J. Phys. Chem. C XXXX, xxx, 000
A
Theoretical Study of the Effect of (001) TiO2 Anatase Support on V2O5
Konstantinos Alexopoulos,† Pawel Hejduk,‡ Malgorzata Witko,‡ Marie-Francoise Reyniers,*,†
and Guy B. Marin†
Laboratory for Chemical Technology, Ghent UniVersity, Krijgslaan 281 (S5), B-9000 Ghent, Belgium, and
Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek 8,
30239 Cracow, Poland
ReceiVed: NoVember 10, 2009; ReVised Manuscript ReceiVed: January 7, 2010
The effect of (001) TiO2 anatase support on the electronic and catalytic properties of a V2O5 monolayer is
analyzed using density functional theory (DFT). The catalyst is represented by both clusters and periodic
slabs. Using two experimentally relevant models of monolayer V2O5/TiO2 (anatase) catalyst, both weak and
strong interactions between a V2O5 monolayer and the TiO2 support have been investigated. In the first model,
where a crystallographic (001) V2O5 layer is placed on top of the (001) TiO2 support, the weak interaction
between vanadia and titania does not result in a major reconstruction of the active phase. Nevertheless, the
changes in the electronic properties of the system are evident. The deposition of the vanadia monolayer on
the titania substrate results in charge redistribution, enhancing the Lewis acidity of vanadium and the chemical
hardness above the vanadyl oxygen, and in a shift of the Fermi level to lower binding energies accompanied
by a reduction in the band gap. In the second model, where the (001) titania anatase structure is extended
with a VO2 film terminated by half a monolayer of vanadyl oxygen, apart from a similar electronic effect, the
strong interaction of the vanadia phase with the titania support resulting from a high order of epitaxy has an
important effect on the structure of the active phase. Atomic hydrogen adsorption is most favorable on the
vanadyl oxygen of all the investigated surfaces, while the adsorption energy on this site increases by ∼10
kJ/mol due to the weak interaction between vanadia and titania and is further increased by ∼50 kJ/mol as a
stronger interaction between the two phases is achieved, all in agreement with the increase in the negative
electrostatic potential above the vanadyl site. The observed trends in the reactivity of the oxygen sites in H
adsorption for the different catalyst models are successfully explained in terms of a frontier orbital analysis.
Introduction
Transition metal oxides are widely used as catalysts for the
oxidation of hydrocarbons. Especially vanadium oxide based
catalysts are among the most active for the oxidation of both
aliphatic and aromatic hydrocarbons. An important example of
such a catalyst is V2O5/TiO2 (anatase), which is used in industry
as an effective catalyst for the production of phthalic anhydride
from o-xylene.1,2 For the anatase support, although the (101)
surface is thermodynamically more stable, the (100) and (001)
faces are found in the industrial TiO2 powders.3 Earlier
experimental studies indicate that this catalytic system is of high
performance when it consists of a monolayer of V2O5 upon a
TiO2 (anatase) substrate, showing activity and selectivity not
observed in the unsupported V2O5 or TiO2 anatase.2,4 The
enhanced catalytic performance can be attributed to a synergetic
effect between the active phase and the support. In order to
unravel the role of the TiO2 support on a V2O5 monolayer
catalyst, ab initio methods can help to provide a better
understanding of the relation between structure and reactivity.
Several theoretical models have been proposed for describing
the V2O5/TiO2 anatase catalyst at different vanadium loadings.
Avdeev and Zhidomirov5 used small cluster models consisting
of monovanadate and divanadate species to model the active
centers of the V2O5/TiO2 catalyst. They found that TiO2 forms
* Corresponding author: tel, +32 9 264 5677; fax, +32 9 264 5824;
e-mail, MarieFrancoise.Reyniers@ugent.be.
†
Laboratory for Chemical Technology, Ghent University.
‡
Institute of Catalysis and Surface Chemistry, Polish Academy of
Sciences.
10.1021/jp910685z
strong bonds with the monomeric and dimeric VOx groups.
Kachurovskaya et al.6 constructed cluster models of the VOx/
TiO2 catalyst based on embedding vanadium ions in the anatase
support. This is the so-called substitution model, as it consists
of replacing a surface Ti atom by a V or VOH unit. Their results
indicated an increased acidity of the VOx/TiO2 catalyst system
as compared to pure V2O5. Additionally they concluded that
including a second titania layer is essential for the modeling of
the anatase support. Besides cluster models, the periodic
approach has also been used to model the V2O5/TiO2 catalyst.
This approach is mostly useful for investigating medium and
high coverages of vanadia on titania. In order to model
coverages of vanadia below the monolayer, Calatayud and
Minot3 have constructed periodic slabs consisting of monomeric
and dimeric vanadia species deposited on titania anatase, which
is an example of the so-called addition model. Moreover, Grybos
and Witko7 used different monomers with the general formula
of VOxHy to construct vanadium oxide monolayers on a TiO2
anatase slab. In both of these studies, the vanadia species are
anchored to the anatase support by strong interactions.
In general, the interaction of the support with the active phase
of the catalyst can be either strong or weak, depending on
whether the presence of the support modifies significantly the
structure of the active phase or not.7 Devriendt et al.8 put several
models9-12 of the V2O5/TiO2 anatase catalyst to the test using
single scattering cluster simulations in conjunction with X-ray
photoelectron diffraction (XPD) measurements. Either these
models consisted of mono-oxo9 (VdO) or dioxo10 (OdVdO)
vanadyl groups centered above four or two anatase surface
XXXX American Chemical Society
Alexopoulos et al.
B J. Phys. Chem. C, Vol. xxx, No. xx, XXXX
oxygen atoms, respectively, or they11,12 assumed that the vanadia
monolayer has a structure similar to the crystalline V2O5.
Although the authors8 concluded that the model resembling a
flattened V2O5 (001) layer11 provided the best fit, this model
needs to be refined in order to eliminate the lattice misfit strain
at the interface. However, according to the same authors,8 the
relaxation of the V2O5 (001) monolayer by means of simulations
based on force fields12 was considered to be too strong, and it
was suggested that a more bulklike V2O5 structure would be
able to explain the experimental XPD patterns. In agreement
with this, X-ray absorption spectroscopy (XAS) measurements13
yielded no structural differences between the fully oxidized
supported vanadium oxide and bulk crystalline V2O5. On the
other hand, results obtained for V2O5/TiO2 anatase by X-ray
photoelectron spectroscopy (XPS), UV photoelectron spectroscopy, reflection high energy electron diffraction, and low energy
electron diffraction measurements14 and periodic DFT calculations15 pointed toward an epitaxial monolayer with a V2O5
stoichiometry. In addition, periodic DFT calculations for thin
vanadia films on Al2O3 support16 yielded similar conclusions,
since a pseudomorphic epitaxial V2O3 layer with oxygen
adsorption oxidizing the outermost V to 5+ is favored. Thus,
the composition of the surface layer is V2O5, but the coordination
of vanadium is different from that in the crystallographic V2O5
(001) layer.
In an attempt to clarify the nature of the interaction between
the support and the active phase, two supported models of a
V2O5 monolayer have been proposed in this study and are
confronted to results available in literature. In the first model,
where a weak interaction between the support and the active
phase is assumed, a crystallographic V2O5 (001) layer is placed
on top of the (001) TiO2 anatase support, which is allowed due
to the small lattice misfit between the two phases.12 In the second
model, where a strong interaction between the two phases is
assumed, the (001) titania anatase structure is extended with a
VO2 film terminated by half of monolayer of vanadyl oxygen,
thus creating a vanadia monolayer that does not resemble the
structure of bulk V2O5 but has the fully oxidized V2O5
stoichiometry.14 Moreover, for both models all the possible
orientations of the active V2O5 phase on the support have been
considered. Apart from the supported catalyst system, models
have also been constructed for the most stable (001) V2O5
surface of the unsupported V2O5 catalyst and for the (001) TiO2
anatase support surface typically found in the industrial TiO2
powders. In order to investigate the influence of the support on
the vanadia monolayer, a comparison of the electronic properties, e.g., atomic charges, bond orders, electrostatic potential,
and density of states, between the supported and the unsupported
catalytic systems is made. Additionally, the adsorption of atomic
hydrogen is used to probe the reactivity of the different active
sites that exist on the vanadia surface.
