Nuclear reorganization parameter

Uie rate of electron transfer (ET) from a donor (D) to an acceptor (A) held at fixed distance and orientation depends on of temperature (7), reaction driving force (-AG°) a nuclear reorganization parameter (X), and an electronic coupling matrix element The reorganization parameter... 

In semiclassical ET theory, three parameters govern the reaction rates the electronic couphng between the donor and acceptor (%) the free-energy change for the reaction (AG°) and a parameter (X.) related to the extent of inner-shell and solvent nuclear reorganization accompanying the ET reaction [29]. Additionally, when intrinsic ET barriers are small, the dynamics of nuclear motion can limit ET rates through the frequency factor v. These parameters describe the rate of electron transfer between a donor and acceptor held at a fixed distance and orientation (Eq. 1),... 

Both the electronic couphng matrix element and the outer-sphere component of the nuclear reorientation parameter are thought to vary with donor-acceptor separation and orientation [29, 49]. It has been shown in studies of Os and Ru-ammines bridged by polyproline spacers that the distance dependence of X can be greater than that of [50]. Dielectric continuum models of solvent reorganization predict that Xg will increase with... 

This chapter concerns the energetics of charge-transfer (CT) reactions. We will not discuss subjects dealing with nuclear dynamical effects on CT kinetics. " The more specialized topic of employing the liquid-state theories to calculate the solvation component of the reorganization parameters is not considered here. We concentrate instead on the general procedure of the statistical mechanical analysis of the activation barrier to CT, as well as on its connection to optical spectroscopy. Since the very beginning of ET research, steady-state optical spectroscopy has been the major source of reliable information about the activation barrier and preexponential factor for the ET rate. The main focus in this chapter is therefore on the connection between the statistical analysis of the reaction activation barrier to the steady-state optical band shape. 

The other model parameters entering Eq. [66] are the nuclear reorganization energies defined through the second cumulants of the reaction coordinate... 

If nuclear-tunneling effects are neglected, then the experimental activation parameters are related to the reorganization parameters by ... 

The mechanism of any catalyzed or noncatalyzed reaction is perhaps the aspect of the reaction most difhcult to understand. The mechanism of a reaction is defined as the detailed description of the electronic, or both electronic and nuclear, reorganization during the course of a reaction. There are several methods or techniques used to diagnose the reaction mechanism, but perhaps the kinetic method is the most important one, which establishes the most refined mechanism at the molecular level for any reaction. The kinetic study provides experimentally determined reaction parameters that could be used to test a proposed reaction mechanism. 

In the high temperature limit where all the nuclear motions coupled to the process can be described classically, the nuclear factor is expressed in terms of only two parameters the driving force of the reaction AG°, and the whole reorganization energy X (expressions (13) and (14)). Detailed calculations carried out in the case of cytochrome c have demonstrated that AG° is a complex quantity, which depends not only on the electronic properties of the redox centers but also on those of the protein and of the surrounding solvent [100]. Usually, AG can be evaluated from measurements of redox potentials and of eventual interaction energies between the different parts of the systems (Appendix). 

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Diakov, Anatoli S., Conversion of the Russian Nuclear Weapons Complex Main Parameters of Minatom Program Reorganization and Conversion of the Nuclear Weapons Complex in 1998-2000, unpublished PowerPoint presentation supplied to authors. 

Fig. 16.2 A model for the energetics of electron transfer reactions. The two potential surfaces are associated with two electronic states that transform to each other when the electron is transferred. The coordinate X stands for the nuclear configuration. The model may be characterized by the curvature of these surfaces, by the energy gap AE between the two electronic origins and by the reorganization energy Ex. Other important parameters that can be expressed in terms of these are the equilibrium configuration shift Ay, — Xa and the activation energy E. ...

The critical parameter is A, the reorganization energy, which represents the energy necessary to transform the nuclear configurations in the reactant and the solvent to those of the product state. It is usually separated into inner, Aj, and outer, Aq, components ... 

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