Theoretical studies Marcus theory

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

The RRKM theory is a ubiquitous tool for studying dissociation or isomerization rates of molecules as a function of their vibrational energy. Still highly active in the theoretical field, Marcus has tackled such issues as the semiclassical theory for inelastic and reactive collisions, devising reaction coordinates, new tunneling paths, and exploring solvent dynamics effects on unim-olecular reactions in clusters. 

The next two chapters are devoted to ultrafast radiationless transitions. In Chapter 5, the generalized linear response theory is used to treat the non-equilibrium dynamics of molecular systems. This method, based on the density matrix method, can also be used to calculate the transient spectroscopic signals that are often monitored experimentally. As an application of the method, the authors present the study of the interfadal photo-induced electron transfer in dye-sensitized solar cell as observed by transient absorption spectroscopy. Chapter 6 uses the density matrix method to discuss important processes that occur in the bacterial photosynthetic reaction center, which has congested electronic structure within 200-1500cm 1 and weak interactions between these electronic states. Therefore, this biological system is an ideal system to examine theoretical models (memory effect, coherence effect, vibrational relaxation, etc.) and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, internal conversion theory, etc.) for treating ultrafast radiationless transition phenomena. 

The mechanism of the electrochemical cleavage of the C-X (X = F, Cl, Br and I) bond has been extensively studied (see for example, Miller and Riekena 1969 Pause et al. 2000 Costentin et al. 2003 Wang et al. 2004 Sanecki and Skital 2007) and theoretical models (Battistuzzi et al. 1993 Kuznetsov et al. 2004 Zhang et al. 2005 Golinske and Voss 2005), mostly based on the Marcus theory (Marcus 1964) for the homogeneous and heterogeneous (electrochemical) electron transfer (ET), have been formulated (Saveant 1987, 2000 Maran et al. 2001 Costentin et al. 2006a, b) and tested with the aim to predict the experimental outcomes. 

The intellectual push to study mixed-valence complexes was provided by the publication in 1967 of two review articles, by Allen and Hush (2) and Robin and Day (3), on the physical properties of mixed-valence systems. These were followed by Hush s publication (4) of his theoretical model of intervalence transitions, which provided a link between the properties of mixed-valence complexes in solution and the Marcus theory of intermolecular electron transfer (5, 6). The review by Robin and Day classified mixed-valence complexes into three types class I,... 

In the kinetic study of ET at OAV interfaces, the experiment seems to have not caught up with the theory. The experimental data is still insufScient for the verification of the Marcus theory. Further experimental approaches as well as theoretical advances are needed. Recently, novel interesting ET systems including metal nanoparticles [63,64]... 

These complexes are excellent models for theoretical studies. The octacyano complexes of molybdenum and tungsten are stable and inert toward substitution reactions and therefore very suitable for theoretical studies of redox reactions and application of the Marcus theory. The photoreactivity of these systems is also proving to be important. The 0X0- and nitridocyano complexes of Mo(IV), W(IV), Tc(V), Re(V), and Os(VI) are very good candidates for kinetic studies of substitution reactions with both mono- and bidentate ligands and are of interest especially in view of the large variations in the observed reactivity. 

Finally, theoretical studies, particularly by Wolfe et al. (26) and more recently by Evleth and co-workers (27), provided some additional justification for our analysis. Quantum calculations of barriers for cross-reactions are in agreement with values that would have been derived from a Marcus theory analysis of other calculated barriers. Jorgensen and co-workers (28, 29) carried this analysis further using statistical mechanics simulations that show that the gas phase potential surface indeed translates into the solution surface in the way that we predicted. (For a dicussion of an alternative way to apply Marcus theory to double-minimum surfaces, as well as a note on Cl + CH3C1, see reference 29a.)... 

A prominent and widely appUed model of electron transfer in organic molecules is Marcus theory. It is thoroughly introduced in Section 4.3.1.1 and hence we concentrate here on its applicabiUty to triplet energy transfer supported by recently reported experimental studies of the temperature dependence of the triplet diffu-sivity and of the effect of disorder on triplet transfer in organic molecules. We would also like to refer the interested reader to a recent overview on experimental and theoretical work concerning a unified description of triplet energy transfer by Kohler and Bassler [30]. 

Hydride transfers are a very important category of reactions in organic and biological chemistry, and can be a model for electrophilic reactions, because they can be viewed as transfer of a proton with a pair of electrons between electron deficient sites [31], A + BH AH + B+. A large number of theoretical studies have addressed this topic, and the theory of Marcus gives a reasonable representation of the relation between rate and... 

ABSTRACT. A theoretical study of the electron self-exchange in porphyrins and in cytochrome c, and of the free-energy dependence of poq)hyrin-cytochrome c systems ows that these reactions are not easily amenable to an explanation in the framework of the theory of Marcus. On the other hand the intersecting-state model can be used to calculate the self-exchange rates and ] ovide an useful rationalization of the free-energy relationsh obs ed in these systems. 

A theoretical study of the hydrolysis of arenediazonium ions, combining Marcus theory with density functional theory (DPT) calculations, indicates the possibility of reaction by an 5 2 pathway, with the transition state (1), rather than an 5 1 pathway There has been a survey of the use of arenediazonium ions in synthetic reactions including their use as aryl radical precursors, aryl cation precursors, and super-electrophiles in transition-metal-catalysed reactions ... 

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