Anisotropic motion

R,1S isomer. However, this proposal is tentative, because X-ray diffraction has shown that another specimen of asperlin, possessing a different crystalline form, has structure 49b. It should be noted that 1 tumbles somewhat anisotropically, with D /D = 1.3, as deduced from C relaxation measurements. If, however, the anisotropic motion of 1 were not properly corrected for, the largest error in the measurement of its interproton distances would not exceed 4%. 

For the relatively rapid anisotropic motion (tc < 3 x 10" s) of spin probes observed on fully hydrated smectites such as montmoril-lonite, hectorite, and beidellite, an external fixed axis system (x1, y, z ) can be defined in addition to the molecule-fixed axes (x, y, z). The angle, 0, between the z and z axes is given by ... 

A variety of relaxation time studies have been performed on toluene. The choice of deuterated toluene avoids certain complicating factors which affect proton NMR studies, such as, dipolar or spin-spin couplings. The dominant relaxation mechanism is quadrupolar and the relaxation times are determined by the reorientation of the C-D bond vector. Relaxation times such as T, are sensitive to the motions of the solvent around the larmor frequency, which is on the order of 14 MHz in this study. T2 measurements may probe slower motions if the molecule undergoes slow and/or anisotropic motion. The relaxation time results presented in Figure 3 are significantly shorter than those found in bulk toluene solutions (18.19). In bulk toluene, the T and T2 values are equal above the melting temperature (1.2.). In this polymer system T2 < T indicative of slow and/or anisotropic reorientation. 

In the atomic model, the tensor fiJk describes the anisotropic motion of an... 

The motional dynamics of O J adsorbed on Ti supported surfaces has been analyzed over the temperature range 4.2-400 K in a recent paper by Shiotani et al. (66). Of the several types of 02, a species noted as 02 (III), and characterized by gxx = 2.0025, gyy = 2.0092, g12 = 2.0271 at 4.2 K, exhibited highly anisotropic motion. While gxx and gzz varied with increasing temperature and were accompanied by drastic line shape changes, gyy was found to remain constant. This observation indicates that the molecular motion of this 02 can be described by rotation about the y axis perpendicular to the internuclear axis of 02 and perpendicular to the surface with the notation given in Fig. 4. The EPR line shapes were simulated for different possible models and it was found that a weak jump rotational diffusion gave a best fit of the observed spectra below 57.4 K, whereas some of the models could fit the data above this temperature. The rotational correlation time was found to range from 10 5 sec (below 14.5 K) to 10 9 sec (263 K), while the... 

The inner coordination spheres of these two complexes are presented in Figure 1. While the Ru-H distance is well defined in the amidinato, it is not in the triazenido complex. Yet reference to Table I indicates that the triazenido structure is better if one uses the unreliable criterion that the lower the R index, the better the structure. In this instance, the low R index in the triazenido complex results from an elaboration of the usual group refinement model (3), allowing for anisotropic motion of the group atoms. This elaboration introduces a large number of additional variables and provides us with an opportunity to lower the R index More importantly, we established that the other features of the structure were virtually unaffected by this elaboration. We conclude that with problems of this type, such an elaboration probably is not justified by the expense involved. Why can t the hydride position be located accurately in the... 

The tris and bis complexes of acetylacetone (2,4-pentanedione) (167) with chromium(III) have been known for many years (168,169).739 The tris compound is generally prepared by the reaction of an aqueous suspension of anhydrous chromium(III) chloride with acetylacetone, in the presence of urea.740 Recently a novel, efficient synthesis of tris(acetylacetonato)chromium-(III) from Cr03 in acetylacetone has been reported.741 The crystal structure of the tris complex has been determined.744 A large anisotropic motion was observed for one of the chelate rings, attributed to thermal motion, rather than a slight disorder in the molecular packing. 

Eq. (3.21) discussed in Section 3.3.2 is only valid if the motion of the molecules under study has no preferential orientation, i.e. is not anisotropic. Strictly speaking, this applies only for approximately spherical bodies such as adamantane. Even an ellipsoidal molecule like trans-decalin performs anisotropic motion in solution it will preferentially undergo rotation and translation such that it displaces as few as possible of the other molecules present. This anisotropic rotation during translation is described by the three diagonal components Rlt R2, and R3 of the rotational diffusion tensor. If the principal axes of this tensor coincide with those of the moment of inertia - as can frequently be assumed in practice - then Rl, R2, and R3 indicate the speed at which the molecule rotates about its three principal axes. 

If the position of the principal axes of the rotational diffusion tensor were known with respect to the molecular coordinates, then the motion of the molecule could be calculated from the measured relaxation times. With simple molecules, however, it is possible to interpret the Tt values qualitatively in terms of an anisotropic motion. 

