Ab Initio Atomistic Thermodynamics for Fuel Cell Catalysis - Fuel Cell Catalysis: A Surface Science Approach - page 144

Again, the latter aspect is a direct consequence of the fact that we have assumed the
electrolyte part of the interface to be fixed. Although the final reduction of the
system size to the electrode surface alone allows the problem to be treated quantum
mechanically, the Gibbs free energy G still depends on the amount of excess charge
on the electrode surface, q e , which changes as the electrode potential is varied.
However, this brings us back to the problem of describing the shape of the potential
drop within the electrode/electrolyte interface, for which, as we have learned already,
no conclusive approach exists at present. In practical calculations, one way out of this
dilemma is to revert to experimental measurements.
Therefore, instead of considering the electrode potential, the surface stability can be
evaluated as a function of any quantity, which allows one to change the excess surface
charge. When performing DFT calculations, this could be realized by adding an exter-
nal electric field perpendicular to the surface plane, E z . Since G and g bulk

Au in (5.21)
describe the Au surface and bulk, respectively, both of which have solid character,
the temperature and activity (pressure) dependence will be rather small, which is
why the DFT energies, which mimic T ¼ 0, can be used instead. Therefore, G can
be replaced by the total energy of the surface, leading to

s e (E z )m e (E z )

g 0 (E z ) ¼ 1
A

E tot (E z ) N Au g bulk (5 : 22)

Au

where we have introduced the excess surface charge density on the electrode surface,
s e , which also depends on the applied electric field.
Figure 5.7 shows the modified surface free energies g 0 calculated for unrecon-
structed and reconstructed Au(100) using DFT. The details can be found in [Jacob,
2007a]. The plot shows that the hexagonal reconstructed surface is more stable over

Figure 5.7 Calculated g 0 versus electric field perpendicular to the surface, E z , for unrecon-
structed and reconstructed Au(100).