Polyatomic systems vibrational energy level

In this chapter we analyzed several developments in SCF approaches to intramolecular dynamics, as pertinent both to the vibrational energy-level structure and to vibrational energy redistribution in polyatomic systems. The emphasis was on methodological progress, and on how the latter throws light on the physical basis for the validity of the method and on possible future applications. The main themes that emerged in the discussion can be summarized as follows. 

Weakly bound systems from van der Waals to strong hydrogen bonds are treated theoretically in ECC in the article by Bogumil Jeziorski Intermolecular Interactions by Perturbation Theory). Related articles are those of Tucker Carrington Vibrational Energy Level Calculations), Wolfgang Domcke Vibronic Dynamics in Polyatomic Molecules), and of Martin Quack Multiphoton Excitation). 

The energy levels of the vibrational modes can be predicted with a reasonable accuracy on the basis of the standard Wilson vibrational analysis (241,244) (called GF analysis). The vibrational motion of atoms in the polyatomic system is approximated by harmonic oscillations in a quadratic force field. Computations of the force constants are the subject of quantum chemistry. 

As already discussed in Section 13.1, the multiphonon pathway for vibrational relaxation is a relatively slow relaxation process, and, particularly at low temperatures the system will use other relaxation routes where accessible. Polyatomic molecules take advantage of the existence of relatively small frequency differences, and relax by subsequent medium assisted vibrational energy transfer between molecular modes. Small molecules often find other pathways as demonstrated in Section 13.1 for the relaxation ofthe CN radical. When the concentration of impurity molecules is not too low, intermolecular energy transfer often competes successfully with local multiphonon relaxation. For example, when a population of CO molecules in low temperature rare gas matrices is excited to the v = 1 level, the system takes advantage ofthe molecular anhannomcity by undergoing an intermediate relaxation of the type... 

This chapter is devoted to recent developments in a class of approximation methods that aim at describing the energy-level structure and dynamics of energy transfer in vibrationally highly excited polyatomic systems. The meth ods that are the subject of the present study are the self-consistent-field (SCF) approximations, in which framework each vibrational mode is described as moving in an effective field obtained by averaging the full potential function... 

When vibrational excitation is supplied to a polyatomic molecule by a technique such as pulsed-laser pumping, the return of the system to equilibrium via collisions is an enormously complex process for a molecule with more than just a few energy levels as should be evident from the data presented for CH4, CD4, CD3H, CHjDj, and CH3F in the preceding section. For example, let = -)- ,(/) be the population density of... 

Table 9.3 compares different ways of storing energy in one particular system (the HF molecule), but we see the same general trends that the correspondence principle predicts for all such systems. Vibrational, rotational, and translational energy levels become more closely spaced as the mass increases (remember that flg and (o both decrease with mass). The degeneracy increases at higher values of the quantum numbers /, n, tty, and n. For polyatomics, such as CO2, we have seen that the vibrational degeneracy also climbs with v. 

Since the lifetimes t are evidently determined by microscopic dynamics rather than by statistics, one must conclude either that statistical theories do not apply to the dissociation of polyatomic vdW molecules or that the lifetimes t are not the predissociation lifetimes (or, possibly, that both statements are true). The first choice — abandoning a statistical description — should not be too upsetting, for two reasons. First, there have been very few tests of statistical theories on a microscopic level, and It Is easy to Imagine that even If a statistical model were microscopically Incorrect It might be valid (on the average) for macroscopic observations. Second, vdW molecules do represent a special class of systems. In which the dissociation energies are very small, and which contain vibrational frequencies In the vdW coordinates which are unusually low. It Is possible that a statistical description not valid for vdU molecule dissociation might still be valid for dissociation of covalent bound species. 

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