Scaling relationships for adsorption energies on transition metal oxide, sulfide, and nitride surfaces.

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Surface Adsorption
DOI: 10.1002/anie.200705739
Scaling Relationships for Adsorption Energies on Transition Metal
Oxide, Sulfide, and Nitride Surfaces**
Eva M. Fern?ndez, Poul G. Moses, Anja Toftelund, Heine A. Hansen, Jos? I. Mart?nez,
Frank Abild-Pedersen, Jesper Kleis, Berit Hinnemann, Jan Rossmeisl, Thomas Bligaard, and
Jens K. Nørskov*
There has been substantial progress in the description of
adsorption and chemical reactions of simple molecules on
transition-metal surfaces. Adsorption energies and activation
energies have been obtained for a number of systems, and
complete catalytic reactions have been described in some
detail.[1–7]Considerable progress has also been made in the
theoretical description of the interaction of molecules with
transition-metal oxides,[8–19]sulfides,[20–25]and nitrides,[26–29]but
it is considerably more complicated to describe such complex
systems theoretically. Complications arise from difficulties in
describing the stoichiometry and structure of such surfaces,
and from possible shortcomings in the use of ordinary
generalized gradient approximation (GGA) type density
functional theory (DFT).[30]
Herein we introduce a method that may facilitate the
description of the bonding of gas molecules to transition-
metal oxides, sulfides, and nitrides. It was recently found that
there are a set of scaling relationhips between the adsorption
energies of different partially hydrogenated intermediates on
transition-metal surfaces.[31]We will show that similar scaling
relationships exist for adsorption on transition metal oxide,
sulfide, and nitride surfaces. This means that knowing the
adsorption energy for one transition-metal complex will make
it possible to quite easily generate data for a number of other
complexes, and in this way obtain reactivity trends.
The results presented herein have been calculated using
self-consistent DFT. Exchange and correlation effects are
describedusing therevised
(RPBE)[32]GGA functional. It is known that GGA func-
tionals give adsorption energies with reasonable accuracy for
transition metals.[32,33]It is not clear, however, whether a
similar accuracy can be expected for the oxides, sulfides, and
Perdew–Burke–Ernzerhof
nitrides, although there are examples of excellent agreement
between DFT calculations andexperiments, for example, with
RuO2 surfaces.[9]In our study we focused entirely on
variations in the adsorption energies from one system to
another, and we expected that such results would be less
dependent than the absolute adsorption energies on the
description of exchange and correlation.
For the nitrides, a clean surface and a surface with a
nitrogen vacancy were studied. For MX2-type oxides or
sulfides, an oxygen- or sulfur-covered surface with an oxygen
or sulfur vacancy was studied. The structures of the clean
surface considered in the present work and their unit cells are
shown in Figure 1. The adsorption energies given below are
for the adsorbed species in the most stable adsorption site on
the surface.
By performing calculations for a large number of tran-
sition-metal surfaces of different orientations,[31]it was found
that the adsorption energy of intermediates of the type AHxis
linearly correlated with the adsorption energy of atom A (N,
O, S) according to Equation (1):
DEAHx¼ gðxÞDEAþ x
ð1Þ
Here the scaling constant is given to a good approxima-
tion by Equation (2) where xmaxis the maximum number of
H atoms that can bond to the central atom A (xmax=3 for A=
N, and xmax=2 for A=O, S), that is, the number of hydrogen
atoms that the central atom Awould bond to in order to form
neutral gas-phase molecules.
gðxÞ ¼ ðxmax?xÞ=xmax
ð2Þ
We have performed similar calculations for the adsorption
of oxygen, sulfur, and nitrogen on a series of transition metal
oxide, sulfide, and nitride surfaces (Figure 2). We find that
scaling relationhips also exist for these systems, which are
considerably more complex than the transition-metal surfa-
ces. Such a correlation between the adsorption energies of O
and OH has previously been found for the MO2oxides.[12]
Furthermore, it can be seen that the scaling constant g(x) is
given to a good approximation by the same expression
[Eq. (2)] as for adsorption on the transition metals. We find
that the mean absolute error (MAE) is lower than 0.19 eV for
all the species considered here. The nitride surfaces present a
poorer correlation than the others, mainly because TiN(100)
is a clear outlier.
