Theory of gold on ceria - Department of Chemistry - UCL

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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

COVER ARTICLE

Jenkins et al.

ong>Theoryong> ong>ofong> ong>goldong> on ceria

1463-9076(2011)13:1;1-T


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PERSPECTIVE

ong>Theoryong> ong>ofong> ong>goldong> on ceria

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 ong>ofong> ceria-supported ong>goldong> clusters as catalysts ong>ofong> the future for important

industrial processes, such as the water gas shift reaction, has prompted a flurry ong>ofong> activity aimed

at understanding the molecular-level details ong>ofong> their operation. Much ong>ofong> this activity has focused

on experimental and theoretical studies ong>ofong> the structure ong>ofong> perfect and defective ceria surfaces,

with and without ong>goldong> clusters ong>ofong> various sizes. The complicated electronic structure ong>ofong> ceria,

particularly in its reduced form, means that at present it is highly challenging to carry out

accurate electronic structure simulations ong>ofong> such systems. To overcome the challenges, the

majority ong>ofong> recent theoretical studies have adopted a pragmatic and ong>ofong>ten controversial approach,

applying the so-called DFT + U technique. Here we will briefly discuss some recent studies ong>ofong>

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 ong>ofong> all bulk metals, ong>goldong> would, until

relatively recently, have seemed an odd choice ong>ofong> material to

investigate for its potential as a catalyst. Since the seminal

work ong>ofong> Haruta, 1 however, it has become clear that ong>goldong>

a London Centre for Nanotechnology and Department ong>ofong> Chemistry,

University College London, London WC1H 0AH

b Department ong>ofong> Chemistry, University ong>ofong> Cambridge, Lensfield Road,

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 ong>ofong> application. 2–19

Today, research into catalysis by ong>goldong> is a thriving field,

driven not only by the economic attractions ong>ofong> the material

(historically one ong>ofong> the more abundant and cheaper ong>ofong> the

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 ong>ofong>

nanoparticulate ong>goldong>, including those based on structural

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 ong>Theoryong> Department.

Angelos Michaelides In 2006 he moved to UCL and

became Prong>ofong>essor in 2009.

Angelos’ current research (www.chem.ucl.ac.uk/ice) involves

the application and development ong>ofong> electronic structure methods

to study catalytic and environmental interfaces.

Stephen Jenkins studied Theoretical

Physics at the University

ong>ofong> Exeter, completing his

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 ong>ofong> the

Cambridge Surface Chemistry

group. His current research (www-jenkins.ch.cam.ac.uk)

includes the fundamentals ong>ofong> adsorption and catalysis, surface

structure and chirality, and the surface and interface properties

ong>ofong> spintronic materials.

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 ong>ofong> the particle/support interaction in

this system, and its effect on catalytic activity. 35–41 In this short

perspective article, we aim to provide a selective but

representative overview ong>ofong> progress in this direction over

recent years, highlighting not only the key areas in which

consensus appears to be emerging, but also what we believe to

be some ong>ofong> the most pertinent open questions that remain.

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Fig. 1 Top: Schematic representations ong>ofong> the stoichiometric (left) and

reduced (right) CeO 2 {111} surface. White atoms are cerium, red atoms

oxygen, and the oxygen vacancy is circled. Bottom: Electronic structure

ong>ofong> the stoichiometric CeO 2 {111} surface (left) and the reduced

surface (right) with occupied states shaded and unoccupied states

unshaded. The density ong>ofong> states for the reduced surface is shown

spin-resolved. The Fermi levels are set at zero and the units ong>ofong> the

energy (y) axis are in eV.

effects (the presence ong>ofong> step and kink sites), on electronic

effects (the presence ong>ofong> non-metallic and/or ionic sites), and

on support effects (either through the stabilisation ong>ofong> unusual

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 ong>ofong> the more exotic materials considered as a possible

support for nanoparticulate ong>goldong> is cerium dioxide

(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 ong>ofong> oxygen vacancies within

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 ong>ofong> two Ce 3+ ions in sites close to (though not

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-ong>ofong>f below the unoccupied f states (see Fig. 1).

