Chemically activated reactions

The recombination A + B AB is the reverse reaction of the unimolecular dissociation of AB. The principle of detailed balancing ties both reactions together by the thermodynamic equilibrium constant ku 

Consequently, /tree is—like k i—pressure dependent. This is obvious for the high-pressure limit when collisions with the bath gas quickly establish a Boltzmann distribution of the population, but Smith et al. [9,10] argue that equation (30) also holds for lower pressures. 

In the introduction we characterized a pressure-dependent reaction as a process that is composed of an excitation step followed by either deactivation or reaction to (often multiple) products. A closer look at the recombination in terms of the underlying scheme of elementary reactions 

Application of the steady-state assumption for [AB ] yields the apparent recombination rate constant for stabilization, defined as d[AB]/ dt = fcrec[A][B], 

If we combine equations (4) and (31) we can show that equation (30) is obtained  

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Kim S K, Guo J, Baskin J S and Zewail A H 1996 Femtosecond chemically activated reactions concept of nonstatistical activation at high thermal energies J. Phys. Chem. 100 9202-5... 

Figure 13. Model potential energy surfaces for competitive dissociation of a chemically activated reaction intermediate to yield two products.

CHEMACT A Computer Code to Estimate Rate Constants for Chemically-Activated Reactions, Dean, A. M Bozzelli, J. W. and Ritter, E. R. Combust. Sci. Tech. 80, 63-85 (1991). A computer code based on the QRRK treatment of chemical activation reactions to estimate apparent rate constants for the various channels that can result in addition, recombination, and insertion reactions. 

Total pressure also affects the rate constant for a class of bimolecular reactions called chemical activation reactions. A generic example is the reaction of molecules A and B to form products D and E, but where an alternate reaction is recombination of the reactants to form the stable molecule C. An example of this type of chemical activation reaction reaction is... 

The theoretical analysis of chemical activation reactions is similar to the Lindemann theory of unimolecular and association reactions. There are a number of competing reaction pathways. Depending on total pressure, concentrations of the participating species, and temperature, the outcome of the competition can change. 

The chemical activation high-pressure rate constant Mmol.oo for formation of product molecules D and E is seen to be inversely proportional to pressure. Stated another way, the product bimol,oo [M] is pressure independent, depending only on temperature. In specifying the rate expression for a chemical activation reaction, one supplies the three Arrhenius parameters for the temperature dependence of the product Mmol.oo [M] as... 

The treatment given in this section is analogous to the Lindemann theory of unimolecu-lar reactions. It provides a general explanation of pressure effects in bimolecular chemical activation reactions. A more sound theoretical treatment of chemical activation kinetics is given in Section 10.5. 

Chemical activation reaction kinetics are illustrated by the reaction... 

Fig. 9.2 Bimolecular rate constant for the chemical activation reaction 9.151 as a function of pressure for three different temperatures.

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

Transition-state theory is based on the assumption of chemical equilibrium between the reactants and an activated complex, which will only be true in the limit of high pressure. At high pressure there are many collisions available to equilibrate the populations of reactants and the reactive intermediate species, namely, the activated complex. When this assumption is true, CTST uses rigorous statistical thermodynamic expressions derived in Chapter 8 to calculate the rate expression. This theory thus has the correct limiting high-pressure behavior. However, it cannot account for the complex pressure dependence of unimolecular and bimolecular (chemical activation) reactions discussed in Sections 10.4 and 10.5. 

Fig. 10.8 Reaction pathways in the QRRK analysis of bimolecular chemical activation reactions.

Pressure effects are also seen in a class of bimolecular reactions known as chemical activation reactions, which were introduced in Section 9.5. The treatment in that chapter was analogous to the Lindemann treatment of unimolecular reactions. The formulas derived in Section 9.5 provide a qualitative explanation of chemical activation reactions, and give the proper high- and low-pressure limits. However, that simple treatment neglected many quantum mechanical effects, namely the energy dependence of various excitation/de-excitation steps. 

This section treats the theory of chemical activation reactions more rigorously, at the same level of approximation as in the discussion of unimolecular reactions in Section 10.4.4. That is, the QRRK theory of chemical activation reactions is developed here. This theory for bimolecular reactions was set out by Dean and coworkers [93,428],... 

