Theory of gold on ceria - Department of Chemistry - UCL
Physical Chemistry Chemical Physics
www.rsc.org/pccp Volume 13 | Number 1 | 7 January 2011 | Pages 1–348
ISSN 1463-9076
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Jenkins et al.
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PERSPECTIVE
Changjun Zhang, a Angelos Michaelides a and Stephen J. Jenkins* b
Received 8th July 2010, Accepted 15th September 2010
DOI: 10.1039/c0cp01123a
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The great promise
industrial processes, such as the water gas shift reaction, has prompted a flurry
at understanding the molecular-level details
on experimental and theoretical studies
with and without
particularly in its reduced form, means that at present it is highly challenging to carry out
accurate electronic structure simulations
majority
applying the so-called DFT + U technique. Here we will briefly discuss some recent studies
Au on CeO 2 {111} that mainly use this methodology. We will show that considerable insight has
been obtained into these systems, particularly with regard to Au adsorbates and Au cluster
reactivity. We will also briefly discuss the need for improved electronic structure methods,
which would enable more rigorous and robust studies in the future.
1. Introductory remarks
Amongst the least reactive
relatively recently, have seemed an odd choice
investigate for its potential as a catalyst. Since the seminal
work
a London Centre for Nanotechnology and Department
University College London, London WC1H 0AH
b Department
Cambridge, CB2 1EW, UK. E-mail: sjj24@cam.ac.uk;
Fax: +44 (0)1223 762829; Tel: +44 (0)1223 336502
nanoparticles can show dramatic chemical activity in certain
contexts when suitably prepared, and this unexpected
observation has prompted concerted efforts both to explain
this phenomenon and to expand its range
Today, research into catalysis by
driven not only by the economic attractions
(historically one
precious metals) but also by its highly desirable propensity to
catalyse reactions at relatively low temperatures. Various
theories have been put forward to explain the activity
nanoparticulate
Angelos Michaelides obtained a
PhD in Theoretical Chemistry in
2000 from Queen’s University
Belfast (supervised by Peijun Hu).
He then moved to David King’s
group in Cambridge and in 2002
was awarded a junior research
fellowship from Gonville and
Caius College. In 2004 he moved
to the Fritz Haber Institute,
Berlin, first as an Alexander von
Humboldt fellow and then later as
a staff scientist, in Matthias
Scheffler’s
Angelos Michaelides In 2006 he moved to UCL and
became Pr
Angelos’ current research (www.chem.ucl.ac.uk/ice) involves
the application and development
to study catalytic and environmental interfaces.
Stephen Jenkins studied Theoretical
Physics at the University
PhD in 1995 (supervised by G.P.
Srivastava and John Inkson).
After a spell as a post-doc in
Exeter, he joined David King’s
group in Cambridge in 1997.
Awarded a Royal Society University
Research Fellowship in 2001,
Stephen was appointed to a University
Lectureship in Physical
Chemistry in 2009, and succeeds
Stephen J. Jenkins David King as head
Cambridge Surface Chemistry
group. His current research (www-jenkins.ch.cam.ac.uk)
includes the fundamentals
structure and chirality, and the surface and interface properties
22 Phys. Chem. Chem. Phys., 2011, 13, 22–33 This journal is c the Owner Societies 2011
great interest from the catalytic viewpoint. 22–34 These studies
in turn have prompted significant theoretical efforts to understand
the physical nature
this system, and its effect on catalytic activity. 35–41 In this short
perspective article, we aim to provide a selective but
representative overview
recent years, highlighting not only the key areas in which
consensus appears to be emerging, but also what we believe to
be some
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Fig. 1 Top: Schematic representations
reduced (right) CeO 2 {111} surface. White atoms are cerium, red atoms
oxygen, and the oxygen vacancy is circled. Bottom: Electronic structure
surface (right) with occupied states shaded and unoccupied states
unshaded. The density
spin-resolved. The Fermi levels are set at zero and the units
energy (y) axis are in eV.
effects (the presence
effects (the presence
on support effects (either through the stabilisation
structural/electronic features, or through reactions occuring
across the particle/support interface itself). The reality may
well be that all such phenomena are important at some time or
another in varying proportions in different scenarios and for
different reactions.
