Electrocatalysis and Catalyst Screening from Density Functional Theory Calculations - Fuel Cell Catalysis: A Surface Science Approach - page 57

In spite of the importance of having an accurate description of the real electrochemical
environment for obtaining absolute values, it seems that for these systems many trends
and relative features can be obtained within a somewhat simpler framework. To make
use of the wide range of theoretical tools and models developed within the fields of
surface science and heterogeneous catalysis, we will concentrate on the effect of the
surface and the electronic structure of the catalyst material. Importantly, we will
extend the analysis by introducing a simple technique to account for the electrode
potential. Hence, the aim of this chapter is to link the successful theoretical surface
science framework with the complicated electrochemical environment in a model
simple enough to allow for the development of both trends and general conclusions.
Once we have developed our basic model and shown how it may be used to estab-
lish trends in electrochemical reactivity, we will take the further step of applying it to
the identification of new bimetallic electrocatalysts. We will introduce simple pro-
cedures to rapidly screen bimetallic alloys for promising electrocatalytic properties,
and we will demonstrate the importance of including estimates of the alloys' stability
in the screening procedure. Finally, we will give examples of successful application of
this method to specific problems in the area of electrocatalyst development.

3.2 THEORETICAL STANDARD HYDROGEN ELECTRODE

Ab initio atomic simulations are computationally demanding; present day computers
and theoretical methods allow simulations at the quantum mechanical level of hun-
dreds of atoms. Since an electrochemical cell contains an astronomical number of
atoms, however, simplifications are essential. It is therefore obvious that it is necessary
to study the half-cell reactions one by one. This, in turn, implies that a reference
electrode with a known fixed potential is needed. For this purpose, a theoretical
counterpart to the standard hydrogen electrode (SHE) has been established
[Nørskov et al., 2004]. We will describe this model in some detail below.
Consider the following reaction:

1

2 H 2 (g) ! H ! H þ (aq) þ e

(3 : 1)

where H is hydrogen bound on the surface. Ignoring the H , we get

1

2 H 2 (g) ! H þ (aq) þ e

(3 : 2)

At the conditions used to define the standard hydrogen electrode potential, T ¼ 300K,
p H 2 ¼ 1 bar, and pH ¼ 0, the reaction free energy of any of these reactions, DG,is
zero. Hence, the free energies of

2 H 2 (g) and H þ (aq) þ e 2 are equal. This defines
U ¼ 0 V. At another potential, the chemical potential of the electrons e 2 is changed
by a factor of 2eU with respect to H 2 in the gas phase. Taking this into account,
the free energy of H adsorbed on the surface can be related to the free energy of H 2

1