Electron dynamical solvent effect

Barbara P F, Walker G C and Smith T P 1992 Vibrational modes and the dynamic solvent effect in electron and proton transfer Science 256 975-81... 

Heitele H (1993) Dynamic solvent effects on electron-transfer reactions. Angew Chem Int Ed Engl 32 359-377... 

In the last two decades, studies on the kinetics of electron transfer (ET) processes have made considerable progress in many chemical and biological fields. Of special interest to us is that the dynamical properties of solvents have remarkable influences on the ET processes that occur either heterogeneously at the electrode or homogeneously in the solution. The theoretical and experimental details of the dynamical solvent effects on ET processes have been reviewed in the literature [6], The following is an outline of the important role of dynamical solvent properties in ET processes. 

The dynamical solvent effects on the kinetics of electron-transfer processes have been reviewed in detail in Refs [24a] and [32] and concisely in Section 3.6 of Ref. [8]. 

The reader is also referred to the innovative nonphotochemical electron transfer studies of Weaver et al. [147], These authors have been exploring dynamical solvent effects on ground state self-exchange kinetics for or-ganometallic compounds. This work has explored many aspects of solvent control on intermediate barrier electron transfer reactions, including the effect on a distribution of solvation times. The experimental C(t) data on various solvents have been incorporated into the theoretical modeling of the ground state electron transfer reactions studied by Weaver et al. [147]. 

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]. 

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. 

H. Heltele, Angew. Chem. Int. Ed. Engl., 32,359 (1993). Dynamic Solvent Effect on Electron-... 

Mu and Schulz [176] have shown that chloro(tetraphenylporphinato)man-ganese(III) complex, in one electron reduction in six aprotic solvents exhibits a dynamic solvent effect, though its inner reorganization energy is larger than the outer... 

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]. 

Electron Transfer Reactions and Exciolexes - Photoinduced electron transfer is one of the most important areas of research. A review of photoinduced electron transfer and electron acceptor complexes usefully surveys the subject . Details of the mechanisms can be obtained by very short time resolution spectroscopy. Dynamic solvent effects on intramolecular electron-transfer involve solvent fluctuations. Time resolved ps emission spectroscopy has been used to examine the kinetics of intramolecular charge transfer in bis(4-aminophenyl)sulphone in ethanol as a function of temperature in this respect 2. it has... 

Weaver M. J. (1992), Dynamical solvent effects on activated electron-transfer reactions— principles, pitfalls, and progress , Chem. Rev. 92,463 80. 

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... 

Quite different behavior is found for the electron transfer reaction between tetrathiofulvalene (TTF) and its cation radical. For this system, there is no correlation between In et and the Pekar factor y (fig. 7.22). However, there is a strong correlation between Inkgt and IniL. These results are consistant with an adiabatic reaction with a dynamic solvent effect. The estimate of A G[s for this... 

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. ... 

There has been a large number of theoretical studies since the inspiring work of Zusman devoted to dynamical solvent effects or, more generally, to effects associated with the competition between electronic transitions at strong coupling and various relaxation modes in the system [76-144]. Ovchinnikova [79] introduced an effective sink approximation to incorporate fast classical vibrational modes into the stochastic model of ET. She... 

For examples see a) Wiederrecht, G.P., M.R Niemczyk, W.A. Svec, and M.R. Wasielewski (1996). Ultrafast photoinduced electron transfer in a chlorophyll-based triad VibrationaUy hot ion pair intermediates and dynamic solvent effects. J. Am. Chem. Soc. 118(1), 81-88 and b) Shiratori, H., T. Ohno, K. Nozaki, I. Yamazaki, Y. Nishimura, and A. Osuka (1998). Coordination control of intramolecular electron transfer in boronate ester-bridged donor-acceptor molecules. Chem. Commun. (15), 1539-1540. 

Dynamical Solvent Ejfect Another critical topic to be considered when studying excited states in solution is the dynamical solvent effect. Electron excitation is an intrinsically dynamic process The full equilibration of solvent degrees of freedom to the excited-state density requires a finite time. It is thus fundamental that the characteristic times of solvent degrees of freedom are properly taken into account. 

Several theoretical approaches to the description of dynamical solvent effects have been proposed within the framework of PCM of other continuum models [41]. The simplest, and most commonly used, treatment involves the definition of two limit time regimes equilibrium (EQ) and nonequilibrium (NEQ). In the former all the solvent degrees of freedom are in equilibrium with the electron density of the excited-state density, and the solvent reaction field depends on the static dielectric constant of the embedding medium. In the latter, only solvent electronic polarization (fast degrees of freedom) is in equilibrium with the excited-state electron density of the solute, while the slow solvent degrees of freedom remain equilibrated with the groimd-state electron density. In the NEQ time regime the fast solvent reaction field is ruled by the dielectric constant at optical frequency (Copt, usually related to the square of the solvent refractive index). 

The NEQ limit is the most suitable to the treatment of the absorption process. The study of the fluorescence process is instead more complex, since in this case dynamical solvent effects cannot be rigorously decoupled from the intramolecular effects due to the motion of the wave-packet (WP) on the excited-state surface. However, it is possible to define some limit reference models, and intuitive consideration of the properties of the solvent and/or the excited potential energy surface is often sufficient to define what is the most suitable to the treat the case under study (see next sections). PCM can be used in conjunction with all the most important excited-state electronic methods. Since we selected TD-DFT as our reference electronic method, we shall treat PCM/TD-DFT in more detail in the next sections. 

On the other hand, most of the above deficiencies are not present in SS approaches, as SS-PCM/TD-DFT, which instead gives a balanced description of strong and weak electronic transitions (see also the results reported below). Several studies (see below) indicate that SS-PCM/TD-DFT provides accurate estimates of dynamical solvent effects on the absorption and emission processes, of solvent reorganization energy, and thus of inhomogeneous broadening. For example, in SS-PCM/TD-DFT 1 is indeed proportional to the square of the dipole moment shift associated with the transition, which is indeed expected to be the leading term in a polar solvent [85,86]. 

Ilya Rips and Joshua Jortner. Dynamic solvent effects on outer-sphere electron transfer. 

M. J. Weaver, Chem. Rev., 92, 463 (1992). Dynamical Solvent Effects on Activated Electron-Transfer Reactions Principles, Pitfalls, and Progress. 

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