Outer transition state

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

It is important to note here that both of the 5-exo radical cyclizations (133—>132—>131, Scheme 27) must proceed in a cis fashion the transition state leading to a strained mms-fused bicy-clo[3.3.0]octane does not permit efficient overlap between the singly occupied molecular orbital (SOMO) of the radical and the lowest unoccupied molecular orbital (LUMO) of the alkene. The relative orientation of the two side chains in the monocyclic radical precursor 134 is thus very significant because it dictates the relationship between the two outer rings (i. e. syn or anti) in the tricyclic product. The cis-anti-cis ring fusion stereochemistry of hirsutene would arise naturally from a cyclization precursor with trans-disposed side chain appendages (see 134). 

The Marcus treatment applies to both inorganic and organic reactions, and has been particularly useful for ET reactions between metal complexes that adopt the outer-sphere mechanism. Because the coordination spheres of both participants remain intact in the transition state and products, the assumptions of the model are most often satisfied. To illustrate the treatment we shall consider a family of reactions involving partners with known EE rate constants. 

Fig. 5. A model for S042- substitution on [Be(H20)4]2+ proceeding from the outer-sphere complex on the left through the transition state at center to the inner-sphere complex at the right of the figure (16, 66).

This problem has been addressed recently197 with model reactions in which the nucleophile (viz. electron donor) is NO-. It has been found that outer-sphere transition states are easier to compute with NO- than with other electron donors, thus allowing a complete characterization of the competition between the various pathways. 

When the fragments X and Y approach one another in the X. .. H. .. Y transition state, their outer electron shells begin to repel one another. It is to be expected that the repulsion will be stronger when the radii of the atoms X and Y is larger. The examples presented in Table 6.7 confirm this conclusion. 

There are two other mechanistic possibilities, halogen atom abstraction (HAA) and halonium ion abstraction (EL), represented in Schemes 4.4 and 4.5, respectively, so as to display the stereochemistry of the reaction. Both reactions are expected to be faster than outer-sphere electron transfer, owing to stabilizing interactions in the transition state. They are also anticipated to both exhibit antiperiplanar preference, owing to partial delocalization over the C—C—Br framework of the unpaired electron in the HAA case or the electron pair in the EL case. Both mechanisms are compatible with the fact that the activation entropies are about the same as with outer-sphere electron donors (here, aromatic anion radicals). The bromine atom indeed bears three electron pairs located in two orthogonal 4p orbitals, perpendicular to the C—Br bond and in one s orbital. Bonded interactions in the transition... 

In the inner-sphere reactions, the process involves a transition state in which a mutual strong penetration of the coordination spheres of the reagents occurs (and, therefore, strong interaction between reagents), whereas in the outer-sphere reactions there is no overlap of the coordination spheres of the reagents (and, therefore, there is weak interaction between reagents). 

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 ... 

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