o …surface-science.uni-graz.at/publications/papers/kressess...ing two vanadium atoms per layer and...

Surface Science 555 (2004) 118–134

www.elsevier.com/locate/susc

V2O3(0 0 0 1) surface terminations: a density functional study

G. Kresse a,*, S. Surnev b, J. Schoiswohl b, F.P. Netzer b

a Institut f€ur Materialphysik, Universit€at Wien and Centre for Computational Materials Science, Sensengasse 8, A-1090 Wien, Austriab Institut f€ur Experimentalphysik, Karl-Franzens-Universit€at Graz A-8010 Graz, Austria

Received 1 October 2003; accepted for publication 4 February 2004

Abstract

Density functional calculations are carried out for the (0 0 0 1) surface of V2O3 in the corundum structure. In thermal

equilibrium with the bulk, the dominant surface termination is characterised by vanadyl (VO) groups adsorbed on the

(0 0 0 1) surface. Under increased oxygen pressure, the calculations predict that a pure oxygen termination is stable,

whereas under very oxygen poor conditions the removal of the oxygen from the VO group can result in a stoichiometric

metal termination. The electronic states in the valence band regime, the oxygen and vanadium core-level binding

energies, and the vibrational spectra are calculated for the bulk and the surface by density functional theory and

compared to recent experimental studies.

� 2004 Elsevier B.V. All rights reserved.

Keywords: Density functional calculations; Vanadium oxide; Surface energy; Surface relaxation and reconstruction

1. Introduction

In the last decades, vanadium oxides have at-

tracted great interest, because of their unique

physical and chemical properties. V2O3, in par-

ticular, shows a number of remarkable properties,

among them phase transitions which can be in-

duced by hydrostatic pressure [1], doping with Cr[2,3] or Ti [4], or temperature [5,6]. The descrip-

tion of these phase transitions was and is subject

of intense research [7–13]. Furthermore, vanadium

* Corresponding author. Tel.: +43-1-4277-51402; fax: +43-1-

4277-9514.

E-mail address: [email protected] (G. Kresse).

0039-6028/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.susc.2004.02.009

oxides play an important role in heterogenous

catalysis, where the multi-valency of vanadium–

evidenced by the large number of oxides with

vanadium oxidation states ranging from 2þ (VO)

and 3þ (V2O3) to 5þ (V2O5)––is believed to play a

key role. Presently, little is known about the

microscopic mechanisms underlying the catalytic

properties of these oxides. A major reason for thelack of understanding is that the microscopic

structure of vanadium oxide surfaces is largely

unknown. Only recently attempts have been made

to bridge this gap by studying the structure and

surface morphology of thin oxide films grown on

well characterised oxidic supports (e.g. TiO2) or

metal supports, such as Au(1 1 1) [14,15], Cu(1 0 0)

[16], Cu3Au(1 0 0) [17], Ni(1 1 0) [18,19], Rh(1 1 1)[20], W(1 1 0) [15], and Pd(1 1 1) [21–27]. Although

the major focus of the latter studies were thin and

ed.

mail to: [email protected]

G. Kresse et al. / Surface Science 555 (2004) 118–134 119

ultrathin layers of vanadium oxides, thicker layers

up to several hundred monolayers were studied as

well. In fact, when vanadium oxide is grown on

Pd(1 1 1), the oxide takes on the structure of bulk

corundum V2O3 for a coverage larger than 3–4

monolayers (ML) [21,23,24]. The V2O3 phasegrows epitaxially on the metal substrate in the

form of three-dimensional (3D) islands, as re-

vealed by low energy electron diffraction (LEED)

and scanning tunnelling microscopy (STM) [21,24,

25,28]. High resolution electron energy loss spec-

troscopy (HREELS) suggests that the surface

contains a large number of VO groups, which was

confirmed by density functional theory (DFT)[24]. A recent comprehensive experimental study

using HREELS, X-ray photo emission spectro-

scopy (XPS) and near-edge X-ray adsorption fine

structure (NEXAFS) came to a similar conclusion

[15]. As already mentioned, density functional

calculations also predict that the VO termination

dominates in the thermodynamic regime where

bulk V2O3 is stable [24], but the theoretical cal-culations also indicate that more oxygen rich ter-

minations are feasible under properly chosen

preparation conditions. These terminations were

indeed prepared successfully recently [28].

The major focus of the present work is a detailed

discussion of the termination of bulk corundum

V2O3 in thermal equilibrium with the surrounding

gas phase as determined using density functionalcalculations. Contrary to previous theoretical

studies [29,30], we will not only concentrate on the

ideal surface terminations, which can be created by

cleaving the bulk V2O3 structure between adjacent

layers, but results for the vanadyl (VO) terminated

surface and a VO2 trilayer reconstruction will be

presented as well. The present study relies on gra-

dient corrected density functionals and periodicslab calculations, the details of which are described

in Section 2. The surface phase diagram of the

(0 0 0 1) surface of bulk V2O3 is presented in Section

3.1, and the electronic properties of the four most

important terminations are discussed in Section

3.2. To facilitate comparison with experiment, the

oxygen and vanadium core-level binding energies

and the vibrational frequencies of those four ter-minations are calculated as well and compared to

experiment where possible (Sections 3.2 and 3.3).

We will finish with discussions and conclusions

(Section 4).

2. Methodology

2.1. First-principles calculations

The present first-principles calculations are

based on density-functional theory (see e.g. Refs.

[31,32]) and are carried out using a plane wave

basis set [33,34]. To determine the ground state

structures, the Vienna ab initio simulation package

(VASP) [35,36] is used. The interaction betweenthe ionic cores and valence electrons is described

by the projector augmented wave (PAW) [37]

method in the implementation of Kresse and

Joubert [38]. For vanadium the 3p, 3d and 4s

electrons and for oxygen the 2s and 2p electrons

are treated as valence. The PAW core radii are set

to 1.2 and 0.8 �A for vanadium and oxygen,

respectively. An energy cutoff of 250 eV was cho-sen for all but a few test calculations. Generalised

gradient approximations (GGA) of Wang and

Perdew [39,40], commonly referred to as PW91,

are used throughout this work.

Motivated by the considerations elaborated

below, spin polarisation was not included in the

present calculations, except when noted. A decisive

reason for this choice is that most experimentswere carried out at ambient temperatures at which

V2O3 is a paramagnetic metal and crystallises in

the rhombohedral corundum structure. It is not a

simple matter to account for this structure ade-

quately in DFT, but non-magnetic calculations

using generalised gradient approximations seem to

give an overall reasonable description of this

phase. The inclusion of (the low energy) long rangemagnetic order, on the other hand, yields to an

insulating behaviour and a monoclinic distortion

[5,6,9]. Furthermore, the precise magnetic ordering

is still a subject of research [9,10,13], and the cal-

culations would be complicated, if one had to

consider various magnetic orderings at the surface.

Finally, the energy differences between non-mag-

netic and magnetic calculations are relativelysmall, and we expect them to have only a small

influence on the surface phase diagram.