One
support for nanoparticulate
(ceria, CeO 2 ). A highly reducible oxide, ceria has found
applications as an oxygen buffer, as a catalyst, as a catalyst
support, and as a solid electrolyte. 20 These uses typically rely
upon the easy creation and diffusion
the material. When the oxide is stoichiometric, the constituent
cerium atoms exist in the Ce 4+ oxidation state, but in the
partially reduced form each missing lattice oxygen atom implies
the existence
necessarily immediately adjacent to 21 ) the vacancy. The stoichiometric
oxide is therefore characterised by a completely empty
f-band (located in an energy gap between the occupied O 2p
states and the unoccupied Ce 5d states) whilst the partially
reduced oxide features highly-localised partially-occupied
f orbitals split-
A variety
suggest that
2. Theoretical approaches
Electronic structure simulations
surfaces are challenging for a number
is the inevitable difficulty
to extended surfaces. This implies that the structures are
complex and system sizes rather large, and that neither
localised nor periodic basis functions are without significant
drawbacks. Second, and more challenging fundamentally, is
the question
method with the requisite accuracy to describe the properties
have been developed, density functional theory (DFT) is the
most popular and robust theoretical approach currently
available for solving the electronic structures
However, DFT with standard exchange–correlation functionals
(e.g. generalised gradient functionals, such as PW91 42
or PBE 43 ) is far from a panacea and suffers from a number
well-known deficiencies. The one most relevant to the present
topic
strongly correlated nature
The problem
explained, though much less easily remedied. Essentially, one
should recall that the electron–electron interactions included
within standard DFT exchange–correlation functionals are
only mean-field approximations to what are, in reality, a set
approach works remarkably well, allowing orbitals to be
calculated within an independent particle picture. In contrast,
however, when an orbital is very highly localised (as occurs,
course, for f orbitals in the cerium atom) the Coulomb
repulsion is sufficient to provide a strong disincentive towards
instantaneous double occupancy
probability
at any given moment is strongly modified by whether another
electron is or is not already there at the time: the motion
electrons then becomes ‘‘strongly correlated’’. Effects
nature cannot be captured by a pure mean-field approach,
since this assumes that electrons can be treated as independent
particles, so standard DFT exchange–correlation functionals
are doomed to failure; a classic example
to be found in NiO, where DFT incorrectly predicts a metallic
bandstructure and must be augmented in some more or less
sophisticated manner in order to achieve a physically reasonable
result. 44
Although alternative explictly correlated electronic structure
methods for solids have recently begun to emerge, e.g. the
Random Phase Approximation 45 and Quantum Monte Carlo, 46
apragmaticad hoc correction known as the ‘‘Hubbard U’’ has
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much more commonly been applied in practical calculations. 47
Its application is, however, not free from controversy, as it
includes within DFT an additional potential, given the symbol U,
which effectively penalises double occupancy
localised orbitals. In doing so, one steps outside the bounds
DFT + U calculations can be considered reliable, so long as
the value
matters, reports in the literature
parameter, U eff , defined as the difference between the spherically
averaged value
parameter, J. In addition, the Hubbard correction is
typically applied only to a subset
strongly localised ones) which in this case corresponds to the
Ce 4f electrons.
The issue
considerable importance in assessing calculations reported in
the literature for ceria. Values employed for cerium oxides
typically range between 3–6 eV. One should note that the
DFT + U approach is generally implemented in the context
either the local density approximation (LDA + U) or the
generalised gradient approximation (GGA + U); 48,49 the
latter may itself be sub-divided according to the particular
flavour
has tended to be
basis
authors have favoured U eff values ranging between 5–6 eV for
LDA + U and between 3–5 eV for GGA + U. 21,53–58 How
well any
surface calculations, however, has proved to be a point
significant contention, as will be seen below. Moreover, it has
been pointed out (e.g. ref. 52) that there probably exists no
single value
properties, which is to say that a value
excellent results for one property (e.g. lattice constant) may
yield poor results for another (e.g. band gap) and vice versa.
3. The nature
without defects
The most stable surface
and it is this that has been the subject
This surface exhibits three-fold rotational symmetry and may
be thought
Removal
undercoordinated cerium atoms to accommodate the two
resulting excess electrons (3Ce 4+ - 2Ce 3+ + Ce 4+ ). An
early confirmation
correlation effects in any theoretical assault on this system
may, however, be gleaned from the fact that standard DFT
calculations incorrectly predict delocalisation
electrons across all three undercoordinated cerium atoms
(3Ce 4+ - 3Ce 3.33+ ). Correct localisation is obtained when
U eff values
energy cost for removal
surface oxygen vacancy) has been calculated by Zhang et al. 63
using GGA + U with U eff = 5 eV to be 2.23 eV; in contrast,
the creation
same work to require an energy
Removal
electronic structure almost indistinguishable from that
single surface oxygen vacancy. 58,62,63 Their energy difference is
on the order
the vacancy formation energy
theoretical conclusions are in good agreement with the elegant
high-resolution scanning tunneling microscopy work
et al., 64 which showed that the two types
oxygen vacancy and subsurface oxygen vacancy) are present
with almost equivalent concentrations. In addition to the
single vacancies, Esch et al. 64 further discovered that upon
prolonged annealing vacancy clusters appear, with linear
vacancy clusters being dominant and triangular vacancy
clusters being the next most abundant. Interestingly, those
vacancy clusters expose exclusively Ce 3+ ions. Because
electrons left behind by the released oxygen atoms are
localised at adjacent Ce ions, these observations suggest that
electron localisation plays an important role in shaping the
vacancy clusters. 64,65
In order to address this issue, Zhang et al. 62 carried out a
systematic DFT + U study on a series
A correlation between the coordination number
ion and the energy
higher the coordination number, the less stable the Ce 3+ ion
would be. Because the Ce ions neighboring the vacancies have
lower coordination numbers than those that are further away
from the vacancies, this correlation explains well the electronic
features
predicted that a triangular surface vacancy cluster is actually
more stable than the linear vacancy clusters, which disagrees
with the experimental observations. Conesa 66 also used
DFT + U to study the defects containing two and three
vacancies. Whilst the author identified a similar correlation
between the coordination number
energies, he also found the electronic configuration with the
lowest energy is not that which contains the Ce 3+ ions located
as immediate neighbors to the vacancies, although the energy
differences between them are small (less than 0.1 eV per
vacancy). Because the reduction
as predicted in Conesa’s work would produce different O
structural features than are observed in the STM images.
