Hindered rotations/translations

If the center of mass of the molecular probe coincides with the Mossbauer nucleus, then the low-energy part of the spectrum monitors exclusively translational modes of the probe molecule thus providing a selective probe for fast translational processes on the lengthscale of several molecular diameters and larger. If, however, the center of mass does not coincide with the Mossbauer nucleus, then hindered rotations, i.e., librations, will contribute to the low-energy DOS. If... 

Of the 3n coordinates needed to describe an n-atom molecule, three are used for center of mass motion, three describe angular displacement (rotation, hindered rotation, or libration) (two if the molecule is linear, 0 if monatomic), the remaining 3n—6 (3n—5, if linear, 3n—3 = 0, if monatomic) describe atom-atom displacements (vibrations). In some cases it may not be possible to separate translation cleanly from rotation and vibration, but when the separation can be made it is a convenience. Elementary treatments assume... 

When the solution is dilute, the three diffusion coefficients in Eq. (40a, b) may be calculated only by taking the intramolecular hydrodynamic interaction into account. In what follows, the diffusion coefficients at infinite dilution are signified by the subscript 0 (i.e, D, 0, D10> and Dr0). As the polymer concentration increases, the intermolecular interaction starts to become important to polymer dynamics. The chain incrossability or topological interaction hinders the translational and rotational motions of chains, and slows down the three diffusion processes. These are usually called the entanglement effect on the rotational and transverse diffusions and the jamming effect on the longitudinal diffusion. In solving Eq. (39), these effects are taken into account by use of effective diffusion coefficients as will be discussed in Sect. 6.3. 

Extending the theory to interpret or predict the rovibrational state distribution of the products of the unimolecular dissociation, requires some postulate about the nature of the motion after the unimolecularly dissociating system leaves the TS on its way to form products. For systems with no potential energy maximum in the exit channel, the higher frequency vibrations will tend to remain in the same vibrational quantum state after leaving the TS. That is, the reaction is expected to be vibrationally adiabatic for those coordinates in the exit channel (we return to vibrational adiabaticity in Section 1.2.9). The hindered rotations and the translation along the reaction coordinate were assumed to be in statistical equilibrium in the exit channel after leaving the TS until an outer TS, the PST TS , is reached. With these assumptions, the products quantum state distribution was calculated. (After the system leaves the PST TS, there can be no further dynamical interactions, by definition.)... 

In the case of crystaUine sohds, more than one equivalent structural unit may be present in the primitive cell. This results in sphttings of the fundamental vibrational modes of these units. In the case of many crystalline solid materials covalent units (e.g. oxo-anions for oxo-salts) are present, together with other groups bonded by ionic bonds (e.g. the cations in the oxo-salts). According to the above group approximation, the internal vibrations of the covalent units can be considered separately from their external vibrations hindered rotations and translations of the group that finally contribute to the lattice vibrations and to the acoustic modes of the unit cell) and those of the other units. The presence of a number of covalent structural units in the primitive cell, causes their internal modes to spHt... 

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. 

The spectra obtained for ice Ih, LDA and HDA, using the TFXA spectrometer at 10K [53] is shown in Fig. 11. Ice Ih is the most common and readily obtainable phase of ice which has now been well studied [14,15,48,49]. Its spectrum has a very simple structure, the translational modes below 40 meV are well separated from the librational modes (or hindered rotations) in the energy region between 65-125 meV (very few system shows similar behaviour and this is due to the large mass difference between O and H). The observed acoustic phonon peak is at 7 meV. The two sharp peaks at 28 and 37 meV are the optic-phonon bands and have an unusual triangular-shape. In contrast, only a single feature appears in the IR spectrum, at 27 meV, and the Raman spectrum has an additional shoulder at 36 meV (see Fig. 10). 

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... 

Can you have spin-lattice relaxation in the absence of the usual sort of molecular motion By the usual sort, we mean nearly free molecular rotations and translations in liquids and gases as well as hindered rotations and translations in solids but not those involving only parts of the molecule like... 

J. S. Waugh and E. I. Fedin, "Determination of hindered rotation barriers in solids," Sov. Phys.-Solid State 4, 1633-1636 (1963). [Translation of Fizika Tverdogo Tela 4, 2233-2237 (1962).]... 

The partition function for a molecule is formed of the partition functions for individual types of energy increments (motions), i.e. from the translational, rotational, internal rotational (free rotation, hindered rotation), vibrational, electronic and nuclear spin partition functions... 

Primary main chain C Hindered rotations, oscillations or translations > 125 May be activated by defects... 

The contributions from translation (3/2i ) and external rotation (3/2/ for non-linear and li for linear species) are known, which leaves five adjustable parameters (oti,o[2,vi,V2, and V3) that are determined via non-linear regression. Note that in this formulation and 2 are not restricted to integer values. The same is true for n, which can take halfinteger values, because each vibrational mode that represents an internal (hindered) rotation is counted as 1 /2 oscillator. The representative frequencies together with their degeneracies are needed as input parameters for multi-frequency QRRK codes. 

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