Methodology
Computational Details. Periodic Calculations. Spin-polarized periodic DFT calculations have been carried out with the
Vienna Ab Initio Simulation Package (VASP) using plane wave
basis sets.17,18 A plane-wave energy cutoff of 400 eV has been
used in all cases. The projector augmented wave method of
Blöchl19 in the implementation of Kresse and Joubert20 has been
chosen to describe the electron-ion interaction. To account for
the nonlocality in the exchange correlation functional, the
generalized gradient approximation (GGA) according to Perdew,
Burke, and Ernzerhof (PBE) has been used.21 The catalyst is
represented as an infinite system with periodic symmetry.22 A
conjugate-gradient algorithm has been utilized to relax the atoms
into their instantaneous ground state, assuming that convergence
is achieved when the forces are below 0.05 eV/Å. The
Monkhorst-Pack division scheme23 has been chosen to generate
a set of k-points within the Brillouin zone. To improve the
convergence with respect to the number of k-points without
affecting the accuracy of the calculation, a Gaussian smearing18,24
of 0.05 eV has been applied. Convergence tests regarding the
number of k-points, the size of the surface slabs, and the
thickness of the vacuum layers have been carried out to ensure
an accurate description of the catalytic system. A 2 × 6 × 6
and a 6 × 6 × 2 k-point mesh was found to be adequate for the
bulk V2O5 and TiO2 anatase, respectively, yielding cohesive
energies that are converged within 1 meV. Accordingly, for the
(1 × 1) primitive surface cell of (001) V2O5 and for the (3 ×
1) supercell of (001) TiO2 a 2 × 6 × 1 k-point mesh was applied,
while a 3 × 3 × 1 k-point mesh was used for the (2 × 2)
supercell of (001) TiO2. A vacuum gap of ∼11 Å was found
sufficient to separate subsequent slabs, yielding surface energies
that are converged within 0.001 J/m2. For the surface calculations, no symmetry was used and a dipole correction was
included. In all cases, the vanadia monolayer is fully relaxed,
while the atoms of the titania support are kept fixed to their
bulk positions. As a second optimization step, some calculations
have also been performed allowing the topmost layer of the
titania support to relax together with the vanadia monolayer,
thus being able to determine the effect of this extra relaxation
on the structure and energetics of the supported system. For
the unsupported vanadia, surface energies are calculated as
∆Esurf )
1
(E - Ebulk)
2A surf
(1)
where A is the surface area, Esurf is the energy of the V2O5
surface unit cell, and Ebulk is the energy of the V2O5 bulk unit
cell. For the supported vanadia monolayer, surface formation
energies25 are calculated as
∆Ef(surf) )
1
[E
- EV2O5(bulk) - ETiO2(001)]
A V2O5/TiO2(surf)
(2)
where A is the surface area, EV2O5/TiO2(surf) is the energy of the
surface cell of the supported vanadia on titania system, ETiO2(001)
is the energy of the (001) TiO2 anatase surface cell, and EV2O5(bulk)
is the energy of the V2O5 bulk unit cell. In addition, adsorption
energies of atomic hydrogen on the surface are calculated as
follows using supercells having surface area of ∼80 Å2
∆Eads ) Evanadia/H - (Evanadia + EH)
(3)
where Evanadia/H refers to the energy of the hydroxylated
unsupported/supported vanadia surface, Evanadia refers to the
energy of the clean unsupported/supported vanadia surface, and
EH refers to the energy of an isolated hydrogen atom. Positive
values of ∆Eads indicate endothermic processes, while negative
values indicate exothermic processes.
After geometry optimization of the periodic models, band
structure calculations have been performed using VASP in order
to map the electronic structure of the investigated systems. The
bands are plotted along directions connecting high symmetry
points inside the irreducible part of the Brillouin zone, which
in all investigated cases is orthorhombic (Figure 1). These graphs
reveal the energy dispersion of each band along different
symmetry lines, thus characterizing the anisotropy of the
material. In order to have a clear separation between the
occupied and unoccupied bands, the energy scale of these graphs
is relative to the Fermi level of each system. Next to that, the
total spin-up and spin-down density of states (DOS) are readily
Effect of (001) TiO2 Anatase Support on V2O5
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX C
V2O5 surface is placed on top of a titania cluster representing
the (001) TiO2 anatase support, the energy change involved in
this process is expressed as follows
∆Ef(cluster) ) E(V10O31H12 /TixOyH2y-4x) E(V10O31H12) - E(TixOyH2y-4x)
Figure 1. First Brillouin zone of the orthorhombic lattice and its high
symmetry points.
obtained from the band structure calculations and can be used
to observe whether there are any unpaired electron states.
However, because band structures and their k-space integrals,
i.e., DOS, do not contain any information about the localization
of the electronic states in real space or to which atom these
states belong to, local or partial DOS (p-DOS) are also calculated
by projecting the plane waves onto specific atomic orbitals.
Moreover, to obtain a measure of the atomic charges for each
periodic model, a Bader analysis26 is performed as implemented
by Henkelman et al.,27 using the charge density calculated by
VASP. In this implementation the core charges are also included
in the partitioning of the charge density, thus increasing the
accuracy of the method. In addition, to have a clear-cut view
of the charge redistribution induced by the bonding between
vanadia and titania, a charge density difference is calculated as
∆F ) FV2O5/TiO2 - FV2O5 - FTiO2
(4)
where F is the charge density calculated by VASP for each
surface model. Finally, the electrostatic potential for the
investigated surface models is also calculated using VASP.
According to literature,28 this property, which describes the
interaction energy of a system with a positive unit charge
(proton), can be used as a DFT based reactivity indicator probing
the hard regions of the surface. More specifically, the region
with the most negative value of the electrostatic potential is
most favorable to undergo a hard electrophilic attack.
Cluster Calculations. According to Sauer and Dobler,29 GGA
functionals like PBE typically used in plane wave calculations
may yield electronic structures that are too delocalized and the
use of hybrid functionals has been recommended in such cases.
Therefore, in order to provide a more localized picture around
the region where the bonding between vanadia and titania takes
place, density functional theory (DFT) cluster calculations have
been performed with Turbomole,30-32 using the hybrid PBE0
functional21 and all-electron triple-ζ plus polarization basis sets33
(TZVP) on all atoms. An advantage of this approach is that
one can use the whole spectrum of quantum-chemical methods
developed for small molecules with relatively minor modifications.34 The catalytic system is represented as clusters cut out
of the catalyst’s surface with the dangling bonds at the cluster
periphery saturated by hydrogen atoms.22 Geometry optimizations were done with Turbomole using the default convergence
criteria, i.e., 10-3 atomic units (0.05 eV/Å) for the maximum
norm of the Cartesian gradient, while single point calculations
were also performed with Gaussian0335 at the PBE0/TZVP level.
The hydrogen-terminating atoms and the atoms belonging to
the titania support were kept fixed during geometry optimization.
In all cases, cluster size convergence tests have been carried
out to ensure an accurate description of the investigated systems.
For the cases where a vanadia cluster representing the (001)
(5)
while the electron density difference is calculated according to
eq 4, using the electron density calculated by Turbomole for
each cluster model.
Atomic charges for the cluster models have been calculated
with Turbomole using a Mulliken population analysis36 and a
modified Roby-Davidson population analysis based on occupation numbers37 and with Gaussian03 using a Bader analysis
based on the same implementation26,27 as for the periodic models.
Next to the atomic charges, Wiberg bond orders38 have been
calculated with Gaussian03 as total per atom in order to probe
the covalent nature of the investigated systems. For all the
aforementioned population analyses, the values are always taken
from the atoms located at the center of the cluster, as they are
the most representative ones. In addition, the electronic structure
of the cluster models is analyzed with Gaussian03 using
electrostatic potential maps, partial densities of states projected
on certain representative atoms (p-DOS), and crystal orbital
overlap populations39 projected on certain representative bonds
(p-COOP). Due to the discrete orbital energy levels of the
cluster, a Gaussian broadening of 0.5 eV is applied for the
construction of p-DOS and p-COOP curves.
Models. Bulk V2O5 and TiO2 Anatase. Bulk V2O5 forms a
layer-type orthorhombic lattice with space group Pmmn (D2h13)
and experimental lattice constants a ) 11.512 Å, b ) 3.564 Å,
and c ) 4.368 Å.40 Its unit cell, V4O10, comprises two formula
units. In the crystal structure (Figure 2), the layers are stacked
in such a way that distorted VO6 octahedra are formed with
V-O bond distances varying between rather small (1.58 Å) and
quite large values (2.79 Å). This large value is indicative of a
weak van der Waals bond, which explains why V2O5 presents
an easy cleavage parallel to the (001) plane.41 On the basis of
their coordination number, three different types of lattice oxygen
are present in this structure, namely, the singly coordinated
vanadyl O(1), the doubly coordinated bridging O(2), and the
triply coordinated bridging oxygen O(3).
On the other hand, anatase TiO2 belongs to the I41/amd
(D4h19) space group with experimental lattice constants a ) b
) 3.787 Å and c ) 9.515 Å.42 Its unit cell, Ti4O8, comprises
four formula units. The structure can be described as composed
of distorted TiO6 octahedra with two different Ti-O distances,
a long one (1.98 Å) involving the two apical oxygens and a
short one (1.93 Å) involving the four equatorial oxygens. In
this bulk structure (Figure 3), there is only one type of lattice
oxygen (i.e., O(3)), which is coordinated to three titanium atoms.
In order to find the equilibrium volume and the bulk modulus
of these systems at zero pressure and temperature, the unit cells
of these bulk structures have been optimized at several volumes
and the results have been fitted to a Murnaghan equation of
state43
E(V) ) E0 +
(
)
B0V (V0 /V)B0′
B0V0
+1 B0′ B0′-1
B0′-1
(6)
where V0 and E0 are the equilibrium volume and energy,
respectively, B0 is the bulk modulus at zero pressure, and B0′ is
the bulk modulus pressure derivative. This fit for both of the
materials is depicted in Figure S1 of the Supporting Information.
Finally, an additional optimization is performed for each bulk
D
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX
Alexopoulos et al.