These apparent disagreements suggest a need for further
experiments and calculations on vacancy clusters. Another
important issue deserving
oxygen vacancies. Experimentally, whilst Namai et al.
reported the defect mobility at room temperature, 67,68
Esch et al. 64 suggested that the diffusion
requires temperature higher than 400 1C. In theory, energy
barriers for vacancy diffusion have been computed with
interatomic potential approaches 69 and DFT methods, 70,71
and the obtained values vary in the range
Nolan et al. 72 employed the DFT + U method to calculate the
diffusion for a single vacancy in a (222) unit cell (CeO 1.96 )
and obtained an energy barrier
calculated barrier in the classical transition-state theory
expression yields a rate
a standard pre-exponential factor
low mobility for the vacancy at room temperature.
24 Phys. Chem. Chem. Phys., 2011, 13, 22–33 This journal is c the Owner Societies 2011
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4. Gold adatoms on stoichiometric ceria surfaces
The first theoretical calculation to address the adsorption
were considered on both the stoichiometric and the partially
reduced CeO 2 {111} surface. Significantly, the adsorption
energy was found to be rather larger when the adatom
occupied an oxygen vacancy site (1.86 eV) than when it sat
atop an oxygen atom on the ideal surface (1.26 eV) pointing
towards a possible role for such vacancies as nucleation sites
for larger clusters. Furthermore, these calculations also
indicated that the charge state
pr
stoichiometric surface, the calculations indicated that the 6s
orbital
adjacent cerium atom upon adsorption (Ce 4+ - Ce 3+ ); the
adatom itself acquired a net positive charge
(see Fig. 2) and was found to retain no net spin, in sharp
contrast to an isolated
a single unpaired spin.
It is worth mentioning that these early calculations for
on ceria were not carried out using the DFT + U technique
that underlies more recent work. Neither, however, were they
carried out without due regard to the issue
In fact, an alternative method
f electrons was employed, via a technical adjustment to the
self-consistency procedure adopted during iterative solution
the Kohn–Sham equations
‘‘pruned density mixing’’. 99 Nevertheless, it is certainly fair to
say that the ‘‘pruned density mixing’’ technique is not trivial to
apply, and that careful adjustment
to achieve convergence in its one application to date. 35 The
DFT + U method suffers from the ambiguity noted above,
regarding the correct choice for U eff , but does benefit from
being by now rather standard, implying both that DFT + U is
readily available as an option in many modern DFT codes, but
also that calculations performed using this method are more
straightforwardly comparable with others in the literature
obtained by similar means; convergence is also routinely
achieved without the extensive optimisation efforts necessary
in application
Fig. 2 Electronic structure
CeO 2 {111} surface (atop site). In (a) the top panel shows the
density
panel
that arises from adsorption
existence
shows net spin associated with this occupied f-orbital, localised on one
from Liu et al. 35 Copyright (2005), American Physical Society.
Fig. 3 Electronic structure
CeO 2 {111} surface (bridge site). In the left panel, the total
density
(PDOS)
rescaled so that characteristic features can be seen more clearly. The
Ce and O atoms in the PDOS refer to the reduced Ce (i.e. Ce 3+ ) and
the O between Ce 3+ and the Au atom, respectively. In the right panel
is depicted the three-dimensional isosurface plot
density (blue areas)
Zhang et al. 55 Copyright (2008), American Chemical Society.
those reasons alone, the present authors have adopted the
GGA + U methodology in all
this system.
Our recent GGA + U (U eff = 5 eV) results 55 for individual
qualitative agreement with the earlier work, albeit the adatom
charge (+0.17|e|) and adsorption energy (0.96 eV) for the atop
site are both rather smaller than before. Upon investigating
alternative adsorption sites, however, we discovered that a
position bridging between two oxygen atoms was, in fact,
preferred (adsorption energy 1.17 eV, adatom charge
+0.32|e|); interestingly, the unpaired spin resulting from
depopulation
not on the nearest cerium atom, but instead upon the third
nearest 55 (see Fig. 3). A very similar configuration (both in
terms
subsequently by Herna´ndez et al., 73 using a near-identical
computational set-up, although they additionally point out
the existence
minima associated with some
considered. Camellone and Fabris 74 also concur with the same
basic picture, using U eff = 4.5 eV.
Castellani et al., 75 however, adopt a mixed methodology
whereby LDA + U (U eff = 5 eV) is used to obtain optimised
geometries, and then a single-point GGA + U (U eff = 3 eV)
calculation is performed to obtain energies, charges and spin
moments. These choices are motivated by evidence from bulk
ceria compiled by Loschen et al., 51 but in light
on the clean reduced surface 57,62 it is questionable whether the
relatively low value
will correctly reproduce the localisation
orbitals. Certainly, the results for
by Castellani et al. 75 are in marked disagreement with those
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Zhang et al., 55 Herna´ndez et al. 73 and Camellone and Fabris, 74
both regarding the location and the charge state
adatom; they conclude that it sits atop an oxygen atom and
remains essentially neutral. Use
by Branda et al. 76 yields a different preferred adsorption
site for Au, bridging between an O and a Ce atom, but again
indicates a neutral charge state; results in line with previous
work 55,73,74 are obtained when a purely GGA + U (U eff =5eV)
approach is adopted. 76 Our view is that the low U eff values
suggested by Loschen et al. 51 are intended to provide a
balanced description
better representation
higher U eff values. Furthermore, the lower lattice constant
achieved through use
would, we believe, tend to favour unphysical delocalisation
their closer proximity. Alternatively, one might say that whilst
charge localisation is most strongly controlled by the choice
U eff , an important secondary effect arises due to the influence
on the stability
Ce 4+ cation (i.e. compressive strain disfavours the reduction
should nevertheless be granted,
constant obtained with LDA + U lies closer to the experimental
value than does that calculated with GGA + U.
