Photo-driven oxidation of water on -Fe2O3 surfaces: An ab initio study
Manh-Thuong Nguyen, Nicola Seriani, Simone Piccinin, and Ralph Gebauer
Citation: The Journal of Chemical Physics 140, 064703 (2014); doi: 10.1063/1.4865103
View online: http://dx.doi.org/10.1063/1.4865103
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THE JOURNAL OF CHEMICAL PHYSICS 140, 064703 (2014)
Photo-driven oxidation of water on α-Fe2 O3 surfaces: An ab initio study
Manh-Thuong Nguyen,1,a) Nicola Seriani,1 Simone Piccinin,2 and Ralph Gebauer3
1
The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
CNR-IOM DEMOCRITOS, c/o SISSA, via Bonomea 265, 34136 Trieste, Italy
3
The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy and
CNR-IOM DEMOCRITOS Simulation Center, 34136 Trieste, Italy
2
(Received 24 November 2013; accepted 27 January 2014; published online 14 February 2014)
Adopting the theoretical scheme developed by the Nørskov group [see, for example, Nørskov et al., J.
Phys. Chem. B 108, 17886 (2004)], we conducted a density functional theory study of photo-driven
oxidation processes of water on various terminations of the clean hematite (α-Fe2 O3 ) (0001) surface,
explicitly taking into account the strong correlation among the 3d states of iron through the Hubbard
U parameter. Six best-known terminations, namely, Fe − Fe − O3 − (we call S1 ), O − Fe − Fe−
(S2 ), O2 − Fe − Fe−(S3 ), O3 − Fe − Fe− (S4 ), Fe − O3 − Fe− (S5 ), and O − Fe − O3 −(S6 ), are
first exposed to water, the stability of resulting surfaces is investigated under photoelectrochemical conditions by considering different chemical reactions (and their reaction free energies) that
lead to surfaces covered by O atoms or/and OH groups. Assuming that the water splitting reaction is driven by the redox potential for photogenerated holes with respect to the normal hydrogen
electrode, UVB , at voltage larger than UVB , most 3-oxygen terminated substrates are stable. These
results thus suggest that the surface, hydroxylated in the dark, should release protons under illumination. Considering the surface free energy of all the possible terminations shows that O3 –S5
and O3 –S1 are the most thermodynamically stable. While water oxidation process on the former requires an overpotential of 1.22 V, only 0.84 V is needed on the latter. © 2014 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4865103]
I. INTRODUCTION
Splitting water photoelectrochemically is a promising
way in which solar energy can be harvested and stored,
through photocurrent-driven chemical bond rearrangements
leading to the formation of molecular hydrogen (2H2 O
→ 2H2 + O2 , E0 = 1.23 V, Standard Hydrogen Electrode,
SHE). This can be used directly as a fuel or as an intermediate
for the production of other fuels. Hematite (α-Fe2 O3 ) has
emerged as a candidate photoanode material1–5 due to several
favorable features: a band gap of around 1.9–2.1 eV, depending on preparation conditions, which allows for a large fraction of the solar spectrum to be absorbed, high chemical stability, abundance, and non-toxicity. On the other hand, the position of the conduction band relative to the normal hydrogen
electrode (+0.2 eV) implies that electrons photogenerated
into hematite cannot reduce protons to molecular hydrogen,
hence an external bias needs to be applied to achieve water
splitting. Moreover, hematite suffers from low electron mobility, low absorption coefficient, high recombination rates, and
slow reaction kinetics, leading to small photocurrent density
and a sizable overpotential of around 0.5–0.6 V.1, 6, 7 Recently,
through doping to increase conductivity, nanostructuring to
reduce recombination, and the use of co-catalysts to improve
the surface reaction kinetics, current densities as high as
3 mA/cm2 were reached with an applied potential of 1.23 V
under standard illumination.8 Several of the factors limiting
the performance of hematite as a photoanode are linked to
a) Electronic mail: [email protected]
0021-9606/2014/140(6)/064703/8/$30.00
surface properties, and our limited knowledge of the structure
of hematite in contact with water under irradiation conditions
has been recognized as a key limitation towards improving
this material.1
The (0001) surface is among the most stable facets of
hematite and has been the focus of a series of studies. These
have been carried out in a wide range of conditions, ranging
from fresh, briefly wetted surfaces to dry and humid air conditions, or in contact with water, and employing various experimental techniques.9–16 Several basic issues regarding surface
terminations of hematite are however still open. As an example, it is reported that single-iron and ferryl (Fe4 + ) terminations are observed to coexist at an oxygen pressure of 10−3
− 1 mbar and a temperature of 1050 K;15 in another
study, however, no iron termination is seen in the oxygen
pressure range of 10−10 to 1 bar and temperature range of
300–823 K.16
Clearly, the relative stability of various surface terminations in contact with water depends on many environmental
variables, including the applied voltage,17 pH, and temperature. It is thus essential to determine the most stable surface termination around the conditions of interest before proceeding to investigate possible mechanisms through which
hematite acts as photocatalyst for water oxidation. To this
end density functional theory (DFT) simulations, in combination with the approach proposed by Nørskov and co-workers
to model the electrochemical environment18 and the effect
of solar illumination,19, 20 can provide valuable insights. Indeed, the surfaces of various transition metal oxides known
to be good water oxidation catalysts have been the focus of
140, 064703-1
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a number of recent works.17 Hematite, in particular, has been
investigated by Hellman and Pala,21 who employed the PBE
exchange and correlation functional to determine, as a function of the applied bias, the relative stability selected terminations of the (0001) surface, and modeled the photo-induced
oxidation of water on the most stable surface under solar illumination. Liao et al.,22 on the other hand, used a DFT+U
description of the electronic structure of the system to model
water oxidation on selected hydroxylated (0001) hematite surfaces.
