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** Glassy modes high-frequency behavior **

The Hamiltonian of this model with a high-frequency mode coh and a single low-frequency exchange mode coi is given by Eq. (4.2.2) in which components have the following form [Pg.89]

This expression refers to diagrams without closed high-frequency loops (Fig. A3.1 a). Thus, provided the inequality fihQK 1 is valid, the GF defined above can be written in the form involving no high-frequency mode operators [Pg.178]

Fig. 2. The different kinds of interactions of the intramolecular high frequency mode that may be seen in the infrared spectra. Interactions with the substrate (a) will boA affect the vibration frequency and the lifetime of the vibrational excitation. |

Although the rotation barrier is chiefly created by the high-frequency modes, it is necessary to consider coupling to low-frequency vibrations in order to account for subtler effects such as temperature shift and broadening of tunneling lines. The interaction with the vibrations q (with masses and frequencies m , tu ) has the form [Pg.121]

The adiabatic approximation in the form (5.17) or (5.19) allows one to eliminate the high-frequency modes and to concentrate only on the low-frequency motion. The most frequent particular case of adiabatic approximation is the vibrationally adiabatic potential [Pg.77]

There are two kinds of damping that are considered within the strong anharmonic coupling theory the direct and the indirect. In the direct mechanism the excited state of the high-frequency mode relaxes directly toward the medium, whereas in the indirect mechanism it relaxes toward the slow mode to which it is anharmonically coupled, which relaxes in turn toward the medium. [Pg.285]

We describe a simple computational example to demonstrate two key features of the new protocol Stability with respect to a large time step and filtering of high frequency modes. In the present manuscript we do not discuss examples of rate calculations. These calculations will be described in future publications. [Pg.278]

There exists an extensive literature on theoretical calculations of the vibrational damping of an excited molecule on a metal surface. The two fundamental excitations that can be made in the metal are creation of phonons and electron-hole pairs. The damping of a high frequency mode via the creation of phonons is a process with small probability, because from pure energy conservation, it requires about 6-8 phonons to be created almost simultaneously. [Pg.24]

The obtained PES forms the basis for the subsequent dynamical calculation, which starts with determining the MEP. The next step is to use the vibrationally adiabatic approximation for those PES degrees of freedom whose typical frequencies a>j are greater than a>o and a>. Namely, for the high-frequency modes the vibrationally adiabatic potential [Miller 1983] is introduced, [Pg.9]

** Glassy modes high-frequency behavior **

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