Electrocatalysis and Catalyst Screening from Density Functional Theory Calculations - Fuel Cell Catalysis: A Surface Science Approach - page 58

in the gas phase at a given potential U via:

DG(U) ¼ DG 0 þ eU (3 : 3)

where DG 0 is the free energy of reaction for

1

2 H 2 ! H

(3 : 4)

at standard conditions. This free energy can be directly calculated using DFT and
standard molecular tables via

DG 0 ¼ DE þ DZPE TDS (3 : 5)

Here DE and DZPE are the differential adsorption energy for H and the difference in
zero point energy for Reaction (3.4) as given by DFT. DS is the difference in entropy.
At a pH different from zero, the entropy for the H þ ion will change. We can correct
expression (3.5) for this effect by adding DG(pH) ¼ 2k B T ln[H þ ].
Equation (3.3) gives the potential dependence of the reaction free energy of
Reaction (3.2). Since this reaction equilibrium defines the standard hydrogen electrode
potential, we now have a direct link between quite simple DFT calculations and the
electrode potential. In a similar way, we can now calculate potential-dependent
reaction free energies for other reactions, such as O þ H þ þ e 2 ! OH or OH þ
H þ þ e 2 ! H 2 O.
At this point, it is appropriate to describe in more detail how to calculate the
relevant reaction energies using DFT. Taking the electrochemical adsorption of
hydrogen as an example, the calculation of the adsorption energy of H should actually
be done not at ultrahigh vacuum (UHV) conditions, but at realistic electrochemical
conditions. This means that we need not only the platinum electrode and the
hydrogen atoms present, but also the electrolyte. To simplify matters, neglecting the
effect of anion, we could divide the effect of the electrolyte on the hydrogen
adsorption energy into two major effects, not necessarily decoupled from each
other: the effect of the liquid surrounding (water) and the effect of electric field
(the electric double layer).
The influence of water can be included by adding water molecules to the DFT cal-
culation. Whereas the interaction with water will be discussed in more detail later, in
short, the water interaction will be most important for adsorbates that easily form
hydrogen bonds, react with water, or form strong ionic bonds to the surface. For
other adsorbates, such as H , the effect of water is negligible [Jerkiewicz, 1998;
Roudgar and Gross, 2005].
The dependence on the electrical field can be approximated either analytically,
e.g., with a dipole field interaction, or by simulations including an external field. In
either case, the electric field would give rise to a correction term, DG field (U ), to be
added to Equation (3.3). As will also be discussed later, this correction will in most
cases be small.