Electron cross-reaction rate constants

The electron self-exchange rate constant for the [Cr(CNdipp)6] couple (CNdipp = 2,6-diisopropylphenyl isocyanide) in CD2CI2 has been measured between -89 and +22 °C using H NMR line-broadening techniques, with an extrapolated value of 1.8 x 10 M s determined for 25 The kinetics of the outer-sphere oxidations of tris(polypyridine)chromium(II) complexes by a series of tris(chelate)cobalt(III) species have been studied in aqueous solution. " The cross-reaction rate constants obey the Marcus relationship, with the exception of [Co(bpy)3] " and [Co(phen)3] ", for which mild nonadiabaticity (/[Pg.18]

The electron self-exchange rate constants evaluated by the Marcus expressions (using cross-reaction data) and those determined experimentally differ in the following cases. Give possible reasons for these differences. 

Some of the new theoretical relations, the cross-relation between the rates of a cross-reaction of two difierent redox species with those of the two relevant selfexchange reactions, were later adapted to non-electron transfer reactions involving simultaneous bond rupture and formation of a new bond (atom, ion, or group transfer reactions). The theory had to be modified, but relations such as the crossrelation or the effect of driving force (—AG°) on the reaction rate constant were again obtained in the theory, in a somewhat modified form. For example, apart from some proton or hydride transfers under special circumstances, there is no predicted inverted effect. Experimental confirmation of the cross-relation followed, and an inverted effect has only been reported for an H+ transfer in some nonpolar solvents. The various results provide an interesting example of how ideas obtained for a simple, but analyzable, process can prompt related, yet different, ideas for a formalism for more complicated processes. 

Marcus theory has been so successful in predicting cross reaction rates in outer-sphere electron transfer reactions that it is often used to give evidence that an outer-sphere reaction is taking place. If the observed rate constant is within an order of magnitude of the calculated rate constant, then it is likely that an outer-sphere mechanism is occurring. In this way, you will use Marcus theory to give evidence for the reaction mechanism assigned to your rate constant, kos, determined in Experiment 5.5. 

O Reactions.—The cross-section for charge transfer between O- ions and 02(3Sy ) has a maximum value of 7.8 x 10-1 cm2 at an energy of 5 keV of the incident ion,289 whereas that for O- and 02(1A4,) was less than 1 x 10-1 cm2. Reaction rate-constants for reactions of O-, OH-, 02-, Cl-, C03-, and 0H-(H20) with H20 have been measured, and association rate-constants for several ions with COa and S02 tabulated.290 The rate of formation of NO+ by the reaction of 0+ with N2 has been commented upon.291 The formation of H02+ and Os+ by the reaction of 02+( 4 ) with H2 and 02 has been reported,292 and 02+-02, NO+-NO interactions have been considered.293 Rate-constants for reactions of O o4 ,) with N2, Ar, Cl, C02, H2, and 02 have been reported,294 and electron-transfer transitions during the collision of 02, N2, NO, and CO with their respective ions discussed.295 The nearly resonant process (107) has been shown not to occur with high efficiency.29 The lifetime of the 3 state of OH+ has been shown to be 900 ns.87... 

The rate constants, 12, of redox reactions proceeding via the outer-sphere mechanism, for example, reaction (50) (105), depend, according to the Marcus theory (85-87) (Eqs. 54 and 55), on the equilibrium constant of the cross-reaction, iiLi2, and on the electron self-exchange rate constants, and 22> of the redox couples. 

The rate constants for the cross-reactions of Cu(I) tetraaza macrocycles with a series of outer-sphere oxidants have been used to determine the electron self-exchange rate constants of several Cu(I)/Cu(II) couples [CuCMe CMJdieneNJ]-"/"-" (fcn = 23 s ), [Cu(Me4[14]-l,3,8,10-... 

The kinetics of several electron transfer reactions of the molybdenum cuboidal system [Mo4S4(edta)2]" ( = 2, 3, 4) with cross-reactants such as [Co(edta)]-, [Fe(edta)]-, [Co(dipic)2] , [Fe(H20)e], and [Pta ] -, have been investigated. The electron self-exchange rate constants determined for the [Mo4S4(edta)2] and [Mo4S4(edta)2] couples, by an application of the Marcus relationship, are 1.5 x 10 and 7.7 x 10 M s , respectively. The rate constants for the outer-sphere oxidation of two dimeric complexes, [MoW 0)2(p-edta-AT,lV )]2- and [W2(0)2(p-0)(p-S)(p-edta-Ar,iV )] -, by [IrCl ] in addic aqueous solution have been measured. While the oxidation of the former complex shows a simple second-order rate law, the kinetics of the oxidation of the latter complex exhibited a rate retardation in the presence of the [IrCl6] complex. 

The rate constant for Reaction 3, however, is far from well established. For example, an experimental value of kz can be estimated from the measured attachment cross-section data of Buchel nikova (4) who observed a maximum cross-section ae, max = 5 X 10 18 cm.2 at 6.4 e.v. for electrons colliding with water molecules. (The cross-section falls below 1 X 10 18 cm.2 at energies lower than 5 e.v.) This suggests that... 

It is now possible to design the experiments using molecular beams and laser techniques such that the initial vibrational, rotational, translational or electronic states of the reagent are selected or final states of products are specified. In contrast to the measurement of overall rate constants in a bulk kinetics experiment, state-to-state differential and integral cross sections can be measured for different initial states of reactants and final states of products in these sophisticated experiments. Molecular beam studies have become more common, lasers have been used to excite the reagent molecules and it has become possible to detect the product molecules by laser-induced fluorescence . These experimental studies have put forward a dramatic change in experimental study of chemical reactions at the molecular level and has culminated in what is now called state-to-state chemistry. 

Fig. 1. The Marcus parabolic free energy surfaces corresponding to the reactant electronic state of the system (DA) and to the product electronic state of the system (D A ) cross (become resonant) at the transition state. The curves which cross are computed with zero electronic tunneling interaction and are known as the diabatic curves, and include the Born-Oppenheimer potential energy of the molecular system plus the environmental polarization free energy as a function of the reaction coordinate. Due to the finite electronic coupling between the reactant and charge separated states, a fraction k l of the molecular systems passing through the transition state region will cross over onto the product surface this electronically controlled fraction k l thus enters directly as a factor into the electron transfer rate constant...

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