Calculated Phase Diagrams for the Electrochemical Oxidation and Reduction of
Water over Pt(111)
Jan Rossmeisl* and Jens K. Nørskov
Center for Atomic-scale Materials Physics, NanoDTU, Department of Physics, Technical UniVersity of
Denmark, DK-2800 Lyngby, Denmark
Christopher D. Taylor,†Michael J. Janik,†and Matthew Neurock†,‡
Department of Chemical Engineering and Department of Chemistry, UniVersity of Virginia,
CharlottesVille, Virginia 22904
ReceiVed: May 24, 2006; In Final Form: August 25, 2006
Ab initio density functional theory is used to calculate the electrochemical phase diagram for the oxidation
and reduction of water over the Pt(111) surface. Three different schemes proposed in the literature are used
to calculate the potential-dependent free energy of hydrogen, water, hydroxyl, and oxygen species adsorbed
to the surface. Despite the different foundations for the models and their different complexity, they can be
directly related to one another through a systematic Taylor series expansion of the Nernst equation. The
simplest model, which includes the potential only as a shift in the chemical potential of the electrons, accounts
very well for the thermochemical features determining the phase-diagram.
The atomic and molecular scale processes that occur at the
interface between a metal surface and an aqueous solution
ultimately dictate the overall electrochemical and electrocatalytic
behavior.1,2The electrochemical potential that forms is the result
of ion gradients that are established across the solution phase,
doping of the solid phase, or through potentiostatic control.
Despite the long and well-established history of electrochemistry
at metal surfaces, a clear theoretical description of atomic and
electronic scale processes that occur on the electrode surface
has yet to be established. The use of molecular dynamics
simulations and Monte Carlo simulations with various levels
of description of the electrode surface and the electrolyte species
has helped to establish the basic concepts surrounding the
Guoy-Chapman theory of ion distributions, emerging theories
regarding water layering, and the structure and behavior of water
close to the electrode.3-5However, phenomena such as chemical
bonding of species to the electrode (chemisorption), ion adsorp-
tion with partial discharge, and chemical reactivity require a
more complete analysis of the changes of the electronic structure
at the electrode surface as well as within the solution phase.
The study of condensed matter interfaces, such as the electrode-
electrolyte interface, has been hindered thus far due to its
complexity and the lack of clear conventions to describe
electrochemical conditions. Recent work, however, indicates that
such conventions are emerging.1,2,6-8It has, for example, been
shown that many of the conventions from heterogeneous
catalysis and gas-phase reactions can be applied to electro-
chemistry.2This requires a reference to connect the gas-phase
surface calculations to those under electrochemical control.
There are various possible choices, however, as to how one
decides upon a good reference state. For example, in the cluster
calculations performed by Anderson et al. the reference state
was determined by estimating ∆G for a product and reactant
state differing by n electrons (i.e., for a one electron transfer, n
) 1, this corresponds to the ionization potential for the cluster).7
The equilibrium potential was then calculated via
where the term 4.6 V is introduced to account for the work
function of the normal hydrogen electrode.9In the proton/
electron-transfer reactions studied in ref 2, the product and
reactant states differ by n(H++ e), which allows a natural
relationship to the normal hydrogen electrode, defined by the
Thus the energy of n(H++ e) can be directly replaced with the
energy of H2. The reaction energies at subsequent potentials
are then directly determined by raising or lowering the reaction
energy in equilibrium with H2 according to the change in
potential relative to the standard hydrogen electrode:
We will refer to this approach as Model 1. Model 2 is derived
from Model 1, and differs only by the inclusion of an electric
field that is used to simulate the change in surface interactions
with the potential, U, for a slab that is initially charge neutral.
Finally, a quite different approach has been adopted by
considering the absolute potential of the interface under
consideration as the work function of a periodic slab representa-
tion of the interface.1,6,10The work function is therefore related
to the normal hydrogen electrode, similar to eq 1, via the
* Address correspondence to this author.
