Resonance unimolecular dissociation rates

Figure A3.12.9. Comparison of the unimolecular dissociation rates for HO2—>H+02 as obtained from the quantum mechanical resonances open circles) and from variational transition state RRKM step...

Dobbyn A J, Stumpf M, Keller H-M and Schinke R 1996 Theoretical study of the unimolecular dissociation HO2—>H+02. II. Calculation of resonant states, dissociation rates, and O2 product state distributions J. Chem. Phys. 104 8357-81... 

In the present review, a new variation on an existing experimental method will be used to show how accurate unimolecular dissociation rate constants can be derived for thermal systems. For example, thermal bimolecular reactions are amenable to study by use of several, now well-known, techniques such as (Fourier transform) ion cyclotron resonance spectrometry (FTICR), flowing afterglow (FA), and high-pressure mass spectrometry (HPMS). In systems where a bimolecular reaction leads to products other than a simple association adduct, the bimolecular reaction can always be thought of as containing a unimolecular... 

B. Unimolecular Dissociation Rates RRKM Theory and Distribution of Resonances... 

Comparison of the HO2 -> H + O2 unimolecular dissociation rates as obtained from the quantum mechanical resonances (kqm, open circles) and from variational transition state RRXM, theory (kuRKM, step function). E,i,f is the threshold energy for dissociation. Also shown is the quantum mechanical average of the as in a AF = 0.075 eV energy interval (kq, solid line) and the experimental prediction (dashed line). Adapted from ref. 122. 

Figure 1 (a) Illustration of the unimolecular dissociation of a reactant molecule ABC into products A and BC. p( ), Rts and Nts are the density of reactant states, the intermolecular distance of the transition state (TS) and the number of open channels at the transition state, respectively. The vertical axis on the left-hand side shows a spectrum dominated by sharp resonances, (b) Schematic representation of the energy dependence of the micro-canonical rate constant k E) (solid line). The dots represent the state-specific quantum mechanical rates kn-... 

In this chapter we elucidate the state-specific perspective of unimolec-ular decomposition of real polyatomic molecules. We will emphasize the quantum mechanical approach and the interpretation of the results of state-of-the-art experiments and calculations in terms of the quantum dynamics of the dissociating molecule. The basis of our discussion is the resonance formulation of unimolecular decay (Sect. 2). Summaries of experimental and numerical methods appropriate for investigating resonances and their decay are the subjects of Sects. 3 and 4, respectively. Sections 5 and 6 are the main parts of the chapter here, the dissociation rates for several prototype systems are contrasted. In Sect. 5 we shall discuss the mode-specific dissociation of HCO and HOCl, while Sect. 6 concentrates on statistical state-specific dissociation represented by D2CO and NO2. Vibrational and rotational product state distributions and the information they carry about the fragmentation step will be discussed in Sect. 7. Our description would be incomplete without alluding to the dissociation dynamics of larger molecules. For them, the only available dynamical method is the use of classical trajectories (Sect. 8). The conclusions and outlook are summarized in Sect. 9. 

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. 

In this chapter, we discussed the principle quantum mechanical effects inherent to the dynamics of unimolecular dissociation. The starting point of our analysis is the concept of discrete metastable states (resonances) in the dissociation continuum, introduced in Sect. 2 and then amply illustrated in Sects. 5 and 6. Resonances allow one to treat the spectroscopic and kinetic aspects of unimolecular dissociation on equal grounds — they are spectroscopically measurable states and, at the same time, the states in which a molecule can be temporally trapped so that it can be stabilized in collisions with bath particles. The main property of quantum state-resolved unimolecular dissociation is that the lifetimes and hence the dissociation rates strongly fluctuate from state to state — they are intimately related to the shape of the resonance wave functions in the potential well. These fluctuations are universal in that they are observed in mode-specific, statistical state-specific and mixed systems. Thus, the classical notion of an energy dependent reaction rate is not strictly valid in quantum mechanics Molecules activated with equal amounts of energy but in different resonance states can decay with drastically different rates. 

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. 

Three-dimensional quantum mechanical calculations have been performed to determine the unimolecular rate constants for the resonances in HOj H + O2 dissociation (Dobbyn et al., 1995). The resonances are not assignable and the fluctuations in the resonance rate constants can be represented by the Porter-Thomas distribution. Equation 8.17. Thus, the unimolecular dissociation of HO2 is apparently statistical... 

In the experimental studies of state specific NO2 unimolecular dissociation (Miy-awaki et al., 1993 Hunter et al., 1993 Reid et al., 1994, 1993), NO2 is first vibra-tionally/rotationally cooled to 1 K by supersonic jet expansion. Ultraviolet excitation is then used to excite a NO2 resonance state which is an admixture of the optically active and the ground electronic states. [It should be noted that in the subpicosecond experiments by Ionov et al. (1993a) discussed in section 6.2.3.1, a superposition of resonance states is prepared instead of a single resonance state.] The NO product states are detected by laser-induced fluorescence. Both lifetime and product energy distributions for individual resonances are measured in these experiments. A stepwise increase in the unimolecular rate constant is observed when a new product channel opens. Fluctuations in the product state distributions, depending on the resonance state excited, are observed. The origin of the dynamical results is not clearly understood, but it apparently does not arise from mode specificity, since analyses of... 

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