Marcus-Gerischer distribution

Semkonductor-Uquid Junction From Fundamentals to Solar Fuel Generating Structures, Fig. 1 Marcus-Gerischer distribution of the density of states for a one-electron charge transfer redox couple (Cu(II)/Cu(I)) in comparison to the band edges of selected semiconductors assuming a sum of the reorganization energies, X, of 2 eV also shown are the redox potentials... 

Gerischer has demonstrated that the potential of a redox electrolyte in solution represents an electrochemical potential [34,35]. The Fermi level of a semiconductor can also be considered as electrochemical potential. Equilibrium formation demands that the electrochemical potentials equilibrate. The schematic in Fig. 1 shows the respective density of states (DOS) of a series of semiconductors and of a redox solution before contact formation. The solution DOS is given by the Marcus-Gerischer theory [27, 36] and is characterized by Gaussian distributions for the oxidized (unoccupied) and reduced (occupied) component of the redox couple (see Eq. 1). 

Marcus[195] gave a quantitative interpretation of this idea and above all, the role of solvent rearrangement within the framework of the absolute rate theory. Later, he also extended these concepts to electrochemical processes[196]. Similar concepts were also developed by Hush[197,198]. An important result of this work was the establishment of the relation between the transfer coefficient for adiabatic reactions and the charge distribution in the transient state. Gerischer[93,199] proposed a very useful and lucid treatment of the process of electron transfer in reactions with metallic as well as semiconductor electrodes. While the works mentioned above were mainly based on transition state theory, a systematic quantum-mechanical analysis of the problem was started by Levich, Dogonadze, and Chizmadzhev[200-202] and continued in a series of investigations by the same group. They extensively used the results and methods of solid state physics, and above all the Landau-Pekar polaron theory[203]. 

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