Unimolecular resonance isolated

Table 8.1. Quantum Mechanical Studies of Positions and Widths of Isolated Unimolecular Resonances. ...

Figure A3.12.8. Possible absorption spectrum for a molecule which dissociates via isolated compound-state resonances. Eq is the unimolecular threshold. (Adapted from [4].)...

The theory of isolated resonances is well understood and is discussed below. Mies and Krauss [79, ] and Rice [ ] were pioneers m treating unimolecular rate theory in temis of the decomposition of isolated Feshbach resonances. 

In indirect methods, the resonance parameters are determined from the energy dependence of the absorption spectrum. An important extra step — the non-linear fit of (t E) to a Lorentzian line shape — is required, in addition to the extensive dynamical calculations. The procedure is flawless for isolated resonances, especially if the harmonic inversion algorithms are employed, but the uncertainty of the fit grows as the resonances broaden, start to overlap and melt into the unresolved spectral background. The unimolecular dissociations of most molecules with a deep potential well feature overlapping resonances [133]. It is desirable, therefore, to have robust computational approaches which yield resonance parameters and wave functions without an intermediate fitting procedure, irrespective of whether the resonances are narrow or broad, overlapped or isolated. 

Unimolecular reactants are energized by a variety of experimental techniques including collisional and chemical activation, internal conversion and intersystem crossing transitions between electronic states, and different photo-activation techniques, which include excitation of isolated resonance states for reactants with a low density of states (see also Sect. 3). Trajectory simulations usually begin with the preparation of an ensemble of trajectories, whose initial coordinates and momenta resemble — as close as possible — those realized in a particular experiment [20,329]. 

The theory of isolated resonances is well understood and is discussed below. Some initial work has been done on the theory of overlapping resonances (Remade et al., 1989 Desouter-Lecomte and Culot, 1993 Someda et al., 1994a,b) and its relation to experiment (Reid et al., 1994). Much of the research of overlapping resonances has its origins in nuclear physics, where the dissociation of a compound nucleus is treated (Ericson, 1960, 1963 Satchler, 1990 Rotter, 1991). For example, fluctuations in product state populations, called Ericson fluctuations (Satchler, 1990 Rotter, 1991), may arise from coherent excitation of overlapping resonances. However, more work needs to be done to develop a complete theory of overlapping resonances and this topic is not discussed here. Mies and Krauss (1966, 1969) and Rice (1971) were pioneers in treating unimolecular rate theory in terms of the decomposition of isolated Feshbach resonances. 

A possible absorption spectrum for a molecule near its unimolecular dissociation threshold is shown in figure 8.1. Below the absorption lines for the molecular eigenstates are very narrow and are only broadened by interaction of the excited molecule with the radiation field. However, above the excited states leak toward product space, which gives rise to characteristic widths for the resonances in the spectrum. Since the line widths do not overlap, the resonances are isolated. Each... 

Theoretical studies (Beswick and Shapiro, 1982 Chu and Datta, 1982 Hutson et al., 1983 Ashton et al., 1983 Schatz et al., 1988) have shown that many van der Waals molecules, such as He—12 and Ar—HCl, dissociate via isolated resonances with state-specific rate constants. The wave functions for the resonances are found to be assignable, so that the unimolecular decomposition is mode specific. However, for the van der Waals molecules ArCl2 (Halberstadt et al., 1992), Arlj (Gray, 1992a) and those formed by rare-gas atoms attached to aromatic molecules (Semmes et al., 1990) there is substantial coupling between zero-order states in forming the resonance states. 

In the previous section excitation of a single, isolated resonance and its ensuing unimolecular decomposition was considered. However, unimolecular dynamics has also been investigated by exciting a superposition of resonance states, which is initially localized in one part of the molecule, for example, a C—H bond. If this superposition contains all the resonance states in the energy width AE of the excitation process, statistical unimolecular decomposition might be expected after complete IVR for the... 

From this discussion it becomes quite clear that the fundamental expression of statistical unimolecular rate theory in equation (46) is an average quantity. When considered as an energy average over many isolated long-lived resonance scattering states in the interval A , one has the inequality (48) ... 

However, it is not possible to recover the nontrivial dependence of k(E, J) on angular momentum J and other good quantum numbers by this procedure. The question has been discussed critically. Formally, one might consider energy to be a sufficient index, if all decaying metastable states correspond to completely separated, isolated resonances. However, in practice this is rather the exception than the rule in unimolecular rate theory. Under normal circumstances one must allow for a dense set of heavily overlapping resonances with a variety of good quantum numbers. 

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