Transition states energy levels

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). 

Figure 11.5 The effects of changes in reactant and transition-state energy levels on reaction rate, (a) A higher reactant energy level (red curve) corresponds to a faster reaction (smaller AG ), (bl A higher transition-state energy level (red curve) corresponds to a slower reaction (larger AG ).

M.S. Zhao, M. Mladenovic, D.G. Truhlar, D.W. Schwenke, O. Sharafeddin, Y. Yan, D.J. Kouri, Spectroscopic analysis of transition state energy levels Bending-rotational spectrum and lifetime analysis of H3 quasibound states, J. Chem. Phys. 91 (1989) 5302. 

Table 14-1. The energy barriers Eb, and transition state energy levels Bps with respect to the energy of the 1-propanol molecule and the Si(001). surface in separation from each other...

Table 14-3. Energy barriers Eb and transition state energy levels EjS for the dissociation processes 1-1 —> F-l and 1-2 —> F-2 at four levels of surface coverage. The reference for die indicated energy values is the energy of the separated subsystems...

The dependence of the energy barriers on the 1-propanol coverage in the interval [0.25 ML, 1.0 ML] is illustrated by Table 14-3, which contains the energy barriers Eb and transition state energy levels Ej-S with respect to the energy of 1-propanol and Si(001) in isolation from each other. Two processes correspond to O-H bond and C-O bond scission. 

The quantization of transition state energy levels is not simply a mathematical device to add quantum effects to the partition functions. The quantized levels actually show up as structure in the exact quantum mechanical rate constants as functions of total energy [51]. The interpretation of this structure provides clear evidence for quantized dynamical bottlenecks, both near to and distant from the saddle points, as reviewed elsewhere [52]. Quantized variational transition states have also been observed in molecular beam scattering experiments [53]. Analysis of the reactive flux in state-to-state terms from reactant states to transition state levels to product states provides the ultimate limit of resolution allowed by quantum mechanics [53,54]. Quantized energy levels of the variational transition state have been used to rederive TST using the language of quantum mechanical resonance scattering theory [55]. 

Note that if we set kt equal to unity and PT( ) to a unit step function at transition state energy level T, Eq. (9) reduces to (8). 

The characterization of transition states as resonances is a useful analytical tool and provides new insights into fundamental problems of chemical reactivity. It has already been used, for example, to lead to a new computational approach for the calculation of anharmonic transition state energy levels by a reformulation of variational transition state theory (88). 

Figure 2 Density of reactive states, p ( ), for Cl + para-H2 with / = 0 on the G3 surface. Heavy solid curve accurate quantal heavy dashed curve fit light dashed curve components of the fit. The energies, state assignments, and transmission coefficients of the quantized transition state energy levels are indicated next to arrows at the energies of the peaks in the components of the fit. 

Sun L, Base WL (2010) Comparisons of classical and Wigner sampling of transition state energy levels for quasiclassical trajectory chemical dynamics simulations. J Chem Phys 133 044313... 

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