In this work, we study the photo-oxidation of water on the
hematite (0001) surface employing DFT+U, i.e., explicitly
including effects of strong correlation among the 3d states of
iron. We examine six different surface terminations, identified
in our earlier work,23 investigating their interaction with water
molecules and proposing possible water dissociation states.
The stability of dissociated-water states on each termination
is evaluated by considering the (voltage-dependent) reaction
free energy. The most stable configurations on each surface
termination are then compared in terms of surface free energy.
The energetics of the full water oxidation reaction cycle on the
thermodynamically most stable surface terminations is then
determined, and compared with previous studies and available
experimental information.
II. METHODOLOGY AND MODELS
Water oxidation is a four-electron semi-reaction leading to the formation of molecular oxygen. While a direct
coupling of two oxygen adsorbates could in principle be a
viable mechanism for the key O–O bond formation step, calculations show that this route has a prohibitively high activation energy.17 A more widely accepted mechanism is on the
other hand a nucleophilic attack of a solvent water molecule
on an oxygen adsorbate, leading to the formation of a hydroperoxo group HOO∗ . As previous studies in this field,17–22
we hence assume the water oxidation mechanism to consists
in the following series of proton-coupled electron transfer
(PCET) steps:
A
→
2H2 O + ()∗ −
B
−
→
HO∗ + H2 O + H+ + e−
O∗ + H2 O + 2(H+ + e− )
−
→
C
HOO∗ + 3(H+ + e− )
D
O2 + 4(H+ + e− ),
−
→
(1)
where ()∗ represents an under-coordinated surface Fe ion, i.e.,
an active surface site, O∗ is an oxygen atom adsorbed at an
active surface site, and A, B, C, D label the reaction steps. C
represents the nucleophilic attack mentioned above. We note
that the step ordering can be different from surface to surface,
as shown below. To calculate the free energy differences between the intermediates in this reaction, we adopt the method
introduced by Nørskov and co-workers.18 The SHE potential,
where the equilibrium 1/2 H2 H+ + e− at p(H2 ) = 1 bar
and T = 298 K is established, is set to be the reference potential, hence has by definition an electrode potential U = 0. For
a PCET, the chemical potentials of electrons and protons do
not need to be known separately, and using the SHE as reference their sum can be taken to be equal to the chemical potential of gas phase hydrogen, which can be easily computed. At
standard conditions (Ub = 0, pH = 0, p = 1 bar, T = 298 K),
the reaction energy free energy of HA∗ → A + H+ + e− can
therefore be calculated as that of HA∗ → A + 1/2H2 . The effect of the external bias Ub (measured against the SHE) is
to modify the chemical potential of the electrons by −eUb ,
while the effect of pH is to modify the chemical potential of
the protons by −kB T ln (10)pH. Accordingly, the reaction free
energy of a PCET step is computed according to
G(Ub , pH) = E + (ZPE − T S)
−eUb − kB T ln(10)pH,
(2)
where the reaction energy E, the zero point energy change
ZPE, and the entropy change S are calculated using DFT.
In this work, we consider only pH = 0. The surrounding water
molecules and the electrolyte can interact with these intermediates, still we assume that such interactions are the same in
all the intermediates, and the relative stability between them
is not affected.