†Department of Chemical Engineering, University of Virginia.
‡Department of Chemistry, University of Virginia.
U/V NHE ) ∆G/nF - 4.6 V(1)
∆G ) ∆G(0) + nF(U NHE)(3)
U/V NHE ) Φ/e - 4.6 V(4)
J. Phys. Chem. B 2006, 110, 21833-21839
10.1021/jp0631735 CCC: $33.50 © 2006 American Chemical Society
Published on Web 10/07/2006
Filhol and Neurock also introduced a scheme to tune the
electrode potential by modifying the surface charge density.1
A second reference is then used to monitor the change in this
potential relative to the potential at some distance from the
electrode in the solution phase. This approach is referred to
herein as Model 3.
In this paper we calculate the phase diagram of Pt(111) in
water as a function of the applied potential for all three different
models to understand the similarities as well as the differences
between them. Only the thermochemistry is considered in this
work, meaning that we do not investigate the mechanisms or
the activation barriers for the phase transitions. In the first
scheme, Model 1, the adsorption energies are treated indepen-
dently of the electrochemical potential, as in the earlier papers2,11
and similar to the scheme developed by Anderson et al.7We
then compare the reaction energies reported using this model
to simulations in which the adsorption energy is allowed to vary
with the electrochemical potential. In this second scheme (Model
2) the potential dependence is estimated by monitoring the
change in adsorption energy of water and its dissociation
products as a function of the electric field. The potential is then
subsequently determined by estimating the double-layer width
and multiplying accordingly. Finally, we compare with the
results obtained using the approach from refs 1, 6, and 10 for
including the electrode potential and a more extensive model
of the electrolyte region, Model 3. These models are described
in more detail in subsequent sections.
For Models 1 and 2 density functional (DFT) calculations
using a plane wave implementation12on a 3-layer 3 × ?3 Pt-
(111) slab were performed on the level of the generalized
gradient approximation Revised-Perdew-Burke-Ernzerhof
(RPBE)13for the exchange-correlation term. A 3 × 4 × 1
Monkhorst-Pack mesh was used to sample the first Brillouin
zone. Ultrasoft pseudopotentials were used to model the ion
cores.14The electronic wave functions can therefore be repre-
sented on plane wave basis set with a cutoff energy of 340 eV.
The electron density is treated on a grid corresponding to a plane
wave cutoff at 500 eV. A Fermi smearing of 0.1 eV and Pulay
mixing is used to ensure a fast convergence of the self-consistent
electron density. The atomic positions were relaxed until the
sum of the absolute forces was less than 0.05 eV/Å. All
calculations were performed with the ASE simulation package.15
Model 3 was examined with the Vienna Ab initio Software
Package,16-19with a 3 × 3 × 1 k-point Monkhorst-Pack20mesh
of the first Brillouin zone and a plane-wave basis with a cutoff
energy of 396.0 eV. Methfessel-Paxton smearing21of order 2
with a value of σ of 0.2 eV was applied to aid convergence.
The model utilized a 3 × 3 periodic simulation cell to capture
the surface periodicity and periodicity of the ice-like water
overlayer at the interface. An interslab spacing of 14.64 Å was
used. Twenty-four water molecules were introduced in this
interlayer volume to give a density of 1 g/cm3. Molecular
dynamics simulations as described in the paper by Filhol and
Neurock1were used to anneal an appropriate water structure
for simulation of the aqueous region.
Results and Discussion
Model 1. The cathodic and anodic activation of water can
lead to various surface intermediates, which we may describe
as different surface phases. Four different states of the surface
are considered herein: the water covered surface (that is, the
clean surface with a water overlayer), the hydrogen covered
surface, the hydroxyl covered surface, and the oxygen covered
surface. A water layer is introduced as described in refs 3 and
22 in order to model the aqueous/metal interphase. The water
layer can point the hydrogen atoms either away from the surface
or toward the surface; these two configurations are very close
in energy. The surface structures are shown in Figure 1.