A valuable analysis has now been provided by Branda
et al., 78 addressing precisely the subtle interplay between
lattice constant and the chosen U eff value in determining
the charge transfer between adatom and surface. They
demonstrate that, for
GGA + U (U eff = 3 eV) consistently predicts zero or minimal
charge transfer at lattice constants in the range 5.35–5.55 eV,
whereas GGA + U (U eff = 5 eV) consistently predicts full
charge transfer at lattice constants above about 5.40 eV
(and very little charge transfer at lattice constants below). If
one accepts the larger U eff value and any reasonable lattice
constant, the unequivocal conclusion is that significant charge
transfer occurs. If, on the other hand, one prefers the smaller
U eff value, the result is a less clearcut preference for a lack
charge transfer, since metastable solutions with some degree
charge transfer lie within a few tens
state. Branda et al. 78 avoid drawing a firm conclusion over
which picture is correct, but we feel it is important to note that
their results obtained at smaller (essentially experimental)
lattice constants reveal an unphysical (albeit small) delocalisation
obtained at larger lattice constants do not.
Out
(U eff = 3 eV) and GGA + U (U eff = 5 eV) calculations for
the clean reduced CeO 2 {111} surface, holding the lattice
constant fixed at the LDA + U (U eff = 5 eV) value reported
by Castellani et al. 75 (i.e. 5.39 A˚ ). In the former case, we find
unphysical delocalisation
atoms, rather than the physically correct solution showing
localisation on just two. Only with the larger U eff value do we
obtain properly localised solutions, and even then only when
the initial guess for the electron distribution is carefully
chosen. It seems clear, therefore, that use
constant (5.39 A˚ ) produces unphysical results unless the higher
U eff valueisusedfortheGGA+U calculations, and risks error
even then. Since we and others have also previously reported 57,62
that GGA + U (U eff = 3 eV) produces similarly spurious results
for oxygen vacancies even at larger lattice constants, it seems to
us on balance that the most consistent choice is to use GGA + U
(U eff E 5 eV) at its own theoretically obtained (albeit somewhat
too large) lattice constant. Such a choice for CeO 2 {111}/Au
leads to adsorption at the bridge site, with full charge transfer
from the
Zhang et al., 55 Hernández et al., 73 Camellone and Fabris, 74 and
Branda et al. 76
As a final comment on the subject
the stoichiometric surface, we note that Branda et al. 78 report
the results
(as opposed to DFT + U) which favour a solution with no
charge transfer over a second solution with strong charge
transfer, but only by a very small margin. Given the uncertainties
inherent in hybrid functional DFT, its application on
ceria systems is not free
et al. 80 and Kullgren et al. 81 have found, whilst hybrid
functionals such as PBE0, 82 HSE 79 or B3LYP 83 give a reasonably
good prediction on bulk CeO 2 and Ce 2 O 3 systems, the
overall description
gaps) can actually be substantially worse than obtained when
using LDA + U or GGA + U with adjustable U parameters.
5. Gold adatoms on defective ceria surfaces
Notwithstanding the complexities
surfaces, it is highly likely that adsorption at defect sites
will play a major (possibly even dominant) role under
Table 1 Calculated adsorption energies for a single
stoichiometric (Stoich.) and defective (O-Vac. and Ce-Vac.)
CeO 2 {111} surfaces. The ‘‘PW91+’’ calculations employed the
‘‘pruned density mixing’’ technique. For the various DFT + U
calculations, we adopt the notation
‘‘Ln’’ indicates LDA + U with U eff = n eV, and ‘‘Gm’’ indicates
GGA + U with U eff = m eV. All the GGA-based calculations used the
PW91 functional, except for those reported by Camellone & Fabris 74
which employed the PBE functional. The notation ‘‘L5 - G3’’ implies
that geometry optimisation was done wholly within the L5 approach
(and at the L5 lattice constant) followed by a single-point calculation
for adsorption energy and electronic structure carried out within the
G3 approach. For the stoichiometric surface, results marked with a
superscript dagger correspond to adsorption atop an O atom, those
marked with a double-dagger are for adsorption in a Ce–O bridge site,
and the remaining plain entries are for adsorption in the O–O bridge
site. In all cases at the O-Vac. and Ce-Vac. surfaces, the adatom bonds
directly into the vacancy site.
Functional Stoich. O-Vac. Ce-Vac.