Figure 2. Crystal structure of V2O5 and its inequivalent oxygen atoms.
Figure 3. Crystal structure of TiO2 anatase.
material at its equilibrium volume, in order to determine the
optimum lattice constants and atomic positions.
(001) V2O5 Surface. Because V2O5 presents an easy cleavage
parallel to the (001) plane, this plane has been used in this study
to model the fully oxidized unsupported vanadia surface.
However, when considering the (001) V2O5 surface, an additional distinction between the oxygen sites within the surface
layer has to be made, owing to the differences in their surface
orientation. As seen in Figure 4, six distinct oxygen sites exist
within a (001) V2O5 layer: singly coordinated O(1)/O(1)′
belonging to a vanadyl group that is either sticking out of the
surface or pointing into the bulk, respectively, doubly coordinated O(2)/O(2)′ bridging two vanadyl groups that are either
pointing into the bulk or sticking out of the surface, respectively,
triply coordinated O(3)/O(3)′ connecting either two vanadyl
groups pointing into the bulk and one vanadyl group sticking
out of the surface or vice versa. Due to this surface site
orientation, the nonaccented oxygen sites are the ones that are
easily accessible to gas-phase molecules and can be considered
as active. On the other hand, the inaccessible sites O(1)′ are
involved in the anchoring of the vanadia overlayer on the
substrate, as will be seen in the modeling of the supported
vanadia surface.
Periodic calculations have been performed for the (001) V2O5
surface using both single layer (V2O5 slab) and double layer
(V2O5-V2O5 slab) slabs, in order to test whether there is any
influence of a second underlying vanadia layer on the surface
properties. In addition, for the cluster calculations, the V10O31H12
(V10) cluster has been used as a realistic model of the (001)
V2O5 surface, as suggested by Hermann et al.44
Weak Interaction Model: One-Layer (001) V2O5/(001) TiO2
Anatase. The first type of supported models originates from
the idea that a fully oxidized vanadia monolayer maintains more
or less its crystallographic V2O5 structure when supported on
titania anatase, which has been supported by experimental
evidence.13 As the interface between the (001) V2O5 monolayer
and (001) TiO2 surface exhibits a very small lattice misfit, it
has been chosen for this kind of modeling. While the surface
unit cell of (001) TiO2 is tetragonal (a ) b ) 3.79 Å), the
surface unit cell of (001) V2O5 is rectangular (a ) 11.51 Å, b
) 3.56 Å). For this reason, two possible orientations of (001)
V2O5 on (001) TiO2 have been considered, as shown in Figure
Effect of (001) TiO2 Anatase Support on V2O5
Figure 4. Side and top view of the (001) V2O5 surface. Oxygen sites
with different coordination (number in parentheses) and different surface
orientation (accented or not) are depicted. Certain angles used in Table
3 are also depicted. A dashed line has been drawn on the side view to
differentiate between the oxygen sites that are pointing into the substrate
and the ones that are pointing toward the vacuum and are easily
accessible to gas-phase molecules.
Figure 5. V2O5-TiO2 slabs. Side view of the two possible orientations
of a (001) V2O5 monolayer supported on (001) TiO2 anatase (weak
interaction with support). Blue balls are vanadium atoms, red balls are
oxygen atoms, and green balls are titanium atoms.
5 (V2O5-TiO2 slabs). As seen in this figure, the vanadia
overlayer is anchored to the titania substrate using half of its
vanadyl groups. Apart from the regions where bonding between
vanadia and titania takes place, there are also large empty
cavities below the vanadia overlayer at the regions where the
vanadyl groups are sticking out of the surface, which is due to
the alternating orientation of the double vanadyl rows on the
vanadia overlayer structure. In addition to the periodic slabs
for this kind of modeling, a series of cluster calculations have
been performed using several cluster models of vanadia on
titania (see Figure S2 of the Supporting Information). These
clusters differ in size and in orientation of the active phase on
the support, so that both effects can be studied for this type of
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX E
modeling. However, due to the prerequisite of fixing the
terminating H atoms, the optimum distance between the vanadia
and titania cluster must be found manually before optimizing
the positions of the atoms in the vanadia layer. This is simply
done by choosing some points with different Ti-O(1)′ distance
and calculating the energy of the system, with the optimum
distance being the one minimizing its formation energy
(∆Ef(cluster)). As seen in Figure S3 of the Supporting Information,
a minimum in the formation energy of the supported cluster
has been found, with the optimized Ti-O distance being 2.25
Å, which is equal to the distance obtained from the periodic
calculations for the respective slab model (V2O5-TiO2 (B)
orientation). Additionally, in order to select the cluster that yields
converged results for this surface system, the dependence of
the properties on the cluster size has been examined. As seen
from Table S1 of the Supporting Information, the data are almost
identical for the two largest clusters (i.e., V10 on Ti10 (B) and
V10 on Ti15 (A)), indicating that convergence of the electronic
and energetic properties is achieved for the V10 on Ti10 cluster
which is used in the following discussion.
Strong Interaction Model: One-Epitaxial Layer V2O5/(001)
TiO2 Anatase. The second approach for modeling the V2O5
monolayer supported on (001) TiO2 anatase is based on results
obtained by several surface characterization techniques14 and
assumes that the presence of the titania anatase support alters
significantly the structure of the fully oxidized vanadia monolayer. This model is constructed by placing half monolayer of
oxygen atoms on top of a pseudomorphic VO2 phase that
extends the (001) TiO2 anatase structure. As illustrated in Figure
6, three possibilities of arranging these on-top oxygen atoms
have been envisaged: one along the diagonal [110] direction
(configuration A), one along the [100] direction (configuration
B), and one along the [010] direction (configuration C). The
resulting structures (VTiO slabs) are also shown in this figure
after allowing the vanadia overlayer to relax. In addition to the
periodic slabs for this kind of modeling, a series of cluster
calculations have been performed using cluster models of
different size (see Figure S4 of the Supporting Information). In
order to select the cluster that can adequately describe this
surface system, the convergence of the properties with cluster
size has been examined. As seen from Table S2 of the
Supporting Information, the data at all levels of analysis are
identical for the two largest clusters (i.e., V4_Ti15 and
V6_Ti16). Convergence of the electronic and energetic properties is thus achieved for the V4_Ti15 cluster, which is used in
the following discussion.
Results and Discussion
Bulk V2O5 and TiO2 Anatase. As seen in Tables 1 and 2,
the calculated values of the lattice parameters, atomic positions,
and bulk moduli are in good agreement with the experimental
values.40,42,45,46 This is an indication that both systems are well
represented using the aforementioned computational methodology.
After the optimization of the bulk structure of V2O5 and TiO2
anatase, band structure calculations have been performed in
order to map the electronic structure of these systems. From
the total spin-up and spin-down density of states (DOS) as
plotted in Figures S5 and S6 for V2O5 and TiO2, respectively,
the diamagnetic character of both materials is observed. For
V2O5 (Figure S5 in the Supporting Information), three characteristic groups of bands are identified around the Fermi level.
A valence band that consists mainly of O 2p states with nonnegligible V 3d contributions is found below the Fermi level.
The calculated valence bandwidth of 4.9 eV is in good
F
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX
Figure 6. VTiO slabs. Schematic representation of different possibilities of arranging a half monolayer of oxygen atoms on top of a
pseudomorphic VO2 phase that extends the (001) TiO2 anatase (white
background) and top view of the resulting models (shaded background)
representing an epitaxial monolayer of V2O5 supported on (001) TiO2
anatase (strong interaction with support). The vanadia overlayer is
represented by a ball and stick model, where the blue balls are the
vanadium atoms and the red balls are the oxygen atoms, whereas the
titania anatase support is depicted as a stick model with red indicating
oxygen and green indicating titanium.
TABLE 1: Experimental versus Calculated Structural
Parameters for Bulk V2O5
experimental
Lattice Parameters (in Å)
11.658
3.575
4.485
a
b
c
11.512a
3.564a
4.368a
V
O(1)
O(2)
O(3)
Wyckoff Positions
(0.10118, 0.25, -0.1083)a
(0.1043, 0.25, -0.469)a
(0.25, 0.25, 0.001)a
(-0.0689, 0.25, 0.003)a
B0
50 ( 2b
a
calculated
(x,y,z)
(0.10179, 0.25, -0.1076)
(0.1047, 0.25, -0.467)
(0.25, 0.25, -0.002)
(-0.0683, 0.25, 0.005)
Bulk Modulus (in GPa)
49
Reference 40. b Reference 45.
