Transition state quantized

Detailed analyses of the above experiments suggest that the apparent steps in k E) may not arise from quantized transition state energy levels [110.111]. Transition state models used to interpret the ketene and acetaldehyde dissociation experiments are not consistent with the results of high-level ab initio calculations [110.111]. The steps observed for NO2 dissociation may originate from the opening of electronically excited dissociation chaimels [107.108]. It is also of interest that RRKM-like steps in k E) are not found from detailed quantum dynamical calculations of unimolecular dissociation [91.101.102.112]. More studies are needed of unimolecular reactions near tln-eshold to detennine whether tiiere are actual quantized transition states and steps in k E) and, if not, what is the origin of the apparent steps in the above measurements of k E). 

King R A, Allen W D and Schaefer H F III 2000 On apparent quantized transition-state thresholds in the photofragmentation of acetaldehyde J. Chem. Phys. 112 5585-92... 

Probing Structures and Dynamics of the Quantized Transition States 140... 

Probing the Structures of Quantized Transition States in the H + D2 Reaction... 

In conclusion, we have demonstrated that the DCS for the H + D2 —> HD + H reaction exhibits pronounced oscillatory structures in the backward scattering direction both in experimental and in theory. The physical origin of this structure has been traced to the opening of a sequence of quantized transition state thresholds. 

Because the total angular momentum and its component are conserved during a collision, we can study the reaction dynamics for each value of 7 and M, independently. Since the results are independent of M, we always set M, - 0, and we will not mention it again (but the existence of the Af, quantum number is the reason for the factor of 27 + 1 in the following sentence). In particular, we can study the 7-specific contributions to the rate constant, k (E) [with k(E) of Eq. (3) being a (27 + l)-weighted sum of individual k (E), to the cumulative reaction probability, N (E), and to the density of reactive states, pJ(E). The influence of quantized transition states on chemical reactivity will be analyzed through studies of k (E). 

In this section we discuss the quantized transition state spectra of H + H2 with emphasis on the assignment of quantum numbers and transmission coefficients. The discussion is focused on the total CRP. Another very important aspect of the H, quantized transition states is their role in determining state-selected and state-to-state transition probabilities we refer the reader to previous discussions (9,16) for that subject. 

The excellent agreement between the quantal and synthetic densities of reactive states in Fig. lb demonstrates that quantized transition states globally control the chemical reactivity. All of the reactive flux, up to an energy of 1.6 eV, can be attributed to contributions from the energy levels of the transition state i.e., there is no noticeable background. Thus, this study (and ones to follow) provides a strong validation for approximate transition state theories that postulate the existence of transition states controlling the reaction dynamics. 

The value of the transmission coefficient kt is shown for each feature in Table 2. (The value of kt for the last feature is greater than 1 because it includes contributions from higher energy transition states that have not been included in the fit.) Many of the values of the transmission coefficients are very close to unity, suggesting that these features correspond to quantized transition states that are nearly ideal dynamical bottlenecks to the reactive flux. Several of the values of kt deviate from unity this could be the result of the assumption of parabolic effective potential barriers or from recrossing or other multidimensional effects. 

Each of the 10 energy levels of the H3 quantized transition state can be associated with a set of linear-triatomic quantum numbers (66) [vjv ] where v, and v2 are the stretch and bend quantum numbers respectively for modes orthogonal to the reaction coordinate... 

We conclude above that the 7 = 0 cumulative reaction probability is globally controlled by quantized transition states, and we have assigned stretch (vj) and bend (v2) quantum numbers for the motion orthogonal to the reaction coordinate. As discussed below, similar conclusions can be reached for the 7 = 1 and 7 = 4 cumulative reaction probabilities. We have obtained spectroscopic constants for the H2 transition state by fitting the E7 values of [00°], [02°], [04°], [10°], [12°], and [20°] for 7 = 0 and [00°] for 7 = 4 by (66)... 

Cuccaro et al. (96) interpreted the time delays in Table 2 as resonances and assigned a value of 0 for the third quantum number v without explanation. We identify these resonances as quantized transition states. The analysis presented above of scattering by one-dimensional barriers, with the conclusion that the v = 0 pole is the most important because it is closest to the real energy axis, supplies a justification for the assignment of the third quantum number. 

Fitting the quantal density by a sum of terms KTpT( ) is difficult because of the large number of transition states for 7 = 4. However, quantized transition state control of chemical reactivity can be assessed for 7 = 4 without identifying all of the individual contributions to the total density by comparing the accurate values of N4(E) with those in the next to last column of Table 4. If the transition states were ideal (kt = 1), the two numbers would be equal. Up to 1.228 eV, the energy of the sixth peak, the numbers are very close at 1.228 eV the accurate value of N4(E) is 24. Thus, the quantized transition states up to 1.228 eV are nearly ideal dynamical bottlenecks. Above 1.228 eV the quantal N4(E) is somewhat smaller than the predicted value, but even at 1.570 eV the difference is only 15%. This difference may be due to the inaccuracy of Eq. (25) at high v2 or to... 

The accurate density of reactive states O + H2, J = 0 is shown in the top left panel of Fig. 5, and results of the quantized transition state theory fit are in Table 6, along with assignments discussed below. The quantal and fitted densities are indistinguishable to plotting accuracy (14), indicating that quantized transition states control the chemical reactivity. The density closely resembles that for the reaction of H with H2 up to about 1.3 eV. Analogous features are associated with the same sets of quantum numbers through the [06°] transition state at 1.218 ev. 

The fit identified 17 features up to 1.9 eV. The width parameter WT generally scales inversely with v, and directly with v2, as expected (14). For many of the states kt is very close to 1.00, and its smallest value is 0.54 (14). Thus many of the quantized transition states are nearly ideal dynamical bottlenecks, and even ones with large bend quantum numbers are quite good. 

Many but not all of the quantized transition states observed in the densities of state-selected reaction probability are observed as peaks in the total density of reactive states. Some highly bend excited states (e.g., [0 12°], and [0 14°]) are observed as peaks only in the state-selected dynamics. If the closely spaced features in the stretch-excited manifolds for p(i are indicative of supernumerary transition states more closely spaced in energy than the variational transition states (which adiabatic transition state theory also suggests), then only some of the supernumerary transition states, in particular S[20°], 5[22°], 5[24°], 5[30°], 5[32°], 5[34°], and 5[36°], are observed in the total density, i.e., only some are of the first kind. The other supernumerary transition states identified in the state-selected dynamics are of the second kind. 

Spectroscopic constants for the variational transition states were obtained by a fit similar to that used for the H + H2 reaction. In this case, noting that quantized transition states are associated with poles of the S matrix having the form... 

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