120 G. Kresse et al. / Surface Science 555 (2004) 118–134

2.2. Bulk V2O3

The structural parameters determined by the

theoretical calculations for rhombohedral V2O3

are summarised in Table 1. In the V2O3 corundumstructure, the oxygen atoms form hexagonal

planes in the (0 0 0 1) direction with three oxygen

atoms per layer in the hexagonal unit cell (com-

pare Fig. 1). Only one structural parameter

determines their position. It is a measure for the

deviation of the hexagonal oxygen layer from

a perfect 2-dimensional hexagonal packing, with

1/3 corresponding to this packing. The vanadiumsub lattice has a honeycomb structure contain-

ing two vanadium atoms per layer and unit cell,

with a slight buckling that is proportional to 2c�

Table 1

Structural parameters of bulk corundum V2O3 as determined exper

various theoretical methods

ux

Exp.a a ¼ 4:94 �A

12c V 0

18e O 0.31220

Exp.b a ¼ 4:951 �A12c V 0

18e O 0.3049

GGA a ¼ 4:820 �A

12c V 0

18e O 0.3278

S-GGAc a ¼ 4:903 �A

12c V 0

18e O 0.3238

S-GGAd a ¼ 4:861 �A12c V 0

18e O 0.3244

LDA a ¼ 4:70 �A

12c V 0

18e O 0.3306

LDA+Ue a ¼ 4:94 �A

12c V 0

18e O 0.3071

The entries in the rows ‘‘12c’’ and ‘‘18e’’ correspond to the Wycoff poaRef. [41].bRef. [42].c Spin-polarised GGA calculations, anti-ferromagnetic (AF) couplid Spin-polarised GGA calculations, ferromagnetic (FM) coupling be PAW LDA+U, U ¼ 3:43, J ¼ 0:93, magnetic ordering as in foo

ðuz � 1=3Þ (exp: 0.40 �A). The reason for the buck-

ling is that one vanadium atom has a vanadium

neighbour in the next V2 layer, whereas the second

vanadium atom has a neighbour in the previous V2

layer (Fig. 1). The GGA as well as the LDA cal-

culations clearly underestimate the buckling andyield a too symmetric position for the oxygen

atoms. Additionally LDA significantly underesti-

mates the volume and the lattice constant a. Forthe structural parameters, the discrepancies are

unusually large for density functional calculations,

which is probably related to the neglect of any

magnetic short range order, strong Coulomb

repulsion between localised electrons and correla-tion effects. When the calculations are carried out

using a long range anti-ferromagnetic order in the

imentally and by present density functional calculations using

uy uz

b ¼ a c ¼ 13:97 �A

0 0.34634

0 0.25000

b ¼ a c ¼ 14:002 �A0 0.34766

0 0.25000

b ¼ a c ¼ 14:37 �A

0 0.34015

0 0.25000

b ¼ a c ¼ 14:183 �A

0 0.34210

0 0.25000

b ¼ a c ¼ 14:37 �A0 0.34042

0 0.25000

b ¼ a c ¼ 14:19 �A

0 0.3391

0 0.25000

b ¼ a c ¼ 13:99 �A

0 0.3489

0 0.25000

sition, the atomic species, and the coordinates in internal units.

ng in the basal plane, ferromagnetic coupling between planes.

etween all V neighbours.

tnote c.

Fig. 1. Model of a five layer thick metal terminated stoichio-

metric V2O3 slab. For the three central layers only sticks rep-

resenting the bonds are shown, whereas a ball and stick model

is used for the surface layers. The rhombus indicates the hex-

agonal unit cell, which contains three oxygen atoms (O3) per

layer.


honeycomb V planes and a FM ordering between

nearest V neighbours of different planes––anordering which is commensurate to the rhombo-

hedral symmetry––a better agreement for the lat-

tice parameters is obtained, but the internal

parameters exhibit a similar discrepancy to experi-

ment as before. In the GGA, however, a ferro-

magnetic coupling between neighbours is even

more stable, with a similar disagreement for the

structural parameters as for non-spin polarisedcalculations. The ferromagnetic order is addition-

ally not compatible to the observed paramagnetic

response, and the FM calculations predict an

insulating ground state. These results indicate that

in DFT spin polarisation does not improve the

description of bulk V2O3, supporting our choice of

a non-spin polarised setup for the surface calcu-

lations.For the structural parameters, substantially

better agreement with experiment can be attained

only by inclusion of an on-site Coulomb repulsion

between electrons, e.g. by a Hubbard U using the

LDA+U method (implementational details can be

found in Refs. [43,44]). The parameters we have

adopted for J and U are roughly identical to the

well accepted values of Ref. [10]. To compensate

for the fact that the PAW spheres are smaller than

the atomic spheres used in Ref. [10], U was in-

creased from 2.9 to 3.4 eV. The LDA+U calcu-

lations predict an insulating ground state in

agreement with Ref. [10], but problematic for the

present application since we seek to describemetallic V2O3. Additionally, application of the

LDA+U method to surface energetics is debat-

able, because U depends on the local oxidation

state of the vanadium atoms, which does change

on the surface as discussed below. A more precise

and proper description of metallic V2O3 would

require to account adequately for electronic cor-

relation effects by e.g. dynamical mean field theory[12], but presently these methods do not allow for

force and stress calculations and are too time

consuming for the surfaces under considerations.

2.3. Slab models

The surface calculations were performed using

generalised gradient corrections and disregardingany magnetic interactions and order, as discussed

in the previous section. They were carried out

using symmetric slabs containing at least seven V2

layers (Fig. 1 shows a five layer slab). The central

vanadium layer and the two neighbouring oxygen

layers were kept frozen in their bulk position. The

stoichiometric surface termination (see Fig. 1) is

obtained by cleaving bulk V2O3 in the mid-planebetween two buckled V atoms. It possesses a single

metal atom above the surface oxygen layer (OS3),

with this V atom located at the usual bulk position

with no vanadium neighbour in the layer S. This

termination will be termed V2O3–V. Other possible

terminations are vanadyl groups, which are mod-

elled by adding one oxygen atom atop the surface

vanadium atom (V2O3–VO), a double metal ter-mination V2O3–V2 and an oxygen termination

(V2O3). To test for convergence with respect to the

slab thickness, several calculations were performed

for nine layer thick slabs, and results agreed usu-

ally within 5 meV per primitive surface cell. Even

for the oxygen rich O3 terminated surface, which

exhibits the largest relaxation, the difference be-

tween seven and nine layer thick slabs was lessthan 10 meV per surface unit cell. The calculations

were performed initially for the primitive surface


unit cell using symmetric slabs. To model recon-

structions, a symmetricffiffiffi3

p�

ffiffiffi3

p� �R30� super-cell

was additionally used. Specifically, the follow-

ing models were considered: starting from the

symmetric primitive V2O3–VO model, affiffiffi3

p�

�ffiffiffi3

pÞR30� super-cell was constructed (containing 3

VO units at both sides of the slab), and then VO

units were removed one by one from both sides of

the slab [V2O3–(VO)x, x ¼ 2=3; 1=3]. Second, oxy-gen atoms were removed from the VO units, to

create a mixed metal/VO termination at the sur-

face [V2O3–Vx(VO)1�x], and, finally, the vanadium

atoms were removed from the surface [V2O3–Vx].

Additionally, oxygen vacancies, adsorption of VOgroups at various other sites, and the structural

model of Niehus et al. [17] were considered but

finally ruled out on energetic grounds. With one

single exception, hydrogen contamination, e.g.

in the form of OH groups, was not considered in

the present work. This is mainly motivated by

the experimental observation, that neither OH

stretch frequencies, nor O-1s core-level bindingenergies characteristic of OH groups were ob-

served under typical UHV preparation conditions

[15,28].

