Valence bond vibration

In the Bom-Oppenlieimer [1] model, it is assumed that the electrons move so quickly that they can adjust their motions essentially instantaneously with respect to any movements of the heavier and slower atomic nuclei. In typical molecules, the valence electrons orbit about the nuclei about once every 10 s (the iimer-shell electrons move even faster), while the bonds vibrate every 10 s, and the molecule rotates... 

The coefficients bi and bf describe the dependence of the potential energy on the atomic vibrational amplitude along the valence bonds. There is a parabolic relationship between the potential energy and the vibration amplitude... 

We demonstrate that the spectral function of valence harmonic vibrations of a diatomic group that effects rotational reorientations is broadened by w. The vector of atom C displacements relative to the atom B (see Fig. A2.1) may be represented as x(t)e(t), where x(t) is the change in the length of the valence bond oriented at the time t along the unit vector e(/). Characteristic periods of valence vibrations are much shorter than periods of changes in unit vector orientations. As a consequence, the GF of the displacements defined by Eq. (4.2.1) can be expressed approximately as ... 

Spectroscopic techniques look at the way photons of light are absorbed quantum mechanically. X-ray photons excite inner-shell electrons, ultra-violet and visible-light photons excite outer-shell (valence) electrons. Infrared photons are less energetic, and induce bond vibrations. Microwaves are less energetic still, and induce molecular rotation. Spectroscopic selection rules are analysed from within the context of optical transitions, including charge-transfer interactions The absorbed photon may be subsequently emitted through one of several different pathways, such as fluorescence or phosphorescence. Other photon emission processes, such as incandescence, are also discussed. 

Fig. 9.3. Rate of increase of the mean square amplitude of thermal vibration with temperature plotted as a function of bond valence. The circles represent the sum of uncorrelated atomic displacements along the bond direction, the lines represent the expected bond vibrational amplitudes calculated from eqn (9.9).

When this kind of interaction occurs between vibrational states instead of electronic states it is called Fermi resonance we shall discuss this later (Sect. 10.8). In fact, the whole qualitative concept of resonance stabilization as used in the valence bond theory is just the same principle in still another guise. 

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