A variety ong>ofong> experimental studies has provided evidence to

suggest that ong>goldong> nanoparticles supported on ceria may be ong>ofong>

2. Theoretical approaches

Electronic structure simulations ong>ofong> nanoparticles on oxide

surfaces are challenging for a number ong>ofong> reasons. First, there

is the inevitable difficulty ong>ofong> describing finite clusters attached

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 ong>ofong> identifying a suitable electronic structure

method with the requisite accuracy to describe the properties

ong>ofong> interest. Of the many electronic structure techniques that

have been developed, density functional theory (DFT) is the

most popular and robust theoretical approach currently

available for solving the electronic structures ong>ofong> solid surfaces.

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 ong>ofong>

well-known deficiencies. The one most relevant to the present

topic ong>ofong> ong>goldong> on ceria is an inability to correctly treat the

strongly correlated nature ong>ofong> the cerium f electrons.

The problem ong>ofong> strongly correlated electrons is easily

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

ong>ofong> complex dynamical phenomena. In most situations, this

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, ong>ofong>

course, for f orbitals in the cerium atom) the Coulomb

repulsion is sufficient to provide a strong disincentive towards

instantaneous double occupancy ong>ofong> that orbital. That is, the

probability ong>ofong> a specific electron being found in such an orbital

at any given moment is strongly modified by whether another

electron is or is not already there at the time: the motion ong>ofong>

electrons then becomes ‘‘strongly correlated’’. Effects ong>ofong> this

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 ong>ofong> such a situation is

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 ong>ofong> highly

localised orbitals. In doing so, one steps outside the bounds

ong>ofong> ‘‘pure’’ DFT, but experience shows that the results ong>ofong>

DFT + U calculations can be considered reliable, so long as

the value ong>ofong> U is appropriately chosen. 97 To further complicate

matters, reports in the literature ong>ofong>ten cite an effective

parameter, U eff , defined as the difference between the spherically

averaged value ong>ofong> U and the screened exchange interaction

parameter, J. In addition, the Hubbard correction is

typically applied only to a subset ong>ofong> orbitals (i.e. the most

strongly localised ones) which in this case corresponds to the

Ce 4f electrons.

The issue ong>ofong> choosing the value ong>ofong> U eff thus assumes

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 ong>ofong>

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 ong>ofong> GGA functional used, which in the present context

has tended to be ong>ofong> either the PW91 or the PBE variety. On the

basis ong>ofong> studies for bulk CeO 2 and bulk Ce 2 O 50–53 3, various

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 ong>ofong> these conclusions may safely be carried over to

surface calculations, however, has proved to be a point ong>ofong>

significant contention, as will be seen below. Moreover, it has

been pointed out (e.g. ref. 52) that there probably exists no

single value ong>ofong> U eff that is optimal for calculation ong>ofong> all material

properties, which is to say that a value ong>ofong> U eff that yields

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 ong>ofong> the clean ceria surface with and

without defects

The most stable surface ong>ofong> ceria is the CeO 2 {111} facet, 57–60

and it is this that has been the subject ong>ofong> most study to date.

This surface exhibits three-fold rotational symmetry and may

be thought ong>ofong> in terms ong>ofong> stacked O–Ce–O trilayers (Fig. 1).

Removal ong>ofong> a single oxygen atom at the surface leaves three

undercoordinated cerium atoms to accommodate the two

resulting excess electrons (3Ce 4+ - 2Ce 3+ + Ce 4+ ). An

early confirmation ong>ofong> the necessity to account for strong

correlation effects in any theoretical assault on this system

may, however, be gleaned from the fact that standard DFT

calculations incorrectly predict delocalisation ong>ofong> these excess

electrons across all three undercoordinated cerium atoms

(3Ce 4+ - 3Ce 3.33+ ). Correct localisation is obtained when

U eff values ong>ofong> around 5 eV are employed. 21,56–58,61,62 The

energy cost for removal ong>ofong> an oxygen atom (i.e. creation ong>ofong> a

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 ong>ofong> a cerium vacancy has been calculated in the

same work to require an energy ong>ofong> 4.67 eV.

Removal ong>ofong> a single subsurface oxygen atom leads to an

electronic structure almost indistinguishable from that ong>ofong> a

single surface oxygen vacancy. 58,62,63 Their energy difference is

on the order ong>ofong> 0.1 eV, which is very small compared to

the vacancy formation energy ong>ofong> well over 2.0 eV. These

theoretical conclusions are in good agreement with the elegant

high-resolution scanning tunneling microscopy work ong>ofong> Esch

et al., 64 which showed that the two types ong>ofong> defect (i.e. surface

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 ong>ofong> vacancy clusters.

