Hindered translations

Anti-HIV-1 env Anti-sense T cells Binds transcript thereby mediating degradation and hindering translation Levine et al. 2006... 

In good agreement with our calculation. In Ref. 14, using the harmonic approximation, the anomalous Isotopic factor for the frequency was Interpreted as due to mixing with the hindered translation. However, as we have shown, the harmonic approximation Is Inappropriate In this case. 

Fig. 18. The hindered translational region of the vibrational spectrum as predicted by the Wores Rice model (from Ref. 64>)...

The preceding suggests that the structure of the density of vibrational states in the hindered translation region is primarily sensitive to local topology, and not to other details of either structure or interaction. This is indeed the case. Weare and Alben 35) have shown that the density of vibrational states of an exactly tetrahedral solid with zero bond-bending force constant is particularly simple. The theorem states that the density of vibrational states expressed as a function of M (o2 (in our case M is the mass of a water molecule) consists of three parts, each of which contains one state per molecule. These arb a delta function at zero, a delta function at 8 a, where a is the bond stretching force constant, and a continuous band which has the same density of states as the "one band Hamiltonian... 

The A defined in Equation 5.30 is not to be confused with the Helmholtz free energy. Should the A frequencies be limited to the external hindered translations and rotations, vi g = vi g = 0, and this is an additional simplification. In some molecules, however, there are isotope sensitive low lying internal modes (often internal rotations or skeletal bends). In that cases both terms in Equation 5.30 contribute. 

The Bartell mechanical model has also been used to estimate the isotope effect on molar volume due to the over all motion (i.e. hindered translation) of molecules interacting in a Lennard-Jones potential. For C6H6/C6D6 one finds AV/V 4 x 10-5, about two orders of magnitude smaller than the contribution of the internal modes (and experiment). We conclude that for all but very light molecules this contribution can be neglected. 

At low temperatures the hydrogen atoms in a hydrogen-palladium system would be expected to form a Debye sublattice, but at higher temperatures when the well known, but little understood, diffusion processes set in, heat capacities characteristic of hindered translation for the hydrogen atoms might be expected. Rapid cooling of a mobile system of hydrogen atoms would be expected to produce nonequilibrium conditions. Experimentally the system does behave somewhat as expected, but some unusual consequences of this situation became evident only after the experimental observations. 

Between 65° and 180° K, the dashed curve, E, is the sum of C and D. This assumes that after the cooperative transition the hydrogen atoms are hindered translators. The barrier is sufficiently high that the effective motion is vibration in a Debye sublattice. Figure 5 gives a theoretical curve calculated in a similar manner between 100° and 300° K. In this case the curve is calculated on the... 

The next developments of the FC approach were in papers by (R. A.) Marcus,41 49 and a later series from the Soviet Union. About the same time Hush50 introduced other concepts, to be discussed below. The early work of Marcus41 considered the Inner Sphere to be invariant with frozen bonds and vibrational coordinates up to the time of electron transfer. The classical subsystem for ion activation has its ground state floating on a continuum of classical levels, i.e., vibrational-librational-hindered translational motions of solvent molecules in thermal equilibrium with the ground state of the frozen solvated ion. 

Spectra of samples in the liquid state (Fig. 2.6-lB) are given by molecules which may have any orientation with respect to the beam of the spectrometer. Like in gases, flexible molecules in a liquid may assume any of the possible conformations. Some bands are broad, since they are the sum of spectra due to different complexes of interacting molecules. In the low frequency region spectra often show wings due to hindered translational and rotational motions of randomly oriented molecules in associates. These are analogous to the lattice vibrations in molecular crystals, which, however, give rise to sharp and well-defined bands. The depolarization ratio p of a Raman spectrum of molecules in the liquid state (Eqs. 2.4-11... 13) characterizes the symmetry of the vibrations, i.e., it allows to differ between totally symmetric and all other vibrations (see Sec. 2.7.3.4). 

From an interpretation of peaks in the far IR spectral region, one can obtain knowledge of hindered translations among water molecules in ionic solutions. Somewhat surprisingly, the force constants associated with such movements are loweredhy the presence of ions because ions free some water molecules from the surrounding solvent structures. Thus, force constants are given by where U is the potential... 

Thus 28 IR active modes are expected to fall in the regions of the vibrations of the orthosilicate anions. Of these, we can expect five modes associated with V3 (asymmetric stretching) and two modes associated with Vi (symmetric stretching), three modes associated with the symmetric deformation (V2) and five with the asymmetric deformation V4, four hindered rotations, four hindered translations, and, finally, five modes associated with Al—O tetrahedra. We actually observe at least 10 components for framework vibrations. Additionally, the low-frequency modes of Na ions are expected to fall in the FIR region [68], where several bands are indeed observed. 

Figure 6 shows the vibrational density of states for confined water (52% hydrated Vycor) as compared with that of bulk water at room temperature [3]. Among striking features of the density of states of confined water are a much attenuated peak associated with the density of states of the hindered translational motions, centered around 6 meV, indicating the reduction of this degree of freedom upon confinement and an up-shift of the librational peak at 70 meV, which signifies the hindrance of the librational motions because of the presence of the surface. The hindrance of the motions increases when the temperature is lowered. 

The crystal data compilation of Donnay and Ondlk ( ) tabulated both ZrCl and ZrBr as cubic structures. Thus, the adopted heat capacity values are estimated so as to parallel those for ZrCl. The heat capacity values below 300 K are calculated by summing contributions due to hindered translations, librations, and internal vibrations of the crystal. The parameters used in the calculations are determined by a correlation with corresponding parameters for ZrCl (6) and a consideration of the sublimation data for ZrBr (6). The high temperature heat capacities are obtained graphically. 

Pal et al., 2002). To understand the different solvation timescales, we have fitted the decay curves to multiexponentials. Four different solvation timescales are identified, from ultrafast to slow components. An ultrafast component with a time constant of 40-50 fs, followed by a fast component at 0.7-1.2 ps was observed. Two slower components with time constants in the range of 6-17 and 42-88 ps were also noticed. Such different solvation timescales arise from the presence of different types of water molecules within the hydration layer (Bandyopadhyay et al., 2005). The initial ultrafast relaxation arises from the high frequency librational (hindered rotation) and intermolecular vibrational (hindered translation) motions of the "free" or bulk-like water molecules. The moderately damped rotational motions of these water molecules contribute to the fast relaxation ( 1 ps). The slowest component observed (42-88 ps) arises from those water molecules which... 

Vibrational modes of water. Shown are the internal modes (a) symmetric stretch, (b) bending, (c) asymmetric stretch, and the librational modes (d) wag, (e) twist, and (f) rock. Not shown are the three hindered translational modes. 

Hindered translation vt Band appears as shoulder of Vl. band V 193 Band appears as shoulder of vl band vw 190 ... 

---