Operator-based Floquet theory in solid-state NMR

Scholz, Ingo; Beek, Jacco D. van; Ernst, Matthias

doi:10.1016/j.ssnmr.2010.04.003

Cited by 113 publications

(102 citation statements)

References 81 publications

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“…For example the averaging of anisotropic interactions by MAS can partly be cancelled by dynamic processes [75,76]. Interference between MAS and RF irradiation is extensively used in solid-state NMR to generate effective Hamiltonians during selected time periods of experiments [77][78][79][80]. Such recoupling processes may be altered by a stochastic dynamics on the same time scale [81,82].…”

Section: Challenges For Measuring Relaxation Parameters In Solidsmentioning

confidence: 99%

“…This is mainly the case for quadrupolar couplings which are often much larger than typical spinning frequencies. For dipolar-coupling and CSA interactions, measuring anisotropic interactions under MAS often requires a recoupling sequence [77][78][79][80], which reintroduces the interaction that is otherwise averaged by MAS in first order on the time scale of τ r . The recoupling can be seen as an interference between two time-dependent processes, the sample rotation and the pulse sequence.…”

Section: Measurements Of Anisotropic Interactions Under Mas Can Be Domentioning

confidence: 99%

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

Schanda

Ernst

2016

Progress in Nuclear Magnetic Resonance Spectroscopy

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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: Challenges For Measuring Relaxation Parameters In Solidsmentioning

confidence: 99%

Section: Measurements Of Anisotropic Interactions Under Mas Can Be Domentioning

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

Self Cite

198

295

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“…The eigenvectors only modify the transition amplitudes and can be ignored in the strong decoupling limit. 32 In common with recent theoretical analyses of heteronuclear decoupling, [33][34][35][36] we use Floquet theory to express the time-dependent Hamiltonian in non-time-dependent form.…”

Section: A Observation Via Heteronucleusmentioning

confidence: 99%

Unexpected effects of third-order cross-terms in heteronuclear spin systems under simultaneous radio-frequency irradiation and magic-angle spinning NMR

Tatton

Frantsuzov

Brown

et al. 2012

The Journal of Chemical Physics

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(2012) 'Unexpected e ects of third-order cross-terms in heteronuclear spin systems under simultaneous radio-frequency irradiation and magic-angle spinning NMR. ', Journal of chemical physics., 136 (8). 084503.Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

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“…The efficiency plot is obtained by carrying out the numerical integrator with different time steps, corresponding to different numbers of evaluations of ( ) H t . However, AHT is not applicable to Hamiltonians with multiple basic frequencies: MAS and radiofrequency irradiation must be synchronized or time-scale separated, multiple irradiations must be synchronized or time-scale separated [79] [80]. Our recent validation of the AHT method probed with quadrupolar nuclei showed that the AHT method becomes less efficient to predict the dynamics of the spin system as the quadrupolar spin nuclei dimension increase [75].…”

Section: Average Hamiltonian Theorymentioning

confidence: 99%

“…This theory provides a more general approach to AHT and has been applied satisfactorily to study important NMR phenomena [79] [80] [83]. The theory delineates the finite-dimensional time-dependent Liouville space onto an infinite-dimensional but time-independent Floquet space.…”

Section: Floquet Theorymentioning

confidence: 99%

Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

Mananga¹,

Moghaddasi²,

Sana³

et al. 2015

WJNST

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This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance in particular. Methods of these expansion schemes used as numerical integrators for solving the time dependent Schrodinger equation are presented. The action of their propagator operators is also presented. We highlight potential future theoretical and numerical directions such as the time propagation calculated by Chebychev expansion of the time evolution operators and an interesting transformation called the Cayley method.

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Operator-based Floquet theory in solid-state NMR

Cited by 113 publications

References 81 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

Unexpected effects of third-order cross-terms in heteronuclear spin systems under simultaneous radio-frequency irradiation and magic-angle spinning NMR

Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

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