A correlation between the coordination number ong>ofong> each Ce 3+

ion and the energy ong>ofong> its f states was identified: specifically, the

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 ong>ofong> the vacancy clusters. However, Zhang et al. 62

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 ong>ofong> Ce 3+ ions and their

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 ong>ofong> Ce ions leads to displacements

ong>ofong> neighboring O atoms, such electronic configurations

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 ong>ofong> further study is the mobility ong>ofong>

oxygen vacancies. Experimentally, whilst Namai et al.

reported the defect mobility at room temperature, 67,68

Esch et al. 64 suggested that the diffusion ong>ofong> oxygen vacancies

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 ong>ofong> B0.5–1.1 eV.

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 ong>ofong> 0.53 eV. Substituting the

calculated barrier in the classical transition-state theory

expression yields a rate ong>ofong> less than 10 8 ps 1 at 300 K (assuming

a standard pre-exponential factor ong>ofong> 10 13 ), which suggests very

low mobility for the vacancy at room temperature.

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4. Gold adatoms on stoichiometric ceria surfaces

The first theoretical calculation to address the adsorption ong>ofong>

ong>goldong> on ceria was that ong>ofong> Liu et al., 35 in which single adatoms

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 ong>ofong> ong>goldong> adatoms could be

prong>ofong>oundly altered by their local environment. On the

stoichiometric surface, the calculations indicated that the 6s

orbital ong>ofong> the ong>goldong> atom became depopulated in favour ong>ofong> an

adjacent cerium atom upon adsorption (Ce 4+ - Ce 3+ ); the

adatom itself acquired a net positive charge ong>ofong> +0.35|e| 98

(see Fig. 2) and was found to retain no net spin, in sharp

contrast to an isolated ong>goldong> atom for which the 6s orbital hosts

a single unpaired spin.

It is worth mentioning that these early calculations for ong>goldong>

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 ong>ofong> strong correlation.

In fact, an alternative method ong>ofong> achieving localisation ong>ofong>

f electrons was employed, via a technical adjustment to the

self-consistency procedure adopted during iterative solution ong>ofong>

the Kohn–Sham equations ong>ofong> DFT, perhaps best described as

‘‘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 ong>ofong> parameters was required

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 ong>ofong> the ‘‘pruned density mixing’’ approach. For

Fig. 2 Electronic structure ong>ofong> a single Au adatom on the stoichiometric

CeO 2 {111} surface (atop site). In (a) the top panel shows the

density ong>ofong> states (DOS) for the clean surface, similar to the bottom left

panel ong>ofong> Fig. 1. The lower panel in (a) shows the spin-polarised DOS

that arises from adsorption ong>ofong> Au in an atop site, highlighting the

existence ong>ofong> a single occupied f-orbital (occ-f). In (b) the blue isosurface

shows net spin associated with this occupied f-orbital, localised on one

ong>ofong> the Ce ions neighbouring the Au adatom. Reprinted with permission

from Liu et al. 35 Copyright (2005), American Physical Society.

Fig. 3 Electronic structure ong>ofong> a single Au adatom on the stoichiometric

CeO 2 {111} surface (bridge site). In the left panel, the total

density ong>ofong> states (DOS) and atom-resolved projected density ong>ofong> states

(PDOS) ong>ofong> the Au adsorbed on the bridge site, the latter ong>ofong> which are

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 ong>ofong> the spin

density (blue areas) ong>ofong> the system. Reprinted with permission from

Zhang et al. 55 Copyright (2008), American Chemical Society.

those reasons alone, the present authors have adopted the

GGA + U methodology in all ong>ofong> their joint publications on

this system.