Liu et al. 35 PW91+ 1.26 w 1.86 —
Chen et al. 84 G5 0.88 w 2.58 5.65
Branda et al. 78 G5 0.96 w — —
Zhang et al. 55 G5 1.17 2.75 5.94
Hernandez et al. 73 G5 1.15 2.41 —
Camellone & Fabris 74 G4.5 1.18 2.29 5.68
Branda et al. 76 G5 1.15 — —
Branda et al. 76 L5 - G3 0.71 ww — —
Castellani et al. 75 L5 - G3 0.66 w — —
Branda et al. 78 L5 - G3 0.61 w — —
Branda et al. 78 G5 0.96 w — —
26 Phys. Chem. Chem. Phys., 2011, 13, 22–33 This journal is c the Owner Societies 2011
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catalytically relevant conditions. Certainly the adsorption
energy associated with depositing single
either cerium or oxygen vacancy sites is agreed to be rather
greater than for the stoichiometric surface. Various calculations
have, for instance, indicated a preference for adsorption
into an oxygen vacancy site relative to the stoichiometric
surface (see Table 1) the most reliable results being, we believe,
those presented recently by Zhang et al. 55 (1.58 eV preference),
Herna´ndez et al. 73 (1.26 eV preference) and Camellone and
Fabris 74 (1.11 eV preference). The work
appears accurately to represent the structure and energetics
the relative preference for that site because the most stable site
for adsorption on the stoichiometric surface is not considered
in that work. The adsorption energy
by Liu et al. 35 for the oxygen vacancy site now looks
conspicuously low in relation to these four GGA + U
Table 2 Calculated charge states for a single
the stoichiometric (Stoich.) and defective (O-Vac. and Ce-Vac.)
CeO 2 {111} surfaces. The key to the ‘‘Functional’’ column is explained
in the caption to Table 1. For the stoichiometric surface, results
marked with a superscript dagger correspond to adsorption atop an
O atom, those marked with a double-dagger are for adsorption in a
Ce–O bridge site, and the remaining plain entries are for adsorption in
the O–O bridge site. In all cases at the O-Vac. and Ce-Vac. surfaces,
the adatom bonds directly into the vacancy site
Functional Stoich. O-Vac. Ce-Vac.
Liu et al. 35 PW91+ +0.35 w 0.58 —
Branda et al. 78 G5 +0.32 w — —
Zhang et al. 55 G5 +0.32 0.62 +1.23
Hernandez et al. 73 G5 +0.34 0.6 —
Branda et al. 76 G5 +0.33 — —
Branda et al. 76 L5 -G3 0.06 ww — —
Castellani et al. 75 L5 - G3 0.02 w — —
Branda et al. 78 L5 -G3 +0.05 w — —
Branda et al. 78 G5 +0.32 w — —
Fig. 4 Electronic structure
vacancy on the CeO 2 {111} surface. In (a) the left panel shows
schematically the structure and the formal charges
the bare vacancy, while the right panel shows the density
(DOS) projected onto the f-orbitals
panel shows the structure and formal charges after adsorption
into the vacancy site, while the right panel shows the DOS projected
onto the f-orbitals
d-orbitals
Hernández et al. 73 Copyright (2009), Royal Society
calculations. All works that address explicitly the calculated
electronic structure, 55,73,74 however, agree with the original
finding
reversed relative to adsorption on the stoichiometric surface;
one
vacancy donates an electron (2Ce 3+ +Ce 4+ - Ce 3+ +2Ce 4+ )
to the adatom, which gains a substantial net negative charge
in the vicinity
(see Table 2 and Fig. 4).
An alternative scenario involves the adsorption
cerium vacancies, the energetics
by Hu and co-workers 84,85 who report an extremely high
adsorption energy
by Zhang et al. 55 confirms a similarly high adsorption energy
(5.94 eV) and adds the observation that the substitutional
atom gains a very large positive charge
and Fabris 74 report an adsorption energy
a site. These high adsorption energies do not, however,
necessarily imply that cerium vacancies will dominate the
adsorption properties
vacancy itself requires significant energy.
In order to address this issue, Zhang et al. 63 extended their
work to include a first-principles thermodynamic analysis
to compete with the stoichiometric surface for
As mentioned in the section dealing with clean surfaces above,
the formation energy for a single cerium vacancy (4.67 eV) far
exceeds that
calculated within the GGA + U (U eff = 5 eV) methodology. 63
Application
conclusion that the free energy
less than that
those found in, for example, the water gas shift (WGS)
reaction (400–800 K, with partial pressure ranging from
1 kPa to 100 kPa). Indeed, the free energy
vacancy is comparable with that
in the relevant range, whereas the cerium vacancy is unstable
by a margin
both cerium and oxygen vacancies together are found to be
unstable by more than 2 eV. Accordingly, one expects that
oxygen vacancies will be abundant under these conditions,
whereas cerium vacancies ought to be extremely rare. The
inclusion
difference to the outcome under WGS conditions. 63 Coupling
the creation
vacant site is strongly disfavoured, from a free energy
perspective, by around 7 eV relative to adsorption
on the stoichiometric surface. And once again, composite
defects involving both cerium and oxygen vacancies together
are also disfavoured. Adsorption
vacancies is, however, still strongly favoured over adsorption
onto the stoichiometric surface, even when the cost
the oxygen vacancy is included within the free energy.
