вход по аккаунту



код для вставкиСкачать
Journal of Physics: Condensed Matter
Related content
Ab initio simulations of water splitting on hematite
To cite this article: Nicola Seriani 2017 J. Phys.: Condens. Matter 29 463002
View the article online for updates and enhancements.
- Polarity of oxide surfaces and
Jacek Goniakowski, Fabio Finocchi and
Claudine Noguera
- Colloidal nanocrystals for
photoelectrochemical and photocatalytic
water splitting
Chethana Gadiyar, Anna Loiudice and
Raffaella Buonsanti
- Recent developments in complex metal
oxide photoelectrodes
Fatwa F Abdi and Sean P Berglund
This content was downloaded from IP address on 27/10/2017 at 08:33
Journal of Physics: Condensed Matter
J. Phys.: Condens. Matter 29 (2017) 463002 (11pp)
Topical Review
Ab initio simulations of water splitting
on hematite
Nicola Seriani
The Abdus Salam ICTP, Strada Costiera 11, 34151 Trieste, Italy
Received 1 December 2016, revised 27 July 2017
Accepted for publication 8 August 2017
Published 20 October 2017
In recent years, hematite has attracted great interest as a photocatalyst for water splitting, but
many questions remain unanswered about the mechanisms and the main limiting factors. For
this reason, density functional theory has been used to understand the optical, electronic and
chemical properties of this material at an atomistic level. Bulk doping can be used to reduce
the band gap, and to increase photoabsorption and charge mobility. Charge transport takes
place through adiabatic polaron hopping. The stable (0 0 0 1) surface has a stoichiometric
termination when exposed to oxygen, it becomes hydroxylated in water, and it has an oxygenrich termination under illumination in a photoelectrochemical setup. On the oxygen-rich
termination, surface states are present that might act as recombination centres for electrons
and holes. On the contrary, on the hydroxylated termination surface states appear only on
reaction intermediates. The intrinsic surface states disappear in the presence of an overlayer of
gallium oxide. The reaction of water oxidation is assumed to proceed by four proton-coupled
electron transfers and it is shown to involve a nucleophilic attack with the formation of an
OOH group. Calculated overpotentials are in the range of 0.5–0.6 V. Open questions and future
research directions are briefly discussed.
Keywords: photocatalysis, hematite, ab initio simulations, density functional theory,
water splitting
(Some figures may appear in colour only in the online journal)
1. Introduction
fuels could play an important role in alleviating the problem of
storing electricity. Moreover, they could be readily used in the
current transportation system. Given the interest in developing processes for the mass production of fuels, it is desirable
to employ the most widely available reactants, and to attain
products with the highest possible energy density. Therefore,
it is considered that the main goal in the field is to produce
hydrocarbons from water and carbon dioxide. For example, if
one considers methane as a product:
The sun irradiates a large amount of energy onto the earth,
and it would be wise to learn to harvest, store and employ this
energy in efficient ways. While photovoltaic devices for the
production of electricity are widespread nowadays and they
are an essential part of electricity production, other applications such as the direct use of solar energy, to perform chemical reactions and to produce fuels, lag behind [1]. Although
the potential of solar energy for this purpose was already recognized a century ago [2], this field did not receive sufficient
attention for a long period of time due to the wide availability
of fossil fuels throughout the twentieth century. Still, solar
2H2 O + CO2 → CH4 + 2O2 .
For this kind of reaction, so far only photoelectrochemical approaches have been successful [3], i.e. through an
© 2017 IOP Publishing Ltd Printed in the UK
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
Figure 1. Scheme of a photoelectrochemical device using hematite
as photoanode and platinum as cathode. Light is absorbed by
hematite and used to oxidize water to oxygen. The resulting
protons are transferred through the electrolyte to the cathode, where
electrons also arrive from the outer circuit, where an external bias
V is applied. At the cathode, protons are reduced to molecular
appropriate combination of photoexcitations and electric
fields. Zero-bias activity is substantial only in the presence of
sacrificial agents [4] that effectively modify the reaction under
study. In this process, water is oxidized to produce gaseous
oxygen, and the resulting protons reduce CO2. In a photoelectrochemical cell, water splitting and oxygen evolution take
place at the photoanode, while CO2 reduction, or hydrogen
evolution, takes place at the cathode (figure 1). Since both
water splitting [5, 6] and CO2 reduction are challenging reactions, it is useful to study them separately. The current review
deals exclusively with the water splitting reaction on a promising material as a photoanode, namely hematite (iron oxide,
α-Fe2O3). Hematite is one of the most interesting candidate
photocatalysts for the water splitting reaction [7, 8]. For the
purpose of this paper, the main reaction to be considered is
Figure 2. Scheme of a electrochemical interface between hematite
and the electrolyte at (a) flat band conditions and (b) in the presence
of band bending. VBM is the valence band maximum, CBM the
conduction band minimum. The dashed arrow indicates the electron
transfer to H+, suppressed by the unfavourable position of the
which is the subject of the present review, other interesting
candidates are BiVO4, ZnO, WO3, MoS2... [10, 11].
Hematite (α-Fe2O3, corundum crystal structure) is considered interesting for its abundance, lack of toxicity, stability under photoelectrochemical conditions, a gap of ∼2 eV
ensuring substantial photoabsorption down to the visible
range, and a favourable position of the edge of the valence
band. Drawbacks include low charge mobility in the bulk,
slow reaction kinetics at the interface, high electron–hole
recombination rates, and a high overpotential necessary to
trigger the water splitting. Substantial efforts are under way
to understand the origins of these limitations, and to modify
hematite to alleviate them. For example, the conduction band
minimum (CBM) lies 0.2 eV below the H2O/H2 redox level,
and transfer of electrons to reduce protons to H2(g) is never
spontaneous in these systems (figure 2(a)). This is one of the
reasons why the application of an external electric bias is a
necessary condition for the reaction to take place. In the presence of an interface with an electrolyte, this picture gets more
complex, because of surface charging effects [12, 13]. Ions
from the solution are adsorbed at the interface, and charge
from dopants reorganize in the solid, with the formation of a
space charge layer depleted of conduction band electrons. In
other words, at a hematite surface under these conditions the
electronic bands are bent upwards (figure 2(b)). This upward
bending is fundamental for our processes, because it drives
photogenerated holes in the bulk torwards the surface, where
they may become available for water oxidation reactions. The
band bending and the width of the space charge layer depend
on properties of the electrolyte, on intrinsic defects in hematite
and on bulk doping, which provide the conduction electrons
2H2 O + 4hν → 2H2 + O2 .
Under alcaline conditions, the electrodes exchange hydroxyl
ions (OH−) with the electrolyte, and the two half-reactions are
4OH− (aq) + 4h+ → 2H2 O + O2 ,
(oxygen evolution reaction, OER, at the photoaonde), and
2H2 O + 2e− → H2 + 2OH− (aq),
(hydrogen evolution reaction, HER, at the cathode). On the
other hand, under acidic conditions, protons or hydronium
ions are the main ions in the electrolyte, and the two halfreactions are
2H2 O + 4h+ → O2 + 4H+ (aq),
(oxygen evolution reaction, OER, at the photoaonde), and
2H+ + 2e− → H2 ,
(hydrogen evolution reaction, HER, at the cathode). Several
alternatives are being intensively investigated as possible
materials for the photoanode. Historically, the first material
to demonstrate sizable activity was titania [9]. Besides titania,
which is still the benchmark material in this field, and hematite
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
water splitting reaction takes place, and the mechanism of the
reaction; photoabsorption, its dependence on impurities, the
formation of excitons, their dissociation, and the dynamics of
This review article aims at providing the most comprehensive view of the research performed on hematite by ab initio
simulations, to clarify the current state of the art, to help
comparisons with experiments, and to underline the open
problems. This differentiates the present paper from excellent reviews published in the past, which either give a general
overview over several different materials [10, 31, 32], or are
more focused on methodological aspects [33]. Moreover, this
paper is made necessary by the high rate of new work appearing on the subject. The article is organized as follows: first,
the basic techniques will be presented, then the results will
be organized in three sections: photoabsorption and charge
dynamics in the bulk; surface structures and their stability
under realistic conditions; reaction mechanism, thermodynamics and kinetics.