Surface phase changes may occur as a consequence of proton
transfer between water and the adsorbents and electron transfer
between the absorbents and the electrode. The reactions con-
necting the different states of the surface can be written such
Here * denotes a free site on the surface, e-is an electron in
the electrode, and H+denotes a proton solvated in the
electrolyte. The chemical potential of the protons in the aqueous
phase and the electrochemical potential of the electrons are
variable parameters that can be used to determine the phase of
the system. The chemical potential of the protons is given by
the pH of the solution. The potential of the electrons is
determined by the bias between the electrode under study and
a reference electrode. The standard hydrogen electrode is used
here as the reference; as such the potential is zero at pH 0, when
Figure 1. Side and top views of the five calculated configurations. From the left: the water layer with the hydrogen pointing up, the water layer
with hydrogen pointing down, chemisorbed atomic hydrogen at the surface with a water layer above, the half dissociated water layer where every
second water molecule is substituted with HO*, and chemisorbed atomic oxygen at the surface with a water layer above. The coverage of H*, OH*,
and O* is1/3of a monolayer. There are four water molecules per unit cell.
H2O + * T OH* + e-+ H+
OH* + * T O* + e-+ H+
* + e-+ H+T H*(7)
21834 J. Phys. Chem. B, Vol. 110, No. 43, 2006
Rossmeisl et al.
protons and electrons are in equilibrium with hydrogen gas at
standard conditions. The chemical potential for electrons at the
electrode is then eU, where U is the bias between the electrodes
as discussed above.
Model 1 includes the effect of solvation and bias according
to the following prescription:
1. By setting the reference potential to that of the standard
hydrogen electrode, we can relate the chemical potential (the
free energy per H) for H++ e-in solution to that of1/2H2in
the gas phase. At pH 0 in the electrolyte and 1 bar of H2in the
gas phase at 298 K the reaction free energy of1/2H2f H++
e-is zero at an electrode potential of U ) 0. At standard
conditions, the free energy ∆G0) ∆G(U ) 0, pH 0, p ) 1
bar, T ) 298 K) for the reaction of *AH f *A + H++ e-can
therefore be calculated as the free energy of the reaction *AH
f *A +1/2H2.
2. To model the water environment of the electrochemical
cell we calculate the binding enthalpies, ∆Ew.water, in the
presence of a layer of water, see the discussion above. (If the
water layer is not included we denote the binding enthalpy ∆E.)
3. ∆Gw.water ) ∆Ew.water + ∆ZPE - T∆S is calculated as
follows: The reaction energy, which refers here to the change
in the electronic energy between the products and the reactants
(∆E for Ni and Au, or ∆Ew.waterfor Pt), is calculated directly
from the DFT results. The effect of water is subsequently taken
into account for the Ni, Au systems by including the interaction
term derived from the Pt calculations. The difference in zero
point energies due to the reaction, ∆ZPE, and the change in
entropy ∆S are determined by using DFT-calculated vibrational
frequencies23and standard tables for the gas-phase molecule.24
4. We include the effect of a bias on all states involving an
electron in the electrode, by shifting the energy of this state by
∆GU) -eU, where U is the electrode potential.
5. At a pH that is different from 0, we can correct for the
free energy of H+ions by the concentration dependence of the
entropy or free energy: ∆GpH(pH) ) -kT ln[H+] ) kT(ln 10)-
pH. In this study we use a pH value of 0.
The reaction free energy is then calculated as
This method is also described in previous publications.2,11,23
In Table 1 the binding enthalpies relative to gas-phase water
and hydrogen are listed, together with the calculated free
energies. Ni(111) and Au(111) are included for comparison. The
phase diagrams for the three metal surfaces at 298 K and pH 0
are shown in Figure 2.