TABLE 2: Experimental versus Calculated Structural
Parameters for Bulk TiO2 Anatase
experimental
a
calculated
a
b
c
Lattice Parameters (in Å)
3.834
3.787a
3.787a
3.834
9.515a
9.628
Ti
O(3)
Wyckoff Positions (x,y,z)
(0, 0.75, 0.1250)a
(0, 0.75, 0.1250)
(0, 0.75, 0.3333)a
(0, 0.75, 0.3328)
B0
Bulk Modulus (in GPa)
179 ( 2b
174
Reference 42. b Reference 46.
agreement with the experimental value of 5.5 eV reported in
literature49,50 (see Table 3). Above the Fermi level, the conduction band, which is mainly dominated by unoccupied V 3d
Alexopoulos et al.
states, is divided into two groups of bands: a narrow feature at
lower energies separated from the broad upper group of bands
by a gap of 0.6 eV. This split-off feature at the bottom of the
conduction band consists of a pair of localized bands, and its
existence has been reported in the literature by several
authors.40,49,51,52 Experimentally, V2O5 is considered to be a
semiconductor with a band gap of about 2.3 eV.48 In agreement
with this, the periodic calculations for bulk V2O5 yield a direct
band gap of 2.2 eV at the Γ-point and an indirect band gap of
1.7 eV that corresponds to a transition between the valence band
maximum (located close to R along the RZ direction) and the
conduction band minimum (located at the Γ-point). However,
it has to be kept in mind that despite of this agreement, pure
DFT methods in general underestimate the band gap of bulk
materials.49,53,54 This is evident in the case of TiO2 anatase
(Figure S6 in the Supporting Information), where the periodic
calculations yield a direct band gap of 2.0 eV at the Γ-point
and an indirect band gap of 1.9 eV corresponding to a S to Γ
transition, while the experimental band gap is 3.2 eV.54,55
Nevertheless, the calculated band gap is in agreement with other
reported calculations.53-56 In addition, the calculated valence
bandwidth of 4.6 eV for bulk TiO2 anatase agrees well with
the experimental value of 4.75 eV, as obtained from XPS
measurements.55,56 Similar to V2O5, the valence band of TiO2
anatase consists mainly of O 2p states with non-negligible Ti
3d contributions located at the bottom of the valence band, while
the conduction band is dominated by unoccupied Ti 3d states.
By comparing the magnitude of the calculated charges on
the V, O and Ti atoms for bulk V2O5 and TiO2 anatase (see
Table 4) with their formal charges (namely, +5, -2, and +4,
respectively), it is found that these systems cannot be considered
as purely ionic and exhibit also a covalent character. This is in
line with a recent experimental study,57 where the electronic
structure of V2O5 has been probed by resonant photoemission
spectroscopy (RPES). RPES results showed that the approximate
charge on the V ion and the O ion in V2O5 is +3 and -1.2,
respectively, indicating that the simple ionic model of bonding
is not valid for such a system.
Overall, with the exception noted earlier, the present calculations describe well the geometric and electronic features of these
well-defined bulk materials.
Unsupported V2O5 Surface. As seen in Tables 3 and 4 (bulk
V2O5 vs V2O5 slab), when the bulk structure is cleaved to create
the (001) V2O5 surface, no major surface relaxations and charge
redistributions occur. A very small surface energy of 0.038 J/m2
is calculated for the relaxed surface slab (Table 5), which is in
good agreement with the reported values41,58 of 0.040 and 0.047
J/m2. In accordance with literature,41,58 the VdO(1) bond lengths
are shorter compared to the calculated bulk structure by less
than 0.01 Å, while the V-O(2) and V-O(3) bond lengths are
larger by the same amount (Table 3). In agreement with the
periodic calculations of Yin et al.,59 when going from bulk to
one-layer V2O5 (Table 4), the negative charge of O(1) slightly
decreases from -0.53 to -0.47 whereas the charges of O(2)
and O(3) slightly increase from -0.80 to -0.83 and from -0.93
to -0.95, respectively, while the positive charge of V slightly
decreases from +1.86 to +1.83. The band structure of the single
(001) V2O5 slab (Figure S7 of the Supporting Information)
resembles much the band structure of bulk V2O5 (Figure S5 of
the Supporting Information), which is to be expected since the
interaction between layers in V2O5 is so weak and all atoms
within the (001) layer are coordinatively saturated. However,
it is worth noting that the states of the single surface layer have
somewhat less dispersion, i.e., they form narrower bands, as
Effect of (001) TiO2 Anatase Support on V2O5
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX G
TABLE 3: Calculated Bond Distances, Angles, and Band Structure for the Periodic Models Considered in This Study
Compared to the Experimental Values of Bulk V2O5
calculated
experimental (bulk V2O5)
V2O5 bulk
V2O5 slab
V2O5-V2O5 slab
V2O5-TiO2 slab (A)
VTiO slab (C)a
VdO(1)
VsO(2)
VsO(3)b
1.58
1.78
1.88/2.02
1.61
1.79
1.89/2.05
Bond Length (Å)
1.60
1.60
1.80
1.80
1.90/2.06
1.89/2.08
1.60
1.82
1.99/1.99
1.60 (1.58)
1.77 (1.77)
1.96/1.97c (1.95/2.00c)
V · · · VdO(1)d
VsO(2)sVe
VsO(3)sVf
89
149
143
89
149
143
Bond Angle (deg)
89
89
146
146
141
142
89
148
149
132
125
155
interlayer distance (Å)
O(1) · · · V, 2.79
O(1) · · · V, 2.87
O(1)′sTi, 2.22
O(3)sTi, 1.97
Fermi level
band gap (indirect/direct)
valence bandwidth
-6.7 ( 0.1g
2.3 ( 0.1h
5.5 ( 0.5i
-8.8
1.7/2.2
4.9
-6.8
0/0.2
6.2
-7.8
0.9/1.4
5.4
O(1)′ · · · V, 2.89
Band Structure (eV)
-8.5
-8.4
2.0/2.2
1.7/1.9
4.5
4.8
a
Values in parentheses from ref 15. b Along [010] direction/perpendicular to [010] direction. c This bond length is between O(3) and the
underlying titanium atom of the support. d This angle is between the vanadyl group and its next neighboring vanadium atom positioned along
the [100] direction (see angle R of Figure 4). e Angle β of Figure 4. f This angle is between O(3) and its two next neighboring vanadium atoms
positioned along the [010] direction (see angle γ of Figure 4). g Reference 47. h Reference 48. i Reference 49.
TABLE 4: Calculated Atomic Charges Originating from a Bader Analysis on the Periodic Models Considered in This Study
V)O(1)/V)O(1)′
model
bulk V2O5
bulk TiO2
V2O5 slab
V2O5-V2O5 slab
V2O5-TiO2 (A) slab
VTiO (C) slab
top layer
bottom layer (fixed)
vanadia overlayer
top titania layer (fixed)
bottom titania layer (fixed)
vanadia overlayer
top titania layer (fixed)
bottom titania layer (fixed)
V2O5 slab
V2O5-TiO2 slab
VTiO slab
orientation
∆Esurf (J/m2)
-0.53
-0.80
1.83
1.86/1.85
1.85/1.93
1.86/1.84
-0.47
-0.49/-0.53
-0.48/-0.62
-0.48/-0.59
-0.83
-0.82/-0.81
-0.83/-0.80
-0.84/-0.85
-0.89
-0.97
-0.77
-0.99
-0.98
1.86
∆Ef(surf) (J/m2)
0.038
(A)
(B)
(A)
(B)
(C)
O(2)/O(2)′
1.86
TABLE 5: Calculated Surface Energy (J/m2) for the
Unsupported (001) V2O5 Slab and Monolayer Formation
Energies (J/m2) for the Supported Periodic Models
Considered in This Study
model
O(1)/O(1)′
0.056
0.070
-0.622
-0.055
-0.698
compared to the bulk. For this reason, a slight decrease of the
valence bandwidth from 4.9 to 4.5 eV and a slight increase of
the indirect band gap from 1.7 to 2.0 eV is observed when going
from bulk to one-layer V2O5 (Table 3). As for bulk V2O5, a
direct band gap of 2.2 eV is calculated at the Γ-point and a
split-off band is again witnessed at the bottom of the conduction
band of the (001) V2O5 surface, being separated from the main
conduction band by a gap of 0.6 eV. Overall, these results are
in agreement with the aforementioned weak interlayer interactions in V2O5.
From Tables 3 and 4 (V2O5 slab vs V2O5-V2O5 slab) it can
be seen that a single layer slab is adequate for modeling the
(001) V2O5 surface, since no significant differences on the
structural and electronic properties of the surface are found for
a two-layer slab. The VdO(1) and VsO(2) bond lengths are
exactly the same, while the VsO(3) bond lengths differ only
by about 0.01 Å. On comparison of the atomic charges for the
one-layer slab with the charges on the atoms exposed to the
-0.49
O(3)/O(3)′
-0.93
-0.96
-0.95
-0.94/-0.93
-0.94/-0.93
-0.96/-0.97
-0.91
-0.98
-0.96
-0.96
-0.97
Ti
1.93
1.97
1.92
1.94
1.94
gas phase (i.e., VdO(1)′, O(1), O(2), O(3)) for the top layer of
the two-layer slab, very small differences of 0.01-0.03 are
found.
In addition to the periodic approach, the properties of the
unsupported vanadia surface have been studied using the V10
cluster (Figure 7).44 Although the Bader analysis for the cluster
yields slightly more localized atomic charges (i.e., of larger
absolute magnitude, namely, about 0.2 larger for V and 0.1
larger for O) as compared with the Bader analysis for the
periodic slab, the trends and differences that exist between
inequivalent ions are maintained (see Tables 4 and 6). According
to the Bader analysis, the charges on O(1), O(2), and O(3) are
-0.52, -0.88, and -1.07, respectively, for the V10 cluster and
-0.47, -0.83, and -0.95 for the V2O5 slab. In both cases
(cluster/slab), the negative charges on the oxygen atoms increase
in the following order, O(1) < O(2) < O(3), and the difference
of the charges between the inequivalent oxygen atoms (e.g.,
O(1)-O(2), O(2)-O(3)) is within the same order of magnitude.