In a rare investigation
surfaces
substitutional
They found that occupancy
nearby lattice O thermodynamically unstable, implying that
substitutional
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by an oxygen vacancy under near-equilibrium conditions. In
effect, therefore, these results indicate that substitution
isolated Au atom into a Ce vacancy is unstable relative to
adsorption
and O vacancy sites. Furthermore, the cost
vacancy in the first place was not included in the analysis, so
the likely concentration
directly addressed. We anticipate that, similar to the {111}
surface, such defects will be rare under conditions relevant to
WGS catalysis. Heavily oxygen-rich conditions would,
course, tend to favour cerium vacancies over oxygen vacancies,
so under such circumstances it may be that substitutional
In the case
with a lower valency (Au + or Au 3+ ), on a Ce 4+ site could
result in an electronic hole localized on the neighbouring
oxygen ion(s). This phenomenon, also referred to as polaronic
localization, is quite common in many metal oxides 87 : despite
the existence
metal ion defect in oxides, the hole-lattice coupling
favours hole localization at a single oxygen, and thus breaks
the space group symmetry. This poses a challenge in theoretical
treatments, as standard DFT
hole localization and the associated lattice distortion. 88–90 The
origin
standard DFT to cancel the electron self-interaction. There
have been some recent theoretical efforts in tackling this
problem, among which the DFT + U approach with the
Hubbard correction applied to the oxygen p orbitals has
shown some promising improvement. 91–94 As the current
DFT + U studies
Ce f orbitals with the Hubbard correction, it would be interesting
to see the effects on electronic structure, ionic structure
and energetics when the correction also applies on the oxygen
p orbitals.
Another category
consideration is to be found in the form
these have been the subject
date. To our knowledge, only Castellani et al. 75 have investigated
the binding
model structure incorporating both convex and concave step
morphology. In most
authors find adsorption energies in the range 0.52–0.69 eV,
with a trivial degree
adsorbate. Although such results would seem distinctive
relative to the findings on planar surfaces reported by the
majority
that the particular methodology employed by Castellani et al. 75
does in fact yield similarly weakly bound and neutral adsorption
for the planar case. Indeed, the clearest message that may
be understood from this work is that Au adsorption in most
the step-related adsorption sites is remarkably unperturbed
relative to the planar surface. 75 We might therefore expect that
calculations performed using methodologies that provide
stronger binding and greater charge transfer on the planar
surface are likely also to do so on the stepped surface;
unfortunately such calculations have not, to our knowledge,
been performed to date. In just one adsorption site, involving
the concave step, is a significantly enhanced adsorption energy
charge transfer that leaves the Au adatom with a significant
positive charge
6. Gold clusters on ceria
Although a great deal
adsorption
(see above) it is
isolated entities are likely to be plentiful under reaction
conditions. In general, we should think in terms
clusters, whose size distribution will depend critically upon
both thermodynamic and kinetic aspects
preparation. Since the adsorption energies reported for
on the stoichiometric and reduced surfaces
below the calculated cohesive energy
that high temperatures will allow sintering, ultimately resulting
in relatively large
in contrast, may kinetically stabilise small particles, and this
may be further accentuated by low
The earliest calculations to address
were those
adatoms were considered (i.e. Au 1 ,Au 2 ,Au 3 and Au 4 clusters).
The first
vacancy site, and the others to progressively occupy adjacent
sites lying nearly atop oxygen atoms. The adsorption energy
for each additional
which was noted to be much higher than the 1.26 eV calculated
in the same work for adsorption on the stoichiometric surface.
It was therefore concluded that, once the number
would grow preferentially around these
rather than nucleating elsewhere on patches
surface. Moreover, although the first
was found to be negatively charged, consistent with its occupation
achieved a net positive charge, in the range +0.10–0.19|e|,
somewhat less than that associated with an isolated
adatom on the stoichiometric surface (+0.35|e|).
Sporadic attention has been paid to cluster morphology on
CeO 2 {111} in subsequent GGA + U calculations, for example
a Au 2 cluster anchored to an oxygen vacancy site was
considered by Camellone et al. 74 (U eff = 4.5 eV) and a Au 3
cluster anchored to a cerium vacancy site studied by
Chen et al. 95 (U eff = 5 eV). These latter authors also reported
calculations on a Au 10 cluster, constructed by depositing a
cluster
performing molecular dynamics as a form
annealing, and then re-optimising; the stability
against others
not discussed. 95
Gold clusters
in very recent work by Zhang et al. 96 based on the
GGA + U (U eff = 5 eV) methodology. Assuming the particles
to be anchored at a single oxygen vacancy, they built up a
sequence
structure before adding another atom and calculating the next
(see Fig. 5). Molecular dynamics calculations were also
28 Phys. Chem. Chem. Phys., 2011, 13, 22–33 This journal is c the Owner Societies 2011
while six other
displayed net positive charges averaging +0.17|e| per atom;
three further
showed a net negative charge averaging 0.03|e|, and the
single
negative charge
the
display a significant positive charge, even for much larger clusters.
