Reorientational relaxation times calculation

Table 4.5-1 gives values for the fit parameters and the reorientational correlation times calculated from the dipolar relaxation rates. 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

In order to extract some more information from the csa contribution to relaxation times, the next step is to switch to a molecular frame (x,y,z) where the shielding tensor is diagonal (x, y, z is called the Principal Axis System i.e., PAS). Owing to the properties reported in (44), the relevant calculations include the transformation of gzz into g x, yy, and g z involving, for the calculation of spectral densities, the correlation function of squares of trigonometric functions such as cos20(t)cos20(O) (see the previous section and more importantly Eq. (29) for the definition of the normalized spectral density J((d)). They yield for an isotropic reorientation (the molecule is supposed to behave as a sphere)... 

In the previous discussion, the electron-nucleus spin system was assumed to be rigidly held within a molecule isotropically rotating in solution. If the molecule cannot be treated as a rigid sphere, its motion is in general anisotropic, and three or five different reorientational correlation times have to be considered 79). Furthermore, it was calculated that free rotation of water protons about the metal ion-oxygen bond decreases the proton relaxation time in aqua ions of about 20% 79). A general treatment for considering the presence of internal motions faster than the reorientational correlation time of the whole molecule is the Lipari Szabo model free treatment 80). Relaxation is calculated as the sum of two terms 8J), of the type... 

Correlation frequencies determined from T1 Tle and T2 relaxation times were plotted against reciprocal temperature and activation energies calculated. The methyl group had a comparatively high activation energy (4.7 kcal/mole) which was attributed to steric hindrance from the reorientation of the two methyls bound to the same carbon and steric hindrance arising from the two phenyl groups on the carbon atom. 

C. An analogous model was considered in Ref. 12b, but an important new step was made. Now it was assumed that the stochastic processes with two different relaxation times correspond to types of motion described by two wells. Two different complex susceptibilities were calculated, which have split Eq. (235) by two similar expressions for reorientation and vibration processes ... 

The linewidth of VH spectrum for the fluid at 7.0 MPa is as broad as about 54 cm (FWHH), from which the rotational relaxation time is calculated to be as short as about 0.3 ps. This may be based upon the fact that the density of the fluid is so low that the molecule can reorientate with small perturbation the collision rate is still low at this density compared with that in the liquid. 

The reorientational dynamics of water molecules has been analyzed by calculating the relaxation times of the molecular dipole vector relative to the laboratory fixed... 

Conformations and Dynamic Situations.—Rotation about single bonds " and partial double bonds, carbonium-ion rearrangements, conformational processes in rings, and spin-lattice relaxation times and the mobility of organic molecules in solution have been reviewed. The proton spin-lattice relaxation of polycrystalline bicyclo[2,2,2]oct-2-ene has been measured and the enthalpy of activation or reorientational motion calculated. 

Table 3.2 Reorientational rotation times in solution, compared with theoretical values for diffusion with slip or stick conditions. Experimental plots for solutes in various low-polar solvents (as in Figure 3.10) show that the rotational relaxation time r is linearly related to the viscosity (r = Zq +Ct], where Tq is small), and depends on no other solvent property. The table compares experimental values of C with values calculated (a) for slip conditions and (b) for stick conditions, the solute molecules being approximated to ellipsoids, with axial ratio a/b. Data from Ref. [16]. See text and Figure 3.11...

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