in the first place. Values of the band bending can be 0.1–1 eV,
and the width of the space charge layer can be 1 nm to 100 nm
[14, 15]. The band bending can be changed by applying an
external electric bias. The band bending is responsible for two
important processes for the reaction: it drives holes towards
the surface, and makes them available for the reaction, and it
drives conduction electrons away from the surface, suppressing electron–hole recombination at the interface. In fact, the
current view on the reaction is the following: upon illumination, holes form and migrate to the surface. There, two different processes compete with each other: the desired process of
hole transfer to the reactants at the interface, and the recombination with conduction electrons. It turns out that hole transfer is extremely slow [16], and recombination dominates in
the absence of an external electric bias [17]. The latter further
lowers the conduction band in the bulk, increasing the band
bending, until recombination is suppressed to a level that photoholes become long lived, up to 3 s [17]. At this stage, hole
transfer to the reactants becomes sizable [18].
Several attempts have been undertaken to modify hematite
to increase the overall efficiency, with some success stories.
Among them, modification of hematite through doping has
been shown to be an effective way to increase photoabsorption, and to decrease the band gap. Usual dopants are titanium
[19], fluorine [4] and tin [20]. Work was also devoted to surface
modifications, with different strategies employed. One strategy is the addition of co-catalysts, like IrOx [21, 22] or cobalt
phosphate [23, 24], which are supposed to lower the barriers
for the reaction steps at the interface. Another is to modify the
electronic states and/or the electrostatics of the interface by
depositing overlayers, e.g. of Al2O3 [25], Ga2O3 [26], nickel
oxide [27] or TiO2 [28]. Even underlayers (i.e. layers deposited on the opposite side with respect to the interface with the
electrolyte) of such oxides seem to have a positive effect [29].
It is still debated what the effect of this modification is, but it
is possible that these deposited oxides create dipoles that drive
holes towards the surface, and further suppress recombination
[30]. Another possibility is that the overlayer makes surface
states (trapping holes at the surface) disappear. We are going
to comment on this hypothesis later.
Designing and implementing solutions to improve the
catalyst’s activity and efficiency must be based on a sound
understanding of the structure of the catalyst under reaction
conditions and of the elementary processes taking place on it.
Given the complexity of the system and processes, methods
able to investigate one aspect of the system at a time can be
extremely useful to divide the overall problem into smaller
pieces that can be characterized successfully before putting
all the elements together for a holistic understanding of water
splitting. In this context, first-principles atomistic simulations
based on density functional theory have proven extremely
useful for their ability to characterize simplified models of the
catalyst and of the interface with great spatio-temporal resolution. Simulations can contribute to the answers for several
questions: understanding the surface termination of hematite
in contact with water, under illumination and in presence of
an external electric bias; nature of the active site where the
2. Computational methods
This manuscript deals with first-principles simulations based
on density functional theory (DFT). These methods are not
going to be introduced here, the reader interested in learning
about the basics can find excellent reviews in the literature
[34–38]. For the purpose of this presentation, it is however
important to stress that the systems dealt with here are nontrivial from the point of view of DFT, mainly because of two
reasons: first, in iron ions the very localized 3d orbitals play a
fundamental role in determining chemical and physical properties, and these very localized orbitals are badly described by
local and semilocal exchange and correlation functionals, due
to their well known self-interaction error [39–43]. Second, the
material under study is embedded in a photoelectrochemical
cell, and describing the stability of surface phases and reaction intermediates implies a correct description of the effects
of illumination, electric bias, pH, and solvation on the free
energies. Often, these environmental conditions are taken into
account through simplified models, and it is not clear how general these approximations are. On the other hand, it has been
shown that, for a wide class of semiconductors, mostly oxides,
their capability for water splitting can be assessed from their
ionization potential and electron affinities only [44].
2.1. Density functional theory for the correct description
of the electronic states
The problem of correctly describing the electronic structure
of the system is particularly serious for the case of small
polarons formed by excess electrons and holes [45–48]. For
this reason, all calculations for this system are performed
by post-DFT methods, including either a Hubbard U correction (DFT + U method) [42, 49, 50], or some fraction of
exact exchange (hybrid functionals) [51, 52], even though the
atomic structure of the system is properly described even at
spin-polarized LDA or GGA level [53]. In hybrid functionals,
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
the exact exchange is applied to all orbitals in a unified framework, which seems to be a more systematic and general
approach, but the cost of hybrid functionals may be prohibitively large for these systems. On the contrary, in DFT + U
the Hubbard U is selectively applied only to a small number
of quasi-atomic orbitals chosen a priori, which seems to be a
more ad hoc approach to the problem, but makes it possible to
simulate these systems with a computational cost comparable
to that of semi-local functionals. For this reason, DFT + U is
by far the most used method, with the Hubbard U corrections
applied only to the 3d states of iron.
Rollmann et al investigated the dependence of bulk properties on the U parameter applied on the 3d states of iron, and
found a value of 4 eV to yield the best agreement with experiments in terms of band gap and magnetic moments [54]. Such
a value is also crucial to correctly describe the system as a
charge transfer insulator, with a O–2p–Fe–3d gap. Smaller
values instead yield a gap due to d–d transitions, as in Mott–
Hubbard insulators. In subsequent work, many papers indicate
a value of 4.3 eV as an optimal value to describe the ground
state of bulk hematite [48], while others propose 4.5 eV [55].
Instead, to obtain the right ordering of the tg and e orbitals in the conduction band, values of U larger than 6 eV or
exact-exchange fractions larger than 30% are necessary [56].
Although the Hubbard U correction is necessary for the electronic and magnetic properties, it does not improve noticeably
the vibrational properties of bulk hematite [57]. Regarding the
thermodynamics of surfaces, DFT + U increases the stability
of the iron termination with respect to semi-local DFT [58],
and the employment of a site-specific value of U at the surface improves the description of the thermodynamics of the
(0 0 0 1), correctly resulting in a metastable ferryl termination
Although the electronic properties of the ground state are
reasonably well described within DFT + U, the formation and
cohesive energies are better reproduced by hybrid functionals
[60]. A hybrid functional of HSE type [61, 62] with a fraction
of 12% of exact exchange reproduces the experimental gap
and correctly identifies hematite as a charge-transfer insulator [63]. The GW approximation [64–66] was tested on the
bulk, with the best results delivered by G0W0 with input from
DFT + U [67]. When starting from DFT + U with U = 4 eV
on the 3d states of iron, G0W0 delivers a band gap of 2.9 eV,
and selfconsistent versions of GW overestimate the gap by an
even larger amount [68].
Figure 3. Scheme of the usually assumed reaction cycle for water
oxidation, consisting of four proton-coupled electron transfers. In
the single-site version presented here, it foresees a nucleophilic
attack with the formation of an OOH intermediate.
(SHE) [12], which is defined as the electrode at which the
reaction of proton reduction is at equilibrium at standard conditions (pH_2 = 1 atm, pH = 0, room temperature)
G(H (aq)) + G(e ) = G(H2 (g)).
Since the free energy of the solvated proton is a property of
the proton in the solution, and the free energy of the hydrogen gas is a property of the gas itself, the statement of equation (7) applied to an electrode should mainly be understood
as a statement about the free energy of the electron, i.e. about
the Fermi level of the electrode and its alignment with the
relevant redox states. The standard hydrogen electrode is in
practice realized by a platinum electrode.
