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Scaling properties of adsorption energies for hydrogen-containing molecules on
transition-metal surfaces
Abild-Pedersen, Frank; Greeley, Jeffrey Philip; Studt, Felix; Rossmeisl, Jan; Fronczek-Munter, Ture
Rønved; Moses, Poul Georg; Skulason, Egill; Bligaard, Thomas; Nørskov, Jens Kehlet
Published in:
Physical Review Letters
Link to article, DOI:
10.1103/PhysRevLett.99.016105
Publication date:
2007
Document Version
Publisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):
Abild-Pedersen, F., Greeley, J. P., Studt, F., Rossmeisl, J., Fronczek-Munter, T. R., Moses, P. G., Skulason, E.,
Bligaard, T., & Nørskov, J. K. (2007). Scaling properties of adsorption energies for hydrogen-containing
molecules on transition-metal surfaces. Physical Review Letters, 99(1), 016105.
https://doi.org/10.1103/PhysRevLett.99.016105
Scaling Properties of Adsorption Energies for Hydrogen-Containing Molecules
on Transition-Metal Surfaces
F. Abild-Pedersen, J. Greeley, F. Studt, J. Rossmeisl, T. R. Munter, P. G. Moses, E. Sku
´
lason, T. Bligaard, and J. K. Nørskov
Center for Atomic-scale Materials Design, Department of Physics, NanoDTU, Technical University of Denmark,
DK-2800 Lyngby, Denmark
(Received 13 February 2007; published 6 July 2007)
Density functional theory calculations are presented for CH
x
, x 0; 1; 2; 3, NH
x
, x 0; 1; 2, OH
x
, x
0; 1, and SH
x
, x 0; 1 adsorption on a range of close-packed and stepped transition-metal surfaces. We
find that the adsorption energy of any of the molecules considered scales approximately with the
adsorption energy of the central, C, N, O, or S atom, the scaling constant depending only on x. A model
is proposed to understand this behavior. The scaling model is developed into a general framework for
estimating the reaction energies for hydrogenation and dehydrogenation reactions.
DOI: 10.1103/PhysRevLett.99.016105 PACS numbers: 82.45.Jn
The formation of a bond between a molecule and a metal
surface is an important phenomenon in a number of pro-
cesses including heterogeneous catalysis [1], contact for-
mation in molecular electronics [2], and anchoring of
biomolecules to solids for sensors and other biomedical
applications [3]. The adsorption energy is a key quantity
describing the strength of the interaction of molecules with
the surface. The adsorption energy can be measured by
advanced surface science techniques [4 –6]. Alternatively,
density functional theory (DFT) offers the possibility of
calculating adsorption energies with reasonable accuracy
[7–11]. While both experiments and DFT calculations are
feasible for a limited number of systems, they can hardly
be performed in detail for all potentially interesting ad-
sorption systems. There is therefore a need for simple
models with the ability to estimate bond energies in a first
screening of interesting systems. A successful model will
also expose the important factors determining the strength
of an adsorbate-surface bond. In the present Letter we will
develop such a model for hydrogen-containing molecules.
We use DFT calculations to derive a number of correlations
between adsorption energies, and we then present a model
to explain them. The model shows how the adsorbate
valency, together with the properties of the d electrons of
the surface, determines the adsorption energy. We further
develop the scaling model into a method for estimating
hydrogenation or dehydrogenation reaction energies for
organic molecules on transition-metal surfaces. The model
is tested against full DFT calculations for reactions of
hydrocarbons, alcohols, thiols, and amino acids.
First, we present results of extensive DFT calculations of
the adsorption energies of CH
x
, x 0; 1; 2; 3, NH
x
, x
0; 1; 2, OH
x
, x 0; 1, and SH
x
, x 0; 1 on a range of
close-packed and stepped metal surfaces. The study in-
volves the close-packed fcc(111), fcc(100), hcp(0001), and
bcc(110) surfaces, and the stepped fcc(211) and bcc(210)
surfaces. Each of the surfaces is modeled by a (2 2)ora
(1 2) surface unit cell for the close-packed and stepped
surfaces, respectively. Each slab has a thickness of three
layers in the direction perpendicular to the close-packed
surface. These slabs are thick enough to capture the trends
in the chemisorption energetics. The adsorbates and the
topmost layer are allowed to relax fully in all configura-
tions, and in the case of Fe, Ni, and Co, spin polarization is
taken into account. The binding energies of the different
species have been taken for the most stable adsorption sites
on all surfaces. The RPBE functional [12] in the general-
ized gradient approximation is used to describe exchange
and correlation effects. The calculational method and setup
is described in Ref. [13].
Figure 1 summarizes the results of the DFT calculations.
