Unimolecular resonance width

Even at room temperature, the sum over the angular momentum may include hundreds of rotational states, depending on the rotational constants. Thus, the temperature and pressure dependent unimolecular rate includes averaging over a very large number of resonance states and therefore a reasonable question is to which extent the quantum mechanical fluctuations can survive this averaging. As was shown by Miller [288], the rate k ni, T) is actually related to the micro-canonical rate constant averaged over the distribution of resonance widths Q k), k v, introduced in Eq. (51),... 

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

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 ... 

Figure 12 Resonance widths F in the unimolecular dissociation of HCO for three progressions, ui, vz, and U3 are the number of quanta in the HC stretching, the CO stretching, and the HCO bending mode, respectively. Comparison between experimental and calculated results. Reprinted, with permission of the American In.stitute of Physics, from Ref. 70...

These experiments stimulated theoretical work by us (9-14), independently by Schinke and co-workers (15-17), and recently both groups (18) to rigorously model this unimolecular dissociation. Ab /wiYio-based potential energy surfaces were constructed by these groups, and used in quantum dynamics calculations to obtain the real energies and widths of the HOCl resonances for OH-overtones. The results of our calculations and their interpretation will be reviewed below. However, before describing that work, we present a short overview of the theory and calculation of unimolecular resonances. 

Tobiason J D, Dunlap J R and Rohifing E A 1995 The unimolecular dissociation of HCO a spectroscopic study of resonance energies and widths J. Cham. Phys. 103 1448-69... 

More recently, Mies and Kraus have presented a quantum mechanical theory of the unimolecular decay of activated molecules.13 Because of the similarity between this process and autoionization they used the Fano theory of resonant scattering.2 Their theory provides a detailed description of the relationships between level widths, matrix elements coupling discrete levels to the translational continuum, and the rate of fragmentation of the molecule. 

If the lifetime of the excited resonance state is too long for direct measurement of the rate via the widths of the spectral features, one can use a third laser (the probe laser in Fig. 11) to resonantly promote the molecules from this level to a rovibrational level in the excited electronic state. The decrease of the total LIF signal as function of the delay time between pump and probe laser reflects the state-specific dissociation rate. The limitation of the SEP technique is that an excited state has to be found, which lives long enough and which is accessible by all three lasers. Molecules, which have been studied by SEP spectroscopy in the context of unimolecular dissociation, are HCO, DCO, HFCO and CH3O. 

Several conclusions can be drawn from Eqs. (76) and (77). First, the influence of fluctuations is the largest when the number of open channels u is of the order of unity, because then the distribution Q k) is the broadest. Second, the effect of a broad distribution of widths is to decrease the observed pressure dependent rate constant as compared to the delta function-like distribution, assumed by statistical theories [288]. The reason is that broad distributions favor small decay rates and the overall dissociation slows down. This trend, pronounced in the fall-of region, was clearly seen in a recent study of thermal rate constants in the unimolecular dissociation of HOCl [399]. The extremely broad distribution of resonances in HOCl caused a decrease by a factor of two in the pressure-dependent rate, as compared to the RRKM predictions. The best chances to see the influence of the quantum mechanical fluctuations on unimolecular rate constants certainly have studies performed close to the dissociation threshold, i.e. at low collision temperatures, because there the distribution of rates is the broadest. 

For a quasi-stationary resonance state the unimolecular reactant moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval t has elapsed t may be called the lifetime of the almost stationary resonance state. The energy spectrum of these states will be quasi-discrete it consists of a series of broadened levels with Lorentzian line-shapes [recall Eq. (4.35)], whose full-width at half-maximum F is related to the lifetime by F = hH. 

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. 

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... 

Computations of shapes and widths of resonance lines have been performed for realistic, nevertheless somewhat marginal, examples of unimolecular breakdown, namely for a resonance in He-Nj scattering and for Xe-Di (see also the... 

Consider again the potential given by equation (10). If its behaviour is examined at large p values, it is seen that it has three symmetric saddles at height (6X ) at p=X, and eventually goes to minus infinity. Therefore all the states which it supports are actually metastable, and they will eventually decay by quantum mechanical tunnelling in other words, they are typical quantum mechanical resonances, to which we may associate a width r and a lifetime =fi/r. This model has already been considered [35,36] for unimolecular reaction theory, where the resonance li fetime is most naturally related to the inverse of the unimolecular rate constants k=x... 

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