Marcus parameter

Modified Marcus Parameters for Proton-Transfer Reactions with Deprotonated Metal Peptide Complexes... 

Fig. 13 Plots of equation (40) to find Marcus parameters from data for the reaction of RY with H20 and OH ...

Marcus parameters lor some proton-transfer reactions [22a,26]... 

Marcus parameters within organic and inorganic mixed valence compounds, as well as to ET between inorganic complexes in solution. ... 

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... 

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

Samec Z, Weber J (1973) The influence of chemisorbed sulfur on the kinetic parameters of the reduction of Fe " ions on a platinum electrode on the basis of the Marcus theory of electron transfer. J Electroanal Chem Interfacial Electrochem 44 229-238... 

Intense ion-ion interactions which are characteristic of salt solutions occur in the concentrated aqueous solutions from which AB cements are prepared. As we have seen, in such solutions the simple Debye-Hiickel limiting law that describes the strength goes up so the repulsive force between the ions becomes increasingly important. This is taken account of in the full Debye-Hiickel equation by the inclusion of a parameter related to ionic size and hence distance of closest approach (Marcus, 1988). 

Azo-bridged ferrocene oligomers also show a marked dependence on the redox potentials and IT-band characteristics of the solvent, as is usual for class II mixed valence complexes 21,22). As for the conjugated ferrocene dimers, 2 and 241 the effects of solvents on the electron-exchange rates were analyzed on the basis of the Marcus-Hush theory, in which the t/max of the IT band depends on (l/Dop — 1 /Ds), where Dop and Ds are the solvent s optical and static dielectric constants, respectively (155-157). However, a detailed analysis of the solvent effect on z/max of the IT band of the azo-bridged ferrocene oligomers, 252,64+, and 642+, indicates that the i/max shift is dependent not only on the parameters in the Marcus-Hush theory but also on the nature of the solvent as donor or acceptor (92). 

According to the Marcus theory [9], the electron transfer rate depends upon the reaction enthalpy (AG), the electronic coupling (V) and the reorganization energy (A). By changing the electron donor and the bridge we measured the influence of these parameters on the charge transfer rate. The re-... 

Fig. 12.2. Free energy data for electron transfer between the protein cytochrome c and the small acceptor microperoxidase-8 (MP8), from recent simulations [47]. Top Gibbs free energy derivative versus the coupling parameter A. The data correspond to solvated cytochrome c the MP8 contribution is not shown (adapted from [47]) Bottom the Marcus diabatic free energy curves. The simulation data correspond to cyt c and MP8, infinitely separated in aqueous solution. The curves intersect at 77 = 0, as they should. The reaction free energy is decomposed into a static and relaxation component, using the two steps shown by arrows a static, vertical step, then relaxation into the product state. All free energies in kcalmol-1. Adapted with permission from reference [88]...

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... 

Fig. 14.6 Experimental and calculated enrichments or depletions of all possible ozone iso-topomers. The labels 6, 7 and 8 represent lsO, 170, and lsO respectively. Ozone (gray bars) was produced in well scrambled oxygen mixtures at about 90 mbar and room temperature (Mauersberger et al. Adv. Atomic Mol. Opt. Phys. 50, 1 (2005)). The calculated values (vide infra) are those of Gao, Y. Q. and Marcus, R. A., J. Chem. Phys. 116, 137 (2002) setting the parameter r = 1.18 (black bars) or r = 1.0 (white bars). A typical symbol, such as 668, denotes an ozone with the isotopic composition 160160180 and consists of a mixture of symmetric (160180160) and asymmetric (160160180) isotopomers (After Gao, Y. Q. and Marcus, R. A., Science 293, 259 (2001))...

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

It is thus, in principle, possible to derive from the potential location and from its shape all the parameters contained in the Marcus-Hush model, namely, the standard potential, , and the intrinsic barrier, AGq (Klinger... 

The pattern for outer-sphere oxidation by Co(NH3)5 compared with Co(en)j+ (usually it is —10 times slower) towards inorganic reductants can be used to support an estimate of the proportion of electron transfer (Marcus-dependent) and charge transfer which Ru(bpy) + displays towards these oxidants (45 and 11%, respectively). Sec. 2.2.1(b). Finally, Eqn. 5.35 can be used to determine K 2 for a reaction in which the other kinetic parameters are known. The value of A, 2 can be used, in turn, to estimate the oxidation potential of one couple, which is normally inaccessible. Thus the potentials of the o-, m- and /7-benzene diol radicals 1T2A4 were determined from kinetic data for the oxidation of the diols (H2A) by Fe(phen) + (5.45) ... 

The activation parameters for the cation-independent pathway ( o) can be accounted for by a modified semiclassical Marcus-Hush theory. Lower enthalpies, and more positive volumes of activation are noted for the M +-catalyzed pathway. - ... 

Ab initio SCRF/MO methods have been applied to the hydrolysis and methanol-ysis of methanesulfonyl chloride (334). ° The aminolysis by aromatic amines of sulfonyl and acyl chlorides has been examined in terms of solvent parameters, the former being the more solvent-dependent process.Solvent effects on the reactions of dansyl chloride (335) with substituted pyridines in MeOH-MeCN were studied using two parameters of Taft s solvatochromatic correlation and four parameters of the Kirkwood-Onsager, Parker, Marcus and Hildebrand equations. MeCN solvent molecules accelerate charge separation of the reactants and stabilize the transition... 

Roenigk, K. F., Jensen, K. F., and Carr, R. W., Rice-Rampsperger-Kassel-Marcus theoretical prediction of high-pressure Arrhenius parameters by nonlinear regression Application to silane and disilane decomposition, J. Phys. Chem. 91, 5732 (1987). 

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