Dynamical solvent effects, rate

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diflfiision control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8. chapter A3.13. chapter B3.3. chapter C3.1. chapter C3.2 and chapter C3.5. 

As can be seen from the numbers, the exponent a is clearly a function of barrier frequency (cob) and its value is decreasing with increase in a>b- For cob — 2 x 1013 s-1, its value almost goes to zero (a < 0.05), which clearly indicates that beyond this frequency the barrier crossing rate is entirely decoupled from solvent viscosity so that one recovers the well-known TST result that neglects the dynamic solvent effects. 

In this chapter we consider dynamical solvent effects on the rate constant for chemical reactions in solution. Solvent dynamics may enhance or impede molecular motion. The effect is described by stochastic dynamics, where the influence of the solvent on the reaction dynamics is included by considering the motion along the reaction coordinate as (one-dimensional) Brownian motion. The results are as follows. 

Dynamic solvent effect — is a phenomenon typical for adiabatic -> electron transfer and -> proton transfer reactions. This effect is responsible for a dependence of the reaction rate on solvent relaxation parameters. The initial search for a dynamic solvent effect (conventionally assumed to be a feature of reaction adiabatic-ity) consisted in checking the viscosity effect. However, this approach can lead to controversial conclusions because the viscosity cannot be varied without changing the -> permittivity, i.e. a dynamic solvent effect cannot be unambiguously separated from a -> static solvent effect [i]. Typically a slower solvent relaxation goes along with a higher permittivity, and the interplay of the two solvents effects can easily look as if either of them is weaker. The problems of theoretical treatment of the dynamic solvent effect of solvents having several relaxation times are considered in refs, [ii-iii]. 

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]. 

In PET, the rate can be markedly affected by the solvent polarity. With the formation of each new charge-transfer intermediate, solvent dipoles undergo reorientation in response to the new charge distribution on the reactants [49]. The solvent response influences the free-energy barrier of the reaction by altering the potential energy surface of the electron transfer. We consider this facet of solvent motion in this section. In a later section, we examine dynamical solvent effects. 

The universality of intermolecular electron transfer (ET) makes the mechanism one of the central questions to be solved in chemistry and biology. ET is strongly influenced by the nature of solvent and its dynamics in solution. Dynamical solvent effects on the course of reaction have recently studied both theoretically [1-5] and experimentally [6-15]. For ET with a rate comparable to the solvent flucmation rate, the motion and structure of the solvent can determine the rate of ET and it becomes the "solvent-controlled" reaction [2,3,6-9]. 

Thermal-induced intramolecular ET reaction is free from above the additional problems when one examines the dynamical solvent effect on the rate. Nevertheless, no quantitative and systematic data for the rate constant exceeding 10" S" have been reported because of experimental difficulties. ... 

Dynamic solvent effects on the large amplitude isomerization rate ... 

Figure 14.5 shows how dynamical solvent effects (corrections to the TST rate) behave as a function of molecule-solvent interactions. Several observations should be pointed out ... 

The Marcus theory, as described above, is a transition state theory (TST, see Section 14.3) by which the rate of an electron transfer process (in both the adiabatic and nonadiabatic limits) is assumed to be determined by the probability to reach a subset of solvent configurations defined by a certain value of the reaction coordinate. The rate expressions (16.50) for adiabatic, and (16.59) or (16.51) for nonadiabatic electron transfer were obtained by making the TST assumptions that (1) the probability to reach transition state configuration(s) is thermal, and (2) once the reaction coordinate reaches its transition state value, the electron transfer reaction proceeds to completion. Both assumptions rely on the supposition that the overall reaction is slow relative to the thermal relaxation of the nuclear environment. We have seen in Sections 14.4.2 and 14.4.4 that the breakdown of this picture leads to dynamic solvent effects, that in the Markovian limit can be characterized by a friction coefficient y The rate is proportional to y in the low friction, y 0, limit where assumption (1) breaks down, and varies like y when y oo and assumption (2) does. What stands in common to these situations is that in these opposing limits the solvent affects dynamically the reaction rate. Solvent effects in TST appear only through its effect on the free energy surface of the reactant subspace. 

