First-Principles Simulation of the Active Sites and Reaction Environment in Electrocatalysis - Fuel Cell Catalysis: A Surface Science Approach - page 120

Using the periodic DFT double-reference model, the reduction of adsorbed O 2
(O 2 ) was found to occur by two sequential steps:

H bulk þ e reference þ O 2 ! H near þ e þ O 2 (4 : 15)

H near þ O 2 þ e ! OOH

(4 : 16)

where H bulk signifies a proton in the bulk electrolyte and H near refers to a proton in the
model unit cell, but as far from the adsorbed O 2 as possible within the model system.
Reaction (4.15) represents the diffusion of the proton from the bulk to the near-surface
region, defined for our purposes as being the initial proton position within the DFT
model unit cell. Within the double-reference model system, the completion of this
diffusion process coincides with the addition of an electron to the model system,
however, whether the electron resides in the electrode, on adsorbed O 2 , or associated
with the nearby proton is observed rather than prescribed. In the initial reactant state
of Reaction (4.15), the energy of the proton and electron are included using a bulk
reference rather than being included directly in the unit cell. This is done by invoking
the equality of the free energy of a proton and electron with a gas phase hydrogen
molecule at NHE conditions [Liu et al., 2003; Nørskov et al., 2004]:

G H þ ,e (U) ¼ G H 2 þ eU (4 : 17)

where U represents the potential relative to the NHE. In the product species of
Reactions (4.15) and (4.16) (“H near þ e 2 þ O 2 ” and OOH ), the proton and electron
are included in the DFT model system and the double-reference method is used to
explicitly consider whether the electron shifts the electrode potential or reduces the
reaction center at a given electrode potential.
Figure 4.14 illustrates the structures considered and the potential dependence of the
free energies of each species. Both of the steps involved in reducing adsorbed O 2 were
found to endothermic at potentials of interest for the ORR, in line with the expectation
that transport of the proton closer to the positively charged surface is successively
more endothermic with increasing proximity. What is surprising, however, from
this plot is the relative slopes of the two reaction steps. The slope of an elementary
reaction free energy with potential is equal to the number of electrons transferred in
that step. Clearly, the first step of moving the proton near to the adsorbed O 2 has a reac-
tion free energy that increases with increasing potential, and, in fact, the slope of this
reaction is exactly 1. This indicates that electron transfer has occurred prior to forming
the OO22H bond. A detailed analysis of charge corroborates that reduction has
occurred and that an additional electron resides in the adsorbate layer near to the
surface as compared with the initial state. The additional electron cannot be directly
assigned to the oxygen molecule, as the electron density increases across various
local water molecules and the added H atom as well, suggesting that electron transfer
to the adsorbed O 2 occurs together with a polarization to stabilize the positive charge
on the hydronium ion. This result can only be attributed to the specific model system
used in this study (i.e., the water structure, O 2 coverage, proton position, and