To account for the effect of solar illumination, we model
the system assuming the driving force for the oxidation is provided by the holes at the valence band maximum of hematite.
Using the experimental evidence that the conduction band of
hematite is at about 0.2 V with respect to NHE and the band
gap is 2.1 eV, the photogenerated holes provide at effective
bias UVB of 2.3 V and pH = 0.1, 5
To calculate the reaction energy E, we employ
first-principles calculations using spin-polarized plane-wave
density functional theory as implemented in the Quantum ESPRESSO package,24 within the framework of
GGA(PBE)+U formalism.25–27 The effective Coulomb repulsion parameter for hematite is usually chosen at
4.0–4.3 eV,28, 29 in our calculations U was set to 4.2 eV. Indeed, this value leads to an energy gap of about 2.0 eV, in
good agreement with experiments. The interactions between
the electrons and ions were represented with ultrasoft pseudopotentials. We used a kinetic energy cutoff of 40 Ry for the
wavefunction and 320 Ry for the charge density. The force
convergence threshold was set at 10−4 eV/Å for structural
optimizations.
We first calculated the bulk structural parameters
considering the 30-atom hexagonal unit cell containing
six Fe2 O3 units with the antiferromagnetic ordering (a
= 5.07 Å, c = 13.90 Å). The surface calculations were performed on a symmetric slab geometry, as shown in Fig. 1. We
considered the 1 × 1 surface unit cell and six terminations
of the hematite surface, which are identified as Fe − Fe −
O3 − (this layer ordering is called S1 ), O1 − Fe − Fe− (S2 ),
O2 − Fe − Fe− (S3 ), O3 − Fe − Fe− (S4 ), Fe − O3 − Fe−
(S5 ), and O − Fe − O3 − (S6 ). In geometry optimizations, all
atoms were allowed to relax. A vacuum layer of 24 Å is added
between slabs and their periodic images to ensure negligible
coupling among them. A 2 × 2 × 1 k-point grid is chosen to
sample the Brillouin zone in the self-consistent calculations.
To compute the ZPE and the entropic term TS for relevant reaction intermediates, we took (average) data from
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FIG. 1. (a) Top view of 1 × 1 surface unit cell of the stoichiometric hematite (0001) surface: O in red and Fe in pink; letters A, B, C indicate iron atoms on and
right under the surface with decreasing z-coordinate. ((b)–(g)) The symmetrical slab model of different terminations. Atoms are shown in their bulk positions,
ferryl groups in (g) are initialized by placing oxygen atoms right above the outermost iron atoms.
Ref. 21. In that work, for each intermediate these quantities were found to change only slightly from termination to
termination. The data used in the present work, presented in
Table I, are very close to the corresponding results reported
by Liao et al.22 We also noticed that the ZPE and the entropic
contributions to the free energy of O∗ , HO∗ , HOO∗ do not
change considerably from surface to surface of different metal
oxides. Finally, the energy of O2 is determined using that of
H2 and H2 O, and data in Table I to avoid inaccurate energy
calculations of this molecule.20
III. SURFACE STABILITY
In this section, we will investigate the coordination of unsaturated iron atoms by water. Owing to the very low dissociation energy barriers of water on hematite,23 the substrates
under study can easily be terminated with O atoms or/and OH
groups upon water contact. Surface iron atoms at S1,5 and
S2,3,6 are not fully coordinated, therefore dissociated water
can bind to them. Water can simply dissociate into H∗ and
HO∗ , or an electrochemical step can take place, leading to
HO∗ and the release of an electron and a proton, or to O∗ and
the release of two electrons and two protons. Considering that
up to three water molecules can dissociate on the unit cell we
are considering, there is clearly a wide range of possible final surface structures, whose relative stability depends on the
applied bias. We explicitly account for all possible dissociation patterns compatible with the initial surface termination
and compute their reaction free energy. We then confine ourselves to the case Ub ≥ UVB = 2.3 V and establish, for each
surface termination, which structure is the most stable. Since
each termination has a different surface energy, in Secs. III A
and III B we will compare the surface free energy of each
TABLE I. Zero point energy and entropic contributions to the free energy,
data taken from Ref. 21.
Intermediate
H2 O
H2
O2
HO∗
HOO∗
O∗
ZPE (eV)
TS (eV)
ZPE-TS (eV)
0.58
0.33
0.10
0.37
0.44
0.07
0.67
0.41
0.64
0.03
0.06
0.02
− 0.09
− 0.07
− 0.54
0.34
0.38
0.05
of these structures to establish the overall most stable surface
structure under the conditions of interest.
