Static solvent effects, transition-state theory

Static solvent effects, transition-state theory 

In this chapter we consider static solvent effects on the rate constant for chemical reactions in solution. The static equilibrium structure of the solvent will modify the potential energy surface for the chemical reaction. This effect can be analyzed within the framework of transition-state theory. The results are as follows. 

The basic expressions for the rate constant within a fully classical version of conventional transition-state theory were derived in Chapter 5. According to Eq. (5.53), we may write 

From this equation originates the statement that the rate constant is determined by the free energy of activation. Furthermore, as also discussed in Section 6.6, the preexponential factor in front of the activation energy AE is related to the entropy of activation. For reactions in solution, it is important to notice that the values of AA , AS , and AEf are determined by the activated complex and the reactant as well as by the surrounding solvent molecules. 

The interaction potential between solvent molecules and between solvent and solute molecules may, in principle, be found by solving the electronic Schrodinger equation, Eq. (3.1), for the solute/solvent system. Thus, the electronic energy (the potential for the nuclear motion) is, for a system with N nuclei, a function of the position vectors of each nucleus, i.e., Un t, r/v). Note that if the whole system is invariant to 

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In our discussion of the transition-state theory with static solvent effects, it was noticed that it is a mean field description where the effects of dynamical fluctuations in the solvent molecule positions and velocities were excluded. 

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... 

First of all, liquid-phase studies generally do not obtain data which allows static and dynamic solvent effects to be separated [96,97], Static solvent effects produce changes in activation barriers. Dynamic solvent effects induce barrier recrossing and can lead to modification of rate constants without changing the barrier height. Dynamic solvent effects are temperature and viscosity dependent. In some cases they can cause a breakdown in transition state theory [96]. 

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