The QRRK treatment of bimolecular chemical activation reactions considers in more detail the energy-dependence of the rate coefficients. Begin by modifying the chemical activation reaction scheme of Eqs. 9.132 to 9.134 to account for the specific energy levels of the rate constants and activated species. 

Chemical activation causes many problems. First of all, rates are now a function of P (as well as 7), adding another dimension to the rate estimation functions. Also, chemically-activated rates depend on properties of the complete adduct molecule, not just some of its functional groups. And, in order to compute the chemically-activated rates, one must enumerate all the important product channels, i.e. identify a large number (Matheu et al., 2003a, b) of different reactions and products, which could be of completely different types. As a result, each chemically-activated reaction has unique rate parameters, not amenable to easy generalization. It would not be practical to compute or to store the rate parameters for every conceivable chemically-activated reaction. 

RMG, which was implemented by Jing Song (2004), uses a version of the rate-based model-construction algorithm described by Susnow et al. (1997), but it treats non-thermalized chemically-activated reaction paths on an equal basis with ordinary thermal reactions, as done by Matheu et al. (Matheu, 2003 Matheu et al., 2003a, b). Byproducts and activated reaction intermediates are... 

Unlike most model-generation software described in the literature, RMG correctly handles pressure and temperature variations it does this by using k(T,P) computed for the chemically-activated reactions at discrete (T,P) to determine coefficients in a Chebyshev form (Venkatesh et al., 1997) suitable for use in the differential equation solver. 

The new RMG software combines high-accuracy chemistry estimation methods (including methods for automatically identifying chemically-activated reaction paths) with the extensible 21st century functional group tree data model described above, so it is now much easier for users to add, modify, and document the chemical assumptions that underlie the models than it was using the previous generation of model-construction software, and the software does not need to be modified or recompiled when new chemistry is added. 

States of unimolecular reactants prepared by collisional energization and chemical activation, reactions (1) and (2), can also be viewed as incoherent superposition states. The most specific excitation will occur when the collision partners are in specific vibrational/rotational states and the relative translational energy is highly resolved. However, even for this situation it is difficult to avoid preparing a superposition state since the collisions have a distribution of orbital angular momentum. 

Using the results obtained on the phenyl system for the dibenzofuran + O2 system, kinetics of each path, as a function of temperature and pressure are determined using bimolecular chemical activation analysis. The high-pressure-limit kinetic parameters from the calculation results are again obtained with cannonical Transition State Theory. QRRK analysis is utilized to obtain k(E) and master analysis is used to evaluate the fall-off behaviour of this complex bimolecular chemical activation reaction [34]. 

High Pressure limit kinetic parameters are obtained from canonical Transition State Theory calculations. Multifrequency Quantum Rice-Ramsperger-Kassel (QRRK) analysis is used to calculate k(E) data and master equation analysis is applied to evaluate fall-off in this chemically activated reaction system. 

Unimolecular dissociation and isomerization reactions of chemically activated and stabilized adduct resulting from addition or combination reactions are analyzed by constructing potential energy diagrams. Some high-pressure rate constants for each channel are obtained from literature or referenced estimation techniques. Kinetics parameters for uni-molecular and bimolecular (chemical activation) reactions are then calculated using multifrequency QRRK analysis iork(E) [199, 200, 63]. 

Multi channel, multi-frequency Quantum RRK calculations are performed for k(E) with master equation analysis for falloff on the chemical activated phenyl peroxy radical [PhOO ] and the intermediates (isomers) in this complex reaction system. This provides an evaluation of the rate constants for the formation of stabilized adducts or reaction products as a function of pressure and temperature. The bi-molecular chemical activated reaction of Phenyl + O2 system is carried out using the CHEMASTER program and incorporates all adducts and product channels illustrated. QRRK with Master equation analysis is used for unimolelcular dissociation of each adduct, but only isomeration to parallel, adjacent products / wells is included in the dissociation of stabilized intermediates. The input file for the phenyl + O2 reaction system is given in the appendix F. 

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