At very negative biases all the metals will adsorb hydrogen,
and at high positive potentials only oxygen will be present on
the surface. However, the potentials at which the phases change
are different for the different metals. Gold is noble and therefore
it needs quite extreme potentials to bind any of the adsorbates.
Nickel on the other hand always has an adsorbate bound to the
surface, whereas platinum is somewhere in between.
Hydrogen starts to adsorb at platinum at a potential close to
U ) 0.09 V, which is consistent with the fact that platinum is
a good catalyst for hydrogen evolution under acidic conditions.25
According to the model, the formation of OH* is down hill in
free energy for potentials above 0.79 V. This value is not
trivially compared to voltammograms on Pt(111). The theoretical
value denotes the potential at which reaction 5 is in equilibrium,
this means that it should be compared with the reversible
potential from the voltammogram. Underpotential deposited
species seen in experiments are most likely due to adsorption
on defects such as steps, and are therefore not relevant for
comparison. The reversible potential for OH adsorption from
experiment is ∼0.8 V,26which is in excellent agreement with
the value prediction with the model of 0.79 V. We therefore
conclude that Model 1 is in excellent qualitative and quantitative
agreement with experimental observations on these points. At
the water decomposition potential surface hydroxyl and surface
oxygen are very close in energy. Both phases, therefore, will
probably coexist. Higher potentials favor the surface oxide.
On the Au substrate, water appears to be the thermodynami-
cally favored state over the entire range of potentials examined
whereas on Ni(111) water is never the most stable structure.
On Ni there is a phase transition from the hydride phase directly
to the hydroxyl phase at 0.19 V. The hydroxyl phase, however,
is only stable within a very narrow window (0.19-0.21 V) as
it further oxidizes to form O*.
Model 2. In Model 1 the only way in which the bias enters
the calculation is through the chemical potential of the electrons
(the -eU term in the free energy). This neglects the fact that
the bias will also give rise to electrical fields at the water-
metal interface and will change the magnitude and structure of
TABLE 1: The Binding Enthalpies at U ) 0 V for
Absorbents without Water from References 2 and 23 and
Enthalpies and Free Energy Changes for Pt with Water As
Shown in Figure 1a
∆Gw.water(Figure 1)0.81 eV
aThe free energies for the adsorbents on Ni (111) and Au(111) are
obtained by assuming that the corrections due to zero point energy,
entropy, and the interaction with water are the same as those for Pt.
∆G(U, pH, pH2)1 bar, T ) 298 K) )
∆Gw.water+ ∆GU+ ∆GpH(8)
Figure 2. The phase diagram showing the free energy for different
surface structures for water at pH 0 in contact with Au(111), Pt(111),
and Ni(111). The figure is based on the free energy values in Table 1
and represents the results of Model 1. The lowest line represents the
thermochemically most stable phase. The crossing of the two bottom
lines indicates a phase change. The free energy for liquid water and
hydrogen gas at standard conditions is defined as ∆G ) 0. The lines
with a slope of 1 eV/V are related to H*: ∆GH*w.water(U) ) ∆GH*w.water-
(0) + eU. The lines with a slope of -1 eV/V are related to OH*:
∆GOH*w.water(U) ) ∆GOH*w.water(0) - eU. The lines with a slope of -2
eV/V are related to O*: ∆GO*w.water(U) ) ∆GO*w.water(0) - 2eU.
Electrochemical Oxidation and Reduction of Water over Pt(111)
J. Phys. Chem. B, Vol. 110, No. 43, 2006 21835
the electronic charge on the surface. Because the liquid phase
has ions and is electrically conducting, this change in charge
on the electrode will be screened by a charge of the same
magnitude but opposite in sign from ions attracted to the near-
surface region. The potential drop outside the electrode is
therefore restricted to this double layer of opposite charges, and
appreciable electrical field strengths can build up in this region.
