Radical pairs potential energy

FIGURE 3. Qualitative energy model of a radical-anion pair in sulfoxides where A = CH3, C2H5 B = SOCH3, "SOC2H5 u is the potential energy R(AB) is the distance between A and B. Reproduced by permission of the authors from Reference 16. 

Fig. 26.—Illustrative representation of the potential energy of the radical-monomer pair as a function of their distance of separation. See text for further explanation.

The participation of such ionic states would load one to expect disproportionation rates to increase in the series CH8, C2H5J iso-C8H7, and ferf-butyl, since the ionization potentials of these radicals form a descending series 10.0 e.v., 8.8 e.v., 7.9 e.v., and 6.9 e.v., respectively. This effect of decreasing ionization potential, which might be expected to push the ion-pair state down in energy, considerably below the radical pair state, is considerably off-set by the increasing value of rt (eqs. 5 and 6). ... 

Fig. 28. Potential energy for the nuclear motion along the reaction coordinate, (a) A monomolecular decay with the formation of radicals (b) a monomolecular decay with the formation of molecules with the paired electrons (E ) = n0a>, = n uj) (c) a monomolecular isomerization...

Depending on the solvent polarity and redox potentials of donor and acceptor, the ions resulting from electron transfer may remain associated either as a contact ion radical pair or as a solvent-separated ion radical pair. In the contact pair electron back-transfer can take place. For such electron back-transfer, the solvent reorganization energy is less than 5% of the total reorganization energy (Serpa Amaut 2000). 

A question that arises in consideration of the annihilation pathways is why the reactions between radical ions lead preferentially to the formation of excited state species rather than directly forming products in the ground state. The phenomenon can be explained in the context of electron transfer theory [34-38], Since electron transfer occurs on the Franck-Condon time scale, the reactants have to achieve a structural configuration that is along the path to product formation. The transition state of the electron transfer corresponds to the area of intersection of the reactant and product potential energy surfaces in a multidimensional configuration space. Electron transfer rates are then proportional to the nuclear frequency and probability that a pair of reactants reaches the energy in which they have a common conformation with the products and electron transfer can occur. The electron transfer rate constant can then be expressed as... 

FIGURE 8. Schematic of the possible energetics of electron transfer along the A- and B-branches of cofactors in the Rb. sphaeroides reaction centre. The free energies of the B-branch radical pairs are higher than that of their A-branch counterparts. Mutations that affect the redox potential of B, Bg, or HbWIII affect electron transfer on one branch only, whereas changes in the redox potential of P will affect electron transfer on both branches. 

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