Hynes [43] has discussed dynamic solvent effects for electron transfer reactions and described the role of solvent friction for both diabatic and adiabatic reactions. In the case of diabatic reactions the rate is strongly dependent on the coupling between the energy surfaces for the reactants and products as expressed through the parameter /j. (see section 7.8D). When is very small, dynamic... 

Photoinduced electron transfer is a subject characterised, particularly at the present time, by papers with a strongly theoretical content. Solvent relaxation and electron back transfer following photoinduced electron transfer in an ensemble of randomly distributed donors and acceptors, germinate recombination and spatial diffusion a comparison of theoretical models for forward and back electron transfer, rate of translational modes on dynamic solvent effects, forward and reverse transfer in nonadiabatic systems, and a theory of photoinduced twisting dynamics in polar solvents has been applied to the archetypal dimethylaminobenzonitrile in propanol at low temperatures have all been subjects of very detailed study. The last system cited provides an extended model for dual fluorescence in which the effect of the time dependence of the solvent response is taken into account. The mechanism photochemical initiation of reactions involving electron transfer, with particular reference to biological systems, has been discussed by Cusanovich. ... 

In all of these cases, the higher the reaction temperature, the higher the pressure required to observe the pressure-induced retardations. This is reasonable because the viscosity decreases with increasing temperature and we were convinced that these retardations were in fact dynamic solvent effects observed for slow thermal reactions for the first time [35]. We are now in a position to examine viscosity dependence of the rate constant. The results obtained for DBNA in DCMP are plotted against viscosity in Fig. 3.8. 

Considering the significant difference in the isomerization rate and in the pressure range where dynamic solvent effects were observed for the two carbocyanines, it is interesting to examine whether the dynamic solvent effect appears at a similar level in the relative time scales of the solvent and the chemical coordinate. It has earlier been shown [20, 21] that the product kxsT x Z can be used in the AH model to describe the balance of the characteristic times of the reaction system and the solvent the greater the product, the higher the anisotropy of the two time scales as... 

The reason for the small rate difference between the two solvents cannot be rationalized at the present level of knowledge. However, the fact that the rate in GTA was larger than that in AcOMe also supports the absence of dynamic solvent effects in GTA at low pressures. 

Several authors [36-38] have measured the pressure/solvent dependency of some unimolecular rate processes of ground-state molecules and all of the authors have interpreted the results as "dynamic solvent effects. However, as a result of our own measurements described in this chapter, we believe that what they observed was static pressure/solvent effects. See also Sect. 3.5. 

The importance of dynamical solvent effects on the rate of charge-transfer... 

If equilibrium solvation is the only cause of the solvent effect then the Mu reaction should also be a factor 35 faster in aqueous solution compared to the gas phase. This was not observed, the increase of its rate constant in water for addition to benzene amounts to only a factor of 3-5 (Figure 8), and it is not limited by diffusion. The difference was ascribed to a dynamic solvent effect and taken as evidence of Kramers solvent friction which increases with frequency and is thus obviously far more important for the reaction of Mu, the lighter isotope [33]. 

On the other hand, the reactions of esters with amines generate the aminolysis products. A theoretical study " on ester aminolysis reaction mechanisms in aqueous solution shows that the formation of a tetrahedral zwitterionic intermediate (Scheme 9.3) plays a key role in the aminolysis process. The rate-determining step is the formation or breakdown of such an intermediate, depending on the pH of the medium. Stepwise and concerted processes have been studied by using computation methods. Static and dynamic solvent effects have been analyzed by using a dielectric continuum model in the first case and molecular dynamics simulations together with the QM/MM method in the second case. The results show that a zwitterionic structure is always formed in the reaction path although its lifetime appears to be quite dependent on solvent dynamics. 

---