Unimolecular resonance overlapping

There are a number of open issues associated with statistical descriptions of unimolecular reactions, particularly in many-dimensional systems. One fundamental issue is to find a qualitative criterion for predicting if a reaction in a many-dimensional system is statistical or nonstatistic al. In a recent review article, Toda [17] discussed different aspects of the Arnold web — that is, the network of nonlinear resonances in many-dimensional systems. Toda pointed out the importance of analyzing the qualitative features of the Arnold web— for example, how different resonance zones intersect and how the intersections further overlap with one another. However, as pointed out earlier, even in the case of fully developed global chaos it remains challenging to define a nonlocal reaction separatrix and to calculate the flux crossing the separatrix in a manydimensional phase-space. 

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. 

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... 

Compared to the large number of experimental studies of state-specific decomposition for van der Waals molecules, there is a paucity of such experimental data for the unimolecular decomposition of covalently bound molecules. This is because, for the latter class of molecules, it is often the case that the molecule s density of states is sufficiently large and its unimolecular lifetime sufficiently short that there is extensive overlapping of the resonance line widths. Experimental studies of state specific unimolecular decomposition are listed in table 8.4. In the following, experimental studies of D2CO, HFCO, and NOj state-specific decomposition are reviewed. 

Several theoretical studies have related resonance widths and the unimolecular rate constant for overlapping resonances.The following discussion focuses on studies based on the random matrix version of Feshbach s optical model,especially the results of Peskin et al ... 

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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