We find for all the molecules studied that the adsorption
energy of molecule AH
x
is linearly correlated with the
adsorption energy of atom A:
E
AH
x
E
A
: (1)
There is some scatter around the linear relations, but we
note that while the adsorption energies vary by several
electron volts over the range of metals considered here,
the mean absolute error (MAE) is only 0.13 eV. Some of
this scatter is related to differences in adsorption sites for
adsorbates with different amounts of hydrogen. CH
3
, for
instance, typically prefers a onefold adsorption site on the
close-packed surfaces while C prefers the threefold site. If
we were to use the adsorption energy of C in the onefold
adsorption site as the reference, the quality of the correla-
tion becomes significantly better (MAE 0:06 eV); see
Fig. 2. We also find that when we use a reference with the
same configuration as the molecule of interest, the scaling
behavior includes alloys with the same accuracy as for the
elemental metals (Fig. 2).
The main observation from Figs. 1 and 2 is that the slope
of the linear relationship in Eq. (1) is given to a good
approximation by the number of H atoms in AH
x
as x
x
max
x=x
max
, where x
max
is the maximum number of H
atoms that can bond to the central atom A (x
max
4 for
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A C, x
max
3 for A N, and x
max
2 for A O; S).
Since x
max
x is the valency of the AH
x
molecule, we
conclude that for the four families of molecules considered
the slope only depends on the valency of the adsorbate. In
the following we will consider a model that allows us to
understand the origin of this effect.
For some of the considered systems, simple valency or
bond-counting arguments [14] can explain the results:
Comparing CH, CH
2
, and CH
3
on the close-packed sur-
faces, we generally find CH (with a valency of 3) to prefer
threefold adsorption sites, CH
2
(valency of 2) to prefer
twofold adsorption, and CH
3
(valency of 1) to prefer one-
fold adsorption. The implication of these trends is that
unsaturated bonds on the carbon atom form bonds to
surface metal atoms; in effect, each unsaturated sp
3
hybrid
on the central C atom binds independently to the d states of
the nearest neighbor metal atoms, consistent with the
slopes in Fig. 1. However, this picture cannot include
adsorbed atomic C. Adsorbed C also adsorbs in a threefold
site (neglecting long range reconstructions), but it does not
have four bonds as would be needed to explain all the C
data in Fig. 1. We also note that the overall scaling behav-
ior is independent of the adsorption geometry and hence
the details of the bonding; see Fig. 2. The scaling in Figs. 1
and 2 must therefore have a more general explanation that
includes the argument above for CH, CH
2
, and CH
3
as a
special case.
We will base our analysis on the d-band model which
has been used quite successfully to understand trends in
adsorption energies from one transition metal to the next
[8,15–19]. According to the d-band model, it is useful to
think of the formation of the adsorbate-surface bond as
taking place in two steps. First, we let the adsorbate states
interact with the transition metal sp states, and then we
include the extra contribution from the coupling to the d
states:
E E
sp
E
d
: (2)
The coupling to the metal sp states usually contributes the
largest part of the bonding and involves considerable hy-
bridization and charge transfer. In terms of variations from
one transition metal to the next it can, however, be consid-
ered to be essentially a constant; the sp bands are broad,
and all the transition metals have one sp electron per metal
atom in the metallic state [20]. According to the d-band
model, the main contribution to the variations in bond
energy from one transition metal to the next comes from
the coupling to the metal d states; the d states form narrow
bands of states close to the Fermi level, and the width and
energy of the d bands vary substantially between transition
metals. According to the d-band model, all the variations
among the metals observed in Fig. 1 should therefore be
given by E
d
. That means that the x dependence of
E
AH
x
x must be given by the d coupling alone: Let us
assume for the moment that the d coupling for AH
x
is
proportional to the valency parameter defined above:
E
AH
x
d
xE
A
d
(3)
Using Eq. (1), this will lead to the kind of relationship in
Fig. 1. We can write the adsorption energy of molecule
AH
x
in terms of the adsorption energy of molecule A as
-6
-5
-4 -3 -2
∆E
C
(eV)
-2.25
-2
-1.75
-1.5
-1.25
-1
-0.75
-0.5
∆E
CH
3
(eV)
Fit: y=0.24x-0.02
Fit: y=0.28x-0.27
Ir
Pt
Pd
Ni
Rh
Ru
Cu
Au
Ag
Ir
RuRh
Pt
Pd
Ni
Cu
Au
Ag
Cu
3
Pt
Pd
3
Au
Cu
3
Pt
Pd
3
Au
Ontop adsorption site
Most stable adsorption site
FIG. 2 (color). Binding energies of CH
3
plotted against the
binding energies of C for adsorption in the most stable sites
(triangles) and in the case where both CH
3
and C have been fixed
in the on-top site (squares).
