Inner transition state

The inner integral on the right-hand side is just e so equation (A3.11.185) reduces to the transition state partition fiinction (leaving out relative translation) ... 

The inner multiple integral is the transition state s density of states at energy , and also the numerator in... 

It is possible to take advantage of the differing characteristics of the periphery and the interior to promote chemical reactions. For example, a dendrimer having a non-polar aliphatic periphery with highly polar inner branches can be used to catalyse unimolecular elimination reactions in tertiary alkyl halides in a non-polar aliphatic solvent. This works because the alkyl halide has some polarity, so become relatively concentrated within the polar branches of the dendrimer. This polar medium favours the formation of polar transition states and intermediates, and allows some free alkene to be formed. This, being nonpolar, is expelled from the polar region, and moves out of the dendrimer and into the non-polar solvent. This is a highly efficient process, and the elimination reaction can be driven to completion with only 0.01 % by mass of a dendrimer in the reaction mixture in the presence of an auxiliary base such as potassium carbonate. 

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).

Electrogenerated monovalent Co complexes of the well-known open chain N202 Schiff base ligands salen (8), salphen (9), and their substituted derivatives undergo oxidative additions with alkyl halides. Reactions of the complex with substrates within the series RBr (R = Pr, Bu, t-Bu) proceed at different rates. The reaction occurs by an inner-sphere alkyl-bridged electron transfer, with a Co1- R+- X-transition state, which is sensitive to distortions of the complex in different configurations.124... 

Fig. 14. Conformations of s,czs-cyclooctadiene-l,5 with calculated angles (inner values) and torsion angles (deg force field of ref. 19) (83). The additional calculated information given is (from top) symmetry, AV, AH (kcal mole-1 T = 298 K reference C2-symmetric distorted boat conformation). The three upper conformations correspond to potential energy minima, the two lower to onedimensional partial maxima (transition states).

B. Structural Models of dcr/Acr Inner-Sphere Electron-Transfer Transition States... 

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 ... 

From a mechanistic point of view [4], there are two extremes conceivable if the interaction between X and Y is weak, [XY] symbolizes a transition state and the reaction (la,a ) is a case of outer-sphere electron transfer. If, however, the interaction is strong enough that it leads to, e.g., covalent-bond formation between X and Y (Eq. 1 b), the product of that interaction is an intermediate ( adduct ) and the overall electron exchange between X and Y (via Eq. lb, b ) is then an example of inner-sphere electron transfer. 

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