Relaxation rate matrix

The only time when the calculated rate constants show any marked sensitivity to the variation of the elements of the relaxation rate matrix is when those elements happen to lie in the region of a bottleneck in the activation process [71.K1]. Thus, we might suppose, conjecturally, that marked deviations from strong collision fall-off behaviour will only occur when severe bottleneck effects are present in the activation processes. 

The second reason is related to the misconception that proton dipolar relaxation-rates for the average molecule are far too complicated for practical use in stereochemical problems. This belief has been encouraged, perhaps, by the formidable, density-matrix calculations " commonly used by physicists and physical chemists for a rigorous interpretation of relaxation phenomena in multispin systems. However, proton-relaxation experiments reported by Freeman, Hill, Hall, and their coworkers " have demonstrated that pessimism regarding the interpretation of proton relaxation-rates may be unjustified. Valuable information of considerable importance for the carbohydrate chemist may be derived for the average molecule of interest from a simple treatment of relaxation rates. 

NMR relaxation of liquids such as water in porous solids has been studied extensively. In the fast exchange regime, the spin-lattice relaxation rate of water in pores is known to increase due to interactions with the solid matrix (so-called surface relaxation ). In this case, T) can be described by Eq. (3.5.6) ... 

Nuclear spin relaxation is considered here using a semi-classical approach, i.e., the relaxing spin system is treated quantum mechanically, while the thermal bath or lattice is treated classically. Relaxation is a process by which a spin system is restored to its equilibrium state, and the return to equilibrium can be monitored by its relaxation rates, which determine how the NMR signals detected from the spin system evolve as a function of time. The Redfield relaxation theory36 based on a density matrix formalism can provide... 

The symbols Rauto and Rcross within the relaxation matrix are the auto- and cross-relaxation rates, respectively. and (l2Z) are the longitudinal magnetizations of spin 1 and 2, respectively, and the brackets indicate averaging over the whole ensemble of spins. Rcross in terms of the spectral densities is given by... 

NMRD studies (0.01-30 MHz) on bentonite suspensions showed that the water-proton spin-lattice relaxation rates are dominated by magnetic interactions with paramagnetic centers entrapped in the mineral matrix (89). The 1/Ti values were linearly dependent on the concentration of the... 

Selected entries from Methods in Enzymology [vol, page(s)] Anisotropy effects, 261, 427-430 determination by dynamic laser light scattering (quasi-elastic light scattering), 261, 432-433 determination for nucleic acids by NMR [accuracy, 261, 432-433 algorithms, 261, 11-13, 425, 430 carbon-13 relaxation, 261, 11-12, 422-426, 431, 434-435 cross-relaxation rates, 261,419-422, 435 error sources, 261, 430-432 phosphorus-31 relaxation, 261, 426-427, 431 proton relaxation, 261,51,418-422 relaxation matrix calculations, 261,12] deuterium solvent viscosity effects, 261,433 effect... 

Cross-relaxation rates and interproton distances in cyclo(Pro-Gly) from the full matrix analysis of NOESY spectrum recorded at Tm = 80 ms and T = 233 K. Cross-relaxation rates are obtained from the volumes shown in table 2 according to eq. (11) by Matlab (Mathworks Inc). Error limits were obtained from eq. (27) with Aa = 0.015 (table 2). 

Cross-relaxation rates, [Pg.296]

Observed agreement between the experimental and model cross-relaxation rates within the estimated error limits confirms validity of the full matrix analysis procedure but not necessarily its usefulness. Namely, the agreement is achieved mainly within the broad limits of cross-relaxation rate errors. Errors span the range 0.25 to 0.62 s but are clustered around the values 0.35 s and 0.55 s All the errors involving cross-relaxation rates of ProH and GlyH are clustered around 0.35 s . This is mainly because... 

In practice, the full matrix analysis is rarely applicable because of spectral overlap and because of the global error propagation. In full matrix analysis all the elements are interconnected and the error in one volume element propagates into all cross-relaxation rates. This property is not favorable in practical situations in which a part of the spectrum may be ill-defined although a good portion of the spectrum is of a satisfactory quality. Then, the more favorable analysis is localized, i.e., errors are confined within respective cross-relaxation rates. However, such analysis is possible only on data in which spin diffusion is not dominant. 

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