For the primitive surface cell, the k-point sam-pling was performed with a grid of 4 · 4 points in

the surface Brillouin zone. In the irreducible wedge

of the Brillouin zone, this grid corresponds to four

k-points: C, (1/4,0,0), (1/2,0,0) and (1/4,1/4,0) withweights of 1, 6, 3, and 6 respectively. For theffiffiffi

3p

�ffiffiffi3

p� �super-cells, a grid of 4 · 4 k-points was

used as well, although results for 2 · 2 k-pointswere identical to within 5 meV per primitive sur-

face cell. To obtain the final phase diagram, all

calculations were finally repeated for consistency

using theffiffiffi3

p�

ffiffiffi3

p� �super-cell. Overall our tests

(nine layers, less k-points) indicate that the errorsfor individual phases are smaller than 10 meV per

surface unit cell (not including possible errors in-

curred by the local density approximation).

2.4. Core-level binding energies and vibrational

spectra

The core-level energies were calculated includ-ing final state effects using a modified projector-

augmented wave method. In this method, a single

core electron is excited from the core to the va-

lence, by generating a core excited PAW potential

in the course of the ab initio calculations. Screen-

ing by the core electrons is not taken into account

(i.e. the other core electrons are kept frozen in the

configuration for which the PAW potential wasgenerated). Screening by the valence electrons is

included, however. Tests, indicating the reliability

of this approach by comparison with full potential

calculations, will be presented elsewhere [45].

The vibrational spectra of the considered oxide

surfaces were calculated using finite differences.

Each atom in the oxide was displaced by 0.02 �A in

each direction. From this calculation the inter-atomic force constants were determined, and the

mass weighted force constant matrix was diag-

onalised. This yields the vibrational frequencies

and the vibrational eigen-modes of the entire slab.

The intensities of the vibrational loss peaks in the

HREELS spectra were estimated by determining

the derivative of the square of the dipole with re-

spect to each vibrational mode (the dynamic di-pole).

2.5. Thermodynamics

To determine the stability of the surface in

contact with the gas phase simple thermodynamic

arguments are used. The formalism has been ap-

plied to a variety of systems before [23,46–49] andis described in detail in Ref. [49]. Here only a very

brief summary is given.

For thermal equilibrium between the gas phase

and the surface, the thermodynamic quantity of

interest is the surface energy

c ¼ GðT ; p; fnxgÞ

�Xx

nxlxðT ; pxÞ!,

A; ð1Þ

where T and p are the temperature and the pres-

sure, G is the Gibbs free energy of the solid

exposing the surface of interest, nx are the numberof particles x in the solid, and lx and px are the

chemical potentials and the partial pressures of the

respective particles in the reservoirs. In the present

case, the Gibbs free energies are calculated for a

number of reconstructions using finite sized sym-

metric slabs as described in the previous section.


For the determination of the area A, the bottom

and the top side of the slab are counted. Vibra-

tional entropy contributions and enthalpy changes

are neglected, and the Gibbs free energies, GðT ; p;fnxgÞ, are approximated by the energies calculatedby density functional theory EðfnxgÞ. A recent

work indicates that this approximation is suffi-

ciently accurate for the present purpose [49].

Two different species were considered: V and O.

In order to deal with only one extensive thermo-

dynamic variable, the chemical potential of vana-

dium is eliminated assuming that the V and O

particle reservoirs are in thermal equilibrium withthe bulk (if this were not the case, the V2O3 crystal

would either grow or decompose). This requires

that the chemical potentials of V and O satisfy [49]

3lO þ 2lV ¼ EV2O3; ð2Þ

where EV2O3is the energy of a bulk V2O3 unit.

Eliminating lV from the equation for the surface

energy, yields the following expression for the

surface energy c:

c ¼ ðEðfnxgÞ � nVEV2O3=2

� ðnO � 3=2nVÞlOÞ=A: ð3Þ

The energies c are plotted versus the chemical

potential of oxygen lO for each phase, and the

surface with the lowest surface energy at a given

chemical potential is the stable ground statestructure at this potential. In the present work, all

energies and chemical potentials are referenced to

1=2EO2i.e. the energy zero is chosen such that

oxygen molecules have zero energy.

For the chemical potential of oxygen a number

of restrictions apply. If the chemical potential of

oxygen is too large, V2O3 is oxidised to V2O4, and

vice versa, if the chemical potential of oxygen weretoo small, V2O3 would be reduced to VO. There-

fore the reactions

V2O3 þ1

2O2 ! 2VO2 and

V2O3 ! 2VOþ 1

2O2

must be endothermic, which can be expressed as

EV2O3þ lO < 2EVO2

and

EV2O3< 2EVO þ lO

or equivalently:

EV2O3� 2EVO < lO < 2EVO2

� EV2O3;

where the formation energies of the oxides must be

calculated per formula unit. In the present case, weobtain values of )3.44 eV for the lower and )2.74eV for the upper bound. The energy diagram,

however, includes values beyond this regime to

access the structure of the surface under non-

equilibrium conditions. An important point is that

the chemical potential at which bulk V2O3 is stable

corresponds to strongly reducing conditions, i.e.

very high temperatures and low oxygen pressures.A temperature of 800 K and a partial oxygen

pressure of 10�10 mbar, for instance, corresponds

to lO � �1:9 eV, which is significantly larger than

the upper bound of stability ()2.74 eV). It is cer-

tainly possible that density functional theory puts

the stability regime of V2O3 at too small chemical

oxygen potentials, and for vanadium oxides, the

errors might well approach several hundred meV,since semi-local density functionals cannot ac-

count adequately for the strong Coulomb repul-

sion between localised d-electrons, which might

prevail even in metallic V2O3. But even allowing

for such a large error, it is unquestionable that

V2O3 is not the thermodynamically stable phase

under ambient conditions, which is of course in

agreement with the experimental observation thatV2O3 is thermodynamically stable only under

strongly reducing conditions e.g. in ultrahigh

vacuum (not precluding its kinetic stability even at

ambient conditions).

3. Results

3.1. Surface phase diagram and geometry

The central result of the present work is shown

in Fig. 2. We will first concentrate on the resultsfor the primitive surface cell, which correspond to

the thin lines. In the regime, where V2O3 is ther-

modynamically stable, i.e. between )3.44 and

)2.74 eV, there is clearly only a single favourable

termination, and this is the VO type termination

-5 -4 -3 -2 -1µ

O(eV)

-2

-1

0

1

2

E (

eV)

..V-O3V

3O

3

..V2O

3-VO

..V2O

3-V

..V2O

3-(VO)

0.66

..V2O

3-(VO)

0.33

VO V2O

3 VO2

V2O

5

..V2O

3-V

3

V

Fig. 2. Surface energy per primitive surface cell versus chemical

potential of oxygen lO for the (0 0 0 1) surface of rhombohedral

V2O3. Thin lines correspond to calculations for the primitive

surface cell, whereas thick shorter lines correspond to ‘‘recon-

structed’’ cells with a periodicity offfiffiffi3

p�

ffiffiffi3

p� �R30�. The thick

lines between V2O3–V and V2O3–VO correspond to mixed

V2O3–Vx(VO)1�x phases. The stability regime of the bulk oxides

are indicated at the bottom of the graph.