In calculations it is often assumed that the reaction proceeds through neutral intermediates only, i.e. each elementary
step consists of a proton-coupled electron transfer (PCET)
(figure 3). In this case, it is not necessary to determine the
chemical potentials of proton and electron separately, but one
can refer to the SHE directly using equation (7), as pioneered
by NØrskov and co-workers [69, 70]. The calculation of the
free energy of the hydrogen gas at standard conditions is then
straightforward and is analogous to standard ab initio thermodynamics [71–73]; the effect of the electric bias φ consists in
a shift of the free energy of the electron, according to
G(H (aq)) + G(e )(T, φ) = G(H2 (g)) − eφ.
This formalism makes it possible to incorporate the main
effects of an applied electric bias on the stability of surface
phases and intermediates at the cost of a single DFT calcul­
ation. O2 and H2O are at equilibrium at a bias of 1.23 V. Usually,
a higher bias is necessary to make all intermediate reaction
steps exothermic, and, in this context, the difference between
the minimal bias necessary to do so and the 1.23 V is termed
the overpotential. The effect of illumination is often treated as
an effective bias, because it creates a ­non-equilibrium situation where the chemical potentials of electrons and holes are
determined by their quasi-Fermi levels. In principle, at satur­
ation with respect to illumination intensity, the maximally
attainable value of their difference is equal to the band gap
2.2. Dealing with the photoelectrochemical conditions
Hematite is interesting as the photoanode in photoelectrochemical cells; many important processes take place at the
interface between the semiconductor and the electrolyte. It is
therefore crucial to determine which is the stable phase for
the surface, and the free energy differences between reaction intermediates at such a surface. To be able to do this, it
is crucial to establish the chemical potentials of the species
involved, i.e. electrons and ions, as a function of variables like
applied electric bias, pH, and temperature. In electrochemistry, the standard reference is the standard hydrogen electrode
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
[74], and often the effect of illumination is assumed to amount
to an effective bias equal to the band gap of the semiconductor
[70]. Although this approach is widely accepted, the photovoltage is unlikely to reach such high values in experiments
[25, 75, 76], due to low photoabsorption, slow kinetics and
recombination processes; the resulting experimental photovoltages are usually a fraction of the band gap. In hematite,
which has a band gap of 2.1 eV, usual photovoltages fall in the
range 0.6–1.0 V [25, 77].
Another important issue in the calculations of free energies
and of the band alignment between bands in solid state and
redox states of the reactant is the fact that the system contains
a liquid phase. While temperature effects have only a minor
effect on the solid phase at room temperature, calculating the
free energy of the whole system would in principle involve
appropriate sampling of the configurations of the liquid.
Methods to do this are firmly established [78], but they are
extremely demanding computationally. For this reason, there
is great interest in the development of good classical interatomic potentials for water and for oxides [79–81]. However, a
large number of ab initio studies are performed with implicit
solvent or without solvent at all. Some tests seem to validate
this approach [82], but this conclusion seems unlikely to hold
in general.
the visible. Catalyst modification through doping may exploit
different strategies: for example, aluminium substitution
does not induce dramatic changes of the electronic structure,
because Al3+ subsitution for Fe3+ does not induce any charge
imbalance, but it introduces strain that favours migration of
small polarons, resulting in an increase of the PEC activity
[88]. Hydrogen [86] and magnesium [89] doping have rather
modest effects. Deposited platinum at the surface leads to a
reduction of the band effective mass, and to the appearance
of mid-gap states [90]. The former should increase conductivity, while the latter might increase recombination. Platinum
also leads to a higher overpotential when deposited at the
surface [91]. The case of niobium is less clear: some experiments indicate an increase of the overpotential [92] while in
others an enchancement of the catalytic activity was observed
[93, 94]. Theory finds an increased overpotential upon Nb
doping [95], and relates this to the large charge donation (niobium is in the formal oxidation state of +5). This high oxidation state (and the multivalent nature of Nb) should favour
electron transfer from water, a crucial step in water oxidation.
In fact, theory and experiment agree that Nb has a beneficial
effect when introduced into the sample beyond the solubility limit, to produce a heterogeneous sample with a doped
part and an alloyed part, which favours charge separation and
could be used to increase hole energy at the interface with
water [96]. Copper doping raises both valence and conduction
band [97], enough to make direct hydrogen production possible in principle. Beside doped systems, also stoichiometric
mixed oxides FeMO3 (M = Sc, Ti, V, Cr, Cu, Cd or In) were
considered [98], leading to a reduction of the band gap or even
to a half-metallic behaviour.
3. Generation and dynamics of excitations in bulk
Bulk hematite has an optical band gap of 2.0–2.2 eV [67, 83],
which implies a substantial absorption in the visible. Still,
since the potential for water oxidation is 1.23 V versus SHE, in
principle it could be advantageous to reduce it further without
compromise on the activity. A second issue regards the fate of
the excitations, with exciton recombination and dissociation
being the first important processes, followed by hole diffusion towards the surface. Possible trapping of holes at surface
states and recombination involving surface holes will be discussed in the next section, devoted to the surface structure.
Photoabsorption has been studied in detail both exper­
imentally and theoretically. It is an indirect band gap semiconductor, which in principle is good to avoid recombination,
but the bands are quite flat, with an average effective mass ∼4
for the electrons and ∼1.5 for the holes [84].
After having clarified the behaviour of perfect hematite,
interest has turned towards defects and dopants. Hematite is
an n-type semiconductor; calculations confirm that oxygen
vacancies are the most stable defect in bulk hematite at room
conditions [85], and decrease the magnetic moment of iron
[86]. On the contrary, at temperatures above 1000 K, which
are commonly reached during synthesis of the material, there
is a competition between oxygen and iron defects, which
might become important if the material is quenched to room
temperature during synthesis, thus freezing in defects, and
leading to Fermi level pinning [87]. The effects of different
dopants on the electronic structure and on photoabsorption
have been under scrutiny. Cation doping, but also anion doping have shown to reduce the gap and to increase absorption in
3.1. Charge transport
The electronic bands are quite flat, with an average effective mass ∼4 for the electrons and ∼1.5 for the holes [84].
On the other hand, excess electrons and holes form small
polarons in hematite [99, 100], and there is agreement that
polaron hopping is the main conduction mechanism. Excess
electrons form small polarons localized on iron ions, which
are reduced from Fe3+ to Fe2+ . The associated signature is
a reduction of the magnetic moment. Employing DFT + U
(U = 4.3 eV) Adelstein et al [48] have calculated a mobility
of 0.009 S*cm2 s−1 for electron polarons in the basal plane at
room temperature, in fair agreement with cluster calculations
[101, 102] and with experiments [103, 104]. Parameters for
Marcus theory were obtained as well, and it was concluded
that the polaron transfer is adiabatic. Charge transport in the
bulk is characterized by strong anisotropy, with conductivity
due to polaron hopping being three orders of magnitude larger
in the basal plane with respect to the (0 0 0 1) direction [102].
This is confirmed by unrestricted Hartree–Fock calculations
[106]. Holes hop from one oxygen site to another, and the
activation energy for hole hopping is at least 0.1 eV higher
than that for electrons.
Doping plays also a role in increasing charge mobility. Silicon, germanium, zirconium, and tin are prefered as
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
a substitute for iron, and act as electron donors, leading to
the formation of an electron polaron on a nearby iron site
[107, 108]. Among them, germanium has the highest solubility [107]. Substitutional titanium acts as an electron donor,
and also increases the electron mobility [97, 109]. Titanium
doping increases the photocatalytic activity and the electron
carrier concentration; in [110], the presence of Ti4+ did not
lead to the formation of Fe2+ ions, but rather to delocalized conduction electrons. On the contrary, earlier studies
[111, 112] reported the formation of a Fe2+ in the immediate
vicinity, while Zn doping would lead to diffuse hole states.
