Elimination reactions computational modeling

A similar computational modelling approach has been shown to be useful, for example, in studying the mechanism of low-temperature oxidation of alkanes (4), pyrolysis of alkanes (5-7), other gas-phase reactions (8), the formation of photochemical smog (9,10), and peroxide decomposition (11), among others. It is not uncommon to begin with all possible species and by permutation and combination derive a complete set of reactions, and then eliminate a subset by chemical... 

This chapter will examine structure correlations pertinent to carbonyl substitution-elimination reactions as well as results of computational studies of potential energy surfaces and transition-state structures for such reactions. We shall then assess the current standing of the original postulates as well as that of the derivative models employed in the discussion of stereoselection and regioselectivity. 

Let us consider one more important aspect. Simplification of the reaction mechanism by elimination of unimportant constituents is one of the methods for the reduction of its mathematical dimensionality [35-40]. In other words, it leads to the reduction of the number of differential (kinetic) equations to be integrated, underlying the reaction mathematical model. Thus, it facilitates computational procedures, as well as it analyses the kinetic model, in terms of both its use of predicting the reaction behavior under new conditions and for its control. Not less important is also that at the available accuracy for the rate constants of individual steps, the descriptive capacity of kinetic models may decrease as its complexity increases (this question will be discussed more thoroughly in Section 3.3). 

Thermal organic reactions are often classified in terms of the molecular and electronic structure of their transition state or reactive intermediate (which is often taken as a model of the transition state). Thus, for instance, one has the Sn2 transition state for concerted bimolecular nucleophilic substitution reactions one has the E2 and Ei transition states in elimination reactions, etc. Given the transient nature of the transition states, the use of quantum chemical methodologies is essential for the determination of their detailed geometrical and electronic structure. Furthermore, the computation of the associated transition vectors provides information on the reactive mode... 

Determination of equilibrium constants and rate constants is cmcial in order to understand the kinetics of an ATRP. Experimentally, the values of feact, deact, and Katrp can be determined by direct analysis of the polymerization mixture, by, for example, EPR, NMR, GC, GPG, and IR or by the study of low MW model compounds. Furthermore, while some side reartions, for example, thermal initiation of monomer, elimination reactions, transfer reactions, degradation of the catalyst, and some physical parameters (e.g., viscosity and inhomogeneity), may have an important effect on the kinetics of an ATRP, the influence of these parameters may also be investigated by model studies or by computer simulation. " ... 

Boulier, F., Lelranc, M., Lemaire, F., Morant, P.-E. Model reduction of chemical reaction systems using elimination. Math. Comput. Sci. 5, 289 (2011)... 

Eq. (122) represents a set of algebraic constraints for the vector of species concentrations expressing the fact that the fast reactions are in equilibrium. The introduction of constraints reduces the number of degrees of freedom of the problem, which now exclusively lie in the subspace of slow reactions. In such a way the fast degrees of freedom have been eliminated, and the problem is now much better suited for numerical solution methods. It has been shown that, depending on the specific problem to be solved, the use of simplified kinetic models allows one to reduce the computational time by two to three orders of magnitude [161],... 

Figure 2 Intermediate in the EPSP synthase pathway, (a) The mechanism of the reaction catalyzed by EPSP synthase is shown. The reaction proceeds by an addition-elimination mechanism via a stable tetrahedral intermediate, (b) A single turnover reaction is shown in which 10- xM enzyme was mixed with 1 OO-m-M S3P and 3.5-riM radiolabeled PEP. Analysis by rapid-quench kinetic methods showed the reaction of PEP to form the intermediate, which then decayed to form EPSP in a single turnover. The smooth lines were computed from a complete model by numerical integration of the equations based on a global fit to all available data. Reproduced with permission from Reference 7.

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