State specific rate constants

If all the resonance states which fomi a microcanonical ensemble have random i, and are thus intrinsically unassignable, a situation arises which is caWtA. statistical state-specific behaviour [95]. Since the wavefunction coefficients of the i / are Gaussian random variables when projected onto (]). basis fiinctions for any zero-order representation [96], the distribution of the state-specific rate constants will be as statistical as possible. If these within the energy interval E E+ AE fomi a conthuious distribution, Levine [97] has argued that the probability of a particular k is given by the Porter-Thomas [98] distribution... 

If the state-specific rate constants are assumed continuous, equation (A3.12.65) can be written as [103]... 

In order to discuss predissociation dynamics, it is also important to derive a state-specific rate constant based on the measurements of absorption and dissociation cross sections. 

Conventional FTIR instruments, in which the interferometer mirror is translated at a constant velocity, are ideally suited to the analysis of steady state infrared emission. However, time resolution of the infrared emission is required in many applications, such as the measurement of absolute rate constants for the formation or subsequent relaxation of a vibrationally excited species. It is then necessary to follow the intensity of the emission (at a particular wavenumber if state-specific rate constants are required) as a function of time. For continuous-wave experiments, crude time resolution... 

At 2000 K and 1 atm, Hollander s state-specific rate constant becomes k. = 1.46 x 1010 exp(-AE/kT) s-1, where AE is the energy required for ionization. For each n-manifold state the fraction ionized by collisions is determined, as well as the fraction transferred to nearby n-manifold states in steps of An = 1. Then the fractions ionized from these nearby n-manifold states are calculated. In this way a total overall ionization rate is evaluated for each photo-excited d state. The total ionization rate always exceeds the state-specific rate, since some of the Na atoms transferred by collisions to the nearby n-manifold states are subsequently ionized. Table I summarizes the values used for the state-specific cross sections and the derived overall ionization and quenching rate constants for each n-manifold state. The required optical transition, ionization, and quenching rates can now be incorporated in the rate equation model. Figure 2 compares the results of the model calculation with the experimental values. 

In what follows, we will discuss the IVR dynamics and VP event for a collinear nonrotating triatomic vdW complex A..BC. For this model, all the complications that arise from the partitioning of the total angular momentum of the complex into the relative angular momentum of the dissociation fragments and intrinsic angular momentum of the diatomic fragment do not appear, and the quantum (Q) state-specific rate constant of the VP event in Eq.(l) can be written in more details as... 

To conclude this section, for many reactant molecules it is expected that a micro-canonical ensemble of resonance states will contain states which exhibit mode-specific decay and can be identified by patterns (i.e., progressions) in the spectrum, as well as unassignable states with random i and, thus, state-specific rate constants with random fluctuations. In general, it is not expected that the ij , which form a microcanonical ensemble, will have identical k which equal the RRKM k(E). 

Figure 8.4 Porter-Thomas distribution of state specific rate constants, Eq. (8.15), for v 1, 2,4, 8, and In these plots x = k and (x) = k (Polik et al, 1990b).

The connection between the Porter-Thomas nonexponential N(r, E) distribution and RRKM theory is made through the parameters k and v. The average of the statistical state-specific rate constants k is expected to be similar to the RRKM rate constant k(E). This can be illustrated (Waite and Miller, 1980) by considering a separable (uncoupled) two-dimensional Hamilton H = + Hy whose decomposition path is... 

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. 

Thus, in the high-pressure limit k(E + dE, while /c(co, E) for the low-pressure limit is one divided by the average of the inverse of the state-specific rate constants. If all the k( are equal, (oo, E) - k(0, E) and normal RRKM behavior is observed. However, for statistical state specificity, where there are random fluctuations in the k , k(u>, E) will be pressure dependent. 

Experimental and theoretical studies in the past decade and a half have shown that deposition of energy in the different degrees of freedom, e.g., translational, vibrational, rotational, electronic, of the reagents of an elementary gas-phase chemical reaction can influence the rate and outcome of this process drastically differently [1-3]. The measurement of state-specific rate constants (or cross sections) has allowed detailed inferences to be made on the dynamics of simple reactions [4-9]. 

A very widely employed method for the measurement of spin-orbit state-specific rate constants is the time-resolved measurement of the concentrations of individual atomic levels after formation of these species from a suitable precursor, either by flash photolysis [13], or, more recently, by laser photodissociation. The concentrations of the various atomic reactant states are monitored by atomic absorption or fluorescence spectroscopy using atomic emission sources [14], or, for spin-orbit-excited states, by observation of the spontaneous infrared emission [15-18]. Recently, Leone and co-workers have utilized gain/absoiption of a colour centre and diode infrared laser to probe the relative populations of ground and spin-orbit excited halogen atoms produced in a chemical reaction [19] and also by photodissociation [20],... 

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