First-Principles Simulation of the Active Sites and Reaction Environment in Electrocatalysis - Fuel Cell Catalysis: A Surface Science Approach - page 100

4.3.3.1 The Vacuum Reference The first reference in the double-reference
method enables the surface potential of the metal slab to be related to the vacuum
scale. This relationship is determined by calculating the workfunction of the model
metal/water/adsorbate interface, including a few layers of water molecules. The
workfunction, 2f Fermi , is then used to calibrate the system Fermi level to an electro-
chemical reference electrode. It is convenient to choose the normal hydrogen electrode
(NHE), as it has been experimentally and theoretically determined that the NHE
potential is 24.8 V with respect to the free electron in a vacuum [Wagner, 1993].
We therefore apply the relationship

f NHE ¼ 4 : 8V f Fermi (4 : 1)

to determine the electrochemical potential of our interfacial model.

4.3.3.2 The Aqueous Reference The vacuum potential of the electron pro-
vides a convenient, absolute reference point for an uncharged system. In the presence
of an electric field, however, the vacuum level is no longer meaningful, as the field
permeates through free space, thus preventing the assignment of a unique free electron
potential. In electrochemical systems, the electric field generated by a charged elec-
trode is rapidly screened by the water molecules and ions in solution. Hence, at a
point in the solution phase some ˚ngstr ¨ms from the surface (typically estimated at
5 - 10 ˚ ), the electrochemical potential will again reach a constant level [Lozovoi
et al., 2001; Sanchez et al., 2004; Taylor et al., 2006b]. Accordingly, we introduce
a second reference point for monitoring the potential within the aqueous region of
the unit cell. The electrochemical potential of this point is calibrated to the value
f W (0) using the vacuum reference introduced above. As the system is subsequently
charged with q electrons, the Fermi level f Fermi (q) of the model electrode/electrolyte
system is measured against this reference point f W (q). The electrochemical potential
of the charged system is therefore given by the relation

f NHE (q) ¼ 4 : 8 [f Fermi (q) f W (q) þ f W (0)] (4 : 2)

4.3.3.3 Establishing the Potential-Dependent Free Energy Thermo
dynamically, a variation of the number of electrons available to a system is equivalent
to operating within the grand canonical ensemble (for a full discussion, see Lozovoi
et al., 2001). Hence the free energy is a function not only of the electronic structure
and field of the nuclei, but also of the electrochemical potential. Furthermore, the
energy of the periodic slab must be corrected for interactions with the homogeneous
background charge that is applied to restore the system to charge neutrality [a correc-
tion of E slab bg (q)]. This latter term is derived in Taylor et al. [2006b] and can be
reduced to the following:

E slab bg (Q) ¼ Q
0

Df shift (q) dq (4 : 3)