Our recent GGA + U (U eff = 5 eV) results 55 for individual

ong>goldong> adatoms on the CeO 2 {111} surface are, indeed, in

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 ong>ofong> the ong>goldong> 6s orbital was found to be located

not on the nearest cerium atom, but instead upon the third

nearest 55 (see Fig. 3). A very similar configuration (both in

terms ong>ofong> energy and electronic structure) was reported

subsequently by Herna´ndez et al., 73 using a near-identical

computational set-up, although they additionally point out

the existence ong>ofong> multiple, slightly less stable, electronic local

minima associated with some ong>ofong> the adsorption sites they

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 ong>ofong> other work

on the clean reduced surface 57,62 it is questionable whether the

relatively low value ong>ofong> U eff used in the GGA + U calculations

will correctly reproduce the localisation ong>ofong> charge on cerium f

orbitals. Certainly, the results for ong>goldong> adsorption presented

by Castellani et al. 75 are in marked disagreement with those ong>ofong>

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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 ong>ofong> the

adatom; they conclude that it sits atop an oxygen atom and

remains essentially neutral. Use ong>ofong> the same mixed methodology

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 ong>ofong> both CeO 2 and Ce 2 O 3 , whereas a

better representation ong>ofong> CeO 2 alone may be achieved with

higher U eff values. Furthermore, the lower lattice constant

achieved through use ong>ofong> LDA + U in the structural calculation

would, we believe, tend to favour unphysical delocalisation

ong>ofong> charge between neighbouring cerium atoms, owing to

their closer proximity. Alternatively, one might say that whilst

charge localisation is most strongly controlled by the choice ong>ofong>

U eff , an important secondary effect arises due to the influence

ong>ofong> strain (relative to the prevailing calculated lattice constant)

on the stability ong>ofong> the large Ce 3+ cation versus the smaller

Ce 4+ cation (i.e. compressive strain disfavours the reduction

ong>ofong> individual ions, Ce 4+ - Ce 3+ , implied by localisation). 77 It

should nevertheless be granted, ong>ofong> course, that the lower lattice

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 ong>goldong> adsorbed atop an oxygen atom,

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 ong>ofong>

charge transfer, since metastable solutions with some degree ong>ofong>

charge transfer lie within a few tens ong>ofong> meV from the ground

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

ong>ofong> charge amongst cerium f orbitals, whereas those

obtained at larger lattice constants do not.

Out ong>ofong> interest, we have now performed GGA + U

(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 ong>ofong> charge amongst three cerium

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 ong>ofong> the lower lattice

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 ong>goldong> adatom to a single cerium atom, as described by

Zhang et al., 55 Hernández et al., 73 Camellone and Fabris, 74 and

Branda et al. 76

As a final comment on the subject ong>ofong> adatom adsorption on

the stoichiometric surface, we note that Branda et al. 78 report

the results ong>ofong> hybrid functional (HSE 79 ) calculations

(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 ong>ofong> problems. Indeed, as Da Silva

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 ong>ofong> the electronic properties (particularly band

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 ong>ofong> ong>goldong> adsorption on stoichiometric

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 ong>goldong> atom on the

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 ong>ofong> Branda et al., 78 whereby

‘‘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 — —

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catalytically relevant conditions. Certainly the adsorption

energy associated with depositing single ong>goldong> adatoms into

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 ong>ofong> Chen et al. 84

appears accurately to represent the structure and energetics

ong>ofong> the ong>goldong> adatom in the oxygen vacancy site, but overstates

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 ong>ofong> 1.86 eV reported

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 ong>goldong> atom adsorbed on

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 ong>ofong> a single Au adatom adsorbed into an O

vacancy on the CeO 2 {111} surface. In (a) the left panel shows

schematically the structure and the formal charges ong>ofong> atoms surrounding

the bare vacancy, while the right panel shows the density ong>ofong> states

(DOS) projected onto the f-orbitals ong>ofong> the two Ce 3+ ions. In (b) the left

panel shows the structure and formal charges after adsorption ong>ofong> Au

into the vacancy site, while the right panel shows the DOS projected

onto the f-orbitals ong>ofong> the single remaining Ce 3+ ion and the s- and

d-orbitals ong>ofong> the Au adatom. Reprinted with permission from

Hernández et al. 73 Copyright (2009), Royal Society ong>ofong> Chemistry.

calculations. All works that address explicitly the calculated

electronic structure, 55,73,74 however, agree with the original

finding ong>ofong> Liu et al. 35 that the direction ong>ofong> charge transfer is

reversed relative to adsorption on the stoichiometric surface;

one ong>ofong> the two reduced cerium atoms associated with the oxygen

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 ong>ofong> 0.60|e| due to filling ong>ofong> the 6s orbital

(see Table 2 and Fig. 4).

