Torsion modes

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

The four steric energy sums in Eq. (4-13) corresponding to sketching, bending, and torsional modes of motion and van der Waals inhamolecultu interaction appear to be about the smallest number one can use in an accurate MM geomehy minimization. 

The solutions to a problem of this magnitude can be found in references [3, 7] and others. Figures 9-16 and 9-17 are torsional mode shape diagrams of some typical systems. While the rigorous solution to the multimass damped system is not within the scope of this book, several interesting points should be made. 

Figures 4 and 5 show the Raman and IR spectra of ce-Ss in the range up to about 100 cm A comparison of these spectra with those presented in Figs. 2 and 3 reveals that the linewidths are much smaller at low temperatures (ca. 0.02-0.2 cm ). The wavenumbers and assignments of the external and torsional modes as reported by Gautier and Debeau [106] and Becucci et al. [107] are listed in Table 3. The spectra in Figs. 4 and 5 clearly demonstrate that there is no gap between the external vibrations and the crystal components of the lowest internal vibration Vg. Moreover, at about 76 cm an IR active lattice mode appears between two components of the fundamental Vg at 74 cm and 79 cm respectively.

Bending and torsion modes are heavily mixed Assignment of the symmetry class based on the observed pressure dependence of Raman intensities has been performed on group theoretical considerations with respect to the molecular geometry [150]... 

While the vibrations (stretching, bending, torsion) in high symmetrical rings (Ss, Ss, S12) are almost uncoupled [80], the vibrations in the low symmetrical Sy ring are heavily mixed, especially the bending and torsional modes [81]. 

The infrared and Raman spectra of trisulfane have been assigned assuming a molecular C2 symmetry [58]. Due to strong coupling between bending and torsion modes the assignment given in Table 6 should be considered as only approximate. 

Many molecules are composed of functional groups (hat can rotate with respect to the rest of the molecule. The classical example is ethane, as the possibility of rotation of one methyl group against the other was recognized long ego. Because the torsional mode does not result in infrared activity, its frequency was estimated from thermodynamic data. 

Dynamic nuclear polarisation (DNP) enhanced 15N CP MAS NMR has been exploited by Mark-Jurkauskas et al.79 in the studies of intermediates of the bacteriorhodopsin photocycle. The data for L intermediate were similar to those found for 13-ds,15-anti retylidene chloride, while those for K intermediate were similar to those of acid blue bacteriorhodopsin in which the Schiff base counterion was neutralised (Table 3). The 15N chemical shifts observed have shown that for bacteriorhodopsin, the Schiff base in K intermediate state loses contact with its counterion and establishes a new one in L intermediate state. The proton energy stored at the beginning in the electrostatic modes has been transformed to torsional modes. The transfer of energy is facilitated by the reduction of bond order alternation in the polyene chain when the counterion interaction is initially broken and is driven by the attraction of the Schiff base to a new counterion. 3D CP MAS experiments of NCOCX, NCACX, CONCA and CAN(CO)CA types have been used in studies of proteorhodopsin.71... 

Although the phase space of the nonadiabatic photoisomerization system is largely irregular, Fig. 36A demonstrates that the time evolution of a long trajectory can be characterized by a sequence of a few types of quasi-periodic orbits. The term quasi-periodic refers here to orbits that are close to an unstable periodic orbit and are, over a certain timescale, exactly periodic in the slow torsional mode and approximately periodic in the high-frequency vibrational and electronic degrees of freedom. In Fig. 36B, these orbits are schematically drawn as lines in the adiabatic potential-energy curves Wo and Wi. The first class of quasi-periodic orbits we wish to consider are orbits that predominantly... 

Terahertz, or far infrared spectroscopy, covers the frequency range from 0.1 to lOTHz (300 to 3cm ) where torsional modes and lattice vibrations of molecules are detected. It is increasing in use in many application areas, including analysis of crystalline materials. Several dedicated conunercial instruments are available which use pulsed terahertz radiation which results in better signal to noise than those using blackbody sources for radiation (and associated with the terminology far infrared spectroscopy). Work using extended optics of FTIR instrumentation as weU as continuous-wave source THz has also been recently reported. ... 

Finally, the zero point vibration corrections (SET V) use to be much larger than the pseudopotential corrections. In the present case, these zero point corrections seems to give rise to unrrealistic values, probably because of the harmonic approximation used in the calculations. The torsion mode as well as its interactions with the remaining modes are indeed very anharmonic. 

PPG (at higher temperatures) behaves like a typical pseudoplastic non-Newtonian fluid. The activation energy of the viscosity in dependence of shear rate (284-2846 Hz) and Mn was detected using a capillary rheometer in the temperature range of 150-180°C at 3.0-5.5 kJ/mol (28,900 Da) and 12-13 kJ/mol (117,700 Da) [15]. The temperature-dependent viscosity for a PPG of 46 kDa between 70 and 170°G was also determined by DMA (torsion mode). A master curve was constructed using the time-temperature superposition principle [62] at a reference temperature of 150°G (Fig. 5) (Borchardt and Luinstra, unpublished data). A plateau for G was not observed for this molecular weight. The temperature-dependent shift factors ax were used to determine the Arrhenius activation energy of about 25 kJ/mol (Borchardt and Luinstra, unpublished data). 

The fundamental vibrations (8 stretching, 10 deformation and 3 torsional modes) of tri-fluoromethyl peroxynitrate (1) can be assigned from the FUR spectrum in the gas phase and FT-Raman spectrum of the liquid. The high-frequency stretching modes are characteristic and easily assigned, except for the Vs(CF3) and Vs(N02) fundamental modes, which overlap in the gas-phase IR spectrum. Near agreement is obtained between the experimental and the theoretically calculated vibrational spectra°°. Due to the Cj symmetry of the molecule, all the fundamental modes (7 stretching, 8 deformation and 3... 

The excited dibromide executes this vibrational mode and the vibrational coherence persists as some trajectories find the C Br bond-cleavage exit channel, a reaction favored when the dihedral angle is close to 60°. The proper phasing of two vibrations, the BrCCC dihedral-angle-modifying torsional mode and the C—Br stretching vibration, leads to the cleavage of the C Br bond. 

In the limiting case of no H-bonding the yXH vibration becomes a low frequency torsional mode of vibration of single molecules the effect of the presence of an H-bond is in this case to increase the restoring force tending to keep the XH bond in a fixed orientation [57 J (i.e. directed towards the Y atoms)— hence the rise in frequency—and to decrease the amplitude, and possibly the anharmonicity, of the vibration. 

At present the body of data on reactions in clusters is insufficient to test the above two microcanonical approaches. For electron transfers in solution it seems clear that the vibrational assistance approach, stemming from Eq. (1.2), with its extensions mentioned earlier, is the one that has been the most successful [27-30]. For slow isomerizations Sumi and Asano have pointed out that an analysis based on Eq. (1.2) was again needed [40]. An approach based on Eq. (1.1) or on its extension to include a frequency-dependent friction, they noted, led to unphysical correlation times [40]. In investigations of fast isomerizations the most commonly studied system has been the photoex-cited trans-stilbene [5, 41-43,46]. Difficulties encountered by a one-coordinate treatment for that system have been reported [4, 8]. Indeed, coherence results for photoexcited cw-stilbene have shown a coupling of a phenyl torsional mode to the torsional mode about the C=C bond [42, 47]. 

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