Electron rate constant, intramolecular

Electron rate constant, intramolecular, 40 175 Electron relaxation times, iron-sulfiir proteins, 47 252-257... 

Figure 2.3 Evidence for the Marcus inverted region from intramolecular electron rate constants as a function of AG° in methyltetrahydrofuran solution at 206 K. Reprinted with permission from G.L. Closs, L.T. Calcaterra, H.J. Green, K.W. Penfield and J.R. Miller, ]. Phys. Chem., 90,3673 (1986). Copyright (1986) American Chemical Society...

Long-distance intramolecular electron transfer can be described in the framework of the Marcus theory 175). In the formulation of Lieber et al. 177), the intramolecular electron rate constant, can be written as... 

A large red shift observed in polar solvents was indicative of the intramolecular charge transfer character of the triplet state. The change of dipole moment accompanying the transition Tj - Tn, as well as rate constants for electron and proton transfer reactions involving the T state of a-nitronaphthalene, were determined. The lower reactivity in polar solvents was attributed to a reduced n-n and increased charge transfer character of the triplet state... 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

In the classical limit where the condition << kgT is met for the trapping vibrations, the rate constant for electron transfer is given by eq. 6. In eq. 6, x/4 is the classical vibrational trapping energy which includes contributions from both intramolecular (X ) and solvent (XQ) vibrations (eq. 5). In eq. 6 AE is the internal energy difference in the reaction, vn is the frequen-... 

In the stepwise case, the intermediate ion radical cleaves in a second step. Adaptation of the Morse curve model to the dynamics of ion radical cleavages, viewed as intramolecular dissociative electron transfers. Besides the prediction of the cleavage rate constants, this adaptation opens the possibility of predicting the rate constants for the reverse reaction (i.e., the reaction of radicals with nucleophiles). The latter is the key step of SrnI chemistry, in which electrons (e.g., electrons from an electrode) may be used as catalysts of a chemical reaction. A final section of the chapter deals... 

The probability of intramolecular energy transfer between two electronic states is inversely proportional to the energy gap, AE, between the two states. The value of the rate constant for radiationless transitions decreases with the size of the energy gap between the initial and final electronic states involved. This law readily provides us with a simple explanation of Kasha s rule and Vavilov s rule. 

In this equation g(r) is the equilibrium radial distribution function for a pair of reactants (14), g(r)4irr2dr is the probability that the centers of the pair of reactants are separated by a distance between r and r + dr, and (r) is the (first-order) rate constant for electron transfer at the separation distance r. Intramolecular electron transfer reactions involving "floppy" bridging groups can, of course, also occur over a range of separation distances in this case a different normalizing factor is used. 

It is too early to draw any conclusions about the insensitivity of the rate constants to the nature of the dipeptide. Differences among the peptides seem to be revealed more in the temperature dependencies of the rate constants for intramolecular electron transfer than in the magnitude of the rate constant itself. Work is in progress on the synthesis of other di-, tri-, and tetra-peptides separating Co(III) and Ru(II) in order to examine the temperature dependence of the intramolecular rate... 

Table 10. A comparison of rate constants for intramolecular electron transfer in Ru(NH3)j-modiiied electron transport metalloproteins, modifications at surface histidine present in native proteins, pH 7. Values of AE° by determined measurements on modified protein except as indicated...

Of course the Co CNHj) breaks down rapidly in acid into Co + and 5NHJ. Precursor complex formation, intramolecular electron transfer, or successor complex dissociation may severally be rate limiting. The associated reaction profiles are shown in Fig. 5.1. A variety of rate laws can arise from different rate-determining steps. A second-order rate law is common, but the second-order rate constant is probably composite. For example, (Fig. 5.1 (b)) if the observed redox rate constant is less than the substitution rate constant, as it is for many reactions of Cr +, Eu +, Cu+, Fe + and other ions, and if little precursor complex is formed, then = k k2kz ). In addition, the breakdown of the successor complex would have to be rapid k > k 2). This situation may even give rise to negative (= A//° +... 

---