Copper doping raises both valence and conduction band [97],
enough to make direct hydrogen production possible in principle. Liao et al proposed Co and Ni as effective dopants to
decrease the overpotential for water splitting [82]. Also tallium increases the electron carrier concentration, by providing
shallow donor levels [113]. Dopants with +2 oxidation states,
such as Mg, Ni, Cu, and Mn2+ trap holes on nearby oxygen
atoms. The multivalent nature of manganese, with the possible
formation of Mn3+ states, creates hole hopping paths with low
transition energy and higher mobility [106]. Beside changes
in mobility due to changes in the electronic structure, dopants
can also act indirectly by changing the lattice parameters. In
the already mentioned case of aluminium, the changes in the
band structure are negligible, but the resulting strain favours
migration of small polarons [88]. Also Ti, Cr, Mn, and Ni were
predicted to have the same effect [109]. Even without doping,
strain is an effective way to change the band gap and the positions of valence and conduction bands [114], although in the
case of ultrathin slabs the effects should be rather detrimental
for the photocatalytic activity [115].
Figure 4. Atomic structures of the most common terminations of
the (0 0 0 1) surface of hematite: (a) stoichiometric iron termination;
(b) hydroxylated termination; (c) O-rich termination. The small
balls are O atoms, the large balls are Fe atoms, the tiny blue balls
are H atoms.
temperature and humidity, and a surface phase diagram has
been calculated for this facet [118, 119], as well as for (0 1 1̄ 2)
[120]. Other common surfaces are (1 0 1̄ 4) and (1 1 2̄ 3) [121].
Calculated formation energies suggest that it should be possible to produce nanoribbons [122].
Investigations range from ultrahigh vacuum (UHV) conditions, to gaseous environment up to electrochemical conditions. Under UHV, the (0 0 0 1) surface displays two possible
terminations, one iron- and the other oxygen-terminated.
Depending on the preparation conditions, only one of them
may appear, but coexistence has been reported repeatedly
[123]. This is in line with DFT calculations, that show that
the stoichiometric, iron-terminated surface is the most stable
under UHV, with the oxygen termination being only few meV
Å higher in energy [124, 125] (figure 4). In fact, coexisting domains of O- and Fe- terminations have been shown to
be energetically more favourable than a single termination
[126], explaining why in many experiments the coexistence is
actually observed. In a wide range of pressures of oxygen, an
experimental surface phase diagram has been established for
(0 0 0 1), showing a sequence of oxygen-, ferryl- and oxygen
terminations at increasing O2 pressure [127]. Others predict
the Fe- termination to be stable in a wider range of chemical
potentials of oxygen [128]. Using GW calculations, the positions of the valence band maximum and the conduction band
minimum were calculated for stoichiometric (0 0 0 1) and (011̄
2) [129], incorrectly resulting in a conduction band favourable
for water reduction. The authors pointed out that hydroxylation of the surface and solvent effects might correct this result.
When water vapour is added, the surface becomes hydroxylated [130, 131]. The initial stages of surface hydroxylation
4. Structure of the surface under reaction
The hematite samples used in the photoelectrochemical
experiments have the appearance of a cauliflower in electron
micrographs, and consist of polycrystals with crystallite sizes
of tens to hundreds of nanometers [7]. Such small crystallite
sizes are crucial to produce good activity, because the diffusion length of holes in hematite amounts to tens of nanometers. The cauliflower shape is quite irregular, and this implies
that the sample exposes several inequivalent crystallographic
facets, and high densities of surface defects, such as edges,
steps, and adatoms. As a first important approximation, most
computational studies (and most surface science studies) focus
on the investigation of the most stable single-crystal surface,
namely of the (0 0 0 1) surface. Ferrer et al [116] calculated
that the surface energies are ordered as (1 0 1̄ 0) > (1 0 1̄ 1) >
(1 1 2̄ 0) > (0 0 0 1)/Fe > (011̄2) > (0 0 0 1)/OH, where (0 0 0 1)/
Fe is the iron termination and (0 0 0 1)/OH is the hydroxylated termination, and all other surfaces are stoichiometric. In
fact, some of the surface energies are so similar that small
differences in temperature and water pressure can induce considerable changes in the equilibrium shape of nanoparticles,
as calculated from Wulff construction [117]. The (1 0 1̄ 0)
surface is hydroxylated to different extents, in dependence of
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
into account an explicit solvent, let us consider the electronic
properties of the neutral surfaces in the next subsection.
have been investigated by DFT by Yin et al on perfect [132]
and defective surfaces [133]. In fact, water dissociation is
facile, with dissociation barriers below 0.3 eV, and negligible
in some cases, even in the absence of surface defects [125].
Still, oxygen vacancies enhance dissociative adsorption [128].
Hydroxylation starts at a relative humidity as low as 1 × 10−7%
[134] at room temperature, while adsorption of molecular
water starts at relative humidities above 2 × 10−5%. The
surface remains fully hydroxylated up to 900 K, above which
iron-terminated and hydrogenated phases are stable [135].
Adsorption of OH and its co-adsorption with Cl induce relaxation of the upper layers of the (0 0 0 1) surface by tenths of
Ångstrom [136].
Nguyen et al [124] performed DFT simulations with the
NØrskov method [69, 70], and found that including illumination in a photoelectrochemical environment results in
deproto­nation of the surface and the creation of an oxygenrich termination. It should also be stressed again that this
computational study takes only neutral surface phases into
account, and a full account of surface charging might modify
this picture. At the same time, a more detailed characterization of a single-crystal surface under reaction conditions is
highly desirable. The most complete study of possible terminations and of their stability under reaction conditions was
performed by Ulman et al [137]; their most stable phase contains a surface species of oxygen with a direct O–O bond,
very similar to a peroxo group. This is a variance from the
results by Yatom et al [138], which excluded the presence of
a peroxo species on the O-termination. It must be said that
the two proposed peroxo structures differ, and it seems likely
to me that the peroxo structure in [138] is simply a higherlying structure than that proposed in [137]. Using vibrational
spectroscopy, surface peroxo species have been observed to
form as intermediates during oxygen evolution on TiO2 [139]
and on cobalt oxide [140], while they were interpreted as trap
states on hematite [141]. On the other hand, Young et al had
proposed peroxo species to be reaction intermediates [143].
However, Ulman et al [137] also found that several terminations are very near in energy, which would make it hard to
determine their exact energy ordering by DFT, and would
make it easy for them to coexist at a real surface. For this reason, invest­igations continue also on the hydroxylated and the
stochiometric terminations.
The (1 1̄ 0 2) surface has also been investigated, in the
clean and in the hydrated case [144] and it is found that, at
room temper­ature, the hydroxylated termination is a metastable phase. Experimentally, it is still possible to produce
it by a careful preparation method [145]. Guo and Barnard
[120, 146] have calculated the phase diagrams of the (0 0 0 1),
(1 0 1 1), (1 0 1 4) and (0 1 1̄ 2) surfaces in the presence of water
vapour and of oxygen, and found that hydroxylation prevails
on all of them at room conditions.
It should be noted, however, that all the previous studies
considered neutral surfaces. The charging state of the surface
in principle depends on pH, applied electric bias and illumination conditions. In fact, the interaction of the surface with a
single molecule strongly depends on the presence of charges
at the surface [105]. However, before surveying studies taking
4.1. Surface states, hole trapping and surface modifications
The electronic structure of the surface plays a crucial role
in the photocatalytic process, as it determines the dynamics
of the reactive holes, which were produced by photoabsorption and exciton dissociation in the bulk. Experimentally, it
has been shown that charge dynamics at the surface is one of
the crucial processes determining the overall kinetics of the
water splitting reaction [147]. Kerisit and Rosso [142] simulated charge transfer in the bulk and at the surface, showing
charge transfer to be heavily dependent on the termination.