A. Fe–Fe–O3 –
We first consider the S1 termination of hematite. The outermost iron atoms of S1 (B and C atoms in Fig. 1) can be
bridged by O atoms and/or OH groups. Given the fact that
each (0001) plane contains at most 3 O atoms per unit cell, at
most 3 water molecules can be dissociated on a 1×1 surface
unit cell of Fe2 O3 (0001). The possible reactions leading to
the adsorption, dissociation, and/or oxidation of water taking
place on this termination can be written as
nm
S1 : S1 + 3H2 O ↔ S1 + nO∗ + mHO∗
Snm
1
+(3 − n − m)H2 O + (2n + m)(H+ + e− ).
(3)
nm
S1
Here, the notation
implies the reaction occurs on the termination S1 , there are n O∗ atoms and m HO∗ groups in the
outermost layer of the resulting surface Snm
1 , with 0 ≤ n, m
≤ 3, and 1 ≤ n + m ≤ 3. The reaction free energy, accordingly, is
GSnm
= ESnm
+ (ZPE − T S)Snm
1
1
1
−(2n + m)eUb .
(4)
Fig. 2(a) shows the dependence of most negative reaction
free energies on Ub , each case of 1, 2,. . . ,6 protons transferred
to the electrolyte. Clearly, surfaces terminated with more O
atoms and less OH groups (i.e., more electrons transferred to
the electrode) become more stable at high applied bias, due
30
to the −eUb term. For Ub equal and larger than UVB , the S1
process has the most negative (free) reaction energy. This scenario is similar to what has been found for RuO2 (110): also in
that case for high enough values of Ub (> 1.4 V) the totally
O∗ -covered surface becomes the most stable.
B. O1 –Fe–Fe–
The S2 can be viewed as S1 covered with one oxygen
atom in each surface unit cell, so in the rest of this subsection
S1 + O∗ implies S2 . This O∗ site can be hydrogenated, forming one HO∗ site. In this case, there are at most two molecules
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C. Surface free energy
S01
1
-3
Having established, in Secs. III A and III B, the most
stable combination of O∗ and HO∗ groups present at the surface of each termination of Fe2 O3 under solar illumination,
we now compare the various terminations Snm
k (k = 1, 2, . . . ,
6) in an effort to establish the overall lowest surface energy
structure of hematite (0001).
The surface free energy is defined as
1
ni μi ,
(7)
γ =
G−
A
i
S02
1
-6
-9
S21
1
S30
1
(a)
S03
1
S12
1
S02
2
-2
S03
2
S21
2
-4
-6
S12
2
S30
2
(b)
S12
3
ΔGS (eV)
0
-1.5
-3
where G is the free energy of our system (the right hand side
of, for instance, Eq. (3)) and μi (ni ) is the chemical potential
(number of atoms) of type i, and A is the total surface area
(which counts twice in our slab model). The free energy of
Sknm is
S21
3
S30
3
(c)
1.5
S10
5
0
= ESnm
+ (ZPE − T S)Snm
,
GSnm
k
k
k
S21
5
S11
5
-1.5
where ESknm is the energy from PBE+U calculations, ZPE and
TS are taken from the surface region of the slab (O∗ , HO∗ ), we
assume that those of the bulk region (the middle of the slabs)
are the same for all the surfaces and do not take into account
this contribution since it does not change the relative stability
among surfaces.
Given the fact that different terminations have a different
number of Fe and O atoms, we need to define the chemical
potential of these species too. Under electrochemical conditions the oxygen and hydrogen chemical potentials are bias
dependent30
S01
5
S30
5
S12
5
(d)
2
S01
6
0
S12
6
S21
6
S30
6
(e)
-2
1.6
1.8
2
2.2
2.4
2.6
2.8
3
Ub (V)
FIG. 2. ((a)–(e)) The relative stability of various water dissociation patterns
on each surface termination against the applied bias, notation Snm
k means
there are n O∗ atoms and m HO∗ groups in the outermost layer of covered
surface k. The dotted vertical line indicates Ub = UVB .
involved in the reaction
nm
μO = GH2 O − GH2 + 2eU,
(9)
2μH = GH2 − 2eU,
(10)
where GX = EX + (ZPE − TS)X (X = H2 O, H2 ). Assuming
Fe and O species to be in thermodynamic equilibrium with
the oxide surface, these two quantities are related through
1
(μFe2 O3 − 3μO )
2
1
= (eFe2 O3 − 3GH2 O + 3GH2 − 6eU ),
(11)
2
where the chemical potential of the bulk μFe2 O3 is approximated as the energy per Fe2 O3 formula unit, eFe2 O3 .
