Vibrational anharmonicity relaxation

Am = (Gm — 2Gm) is the vibrational anharmonicity. This Hamiltonian describes excitons as oscillator (quasiparticle) degrees of freedom. Hb represents a bath Hamiltonian. We shall not specify it and merely require that it conserves the number of excitons. The bath induces relaxation kernels. The structure of the final expression is independent of the specific properties of the bath the latter only affects the microscopic expression for the relaxation kernels (51). 

Due to vibrational anharmonicity, this transfer is resonant only for the K = 1 exchange, which has been considered in a previous section, but it remains, in the liquid, faster by several orders of magnitude than V-T relaxation for diatomics. Relaxation of highly excited I2 and Br2 close to the vibrational dissociation limit has been observed in the dense gas (at liquid densities). These indirect measurements of T, were correlated with the gas diffusion coefficient and should hence be more reasonably accounted for in the framework of an isolated binary interaction model. This interesting exjjerimental system raises the question of the influence of the change in molecular dimensions in higher excited states, due to anharmonicity, on the efficiency of collisional deexcitation. This question could jjerhaps be answered by more precise direct relaxation measurements. 

For polyatomics, ordinarily only the last two terms of equation (C3.5.6), the eubie and quartie anharmonic terms, need be considered 134]. In a eubic anharmonic process, excited vibration Q relaxes by interaeting with two other states, say another vibration o and one phonon (or alternatively two phonons). In the quartie proeess, Q relaxes by interacting with three other states, say two vibrations and one phonon. The total rate eonstant for energy loss from Q for cubic... 

Molecular motions (rotation, translation, and vibration) of a water molecule also turn out to be quite different from those of other common liquids. Here all the six unique features of an individual water molecule outlined in Chapter 1 manifest themselves in diverse ways. As we discuss below, not only is the mechanism of displacements of individual water molecules different, but the collective dynamics and dynamical response of bulk water are also different. For example, the rotational motion of an individual water molecule contains a surprising jump component and vibrational energy relaxation of the O—H mode involves a cascading effect mediated by anharmonicity of the bond. These motions are reflected in many important processes such as electrical conductivity, solvation dynamics, and chemical reactions in aqueous medium. 

A convincing example illustrating the effect of vibrational anharmonicity on the probability of vibrational energy transfer has been reported [175] for vibrational relaxation of CO. The CO molecules on high-lying vibrational levels (4 < v < 13) are produced in the O—CS2 system by the reactions... 

Treanor C E, Rich J W and Rehm R G 1968 Vibrational relaxation of anharmonic oscillators with exchange-dominated collisions J. Chem. Phys. 48 1798-807... 

The book thus embraces an extended study on a variety of issues within the theory of orientational ordering and phase transitions in two-dimensional systems as well as the theory of anharmonic vibrations in low-dimensional crystals and dynamic subsystems interacting with a phonon thermostat. For the sake of readability, the main theoretical approaches involved are either presented in separate sections of the corresponding chapters or thoroughly scrutinized in appendices. The latter contain the basic formulae of the theory of local and resonance states for a system of bound harmonic oscillators (Appendix 1), the theory of thermally activated reorientations and tunnel relaxation of orientational... 

The heat capacity models described so far were all based on a harmonic oscillator approximation. This implies that the volume of the simple crystals considered does not vary with temperature and Cy m is derived as a function of temperature for a crystal having a fixed volume. Anharmonic lattice vibrations give rise to a finite isobaric thermal expansivity. These vibrations contribute both directly and indirectly to the total heat capacity directly since the anharmonic vibrations themselves contribute, and indirectly since the volume of a real crystal increases with increasing temperature, changing all frequencies. The constant volume heat capacity derived from experimental heat capacity data is different from that for a fixed volume. The difference in heat capacity at constant volume for a crystal that is allowed to relax at each temperature and the heat capacity at constant volume for a crystal where the volume is fixed to correspond to that at the Debye temperature represents a considerable part of Cp m - Cv m. This is shown for Mo and W [6] in Figure 8.15. 

An additional point that should be considered is that in the harmonic oscillator approximation, the selection mle for transitions between vibrational states is Ay = 1, where v is the vibrational quantum number and Ay > 1, that is, overtone transitions, which involve a larger vibrational quantum number change, are forbidden in this approximation. However, in real molecules, this rule is slightly relaxed due to the effect of anharmonicity of the oscillator wavefunction (mechanical anharmonicity) and/or the nonlinearity of the dipole moment function (electrical anharmonicity) [55], affording excitation of vibrational states with Ay > 1. However, the absorption cross sections for overtone transitions are considerably smaller than for Ay = 1 transitions and sharply decrease with increasing change in Av. 

A non-perturbative theory of the multiphonon relaxation of a localized vibrational mode, caused by a high-order anharmonic interaction with the nearest atoms of the crystal lattice, is proposed. It relates the rate of the process to the time-dependent non-stationary displacement correlation function of atoms. A non-linear integral equation for this function is derived and solved numerically for 3- and 4-phonon processes. We have found that the rate exhibits a critical behavior it sharply increases near a specific (critical) value(s) of the interaction. 

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