Vibrational states energy

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

FIGURE 7.10 An energy level diagram for a molecule or complex ion showing the vibrational energy states superimposed on the electronic states. 

Gray, S. K., and Child, M. S. (1984), The Vibrational Energy States of Two Coupled Modes in Formaldehyde Classical, Quantum and Semiclassical Analysis, Mol. Phys. 53,961. 

While the harmonic oscillator is a good approximation to the behavior of a molecule in the lower vibrational energy states, marked deviations occur at higher energies. At the lower energy levels the change in the distance between the atomic centers during the... 

Absorption of infrared radiation causes transitions between vibrational energy states of a molecule. A simple diatomic molecule, such as H—Cl, has only one vibrational mode available to it, a stretching vibration somewhat like balls on the ends of a spring ... 

Figure 29. Relative cross sections for collisional dissociation of CHjBr in selected vibrational-energy states as function of kinetic energy. Data were obtained by photoion photoelectron coincidence technique and were analyzed by assuming only backscattering in center of mass. Maxima of curves were normalized to same relative cross section.86b...

It is demonstrated that the formula for the vibrational energy states of a diatomic molecule should be written as En/hc = Go ioj n - - 1/2) — (OeX (n + 1/2) with non-zero Go. Go values are evaluated for some diatomic hydrides and the effect of Go on the theoretical calculation of isotopic exchange equilibrium constants is shown. 

In the literature it is seen that some approximate formulas for energy eigenvalues E(v, J) for diatomics have been obtained. In fact, this is the traditional approach for chemists and physicists who study vibrations of molecules only in the lowest few vibrational energy states. For such vibrations the diatomic potential is well approximated by the harmonic oscillator with smaller anharmonic corrections, i.e., the Dunham (D) expression (see Section II,A) serves as a good approximation for that... 

As discussed in Chapter 2, atmospheric molecules are characterized by discrete rotational and vibrational energy states, and by their electronic configurations (see Figure 4.1). The absorption of photons can induce transitions between ground and excited states. The difference between rotational energy levels are much smaller than those of the vibrational... 

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