According to their calculations, terminal iron atoms could
act as electron traps at the surface. Le Formal et al employed
transient absorption spectroscopy, transient photocurrent
spectroscopy, and electrochemical impedance spectroscopy,
to characterize the electron–hole recombination at the interface, and found a time scale of 10 ms to 1 s for the process,
dependent on the applied electric bias, and they attribute it to
recombination of electrons from the conduction band of bulk
hematite with long-lived holes accumulated at the interface
[148] and argue that the main role of the applied bias is to
suppress such recombination by increasing the space charge
layer. Accumulation of holes at the surface has been shown
to take place until the reaction sets in, leading to a release
of the charges [149]. Using near-edge x-ray absorption fine
structure spectroscopy (NEXAFS), Braun et al have observed
the appearance of two distinct hole states at the surface [150].
The picture was made more precise by x-ray photoelectron
spectroscopy, suggesting that the surface contains Fe2+ ions
which oxidize to Fe3+ during anodization [151], leading to
the formation of a hole-doped film at the hematite surface.
Given the importance of hole accumulation at the interface,
great attention has been devoted to the investigation of surface
states. A surface state was identified in NEXAFS [152]. In
calculations on the (0 0 0 1) surface, a surface state lies 0.4 eV
above the top of the valence band in DFT + U and 2 eV above
the VBM in G0W0 [68]. According to Ulman et al [137], a
surface state is present on the stoichiometric termination and
on the O-termination stable under reaction conditions, but not
on the hydroxylated surface. These differences are crucial also
for the interpretation of the role of the surface states. Some
consider them to be electron–hole recombination centers
[153], responsible for sluggish charge transfer to the reactants
and for increased recombination. Others find evidence that
they could be a signature of reaction intermediates: the calcul­
ations by Yatom et al [138] suggest that the spectroscopically
observed surface state where holes are accumulated is related
to the formation of FeIV = O as a reaction intermediate. In
this interpretation the surface state would not be a trap and
a recombination center, but the spectroscopic signature of a
reaction intermediate.
Following the interpretation of the surface states as hole
traps and recombination centers, oxide overlayers were
deposited that led to the disappearance of the surface state, to
an increased activity and to a lower overpotential. Overlayers
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
of isostructural alumina [25] and of gallium oxide, but also of
TiO2 [28] display this effect. One should be cautious in interpreting this as a demonstration that the overlayers increase
the activity through the suppression of surface states. In fact,
it was argued that the main effects of these overlayers could
be to deplete the oxide of electrons near the surface through
electrostatic interactions, thereby suppressing electron–hole
recombination [30]. Overlayers of gallium oxide or of aliminium oxide are attractive also for simulations, because gallium
oxide and aluminium oxide are isostructural to hematite with
a strain smaller than 1%. When the stoichiometric termination of (0 0 0 1) is covered with a monolayer of Ga2O3, the
surface state disappears [154]. The same calculations show
that the overpotential, as calculated in the NØrskov approach,
increases in presence of the Ga2O3 overlayer. It should be
noted that the surface state does not disappear on the O-rich
surface believed to be stable under photoelectrochemical conditions [137].
In the presence of an incomplete alumina overlayer, the
reaction does not take place on the alumina but on the exposed
part of the hematite surface, in a neighbourhood of the overlayer [155]. Still, alumina contributes to a decrease in the
overpotential by decreasing the work function of the hematite surface [155]. The increased work function is related to a
higher-lying hole state at the surface, i.e. to a stronger driving
force to steer the holes towards the surface. Another important
effect of alumina and gallium oxide could be that of decreasing the effective masses and increase the charge mobility [84].
There are thus many mechanisms by which overlayers could
increase the activity of the photocatalyst, beside quenching
surface states.
liquid. Also on (1 1̄ 0 2) the interface is very dynamic with frequent exchanges between terminal aquo groups and adsorbed
water [160]. Another important issue that was not adequately
addressed is the charging state of the surface, which was
shown to influence interaction with water at the level of single
molecules [105].
5. Reaction mechanism
Mechanistic studies have dealt with the reaction mechanism
on different terminations. The reaction leads to oxygen evo­
lution on hematite, while hydrogen evolution takes place on
the cathode. Calculations have shown that, besides the position
of the conduction band, the barriers for hydrogen formation
are also too high on hematite [161]. All studies assume that
the overall reaction consists of four successive proton-coupled
electron transfer (PCET) steps. From the exper­imental point
of view, there are no clear signatures supporting or contrasting
this assumption. There are experimental signatures indicating
hole transfer from the surface to the reactants as the rate-limiting step in the reaction [16, 17, 162].
An important point regards the presence of a nucleophilic
attack in the mechanism, i.e. of a step
O ∗ + H2 O → OOH ∗ + H+ + e− ,
where the second oxygen atom binds to the first directly from
the solution. Zhang et al [163] compared this reaction mech­
anism with one where the O–O bond formation takes place
between two adjacently adsorbed O atoms; on the (1 1 2̄ 0)
surface, the O–O bond formation between two adjacently
adsorbed O atoms is competing with the OOH formation at
a single site, while for other surfaces OOH formation is the
most probable mechanism. On (0 0 0 1), this leads to a calculated overpotential of 0.6 V [137] on the O-rich termination
which is found to be stable under photoelectrochemical conditions. Among defect-free surfaces, the lowest overpotential
0.52 V was calculated for the (1 0 1̄ 0) [164], thanks to adsorbate-adsorbate interaction.
A very important distinction among the different studies is
the termination on which the reaction takes place. Many studies on (0 0 0 1) were devoted to water splitting on a hydroxylated surface [138, 165]; they found the surface states to be
present only on the reaction intermediate Fe = O. On the
other hand, in a photoelectrochemical cell under illumination,
the most stable termination is oxygen-rich [124, 137, 166].
There, a surface state is present intrinsically at the surface and
is not related to a reaction intermediate [137]. A high-valent
FeIV = O iron-oxo reaction intermediate was identified by inoperando infrared spectroscopy [141, 167].
Effects of surface modifications on the overpotential have
also been taken into account. Oxygen vacancies are the most
stable intrinsic defects [85], and they are also the most effective in lowering the overpotential [163, 168]. Hellman et al
[169] calculated the onset potential for water oxidation on
hydroxyl- and oxygen-terminated (0 0 0 1), and found values
of 1.79 V and 2.09 V versus SHE, respectively. Oxygen vacancies shifted them to 3.09 V and 1.83 V. Comparison with their
own measurements, and corrections due to pH, led them to
4.2. Explicit solvent
In the last two years, papers have appeared tackling the problem of simulating the solvent explicitly, and of assessing its
role in the surface structure and reactivity. While some work
has been done on the structure of the interface by molecular dynamics with classical interatomic potentials [156], this
review focuses on the ab initio MD calculations. English et al
investigated the structure of the solvent at the interface, spontaneous water dissociation there, proton swapping, and the
interactions of oxygen from the water with iron ions [157].
