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in the previous section. Only the bonding part is filled, and, since it lies well below the
Fermi level, the electronic energy of the transition state is significantly reduced.
A natural question is: for a given width of a d-band and a fixed interaction strength,
what is the optimum position of the center of the band for catalysis? As Fig. 2.19a
shows, this is near the Fermi level—a fact that is easy to understand in terms of the
splitting mechanism. Conversely, for a fixed position of the band, an increase in the
coupling strength can reduce the activation energy significantly. In the model calculation
presented here, the activation energy is reduced by more than 1 eV; thus, a process that at
sp-metals is practically too slow to be observable can become quite fast at transition
metals. Of course, this is exactly what is observed for the hydrogen oxidation reaction:
at sp-metals such as mercury and lead it is extremely slow, while at platinum, palladium,
and several other transition metals it is very fast. Indeed, a first application of our model to
the hydrogen oxidation on a series of metals shows a good correlation with experimental
results [Santos and Schmickler, 2007a, b, c; Santos and Schmickler, 2008].
2.9 CONCLUSIONS
Electrochemical electron transfer reactions take place at the interface between an
electrode and a solution, and therefore they are governed by the interaction of the reac-
tant both with the solvent and with the electrode. To a good approximation, the inter-
action of ions with the solvent can be treated by classical statistical mechanics, while
the chemical interaction between a reactant and a metal electrode must be calculated by
advanced quantum chemical methods, which have only become available during
the last decade. Therefore, it is logical that the theory of electron transfer at first
focused on the solvent reorganization, and that the electrode was simply considered
as a reservoir of electrons. This is the essence of the theories of outer sphere electron
transfer reactions originated by Marcus and Hush. Since in this class of reactions
the reactants are not adsorbed, they interact relatively weakly with the metal.
Indeed, most reactions of this type seem to fall into the class of weakly adiabatic inter-
actions, which are sufficiently strong to ensure adiabaticity, but too weak to affect the
energy of activation. Therefore, these theories are quite successful for outer sphere
reactions, and for a long time they formed the basis of our understanding of electro-
chemical electron transfer.
Reactions of practical interest involve the breaking or formation of chemical bonds,
which require extra energy. The theory of Sav´ant and its subsequent developments
are an ingenious extension of the Marcus - Hush type of theory to the breaking of a
simple bond. The binding energy enters into the energy of activation, but the inter-
action with the metal electrode is still assumed to be weak, i.e., the reactants are not
adsorbed. In this sense, the reaction is not catalyzed by the electronic interaction
with the metal.
In a simple ion transfer reaction, the distance of the reactant to the surface changes,
and it becomes quite strong when it is actually in contact with the metal. Thus, a full
description requires a good treatment of the interaction both with the solvent and with
the metal. Nevertheless, the energy of activation is mainly determined by the partial
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