduce the chemical-shift scaling factor distortions generated by phase transients such that high-quality, high-resolution H-1 NMR spectra can be acquired at arbitrary RF offsets

Quasi-equilibria in reduced Liouville spaces

International audienceThe quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed

Improved Phase-Modulated Homonuclear Dipolar Decoupling for Solid-State NMR Spectroscopy from Symmetry Considerations

We explore the effects of symmetry on the performance of phase-modulated homonuclear dipolar decoupling in ¹H solid-state NMR. We demonstrate that the symmetry of the DUMBO family of decoupling sequences is the result of two well-defined symmetry expansions. The first is an antipalindromic expansion that arises from the symmetrization step that was built into the original architecture of the DUMBO sequence. The second is a mirror-pair expansion that inverts the sign of the phase modulation in the second half of the pulse sequence relative to the first. The combination of these two symmetry expansions generates a sequence of four Lee–Goldburg-type rotations in the rotating frame. The axes of rotation, oriented at the magic angle, are separated in the transverse plane by 2α, where α is chosen to minimize the sensitivity of the sequence to instrument imperfections such as rf inhomogeneity. The efficiency of the DUMBO symmetry for decoupling is demonstrated experimentally, and the effect of the α-phase-shift parameter is investigated. A new decoupling sequence (LG4) that combines the DUMBO symmetry with α = 55° is introduced and is shown to produce very efficient decoupling as well as a nearly 2-fold increase in coherence lifetimes when compared to standard PMLG/FSLG decoupling

Quasi-equilibria in reduced Liouville spaces

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4726162

Protein dynamics. Direct observation of hierarchical protein dynamics.

International audienceOne of the fundamental challenges of physical biology is to understand the relationship between protein dynamics and function. At physiological temperatures, functional motions arise from the complex interplay of thermal motions of proteins and their environments. Here, we determine the hierarchy in the protein conformational energy landscape that underlies these motions, based on a series of temperature-dependent magic-angle spinning multinuclear nuclear-magnetic-resonance relaxation measurements in a hydrated nanocrystalline protein. The results support strong coupling between protein and solvent dynamics above 160 kelvin, with fast solvent motions, slow protein side-chain motions, and fast protein backbone motions being activated consecutively. Low activation energy, small-amplitude local motions dominate at low temperatures, with larger-amplitude, anisotropic, and functionally relevant motions involving entire peptide units becoming dominant at temperatures above 220 kelvin

Macroscopic nuclear spin diffusion constants of rotating polycrystalline solids from first-principles simulation

A method for quantitatively calculating nuclear spin diffusion constants directly from crystal structures is introduced. This approach uses the first-principles low-order correlations in Liouville space (LCL) method to simulate spin diffusion in a box, starting from atomic geometry and including both magic-angle spinning (MAS) and powder averaging. The LCL simulations are fit to the 3D diffusion equation to extract quantitative nuclear spin diffusion constants. We demonstrate this method for the case of H-1 spin diffusion in ice and L-histidine, obtaining diffusion constants that are consistent with literature values for H-1 spin diffusion in polymers and that follow the expected trends with respect to magic-angle spinning rate and the density of nuclear spins. In addition, we show that this method can be used to model C-13 spin diffusion in diamond and therefore has the potential to provide insight into applications such as the transport of polarization in non-protonated systems. (C) 2015 Elsevier Inc. All rights reserved