Von Rudorff et al investigated the hematite-water interface for
a hydroxylated (0 0 0 1) surface [158]. Only half of the terminal protons point towards the solvent, while the others lead
to in-plane hydrogen bonds. A pattern of bonds exist for 1 ps
and then converts quickly into another surface pattern, and the
lifetime of the in-plane hydrogen bonds is shorter than in bulk
water (80 fs versus 150 fs). Moreover, the solvation structure
of the interface with water strongly depends on the termination [159]: on the iron termination, −O− and −OH+
2 appear
by autoionization of neutral OH groups, while this does not
happen on the O-termination [159]. Notably, the proton dissociated from the OH group remains at the surface rather than
being released into the liquid as hydronium. Moreover, with
the Fe-termination water is much less ordered at the interface,
leading to a lower number of protons pointing towards the
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
[4] Hu Y-S, Kleiman-Shwarsctein A, Stucky G D and
McFarland E W 2009 Chem. Commun. 2009 2652
[5] Osterloh F E and Parkinson B A 2011 MRS Bull. 36 17
[6] Dau H, Limberg C, Reier T, Risch M, Roggan S and Strasser P
2010 ChemCatChem 2 724
[7] Sivula K, Le Formal F and Grätzel M 2011 ChemSusChem
4 432
[8] Katz M J, Riha S C, Jeong N C, Martinson A B F, Farha O K
and Hupp J T 2012 Coord. Chem. Rev. 256 2521
[9] Fujishima A and Honda K 1972 Nature 238 37
[10] Bhatt M D and Lee J S 2015 J. Mater. Chem. A 3 10632
[11] Maeda K and Domen K 2007 J. Phys. Chem. C 111 7851
[12] Bisquert J 2015 Nanostructured Energy Devices (Boca Raton,
[13] Chatman S, Zarzycki P and Rosso K M 2013 Phys. Chem.
Chem. Phys. 15 13911
[14] Zandi O, Schon A R, Hajibabaei H and Hamann T W 2016
Chem. Mater. 28 765
[15] Chatman S, Pearce C I and Rosso K M 2015 Chem. Mater.
27 1665
[16] Cowan A J, Barnett C J, Pendlebury S R, Barroso M, Sivula K,
Grätzel M, Durrant J R and Klug D R 2011 J. Am. Chem.
Soc. 133 10134
[17] Pendlebury S R, Barroso M, Cowan A J, Sivula K, Tang J,
Grätzel M, Klug D and Durrant J R 2011 Chem. Commun.
47 716
[18] Braun A, Hu Y, Boudoire F, Bora D K, Sarma D D, Grätzel M
and Eggleston C M 2016 Cat. Today 260 72
[19] Carbonare N D, Boaretto R, Caramori S, Argazzi R,
Colle M D, Pasquini L, Bertoncello R, Marelli M,
Evangelisti C and Bignozzi C A 2016 Molecules 21 942
[20] Orlandi M et al 2016 Electrochim. Acta 214 345
[21] Tilley S D, Cornuz M, Sivula K and Grätzel M 2010
Angew. Chem. Int. Ed. 49 6405
[22] Badia-Bou L, Mas-Marza E, Rodenas P, Barea E M,
Fabregat-Santiago F, Gimenez S, Peris E and Bisquert J
2013 J. Phys. Chem. C 117 3826
[23] Klahr B, Gimenez S, Fabregat-Santiago F, Bisquert J and
Hamann T 2012 J. Am. Chem. Soc. 134 16693
[24] Zhong D K and Gamelin D R 2010 J. Am. Chem. Soc.
132 4202
[25] Le Formal F, Tetreault N, Cornuz M, Moehl T, Grätzel M and
Sivula K 2011 Chem. Sci. 2 737
[26] Hisatomi T, Le Formal F, Cornuz M, Brillet J, Tetreault N,
Sivula K and Grätzel M 2011 Energy Environ. Sci. 4 2512
[27] Malara F, Fabbri F, Marelli M and Naldoni A 2016 ACS Catal.
6 3619
[28] Yang X, Liu R, Du C, Dai P, Zheng Z and Wang D 2014 ACS
Appl. Mat. Interfaces 6 12005
[29] Carbonare N D, Carli S, Argazzi R, Orlandi M, Bazzanella N,
Miotello A, Caramori S and Bignozzi C A 2015
Phys. Chem. Chem. Phys. 17 29661
[30] Barroso M, Mesa C A, Pendlebury S R, Cowan A J,
Hisatomi T, Sivula K, Grätzel M, Klug D R and Durrant J R
2012 Proc. Natl Acad. Sci. 109 15640
[31] Pham T A, Ping Y and Galli G 2017 Nat. Mater. 16 401
[32] Nellist M R, Laskowski F A L, Lin F, Mills T J and
Boettcher S W 2016 Acc. Chem. Res. 49 733
[33] Zhang X and Bieberle-Hütter A 2016 ChemSusChem 9 1223
[34] Jones R O and Gunnarsson O 1989 Rev. Mod. Phys. 61 689
[35] Payne M C, Teter M P, Allan D C, Arias T A and
Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045
[36] Kohn W, Becke A D and Parr R G 1996 J. Phys. Chem.
100 12974
[37] Hafner J 2000 Acta Mater. 48 71
[38] Capelle K 2006 Braz. J. Phys. 36 1318
[39] Perdew J P and Zunger A 1981 Phys. Rev. B 23 5048
[40] Anisimov V I, Zaanen J and Andersen O K 1991 Phys. Rev. B
44 943
conclude that water oxidation takes place on the oxygen termination, in presence of oxygen vacancies. Oxygen vacancies
lower the overpotential also on other surfaces, leading to the
lowest ever calculated overpotential of 0.47 V for the (1 1 2̄ 0)
surface [163]. Co-presence of iron vacancies and Ti dopants
have been shown to decrease the overpotential, while suppressing the first hydrogen cleavage, but making the final oxygen release energetically more favourable [170]. Experiments
have shown that improvements are observed only when doping concentrations are low (<1 cation%) [171].
6. Conclusions
Ab initio calculations of hematite as a photocatalyst for water
splitting have contributed to the characterization of its bulk
and surface. DFT + U and hybrid functionals are necessary
to reproduce the charge-transfer insulator nature of this oxide.
Charge transport in the bulk is hindered by the high effective masses and the high barriers for polaron hopping, but
doping can have a positive effect by increasing the density
of charge carriers, and by modifying the barriers for polaron
hopping. The most stable (0 0 0 1) surface has a stoichiometric
termination when exposed to oxygen, it becomes hydroxylated in water, and it has an oxygen-rich termination under illumination in a photoelectrochemical setup. Surface states are
instrinsic surface properties on the oxygen-rich termination,
but are a signature of reaction intermediates on the hydroxylated termination. The intrinsic surface states on the stoichiometric termination disappear in the presence of an overlayer
of gallium oxide. Regardless of the surface termination, the
reaction is assumed to proceed by four proton-coupled electron transfers. The most likely mechanism involves a nucleophilic attack leading to the formation of an OOH group at the
surface, with an overpotential of 0.5–0.6 V.
Calculations have contributed to clarify many mechanistic
aspects of the reaction, and to interpret experimental results.
Some of the predictions from theory still need confirmation
from experiments, specifically those regarding the nature of
the surface termination under reaction conditions, and the
identity of reaction intermediates. On the other hand, the role
of the solvent and of the structure of the electrochemical interface in the reaction need to be investigated further.
I would like to thank Narjes Ansari, Matteo Farnesi
Camellone, Stefano Caramori, Ralph Gebauer, Simone
Piccinin, Emiliano Poli, Kevin Sivula, and Kanchan Ulman
for fruitful discussions.
[1] Blankenship R E et al 2011 Science 332 805
[2] Ciamician G 1912 Science 36 385
[3] Walter M G, Warren E L, McKone J R, Boettcher S W, Mi Q,
Santori E A and Lewis N S 2010 Chem. Rev. 110 6446
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
[79] van Duin A C T, Dasguotam S, Lorant F and Goddard W A
2001 J. Phys. Chem. A 105 9396
[80] Tangney P and Scandolo S 2002 J. Chem. Phys. 117 8898
[81] Pinilla C, Irani A H, Seriani N and Scandolo S 2012 J. Chem.
Phys. 136 114511
[82] Liao P, Keith J A and Carter E A 2012 J. Am. Chem. Soc.
