Torsional vibrations, anharmonic

The spectral changes in the frequency range of 150-280 cm , which characterizes a torsional vibrations in the CH2 sequences contacted with the CONH group, also point to an elevated mobility of chains in Nylon 12 prestrained, while the breaking of H-bonds (110 cm band) in this polymer may be ob rved only for loaded sample (Fig. 33, curve 5). Also the FIR spectra of loaded Nylon 12 show a narrowing of the translational and torsional vibration bands which is connected with a decrease in the amplitudes (and anharmonicity) of these motions because of an increase in the chain rigidity uncter Vision on account of so-called nechanical vitrification ... 

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. 

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. 

Like the rXH absorption bands, the yXH bands become markedly broader as their frequency drops. This behaviour also appears to be explicable in terms of an increasing amplitude and anharmonicity of the yXH vibrations leading to interaction with y or <5 (RXH YR ) modes or (in the limiting case of no H-bond) with torsional motions of the RXH molecule as a whole. 

In fact, the frequency ofthe torsional oscillation mode V4 is found to be more than double that ofthe ground state. The frequency ofthe torsional oscillation mode was reevaluated by Mukheijee et al [56], using a very accurate representation of the one-dimensional vibrational Hamiltonian of the non-rigid rotor in terms of a Fourier series [76-78], and other spectroscopic parameters calculated for the first time taking care of anharmonicity. A new assignment of the experimental spectrum was given. The results are displayed in Table 8. For reference purpose the vibrational frequencies of the ionic states are also listed... 

A molecule-independent, generalized force field for predictive calculations can be obtained by the inclusion of additional terms such as van der Waals and torsional angle interactions. This adds an additional anharmonic part to the potential (see below) but, more importantly, also leads to changes in the whole force field thus the force constants used in molecular mechanics force fields are not directly related to parameters obtained and used in spectroscopy. It is easy to understand this dissimilarity since in spectroscopy the bonding and angle bending potentials describe relatively small vibrations around an equilibrium geometry that, at least... 

To calculate n E-E, the non-torsional transitional modes have been treated as vibrations as well as rotations [26]. The former approach is invalid when the transitional mode s barrier for rotation is low, while the latter is inappropriate when the transitional mode is a vibration. Harmonic frequencies for the transitional modes may be obtained from a semi-empirical model [23] or by performing an appropriate normal mode analysis as a function of the reaction path for the reaction s potential energy surface [26]. Semiclassical quantization may be used to determine anharmonic energy levels for the transitional modes [27]. 

So far we have discussed statistical and dynamical theories that have largely been based on a quadratic expansion of the PES about the reaction path (albeit with a limited account of anharmonicity in some vibrational modes). Still within that same spirit, very anharmonic vibrations such as intramolecular hindered rotations (torsional motion) have been treated more realistically [56,110,138]. However, in many... 

Figure 4 Plots of the potential energy V for a system that simultaneously experiences uncoupled twofold torsional oscillation along qi and anharmonic vibration along 2- total energy exceeds the barrier hei t, but if insu Bcient energy is allocated to qi (shown as case T ), the molecule will be trapped within one isomer for all time. If sufficient energy is allocated to (shown as case R ), the molecule will react and back-react repeatedly. If the energy allocated to equals the energy height of the barrier (shown as case S ) the molecule will approach infinitely dose to the transition state at q in the limit of infinite time.

Our approach to the treatment of torsional anharmonicity makes use of the vibrationally adiabatic approximation. We originally introduced this analysis in our previous treatment of the HO2 + HO2 reaction where torsional motion played a key role. The adiabatic approximation is a common scheme to treat mode coupling for systems that exhibit a separation of timescales. Since torsional motion is typically a very low frequency molecular vibration, the adiabatic approximation appears well suited to this problem. Hence we take the torsional coordinate, t, as slow while the remaining normal modes are fast . 

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