FIG. 1 (color). Adsorption energies of CH
x
intermediates
(crosses: x 1; circles: x 2; triangles: x 3), NH
x
inter-
mediates (circles: x 1; triangles: x 2), OH, and SH inter-
mediates plotted against adsorption energies of C, N, O, and S,
respectively. The adsorption energy of molecule A is defined as
the total energy of A adsorbed in the lowest energy position
outside the surface minus the sum of the total energies of A in
vacuum and the clean surface. The data points represent results
for close-packed (black) and stepped (red) surfaces on various
transition-metal surfaces. In addition, data points for metals in
the fcc(100) structure (blue) have been included for OH
x
.
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E
AH
x
E
AH
x
d
E
AH
x
sp
xE
A
d
E
AH
x
sp
xE
A
; (4)
where E
AH
x
sp
xE
A
sp
is independent of the metal
in question. The parameter can be read off Fig. 1 for each
AH
x
=A combination; see Eq. (1). The parameter can be
obtained from calculations on any transition metal. In the
following all model data presented are obtained using
Pt(111) as the reference system.
The basic question remains, why the coupling to the d
states should scale with the valency of the adsorbate as in
Eq. (1). We cannot provide a general rigorous proof of the
scaling, Eq. (1), and most likely no such proof exists—the
scatter in Fig. 1 indicates that the linear relationship is only
approximate. What we will do, however, is show that
Eq. (1) should hold approximately for the kind of systems
investigated in Fig. 1.
The coupling of the adsorbate states to the d band has
two contributions [15,16,21], E E
hyb
d
E
orth
d
. The
first term describes the energy change associated with the
formation of bonding and antibonding states. Since the d
coupling can often be described in second order perturba-
tion theory [8,15,21], we can write E
hyb
d
/ E
orth
d
/ V
2
ad
,
where V
ad
is the Hamiltonian matrix element between the
adsorbate and the metal d states [21]. If there is more than
one adsorbate state, the total interaction energy will scale
with the sum of contributions from the adsorbate states,
V
2
ad
P
i
V
2
a
i
d
. We suggest that V
2
ad
/ for the kind of
systems considered in Fig. 1, and this directly gives the
relation of Eq. (1). The reason is given in the following.
The coupling strength V
2
ad
fr
ai
g is a function of the
number of metal neighbors and their distances to the
adsorbate. Since the d coupling is usually a minor pertur-
bation to the bond energy, it is the sp coupling which
primarily determines the adsorption bond lengths, r
ai
.
As H atoms are added to the central C, N, O, or S atom,
the adsorption bond lengths increase and the coupling
strength decreases. The effective medium theory (EMT)
[22] provides a simple way of quantifying this effect. In the
EMT the bonding of an atom A to other atoms in the
vicinity is approximated by the interaction of A with a
homogeneous electron gas (the effective medium) of a
density given by a spherical average n of the density
provided by the surrounding atoms: E E
hom
n.
Such a local density approximation for the interaction
energy gives a good description of general trends in bond-
ing, including bond lengths of atoms in metals, adsorbates
on metal surfaces, and of molecules [22–24]. The energy
of embedding an atom in a homogeneous electron gas,
E
hom
n, generally has a minimum for a particular elec-
tron density, n
0
, and the equilibrium geometry of atom A is
given by the position where A experiences the optimum
electron density, n n
0
.
Consider for instance a C atom outside a metal surface.
The adsorption bond length is given by the distance outside
the surface where the electron density from the surface
around the C atom is n
surf
n
0
. Now add H atoms to the C
atom. Each H atom will provide electron density to the C
atom, and the electron density needed from the surface to
reach n n
0
is smaller. For a fixed adsorption site (one-,
two-, or threefold), the bond length between the surface
atoms and the C atom must therefore increase. Alterna-
tively, the adsorption site can change as in the case of CH,
CH
2
, and CH
3
discussed above. In that case we would then
expect the C-metal bond length to be independent of x,
since the change in metal coordination number corre-
sponds exactly to the increase in the H coordination num-
ber for this sequence of systems. This is precisely what we
find in the calculations. Returning to the general case, the
electron density from the surface n
surf
needed to obtain
n n
0
will continue to decrease as the number x of H
atoms increases. When x 4 the H atoms must contribute
all the electron density needed for the central C atom,
4n
H
n
0
, since a methane molecule does not bind to the
surface at all (neglecting van der Waals interactions). The
density contribution from the surface at the equilibrium
site for CH
x
is therefore
n
surf
x
max
x
x
max
n
0
xn
0
: (5)
The linear dependence on x in Eq. (5) is based on the
reasonable assumption that the contribution to the electron
density is the same for all x H atoms, and that the total
density should add up to n
0
[25]. The electron density n
can be viewed as a generalized bond order [26,27], and the
requirement that n n
0
is then an example of bond order
conservation.
