Spectral densities and nuclear spin relaxation in solids

Beckmann, Peter A.

doi:10.1016/0370-1573(88)90073-7

Cited by 253 publications

(236 citation statements)

References 134 publications

(195 reference statements)

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“…The simplest model that involves this parameter is the Davidson-Cole spectral density which finds widespread use in the modeling of both nuclear spin relaxation and dielectric relaxation experiments [7]. One interpretation of this model is that there is a distribution of reorientational barriers with the additional parameter characterizing the width of the The general model of nuclear spin relaxation for spin-1/2 systems, the BlochWangsness-Redfield model [4,[11][12][13][14], which provides the basic relaxation equations, is very robust.…”

Section: Discussionmentioning

confidence: 99%

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Methyl and t-butyl reorientation in an organic molecular solid

Beckmann¹,

Dougherty²,

Kassel³

2009

Solid State Nuclear Magnetic Resonance

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We have determined the molecular and crystal structure of 4,5-dibromo-2,7-di-tbutyl-9,9-dimethylxanthene and measured the 1 H spin-lattice relaxation rate from 87 to 270 K at NMR frequencies of /2 = 8.50, 22.5, and 53.0 MHz. All molecules in the crystal see the same intra and intermolecular environment and the repeating unit is half a molecule. We have extended models developed for 1 H spin-lattice relaxation resulting from the reorientation of a t-butyl group and its constituent methyl groups to include these rotors and the 9-methyl groups. The relaxation rate data is well-fitted assuming that the t-butyl groups and all three of their constituent methyl groups, as well as the 9-methyl groups all reorient with an NMR activation energy of 15.8 ± 1.6 kJ mole . Only intramethyl and intra-t-butyl intermethyl spinspin interactions need be considered. A unique random-motion Debye (or BPP) spectral density will not fit the data for any reasonable choice of parameters. A distribution of activation energies is required.

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Section: Discussionmentioning

confidence: 99%

“…There are, then, three mean times between hops in the perfect crystal; If all molecules are truly equivalent (as suggested by the X-ray study, which uses a small single crystal), then the correlation functions for the three motions will be g(t, [7],…”

Section: Spin-lattice Relaxation Theory Reviewmentioning

confidence: 99%

Methyl and t-butyl reorientation in an organic molecular solid

Beckmann¹,

Dougherty²,

Kassel³

2009

Solid State Nuclear Magnetic Resonance

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“…J(ω, τ ) is the spectral density, 54 which can be interpreted conceptually as the distribution of methyl group rotation (angular) frequencies, ω, with τ −1 being the mean (angular) frequency. This frequency ω/2π is not to be confused with the NMR frequency ω 0 /2π .…”

Section: Theoretical Expressions For the Relaxation Rate And The Omentioning

confidence: 99%

“…The simplest random hopping motion models for an ensemble of methyl rotors all characterized by the same environment and therefore by the same NMR activation energy, E NMR , predicts that J(ω, τ ) is given by the Debye (or Poisson or Bloembergen-Purcell-Pound) spectral density 31,32,54 …”

Section: Theoretical Expressions For the Relaxation Rate And The Omentioning

confidence: 99%

Methyl group rotation, 1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation

Beckmann

Schneider

2012

The Journal of Chemical Physics

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We report 1 H spin-lattice relaxation measurements in polycrystalline 4,4 -dimethoxybiphenyl at temperatures between 80 and 300 K at NMR frequencies of ω 0 /2π = 8.50, 22.5, and 53.0 MHz. The data are interpreted in terms of the simplest possible Bloch-Wangsness-Redfield methyl group hopping model. Different solid states are observed at low temperatures. The 1 H spin-lattice relaxation is nonexponential at higher temperatures where a stretched-exponential function fits the data very well, but this approach is phenomenological and not amenable to theoretical interpretation. (We provide a brief literature review of the stretched-exponential function.) The Bloch-Wangsness-Redfield model applies only to the relaxation rate that characterizes the initial 1 H magnetization decay in a high-temperature nonexponential 1 H spin-lattice relaxation measurement. A detailed procedure for determining this initial relaxation rate is described since large systematic errors can result if this is not done carefully.

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“…(19) First, note that the length is not defined by κ850, such that a n must be determined separately.…”

Section: A Two Relaxation Rate Constantsmentioning

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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Spectral densities and nuclear spin relaxation in solids

Cited by 253 publications

References 134 publications

Methyl and t-butyl reorientation in an organic molecular solid

Methyl and t-butyl reorientation in an organic molecular solid

Methyl group rotation, 1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation

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

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