Vibrational anharmonicity modes

The anharmonic modes for both the a symmetric and 67 asymmetric CH stretching vibrations have been explored. In order to perform a reasonable anharmonic treatment, we had to take into account the stretching of the bonds to larger elongations than for the harmonic description where displacements can be confined close to the equilibrium geometry. Consequently, correlation effects were included in the determination of the potential surface. The electronic calculations were carried out at the MP2 level, which insures a good description of the CH bond potential towards dissociation. A double zeta... 

In the hydrate lattice structure, the water molecules are largely restricted from translation or rotation, but they do vibrate anharmonically about a fixed position. This anharmonicity provides a mechanism for the scattering of phonons (which normally transmit energy) providing a lower thermal conductivity. Tse et al. (1983, 1984) and Tse and Klein (1987) used molecular dynamics to show that frequencies of the guest molecule translational and rotational energies are similar to those of the low-frequency lattice (acoustic) modes. Tse and White (1988) indicate that a resonant coupling explains the low thermal conductivity. 

From (8.23) and (8.24) one can see two special cases when the potential becomes separable. In the first case c12 = 0, we have two independent anharmonic modes, each having two equilibrium positions. In the second case, the angular part of the potential (8.23) Vr is zero, and the motion breaks up into radial vibration in the double well V0(q) and a free rotation, i.e. propagation of the waves of transverse displacements along the ring. The latter case is called free pseudorotation. Since the displacements of atomic groups in the wave are purely transverse, they do not contribute to the total angular momentum. 

The experimental data was fitted, as shown in Fig. 5.10, to a convolution of this response function with the instrument response function. As the result, the decay time T-2/2 was estimated to be 1.1 0.1 ps. Recently, the population lifetime Ti of G-phonons was measured by incoherent time-resolved anti-Stokes Raman scattering and the lifetime was found to be 1.1-1.2 ps in semiconducting SWNTs [57]. Therefore, one can reasonably assume ipu Ti at room temperature. This result is consistent with the conventional Raman line width of semiconducting SWNTs [58]. The observed short lifetime of the G-phonons implies anharmonic mode coupling between G-phonons and RBM-phonons [59]. In fact, a frequency modulation of the G mode by the RBM has been reported, suggesting the anharmonic coupling between these vibrations [56]. 

In contrast, in the low pressure limit, the rate coefficient is effectively proportional to the state density at the dissociation threshold and there is no cancellation from the transition state number of states. However, in this instance a different sort of cancellation may occur. In particular, for bond stretching modes the vibrational anharmonicities tend to increase the state density, while for some other modes, such as out-of-plane bends, the anharmonicities tend to... 

The vibrational spectra S co) after the second pulse in the cases of t = 134 and 201 fs are shown in Fig. 7.8, which clearly indicate that the amplitude of the hg(l) mode is enhanced for t = 134 fs and the predominant mode is switched to the ag(l) mode for t = 201 fs. In short, a Raman active mode is strongly excited if r is chosen to equal an integer multiple of its vibrational period TVib, and the energy of the mode takes the minimum if x is equal to a half-integer multiple of Tvib. This is known to be valid for the harmonic oscillator model. We proved that this is also the case for the potential surface of highly excited Ceo which includes anharmonic mode couplings by nature. 

The methods of Nonlinear Dynamics(8) can be applied to gain new theoretical insight into the underlying dynamics in terms of the molecular phase space structure. In particular, the existence of low order Fermi resonances between vibrationally anharmonic local (or normal) modes or between bending vibrations and rotations, can cause dramatic changes in phase space structure, manifest in the breakdown... 

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