Electron transfer relaxation

Keywords Excited-state intramolecular proton transfer Fluorescence dye Photoinduced electron transfer Proton coupled electron transfer Relaxation dynamics... 

Figure 1.1. Variation in entropies of activation ( S /R) with donor-acceptor, center-to-center separation (tda)- Open squares refer to electron transfer relaxation in [(NH3)50s(iso(pro) )Co(NH3)5] complexes based on data from Isied et alS" Closed squares refer to electron transfer relaxation in [(NH3)50s(iso(pro) )Ru(NH3)5] based on data from Isied et Values of = 9.5,12.2,14.8,18.1, and 21.2 A for n = 0,1,2,3, and 4, respectively, based on Isied et Since no corrections have been made for any differences in A5° or for...

The authors interpret this in terms of a hyperconjugative component of the through-bond coupling and its solvational perturbation. That the ratio of k2 is approximately correlated with the static dielectric constant of the solvent (see Table 1.1) could arise from a more mundane dependence of the electron transfer relaxation rate constant on k u. Thus, when Eq. (2) holds the nuclear contribution to the rate constant ratio becomes the relationship in Eq. (3). One does not... 

The relaxation of the open circuit potential Fqc following an ILIT perturbation is a function of the thermal relaxation back to the initial isothermal condition and the kinetics of an electron-transfer relaxation that is characterized by the experimentally measured rate constant (see Sec. IV.D)—km is a function of the electron-transfer resistance (units ohm cm ), the film capacitance, C (units F/cm ), and the redox or pseudo- capacitance, (units F/cm ) (as before, the superscript i denotes the equilibrium value of the variable prior to the perturbation). The equivalent circuit for this relaxation, shown in Fig. 8, includes the area, a (units cm ), so that the circuit element Rf. /a has the units of ohms and a C and a have the units of farads. The electron-transfer resistance... 

B V/K Coefficient for the amplitude of the open-circuit thermal response effected by an electron-transfer relaxation [see Eqs. (48)-(56) and (58)]... 

Utilizing FT-EPR teclmiques, van Willigen and co-workers have studied the photoinduced electron transfer from zinc tetrakis(4-sulfonatophenyl)porphyrin (ZnTPPS) to duroquinone (DQ) to fonn ZnTPPS and DQ in different micellar solutions [34, 63]. Spin-correlated radical pairs [ZnTPPS. . . DQ ] are fomied initially, and the SCRP lifetime depends upon the solution enviromnent. The ZnTPPS is not observed due to its short T2 relaxation time, but the spectra of DQ allow for the detemiination of the location and stability of reactant and product species in the various micellar solutions. While DQ is always located within the micelle, tire... 

Figrue BE 16.20 shows spectra of DQ m a solution of TXlOO, a neutral surfactant, as a function of delay time. The spectra are qualitatively similar to those obtained in ethanol solution. At early delay times, the polarization is largely TM while RPM increases at later delay times. The early TM indicates that the reaction involves ZnTPPS triplets while the A/E RPM at later delay times is produced by triplet excited-state electron transfer. Calculation of relaxation times from spectral data indicates that in this case the ZnTPPS porphyrin molecules are in the micelle, although some may also be in the hydrophobic mantle of the micelle. Furtlier,... 

In Debye solvents, x is tire longitudinal relaxation time. The prediction tliat solvent polarization dynamics would limit intramolecular electron transfer rates was stated tlieoretically [40] and observed experimentally [41]. 

This lineshape analysis also implies tliat electron-transfer rates should be vibrational-state dependent, which has been observed experimentally [44]- Spin-orbit relaxation has also been identified as an important factor in controlling tire identity of botli electron and vibrational-state distributions in radiationless ET reactions. 

Figure C3.2.12. Experimentally observed electron transfer time in psec (squares) and theoretical electron transfer times (survival times, Tau a and Tau b) predicted by an extended Sumi-Marcus model. For fast solvents tire survival times are a strong Emction of tire characteristic solvent relaxation dynamics. For slower solvents tire electron transfer occurs tlirough tire motion of intramolecular degrees of freedom. From [451.

Dicarbocyanine and trie arbo cyanine laser dyes such as stmcture (1) (n = 2 and n = 3, X = oxygen) and stmcture (34) (n = 3) are photoexcited in ethanol solution to produce relatively long-Hved photoisomers (lO " -10 s), and the absorption spectra are shifted to longer wavelength by several tens of nanometers (41,42). In polar media like ethanol, the excited state relaxation times for trie arbo cyanine (34) (n = 3) are independent of the anion, but in less polar solvent (dichloroethane) significant dependence on the anion occurs (43). The carbocyanine from stmcture (34) (n = 1) exists as a tight ion pair with borate anions, represented RB(CgH5 )g, in benzene solution photoexcitation of this dye—anion pair yields a new, transient species, presumably due to intra-ion pair electron transfer from the borate to yield the neutral dye radical (ie, the reduced state of the dye) (44). 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

The reactions of electron transfer and vibronic relaxation are ubiquitous in chemistry and many review papers have dealt with them in detail (see, e.g., Ovchinnikov and Ovchinnikova [1982], Ulstrup [1979]), so we discuss them to the extent that the nuclear tunneling is involved. 

Theoretical models available in the literature consider the electron loss, the counter-ion diffusion, or the nucleation process as the rate-limiting steps they follow traditional electrochemical models and avoid any structural treatment of the electrode. Our approach relies on the electro-chemically stimulated conformational relaxation control of the process. Although these conformational movements179 are present at any moment of the oxidation process (as proved by the experimental determination of the volume change or the continuous movements of artificial muscles), in order to be able to quantify them, we need to isolate them from either the electrons transfers, the counter-ion diffusion, or the solvent interchange we need electrochemical experiments in which the kinetics are under conformational relaxation control. Once the electrochemistry of these structural effects is quantified, we can again include the other components of the electrochemical reaction to obtain a complete description of electrochemical oxidation. 

FIGURE 34.3 Electron energy diagram. A fluctuation of the solvent polarization brings the energy levels and to the resonance position. After the electron transfer, the occupied energy level relaxes to its equilibrium position for the reduced form Ared-... 

Only if one takes into account the solvent dynamics, the situation changes. The electron transfer from the metal to the acceptor results in the transition from the initial free energy surface to the final surface and subsequent relaxation of the solvent polarization to the final equilibrium value Pqj,. This brings the energy level (now occupied) to its equilibrium position e red far below the Fermi level, where it remains occupied independent of the position of the acceptor with respect to the electrode surface. 

For simple outer-sphere electron transfer reactions, the effective frequency co is determined by the properties of the slow polarization of the medium. For a liquid like water, where the temporal relaxation of the slow polarization as a response to the external field is single exponential, tfie effective frequency is equal to... 

In bulk solution dynamics of fast chemical reactions, such as electron transfer, have been shown to depend on the dynamical properties of the solvent [2,3]. Specifically, the rate at which the solvent can relax is directly correlated with the fast electron transfer dynamics. As such, there has been considerable attention paid to the dynamics of polar solvation in a wide range of systems [2,4-6]. The focus of this chapter is the dynamics of polar solvation at liquid interfaces. 

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