Marcus activated complex

Modem electron transfer tlieory has its conceptual origins in activated complex tlieory, and in tlieories of nonradiative decay. The analysis by Marcus in tire 1950s provided quantitative connections between the solvent characteristics and tire key parameters controlling tire rate of ET. The Marcus tlieory predicts an adiabatic bimolecular ET rate as... 

In the (semi-)classical models of ETR (Marcus the Russian school), redox orbitals of reactants overlap at a close separation, followed by swift electron transfer. The activated complex, considered in equilibrium with the reactants, consists of these overlapping orbitals. In the tunneling model, the electron penetrates... 

Marcus uses the Born-Oppenheimer approximation to separate electronic and nuclear motions, the only exception being at S in the case of nonadiabatic reactions. Classical equilibrium statistical mechanics is used to calculate the probability of arriving at the activated complex only vibrational quantum effects are treated approximately. The result is... 

It should be noted that application of the Marcus theory to these reactions is much more straightforward than application to reactions in solution. Since we are dealing with a single unimolecular step, namely, rearrangement of the reactant complex to the product complex, we need not be concerned with the work terms (2) which must be included in treatments of solution-phase reactions. These terms represent the work required to bring reactants or products to their mean separations in the activated complex, and include Coulombic and desolvation effects. 

A) In activated complex theory the rate constant can be expressed in terms of the free energy F of a system hypothetically constrained to exist on a certain hypersurface, the activated complex,99 cf. Marcus, R. A., J. Chem. Phys. 41, 2624 (1964). F can be expressed in terms of the free energy F of a system centered on that hypersurface (5). The difference between F and F contributes a factor to p. A second factor in p arises from the fluctuations in the separation distance of the reactants in the activated complex (5). 

The RRKM (after Rice, Ramsperger, Kassel, and Marcus) theory is, basically, transition-state theory (see, in particular, the description in Section 6.2) applied to a unimolecular reaction. Thus, one focuses on the activated complex... 

Nowadays, the basic framework of our understanding of elementary processes is the transition state or activated complex theory. Formulations of this theory may be found in refs. 1—13. Recent achievements have been the Rice—Ramsperger—Kassel—Marcus (RRKM) theory of unimol-ecular reactions (see, for example, ref. 14 and Chap. 4 of this volume) and the so-called thermochemical kinetics developed by Benson and co-workers [15] for estimating thermodynamic and kinetic parameters of gas phase reactions. Computers are used in the theory of elementary processes for quantum mechanical and statistical mechanical computations. However, this theme will not be discussed further here. 

This matrix can be used for molecules without internal rotation or for activated complexes having two degrees of freedom of internal rotational freedom for which the relevant expressions simplify, as may be seen from the formulation of Marcus.17... 

Marcus, R. A.. Generalization of activated-complex theory. III. Vibrational adia-baticity. separation of variables, and a connection with analytical mechanics, J. Chem. Phys., 43. 1598-1605 (1965). 

The encounter complexes exhibit high degrees of charge-transfer [20, 91], and on the basis of absorption and emission data electronic coupling matrix elements for similar complexes (exciplexes) have been determined [205] which are comparable to those of mixed-valence metal complexes commonly used as prototypical models for the bridged-activated complex in inner-sphere electron transfers [2, 26, 197]. Accordingly, we ascribe the unusually high rate constants, their temperature-independence, and their on-Marcus behavior to an inner-sphere electron transfer process [31]. 

The theoretical description of the kinetics of electron transfer reactions starts fi om the pioneering work of Marcus [1] in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37-41] avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle... 

Marcus LFER. Oxidation-reduction reactions involving metal ions occur by (wo types of mechanisms inner- and outer-sphere electron transfer. In the former, the oxidant and reductant approach intimately and share a common primary hydration sphere so that the activated complex has a bridging ligand between the two metal ions (M—L—M ). Inner-sphere redox reactions thus involve bond forming and breaking processes like other group transfer and substitution rcaclions, and transition-state theory applies directly to them. In outer-sphere electron transfer, the primary hydration spheres remain intact. The... 

Recent extensions to bimolecular reactions include a study by Marcus (1970) on the relation between state-selected cross sections of endothermic reactions and rate constants of exothermic reactions. This study was prompted by the investigation of Anlauf et al. (1969), and applied a micro-canonical activated-complex theory to bimolecular reactions. 

W. H. Wong and R. A. Marcus, Concept of minimum state density in the activated complex theory of bimolecular reactions, J. Chem. Phys. 55 5625 (1971). 

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