If the average width of the double layer is d, then the average
change in the field is of the order δ? ∼ δU/d. Typically d is
believed to be of the order of a few angstroms, here it is assumed
to be 3 Å.
The simplest way of accounting for the local field effects
induced by a change in bias is to approximate it by a constant
field given by the bias as ? ) U/d. Such a constant field can be
imposed in the DFT calculation and the electrostatic effects
estimated in this way.27Including this correction comprises
The static response of any system to an electric field can be
expanded in the field strength. The energy change of a slab
with adsorbates and a water layer due to an external field, ?,
can be written
where µ is the dipole moment of the slab in the direction of the
field, and R denotes the static polarizability. We have calculated
the energy change due to an external field on the clean slab,
and the results are presented as a function of the applied field
in Figure 3. Since the clean slab has inversion symmetry, there
is no permanent dipole moment and only the polarizability
contributes to the energy change.
Next we consider the response of the metal slab with the
water layer to variation of the surface field. Figure 4 depicts
the field-induced change in the energy of a slab in contact with
a water layer in which the H atoms point up or down (as in the
structures shown in Figure 1). Here we subtract the response
from the clean slab to obtain the response of the water overlayer
alone. The two different water configurations have dipole
moments in different directions, and therefore the µ? term is
different for the two configurations. It should be noted that the
hydrogen-end down structure for adsorbed water is stable up
until about +0.1 V. At higher potentials, water is oriented with
its oxygen end toward the surface. This change in water structure
as a function of potential is known as the water flip-flop
mechanism (also found for water over Pd1and with molecular
dynamics simulations28and cluster calculations29and X-ray
surface studies by Toney30). The adsorption energy of the water
layer is calculated as follows: ∆Ewater layer(?) ) Etotal(?) - Eslab-
(?) - Eslab- 4Ewater in a vacuum, where Etotal(?) is the total energy
of the water covered surface, Eslab(?) + Eslabdenotes the total
energy of the clean surface at a given field strength, and Ewater
ina vacuumis the energy of a water molecule in a vacuum.
Finally we have included the adsorbed species, and calculated
the corresponding field-induced change in the adsorption energy.
In these calculations we have subtracted the response of the
water overlayer, since it is present in all the surface phases.
The exception is adsorbed OH* where no polarization of the
water is corrected for, since the water molecules’ dipoles are
close to parallel with the surface.
The binding enthalpy at a given field strength is calculated
by using the equation
where Etotal(?) is the total energy of the system, ∆Ewater layer(?)
is the adsorption enthalpy of the water layer, shown in Figure
4, and Eslab(?) denotes the total energy of the clean platinum
slab. The changes in Ew.water(?) are shown in Figure 5 for H*,
OH*, and O*. The results in Figure 5 indicate that the effect of
field strength on the adsorption of H, OH, and O is small.
In Model 2 we include the effect of the electrical field
assuming that the width of the double layer is d ) 3 Å. The
corresponding phase diagram for Pt(111) in shown in Figure 6.
The results presented in Figure 6 show that Model 2 closely
replicates Model 1, except for the stabilization of adsorbed OH,
so that there is now a window of potentials where OH* is the
most stable surface species.
Model 3. The third model presented in this paper is based
upon the strategy developed for considering the activation of
water on Pd(111).1An electric field is induced at the interface
by changing the number of electrons available to the metal of
the electrochemical system. This effectively introduces a surface
charge density of q/2A, where q is the charge applied and A is
the area of the slab face. To maintain cell neutrality, and thereby
meet the requirements for periodic calculations, a homogeneous
Figure 3. The total energy change for the Pt(111) slab as a function
of the external field, Eslab(?). The clean Pt surface does not have a
permanent dipole moment, so in this case only the polarization term
has a contribution to the total energy. The calculated points are fit to
a parabola represented with the solid line. This contribution to the total
energy is subtracted in the binding energies.