Combining Eqs. (7) and (9)–(11), the surface free energy
of Sknm reads
μFe =
S2 : S1 + O∗ + 2H2 O ↔ S1 + nO∗ + mHO∗
Snm
2
+(3 − n − m)H2 O + (2n + m − 2)(H+ + e− ).
(5)
In this case, the reaction free energy is
GSnm
= ESnm
+ (ZPE − T S)Snm
2
2
2
−(2n + m − 2)eUb ,
(8)
(6)
where the non-negative integer numbers n, m satisfy 2 ≤ n
+ m ≤ 3. Also in this case, the fully oxidized S30
2 structure, associated with 4 protons transferred to the electrolyte
and 4 electrons transferred to the electrode, corresponding to
the most negative reaction energy with Ub larger than UVB
(Fig. 2(b)).
For the cases of S3 , S5 , and S6 , reaction equations and
reaction free energy equations are provided in the Appendix.
It also appears that S30
3,5,6 surfaces are the most stable ones
where Ub > UVB .
1
[GSnm
k
2A
1
− nFe (eFe2 O3 − 3GH2 O + 3GH2 ) − nO (GH2 O − GH2 )
2
1
−nH GH2 + (3nFe − 2nO + nH )eU ],
(12)
2
where nFe , nO , and nH are, respectively, the numbers of Fe, O,
and H atoms in Snm
k .
For each termination Si , we now consider the most favorable water dissociation pattern determined in Secs. III A and
30
30
30
30
III B, namely, S30
1 , S2 , S3 , S5 , and S6 . We also examine
S4 , which has not been investigated in this work so far. By
γSnm
=
k
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γ(eV/Å2 )
0.2
PCET steps leading to water oxidation is the following:
S30
5
S21
5
S20
5
S03
5
S30
1
0.1
3O∗ + 2H2 O
C1
2O∗ + HOO∗ + H2 O + (H+ + e− )
−
→
D1
−→ 2O∗ + ()∗ + O2 + H2 O + 2(H+ + e− )
0
A1
2O∗ + HO∗ + O2 + 3(H+ + e− )
−
→
B1
3O∗ + O2 + 4(H+ + e− ),
−
→
-0.1
-0.2
1.6
1.8
2
2.2
2.4
Ub (V)
2.6
2.8
3
FIG. 3. Surface free energies against the applied bias of most negative (3nFe
∗
∗
− 2nO ) + nH surfaces, notation Snm
k means there are n O atoms and m HO
groups in the outermost layer of covered surface k. The dotted vertical line
indicates Ub = UVB .
30
30
30
definition, S30
1 , S2 , S3 , and S4 are identical, and so are S5
30
and S6 . Fig. 3 shows the dependence of surface free energies
of these structures on applied bias. The vertical bar at 2.3 V
indicates the bias UVB provided by photogenerated holes in
hematite, as discussed in Sec. II. At these conditions, S30
5 is
the most stable surface structure, closely followed by S30
1 .
This can be rationalized by taking a closer look at the expression for surface free energy γ in Eq. (11): the coefficient of
the bias dependent term is (3nFe − 2nO + nH ), which is minimized in S30
5 , where it has a value of −6. For large enough
biases, this structure is therefore bound to become the most
favorable among those considered in this work. As shown in
Fig. 3, this happens at a bias just below UVB .
These results highlight the importance of taking into account the bias, i.e., the precise photoelectrochemical conditions: here we show, in agreement with Ref. 21, that under illumination the stable phases are hydrogen free. On
the contrary, calculations at zero bias predict a hydroxylated
surface.12, 21, 23, 31, 32 In fact, to the best of our knowledge all
experimental studies investigating in detail the hydroxylation
state of the surface are conducted in contact with water vapour
and not in liquid water.12, 14, 33 While in all these cases a hydroxylated surface was found, our calculations imply that the
surface would lose protons when put in liquid water under illumination. Proton release is not an uncommon process. In
Ref. 34, it was noted that protons may be easily released by
the (0001) surface of hematite upon change of pH. Experiments on hematite in liquid water under controlled conditions
of illumination and bias would be necessary to test our calculations.