An alternative scenario involves the adsorption ong>ofong> ong>goldong> into

cerium vacancies, the energetics ong>ofong> which were first considered

by Hu and co-workers 84,85 who report an extremely high

adsorption energy ong>ofong> 5.65 eV in this site. Subsequent work

by Zhang et al. 55 confirms a similarly high adsorption energy

(5.94 eV) and adds the observation that the substitutional ong>goldong>

atom gains a very large positive charge ong>ofong> +1.23|e|. Camellone

and Fabris 74 report an adsorption energy ong>ofong> 5.68 eV for such

a site. These high adsorption energies do not, however,

necessarily imply that cerium vacancies will dominate the

adsorption properties ong>ofong> ong>goldong>, since the creation ong>ofong> a cerium

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 ong>ofong>

ong>goldong> adsorption, allowing both oxygen and cerium vacancies

to compete with the stoichiometric surface for ong>goldong> adatoms.

As mentioned in the section dealing with clean surfaces above,

the formation energy for a single cerium vacancy (4.67 eV) far

exceeds that ong>ofong> a single oxygen vacancy (2.23 eV) when

calculated within the GGA + U (U eff = 5 eV) methodology. 63

Application ong>ofong> thermodynamic arguments then leads to the

conclusion that the free energy ong>ofong> an oxygen vacancy is much

less than that ong>ofong> a cerium vacancy, under conditions similar to

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 ong>ofong> the oxygen

vacancy is comparable with that ong>ofong> the stoichiometric surface

in the relevant range, whereas the cerium vacancy is unstable

by a margin ong>ofong> around 8 eV. Even composite defects including

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 ong>ofong> ong>goldong> within the model makes only a quantitative

difference to the outcome under WGS conditions. 63 Coupling

the creation ong>ofong> a cerium vacancy with ong>goldong> adsorption into the

vacant site is strongly disfavoured, from a free energy

perspective, by around 7 eV relative to adsorption ong>ofong> ong>goldong>

on the stoichiometric surface. And once again, composite

defects involving both cerium and oxygen vacancies together

are also disfavoured. Adsorption ong>ofong> ong>goldong> into oxygen

vacancies is, however, still strongly favoured over adsorption

onto the stoichiometric surface, even when the cost ong>ofong> creating

the oxygen vacancy is included within the free energy.

In a rare investigation ong>ofong> the less stable {110} and {100}

surfaces ong>ofong> CeO 2 , Nolan et al. 86 considered the effect ong>ofong>

substitutional ong>goldong> on the formation ong>ofong> oxygen vacancies.

They found that occupancy ong>ofong> a Ce site with Au rendered

nearby lattice O thermodynamically unstable, implying that

substitutional ong>goldong> would almost inevitably be accompanied

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by an oxygen vacancy under near-equilibrium conditions. In

effect, therefore, these results indicate that substitution ong>ofong> an

isolated Au atom into a Ce vacancy is unstable relative to

adsorption ong>ofong> Au into a composite defect comprising both Ce

and O vacancy sites. Furthermore, the cost ong>ofong> creating the Ce

vacancy in the first place was not included in the analysis, so

the likely concentration ong>ofong> substitutional Au defects cannot be

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, ong>ofong>

course, tend to favour cerium vacancies over oxygen vacancies,

so under such circumstances it may be that substitutional

ong>goldong> becomes important.

In the case ong>ofong> Au substituting Ce, there is another dimension

ong>ofong> complexity worthy ong>ofong> our attention. Substitution ong>ofong> Au,

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 ong>ofong> several equivalent oxygen sites surrounding a

metal ion defect in oxides, the hole-lattice coupling ong>ofong>ten

favours hole localization at a single oxygen, and thus breaks

the space group symmetry. This poses a challenge in theoretical

treatments, as standard DFT ong>ofong>ten fails to predict the correct

hole localization and the associated lattice distortion. 88–90 The

origin ong>ofong> this problem has been tracked back to the inability ong>ofong>

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 ong>ofong> ceria-based systems ong>ofong>ten treat only the

