Rotational move

As viewed m the drawing a 120° counterclockwise rotation of C 4 places its hydroxyl group m the proper position At the same time this rotation moves the CH2OH group to a position such that it will become a substituent that is up on the five membered ring The hydrogen at C 4 then will be down m the furanose form... 

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A Novel Algorithm Based on a Parallel-Rotation Move for... 

The right-handed sense of a helix traces out a clockwise rotation moving away from the observer the left-handed sense of a helix traces out an anticlockwise rotation moving away from the observer, e.g., the. ..TG TG TG. .. helix of isotactic polypropene is left-handed. 

In summary, the recommended implementation for concerted rotation moves in MC simulations uses ... 

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If the angle (3 is much less than 1, then, in accord with Figs. 7 and 9, the most part of the rotators move freely under effect of a constant potential U0, since their trajectories do not intersect the conical cavity. A small part of the rotators moves along a trajectory of the type 1 shown in Fig. 10. However, at d > (3—that is, in the most part of such a trajectory—they are affected by the same constant potential U0- Therefore, for this second group of the particles the law of motion is also rather close to the law of free rotation. For the latter the dielectric response is described by Eq. (77). We shall represent this formula as a particular case of the general expression (51), in which the contributions to the spectral function due to longitudinal A) and transverse KL components are determined, respectively, by the first and second terms under summation sign. Free rotators present a medium isotropic in a local-order scale. Therefore, we set = K . Then the second term... 

This model32 was termed the hat model (VIG, pp. 326,465) [62], since the potential profile resembles a hat. The low-energy dipoles move inside such a well, while the high-energy dipoles (= the rotators ) move over the potential... 

A simplified version of this model, termed the hybrid model (VIG, p. 305) [32-34, 39] (see also Section IV.E) was proposed for the case of a small cone angle p. In this model the rotators move freely over the barrier U0 as if they do not notice the conical surface the librators move in the diametric sections of a cone—that is, they librate. The hybrid model was widely used for investigation of dielectric relaxation in a number of nonassociated and associated liquids, including aqueous electrolyte solutions (VIG, p. 553) [53, 54]. The hat model was recently applied to a nonassociated liquid [3] and to water [7, 12c]. 

A. Previous models of water (see 1-6 in Section V.A.l) and also the hat-curved model itself cannot describe properly the R-band arising in water and therefore cannot explain a small isotope shift of the center frequency vR. Indeed, in these models the R-band arises due to free rotors. Since the moment of inertia I of D20 molecule is about twice that of H20, the estimated center of the R-band for D20 would be placed at y/2 lower frequency than for H20. This result would contradict the recorded experimental data, since vR(D20) vR(H20) 200 cm-1. The first attempt to overcome this difficulty was made in GT, p. 549, where the cosine-squared (CS) potential model was formally (i.e., irrespective of a physical origin of such potential) applied for description of dielectric response of rotators moving above the CS well (in this work the librators were assumed to move in the rectangular well). The nonuniform CS potential yields a rather narrow absorption band this property agrees with the experimental data [17, 42, 54]. The absorption-peak position Vcs depends on the field parameter p of the model given by... 

Another method uses an inclined disk, as shown in Fig. 6.28. Moist powder is applied to the pan. A small particle falls into the pan and grows as it rotates. In a different adaptation, a drop of hydrogel emerges from the center as the plane rotates. Moving under centripetal force, the drop hardens, becomes spherical, and finally falls of the plate. 

The features of this model, which initially were formulated due to a rather abstract reasoning, hardly could be reconciled with the structures of these fluids. It was supposed that a more realistic intermolecular potential should be used, in which one should disregard contributions to spectra (i) of the uprecessors, performing rotation in a parabolic part of the well around its symmetry axis and (ii) of the rotators moving with constant angular velocity over a potential barrier through a complete circle. 

Equations (213) coincides with (202) if we exclude from consideration in the last formula the dipoles (termed rotators ) moving outside the well and having energy greater than u. Setting also to zero the projection / of the momentum onto the plane of rotation, we find that the formula (160) from GT2 reduces to (215). 

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