134 13296
[83] Merchant P, Collins R, Kershaw R, Dwight K and Wold A
1979 J. Solid State Chem. 27 307
[84] Neufeld O and Toroker M C 2016 J. Chem. Phys.
144 164704
[85] Nguyen M-T, Seriani N and Gebauer R 2014
ChemPhysChem 15 2930
[86] Cava C E, Roman L S and Persson C 2013 Phys. Rev. B
88 045136
[87] Lee J and Han S 2013 Phys. Chem. Chem. Phys. 15 18906
[88] Kleiman-Shwarsctein A, Huda M N, Walsh A, Yan Y,
Stucky G D, Hu Y-S, Al-Jassim M M and McFarland E W
2010 Chem. Mater. 22 510
[89] Kosa M, Barad H N, Singh V, Kellerm K D A, Rühle S,
Anderson A Y, Zaban A and Major D T 2016 Phys. Chem.
Chem. Phys. 18 781
[90] Neufeld O and Toroker M C 2015 Phys. Chem. Chem. Phys.
17 24129
[91] Neufeld O and Toroker M C 2015 J. Phys. Chem. C 119 5836
[92] Aroutiounian V M, Arakelyan V M, Shahnazaryan G E,
Stepanyan G M, Khachaturyan E A, Wang H and
Turner J A 2006 Sol. Energy 80 1098
[93] Sanchez C, Sieber K D and Somorjai G A 1988 J.
Electroanal. Chem. Interfacial Electrochem. 252 269
[94] Aroutiounian V M, Arakelyan V M, Shahnazaryan G E,
Stepanyan G M, Khachaturyan E A and Turner J A 2006
C. R. Chim. 9 325
[95] Yatom N and Toroker M C 2015 Molecules 20 19900
[96] Yatom N and Toroker M C 2016 Phys. Chem. Chem. Phys.
18 16098
[97] Meng X-Y, Qin G-W, Li S, Wen X-H, Ren Y-P, Pei W-L and
Zuo L 2011 Appl. Phys. Lett. 98 112104
[98] Yang H, Mi W-B, Bai H-L and Cheng Y-C 2012 RSC Adv.
2 10708
[99] Rettie A J E, Chemelewski W D, Emin D and Mullins C B
2016 J. Phys. Chem. Lett. 7 471
[100] Rosso K M and Dupuis M 2006 Theor. Chem. Acc. 116 124
[101] Rosso K M, Smith D M A and Dupuis M 2003 J. Chem.
Phys. 118 6455
[102] Iordanova N, Dupuis M and Rosso K M 2005 J. Chem. Phys.
122 144305
[103] Warnes B M, Aplan F F and Simkovich G 1984 Solid State
Ion. 12 271
[104] Zhao B, Kaspar T C, Droubay T C, McCloy J, Bowden M E,
Shutthanandan V, Heald S M and Chambers S A 2011
Phys. Rev. B 84 245325
[105] Negreiros F R, Pedroza L S and Dalpain G M 2016 J. Phys.
Chem. C 120 11918
[106] Liao P and Carter E A 2012 J. Appl. Phys. 112 013701
[107] Zhou Z, Huo P, Guo L and Prezhdo O V 2015 J. Phys. Chem.
C 119 26303
[108] Liao P, Toroker M C and Carter E A 2011 Nano Lett. 11 1775
[109] Huda M N, Walsh A, Yan Y, Wei S-H and Al-Jassim M M
2010 J. Appl. Phys. 107 123712
[110] Kronawitter C X et al 2014 Energy Environ. Sci. 7 3100
[111] Velev J, Bandyopadhyay A, Butler W H and Sarker S 2005
Phys. Rev. B 71 205208
[112] Bandyopadhyay A, Velev J, Butler W H, Sarker S K and
Bengone O 2004 Phys. Rev. B 69 174429
[113] Li H, Niu D, Liu D, Huang W and Zhang X 2017 J. Mol.
Struct. 1139 104
[114] Chen L, Shi C-M, Li X-L, Mi Z-S, Wang D-C, Liu H-M and
Qiao L-J 2017 Materials 10 273
[41] Anisimov V I, Aryasetiawan F and Lichtenstein A I 1997 J.
Phys.: Condens. Matter 9 767
[42] Anisimov V I, Korotin M A, Mylnikova A S,
Kozhevnikov A V, Korotin D M and Lorenzana J 2004
Phys. Rev. B 70 172501
[43] Kummel S and Kronik L 2008 Rev. Mod. Phys. 80 3
[44] Stevanovic V, Lany S, Ginley D S, Tumas W and Zunger A
2014 Phys. Chem. Chem. Phys. 16 3706
[45] Deskins N A and Dupuis M 2007 Phys. Rev. B 75 195212
[46] Setvin M, Franchini C, Hao X-F, Schmid M, Janotti A,
Kaltak M, Van de Walle C G, Kresse G and Diebold U 2014
Phys. Rev. Lett. 113 086402
[47] Seriani N, Pinilla C and Crespo Y 2015 J. Phys. Chem. C
119 6696
[48] Adelstein N, Neaton J B, Asta M and De Jonghe L C 2014
Phys. Rev. B 89 245115
[49] Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J and
Sutton A P 1998 Phys. Rev. B 57 1505
[50] Cococcioni M and De Gironcoli S 2005 Phys. Rev. B
71 035105
[51] Becke A D 1993 J. Chem. Phys. 98 1372
[52] Adamo C and Barone V 1999 J. Chem. Phys. 110 6158
[53] Alvarez-Ramirez F, Martinez-Magadan J M, Gomes J R B and
Illas F 2004 Surf. Sci. 558 4
[54] Rollmann G, Rohrbach A, Entel P and Hafner J 2004 Phys.
Rev. B 69 165107
[55] Guo H and Barnard A S 2011 Phys. Rev. B 83 094112
[56] Canepa P, Schofield E, Chadwick A V and Alfredsson M 2011
Phys. Chem. Chem. Phys. 13 12826
[57] Blanchard M, Lazzeri M, Mauri F and Balan E 2008 Am.
Mineral. 93 1019
[58] Rohrbach A, Hafner J and Kresse G 2004 Phys. Rev. B
70 125426
[59] Huang X, Ramadugu S K and Mason S E 2016 J. Phys. Chem.
C 120 4919
[60] Zhou Z, Shi J and Guo L 2016 Comput. Math. Sci. 113 117
[61] Heyd J, Scuseria G E and Ernzerhof M 2003 J. Chem. Phys.
118 8207
[62] Paier J, Marsman M, Hummer K, Kresse G, Gerber I C and
Angyan J G 2006 J. Chem. Phys. 124 154709
[63] Pozun Z D and Henkelman G 2011 J. Chem. Phys.
134 224706
[64] Hybertsen M S and Louie S G 1986 Phys. Rev. B 34 5390
[65] Onida G, Reining L and Rubio A 2002 Rev. Mod. Phys.
74 601
[66] Shishkin M and Kresse G 2007 Phys. Rev. B 75 235102
[67] Liao P and Carter E A 2011 Phys. Chem. Chem. Phys.
13 15189
[68] Yatom N and Toroker M C 2016 Catal. Lett. 146 2009
[69] NØrskov J K, Rossmeisl J, Logadottir A, Lindqvist L,
Kitchin J R, Bligaard T and Jonsson H 2004 J. Phys. Chem.
B 108 17886
[70] Valdes A, Qu Z-W, Kroes G-J, Rossmeisl J and NØrskov J K
2008 J. Phys. Chem. C 112 9872
[71] Reuter K and Scheffler M 2003 Phys. Rev. B 68 045407
[72] Rogal J, Reuter K and Scheffler M 2004 Phys. Rev. B
69 075421
[73] Seriani N 2009 Nanotechnology 20 445703
[74] Gerischer H 1990 Electrochim. Acta 35 1677
[75] Scheuermann A G, Lawrence J P, Kemp K W, Ito T, Walsh A,
Chidsey C E D, Hurley P K and McIntyre P C 2016 Nat.
