Transition state theory condensed-phase reactions

The solvent effects are essentially of two types physical, when they allow the reactants to show a different behaviour with respect to the gas phase, and chemical, when the solvent itself participates in the reaction. Moreover, it is generally observed, for reactions in the condensed phase that the conversion rate constants are better described by transition state theory than for reactions in the gas phase [8], a consideration that enforces the importance of determining energy diagrams like that of Figure 1 by quantum theory calculations. 

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877... 

When F is equal to unity, the equation reduces to the rate expression of the well-known transition state theory. In most of the cases considered in this book, we will deal with reactions in condensed phases where F is not much different from unity and the relation between k and Ag follows the qualitative role given in Table 2.1. 

S. C. Tucker, Variational transition state theory in condensed phases, vaNew Trends in Kramers Reaction Rate Theory, P. Hanggi and P. Talkner (eds.), Kluwer Academic, The Netherlands, 1995, pp. 5—4-6. 

Although possessing certain inherent limitations (Benson, 1960a), transition state theory seems adequate to permit the quantitative computation of kinetic parameters from first principles. As we have seen, however, practical application of the theory is impeded by incomplete information about the molecular properties of the activated complex and, for reactions in solution, the lack of a quantitative description of molecular interactions in condensed phases. It would be highly useful, therefore, to have some other basis on which to assess... 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

In Chapter 5, attention is directed toward the direct calculation of k(T), i.e., a method that bypasses the detailed state-to-state reaction cross-sections. In this approach the rate constant is calculated from the reactive flux of population across a dividing surface on the potential energy surface, an approach that also prepares for subsequent applications to condensed-phase reaction dynamics. In Chapter 6, we continue with the direct calculation of k(T) and the whole chapter is devoted to the approximate but very important approach of transition-state theory. The underlying assumptions of this theory imply that rate constants can be obtained from a stationary equilibrium flux without any explicit consideration of the reaction dynamics. 

Chapters 9-11 deal with elementary reactions in condensed phases. Chapter 9 is on the energetics of solvation and, for bimolecular reactions, the important interplay between diffusion and chemical reaction. Chapter 10 is on the calculation of reaction rates according to transition-state theory, including static solvent effects that are taken into account via the so-called potential-of-mean force. Finally, in Chapter 11, we describe how dynamical effects of the solvent may influence the rate constant, starting with Kramers theory and continuing with the more recent Grote-Hynes theory for... 

Continuum solvation models can be used to predict the free energy of activation of chemical reactions and the effective potential for condensed-phase tunneling, and they can therefore be combined with transition state theory to predict chemical reaction rates. 

T. D. (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions,... 

We present an overview of variational transition state theory from the perspective of the dynamical formulation of the theory. This formulation provides a firm classical mechanical foundation for a quantitative theory of reaction rate constants, and it provides a sturdy framework for the consistent inclusion of corrections for quantum mechanical effects and the effects of condensed phases. A central construct of the theory is the dividing surface separating reaction and product regions of phase space. We focus on the robust nature of the method offered by the flexibility of the dividing surface, which allows the accurate treatment of a variety of systems from activated and barrierless reactions in the gas phase, reactions in rigid environments, and reactions in liquids and enzymes. 

E. Poliak, J. Chem. Phys., 95,533 (1991). Variational Transition State Theory for Reactions in Condensed Phases. 

Reactions in liquids differ markedly from reactions in the gas phase because of the presence of solvent molecules, which are always in intimate contact with the reactants and, in fact, often interact strongly with them. The most important consequence of this interaction is that ions are often stable species in liquid systems. This is because the energy required to dissociate molecules into ions is usually more than compensated by the energy released from the process of ion solvation. According to the results obtained earlier, Eqs. (2-69) and (2-95), the specific rate constant in condensed phases for a nonideal system can be expressed in terms of transition-state theory as... 

The thermodynamic formulation of reaction rates is also particularly useful in discussing rates in ideal solutions. Indeed, the concept of collision between molecules and the derivations of the kinetic theory of gases seem to be useless in the condensed state. Yet, the results of transition-state theory are not limited to the treatment of ideal gas mixtures. In particular, these results can also be couched in the language of the colU on theory. This may appear surprising since the concept of collision in condensed phases is not a fruitful one. Yet it is found that normal reactions in solution exhibit a rate constant described by (2.5.3) with a probability factor P close to unity. 

A theory appropriate for describing reactions in dilute gases cannot be easily extended to reactions taking place in condensed phase. The spirit of transition state theory can be applied to ion reactions in electrolytes, if the concentrations are replaced by the practically useful, but theoretically not well-founded notion of activity . Since the activity coefficients of each ionic species is a function of the quantities of all ionic species present, the picture of collisions among the individuals of finite discrete qualities cannot be maintained rigorously. 

For gas phase reactions, the reaction can be viewed as a scattering event and k T) can be calculated from scattering properties. However, a more intuitive approach is to calculate the thermal rate constant directly from a simulation of the dynamics in the vicinity of the reaction barrier. This approach has a number of advantages it decreases the numerical effort compared to a full scattering calculation, enables an equivalent treatment of reactions in gas and condensed phase, and results in a very intuitive interpretation based on ideas adopted from transition state theory. The present article intends to... 

Tmhlar DG, Gao JL, Garcia-Viloca M, Alhambra C, Corchado J, Sanchez ML, Poulsen TD (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions, hit J Quantum Chem 100(6) 1136-1152... 

The potential of mean force, the technical term for the free energy along the reaction coordinate, is an essential ingredient in a correct application of transition state theory to processes in the condensed phase. We need the potential of mean force for two purposes. First, to know the location of the bottleneck to reaction, the transition state. Except when it is dictated by symmetry, as in symmetric exchange, the transition state in the presence of a solvent is not necessarily the same as in the gas phase. Second, we need to know the height of the barrier. 

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