Provide an example of the inner-sphere and outer-sphere mechanisms in the Marcus theory.

The Marcus theory explains electron transfer reactions through inner-sphere and outer-sphere mechanisms.

Inner-sphere mechanisms involve direct contact between the donor and acceptor molecules, with the transfer of an electron occurring through a coordinated bond. This type of mechanism is more likely to occur when the donor and acceptor molecules are close in proximity and have compatible coordination geometries. The coordinated bond can be formed through ligands or solvent molecules, and the transfer of the electron can result in a change in the oxidation state of the donor and acceptor molecules.

Outer-sphere mechanisms involve the transfer of an electron through a solvent or medium that surrounds the donor and acceptor molecules. This type of mechanism is more likely to occur when the donor and acceptor molecules are further apart and have incompatible coordination geometries. The transfer of the electron can result in a change in the electrostatic potential of the solvent or medium, which can affect the rate of the reaction.

Overall, the Marcus theory provides a framework for understanding electron transfer reactions and the factors that influence their rates. By considering the inner-sphere and outer-sphere mechanisms, scientists can better predict and control these reactions in various applications, such as energy conversion and storage.