Mater. 15 99
[76] Scheuermann A G, Chidsey C E D and McIntyre P C 2016 J.
Electrochem. Soc. 163 H192
[77] Du C, Yang X-G, Mayer M T, Hoyt H, Xie J, McMahon G,
Bischoping G and Wang D-W 2013 Angew. Chem. Int. Ed.
52 12692
[78] Wu Y, Chan M K Y and Ceder G 2011 Phys. Rev. B
83 235301
Topical Review
J. Phys.: Condens. Matter 29 (2017) 463002
[146] Guo H and Barnard A S 2012 J. Colloid Interface Sci.
386 315
[147] Klahr B, Gimenez S, Fabregat-Santiago F, Hamann T and
Bisquert J 2012 J. Am. Chem. Soc. 134 4294
[148] Le Formal F, Pendlebury S R, Cornuz M, Tilley S D,
Grätzel M and Durrand J R 2014 J. Am. Chem. Soc.
136 2564
[149] Le Formal F, Pastor E, Tilley S D, Mesa C A,
Pendlebury S R, Grätzel M and Durrant J R 2015 J. Am.
Chem. Soc. 137 6629
[150] Braun A, Sivula K, Bora D K, Zhu J, Zhang L, Grätzel M,
Guo J and Constable E C 2012 J. Phys. Chem. C
116 16870
[151] Gajda-Schrantz K, Tymen S, Boudoire F, Toth R, Bora D K,
Calvet W, Grätzel M, Constable E C and Braun A 2013
Phys. Chem. Chem. Phys. 15 1443
[152] Bora D K et al 2011 J. Phys. Chem. C 115 5619
[153] Sivula K 2013 J. Phys. Chem. Lett. 4 1624
[154] Ulman K, Nguyen M-T, Seriani N and Gebauer R 2016 J.
Chem. Phys. 144 094701
[155] Neufeld O, Yatom N and Toroker M C 2015 ACS Catal.
5 7237
[156] Kerisit S 2011 Geochim. Cosmochim. Acta 75 2043
[157] English N J, Rahman M, Wadnerkar N and MacElroy J M D
2014 Phys. Chem. Chem. Phys. 16 14445
[158] von Rudorff G F, Jakobsen R, Rosso K M and Blumberger J
2016 J. Phys. Chem. Lett. 7 1155
[159] von Rudorff G F, Jakobsen R, Rosso K M and Blumberger J
2016 J. Phys.: Condens. Matter 28 394001
[160] McBriarty M E, von Rudorff G F, Stubbs J E, Eng P J,
Blumberger J and Rosso K M 2017 J. Am. Chem. Soc.
139 2581
[161] Pan H-J, Meng X-Y and Qin G-W 2014 Phys. Chem. Chem.
Phys. 16 25442
[162] Klahr B M and Hamann T W 2011 J. Phys. Chem. C
115 8393
[163] Zhang X, Klaver P, van Santen R, van de Sanden M C M and
Bieberle-Hütter A 2016 J. Phys. Chem. C 120 18201
[164] Zhang X, Cao C and Bieberle-Hütter A 2016 J. Phys. Chem.
C 120 28694
[165] Iandolo B and Hellman A 2014 Angew. Chem. Int. Ed.
53 13404
[166] Hellman A and Pala R G S 2011 J. Phys. Chem. C
115 12901
[167] Cowan A J 2016 Nat. Chem. 8 740
[168] Nguyen M-T, Piccinin S, Seriani N and Gebauer R 2015 ACS
Catal. 5 715
[169] Hellman A, Iandolo B, Wickman B, Grönbeck H and
Baltrusaitis J 2015 Surf. Sci. 640 45
[170] Toroker M C 2014 J. Phys. Chem. C 118 23162
[171] Malviya K D, Klotz D, Dotan H, Shlenkevich D,
Tsyganok A, Mor H and Rothschild A 2017 J. Phys.
Chem. C 121 4206
[115] Dahan M H and Toroker M C 2017 J. Phys. Chem. C
121 6120
[116] Ferrer M M, Gouveia A F, Gracia L, Longo E and Andres J
2016 Model. Simul. Mater. Sci. Eng. 24 025007
[117] Guo H, Xu H and Barnard A S 2013 Energy Environ. Sci. 6 561
[118] Guo H and Barnard A S 2011 J. Phys. Chem. C 115 23023
[119] Guo H and Barnard A S 2012 J. Phys. Chem. C 116 15854
[120] Guo H and Barnard A S 2012 J. Mater. Chem. 22 161
[121] Chan J Y T, Ang S Y, Ye E Y, Sullivan M, Zhang J and Lin M
2015 Phys. Chem. Chem. Phys. 17 25333
[122] Wanaguru P, An J and Zhang Q-M 2016 J. Appl. Phys.
119 084302
[123] Eggleston C M, Stack A G, Rosso K M, Higgins S R,
Bice A M, Boese S W, Pribyl R D and Nichols J J 2003
Geochim. Cosmochim. Acta 67 985
[124] Nguyen M-T, Seriani N, Piccinin S and Gebauer R 2014 J.
Chem. Phys. 140 064703
[125] Nguyen M-T, Seriani N and Gebauer R 2013 J. Chem. Phys.
138 194709
[126] Kiejna A and Pabisiak T 2013 J. Phys. Chem. C 117 24339
[127] Barbier A, Stierle A, Kasper N, Guittet M-J and Jupille J
2007 Phys. Rev. B 75 233406
[128] Ovcharenko R, Voloshina E and Sauer J 2016 Phys. Chem.
Chem. Phys. 18 25560
[129] Toroker M C, Kanan D K, Alidoust N, Isseroff L Y, Liao P
and Carter E A 2011 Phys. Chem. Chem. Phys. 13 16644
[130] Trainor T P, Chaka A M, Eng P J, Newville M,
Waychunas G A, Catalano J G and Brown G E 2004 Surf.
Sci. 573 204
[131] Liu P, Kendelewicz T, Brown G E, Nelson E J and
Chambers S A 1998 Surf. Sci. 417 53
[132] Yin S, Ma X and Ellis D E 2007 Surf. Sci. 601 2426
[133] Yin S and Ellis D E 2008 Surf. Sci. 602 2047
[134] Yamamoto S et al 2010 J. Phys. Chem. C 114 2256
[135] Souvi S M O, Badawi M, Paul J-F, Cristol S and Cantrel L
2013 Surf. Sci. 610 7
[136] Pang Q, DorMohammadi H, Isgor O B and and Arnadottir L
2017 Comput. Theor. Chem. 1100 91
[137] Ulman K, Nguyen M-T, Seriani N, Piccinin S and Gebauer R
2017 ACS Catal. 7 1793
[138] Yatom N, Neufeld O and Toroker M C 2015 J. Phys. Chem.
C 119 24789
[139] Nakamura R and Nakato Y 2004 J. Am. Chem. Soc. 126 1290
[140] Zhang M, de Respinis M and Frei H 2014 Nat. Chem. 6 362
[141] Zandi O and Hamann T W 2016 Nat. Chem. 8 778
[142] Kerisit S and Rosso K M 2006 Geochim. Cosmochim. Acta
70 1888
[143] Young K M H, Klahr B M, Zandi O and Hamann T W 2013
Catal. Sci. Technol. 3 1660
[144] Lo C S, Tanwar K S, Chaka A M and Trainor T P 2007 Phys.
Rev. B 75 075425
[145] Tanwar K S, Catalano J G, Petitto S C, Ghose S K, Eng P J
and Trainor T P 2007 Surf. Sci. 601 L59
Без категории
Размер файла
875 Кб
2faa84d9, 1361, 648x
Пожаловаться на содержимое документа