∆E(?) ) µ? -1/2R?2+ ... (9)
Figure 4. The adsorption enthalpy of the water layers (per four water
molecules) as a function of the applied field, ∆Ewater layer(?). Red is the
water with hydrogen pointing up away from the metal surface and black
is the water with hydrogen pointing toward the surface. The structures
are allowed to relax, but only a minor relaxation is taking place. The
potential of the electrode we estimate by assuming a 3.0 Å thick double
layer, U is then 3 Å times the field. The estimated values of the potential
are shown on the upper x-axis.
∆Ew.water(?) ) Etotal(?) - Etotal(0) + ∆Ew.water(0) -
∆Ewater layer(?) + ∆Ewater layer(0) - Eslab(?) (10)
21836 J. Phys. Chem. B, Vol. 110, No. 43, 2006
Rossmeisl et al.
countercharge of uniform charge density -q/AL is distributed
across the entire supercell, where L is the cell height. The
interlayer space is then completely saturated with H2O at a
density of 1 g/cm3. In this way the homogeneous countercharge
is embedded within a dielectric environment, and therefore has
a screened electrostatic interaction with the slab. Previous
calculations showed that the field which is induced in this way
closely replicates the double layer environment that results from
a true polarization by actual ions in the outer Helmholtz plane,
assuming that the unit cell that is used is of appropriate size.6
The supercell geometry that is shown in Figure 7 is used
here to model the activation of water over Pt(111). Panels a-d
in Figure 8 depict the optimized adsorption geometries for the
surface hydrogen, surface hydroxyl, and surface oxygen phases.
In the absence of an applied potential, water and hydroxyl adsorb
at the atop sites, as has been shown previously31for water and
hydroxyl adsorption on Pt(111), whereas oxygen and hydrogen
adsorb at 3-fold hollow sites.32As in Model 2, the hydrogen
atom was placed at the Pt(111)/water interface where the water
has its hydrogen atoms directed toward the metal surface. The
energies of the systems were then calculated at potentials
corresponding to surface charges of -15 through to +15 µC/
cm2. This is accomplished by either adding or subtracting
between 0, 0.5, or 1 electrons to or from the number of electrons
required for neutrality within the unit cell. As in Models 1 and
2, the difference of a proton and electron between the phases is
remedied by the addition of H2 energies where appropriate,
modified by the electrochemical potential of the phase (eqs 2
and 3). In this model (Model 3), the electrochemical potential
is determined by the direct reference to the electrostatic potential
drop observed across the interface, as obtained by Poisson’s
equation applied to the self-consistent electron density of the
system. In this way the work function is determined for the
metal/electrolyte system, which can then be straightforwardly
related to the electrochemical potential via
where ∆Φ|slab,vacrefers to the work function of the metal in a
vaccuum. The potentials calculated in this way are clearly
dependent upon the exact configuration of the water molecules
and adsorbate species within the unit cell. Variations in the
configurations used indicate that the total error introduced in
the potential is in fact considerable and of the order of 0.3 V.
For charged phases, it is not possible to make such a direct
work function measurement, due to the presence of electric field
effects throughout the vacuum region within the periodic
simulation. Equation 5 therefore only applies to the neutral slab
case. The potential for the charged slabs is determined conse-
quently by reference to the potential of the solution layer in the
The energy of the slab is then corrected to remove the energy
contribution from the background countercharge, and the excess
electrons such that the energies of the variously charged slabs
are directly comparable.
More details on this model can be found in a separate
Figure 5. The adsorption enthalpy of the intermediates as functions
of the applied field, calculated in the presence of water, ∆Ew.water(?).
The potential of the electrode, U, was estimated by multiplying the
thickness of the double layer (assumed here to be 3.0 Å) by the field
that is reported here in terms of V/Å. The estimated values of the
potential are shown on the upper x-axis.
