Kinetics Based on Rate Constants or Energies

The linear -representation is designed for studies that put emphasis on reactants and products, while the circular -representation places attention on the catalyst and its cychc nature. In addition, the circular representation can work 

1) Interestingly, an electrical field can affect the efficiency of a catalytic cycle. For instance, Shaik et al calculated its effect on a model of a P450 enzyme, reachii the conclusion that the force and the direction of the field can influence selectivity in the oxidation process [ 12]. 

2) The Curtin-Hammett principle is an old example of the simplicity of an energy-based analysis instead of one using rate constants. This principle states that the selectivity can be defined by the relative height of the selectivity determinii transition states, which is conceptually easier than having to take into account four rate constents  

3) TST has a limited accuracy, sometimes not better than an order of magnitude [8]. Nevertheless, in the arena of tfieoretical catalysis, this is not the only source of errora. The quantum mechanical electronic structure methods used to model reaction profiles Imve similar accuracy. To this we have to add the solvation generally using a continuum 

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A combustion chamber can be ealeulated either based on kinetic theory (reaction rate equations) or a ehemical equilibrium constant. Knowledge about the exact value of partial pressures of the reactants is unnecessary this time, and simple calculations based on minimize of Gibbs free energy can be used. 

Finally, accurate theoretical kinetic and dynamical models are needed for calculating Sn2 rate constants and product energy distributions. The comparisons described here, between experimental measurements and statistical theory predictions for Cl"+CHjBr, show that statistical theories may be incomplete theoretical models for Sn2 nucleophilic substitution. Accurate kinetic and dynamical models for SN2 nucleophilic substitution might be formulated by introducing dynamical attributes into the statistical models or developing models based on only dynamical assumptions. 

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. 

Mathematically, the combustion process has been modelled for the most general three-dimensional case. It is described by a sum of differential equations accounting for the heat and mass transfer in the reacting system under the assumption of energy and mass conservation laws At present, it is impossible to obtain an analytical solution for the three-dimensional form. Therefore, all the available condensed system combustion theories are based on simplified models with one-dimensional or, at best, two-dimensional heat and mass transfer schemes. In these models, the kinetics of the chemical processes taking place in the phases or at the interface is described by an Arrhenius equation (exponential relationship between the reaction rate constant and temperature), and a corresponding reaction order with respect to reactant concentrations. 

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