Local-mode limit basis

To illustrate the first point concerning a spectator bond for the abstraction reaction, Fig. 17 shows the total reaction probability for the abstraction reaction as a function of the translational energy for total angular momentum J = 0 on the YZCL2 PES with the H20 reactant in the ground rovibrational state [the (00)(0) state in the local mode notation], where the uncleaved bond OHb is treated in various ways. Using a limited number of one or five vibrational basis functions, VBF(OHb) = 1 or 5, means that the OHb bond is unreactive, a spectator. The abstraction reaction probability... 

The fact that both the local- and the normal-mode limits are contained within the algebraic approach allows one to study in a straightforward way the transition from one to the other. It is convenient to use, for this study, the local basis [Eq. (4.17)] and diagonalize the Hamiltonian for two identical bonds... 

With this definition, due to Child and Halonen (1984), local-mode molecules are near to the = 0 limit, normal mode molecules have —> 1. The correlation diagram for the spectrum is shown in Figure 4.3, for the multiplet P = va + vb = 4. It has become customary to denote the local basis not by the quantum numbers va, vh, but by the combinations... 

To sum up, we have developed a general non-perturbative method that allows one to calculate the rate of relaxation processes in conditions when perturbation theory is not applicable. Theories describing non-radiative electronic transitions and multiphonon relaxation of a local mode, caused by a high-order anharmonic interaction have been developed on the basis of this method. In the weak coupling limit the obtained results agree with the predictions of the standard perturbation theory. 

An excellent example of non-accidental intramolecular resonance is provided by a polyatomic molecule with two chemically identical bonds. The spectrum and dynamics of such a molecule may equally well be described by an effective Hamiltonian expressed in basis sets corresponding to either of two opposite limiting cases normal mode (H -,RMAL) and local mode (Hlocal)-... 

As mentioned in the introduction, the above discussion of the small-, large-, and intermediate-molecule limits of electronic relaxation processes can also be utilized with very minor modifications to discuss the phenomena of intramolecular vibrational relaxation in isolated polyatomic mole-cules. ° Figure 4 is still applicable to this situation. The basis functions are now taken to be either pure harmonic vibrational states, some local-mode vibrational eigenfunctions, or some alternative nonlinear mode-type wave-functions. In the following the nomenclature of vibrational modes is utilized, but its interpretation as normal or local can be chosen to suit the circumstances at hand. 

Figure 13. Spectrum of a planar triatomic molecule in the local limit. N = 100, A = -3 cm , and A = 3 cm . (t)j, v, v,) is the degeneracy local mode notation (see the text). The degeneracy associated with the true local mode basis appears in brackets, p is the total number of stretching vibrational quanta in a given polyad.

The H2S abatement efficiency was excellent. The concentration of H2S in the treated gas averaged about 2 parts per million. This removal was better than Stretford and allowed the unit to operate at full capacity. Previously, when the unit operated in the Stretford mode, absorption efficiency fell off whenever the liquid circulation rate exceeded 15% of pump capacity. This resulted in occasional non-compliance with local emission standards and set a practical operating limit for the unit that was well below the design basis capacity. 

---