From the calculation of the electrostatic potential for the V10
cluster, the location of the most negative electron potential is
found to be close to the vanadyl oxygens, which is in agreement
with the result obtained for the one-layer (001) V2O5 slab (Figure
8a vs Figure 9a). Moreover, the energy of the HOMO level for
the V10 cluster (-8.3 eV, Table 6) is in good agreement with
the calculated Fermi level of the one-layer V2O5 slab model
(-8.5 eV, Table 3), while the band gap of the cluster (3.9 eV,
Table 6) is larger than the one determined with the periodic
approach (2.2 eV, Table 3). In agreement with the periodic
calculations on the (001) V2O5 surface (Figure 10), the calculated
H
Alexopoulos et al.
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX
as Lewis acid sites. As seen in both cases from the projected
DOS of Figures 10 and 11, the electronic states of O(1) are
more localized in the center of the valence band having no
contribution at the bottom of the valence band, while those of
O(2) and O(3) are dispersed throughout the valence band with
higher densities near its edges (i.e., close to the Fermi level
and at the bottom of the valence band). Overall, there is a close
resemblance of the properties of the V10 cluster compared to
the V2O5 slab, thus justifying the modeling of the extended (001)
V2O5 surface using such a cluster.
Therefore, the chemical bonding at this surface can be
addressed using Wiberg bond order indices (Table 6) and
projected DOS and COOP curves (Figure 11) calculated for
the V10 cluster. According to the Wiberg bond order indices,
the covalent nature of the bonds linking the different oxygen
sites with their neighboring vanadium atoms decreases with
coordination number. The total bond orders of 2.12 for O(1),
of 1.84 for O(2), and of 1.62 for O(3) are in agreement with
the corresponding increase of the ionic character of the oxygen
center as expressed by the atomic charges, i.e., Bader charges
of -0.52 for O(1), of -0.88 for O(2), and of -1.07 for O(3).
In accordance with chemical intuition based on simple valence
concepts, the Wiberg bond order analysis yields clearly a double
bond (2.12) between V and O(1), two almost single bonds (0.92/
0.92) linking O(2) to two V atoms, and three bonds, each being
much weaker than a single bond (0.62/0.59/0.41), linking O(3)
to three V atoms. In addition, using the COOP in conjunction
with the DOS (Figure 11), the extent to which specific states
contribute to a bond between atoms can be analyzed. It is worth
noticing that in all cases the bonding contributions (positive
COOP curve) arising from the hybridization of V and O states
to form V-O bonds dominate the high energy region of the
valence band and decrease when going toward the top of the
valence band (close to the Fermi level), where the interaction
appears to be slightly bonding for the VdO(1) pair, nonbonding
(zero COOP curve) for the V-O(2) pair, and even slightly
antibonding (negative COOP curve) for the V-O(3) pair. The
Figure 7. Size converged cluster models used to represent the (001)
V2O5 surface (V10), a single layer of (001) V2O5 supported on (001)
TiO2 anatase (V10 on Ti10), and an epitaxial monolayer of V2O5
supported on (001) TiO2 anatase (V4_Ti15).
DOS for the V10 cluster (Figure 11) shows that the valence
band consists mainly of O states with non-negligible V
contributions, while the conduction band is dominated by V
providing unoccupied states to additional electrons, thus acting
TABLE 6: Calculated Atomic Charges (q), Total Bond Orders (BO) per Atom and Energy Levels (HOMO, LUMO) for the
Cluster Models Considered in This Studya
vanadia overlayer
model
V10
electronic
properties
qMulliken
qRoby-Davidson
qBader
∑(BO)Wiberg
Ti10
qMulliken
qRoby-Davidson
qBader
∑(BO)Wiberg
Ti15
qMulliken
qRoby-Davidson
qBader
∑(BO)Wiberg
V10 on Ti10 qMulliken
qRoby-Davidson
qBader
∑(BO)Wiberg
V4_Ti15
qMulliken
qRoby-Davidson
qBader
∑(BO)Wiberg
a
V
O(1)/O(1)′
1.47
1.71
2.00
4.68
-0.29
-0.29
-0.52
2.12
1.59
1.76
2.12
4.55
1.38
0.92
2.03
5.34
-0.32
-0.33
-0.65
2.15
-0.34
-0.20
-0.54
2.32
O(2)
top titania layer
O(3)
Ti
O(2)
O(3)
bottom titania layer
Ti
O(2)
O(3)
-0.65 -0.89
-0.72 -1.12
-0.88 -1.07
1.84
1.62
-0.66
-0.66
-0.87
1.84
-0.56
-0.38
-0.86
2.16
-0.90
-1.07
-1.04
1.64
-0.83
-0.66
-1.04
2.04
1.72
1.15
2.08
3.47
1.69
1.09
2.09
3.42
1.65
0.86
2.13
3.63
2.00
0.88
2.12
4.19
-0.81
-0.69
-1.05
1.65
-0.80
-0.72
-1.06
1.66
-0.71
-0.60
-1.01
1.66
-0.96
-0.60
-1.05
2.00
-0.88
-0.37
-1.01
1.78
-0.92
-0.58
-1.01
1.77
-0.91
-0.54
-1.01
1.81
-0.94
-0.46
-1.02
2.08
1.70
1.16
2.11
3.47
1.72
1.09
2.07
3.42
1.67
1.06
2.14
3.42
1.69
1.12
2.11
3.83
-0.81
-0.73
-1.06
1.65
-0.80
-0.69
-1.05
1.66
-0.82
-0.74
-1.08
1.63
-0.80
-0.67
-1.07
1.89
-0.89
-0.41
-1.00
1.78
-0.91
-0.56
-1.01
1.77
-0.88
-0.61
-1.03
1.77
-0.89
-0.50
-1.04
1.98
HOMO (eV) LUMO (eV) gap (eV)
-8.30
-4.40
3.90
-7.08
-3.27
3.81
-7.00
-3.21
3.78
-6.17
-4.98
1.19
-7.11
-5.02
2.09
The values of the electronic properties are always taken from the atoms located at the center of the cluster (see Figure 7), as they are the
most representative ones.
Effect of (001) TiO2 Anatase Support on V2O5
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX I
Figure 8. Isocontours (shown with white color) of the electrostatic potential calculated for the V2O5 (a), V2O5-TiO2 (b), and VTiO (c) slab
models. Blue balls are vanadium atoms, red balls are oxygen atoms, and green balls are titanium atoms.
Figure 9. Contour plots of the electrostatic potential (values in electronvolts, contour increment 0.27 eV) for the unsupported V10 (a) cluster, and
the supported V10 on Ti10 (b), and V4_Ti15 (c) clusters. Blue contours indicate a positive potential while red contours indicate a negative potential.
fact that there are almost no V states close to the Fermi level,
while O states exist in this region, is indicative of the presence
of oxygen lone pair electrons, which is responsible for the Lewis
basic character of these oxygen centers. On the other hand, clear
antibonding V-O states are observed above the band gap rising
abruptly above the lower split-off band of the conduction band.
The fact that no major antibonding V-O contributions are
observed for this unoccupied split-off band shows that some
additional electrons can be accommodated by the vanadia
surface without influencing much its V-O bonds. These
unoccupied V states are responsible for the Lewis acidity of
the vanadia surface.
Supported V2O5 Surface: Weak Interaction with Support.
As already mentioned in the methodology, two possible orientations of the vanadia monolayer on the titania support have been
envisaged (see Figure 5). From the periodic calculations with
these slab models, the following surface formation energies have
been obtained at 0 K after relaxation of the vanadia monolayer
(Table 5): ∆Ef(surfA) ) 0.056 J/m2, ∆Ef(surfB) ) 0.070 J/m2, and
after including the relaxation of the top titania layer: ∆Ef(surfA)
) 0.027 J/m2, ∆Ef(surfB) ) 0.029 J/m2. This leads to the
conclusion that there is almost no influence of the orientation
of the active phase with respect to the support on the energetics
of this system. Nevertheless, since orientation (A) is slightly
more favorable based on the formation energies at 0 K, the
V2O5-TiO2 slab (A) has been chosen to analyze further the
properties of this system when using the periodic approach.
Moreover, as the relaxation of the top titania layer causes no
significant changes in the geometry of the active phase and in
the electronic properties of the supported system (see Table S3
of the Supporting Information), it has not been considered in
the following discussion.
Some of the properties of the selected periodic model are
summarized in Tables 3 and 4 together with the ones of the
unsupported case (V2O5-TiO2 slab (A) vs V2O5 slab). As seen
in Table 3, compared to the unsupported vanadia slab, the
VdO(1) bond length remains the same, the VsO(2) bond length
increases slightly by 0.02 Å, while the largest structural change
in the surface active sites is witnessed for O(3). Both bonds
between O(3) and the vanadyl groups pointing into the substrate
(VdO(1)′) are elongated by 0.09 Å, which is related to the fact
that these vanadyl groups are weakly bonded with titania
(Ti-O(1)′ interlayer bond of 2.22 Å), and this bond elongation
is partially compensated by a bond contraction of 0.07 Å
between O(3) and the vanadyl group sticking out of the surface.