(concentrating on the thin lines only). This is in

complete agreement with the earlier observation

of an intensive V@O stretch mode observed in

HREELS for the thick V2O3 films grown on

Pd(1 1 1) [24,25], and with a recent work of Dupuis

et al. [15]. In STM the VO groups are imaged

under most tunnelling conditions as bright blobswith (1 · 1) periodicity and a rather strong corru-

gation, which is confirmed by the STM simula-

tions (see Fig. 3(b) of Ref. [24] and Fig. 11 of Ref.

[25]). More details on the experimental STM re-

sults are reported in Ref. [28].

The two other relevant terminations are the

metal termination and the O3 termination. The

oxygen rich termination can be stabilised whenoxygen is offered to the surface, whereas the metal

termination requires a strongly reducing environ-

ment. Producing the metal terminated surface by

heating is predicted to be impossible, since a suffi-

ciently reducing environment cannot be obtained

by heating in UHV. A temperature of 1000 K and a

partial oxygen pressure of 10�12 mbar, for instance,

corresponds to lO � �2:6 eV, which is still way offfrom the required chemical potential of )4 eV. This

theoretical prediction agrees with the experimental

observation that reduction of the V2O3–VO ter-

mination to V2O3–V is not possible in UHV by

heating (except electron bombardment) [15]. The

oxygen rich termination, on the other hand, is

stable already for an oxygen chemical potential of)2.0 eV, which is actually realizable under typical

UHV conditions. Nevertheless, it is important to

keep in mind that kinetic limitations are also rele-

vant. The transition from a VO termination to an

O3 termination involves significant barriers, since

the VO groups must be oxidised to V2O3, and the

oxidised groups must attach to existing steps or

form islands on the surface. In any case, oxygenmust be supplied for the oxidation from VO to

V2O3 either by dissociation of oxygen molecules or

by migration of oxygen from the bulk to the sur-

face. This is a complex, possibly activated process,

which is beyond the scope of the present work. The

thermodynamics is however clear and favours the

VO termination, when the surface is in thermal

equilibrium with bulk V2O3, and the O3 termina-tion under typical oxygen rich ambient or even not

too reducing UHV conditions.

A further observation is that the thermody-

namically stable O3 termination is not simply a

continuation of the bulk corundum V2O3 struc-

ture, which would correspond to a � � �V2O3–V2O3–

V2O3 stacking. Instead, a vanadium atom from the

second V2 layer (S-1) pops up into the first surfaceV2 layer (see Fig. 3). The shifted metal atom is the

one with a neighbour in the third vanadium layer

(S-2) and no V neighbour above (S). By migration

into the S layer, one metal–metal dimer bond be-

tween the S-1 and S-2 layers is cleaved and a

stacking sequency of � � �V2O3–V–O3V3O3 is ob-

tained. The first three layers (O3V3O3) exhibit now,

except for a small buckling, a hexagonal arrange-ment. The reason for the increased stability of this

particular reconstruction is most likely its lower

Madelung energy: originally the O3 termination is

profoundly polar and possesses a large surface

dipole moment. The alternative lower energy

reconstruction, however, can be envisaged as an

assembly of the non-polar single V terminated

surface V2O3–V and a non-polar hexagonal VO2

trilayer adsorbed on top of the metal terminated

surface. The stability of this particular hexagonal

Fig. 3. (a) Ideal O3 termination of corundum, and (b) ener-

getically most stable termination.


VO2 trilayer has already been established in pre-

vious work theoretically [23] as well as experi-

mentally [24]. A freestanding monolayer of this

type adopts a lattice constant of 2.87 �A [23,24]. On

bulk V2O3 it is slightly compressed to a lattice

constant of 2.78 �A (theory) and rotated by 30�with the

ffiffiffi3

p�

ffiffiffi3

p� �R30� superstructure fitting

onto the substrate. It is noted that this type of

Table 2

Interlayer distances and buckling DV of the V2O3(0 0 0 1) surface for

� � �V2O3–VO � � �V2O3–V

O–V 1.610

V–OS3 0.754 0.354

OS3–V

Sx 1.130 1.232

VSx–O

S�13 1.220 1.241

OS-13 –VS�1

y 1.193 1.201

VS-1y –OS�2

y 1.200 1.199

DV Sx 0.140 0.109

DV S-1y 0.205 0.189

In the bulk, the distance between the oxygen and vanadium layers is 1.1

and 3 for illustration and labelling.

reconstruction occurs even locally, whenever

vanadium ad-atoms are not present above the

topmost O3 layer.

In Table 2 the distances between the layers and

the buckling in the vanadium layers are collected.

For the most important termination � � �V2O3–VO,the VO bond length is 1.61 �A, and the dimer is

located 0.75 �A above the topmost oxygen layer

(OS3). The O3–V2 interlayer distances exhibit an

oscillatory behaviour, with the first interlayer dis-

tance too short and the second one too large. The

oscillatory behaviour continues into the bulk but

falls off very rapidly. The ideal O3 termination

(labelled � � �V2O3 in Table 2) exhibits a similarbehaviour, with the first interlayer distance sub-

stantially decreased, and the second one increased

by 0.15 �A. The oscillations now fall off slowly into

the bulk. This type of oscillations are common to

oxygen rich polar terminations and allow for a

reduction of the surface dipole moment, since the

layer pairing reduces the net dipole moment of the

surface, in turn reducing the Madelung energy ofthe slab. The determined geometries agree well

with the results of Czekaj et al. [29,30], although

Czekaj et al. applied clusters instead of periodic

slabs. For the V2O3 termination, they found dis-

tances of 0.842 and 1.333 �A for the OS3–V

S2 and V

S2–

OS�13 spacings [29] compared to 0.852 and 1.357 �A

in the present case (note that we specify the dis-

tances with respect to the average position of the Vatoms in one V2 layer). However, details such as

the buckling are not exactly reproduced, which we

relate to finite size effects, that were certainly

present in the previous cluster study.

four terminations (all entries in �A)

� � �V2O3 � � �V–O3V3O3

0.852 1.049

1.357 1.184

1.138 1.443

1.213 1.063

0.143 0.387

0.215 –

97 �A and the buckling in the V layer, DV , is 0.200 �A. See Figs. 1


For the reconstructed O3 termination with the

VO2 trilayer (� � �V–O3V3O3) the distances between

the oxygen and vanadium layers differ also quite

substantially from the bulk. At the surface the tri-

layer adopts a layer distance that is similar to the

layer distance of a free standing trilayer with thesame lattice constant (1.06�A), whereas the distanceVS3–O

S�13 is slightly expanded (1.184 �A). The spac-

ing between the VO2 trilayer and the V atom (OS�13 –

VS�1) is particularly large, since the trilayer is only

relatively weakly bound to the V2O3–V surface.

Finally, for the single metal termination

(� � �V2O3–V), we observe that the V metal atom is

retracted into the surface with a distance of 0.354�A between the metal atom and the top most oxy-

gen layer. Otherwise the layer distances change

only little compared to the bulk. This behaviour is

similar to Al2O3 [48] and was also observed in the

cluster calculations, where the interlayer spacing

for the metal termination were 1.115 and 1.091 �A,fairly close to our values of 1.232 and 1.241 �A. Ourdistances are, however, consistently larger, and thesingle surface V atom sinks much deeper into the

surface than in the cluster study.