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 ong>ofong> surface defect worthy ong>ofong> serious

consideration is to be found in the form ong>ofong> step sites, but

these have been the subject ong>ofong> comparatively little study to

date. To our knowledge, only Castellani et al. 75 have investigated

the binding ong>ofong> Au adatoms at step sites, working with a

model structure incorporating both convex and concave step

morphology. In most ong>ofong> the adsorption sites considered, these

authors find adsorption energies in the range 0.52–0.69 eV,

with a trivial degree ong>ofong> charge transfer between surface and

adsorbate. Although such results would seem distinctive

relative to the findings on planar surfaces reported by the

majority ong>ofong> recent works 35,55,73,74 it should, however, be noted

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 ong>ofong>

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

ong>ofong> 2.36 eV reported by Castellani et al., 75 accompanied by a

charge transfer that leaves the Au adatom with a significant

positive charge ong>ofong> +0.32|e|.

6. Gold clusters on ceria

Although a great deal ong>ofong> attention has been lavished on the

adsorption ong>ofong> single ong>goldong> adatoms on ceria surfaces

(see above) it is ong>ofong> course essential to ask whether these

isolated entities are likely to be plentiful under reaction

conditions. In general, we should think in terms ong>ofong> ong>goldong>

clusters, whose size distribution will depend critically upon

both thermodynamic and kinetic aspects ong>ofong> the surface

preparation. Since the adsorption energies reported for ong>goldong>

on the stoichiometric and reduced surfaces ong>ofong> ceria fall well

below the calculated cohesive energy ong>ofong> bulk ong>goldong>, it is expected

that high temperatures will allow sintering, ultimately resulting

in relatively large ong>goldong> particles. Low temperature preparation,

in contrast, may kinetically stabilise small particles, and this

may be further accentuated by low ong>goldong> loading.

The earliest calculations to address ong>goldong> clusters on ceria

were those ong>ofong> Liu et al. 35 on CeO 2 {111}, where up to four

adatoms were considered (i.e. Au 1 ,Au 2 ,Au 3 and Au 4 clusters).

The first ong>ofong> these adatoms was assumed to occupy an oxygen

vacancy site, and the others to progressively occupy adjacent

sites lying nearly atop oxygen atoms. The adsorption energy

for each additional ong>goldong> atom was in the range 1.84–2.45 eV,

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 ong>ofong> adsorbed

ong>goldong> atoms exceeded the number ong>ofong> oxygen vacancies, clusters

would grow preferentially around these ong>goldong>-filled vacancies,

rather than nucleating elsewhere on patches ong>ofong> stoichiometric

surface. Moreover, although the first ong>goldong> atom in each cluster

was found to be negatively charged, consistent with its occupation

ong>ofong> an oxygen vacancy site, the additional ong>goldong> atoms all

achieved a net positive charge, in the range +0.10–0.19|e|,

somewhat less than that associated with an isolated ong>goldong>

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 ong>ofong> assumed shape onto the stoichiometric surface,

performing molecular dynamics as a form ong>ofong> simulated

annealing, and then re-optimising; the stability ong>ofong> this cluster

against others ong>ofong> differing size and general shape was, however,

not discussed. 95

Gold clusters ong>ofong> up to 11 atoms were studied more systematically

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 ong>ofong> clusters, one ong>goldong> atom at a time, optimising each

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 ong>goldong> atoms in the first layer ong>ofong> the cluster

displayed net positive charges averaging +0.17|e| per atom;

three further ong>goldong> atoms in the second layer ong>ofong> the cluster

showed a net negative charge averaging 0.03|e|, and the

single ong>goldong> atom in the third layer ong>ofong> the cluster had a net

negative charge ong>ofong> 0.12|e|. These results strongly suggest that

the ong>goldong> layer in immediate contact with the ceria surface will

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 ong>ofong> the

Au 7 case. For the larger clusters, Au 10 and Au 11 , it is possible

to discern the beginnings ong>ofong> face-centred cubic (fcc) and

hexagonal close-packed (hcp) stacking patterns, and it is

notable that these have very similar energies; the preference

for fcc stacking in bulk ong>goldong> must emerge at rather larger

cluster sizes. This observation raises the fascinating prospect

that the smallest ong>goldong> clusters (we speculate that this means

those having fewer than about 35 atoms) may exhibit fcc/hcp

polymorphism. This in turn may have catalytic consequences,

in terms ong>ofong> the number and type ong>ofong> active step and kink sites

exposed by the clusters. We believe that state-ong>ofong>-the-art

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 ong>ofong> Zhang et al. 96 also confirmed that unusual