Overall, the structure of the supported vanadia overlayer in this
J
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX
Alexopoulos et al.
Figure 10. Projected DOS for the unsupported V2O5 slab and the supported V2O5-TiO2 and VTiO slabs. In all cases, a Gaussian broadening of
0.5 eV is applied and the Fermi level is indicated by a dotted vertical line.
Figure 11. Projected DOS (full lines) and COOP (dashed lines) for the unsupported V10 cluster and the supported V10 on Ti10 and V4_Ti15
clusters. In all cases, a Gaussian broadening of 0.5 eV is applied and the Fermi level is indicated by a dotted vertical line.
model does not deviate much from the unsupported case, which
is indicative of a weak interaction with the support. However,
focusing on the electronic properties when going from the
unsupported case to the supported case, certain changes can be
observed, with the most obvious ones being related to the band
structure. The direct band gap at the Γ-point for the supported
slab (0.2 eV) is found to be 2.0 eV smaller than the one for the
unsupported slab (2.2 eV), while no indirect band gap is
observed for the supported slab as opposed to the unsupported
case (2.0 eV). In addition, the Fermi level of the supported slab
(-6.8 eV) moves to lower binding energies as compared to the
one of the unsupported slab (-8.5 eV). This substantial decrease
in the band gap together with the energy shift of the Fermi level
can be an indication of a change in the reactivity of the surface.
As seen from Figure S8 of the Supporting Information, due to
the additional electronic states coming from the support, the
number of bands has increased considerably, leading to an
increase in the valence bandwidth (6.2 eV) as compared to the
unsupported case (4.5 eV). Similar to the unsupported slab, the
valence band of the supported slab mainly consists of O 2p
states with non-negligible metal (V, Ti) contributions at the
bottom of the band, whereas the conduction band is dominated
by unoccupied metal (V, Ti) 3d states. While the unoccupied
Ti 3d states are located well above the Fermi level at the top of
the conduction band, the unoccupied V 3d states are located
below the Ti 3d states at the bottom of the conduction band
ending at the Fermi level. Compared to the unsupported vanadia
slab, a split-off band is again witnessed at the bottom of the
conduction band of the supported vanadia slab, only this time
being located directly above the Fermi level and being separated
Effect of (001) TiO2 Anatase Support on V2O5
from the main conduction band by a gap of 0.5 eV, i.e., 0.1 eV
smaller than for the unsupported case. As seen in Table 4, when
going from the unsupported to the supported slab, the largest
changes in the atomic charges are obtained for the oxygen atoms
at the interface. A distinct example is the increase in the negative
charge (from -0.47 to -0.59) of the vanadyl oxygen (O(1)′)
of the vanadia overlayer which is bonded with the titania
support. To obtain a more clear view of the charge redistribution
induced by the weak interaction between vanadia and titania,
the charge density difference (eq 4) is calculated for different
regions of the V2O5-TiO2 (A) slab model (see Figure 12,
V2O5-TiO2 slab). As seen from the magnitude of the plotted
contours (part b vs c of Figure 12), most charge redistribution
occurs in the bonding region between vanadia and titania. In
this region (see Figure 12b), vanadia seems to be losing some
charge density, especially from the VdO(1)′ bond, in order to
create the new bond between O(1)′ and Ti. On the other hand,
a small gain of electron density is observed close to the vanadyl
oxygens (O(1)) that are pointing out of the surface (see Figure
12c). This is also evidenced by comparing the electrostatic
potential maps of the unsupported and supported vanadia
monolayer slabs. As seen in parts a and b of Figure 8, the
magnitude of the negative electrostatic potential located above
and in between the O(1) vanadyl oxygens increases upon
deposition of vanadia on titania, i.e., -2.7 eV for the unsupported and -4.1 eV for the supported vanadia slab.
In addition to the periodic approach, the properties of the
weak-interaction supported vanadia surface have been studied
using the V10 on Ti10 cluster (Figure 7). The energy of the
HOMO level for the V10 on Ti10 cluster (-6.2 eV, Table 6) is
in good agreement with the calculated Fermi level of the
V2O5-TiO2 slab model (-6.8 eV, Table 3). The band gap of
the cluster (1.2 eV, Table 6) is larger than the one determined
with the periodic approach (0.2 eV, Table 3), which was also
the case for the unsupported system and can be attributed to
the hybrid nature of the functional used for the cluster
calculations. A comparison between the slab calculation (Figure
10, V2O5-TiO2 slab) and the cluster calculation (Figure 11, V10
on Ti10 cluster) yields very small differences in the valence
band widths and qualitative agreement as to the energy variation
of the p-DOS. Moreover, the charge density difference calculated for the slab model (Figure 12a, V2O5-TiO2 slab) is very
similar to the one calculated for the cluster model (Figure 12a,
V10 on Ti10 cluster). The largest difference is seen for the
orientation of the V 3d orbitals that are gaining electron density
upon deposition of the vanadia monolayer on the titania support
(i.e., dxy for the slab vs dyz for the cluster). According to the
Bader analysis, the charges on O(1)′, O(2), O(3) of the vanadia
overlayer are respectively -0.65, -0.87, -1.04 for the V10
on Ti10 cluster (Table 6), while the respective charges amount
to -0.59, -0.84, -0.96 for the V2O5-TiO2 slab (Table 4).
Therefore, the trends and differences that exist between the
inequivalent oxygen atoms are maintained in both modeling
approaches (cluster and slab), and an overall close resemblance
is found between the properties of V10 on Ti10 cluster vs
V2O5-TiO2 slab.
Comparing the supported cluster with the vanadia and titania
clusters (V10 on Ti10 vs V10 and Ti10), it can be seen from
the Mulliken population analysis in Table 6 that there is a charge
transfer from vanadium, whose charge increases from +1.47
to +1.59, to titanium, whose charge decreases from +1.72 to
+1.65, through the vanadyl oxygen sticking into the substrate,
whose charge slightly increases from -0.29 to -0.32. Furthermore, to verify the results obtained from the atomic charges of
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX K
the Mulliken population analysis, a modified Roby-Davidson
population analysis based on occupation numbers was carried
out. In contrast to the Mulliken population analysis, it is worth
mentioning that based on the modified Roby-Davidson population analysis the calculated atomic charges on vanadium (+1.71)
for the unsupported V10 cluster and on titanium (+1.15) for
the Ti10 cluster agree with the order as expected from the formal
oxidation states for these metal centers, i.e., Vx+, Tiy+ with x >
y. However, when comparing the supported cluster with the
vanadia and titania clusters, the modified Roby-Davidson
population analysis points again to a charge transfer from
vanadium, whose charge increases from +1.71 to +1.76, to
titanium, whose charge decreases from +1.15 to +0.86, through
the vanadyl oxygen sticking into the substrate, whose charge
slightly increases from -0.29 to -0.33, all in agreement with
the Mulliken population analysis. Moreover, when going from
the unsupported to the supported system, the changes in the
total bond orders per atom fully agree with the results previously
obtained for the charge redistribution using either a Mulliken
or a modified Roby-Davidson population analysis. The total
bond order around vanadium decreases from 4.68 to 4.55,
indicating a loss in electron density around this atom, while
the total bond order per atom increases around titanium from
3.47 to 3.63 and around the vanadyl oxygen sticking into the
substrate from 2.12 to 2.15, indicating a gain in electron density
around these atoms. The new bond that is formed between O(1)′
and Ti is rather weak with a bond order of 0.23, while the
VdO(1)′ bond is slightly weakened with a bond order of 1.92.
The aforementioned charge depletion from vanadium followed
by charge accumulation at the vanadia-titania interface is also
indicated by the Bader analysis when going from the unsupported to the supported vanadia cluster. The positive charge on
vanadium increases from +2.00 to +2.12 while the negative
charge of the vanadyl oxygen sticking into the titania support
increases from -0.52 to -0.65. However, a slight increase of
the positive charge on titanium at the interface (from +2.08 to
+2.13) is observed from the Bader analysis, which is in
disagreement with what is found from the other three population
analysis methods but is in good agreement with the loss of
electron density around the titanium atom as witnessed from
the charge density difference plot for this kind of system (see
Figure 12b). Comparing the contour graphs of the electrostatic
potential for the unsupported and supported vanadia cluster
(parts a vs b of Figure 9), a small increase in the positive charge
above the vanadium atoms is observed, which is in accordance
with the loss of electron density in this region as witnessed from
the charge density difference plot for this system (see Figure
12b). Finally, on comparison of the DOS and COOP curves
between the V10 and the V10 on Ti10 cluster (Figure 11), it
can be seen that most changes are observed for the occupied
O(1)′ states whose stability increases after their interaction with
the support, while the rest remain to a large extent the same.