Figure 6. The electrochemical phase diagram for the reduction and
oxidation of water over Pt(111) at pH 0 as a function of bias. The red
lines are the results from Model 2, while the black dotted lines represent
the results from Model 1 also shown in Figure 2 (middle section). There
is a very good agreement between the two model phase diagrams, which
indicates that the adsorption enthalpies are almost conserved when the
potential is changed. However, OH* is stabilized so that it is present
on the surface around 0.8 V. The dashed lines that result from Model
1 are the following: GH(U) ) EH(0) + 0.24 eV + eU, GOH(U) ) EOH-
(0) - 0.24 eV - eU, and GO(U) ) EO(0) + 0.05 eV - 2eU. The red
lines which refer to Model 2 ar ethe following: GH(U) ) EH(U) +
0.24 eV + eU, GOH(U) ) EOH(U) - 0.24 eV - eU, and GO(U) )
EO(U) + 0.05 eV - 2eU.
Figure 7. Supercell system used to describe the metal/solution interface
in Model 3. Three supercells are shown.
U0) ∆Φ|slab,vac- 4.6 V NHE (11)
Uq) ∆Φ|slab,solution- Φsoln,0+ U0
E ) Eslab-∫0
q〈V(q)〉 dq + qU
Electrochemical Oxidation and Reduction of Water over Pt(111)
J. Phys. Chem. B, Vol. 110, No. 43, 2006 21837
The phase diagram for water over Pt(111) derived with Model
3 is presented in terms of absolute (atomization) energies in
Figure 9a, and in terms of binding energies in Figure 9b. The
free energy corrections based on the zero point energies and
entropic terms used in the previous two models have been
applied.2The equilibrium potential for the adsorption of
hydrogen is +0.16 V and that for oxygen adsorption is +0.5 V
NHE. As observed in Models 1 and 2, the regions for oxygen
and hydroxyl adsorption are quite close, and water activation
to form the hydroxyl overlayer is not exothermic until 0.63 V
NHE. These observations are qualitatively similar to those
provided by Model 2 [recall 0.08 V (H*), 0.74 V (OH*), and
0.82 V (O*)], but contain shifts which are likely due to the
difference in exchange-correlation functional and in interactions
between the environment water and the adsorbates between the
two approaches. For example, as in Model 1 above, Model 3
predicts that O formation will thermodynamically precede OH
formation on Pt(111), although since the formation of O is
expected to be a stepwise procedure, realistically the two species
will be present on the surface at the same time, depending on
the kinetics of OH dissociation over the Pt(111) surface.
Furthermore, changes in the number of hydrogen bonds between
Models 1, 2, and 3 can modify adsorption energies by as much
as -0.2 eV per additional hydrogen bond. A close examination
of the many configurational arrangements of water possible
about the adsorbate species is required to discern these subtle
effects. The best approach may therefore involve the coupling
of one or more of the models in this paper with a molecular
dynamics simulation to determine statistics-based estimates of
the adsorption free energies. Molecular dynamics simulations
will also improve the sampling of the zero charge potential used
as the reference potential for each phase.
It is also instructive to directly compare the results of Model
3 with those obtained by the computationally simpler approach
of Model 1. Since this model utilizes a different exchange-
correlation functional and a different solvation environment for
the adsorbed species than Models 1 and 2, we have reapplied
the methodology of Model 1 to calculating a phase diagram
based on the atomic configuration optimized under neutral slab
conditions as displayed in Figure 8. These energies are shown
as the dotted lines appearing in Figure 9b. The phase diagram
of Model 1 closely resembles that of Model 3. However, a small
linear deviation from the unity slope predicted by the Nernst
law occurs due to the interaction between the dipole of
adsorbents and the field, as also seen in Model 2. There is
qualitative agreement between the slopes found in Model 2 and
Model 3 except for hydroxyl on the surface. This disagreement
is probably due to the small number of water molecules included
in Models 1 and 2. Model 2 shows that the nonunity slope is a
consequence of the interactions between the field and the dipole
moment (see eq 9). This means that whenever a nonunity slope
is observed it need not indicate a partial charge transfer, but
rather a dipole moment. Gibb’s relation can be written as
as ? ) ∆U/d as given above (recall that d is the width of the
double layer, ? is the applied electric field, and ∆µ is the change
in dipole moment for the reaction). We note that the dipole
moment is a physical observable that can be measured as a
work-function change or calculated directly as described above.
