A molecular orbital approach to electron-transfer reactions between transition-metal ions in solution

Abstract

We present a general scheme to rationalize the kinetic behavior of transition-metal redox systems in solution as a function of the detailed electronic configurations of donor and acceptor species. For the inner-sphere route, proceeding usually via atom transfer, simple molecular orbital arguments are used to predict for which electronic configurations LSM1-X-MZL5 complexes will be stable at the symmetric geometry. The results are supported by comparison with known crystal structures. For these electronic configurations then the symmetric structure corresponds to an inner-sphere intermediate, sometimes observed spectroscopically or inferred kinetically in the experimental environment. For other configurations the symmetric structure corresponds to a transition state which is never observed experimentally. The kinetic behavior of a large number of redox systems may be rationalized just on this basis. It is suggested that the normal dependence of reaction rate on bridging ligand X (I- > Br- > C1- > F) arises when the rate-determining step involves a transition state (we call this type I) and the inverse order when the rate-determining step involves intermediate decay (type 11). The dependence of reaction rate upon substituent in some carboxylate-bridged systems is also examined, and the effects of nonbridging ligands are analyzed by extending earlier ideas of Orgel. Two types of electron transfer are delineated. Smooth transfer occurs when the nature of the HOMO gradually changes as the bridge ligand is transferred and corresponds to a symmetry-allowed process. Sudden transfer occurs via an electron jump from one orbital to another, and atom transfer here is not necessary for electron transfer. Cases are observed experimentally where atom transfer does not occur. The results of the inner-sphere case are applied to outer-sphere reactions with some qualifications, and some interesting parallels are drawn. The effect of extra ions added to the solution are analyzed in molecular orbital terms, and three catalytic effects are revealed. The added species may hold together the two reacting ions as an electrostatic “glue” (if of the correct charge); it may reduce the barrier to reaction and also may ensure adiabatic behavior. It is pointed out that water itself is probably an excellent catalyst of this sort. The molecular orbital approach to inner- and outer-sphere reactions gives a ready explanation for the anomalous behavior (on the Marcus theory) of the CO~~,’I~(H~O)~ system where a spin change occurs in the reaction coordinate.