The S30
5 structure, therefore, will be our starting point in
Sec. IV for a mechanistic study, followed by a comparison
with the S30
1 , the second most favorable structure, that has also
been the subject of the work by Hellman and Pala.21
IV. PHOTO-OXIDATION OF WATER
The S30
5 structure, identified in Sec. III as the most favorable under photo-illumination, has no under-coordinated Fe
sites, but rather is fully oxygen terminated. A possible set of
(13)
where in step C1 , the hydroperoxo intermediate HOO∗ is
formed by the combination of an available O∗ site and a OH
group. In our geometry optimizations, however, HOO∗ appears to be highly unstable. We considered several starting
geometries for the (2O∗ + HOO∗ ) complex, but upon optimizing the ionic positions this structure relaxed either into
(HOO∗ + O2 ) or (O∗ + HO∗ + O2 ). On S30
5 , therefore, the
presence of an hydroperoxo drives an atomic rearrangement
leading to the spontaneous formation of molecular oxygen,
without any kinetic barrier. Moreover, we also found that the
3O∗ structure can relax to O∗ + O2 with a negligible barrier
and an energy gain of 3.72 eV. This suggests that our initial
structure S30
5 contains an unfavorable structural motif, namely,
three O∗ on an Fe adatom. In light of these observations, we
can consider alternative water oxidation mechanisms on S5 ,
where O2 is formed through a direct coupling of two neighboring oxygens adsorbed on the surface, rather than through
a hydroperoxo
O∗ + 2()∗ + 2H2 O
C2
−
→ O∗ + HO∗ + ()∗ + H2 O + (H+ + e− )
D2
−→ 2O∗ + ()∗ + H2 O + 2(H+ + e− )
−
→
A2
2O∗ + HO∗ + 3(H+ + e− )
B2
O∗ + O2 + 4(H+ + e− ),
−
→
(14)
or
O∗ + 2()∗ + 2H2 O
C3
−
→ O∗ + HO∗ + ()∗ + H2 O + (H+ + e− )
D3
−→
O∗ + 2HO∗ + 2(H+ + e− )
−
→
A3
2O∗ + HO∗ + 3(H+ + e− )
B3
O∗ + O2 + 4(H+ + e− ).
−
→
(15)
∗
In steps C2,3 , a OH group binds to an empty () site, a
proton is transferred to the electrolyte. The difference between these two mechanisms is just in the intermediates
formed in step D: in D2 a HO∗ group is oxidized to O∗ resulting in 2O∗ on the surface, while in D3 a solvent water
molecule is oxidized to HO∗ , resulting in two HO∗ on the
surface.
Both sets of reactions listed above yield essentially identical energetics, as shown in Fig. 4 (top panel). Step C2,3 , leading to the formation of O∗ + HO∗ adsorbates, corresponds to
the highest reaction energy of the whole process, 2.45 eV.
An applied applied bias of UVB = 2.3 V is therefore not
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O∗ + 2HO∗
A2,3
(H+ + e− )
2O∗ + HO∗
Ub = 0.0 (V)
ΔG(eV)
6
D2,3
4
B2,3
2
Ub = 1.23 (V)
0
Ub = 2.3 (V)
Ub = 2.45 (V)
-2
-4
+H2 O
O2 + (H+ + e− )
(H+ + e− )
2O∗ +∗
C2,3D2,3 A2,3 B2,3
(H+ + e− ) C2,3
+
O∗ + 2∗
A1
+H2 O
O2 + (H+ + e− )
+H2 O
O∗ +∗
(H+ + e− )
∗
4
ΔG(eV)
D1
Ub = 0.0 (V)
HO∗
2
Ub = 1.23 (V)
0
-2
Ub = 2.3 (V)
-4
C1 D1
B1
(H+ + e− )
OH∗
there are available O∗ sites on S30
1 and no undercoordinated Fe
sites, in the first step (C), a water molecule attacks an O∗ site
resulting in a hydroperoxo HOO∗ intermediate. The reaction
free energy of this step is 1.56 eV. The second step (D) leads
to the release of an oxygen molecule, creating an empty site
()∗ . The free energy change of this step is just 0.21 eV. Next,
in step A a second water is oxidized, with a HO∗ group filling
up the ()∗ site, with an 1.11 eV cost. Finally, the hydroxo intermediate is converted to O∗ through the fourth PCET step,
completing the 4-electron reaction. The free energy cost of
the last step (B) is 2.07 eV, making this the most demanding
step of the catalytic cycle promoted by S30
1 . The redox potential generated by photogenerated, UVB = 2.3 V, is hence
enough to make all reaction steps exothermic, i.e., this water
oxidation cycle can proceed under photo-illumination conditions. The energetics and the geometry of the intermediates
for this reaction cycle are shown in Fig. 4 (bottom panel). The
theoretical overpotential for this cycle is therefore 2.07−1.23
= 0.84 V.