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Fig. 5 Au clusters anchored to an O vacancy on CeO 2 {111}. Planar
two-dimensional clusters are denoted with a superscript (a). Clusters
forming a series leading eventually to hcp stacking are given a superscipt
(b), and those forming a series leading eventually to fcc stacking
are highlighted with a superscript (c). Reprinted with permission from
Zhang et al. 96 Copyright (2009), American Chemical Society.
performed for some clusters, to test stability against unexpected
rearrangements. Both two- and three-dimensional
clusters were considered, and the latter was found to be
energetically favoured in general, with the exception
Au 7 case. For the larger clusters, Au 10 and Au 11 , it is possible
to discern the beginnings
hexagonal close-packed (hcp) stacking patterns, and it is
notable that these have very similar energies; the preference
for fcc stacking in bulk
cluster sizes. This observation raises the fascinating prospect
that the smallest
those having fewer than about 35 atoms) may exhibit fcc/hcp
polymorphism. This in turn may have catalytic consequences,
in terms
exposed by the clusters. We believe that state-
scanning transmission electron microscopy may now be
approaching sufficient resolution to confirm or refute these
intriguing structural predictions.
In addition to the structural issues raised by these cluster
studies, the work
electronic properties were retained even for the largest clusters
considered. Specifically, although the net negative charge
residing on the
was found typically to be lessened by the addition
atoms in direct contact with the oxide remained high. In the
hcp-stacked Au 11 cluster, for example, the
directly on top
negative charge
7. Reaction mechanisms
The first theoretical discussion
(i.e. CO + H 2 O - CO 2 + H 2 ) on a planar Au 4 cluster
anchored at an oxygen vacancy on CeO 2 {111}. 35 The first step
in the proposed mechanism involved adsorption
one
negative one that sits in the vacancy site itself, with an
adsorption energy
one
state, namely that it strongly affects adsorption energies.
Indeed, Liu et al. 35 reported that CO adsorption energies on
single adatoms ranged from 0.09 eV in the case
charged Au located in an oxygen vacancy site, through to
2.37 eV in the case
oxygen atom on the stoichiometric surface. The lesser positive
charges found for Au atoms in the basal layer
likely to provide moderate adsorption energies,
value quoted above for the Au 4 cluster is probably fairly typical.
After adsorption
proposed by Liu et al. 35 is partially dissociative adsorption
H 2 O, calculated to be almost thermoneutral, and with an
activation barrier
moiety can then react with CO to form COOH, via a transition
state activated by just 0.10 eV, releasing 0.37 eV at this step.
Fig. 6 Reaction mechanism for the WGS reaction at a model Au 4
cluster anchored to an O vacancy on CeO 2 {111}. After initial adsorption
reaction
from COOH to form gas-phase CO 2 , and finally recombinative
desorption
Copyright (2005), American Physical Society.
This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 22–33 29
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A barrier
H from COOH onto the cluster, in an almost thermoneutral
step that releases CO 2 into the gas phase. And finally,
recombination
input
onto the cluster involves only a very small binding energy, it is
far from inevitable that there will a reasonable probability
each one encountering a CO molecule on the same cluster
during its short adsorbed lifetime; clearly this will depend
sensitively upon the lifetime
temperature. The observation that the adsorption energy
CO (1.22 eV) exceeds the highest reaction barrier (1.08 eV) is
therefore highly relevant, implying that a favourable state
affairs can be achieved through selection
temperature for the reaction, without recourse to prohibitive
pressures. The efficacy
reaction is therefore explicitly linked to the unusual charge
state
More recent work, by Camellone and Fabris, 74 confirms
through the use
conclusions asserted by Liu et al. 35 via ‘‘pruned density mixing’’
for the dependence
state. Specifically, they report that adsorption
single Au adatom initially located in its favoured bridge site on
the stoichiometric CeO 2 {111} surface results in a spontaneous
relocation
oxygen atom, with an adsorption energy
cluster, anchored at an oxygen vacancy site, the preferred
adsorption geometry features CO bound to the Au atom
furthest from the vacancy, and with a somewhat lower
adsorption energy
that the Au atom in question has a lower positive charge than
that
negatively charged single Au adatoms found anchored into
oxygen vacancies are again reported as essentially inert
towards CO adsorption. 74
Alternative pathways for the WGS reaction on CeO 2 {111}
have been investigated by Chen et al., 95 working with both a
Au 3 cluster anchored at a cerium vacancy and with a Au 10
cluster located on the stoichiometric surface (GGA + U,
U eff = 5 eV). They consider first a ‘‘redox’’ mechanism, in
which H 2 O dissociates stepwise at an oxygen vacancy site
resulting finally in filling
creation
then desorb from the cluster, whilst CO is proposed to be
oxidised by an O atom from the lattice, thus regenerating an
oxygen vacancy adjacent to the cluster. Details
oxidation step itself are not reported, as the authors focus
instead upon the OH dissociation step, which they believe to
be kinetically limiting. To avoid the necessity for OH dissociation
involving only the oxide substrate or the
Chen et al. 95 secondly consider a ‘‘formate’’ mechanism, in
which CO adsorbed on the cluster first abstracts H from OH
adsorbed at an oxide oxygen vacancy, then reacts with the
remaining O atom. The result is once again to fill the vacancy,
but this time by creating a formate moiety adsorbed adjacent
to the cluster; this in turn can decompose via various routes to
produce gas-phase CO 2 and H 2 . The calculated activation
energy
Fig. 7 Reaction mechanism for CO oxidation at Au adsorbed on
stoichiometric CeO 2 {111}. After initial adsorption
spillover step leads to a metastable configuration in which the molecule
binds not only to Au but also to a lattice O atom. In the
subsequent oxidation step, this lattice O atom forms part
the departing CO 2 molecule, leaving an O vacancy into which the
Au atom migrates. Reprinted with permission from Camellone and
Fabris. 74 Copyright (2009), American Chemical Society.
those calculated for OH dissociation in the ‘‘redox’’ pathway.
