NMR relaxation theory

There are many people whom I admire enormously. I ve already mentioned Richard Ernst. Then there is Nicolaas Bloembergen, born in The Netherlands. This man is also phenomenal. Not only did he get the Nobel Prize for nonlinear optics, but as a graduate student he also developed NMR relaxation theory, pretty much from scratch. Considering how little was known at... 

Accurate values of quadrupolar coupling constants (QCC) [40] are essential to link the calculated values of correlation times to experimental relaxation times. Because all the coupling constants in NMR relaxation theory are used as squared, the values should be as correct as possible. 

The fundamentals of NMR relaxation theory have been presented in many places [6-9], and there is no space here to give more than a taste of whaf is involved. The rate of ref urn of a spin system to equilibrium is determined by the time-dependent magnetic fields experienced at each atomic nucleus, arising from molecular motions. The ability of this stochastic, fluctuating field fo induce spin... 

Fischer, M.W.F., Majumdar, A., Zuiderweg, E.R.P. Protein NMR relaxation Theory, applications and outlook. Prog. Nucl. Magn. Reson. Spectrosc. 1998,33,207-72. 

A good introductory treatment of the density operator formalism and two-dimensional NMR spectroscopy, nice presentation of Redfield relaxation theory. 

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

Recent solid state NMR studies of liquid crystalline materials are surveyed. The review deals first with some background information in order to facilitate discussions on various NMR (13C, ll, 21 , I9F etc.) works to be followed. This includes the following spin Hamiltonians, spin relaxation theory, and a survey of recent solid state NMR methods (mainly 13C) for liquid crystals on the one hand, while on the other hand molecular ordering of mesogens and motional models for liquid crystals. NMR studies done since 1997 on both solutes and solvent molecules are discussed. For the latter, thermotropic and lyotropic liquid crystals are included with an emphasis on newly discovered liquid crystalline materials. For the solute studies, both small molecules and weakly ordered biomolecules are briefly surveyed. 

Lauffer RB (1987) Paramagnetic metal complexes as water proton relaxation agents for NMR imaging theory and design. Chem. Rev. 87 901-927. 

Figure 2. Fluorine NMR relaxation times for a sample of Linde molecular sieve 13X containing about 6.6 molecules of SFg per cage O, spin lattice relaxation time , spin-spin relaxation time T2 characterized by exponential decay V and A, T2 characterizedby two relaxation times ticked O, decay as r2. Solid lines are theory to the left of 10Z/T = 6 based on molecular diffusion to the right of 10Z/T controlled by Tu. For dashed lines see text (20)...

Carbon-13 rotating-frame relaxation rate measurements are used to elucidate the mechanism of gas transport in glassy polymers. The nmr relaxation measurements show that antiplasticization-plasticization of a glassy polymer by a low molecular weight additive effects the cooperative main-chain motions of the polymer. The correlation of the diffusion coefficients of gases with the main-chain motions in the polymer-additive blends shows that the diffusion of gases in polymers is controlled by the cooperative motions, thus providing experimental verification of the molecular theory of diffusion. Carbon-13 nmr relaxation... 

Noting the similarity between NMR relaxation and dielectric relaxation effects, Bloembergen, Purcell, and Pound (35) adapted the Debye theory for the latter to the problems of the former to obtain equation (2). 

It is evident that simple theories of molecular motion are not adequate to explain experimental nmr relaxation parameters in certain polymer systems as well as in some highly associated small molecules. As field dependent nmr relaxation studies become more widespread, the observation of these relaxation characteristics will undoubtedly be found more general than is currently thought. 

The serial publications listed in Section 1.3 contain a number of articles on various aspects of relaxation. The Encyclopedia of NMR includes 13 articles under titles beginning with the word Relaxation and several other related articles, including Nuclear Overhauser Effect," Carbon-13 Relaxation Measurements,100 Paramagnetic Relaxation in Solution,101 Brownian Motion,102 and Spin—Rotation Relaxation Theory.103 Many of these articles are based on density matrix formulations, which can readily be understood with the background provided in Chapter 11. 

The primary key to this successful cowork (Figure 1) is the matching of time scales, accessed using MD simulations and NMR relaxation experiments. Correlation times (characteristic motional time constants) for translational, angular rotational and reorientational motions are a few of the basic components in the relaxation theories. These quantities are standard dynamical properties, obtained in MD simulations. The real gain in using MD is that it can be used to calculate not only the various correlation times, but even the entire correlation functions, whose shapes and other characteristic features are a very rich source of informa-... 

We will present the topic by introducing the nuclear spins as probes of molecular information. Some basic formal NMR theory is given and connected to MD simulations via time correlation functions. A large number of examples are chosen to demonstrate different possible ways to combine MD simulations and experimental NMR relaxation studies. For a conceptual clarity, the examples of MD simulations presented and discussed in different sections, are arranged according to the specific relaxation mechanisms. At the end of each section, we will also specify some requirements of theoretical models for the different relaxation mechanisms in the light of the simulation results and in terms of which properties these models should be parameterized for conceptual simplicity and fruitful interpretation of experimental data. 

RllO R. Sharp, L. Lohr and J. Miller, Paramagnetic NMR Relaxation Enhancement. Recent Advances in Theory , p. 115 Rill V. A. Mandelshtam, FDM. The Filter Diagonalization Method for Data Processing in NMR Experiments , p. 159 R112 D. M. Korzhnev, M. Billeter, A. S. Arseniev and V. Y. Orekhov, NMR Studies of Brownian Tumbling and Internal Motions in Proteins , p. 197 R113 M. Pons and O. Millet, Dynamic NMR Studies of Supramolecular Complexes , p. 267... 

Halle, B., Carlstrom, G., Anderson, T., Wennerstrom, H., and Lindman, B. NMR of water nuclei in heterogeneous systems-relaxation theory and oxygen-17 data from aqueous solutions of proteins, polyelectrolytes and micelles. Biophysics of Water, E Franks, ed., Wiley, New York, pp. 221, 1982. 

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