[*] Dr. E. M. Fern?ndez, P. G. Moses, A. Toftelund, H. A. Hansen,
J. I. Mart?nez, Dr. F. Abild-Pedersen, Dr. J. Kleis, Prof. J. Rossmeisl,
Prof. T. Bligaard, Prof. J. K. Nørskov
Center for Atomic-scale Materials Design
Department of Physics, Technical University of Denmark
DK-2800 Lyngby (Denmark)
Fax: (+45) 4593-2399
E-mail: norskov@fysik.dtu.dk
Dr. B. Hinnemann
Haldor Topsøe A/S, Nymøllevej 55, DK-2800 Lyngby (Denmark)
[**] The Center for Atomic-scale Materials Design is funded by the
Lundbeck Foundation. We wish to acknowledge additional support
from the Danish Research Agency through grant 26-04-0047 and the
Danish Center for Scientific Computing through grant HDW-0107-
07.
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It is interesting to compare the results of Figure 2 with the
equivalent results for adsorption on the transition metals
(Figure 3). It is found that the linear relationships for the
nitrides are essentially the same for the two classes of systems.
For the oxides, and partially for the sulfides, the results for the
compounds are shifted from those on the transition metals.
We trace this difference to a difference in the adsorption sites
on the two kinds of systems. On the transition-metal surfaces,
O and OH are generally found to coordinate with more than
one metal neighbor. On the other hand, on the oxide surfaces
the O atoms are generally coordinated to a single metal atom.
If we use the adsorption energies for O and OH on the
transitionmetals, where they areforced to adsorbin an on-top
manner, the results now fall on the
samelineas
(Figure 3). For the sulfides, the S
atom also adsorbs at a different
site than on the transition metal. If
the same adsorption site on the
metal is considered the data agree,
as for the oxides, with the results
obtained for adsorption onto the
sulfide surface.
The results of Figures 2 and 3
are remarkable and indicate that
the nature of the adsorption bond
is similar for the transition metals
and the compounds. For the tran-
sition-metal surfaces, the scaling
relationships can be understood
within the d-band model.[34–39]The
variation in adsorption energies
for a given atom or molecule
among the transition metals is
mainly given by the variations in
the strength of the coupling of the
valence states of the adsorbate
with the d states of the transition
metal.Thevariations
adsorption energy of an atom A
from one transition-metal surface
to the next reflect this. If H atoms
are now added to atom A, the
ability of A to couple to the metal
fortheoxides
inthe
d states decreases, either because the modified A states can
couple to fewer d states or because the bonds become
longer.[31]The principle of bond-order conservation would
indicate that the weakening of the bond strength is propor-
tional to the number of H atoms added, which corresponds to
Equation (2).[31]The scaling behavior observed in Figures 2
and 3 indicates that similar arguments should hold for
adsorption on transition-metal oxides, sulfides, and nitrides.
The key to understanding this can be found in recent work by
Ruberto and Lundqvist,[40]in which they show that a suitably
modified d-band model can be used to understand trends in
adsorption energies on transition-metal carbides and nitrides.
Figure 1. Structures used to describe the surfaces of the transition-metal nitrides, oxides and sulfides. a) Fcc-like structure for the M2N (100)
surface, M=Mo and W. Dark and light blue spheres represent metal and N atoms, respectively. b) Fcc-like rock-salt structure for the TiN (100)
surface. Dark blue and gray spheres represent Ti and N atoms, respectively. c) Rutile-like (110) surface for the PtO2surface. Red and white
spheres represent O and metal atoms, respectively. d) Perovskite structure for the LaMO3(100) surface, with M=Ti, Ni, Mn, Fe, and Co. Red,
purple, and violet spheres represent O, La, and metal atoms, respectively. e) Hcp-like (?1010) surfaces for NbS2, TaS2, MoS2, WS2, Co-Mo-S, Ni-
Mo-S, and Co-W-S. Yellow and green spheres represent S and metal atoms, respectively. The black dashed boxes indicate the unit cell.
Figure 2. Adsorption energies of NH and NH2intermediates over nitrides, an OH intermediate over
oxides, and an SH intermediate over sulfides plotted against adsorption energies of N over nitrides, O
over oxides, and S over sulfides, respectively. The adsorption energy of AHxis defined as: DEAHx=
E(AHx*)+(xmax?x)/2E(H2)?E(*)?E(AHxmax) where E(AHx*) is the total energy of an AHxintermediate
adsorbed on the most stable adsorption site, E(*) is the total energy of the surface without the A atom
adsorbed, and E(H2) and E(AHxmax) are the total energies of the hydrogen molecule and the AHxmax
molecule in a vacuum, respectively.