In order to explore surfaces with mixed termi-

nations, i.e. a combination of VO ad-groups and

V ad-atoms, and a lower concentration of VO

groups, calculations for affiffiffi3

p�

ffiffiffi3

p� �R30� super-

cell were performed. As already mentioned above,

for each ad-group (or ad-atom) removed above thesurface O3 layer, a V atom from the S-1 layer

moved into the S layer to create the aforemen-

tioned hexagonal VO2 trilayer locally. The energy

of the corresponding phases are shown using thick

lines in Fig. 2. The GGA calculations show that

the VO groups are progressively removed, when

the oxygen pressure increases. This behaviour is at

first sight somewhat counterintuitive, becauseusually one would expect that oxidation increases

the number of adsorbed species on the surface. For

the particular case of V2O3, however, oxidation

has the opposite effect, since the oxygen rich ter-

mination corresponds to a perfect essentially flat

O3 surface, whereas VO groups reduce the local

oxygen content on the surface, as these groups are

under-stoichiometric with respect to V2O3.Furthermore, the GGA calculations predict

that an intermediate coverage of 2/3 ML VO is

energetically so favourable that the full VO ter-

minated surface cannot be attained. This is in

contrast to the experimental STM findings, that

clearly show a (1 · 1) VO termination upon reduc-

tion of the surface in UHV [28]. The reason for the

incorrect stability of this particularffiffiffi3

p�

ffiffiffi3

p� �-

R30�–2VO reconstruction in the DFT calculations

is somewhat difficult to disentangle, but it seems to

originate from an interplay of the structural

changes upon VO adsorption and the lattice mis-

match between the unsupported trilayer (GGA:

a ¼ 2:87 �A) and the underlying corundum lattice

(GGA: a ¼ffiffiffi3

p� 2:78 �A). When the calcula-

tions are performed for the experimental in-planelattice constant of bulk V2O3 (exp: a ¼

ffiffiffi3

p� 2:85

�A), the entirely VO covered surface is found as a

stable phase, and theffiffiffi3

p�

ffiffiffi3

p� �R30�–2VO andffiffiffi

3p

�ffiffiffi3

p� �R30�–1VO phases become intermediate

stable phases at higher oxygen pressures. In this

case agreement with experiment is reasonable,

although the stability regime of theffiffiffi3

p�

ffiffiffi3

p� �-

R30�–2VO phase seems to remain somewhat toolarge. The calculations at the expanded lattice

constant suggest that small errors in the lattice

constants are one reason for the incorrect domi-

nance of the reconstruction. We cannot rule out

that correlation effects and magnetic short range

order also influences the surface phase diagram,

but these effects are beyond the limits of pres-

ent density functionals, as discussed in the Sec-tion 2.2.

At very reducing conditions, finally, one more

phase is calculated to be metastable. It is a hexa-

gonal metallic vanadium over-layer, with three V

atoms per surface unit cell. The distance between

the V atoms is roughly 2.78 �A, which implies that

the structure is characterised by a sizeable V–V

bond strength in the metallic over-layer. Thisphase was included in the search, since it has been

prepared by V evaporation onto a VO covered

V2O3 surface [28]. Alternatively a double metal

termination with two V atoms was also considered

but finally disregarded on energetic grounds (its

phase line lies above 3.0 eV for relevant oxygen

potentials). But even the metallic hexagonal V

over-layer is thermodynamically not stable, since itoccurs only in a regime, where bcc V is already

stable as well. This implies that the metallic over-


layer was only kinetically stable in the experiment.

Its structure is characterised by a distance of 1.23�A between the metal ad-layer and the topmost

oxygen layer. The two vanadium ad-atoms with

neighbours in the surface layer (S) are 0.1 �A higher

than the third vanadium atom without a neighbourbelow. In the experiment a slight apparent height

difference––albeit only 0.02 �A––was also observed

under appropriate tunnelling conditions [28].

At this point it is instructive to compare the

predicted transition temperatures with the experi-

mental findings. Schoiswohl et al. prepared an

oxidised surface with an average vanadyl coverage

of 0.5 ML per surface unit cell [28]. Upon reduc-tion, the structure reverted to the (1 · 1) vanadylterminated surface at a transition temperature of

650 �C in UHV. Assuming a residual oxygen

pressure of 10�15 mbar this transition temperature

corresponds to an oxygen potential of )2.4 eV.

Our predicted transition potential however lies

below )3.5 eV. For the 0.5 ML vanadyl covered

surface, on the other hand, the experimentalpreparation conditions of 500 �C and 10�6 mbar

correspond to a chemical potential of )1.45 eV,

whereas in the GGA the transition between the

V2O3–(VO)0:66 and V2O3–(VO)0:33 structure occurs

at )1.65 eV. Although direct comparison between

theory and experiment is difficult, since theffiffiffi3

p�

ffiffiffi3

p� �R30�–2VO reconstruction incorrectly

dominates the phase diagram, it seems that tran-sitions occur at too negative potentials using the

GGA. Generally, the oxygen rich terminations are

therefore too stable in GGA, or crossly simplified,

in theory oxygen adsorption is too favourable on

the surface. We will come back to this point in the

conclusions.

A final comment concerns the formation of

hydroxyl groups on the surface. As already men-tioned in Section 2.3, no experimental evidence of

OH groups was found for vanadium oxides pre-

pared under UHV conditions. Nevertheless, we

determined the adsorption energy of H2 on the

vanadyl terminated surface, which leads to the

formation of a V–OH group. The calculated

adsorption energy was found to be only 300 meV

per H2 molecule. In combination with the ther-modynamic arguments discussed in Section 2.5

and Refs. [50,51], one finds that under typical

UHV conditions hydroxyl groups can be ruled

out, since the entropy contribution of H2 or H2O

in the gas phase is too large.

3.2. Electronic properties and surface core-level

shifts

For the discussion of the electronic properties

we have to be aware that density functional theory

can only give tentative results for oxides with a

sizeable on-site Coulomb repulsion between elec-

trons [10]. We nevertheless believe that some of the

features discussed below are important for the

interpretation of the experimental results.For the four important terminations of

V2O3(0 0 0 1), the local electronic densities of states

(DOS) are shown in Fig. 4. The layer resolved

DOS was determined by calculating the densities

of states inside the atom centred PAW spheres,

which have a radius of 1.2 and 0.8 �A for V and O,

respectively. Averages over all atoms in one par-

ticular layer were performed. As reference, we willuse the DOS for the S-2 layer of V2O3–VO, which

is virtually identical to bulk V2O3 (thick lines in

Fig. 4(b)). The displayed energy regime is charac-

terised by two regions. Between )8 and )3 eV, theoxygen 2p states dominate the DOS, exhibiting a

sizeable hybridisation with the vanadium states.

