Spin-Lattice Relaxation in Periodically Perturbed Systems

Haeberlen, Ulrich; Waugh, J. S.

doi:10.1103/physrev.185.420

Cited by 151 publications

(87 citation statements)

References 14 publications

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“…In isotropic liquids, the spectral density functions J(ω) are independent of the values of m but they can differ in solids. Magic-angle spinning leads to a modification of the sampling of the spectral-density functions [63]. In principle, all frequencies are sampled at ω i ±nω r where n can take the values 1 and 2 since most anisotropic interactions in NMR are second-rank tensors.…”

Section: Relaxation In Solidsmentioning

confidence: 99%

Studying dynamics by magic-angle spinning solid-state NMR spectroscopy: Principles and applications to biomolecules

Schanda

Ernst

2016

Progress in Nuclear Magnetic Resonance Spectroscopy

190

295

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Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.

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Section: Relaxation In Solidsmentioning

confidence: 99%

Studying dynamics by magic-angle spinning solid-state NMR spectroscopy: Principles and applications to biomolecules

Schanda

Ernst

2016

Progress in Nuclear Magnetic Resonance Spectroscopy

190

295

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“…5, 6, the decoupling error with the sequences 24s and 48s saturates at around twenty times that for the sequences 8s, 16a, while with τ c = 32τ p and the same B 0 = 0.1/τ p , the decoupling error is comparable to that in Figs. 5,6. Note that these decoupling errors are still small compared to the fidelity loss due to redistribution of the decoherence rates over directions, which for these sequences is identical to that of sequences 8s, 16a with the symmetrizing pulse F 1 [see Fig.…”

Section: Simulationsmentioning

confidence: 69%

“…The approach was to design a decoupling sequence effective for a closed system with the "frozen" bath, where each term in the bath-coupling Hamiltonian H SB [Eq. (5)] is replaced by the corresponding term with a non-zero c-number coefficient in Eq. (3) [e.g.,b α n → B α n ,  α,β n,n ′ → J α,β n,n ′ , etc., with the matching indices.]…”

Section: Model a Hamiltonianmentioning

confidence: 99%

“…Dynamical decoupling [1,2,3] (DD) can be very effective in protecting coherence of a quantum system against low-frequency environment [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. This, combined with low resource requirement, makes it attractive as the first-level coherence protection technique, in combination with quantum error correcting codes [26,27] (QECC).…”

Section: Introductionmentioning

confidence: 99%

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Soft-pulse dynamical decoupling with Markovian decoherence

Pryadko

Quiroz

2009

Phys. Rev. A

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We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape, and for several sequences of π-and π/2-pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal δ-pulses, it can be substantially improved by shaping.

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“…where ωr and ω1 are the MAS frequency and the spin-lock field-strength, in angular-frequency units 21,22 (for a homonuclear spin-pair see 23 ). Although other relaxation experiments are possible, only R1 and R1 ρ data will be used as examples in this study.…”

Section: Relaxation Formalismmentioning

confidence: 99%

Optimized “detectors” for dynamics analysis in solid-state NMR

Smith

Ernst

Meier

2018

The Journal of Chemical Physics

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Relaxation in nuclear magnetic resonance (NMR) results from stochastic motions that modulate anisotropic NMR interactions. Therefore, measurement of relaxation-rate constants can be used to characterize molecular-dynamic processes. The motion is often characterized by Markov processes using an auto-correlation function, which is assumed to be a sum of multiple decaying exponentials. We have recently shown that such a model can lead to severe misrepresentation of the real motion, when the real correlation function is more complex than the model. Furthermore, multiple distributions of motion may yield the same set of dynamics data. Therefore, we introduce optimized dynamics 'detectors' to characterize motions which are linear combinations of relaxation-rate constants. A detector estimates the average or total amplitude of motion for a range of motional correlation times. The information obtained through the detectors is less specific than information obtained using an explicit model, but this is necessary because the information contained in the relaxation data is ambiguous, if one does not know the correct motional model. On the other hand, if one has a molecular dynamics trajectory, one may calculate the corresponding detector responses, allowing direct comparison to experimental NMR dynamics analysis. We describe how to construct a set of optimized detectors for a given set of relaxation measurements. We then investigate the properties of detectors for a number of different data sets, thus gaining insight into the actual information content of the NMR data. Finally, we show an example analysis of Ubiquitin dynamics data using detectors, using the DIFRATE software.2

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Spin-Lattice Relaxation in Periodically Perturbed Systems

Cited by 151 publications

References 14 publications

Studying dynamics by magic-angle spinning solid-state NMR spectroscopy: Principles and applications to biomolecules

Studying dynamics by magic-angle spinning solid-state NMR spectroscopy: Principles and applications to biomolecules

Soft-pulse dynamical decoupling with Markovian decoherence

Optimized “detectors” for dynamics analysis in solid-state NMR

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