However, the most important change is the shift in the energy
positions of the HOMO, from -8.3 to -6.2 eV, and of the
LUMO, from -4.4 to -5.0 eV. As the LUMO eigenvalue
corresponds to the energy change on addition of an incremental
negative charge to the model and can be used as a measure of
the Lewis acidity,60 it can be concluded from the observed shift
of the LUMO that the Lewis acidity of the vanadium atoms
becomes stronger upon deposition of vanadia on titania, which
is in agreement with the changes in the electrostatic potential
(part a vs b of Figure 9) and with the charge redistribution
calculated using atomic charges and charge density difference
maps (Figure 12b).
L
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX
Alexopoulos et al.
Figure 12. Charge density difference plot calculated according to eq 4 for the V2O5-TiO2 slab model (a, isocontour value of 0.03 e/Å3) and for the V10 on Ti10 cluster (a, isocontour value of 0.05 e/Å3).
Blue contours indicate a gain of electron density, while red contours indicate a loss of electron density. The contour maps are plotted for two regions (only the most representative one for the cluster model)
where the vanadyl oxygens of the (001) V2O5 monolayer are pointing inward to the (001) TiO2 anatase (b, contour increment 0.01 e/Å3) and outward to the vacuum (c, contour increment 0.001 e/Å3).
Effect of (001) TiO2 Anatase Support on V2O5
Supported V2O5 Surface: Strong Interaction with Support.
As already mentioned, three possible configurations of the
vanadia monolayer on the titania support have been investigated
(see Figure 6). From the calculated surface formation energies
at 0 K after relaxation of the vanadia monolayer of the slab
models (Table 5), it is found that the most stable configuration
is C with ∆Ef(surfC) ) -0.698 J/m2, followed closely by
configuration A with ∆Ef(surfA) ) -0.622 J/m2, while configuration B with ∆Ef(surfB) ) -0.055 J/m2 is the least stable.
Including the relaxation of the top titania layer does not change
this order in stability, yielding the following surface formation
energies: ∆Ef(surfA) ) -0.562 J/m2, ∆Ef(surfB) ) -0.202 J/m2,
∆Ef(surfC) ) -0.659 J/m2. Therefore, configuration C is chosen
to represent the strong interaction model. Moreover, apart from
a slight elongation of the V-O(3) distances, the relaxation of
the top titania layer causes no other significant changes in the
geometry of the active phase and in the electronic properties of
the supported system (see Table S3 of the Supporting Information), and hence it has not been considered in the following
discussion.
As seen from Figure 6, this fully oxidized vanadia monolayer
is composed of O(1)dVsO(2)sVdO(1) groups which are
connected to each other along the [010] direction via surface
O(3) sites, thus forming rows along this direction. Apart from
bridging two vanadium atoms, the triply coordinated surface
O(3) sites are also bonded to the underlying titanium atoms of
the support. The vanadium atoms are coordinated to four oxygen
atoms within the vanadia overlayer (i.e., one O(1), one O(2),
and two O(3)) and to one O(2) atom of the (001) TiO2 support,
keeping the coordination number to five. The strong interaction
between the vanadia monolayer and the support leads to a much
higher epitaxy as compared to the weak interaction model
discussed above. It is worth mentioning that Vittadini and
Selloni,15 using theoretical calculations with a different approach
for the construction of the model, i.e., via polymerization of
vanadia monomers followed by elimination of the residual
surface OH groups, reported a structure for the supported
monolayer V2O5 that is in accordance with what is found in
the present study. As illustrated in Table 3, similar bond lengths
were obtained by Vittadini and Selloni.15 Overall, by comparing
the surface formation energies (Table 5), it can be concluded
that this configuration, i.e., VTiO slab (C), is at 0 K the most
favorable structure for the oxidized vanadia monolayer among
the investigated interface models.
The properties of the selected periodic model are summarized
in Tables 3 and 4, where distinct differences with the other
models can be observed (VTiO slab (C) vs V2O5-TiO2 slab
(A) and/or V2O5 slab). As seen in Table 3, although the VdO(1)
bond lengths for this model are the same as for the unsupported
and supported (001) V2O5 surface (1.60 Å in all cases), the
vanadyl groups in this case are tilted, i.e., V · · · VdO(1): 132°
in the VTiO slab instead of 89° in both V2O5 and V2O5-TiO2
slab. Moreover, the V-O(2) bonds of the VTiO slab are shorter
(1.77 Å in the VTiO slab, 1.80 Å in the V2O5 slab, and 1.82 Å
in the V2O5-TiO2 slab) and thus stronger compared to the other
two cases. In addition, the V-O(3) bond lengths along the [010]
direction scale as follows for the different surface models: 1.90
Å (V2O5) < 1.96 Å (VTiO) < 1.99 Å (V2O5-TiO2), with their
strength increasing in the opposite manner. As a sign of stronger
interaction between the vanadia monolayer and the titania
support, the interlayer distance of the VTiO slab is shorter (1.97
Å) than the one of the V2O5-TiO2 slab (2.22 Å). The most
characteristic features obtained from the band structure calculations are also reported in Table 3, where a shift in the Fermi
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX M
level to lower binding energies (from -8.5 to -7.8 eV) is
observed when comparing the unsupported V2O5 with the
supported VTiO model. The direct band gap at the Γ-point for
the VTiO slab (1.4 eV) is found to be 0.8 eV smaller than the
one for the unsupported slab (2.2 eV), while the indirect band
gap for the supported slab (0.9 eV, corresponding to a Y f Γ
transition) is found to be 1.1 eV smaller than the one for the
unsupported case (2.0 eV, corresponding to a R f Γ transition).
As seen from Figure S9 of the Supporting Information, similar
to the V2O5 and V2O5-TiO2 slab, the valence band of the
supported VTiO slab is mainly occupied by O 2p states with
non-negligible metal (V, Ti) contributions at the bottom of the
band, while the conduction band is dominated by unoccupied
metal (V, Ti) 3d states. Like the V2O5-TiO2 slab, the bottom
of the conduction band is dominated by empty V 3d states.
Therefore, both weak and strong interaction between the two
phases result in a smaller band gap for the supported system,
while empty vanadium levels are located below the ones
belonging to titanium, in agreement with what has been reported
by Haber and Witko61 for the V2O5/TiO2 system. A noticeable
difference between the two cases of the supported vanadia
monolayer is that the weak interaction model exhibits a wider
valence band (6.2 eV) than the strong interaction model (5.4
eV), which can be attributed to less mixing of bands between
the vanadia and the titania phase resulting in a more or less
simple superposition of bands that is indicative of the weak
interaction between these two phases. Compared to the V2O5
and the V2O5-TiO2 slab, a split-off band is again witnessed at
the bottom of the conduction band of the VTiO slab, only this
time being separated from the main conduction band by a much
smaller gap (0.05 eV) than in the case of the unsupported (0.6
eV) and supported (001) V2O5 surface (0.5 eV). The results of
the Bader analysis are summarized in Table 4, where no
significant differences in the charges of the surface oxygen atoms
exist between the V2O5, V2O5-TiO2, and VTiO slab, with the
largest change being a decrease in the charge of the O(2) site
when going from V2O5 (-0.83) to VTiO (-0.77). However, as
seen in Figure 8, the magnitude of the negative electrostatic
potential located above and in between the vanadyl oxygens
sticking out of the surface is not only increasing upon deposition
of vanadia on titania (-2.7 eV for the unsupported V2O5 slab
and -4.7 eV for the supported VTiO slab), but also increasing
as the epitaxy of the monolayer on the support becomes higher
(-4.1 eV for the supported V2O5-TiO2 slab and -4.7 eV for
the supported VTiO slab).
In addition to the periodic approach, the properties of the
supported vanadia-strong interaction surface have been studied
using the V4_Ti15 cluster (Figure 7). According to the Bader
analysis, the charges on O(1), O(2), and O(3) of the vanadia
overlayer are -0.54, -0.86, and -1.04, respectively, for the
V4_Ti15 cluster (Table 6), while the respective charges are
-0.49, -0.77, and -0.96 for the VTiO slab (Table 4).
Therefore, the trends and differences that exist between the
inequivalent oxygen atoms are maintained in both modeling
approaches (cluster and slab). Moreover, from the calculation
of the electrostatic potential for the V4_Ti15 cluster, the location
of the most negative electron potential at the vanadia surface is
found to be close to the vanadyl oxygens, which is in agreement
with the result obtained for the VTiO slab (Figure 8c vs Figure
9c). The energy of the HOMO level for the V4_Ti15 cluster
(-7.1 eV, Table 6) is in good agreement with the calculated
Fermi level of the VTiO slab model (-7.8 eV, Table 3). The
band gap of the cluster (2.1 eV, Table 6) is larger than the one
determined with the periodic approach (1.4 eV, Table 3), which
N
Alexopoulos et al.
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX
TABLE 7: Calculated Hydrogen Adsorption Energies on Different Oxygen Sites and Models
this work
Hermann et al.a
Yin et al.b
Goclon et al.c
∆Eads (kJ/mol)
V2O5 slab
V2O5-TiO2 slab
VTiO slab
V10 cluster
V2O5 slab
V2O5-V2O5 slab
O(1) + H f O(1)*H
O(2) + H f O(2)*H
O(3) + H f O(3)*H
-277
-268
-252
-286
-276
-286
-340
-260
-265
-294
-266
-241
-271
-253
-249
-290
-269
-251
a
Reference 44. b Reference 59. c Reference 62.
was also the case for the unsupported vanadia and for the
supported vanadia-weak interaction model. Finally, a comparison of the slab calculation (Figure 10, VTiO slab) with the
cluster calculation (Figure 11, V4_Ti15 cluster) yields very small
differences in the valence band widths and qualitative agreement
as to the energy variation of the p-DOS. Therefore, an overall
close resemblance is found between the properties of V4_Ti15
cluster and the VTiO slab.