Since we are using EMT to model the sp contribution to
the bonding, n
surf
denotes the sp electron density outside
the surface. The decay length of n
surf
outside the surface is
given asymptotically by the work function (the energy of
the Fermi level relative to vacuum). Since the d states have
energies close to the Fermi level as well, their decay length
is roughly the same. That means that to a first approxima-
tion V
2
ad
scales with n
surf
. We have therefore shown that the
following relations hold approximately,
E
d
x/V
2
ad
x/n
surf
x/
x
max
x
x
max
x; (6)
which implies Eq. (1).
Given the understanding provided above, we can try to
generalize the findings in Fig. 1. For any hydrogenation or
dehydrogenation reaction of molecules bonding to a
transition-metal surface via C, N, O, or S atoms, we should
be able to estimate the reaction energy for all transition
metals given the reaction energy for just one metal. For
each atom A
i
i 1; ...;N bonding to the surface, we
determine the change
i
in the valence parameter during
the reaction, and we can then estimate variation in the bond
energy for the full system from the variations in the bond
energies of the A
i
:
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E
X
N
i1
i
E
A
i
i
X
N
i1
i
E
A
i
: (7)
The change in the parameter for the particular reaction
needs to be calculated once and for all by calculating the
reaction energy for one single metal. In Fig. 3, we compare
the model to complete DFT calculations for hydrogenation
or dehydrogenation of a series of hydrocarbons, alcohols,
thiols, and amino acids. In each case, we have calculated
from Pt(111) data. The agreement between the model
and the full DFT calculations indicates that the model has
the power to describe both the absolute magnitude and the
trends in reaction energies for hydrogenation or dehydro-
genation reactions of a number of organic molecules on
transition-metal surfaces. We note that the scaling relations
can easily be generalized so that the adsorption energy of
any hydrogenated species AH
y
is used as the reference
instead of A.
By combining the present model with the Brønsted-
Evans-Polanyi –type correlations that have been estab-
lished between activation barriers and reaction energies
for surface reactions [8,10,11], it will be possible to esti-
mate the full potential energy diagram for a surface cata-
lyzed reaction for any transition metal on the basis of the C,
N, O, and S chemisorption energies and a calculation for a
single metal. We suggest that this will be a useful tool in
screening for new catalysts. Such estimates can subse-
quently be followed up by full DFT calculations and ex-
periments for the most interesting systems.
The Center for Atomic-scale Materials Design is spon-
sored by the Lundbeck Foundation. Additional support
from the Danish Research Councils and the Danish
Center for Scientific Computing are also acknowledged.
[1] Z. Ma and F. Zaera, Surf. Sci. Rep. 61, 229 (2006).
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102, 8801 (2005).
[3] B. Kasemo, Surf. Sci. 500, 656 (2002).
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797 (1998).
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(2004).
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31, 669 (2006).
[8] B. Hammer and J. K. Nørskov, Adv. Catal. 45, 71 (2000).
[9] J. Greeley and M. Mavrikakis, J. Phys. Chem. B 109, 3460
(2005).
[10] V. Pallassana and M. Neurock, J. Catal. 191, 301 (2000).
[11] A. Michaelides et al., J. Am. Chem. Soc. 125, 3704
(2003).
[12] B. Hammer, L. Hansen, and J. K. Nørskov, Phys. Rev. B
59, 7413 (1999).
[13] T. Bligaard et al., J. Catal. 224, 206 (2004).
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Chem. Soc. 122, 4129 (2000).
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(1995).
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4744 (2000).
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[20] O. K. Andersen, O. Jepsen, and D. Glo
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Surface Reactions (Kluwer, Dordrecht, 1997).
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24, 3037 (1981).
[25] NH
3
, H
2
O, and H
2
S do bind weakly to the surface. This
bonding by lone pairs cannot be described in the simplest
EMT model. The bond lengths to the surface of the fully
hydrogenated species are, however, significantly larger
than for any of the less hydrogenated species, and the
density contribution from the surface is small. This is
therefore a small correction to the scaling picture devel-
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-1.5 -1 -0.5 0 0.5 1 1.5 2
∆E
reaction
model
(eV)
-1.5
-1
-0.5
0
0.5
1
1.5
2
∆E
reaction
DFT
(eV)
CH
3
OH(g)+
*
-->CH
3
O
*
+1/2H
2
(g)
C
*
H
2
-CH-C
*
H
2
-->C
*
H-CH-C
*
H
2
+1/2H
2
(g)
CH
3
SH+
*
-->CH
3
S
*
+1/2H
2
(g)
Cysteine+
*
-->S
*
-CH
2
-CH(NH
2
)-COOH+1/2H
2
(g)
C
2
H
4
+H
*
-->C
*
-CH
3
+H
2
(g)
FIG. 3 (color). Calculated reaction energies for a series of
dehydrogenation reactions plotted against the model predictions.
The model data have been generated using calculated Pt(111)
data as reference.
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