The authors conclude that both pathways are limited by the
need to refill oxygen vacancies, since their view is that the
substrate is the proximal source
step. 95 This is a fundamental difference from the pathway
proposed by Liu et al. 35 in which OH adsorbed on the cluster
supplied the necessary oxygen atom (without itself dissociating
prior to CO oxidation) and the substrate was not directly
involved other than to induce a positive charge state on the
Camellone and Fabris, 74 meanwhile, have proposed a
detailed mechanism for CO oxidation at a single Au adatom
on the stoichiometric surface (see Fig. 7). Such a mechanism
could constitute the CO oxidation step within the ‘‘redox’’
WGS pathway proposed by Chen et al., 95 or could indeed
stand alone in a process
After initial adsorption
molecule rotates towards the surface in a ‘‘spillover’’ step,
surmounting an activation barrier
eventually a metastable state in which the molecule bonds not
only to the Au adatom but also to one
atoms. The conversion to this metastable state is endothermic
by 0.24 eV, and subsequent extraction
atom to form desorbing CO 2 requires an activation energy
only another 0.24 eV. The Au adatom left behind by the
departing CO 2 molecule migrates into the nascent oxygen
vacancy during this last step. As a means
therefore, this process is inherently self-limiting, since further
CO cannot adsorb on Au located in such a site. The authors
suggest, however, that clusters
spillover to occur whilst being relatively more resistant to
deactivation. 74 Such a situation might, for instance, allow
sufficient time for the vacancy to be refilled, either directly
by dissociation
adsorption and dissociation
‘‘formate’’ pathways
In addition, Camellone and Fabris 74 report on a highly
exothermic (by 3.24 eV) and barrierless oxidation
CO 2 by lattice oxygen when interacting with substitutional Au
located in a cerium vacancy (see Fig. 8). It is suggested that
molecular O 2 can then adsorb in the oxygen vacancy created
30 Phys. Chem. Chem. Phys., 2011, 13, 22–33 This journal is c the Owner Societies 2011
systems, resolving many
have stimulated so much active debate.
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Fig. 8 Reaction mechanism for CO oxidation at Au substituted for
Ce on CeO 2 {111}. Step A involves abstraction
forming gas-phase CO 2 . Step B covers the adsorption
into the O vacancy created in the previous step, including thermoneutral
in situ rearrangement. Step C involves abstraction
the adsorbed O 2 molecule by CO, forming gas-phase CO 2 . The surface
at the end
Energy is in eV. Reprinted with permission from Camellone and
Fabris. 74 Copyright (2009), American Chemical Society.
by this first oxidation step, with an adsorption energy
1.18 eV, and that a further CO molecule can then abstract
an oxygen atom from this molecule in a second oxidation step
leading to CO 2 (exothermic by 2.76 eV and again barrierless).
The final state
the catalytic cycle is closed, with an overall release
3.59 eV per CO 2 molecule formed (including the contribution
from the O 2 adsorption energy). These results show substitutional
oxidation, although it remains uncertain whether such sites
typically exist in substantial concentration under realistic
reaction conditions.
8. Conclusions
In this brief perspective article we have discussed some
recent theoretical studies
ceria. In view
have
found within the wide literature on this topic. Inevitably, the
views we have put forward reflect primarily our own accumulated
experience
than a settled consensus accepted by all workers in the field.
We hope, however, that the current review will serve to point
readers in the direction
therein, which will reveal both the great progress that has
recently been made (for example in predicting realistic adsorption
geometries for small
for important catalytic reaction pathways, and the role
different vacancies in modulating the properties
the significant work that still remains to be done. Indeed, the
work carried out to date in this area has not been free from
controversies. Mainly these have focussed upon discussions
over what might be the best value
implications
and energetics. Such discussions arise because, as is widely
recognised, DFT + U is merely an ad hoc pragmatic approach
to a pr
useful approach we currently have available in the light
contemporary computational resources. We hope, however,
that more rigorous approaches will soon be applied to these
Acknowledgements
We warmly thank Ricardo Grau-Crespo and Franscesc Illas
for constructive criticism on a draft version
S.J.J. is grateful to The Royal Society for a University
Research Fellowship; C.Z. thanks the Isaac Newton Trust
for post-doctoral funding; and A.M.’s work is supported by
the EURYI scheme (www.esf.org/euryi), EPSRC and the
European Research Council.
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98 The charge on the atoms is typically estimated in such calculations
with a scheme such as Mulliken or Bader charge analysis.
99 In order to avoid problematic oscillations in the approach to selfconsistency,
it is standard practice in DFT to mix the electron
density calculated at each new iteration with some contribution from
previous iterations, prior to using this in formulating the potential to
be employed in calculating the next iteration. In essence, the work
Liu et al. 35 ‘‘switched
(i.e. those corresponding to large reciprocal lattice vectors and/or
those whose magnitudes varied dramatically from one iteration to
the next, the latter criterion being continually reassessed dynamically
during the course
localised behaviour for the f electrons, whilst still benefitting from
improved convergence properties for the s, p anddelectrons.
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