Further analysis using cluster calculations has been performed
to compare the electronic and bonding properties of the
V4_Ti15, V10 and V10 on Ti10 models. When going from V10
to V4_Ti15, a clear decrease of the magnitude of the atomic
charges on vanadia occurs as calculated from the modified
Roby-Davidson analysis (from +1.71/-0.29/-0.72/-1.12 at
V10 to +0.92/-0.20/-0.38/-0.66 at V4_Ti15 for V/O(1)/O(2)/
O(3), respectively). This is accompanied by a respective increase
in the total Wiberg bond orders (from 4.68/2.12/1.84/1.62 at
V10 to 5.34/2.32/2.16/2.04 at V4_Ti15 for V/O(1)/O(2)/O(3),
respectively), thus enhancing the covalent character of the V-O
bonding at the vanadia surface at the expense of the ionic
bonding. By comparing the bond orders of the interlayer bonds
for V4_Ti15 (0.68) and V10 on Ti10 (0.23), it is clear that the
O(3)-Ti bond of V4_Ti15 is much stronger than the O(1)′-Ti
bond of V10 on Ti10, justifying their characterization as models
of strong and weak interaction with the support, respectively.
Comparing the DOS and COOP curves between the V10 and
the V4_Ti15 cluster, most changes in the shape of these curves
are observed for the occupied O(2) states whose stability
increases in accordance with the increase of the bond order of
V-O(2) from 0.92 in V10 to 1.08 in V4_Ti15, while the rest
remain to a large extent the same. However, the most important
change is the shift in the energy positions of the HOMO from
-8.3 to -7.1 eV and of the LUMO from -4.4 to -5.0 eV.
Like in the case of the V10 on Ti10 cluster, the observed shift
of the LUMO when going from the V10 to the V4_Ti15 cluster
indicates that the Lewis acidity of the vanadia centers becomes
stronger upon deposition of vanadia on titania, regardless of
the way those two phases interact, i.e., weak or strong
interaction. The increased acidity of the VOx/TiO2 catalyst
system compared to pure V2O5 was also observed by Kachurovskaya et al.6 using cluster models constructed by replacing
a surface titanium atom by a vanadium atom.
Hydrogen Adsorption. As already mentioned there are
several inequivalent active sites available on the vanadia surface.
To test their reactivity for activating a C-H bond of a
hydrocarbon, hydrogen adsorption has been used as a probe
reaction.22 However, it is worth mentioning that because the
active phase is modeled as a vanadia monolayer, there are no
V-O-Ti active sites, as proposed in literature for V2O5/TiO2
catalysts with less than a monolayer of vanadia.62 As shown in
Table 7, for all sites of the supported and unsupported vanadia
monolayer, hydrogen adsorption is an exothermic process. For
the unsupported vanadia the adsorption energies at the different
sites are in good agreement with other periodic and cluster
calculations (see Table 7).44,59,63 The vanadyl oxygen (O(1)) is
Figure 13. Calculated adsorption energy of hydrogen vs average V-O
bond distance.
the most favorable one for H adsorption, and the adsorption
energy on this site increases upon deposition of the vanadia
monolayer on the titania anatase support and is further increased
as a higher epitaxy of vanadia on titania is achieved (V2O5,
-277 kJ/mol; V2O5-TiO2, -286 kJ/mol; VTiO, -340 kJ/mol),
which correlates well with the increase in the negative electrostatic potential above this site (see Figure 8). Interestingly
enough, as mentioned in literature,64 H adsorption on vanadia
follows the same trend as H+ adsorption, thus such a correlation
is to be expected. On the bridging oxygen sites, O(2) or O(3),
the observed trend in the adsorption energies when going from
the unsupported to the supported vanadia correlates well with
the V-O distances (Figure 13), since upon H adsorption these
bonds have to be elongated. With this rationale, the shorter the
bonds (i.e., V-O(2), 1.82 Å (V2O5-TiO2) > 1.80 Å (V2O5) >
1.77 Å (VTiO); average V-O(3), 1.99 Å (V2O5-TiO2) > 1.96
Å (VTiO) > 1.95 Å (V2O5)), the stronger they are and the
more the energy that needs to be used to elongate them, thus
yielding a lower adsorption energy (i.e., O(2), -276 kJ/mol
(V2O5-TiO2), -268 kJ/mol (V2O5), -260 kJ/mol (VTiO); O(3),
-286 kJ/mol (V2O5-TiO2), -265 kJ/mol (VTiO), -252 kJ/
mol (V2O5)). Another possible and more general way of
explaining the observed reactivity of the oxygen sites in H
adsorption for the different catalyst models is in terms of frontier
orbital analysis and models based on band-orbital mixing.34,39
As the most important bonding interactions are between frontier
orbitals, it can be expected that the adsorption energy of the
same adsorbate (i.e., H) on the oxygen sites of the different
catalyst models is related to the energy positions of the metal
oxide’s occupied and unoccupied states. Such a correlation is
illustrated in Figure 14, where the calculated adsorption energy
of H is plotted versus the band gap between the lowest
unoccupied band, i.e., Vt2g, and the highest occupied band, i.e.,
Op, for each oxygen site and different catalyst models. From
this figure it is observed that the adsorption energy becomes
more exothermic when the highest occupied oxygen band moves
to lower binding energies and/or the lowest unoccupied vanadium band moves to higher binding energies. Finally, as seen
in Table S3 of the Supporting Information, the additional
relaxation of the topmost titania layer does not result in major
Effect of (001) TiO2 Anatase Support on V2O5
J. Phys. Chem. C, Vol. xxx, No. xx, XXXX O
well with the energy positions of the frontier orbitals of the
metal oxide, since the adsorption energy of H becomes more
exothermic when the highest occupied oxygen band moves to
lower binding energies and/or the lowest unoccupied vanadium
band moves to higher binding energies.
Acknowledgment. The European Community (FP6 Network
of Excellence IDECAT (NMP3-CT-2005-0113)) is acknowledged for financial support.
Figure 14. Calculated adsorption energy of hydrogen vs V-O band
gap (between lowest unoccupied band, i.e., Vt2g, and highest occupied
band, i.e., Op, for each oxygen site), where ε corresponds to the energy
position of the center of each band (estimated using the function centroid
of the respective p-DOS curve).
changes in the adsorption energies of hydrogen, apart from an
increase in the adsorption energy of 9 kJ/mol for the O(3) site
of the VTiO (C) model.
Conclusions
Cluster and periodic DFT calculations have been performed
to analyze the effect of (001) TiO2 anatase support on the
structure and properties of a fully oxidized V2O5 monolayer.
Both theoretical approaches arrive at the same qualitative results.
In accordance with experimental evidence, two different models
of the monolayer V2O5/TiO2 (anatase) catalyst have been
investigated. In the first one, the vanadia monolayer maintains
its crystallographic (001) V2O5 structure when supported on
titania anatase. Although the interaction between the two phases
is rather weak in this model, it is still enough to induce a charge
redistribution that enhances the Lewis acidity of vanadium. In
the second model, the presence of the titania anatase support
alters significantly the structure of the fully oxidized vanadia
monolayer, resulting in a stronger interaction and achieving a
much higher epitaxy. On the basis of the surface formation
energies at 0 K, the strong interaction model has the most
favorable configuration for the structure of the supported
oxidized vanadia monolayer.
The electronic structure of the investigated systems has been
characterized in detail using band structure calculations. Compared to the unsupported vanadia, both weak and strong
interaction models result in a shift of the Fermi level to lower
binding energies together with a reduced band gap, which can
lead to possible changes in the reactivity of the catalyst
depending also on the adsorbate. In both cases, the shift of the
lowest unoccupied V states to higher binding energies upon
deposition of vanadia on titania indicates that the Lewis acidity
of vanadium becomes stronger. Moreover, the electrostatic
potential proves to be a useful reactivity descriptor, indicating
the electron-rich regions. A hard electrophilic attack will occur
close to the vanadyl oxygens for any case, while the deposition
of a vanadia monolayer on titania anatase increases the chemical
hardness of the vanadyl site for both weak and strong interaction
models. It is also observed that the higher the epitaxy with the
support, the more electron rich the vanadyl region is. Therefore,
atomic hydrogen adsorption at 0 K is most favorable at the
vanadyl site of the supported vanadia monolayer with the highest
epitaxy. In conclusion, the observed reactivity of the oxygen
sites in H adsorption for the different catalyst models correlates
Supporting Information Available: Optimization of the unit
cell volume of bulk V2O5 and TiO2 anatase, optimization of
the vanadia-titania distance using cluster calculations, band
structures of the periodic models, overview of all cluster models
used together with their electronic properties, effect of relaxation
on geometric/electronic/energetic data obtained using periodic
calculations, and atomic coordinates of the selected catalyst
models. This material is available free of charge via the Internet
at http://pubs.acs.org.
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