Spin-lattice relaxation times of carbon-13 in different polypropylene stereosequences differ slightly while nuclear Overhauser enhancements are almost identical (1.8-2.0) [533] isotactic sequences display larger Tx values than the syndiotactic stereoisomers. Other vinyl polymers behave correspondingly [534]. Carbon-13 spin-lattice relaxation times further indicate that dynamic properties in solution depend on configurational sequences longer than pentads. The ratio 7J(CH) 7J(CH2) varies between 1.6 to 1.9 thus, relaxation can be influenced by anisotropic motions of chain segments or by unusual distributions of correlation times [181],... 

EPR spectroscopy has been used to study rotation on vanadyl (V02+) analogues of Gd(III) chelates [73-76]. Vanadyl EPR line shapes are sensitive to rotation, they even allow for the distinction of isotropic and anisotropic motions. One concern about this technique is that substituting the trivalent Gd ion with the divalent vanadyl may modify the rotational dynamics of the complex. 

Multispin systems 242 Anisotropic motion 242 The methyl group 244... 

Current theoretical work on relaxation apparently centres on two issues, the problems of cross relaxation and cross correlation in multispin systems and the effect of anisotropic motion on nuclear relaxation. Both lines of effort come together in very recent theoretical and experimental work on the relaxation behaviour of the methyl group to which in the past three years alone more than 10 papers have been devoted. 

Slight anisotropic motion was assumed in a paper related to steroid relaxation since in several steroids, e.g. [11], C-3 shows a somewhat smaller... 

When the overall motion is not isotropic, the diagonal elements of the rotational diffusion tensor are no longer equivalent and rotation about the three principal axes of the diffusion tensor may be described by different diffusion coefficients or correlation times. For anisotropic motion, the correlation time in Eqs. 16 and 25 is an effective correlation time, r ff, containing contributions from the various modes of reorientation. Partitioning of the various components of rff can be achieved through appropriate dynamic models. The simplest case of anisotropic motion is that for a symmetric-top molecule. The r ff of a rigid ellipsoid is expressed in terms of two parameters, Dn and DL these two parameters respectively describe the rotational diffusion about the C3 symmetry axis (major axis) and the two perpendicular axes (minor axes), which are assumed to be equivalent25-44 (Fig. 4) ... 

Fig. 4.—Molecular shapes and correlation times for isotropic and anisotropic motion, (a) Spherical molecule (b) axially symmetric molecule (c) asymmetric molecule.

Woessner47 has also treated the case of a methyl group attached to an axially symmetric ellipsoid, whereas Levy et al.66 derived equations for the methyl internal rotation superposed on a fully anisotropic motion. The effect of anisotropic reorientation can dramatically alter the relationship between rigidly held methine, methylene, and methyl C—H vectors. Deviation from the ratio T,(CH)/ T,(CH3) = 3 can be considerable, depending on the relative orientation of C—H vectors with respect to the principal diffusion axes. 

A nuclear magnetic relaxation study85 of lactose (17), which is a basic constituent disaccharide unit of all gangliosides, demonstrates that this molecule reorients anisotropically. The favored axis of molecular reorientation appears to lie along the axis of the molecule and therefore is reflected in the shorter T, value at C-4 of the galactose residue. The apparent differences between the relaxation times observed for the C-l resonances of the a (17a) and /3 (17b) isomers may also be reflected in their differing C—H orientations relative to the anisotropic axis. Similar anisotropic motion was observed for methyl /3-lactoside,85 methyl /3-cellobioside,84 and other disaccharide derivatives in solution. 

The presence of anisotropic motion along the molecular length is suggested for trisaccharide 15 as the anomeric carbons of the a and j8 anomers show different Tl values.85 A smaller T, for the C-l carbon of the a anomer (0.11s) relative to that of the j3 anomer (0.24 s) indicates a close correspondence between the equatorial C-H vector in the a-anomer and the favored axis of rotation. By contrast, relaxation studies on sucrose14,106 (7) did not reveal anisotropic motion (however, see below). 

T2, and the nuclear Overhauser enhancement, NOE, comprise a set of parameters which characterize molecular motions. In the case of simple isotropic motion, the dependence is in terms of a single correlation time characterizing the exponential decay of the autocorrelation function. However, in many instances, the assumption of isotropic motion is not valid. For rigid systems, the relaxation behavior can then often be predicted by assuming simple anisotropic motion (1 ). Often, superposition of two or more independent motions must be used to satisfactorily interpret observed relaxation behavior. Recently, however, the wide-... 

These equations describe the reptation normal relaxation modes, which can be compared with the Rouse modes of the chain in a viscous liquid, described by equation (2.29). In contrast to equation (2.29) the stochastic forces (3.47) depend on the co-ordinates of particles, equation (3.48) describes anisotropic motion of beads along the contour of a macromolecule. 

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