Coupling of Vibrations

The coupling of vibrational and electronic motions in degenerate electronic states of inorganic complexes, part 1 state of double degeneracy. A. D. Liehr, Prog. Inorg. Chem., 1962, 3, 281-314 (25). 

Fig. 8. Scattering the transition state from the surface. Measured vibrational distribution of NO resulting from scattering of laser-prepared NO(v = 15) from Au (111) at incidence = 5 kJ mol-1. Only a small fraction of the laser-prepared population of v = 15 remains in the initial vibrational state. The most probable scattered vibrational level is more than 150 kJ mol-1 lower in energy than the initial state. Vibrational states below v = 5 could not be detected due to background problems. These experiments provide direct evidence that the remarkable coupling of vibrational motion to metallic electrons postulated by Luntz et al. can in fact occur. (See Refs. 44 and 59.)...

Hence, according to the symmetry selection rule, n —> n transitions are allowed but n —> ti transitions are forbidden. However, in practice the n —> it transition is weakly allowed due to coupling of vibrational and electronic motions in the molecule (vibronic coupling). Vibronic coupling is a result of the breakdown of the Born-Oppenheimer approximation. 

The conclusion that variations in the coupling of vibrational modes in these dimers is not responsible for the entire frequency shift is an important point in that it justifies the search for a chemical rationale of the bonding differences in Mo2Xf and Mo2(02CR)4. The authors suggest that 6 bonds may make an important bonding contribution in rhenium dimers and molybdenum carboxylates to account for Fmm near 4.5 mdyne A-1. Furthermore, it is proposed that such a 6 component would probably not contribute significantly in the molybdenum halides where is near 3.5 mdyne A"1, possibly... 

Vibrational (Vibronic) Structure.—The sub-bands associated with any electronic transition due to coupling of vibrational transitions with the electronic transition. 

In each model the coupling of vibrations is taken into account by the addition of crossterms. Two important facts arise from this and a general appreciation of Eqs. 2.34-2.36 ... 

The full Hamiltonian is the sum of the free system Hamiltonian H the intersystem electron-electron interaction Hamiltonian He, the vibron Hamiltonian Hy including the electron-vibron interaction and coupling of vibrations to the environment (dissipation of vibrons), the Hamiltonians of the leads Hr, and the tunneling Hamiltonian Ht describing the system-to-lead coupling... 

If the mechanical degrees of freedom are coupled strongly to the environment (dissipative vibron), then the dissipation of molecular vibrations is determined by the environment. However, if the coupling of vibrations to the leads is weak, we should consider the case when the vibrations are excited by the current flowing through a molecule, and the dissipation of vibrations is also determined essentially by the coupling to the electrons. Here, we show that the effects of vibron emission and vibronic instability are important especially in the case of electron-vibron resonance. 

Liehr, Andrew D., The Coupling of Vibrational and Electronic Motions in Degenerate Electronic States of Inorganic Complexes. Part I. States of... 

Figure 10 A typical trajectory showing rotational excitation accompanying vibrational de-excitation (i.e. a vibration to rotational energy transfer) [71]. The top panel shows the evolution in the Z (molecule-surface distance) and r (molecular bond length) coordinates. In the lower panel, the motion is projected onto the r — 0 (molecular bond orientation) plane. Coupling of vibrations and rotations occurs because the molecule attempts to dissociate at an unfavourable bond angle.

It must, however, be borne in mind that minor shifts and weak splittings of the IR bands may arise on account of lowering of site symmetry because of strong lattice effects or of coupling of vibrations between perchlorate groups or from a purely isotopic effect within the group (15, 16). For example, the broad and strong band due to the v mode of ionic perchlorate is often split because of lattice effects. Despite these limitations, with a little care and caution, coordinated and noncoordinated perchlorate(s) are conveniently identified by IR spectroscopy. 

The infrared and Raman spectra of ice is complicated by inter- and intramolecular coupling of vibrations (Bertie, 1968). However, the problem of spectral analysis is simplified by measuring the spectra of, for example, dilute H20 in D20 ice (Homig et al., 1958). In this... 

When you heat a crystalline solid the kinetic energy and hence the amplitude of the oscillations of the molecules increases. The material expands. As it does so the attractive force between the molecules decreases (see Chapter 8, page 208). At the melting temperature this force of attraction is not enough to keep the molecules in place and the material melts. Now the motion becomes a complex coupling of vibrational oscillations and translational movement, as holes" open up as a result of random displacements of neighbors. Clearly, there has to be enough empty space" in the material as a whole for this to occur. 

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