Note that the experimental overpotential of 0.5–0.6 V
has been measured at pH = 13.6,1, 35 while our calculations
are performed at pH = 0. On the one hand, however, the
valance band position of hematite is pH dependent. On the
other hand, the reaction free energy in each step, assumedly,
has the same pH dependence. The experimental overpotential
at pH = 0 is thus about 0.6 V, with which our calculated one
is in agreement. Our result is also in good agreement with the
0.77 V overpotential obtained by Liao et al.,22 who explicitly
accounted for the effect of solvent water molecules using a
single water overlayer.
A1 B1
V. DISCUSSION
(H+
HOO∗
+
e− )
C1
+H2 O
O∗
FIG. 4. Reaction intermediates and reaction free energy diagrams in the case
30
∗
∗
of S30
5 (top, black bars imply intermediate O + HO ) and S1 (bottom).
sufficient to make every step downhill in energy, and the
overall process on this surface structure would have a 2.45–
1.23 = 1.22 V theoretical overpotential at pH = 0. Notice
how the last step in Fig. 4 (top panel), even at zero bias,
is highly favorable. Consistently with the observations made
above, this shows that rather than packing three ligands on
a single Fe adatom, the system gains energy by releasing
molecular oxygen and reducing the number of ligands on
Fe. The results of Sec. III, showing that within the set of
structures considered S30
5 was the most favorable when a bias
UV B is applied, suggested a starting point for the water oxidation cycle that proved to be unstable towards O2 release.
We therefore conclude that S30
5 is unlikely to be a structure
visited by the system under photo-illumination conditions,
and that alternative paths on S5 lead to prohibitively high
overpotentials.
We turn next to S30
1 as the starting surface for the oxidation process, since our calculations predict this to be the second most favorable surface structure at a bias equal to UVB .
We consider the four-step process described by Eq. (2). Since
Of the six terminations S1−6 , the single iron terminated
S5 appears to be the most stable one in a wide range of
oxygen chemical potentials, close to the upper limit. Upon
water adsorption and dissociation, this surface can easily be
hydrogenated and/or hydroxylated.23 Under the photoelectrochemical conditions, we found that all the surface terminations are terminated with oxygen. The high redox potential for the photogenerated holes strongly destabilize the
adsorbed hydrogen atoms at the surface, transferring them to
the electrolyte.
Under the conditions we investigated in this work, S30
1
and S30
5 are the most stable terminations. This is in agreement with the results by Hellman and Pala,21 who concluded,
however, that a UVB of 2.3 V is not sufficient to make every reaction step on S30
1 (or S4 ) downhill in energy. Hellman and Pala21 found that a minimal UVB of 3.0 V is required, while our calculations show that the most demanding step has a free energy cost of 2.07 eV. We believe that
this discrepancy is due to the different choice of electronic
structure approach used: DFT-GGA by Hellmann and Pala,21
DFT+U in our case. It is well known that the Hubbard term U
has a strong effect on the energy differences associated with
changes of oxidation states in transition metal elements.36 A
relevant example, in this context, is the comparison between
DFT-GGA and DFT+U for water oxidation on cobalt oxide
surfaces: Nørskov and co-workers37 showed that quantitative
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064703-7
Nguyen et al.
agreement with experiments can only be obtained by the latter
method, with a value of U of 3.52 eV. In the case of hematite,
earlier works show that a good description of the electronic
structure30 and energetics36 require a Hubbard term U of
around 4 eV.
Another important problem we can discuss on the basis
of our calculations is what happens to a hydrogenated surface
when light is turned on. This question is highly relevant
because hydrogenated terminations were observed in the
dark.21 According to our calculations for photoelectrochemical conditions, upon irradiation, hydrogen is transferred to the
electrolyte, making the electrode more oxygen terminated.
Starting from the hydrogenated terminations of Ref. 21, this
process will lead to oxygen-terminated configurations different from the stable S30
1 . Therefore, it is possible that further
reactions will take place in order for the surface to form
the stable termination. For example, for starting structures
ij
ij
of the X − Fe − O3 − Fe − Fe− kind (S5 , S6 ) where X
indicates O atoms or/and OH groups, a possible scenario is
that the (X − Fe) complex will be removed, thereby forming
the stable termination and setting up the steady state of the
electrode under illumination, with 3 oxygen atoms binding to
double iron sites, S30
1 (or O3 − S1 ).