electronic properties were retained even for the largest clusters

considered. Specifically, although the net negative charge

residing on the ong>goldong> atom sitting directly in the vacancy site

was found typically to be lessened by the addition ong>ofong> more

ong>goldong> neighbours, the net positive charge found on other ong>goldong>

atoms in direct contact with the oxide remained high. In the

hcp-stacked Au 11 cluster, for example, the ong>goldong> atom located

directly on top ong>ofong> the central oxygen vacancy retained a net

negative charge ong>ofong> 0.03|e|(cf. 0.62|e| for a single ong>goldong> atom),

7. Reaction mechanisms

The first theoretical discussion ong>ofong> a reaction occurring on a

ong>goldong> particle at a ceria surface addressed the WGS process

(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 ong>ofong> CO onto

one ong>ofong> the positively charged Au atoms clustered around the

negative one that sits in the vacancy site itself, with an

adsorption energy ong>ofong> 1.22 eV. 35 This immediately highlights

one ong>ofong> the most important consequences ong>ofong> the Au charge

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 ong>ofong> negatively

charged Au located in an oxygen vacancy site, through to

2.37 eV in the case ong>ofong> positively charged Au located atop an

oxygen atom on the stoichiometric surface. The lesser positive

charges found for Au atoms in the basal layer ong>ofong> clusters are thus

likely to provide moderate adsorption energies, ong>ofong> which the

value quoted above for the Au 4 cluster is probably fairly typical.

After adsorption ong>ofong> CO, the next stage in the mechanism

proposed by Liu et al. 35 is partially dissociative adsorption ong>ofong>

H 2 O, calculated to be almost thermoneutral, and with an

activation barrier ong>ofong> 0.59 eV (see Fig. 6). The resulting OH

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

ong>ofong> CO, subsequent steps involve dissociative adsorption ong>ofong> H 2 O,

reaction ong>ofong> the resulting OH moiety with CO to form COOH, loss ong>ofong> H

from COOH to form gas-phase CO 2 , and finally recombinative

desorption ong>ofong> H 2 . Reprinted with permission from Liu et al. 35

Copyright (2005), American Physical Society.

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A barrier ong>ofong> 1.08 eV must then be overcome in order to remove

H from COOH onto the cluster, in an almost thermoneutral

step that releases CO 2 into the gas phase. And finally,

recombination ong>ofong> H adatoms to give gas-phase H 2 requires

input ong>ofong> 0.90 eV. Since the adsorption ong>ofong> an H 2 O molecule

onto the cluster involves only a very small binding energy, it is

far from inevitable that there will a reasonable probability ong>ofong>

each one encountering a CO molecule on the same cluster

during its short adsorbed lifetime; clearly this will depend

sensitively upon the lifetime ong>ofong> adsorbed CO at the ambient

temperature. The observation that the adsorption energy ong>ofong>

CO (1.22 eV) exceeds the highest reaction barrier (1.08 eV) is

therefore highly relevant, implying that a favourable state ong>ofong>

affairs can be achieved through selection ong>ofong> an appropriate

temperature for the reaction, without recourse to prohibitive

pressures. The efficacy ong>ofong> ong>goldong> clusters on ceria for the WGS

reaction is therefore explicitly linked to the unusual charge

state ong>ofong> its constituent atoms. 35

More recent work, by Camellone and Fabris, 74 confirms

through the use ong>ofong> GGA + U (U eff = 4.5 eV) the qualitative

conclusions asserted by Liu et al. 35 via ‘‘pruned density mixing’’

for the dependence ong>ofong> CO adsorption energy on the Au charge

state. Specifically, they report that adsorption ong>ofong> CO onto a

single Au adatom initially located in its favoured bridge site on

the stoichiometric CeO 2 {111} surface results in a spontaneous

relocation ong>ofong> the adatom into a neighbouring site atop an

oxygen atom, with an adsorption energy ong>ofong> 2.48 eV. On a Au 2

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 ong>ofong> 1.60 eV, consistent with the assumption

that the Au atom in question has a lower positive charge than

that ong>ofong> a single adatom on the stoichiometric surface. The

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 ong>ofong> the vacancy with the O atom, and

creation ong>ofong> an H 2 molecule on the cluster. The H 2 molecule can

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 ong>ofong> the CO

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 ong>goldong> cluster,

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 ong>ofong> formate production is, however, even higher than

