Marcus model

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.

Fig. 12. Marcus model of two harmonic terms in the limit of strong coupling. Reorganization energy E, is shown.

Interfacial electron transfer, Marcus model inapplicability, 513 Interfacial parameter... 

Mandelbrot, on fractal surfaces, 52 Mao and Pickup, their work on the oxidation of polypyrrole, 587 Marcus model, inapplicability for interfacial electron transfer, 513 Mechanical breakdown model for passivity, 236... 

Marcus model for flat interfaces [Eqs. (17)-(19)], it was realized that the continuum model for a mixed solvent layer also approaches these experimental values [3-6]. 

The coordinate pertaining to solvent reorganization, z, is the same fictitious charge number as already considered in the Hush-Marcus model of outer-sphere electron transfer (Section 1.4.2), and so is the definition of 2q [equation (1.27)] and the difference between the Hush and Marcus estimation of this parameter. The coordinated describing the cleavage of the bond is the bond length, y, referred to its equilibrium value in the reactant, yRX. Db is the bond dissociation energy and the shape factor ft is defined as... 

This equation, based on the Marcus model, therefore gives us a relationship between the kinetics (kEr) and the thermodynamic driving force (AG°) of the electron-transfer process. Analysis of the equation predicts that one of three distinct kinetic regions will exist, as shown in Figure 6.24, depending on the driving force of the process. 

The Marcus model of intermolecular ET refers to reaction (17) and is detailed in Fig. 1. 

Fig. 1 The Marcus model of intramolecular electron transfer, involving two colliding spheres of charges Zi and Z2 and radii r, and r2.

It is important to remember that the Marcus model refers to a weakly electronically coupled model, as embodied in the term outer-sphere ET. Thus it must be assumed that the electronic overlap between the two reactants is so small that no quantum-chemical effects ensue, yet that there must be enough overlap for the transmission coefficient k of the Eyring equation to be equal to 1 (the reaction must be adiabatic). Usually, this minimum overlap requirement is put at a fairly low level, around 0.1 kcal mol-1, which causes no problems for most reactions involving at least one organic species. 

The simple, classical Marcus model gives predictions that are one to two orders of magnitude too large for both k- and... 

For one-electron electrochemical reactions, the harmonic oscillator ("Marcus ) model (21) yields the following predicted dependence of AG upon the electrode potential ... 

Marcus model all fall on a common curve (shown as a solid line in Figure 3) when presented in this manner (27). [Omitted from... 

An important aspect of the Gao-Marcus model is that it provides a theoretical structure for the understanding of quantum state density isotope effects in general, and is not specifically confined to the formation of ozone itself. This feature is important because as discussed above we are now aware that MIF s occur widely in nature. The theory aids in prediction of where MIF s will be likely found, and once found, in rationalizing how they were chemically produced. 

Smith BB, Halley JW, Nozik AJ (1996) On the Marcus model of electron transfer at immiscible liquid interface and its application to the semiconductor liquid interface. Chem Phys 205 245-267... 

In the 2-level limit a perturbative approach has been used in two famous problems the Marcus model in chemistry and the small polaron model in physics. Both models describe hopping of an electron that drags the polarization cloud that it is formed because of its electrostatic coupling to the enviromnent. This enviromnent is the solvent in the Marcus model and the crystal vibrations (phonons) in the small polaron problem. The details of the coupling and of the polarization are different in these problems, but the Hamiltonian formulation is very similar. ... 

An alternative but related approach has been taken by Silbey and Suarez in their study of hydrogen hopping in solids. Instead of a Marcus model they used the spin-boson Harrriltonian with a turmeling sphtting that has the form Eq. (30). The envirorrment as described in the spin-boson Hamiltorrian has not only slow dyrramics (as in the Marcus model), but fast modes as well. 

It was found that over a narrow free energy range rapidly increases with asymptotically approaching a limiting value smaller than . Although the observed behavior remains in accordance with the Marcus model prediction, it was, somewhat unexpectedly, found that not the electron annihilation energetics is a only factor... 

Figure 17.6 Free energy curves for reactant and product states of an electron transfer process in the kinetic regimes of the Marcus model.

Bond-breaking reaction, 1518 potential energy curves, 1519 bond activation, 1519 George-Griffith model, 1519 Wiss—Marcus model, 1519 Bond strength, in electrocatalysis, 1287 Boulders, electrodeposition, 1336 Bowden, 1402... 

V. Levich and R. R. Dogonadze, Dokl. Akad. Nauk. SSSR 124 123 (1959). Hamiltonian formulation for electron transfer dielectric polarization approach. Quantum aspects of Weiss-Marcus model developed. 

According to the Marcus model, the standard rate constant, ks, for reaction (4.9) can be expressed as follows if the reaction is an adiabatic outer-sphere process 6 ... 

J. Troe Professor Marcus, you were mentioning the 2D Sumi-Marcus model with two coordinates, an intra- and an intermolecu-lar coordinate, which can provide saddle-point avoidance. I would like to mention that we have proposed multidimensional intramolecular Kramers-Smoluchowski approaches that operate with highly nonparabolic saddles of potential-energy surface [Ch. Gehrke, J. Schroeder, D. Schwarzer, J. Troe, and F. Voss, J. Chem. Phys. 92, 4805 (1990)] these models also produce saddle-point avoidances, but of an intramolecular nature the consequence of this behavior is strongly non-Arrhenius temperature dependences of isomerization rates such as we have observed in the photoisomerization of diphenyl butadiene. 

The Bronstcd relation, statistical factors, and the acidity of solvent-derived species (H and H20) 345 Mechanism of the uncatalyzed reaction 348 The Marcus model of proton transfer 350... 

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