The anti-bonding O-2p metal-eg states are located

well above the Fermi-level between 2 and 5 eV andare labelled ‘‘eg’’ (commonly referred to as cubic

eg). They contain a sizeable contribution from O-

2p states. At the Fermi-level up to an energy of 2

eV, the vanadium t2g orbitals dominate, again withsome admixture of O-2p states. Since the crystal

field for vanadium does not posses a perfect

rhombohedral symmetry but a lower trigonal

symmetry in V2O3, these states split into a singlea1g orbital which is oriented perpendicular to the

hexagonal basal plane of V2O3 and double

degenerated epg orbitals oriented towards the faces

and edges of the oxygen octahedrons roughly in

the basal plane of V2O3 [10,13]. The two peaks at

)1 and 0 eV are dominated by these epg states,

whereas the peak at 1.5 eV is deriving mainly from

the a1g orbital. In the bulk, the metal-dominatedconduction band is occupied by two electrons,

since the formal oxidation state of vanadium in

0

0.4

0.8

1.2

1.6

2

2.4

0

0.4

0.8

1.2

1.6

2

2.4

Den

sity

of

Stat

es (

stat

es/e

V)

VO

-8 -6 -4 -2 0 2 4Energy (eV)

0

0.4

0.8

1.2

1.6

2

2.4 S-1

S

...V2O3-VV

0

0.4

0.8

1.2

1.6

2

2.4

0

0.4

0.8

1.2

1.6

2

2.4

Den

sity

of

Stat

es (

stat

es/e

V)

VO

-8 -6 -4 -2 0 2 4Energy (eV)

0

0.4

0.8

1.2

1.6

2

2.4 S-2

S-1

...V2O3S

0

0.4

0.8

1.2

1.6

2

2.4

0

0.4

0.8

1.2

1.6

2

2.4

Den

sity

of

Stat

es (

stat

es/e

V)

VO

-8 -6 -4 -2 0 2 4Energy (eV)

0

0.4

0.8

1.2

1.6

2

2.4 S-2

S-1

...V-O3V3O3S

0

0.4

0.8

1.2

1.6

2

2.4

0

0.4

0.8

1.2

1.6

2

2.4

Den

sity

of

Stat

es (

stat

es/e

V)

VO

-8 -6 -4 -2 0 2 4Energy (eV)

0

0.4

0.8

1.2

1.6

2

2.4 S-2

S

...V2O3-VO VO

O-2p egt

2g

egπ

a1g

eg

t2g

(c) (d)

(a) (b)

Fig. 4. Electronic densities of states for the (a) � � �V2O3–V, (b) � � �V2O3–VO, (c) � � �V2O3 and (d) � � �V–O3V3O3 termination of

V2O3(0 0 0 1).



V2O3 is 3þ. We can determine a measure of the

local valency by integrating the number of states

between the onset of the metal-d states around )2eV and the Fermi-level for a particular vanadium

atom. In this way, a value of 1.6 is determined for

a vanadium atom in bulk V2O3, in good agreementwith the expected value of two. It is important to

emphasise that the number of electrons in the

conduction band corresponds precisely to the

oxidation state: in V2O3, VO2 and V2O5 two, one

and zero electrons (counted per V atom) occupy it.

Our value (1.6) deviates from two, because oxygen

states contribute to the conduction band states

(dashed line), and because the local-density ofstates is calculated inside spheres that do not cover

the entire space. Even with this restriction, the

number of conduction band d-electrons in the

proximity of a particular V atom is a rather

unbiased measure for the local oxidation state of

this V atom.

At the surface, the density of states is pro-

foundly changed, with marked differences betweenthe different terminations. For the stoichiometric

� � �V2O3–V termination, the surface V atom exhib-

its a quite different local geometry than the V atom

in bulk V2O3. As a result of the reduced coordi-

nation the local DOS is narrower, and a sharp

peak is visible at 2 eV, where a gap existed in the

bulk. The number of conduction band d-electrons

is slightly reduced to 1.4 at the topmost vanadiumatom. A bulk like DOS is obtained rapidly after

few layers, with the structure of the DOS in the S-1

layer already largely reminiscent of the DOS in the

bulk, although the gap between the t2g and eg statesis not yet visible. For the VO termination, bulk

like behaviour is even more rapidly attained. Al-

ready in the S-1 layer (not shown) the DOS is

virtually identical to the bulk. At the surface the Vatom now possesses a tetrahedral coordination,

which implies that two eg states are located around

the Fermi-level, whereas triple degenerated t2gstates are located well above 2 eV. A small gap

separates both bands. The number of conduction

band d-electrons is reduced to 0.4 in the vanadyl

group. In fact, formally one would expect an oxi-

dation state of roughly 5þ for the vanadium atomin the VO unit corresponding to zero d-electrons in

the conduction band, but this value is not quite

reached. In the O-2p valence band, the VO unit

has a clear signature as well. For oxygen in the VO

group, the centre of the O-2p states is located at

roughly )5 eV, at smaller binding energies than in

the bulk ()6 eV). Two sharp peaks, one at )4 eV,and an even more pronounced one at )3 eV at thevalence band edge are unique to the VO termina-

tion. Both features have been observed in grazing

incidence photoelectron spectra by Dupuis et al.

[15]. In the experiment the first peak was located

at the upper edge of the O-2p band at roughly

)3.7 eV, whereas the second one was positioned at

)5 eV. Generally the GGA O-2p band is shifted

somewhat compared to the experiment (a commonproblem related to the local density approxima-

tion), but the present results otherwise agree with

experiment.

For the conventional V2O3 termination, we

note a significant shift of the conduction band

states towards the right at the surface, which is a

result of the increased oxidation state of the

vanadium atoms in the S layer. The number of d-electrons in the conduction band is 0.55 for the

vanadium atoms in the layer S, which again points

towards an oxidation state close to 5þ. As for the

VO termination, the centre of mass of the O-2p

band has shifted significantly towards the right

(smaller binding energies). At the edge of the bulk

O-2p band a single sharp peak in the DOS is dis-

cernable at )3.5 eV, which is indicative for thistype of termination.

The � � �V–O3V3O3 termination, on the other

hand, shows features that deviate clearly from the

ideal O3 termination. The first notable point is that

the average number of conduction band d-elec-

trons in the S layer is now 1.0. This agrees with the

expected valency of a free standing VO2 trilayer

with a formal oxidation state of 4þ for the Vatoms. The three atoms in the S layer are however

rather distinct in terms of their electronic and

electrostatic properties. The one with a V atom

below shows a larger oxidation state closer to 5þ

and has only 0.6 electrons in the d-band, while the

other two are closer to 3þ with 1.2 electrons in the

d-band. Since the oxygen coordination of the V

atoms in the surface layer is octahedral, we find agap between the t2g and eg states. The centre of theO-2p states is again shifted towards the right, but


contrary to the previous two cases, no sharp fea-

tures are observable in the DOS. For the single

vanadium atom below the trilayer (S-1) a valency

of 1.0 is calculated which points towards an oxi-

dation state close to 4þ.

The binding energy shifts of the core electronsat the surface are closely related to the changes in

the valence band regime. When the oxidation

state of vanadium increases, the core-levels shift

towards larger (more negative) binding energies.

This behaviour is common to and well known for

(transition) metal oxides, and usually explained

by the observation that a reduction of the d

electron population causes a larger ionicity and inturn a stronger binding of the core electrons to

the ionic core. For a material with a strong

covalent bonding, such as V2O3, the situation is

somewhat more complicated as illustrated in Fig.

