The theory of the Fe2+–Fe3+ electron exchange in water

The rate constant for the Fe2+–Fe3+ electron exchange is formulated as k23= ∫ 0∞g23(r) k̂23(r) 4πr2 dr, a form which also is used to analyze the data for the nuclear spin relaxation in Al3+ induced by collision with Ni2+. It is assumed that the equilibrium pair correlation function g23(r) is the same function of ionic composition and temperature in the two cases and that in the spin relaxation process the local rate constant k̂23(r) has the form that may be deduced from the Solomon–Bloembergen equations. In the case of the exchange reaction the theory of k̂23(r) is developed with respect to the contributions from slow inner shell or outer shell reorganization (activation) dynamics. It is concluded that in the present case these complications are not important and that the controlling dynamics is the crossing from the reactant to the product diabatic Born– Oppenheimer surface. Neither the exchange nor the spin relaxation data can be accounted for if the smallest metal–metal distance in collisions is that given by the closest approach of the envelopes of the M(H2O)6n+ complexes. However, allowing for overlap of the envelopes as one complex pokes into the interstices of the other reduces the distance of closest approach from 6.9 to 4.5 Å. Then one can find Gurney type models for the ion–ion forces in solution such that the model calculations are in good agreement with the experimental exchange and relaxation rate constants and their dependence on temperature and ionic strength, as far as the limited data for the last allow.