Finally, we comment on effects on the overpotential of
water overlayers, which are not considered in our calculations. The interaction of water overlayers with fully oxygenterminated surfaces is mostly hydrogen bonding. Moreover,
the number of such hydrogen bonds in each unit cell can be
assumed the same. To a first approximation, the overall effect of the presence of water layer would be similar for all
the intermediates, hence their relative energies would result
in minor differences compared to the vacuum case we studied in this work. In agreement with these considerations, Liao
et al.22 have shown that introducing a water monolayer only
slightly changes the overpotential (0.06 V).
VI. SUMMARY
We have studied the photo-oxidation of water on the
(0001) facet of hematite considering five ideal and one ferryl surface terminations. Upon water contact, these terminations can easily be covered with O atoms and/or OH groups.
Under photo-illumination conditions, we have shown that the
water oxidation reaction takes place on a full oxygen covered
surface, in agreement with what found also on other transition metal surfaces.17 The reaction proceeds with a theoretical overpotential of around 0.8 V at pH = 0, with the energetically most demanding step being the oxidation of a Fe–OH
group to Fe–O. A comparison of our DFT+U results with earlier DFT-GGA simulations enabled us to highlight the importance of properly accounting for electron correlation effects
in reactions involving changes of oxidation states in transition
metals.
J. Chem. Phys. 140, 064703 (2014)
APPENDIX: WATER ON S3 , S5 , AND S6
In this appendix, reaction equations and reaction free
energy equations of water on S3 (O2 − Fe − Fe−), S5 (Fe −
O3 Fe−), and S6 (Fe − O3 Fe−) are provided.
1. O2 –Fe–Fe–
Similar to the case of S2 , S3 can be viewed as S1 covered with two oxygen atoms, S1 + 2O∗ . This termination, as
mentioned above, can be created by removing one of the outermost oxygen atoms (in each unit cell) of the fully oxygencovered termination S4 , i.e., creating a “vacancy” and leaving
both iron atoms B and C incompletely coordinated. The dissociation of one water molecule can take place at this active
“vacancy” site. It turns out that only three reactions, where a
single water molecule is involved, are to be considered
nm
S3 : S1 + 2O∗ + H2 O ↔ S1 + nO∗ + mHO∗
Snm
3
+(2 − m)(H+ + e− ),
(A1)
where 0 ≤ m ≤ 2 and n + m = 3. The reaction free energy is
given by
GSnm
= ESnm
+ (ZPE − T S)Snm
3
3
3
−(2 − m)eUb .
(A2)
In this case, the most negative reaction energy is in the
30
S3 process (Fig. 2(c)).
2. Fe–O3 –Fe–
In this termination, an iron atom (A) is present on the top
layer of S5 in each surface unit cell, hence at most 3 water
molecules are dissociated
nm
S5 : S5 + 3H2 O ↔ S5 + nO∗ + mHO∗
Snm
5
+(3 − n − m)H2 O + (2n + m)(H+ + e− ), (A3)
where the two non-negative integer numbers n, m satisfy 1
≤ n + m ≤ 3. This shares the same reaction free energy equation with S1 ,
GSnm
= ESnm
+ (ZPE − T S)Snm
5
5
5
−(2n + m)eUb .
(A4)
Fig. 2(d) shows that S30
5 is the most stable structure where
Ub > UVB .
ACKNOWLEDGMENTS
We acknowledge the CINECA Award H2OSPLIT HP10B6BMAA, 2013, for the availability of high performance computing resources and support.
3. O–Fe–O3 –
Finally, we considered the ferryl termination, S6 , which
can be written as S5 + O∗ . We consider the following
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064703-8
Nguyen et al.
J. Chem. Phys. 140, 064703 (2014)
15 C.
reactions:
nm
S6
∗
∗
∗
: S5 + O + 2H2 O ↔ S5 + nO + mHO
Snm
6
+(3 − n − m)H2 O + (2n + m − 2)(H+ + e− ),
(A5)
where 2 ≤ n + m ≤ 3. The reaction free energy is
GSnm
= ESnm
+ (ZPE − T S)Snm
6
6
6
−(2n + m − 2)eUb .
(A6)
The S30
6 termination is determined to be the most stable
one for Ub > UVB (Fig. 2(e)).
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