5. On the left-hand side, the situation for vana-

dium in the oxidation state 3þ is illustrated. The

oxygen-2p states hybridise with the V states and

an O-2p dominated metal-d hybrid band devel-ops, whereas the anti-bonding metal dominated

hybrid orbitals are found mostly above the Fermi-

level. The total number of d-electrons in the

conduction band is two, which determines the

position of the Fermi-level. When the oxidation

state of vanadium increases from 3þ to 4þ or 5þ,

e.g. by increasing the oxygen content in the

vicinity of a particular vanadium atom, the V

Fig. 5. Schematic representation of the level shifts in vanadium

oxides upon change of the oxidation state. Dark thick lines and

areas correspond to oxygen derived states, whereas light areas

correspond to V derived states. Note that the O-2p derived

valence band contains a sizeable contribution from V-d states,

as well as the conduction bands contain a contribution from the

O-2p states. (For a colour version of the figure, see the online

paper. Dark corresponds to red, light corresponds to blue.)

atom has to donate more charge from the t2gderived conduction band to the surrounding

oxygen atoms. This loss of local charge (increased

ionicity) makes the electrostatic potential at the

vanadium atom in turn attractive (dV in Fig. 5)

counterbalancing the charge flow. In hand withthis attractive potential a proportional increase of

the core-level binding energies is observed. Up to

this point, the arguments are identical to those for

a purely ionic bonding. The down shift of the

vanadium d-levels towards larger binding ener-

gies, however, also increases the hybridisation

between the O-2p states and the V-d states, since

they are now closer in energy. In turn, the metalcontribution (mostly cubic eg) to the valence band

increases (hatched area), causing a back donation

of charge to the V atom. In a self-consistent cal-

culation, as performed here, the total number of d-

electrons therefore remains roughly identical for

any oxidation state and is calculated to be 3.45–

3.65 in the V PAW sphere. It is only the number

of electrons in the t2g dominated conduction bandthat decreases when the oxidation state increases,

which is almost entirely compensated by an in-

crease of d-electrons in the valence band (cubic

eg). As we will show later, the shift of the centre

of the V-d band dV is almost exactly identical to

the calculated V-2p core-level shifts.

The calculated core-level shifts are shown in

Table 3. The stoichiometric termination � � �V2O3–V exhibits essentially no shift in neither the V-2p

nor the O-1s binding energies. A substantial shift

of 0.9–1.0 eV is, however, calculated for both the

VO termination and the ideal bulk V2O3 termi-

nation. In these cases, the shift is observed for

the outermost vanadium layer (S) and the V

atom in the vanadyl group, respectively. For the

trilayer terminated surface (� � �V–O3V3O3), thecalculated shifts are significantly smaller than for

the other two surfaces, which can be considered

as a fingerprint of this particular termination.

The shift is additionally only observed for the V

atom with a direct vanadium neighbour in the S-

1 layer and this S-1 atom, whereas the other two

V atoms exhibit essentially no core-level bind-

ing energy shift with respect to the bulk. Theaverage d-band shift, which was determined by

evaluating

Table 3

V-2p and O-1s surface core-level shifts (SCLS) and vanadium d-band centre for various terminations of V2O3

� � �V2O3–V � � �V2O3–VO � � �V2O3 � � �V–O3V3O3

SCLS V-2p

V )0.01 0.92

VS 0.00 0.12 0.97 0.65/2· 0.09VS-1 )0.02 0.02 0.13 0.53

SCLS O-1s

O )1.40OS

3 0.18 )0.31 )0.97 )0.77OS-1

3 )0.04 )0.02 )0.40 )0.41OS-2

3 )0.01 0.01 )0.08 )0.51

d-band centre

V )0.27 0.87

VS 0.06 0.12 1.04 0.86/2· 0.12VS-1 )0.06 0.02 0.02 0.57

As reference the bulk V2O3 core-levels and d-band centres are used. For structurally inequivalent atoms in one layer, the shifts were

averaged, except when more then one value is specified. Differences between averaged shifts never exceed 100 meV.


�R eF�1 ndðeÞðe � eFÞdeR eF

�1 ndðeÞdeþR eF�1 nV2O3

d ðeÞðe � eFÞdeR eF�1 nV2O3

d ðeÞde

is also summarised in Table 3. The function ndðeÞ isthe local density of d-states for each metal atom

inside the PAW sphere and corresponds to thecurves shown in Fig. 4, and nV2O3

d ðeÞ is the bulk

reference. It is obvious that the d-band centre

moves in almost exactly the same manner as the

core-level binding energies in the final state

approximation, confirming our previous discus-

sion. With the exception of the vanadyl terminated

surface, the core-level binding energy shifts in the

initial state approximation (not shown) are alsowithin 0.2 eV of both values, which indicates that

initial state effects dominate the core-level shifts in

this particular case.

When we compare our results with the exper-

imental data of Refs. [15,28], we unfortunately

note a relatively large discrepancy between theory

and experiment for the absolute magnitude of the

core-level binding energy shifts of the vanadylterminated surface. Density functional theory

predicts a shift of 1 eV, whereas the experimental

shift is close to 2 eV for the vanadyl group.

Additionally the O-1s binding energy depends

strongly on the surface termination, whereas exper-

imentally the O-1s binding energies at the surface

are seemingly identical to those in the bulk

[15,28]. To understand this discrepancy, one has

to realize that the exact magnitude of the shift

depends on the precise structure of the conduc-

tion band and on the capability of the V atoms to

hybridise with the O-2p states (covalency), as we

have discussed before. Both features are possiblyinfluenced by the strong Coulomb repulsion be-

tween d-electrons, which are not adequately ac-

counted for by standard density functional

theory. To test this hypotheses, we relaxed the

vanadyl terminated and the trilayer terminated

(� � �V–O3V3O3) surface using the LDA+U meth-

od and inspected the core-level shifts in the final

state approximation. The calculated V-2p shiftswere now 1.86 and 0.74 eV, for the vanadyl and

trilayer terminated surface, respectively. Simulta-

neously, the O-1s core-level binding energies be-

came within 0.2 eV (0.4 eV) identical to the V2O3

bulk values for the VO (trilayer) termination.

Although the precise values should be interpreted

with care, the calculations suggest that an on site

Coulomb repulsion can have a large influence onthe core-level binding energies. The crucial effect

of the U is that it favours entirely filled or entirely

empty V-d orbitals. Therefore, the back-donation

of charge to the cubic eg states, which has been

discussed in Fig. 5, is more difficult for the

LDA+U calculations. This implies that the cen-

tre of the metal d-states has to shift to higher

binding energies in the LDA+U method for the

Table 4

Vibrational frequencies of dipole active modes as calculated by GGA for the four important surface terminations

� � �V2O3–V � � �V2O3–VO � � �V2O3 � � �V–O3V3O3

O3–V stretch V–O stretch O3–V2 stretch O3–V3 stretch

87 meV 135 meV 87 meV 81 meV

V2 plane O3–VO stretch O3–V2 stretch O6–V(S-2)a

61 meV 82 meV 81 meV 78 meV

aThe six O neighbours of the V atom in the S-2 layer vibrate towards this V atom.


charge donation to the cubic eg states to occur. In

short, the U makes the bonding more ionic and

less covalent, causing an increased V-2p and

smaller O-1s core-level shift in the vanadyl group,

as observed experimentally.