Fig. 7 Reaction mechanism for CO oxidation at Au adsorbed on

stoichiometric CeO 2 {111}. After initial adsorption ong>ofong> CO on Au, the

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 ong>ofong>

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 ong>ofong> oxygen in the CO oxidation

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

ong>goldong> cluster.

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 ong>ofong> CO oxidation by molecular O 2 .

After initial adsorption ong>ofong> CO (exothermic by 2.48 eV) the

molecule rotates towards the surface in a ‘‘spillover’’ step,

surmounting an activation barrier ong>ofong> 0.86 eV and achieving

eventually a metastable state in which the molecule bonds not

only to the Au adatom but also to one ong>ofong> the lattice oxygen

atoms. The conversion to this metastable state is endothermic

by 0.24 eV, and subsequent extraction ong>ofong> the lattice oxygen

atom to form desorbing CO 2 requires an activation energy ong>ofong>

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 ong>ofong> CO oxidation,

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 ong>ofong> Au atoms might allow

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 ong>ofong> molecular O 2 in some manner, or via the

adsorption and dissociation ong>ofong> H 2 O as part ong>ofong> the ‘‘redox’’ or

‘‘formate’’ pathways ong>ofong> the WGS reaction. 95

In addition, Camellone and Fabris 74 report on a highly

exothermic (by 3.24 eV) and barrierless oxidation ong>ofong> CO to

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 ong>ofong> the intriguing controversies that

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 ong>ofong> lattice O by CO,

forming gas-phase CO 2 . Step B covers the adsorption ong>ofong> molecular O 2

into the O vacancy created in the previous step, including thermoneutral

in situ rearrangement. Step C involves abstraction ong>ofong> O from

the adsorbed O 2 molecule by CO, forming gas-phase CO 2 . The surface

at the end ong>ofong> Step C has returned to its condition at the start ong>ofong> Step A.

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 ong>ofong>

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 ong>ofong> the surface is identical to the initial state, so

the catalytic cycle is closed, with an overall release ong>ofong> around

3.59 eV per CO 2 molecule formed (including the contribution

from the O 2 adsorption energy). These results show substitutional

ong>goldong> in cerium vacancies to be highly active towards CO

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 ong>ofong> the

recent theoretical studies ong>ofong> relevance to ong>goldong> at the surface ong>ofong>

ceria. In view ong>ofong> our aim to highlight only the key issues, we

have ong>ofong> course barely scratched the surface ong>ofong> the details to be

found within the wide literature on this topic. Inevitably, the

views we have put forward reflect primarily our own accumulated

experience ong>ofong> calculations on the ong>goldong>/ceria system, rather

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 ong>ofong> the original works, and references

therein, which will reveal both the great progress that has

recently been made (for example in predicting realistic adsorption

geometries for small ong>goldong> clusters, plausible mechanisms

for important catalytic reaction pathways, and the role ong>ofong>

different vacancies in modulating the properties ong>ofong> ong>goldong>) and

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 ong>ofong> U to use, and the physical

implications ong>ofong> this choice in terms ong>ofong> adsorption structure

and energetics. Such discussions arise because, as is widely

recognised, DFT + U is merely an ad hoc pragmatic approach

to a prong>ofong>ound many-body problem. It is nevertheless the most

useful approach we currently have available in the light ong>ofong>

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 ong>ofong> this work.

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

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it is standard practice in DFT to mix the electron

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previous iterations, prior to using this in formulating the potential to

be employed in calculating the next iteration. In essence, the work ong>ofong>

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those whose magnitudes varied dramatically from one iteration to

the next, the latter criterion being continually reassessed dynamically

during the course ong>ofong> the calculation). The result is to ‘‘lock-in’’

localised behaviour for the f electrons, whilst still benefitting from

improved convergence properties for the s, p anddelectrons.

This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 22–33 33

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