The surface energy profiles in Figure 9a are well-ap-
proximated by a quadratic expansion about the potential of zero
charge, with the second-order coefficient given by the capaci-
tance of the interface, C ) -∂2G/∂U2:
The reaction energy plots in Figure 9b are linear, however,
which suggests that the second-order term, the capacitance, is
Figure 8. Snapshots indicating the adsorption geometry of (a) water, (b) oxygen, (c) hydroxyl, and (d) hydrogen for the neutral slabs utilized in
dissociation and hydrogen ion adsorption on Pt(111) as determined with
Model 3. Phase energies are shown in panel a, and reaction energies,
relative to the inert H2O phase, in panel b. Dashed lines in panel b
indicate energies determined with Model 1, for the surface/solvent
ensembles treated in Model 3.
Potential-dependent energies for water and hydroxyl
F(n +∆µ/d) ) ∆G/∆U
G ) G0- C/2(U - U0)2
21838 J. Phys. Chem. B, Vol. 110, No. 43, 2006
Rossmeisl et al.
close to being constant between the phases (the inferred
capacitances are all close to 17 µF/cm2). If this were not the
case, a second-order expansion of the Nernst equation would
∆G(U) ) ∆G(U0) + F(n + ∆µ/d)(U - U0) +
Such an expansion may be required when a reaction involves
considerable change in the surface dipole, either by the
rearrangement of ions at the interface, or by species containing
zwitterionic forms that are altered upon adsorption (such as
amino acids). It can also be seen that this expansion is the
equivalent of eq 9, but expanded in terms of the electrochemical
potential, rather than the electric field.
We have presented three different models for the description
of the complex thermochemistry of water interacting with a Pt-
(111) surface as a function of electrical bias. The three models
differ considerably in complexity and in the amount of
computational resources necessary to model and it is therefore
important to compare the results of the different models to obtain
an idea of the strengths and weaknesses. It is clear that for the
systems considered here, the three models give nearly the same
results. Polarization of the interface by using either Model 2 or
Model 3 leads to only small changes in the adsorption energy
of OH, H, and O relative to H2O. Since Model 1 is much simpler
to apply, this suggests that it is a good starting point for these
kinds of investigations, in particular for screening and trend
We anticipate that Model 1 will fail for systems (adsorbates)
with large dipole moments. Here Model 2 or 3 must be applied.
Quantitative differences between the results of Model 2 and
Model 3 presented here are likely due to the difference in net
water structure at the interface used in these static calculation
methods and different exchange-correlation functionals used.
Therefore, further research is needed to assess the complex role
of hydrogen bonding to stabilize surface intermediates and to
improve the estimation of these effects by static methods. For
this kind of investigation, and investigations of the kinetics of
surface processes involving a charge transfer between the slab
and the electrolyte, Models 1 and 2 will not be sufficient, since
they can only describe the thermochemistry. Here Model 3 or
some other model that properly treats the charge state of the
surface must be used.
Acknowledgment. This work was supported by the Director,
Office of Science, Office of Basic Energy Sciences, Division
of Materials Sciences, U.S. Department of Energy under
Contract No. DE-AC03-76SF00098 and the U.S. Army Re-
search Office MURI grant number DAAD19-03-1-0169, by The
Danish Research Council through the NABIIT program, and
the Danish Center for Scientific Computing.
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1/2∆CF(U - U0)2(16)
Electrochemical Oxidation and Reduction of Water over Pt(111)
J. Phys. Chem. B, Vol. 110, No. 43, 2006 21839