Finally, relevant for the interpretation of the

experimental results is the intermediate surface

core-level shift for the trilayer � � �V–O3V3O3 ter-mination. In the GGA (LDA+U) calculations the

V-2p shift is 0.65 eV (0.74 eV). As already pointed

out before the intermediate shift is associated with

vanadium atoms with an oxidation state of 4þ in

the VO2 trilayer. Such an intermediate shift has

indeed been observed experimentally upon partial

removal of VO groups [28] and seems to be

indicative of the existence of the trilayer structure.

3.3. Vibrational frequencies

The determination of the vibrational frequen-cies proceeded in two steps. First, as a reference,

the bulk vibrational spectra was calculated, and

second all vibrational modes of the considered

slabs were determined. For the bulk, only two

modes were calculated to have a significant dipole

intensity with contributions parallel to the c-axis(orthogonal to the hexagonal planes). These two

modes have frequencies of 63.3 meV (511 cm�1)and 46.2 meV (335 cm�1) and correspond well to

two bulk loss peaks at 65 and 47 meV found in a

recent HREELS study [15]. However one experi-

mentally observed loss peak at 81 meV, which was

associated with bulk like phonons, is not found

theoretically. In fact, the maximum vibrational

frequencies of bulk V2O3 is calculated to be

around 72 meV (580 cm�1) which seems to pre-clude that the loss peaks at 81 meV can stem from

bulk like phonons.

For the four important surface terminations,

the frequencies of dipole active modes are sum-

marised in Table 4. Remarkably, for any termi-

nation but the rather unfavourable V termination,

an intensive mode at 81 meV is predicted. It has a

similar origin in all three cases. For the VO ter-

mination, it originates from the three oxygen

atoms below the VO molecule, which vibrateparallel to their oxygen–vanadyl bond. For the

� � �V2O3 termination, two modes at 87 and 81 meV

are found with similar eigen-modes. In one case

the three topmost O atoms vibrate against the

topmost V atom in the S layer, whereas for the

lower frequency they vibrate against the second

somewhat retracted V atom. For the � � �V–O3V3O3

termination, finally, the mode originates againfrom the three topmost oxygen atoms vibrating

now dominantly normal to the surface.

The calculations therefore suggest, that the loss

peak observed at 81 meV derives essentially from

the surface oxygen atoms moving in phase and

perpendicular to the c-axis, but further theoreticaland experimental work will be required to confirm

this conjecture unambiguously. The other impor-tant result is the calculated vanadyl stretch mode

at 135 meV, which agrees reasonably well with a

peak at 127 meV observed in HREELS and

infrared adsorption spectra [15,28]. Unfortunately,

the other frequencies are lying too close in energy

to allow for an unambiguous identification of

specific surface reconstructions using vibrational

techniques.

4. Conclusion

In this work we have presented a detailed study

of the surface structure and energetics of


V2O3(0 0 0 1), as obtained by density functional

theory. The most relevant result of the study is

that ideal bulk terminations are rather unfavour-

able for V2O3(0 0 0 1). Instead, the surface either

adopts a hexagonal trilayer structure or a vanadyl

terminated modification. The latter structure canbe regarded as the ideal single metal terminated

surface, with one additional oxygen atom ad-

sorbed on top of the outermost V atom. It is the

dominant and stable phase, if the surface is in

thermal equilibrium with the V2O3 bulk. Under

oxygen rich conditions, the VO groups can be re-

moved and are replaced by a previously unknown

trilayer structure. There are several ways to con-ceptually build this structure. Either one starts out

from the ideal oxygen terminated surface with a

stacking sequence of � � �V2O3–V2O3–V2O3 and

moves one subsurface vanadium atom into the

surface plane to form � � �V2O3–V–O3V3O3, or one

envisages it as an assembly of the non-polar single

V terminated surface V2O3–V and a non-polar

hexagonalffiffiffi3

p�

ffiffiffi3

p� �R30� VO2 trilayer adsorbed

on top of this metal terminated surface. The later

construction method indicates that the oxygen

atoms in the trilayer have an oxidation state close

to 4þ, which is in fact confirmed by the theoretical

calculations. At this point, the existence of the

trilayer structure is a theoretical prediction, but

some experimental evidence––in particular, the

observed surface core-level shifts suggesting a VO2

stoichiometry for the oxidised surface––can be

reconciled with this model.

In agreement with the energetic DFT consid-

erations, a recent comprehensive LEED, STM,

HREELS and XPS study indicates a (1 · 1) VOterminated surface to be stable over a relatively

wide range of reducing UHV conditions. The only

model that is compatible with this experimentalstructure is the (1 · 1) VO terminated surface

considered here. It is capable to reproduce the

V@O stretch mode and the experimental STM

images, which show a single bright blob corre-

sponding to the vanadyl group [24,25]. Agreement

with experiment for the valence band spectra is

also satisfactory. The experimental V-2p core-level

binding energy shifts in the V@O group, which aremeasured to be 2 eV, are however not reproduced.

The GGA calculations predict a smaller shift of 1

eV, which is accompanied by an opposite shift of

)1 eV for the oxygen atoms in the vanadyl group,

that is not observed experimentally. The reason for

the discrepancy seems to lie in the inability of

present density functionals to describe electronic

exchange and correlation effects sufficiently well.Inclusion of an on-site Coulomb repulsion be-

tween the localised d-electrons by means of the

LDA+U method yields a larger V-2p core-level

binding energy shift of 1.8 eV and a smaller shift of

the O-1s core-level (0.2 eV) for the vanadyl group.

LDA+U is however too crude an approach, as it

predicts a semiconducting bulk oxide, whereas

experimentally rhombohedral V2O3 is a metal. Thecrucial effect of the U is a reduction of the covalent

bonding between the vanadium and oxygen atoms,

since in the LDA+U, hybridisation between the

cubic eg states and O-2p orbitals is supressed. The

reduced covalency causes an increased V-2p and

smaller O-1s core-level shift in the vanadyl group,

as observed experimentally. In summary, these

arguments indicate that the oxygen vanadiumbond is too covalent in present semi-local density

functionals.

Another point concerns details of the predicted

surface phase diagram. When the chemical po-

tential of oxygen is increased (for instance by

increasing the partial oxygen pressure), theory and

experiment agree that VO groups are progressively

removed from the surface. But theory puts thetransition points at too low oxygen potentials, i.e.

GGA predicts that the surface is easier oxidised

than in reality. This problem is even encountered

for the bulk phases, as the stability of oxygen rich

phases seems to be overestimated with the present

semi-local density functionals. Furthermore, the

GGA calculations indicate that affiffiffi3

p�

ffiffiffi3

p� �-

R30�–2VO reconstruction is stable under mostrelevant conditions, its stability even exceeding

that of the entirely VO covered surface. In the

experiments, however, the (1 · 1) vanadyl coveredsurface can be attained under typical UHV con-

ditions [28]. One might argue again that this is a

result of the overestimation of the vanadium–

oxygen bond strength in present semi-local density

functionals.Hence, the present calculations suggest that

semi-local density functionals can give only a


qualitative picture of the energetics and structure

of a correlated oxide, but predictions on spectro-

scopic details or quantitative predictions for

transition temperatures are not yet possible. Bulk

V2O3 and its surfaces still present a challenge to

theory.

Acknowledgement

This work has been supported by the Austrian

FWF.

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