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The strength of the scaling relationships is shown by the
following example. If one has a calculated or an experimental
adsorption energy of an adsorbate AHx(DEAHx
transition metal or transition-metal compound M1, we can
estimate the energy DEAHx
M2
of the same intermediate on
another system M2 from the adsorption energies of atom A
on the two systems, by using Equation (3).
M1) for one
DEAHx
M2¼ DEAHx
M1þ gðxÞðDEA
M2?DEA
M1Þ
ð3Þ
g(x) is a rational number given by Equation (2). If we
have a database of atomic adsorption energies for a number
of systems, we may then estimate the adsorption energy of a
number of intermediates. This opens the possibility of
obtaining an overview of adsorption energies on oxides,
sulfides, and nitride surfaces on the basis of a few calculations.
In summary, density functional theory calculations on the
adsorption of O, OH, S, SH, N, NH, and NH2on a range of
transition metal oxide, sulfide, and nitride surfaces have been
presented. It is shown that the adsorption energies DEAHxof
AHxintermediates scale with the adsorption energies DEAof
the A atoms according to the equation DEAHx=g(x)DEA+ x,
where the proportionality constant g(x) is independent of the
metal and only depends on the number of H atoms in the
molecule.
Experimental Section
The results presented herein
were calculated using self-con-
sistent DFT. The ionic cores
and their interaction with the
valence electrons are described
by ultrasoft pseudopotentials
(soft pseudopotential for S),[41]
and the valence wave functions
are expanded in a basis set of
plane waves with a kinetic
energy cut-off of 350–400 eV.
The electron density of the
valence states was obtained by
a self-consistent iterative diag-
onalization of the Kohn–Sham
Hamiltonian with Pulay mixing
of the densities.[42]The occupa-
tion of the one-electron states
was calculated using an elec-
tronic temperature of kBT=
0.1 eV (0.01 eV for the mole-
cules in a vacuum); all energies
were extrapolated to T=0 K.
The ionic degrees of freedom
were relaxed using the quasi-
Newton minimization scheme,
until the maximum force com-
ponent was
0.05 eV??1.Spin
moments for the oxides, Co-
Mo-S, Ni-Mo-S, and Co-W-S
weretaken
Exchange and
effects are described using the
RPBE[32]GGA functional.
We used the periodic slab
approximation, and the unit
smaller than
magnetic
intoaccount.
correlation
cells considered were modeled by a (2?2) unit cell for the nitrides
and perovskite-type oxides, a (2?1) unit cell for PtO2, a (2?1) unit
cell for Co-W-S and MS2surfaces with M=Mo, Nb, Ta, and W, and a
(4?1) unit cell for the M-Mo-S surface with M=Ni and Co. A four-
layer slab for the nitrides and perovskite-type oxides, a four trilayer
slab for PtO2-type oxides, and an 8 or 12 layer slab for sulfides were
employed in the calculations. Neighboring slabs were separated by
more than 10 ? of vacuum.The results for the MO2surfaces with M=
Ir, Mn, Ru, and Ti are taken from Refs. [12,15] The adsorbate
together with the two topmost layers for the nitrides and perovskite-
type oxides, the two topmost trilayers for MO2oxides, and all layers
for the sulfides were allowed to fully relax. The Brillouin zone of the
systems was sampled with a 4?4?1 Monkhorst-Pack grid for the
nitride and oxide surfaces and with a 6?1?1 (4?1?1) grid for the
2?1 (4?1) supercell of the sulfide surfaces.
Received: December 14, 2007
Revised: March 28, 2008
Published online: && &&, 2008
.
surface chemistry · transition metals
Keywords: adsorption · density-functional calculations ·
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Figure 3. Adsorption energies of NH and NH2intermediates on transition metal nitride and transition-metal
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Communications
Surface Adsorption
E. M. Fern?ndez, P. G. Moses,
A. Toftelund, H. A. Hansen, J. I. Mart?nez,
F. Abild-Pedersen, J.Kleis, B.Hinnemann,
J. Rossmeisl, T. Bligaard,
J. K. Nørskov*
&&&&—&&&&
Scaling Relationships for Adsorption
Energies on Transition Metal Oxide,
Sulfide, and Nitride Surfaces
Getting on top of things: DFT calcula-
tions have been used to study the
adsorption energies of O, OH, S, SH, N,
NH, and NH2on transition metal oxide,
sulfide, and nitride surfaces. A scaling
relationship was found between the
adsorption energies of the intermediates
and the adsorption energies of the atoms
which is independent of the metal and
only depends on the number of H atoms
in the molecule (see graph).
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