JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 7
15 FEBRUARY 2003
Density functional calculations of hydrogen adsorption
on palladium–silver alloy surfaces
O. M. Løvvika)
Department of Physics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway
R. A. Olsen
Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
共Received 26 August 2002; accepted 19 November 2002兲
Palladium–silver alloy surfaces with and without adsorbed hydrogen have been studied through
density functional theory within the generalized gradient approximations employing a slab
representation of the surface. Our calculated lattice constants are in good agreement with
experimental data, but we find a substantially lower surface energy for Ag共111兲 and Pd共111兲 than
experiments. We have calculated adsorption energies of hydrogen on several sites on various alloy
surfaces, and found that threefold hollow sites with as many palladium neighbors as possible are
preferred. The difference in adsorption energy is so large that we expect trapping of hydrogen
around palladium atoms in the surface, possibly resulting in a lower diffusion constant of hydrogen
at low coverage on alloy surfaces than on the pure Pd and Ag surfaces. Assuming that the adsorption
energy has contributions from geometric 共‘‘ensemble’’兲 and electronic 共‘‘ligand’’兲 effects, we found
the geometric contribution to dominate. For the geometric contribution it is seen that the binding
strength increases as the d-band center moves toward the Fermi level, a result also found by a
number of other theoretical studies. However, for the electronic contribution we found that the
variation of the adsorption energy as a function of the d-band center was opposite that reported by
others: We saw that hydrogen binds less strongly to the surface as the d-band center moves toward
the Fermi level. This could possibly be explained by a large variation of the interaction between the
metal sp band and hydrogen. © 2003 American Institute of Physics.
关DOI: 10.1063/1.1536955兴
I. INTRODUCTION
the surface. We have, however, previously shown that it is
possible to describe quite accurately many of the bulk properties of palladium–silver alloys with and without hydrogen
by using periodicity and small unit cells.7 We expect the
same to be the case at the surface, since varying the size and
composition of the unit cell gives a number of different adsorption sites and electronic surroundings. This should put us
in a position to give reasonable estimates of what kind of
sites hydrogen prefers, and how surface diffusion most probably takes place on the alloy surface. This means that a periodic study like the present one should be well justified, at
least as long as the excess of silver atoms at the surface is
taken into account.
There has lately been published a number of theoretical
studies on alloy surfaces based on density functional theory
共DFT兲 共see, for instance, Refs. 8 –20兲. No studies have so far
to our knowledge presented results on palladium–silver alloy
surfaces, but Liu and Nørskov have studied the adsorption of
carbon monoxide, oxygen, and nitrogen on various gold–
palladium alloy surfaces.17 They were able to separate the
adsorption properties into geometric and electronic effects by
varying the gold content of the surface, and found that both
effects contributed to stronger binding of the adsorbate as the
center of the d band moved toward the Fermi level. We shall
see that we find the same trend for the geometric contribution, while the electronic contribution is the opposite for hydrogen adsorption on palladium–silver alloy surfaces.
The interest in hydrogen at alloy surfaces is large and
increasing, both because of the interesting properties of such
systems from a fundamental point of view,1 and also because
of important applications within fields such as heterogeneous
catalysis, hydrogen storage in metal hydrides, and hydrogen
diffusion membranes.2
Palladium–silver alloys are of particular interest for
membranes—a typical industrial metal based hydrogen selective membrane consists of Pd77Ag23 . 3,4 Such membranes
are thus relatively well studied, but the understanding of the
microscopic properties is still quite crude. One intention of
the present study is to increase our detailed knowledge of
hydrogen interacting with the surface of palladium–silver
alloys, a system providing both a rich experimental basis and
a challenge to thorough theoretical studies.
There has not been measured any ordered phases in
PdAg alloys, but a recent theoretical study has predicted
three different ordered structures.5 Experiments on the surface of such alloys show that it is dominated by silver. 共The
共111兲 surface of Pd67Ag33 contains, for instance, 5.2%
palladium.6兲 To be truly realistic, a model describing such
alloys should thus include both the possibility of random
distribution of atoms in the bulk and excess of silver atoms at
a兲
Electronic mail: o.m.lovvik@fys.uio.no
0021-9606/2003/118(7)/3268/9/$20.00
3268
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 118, No. 7, 15 February 2003
Hydrogen adsorption on palladium–silver alloys
3269
TABLE I. The bases that were used to calculate the adsorption energies 共1兲, the cohesive properties 共2兲, and a
basis that was used as a reference 共3兲. The numbers refer to the exponent of a STO, while NAO designates a
numerical atomic orbital. All bases have orbitals up to 3d frozen.
Basis
4s
4p
4d
5s
5p
4f
1
2
3
NAO
NAO, 3.9
NAO, 2.1, 6.2
NAO
NAO, 2.7
NAO, 1.35, 3.9
NAO, 1.5
NAO, 1.5
NAO, 1.45, 4.9
NAO, 1.8
NAO, 1.8
NAO, 0.9, 2.6
1.8
1.0, 2.0
1.5
1.5
II. METHOD
Our calculations are performed using ADF-BAND,21,22 employing the generalized gradient approximation 共GGA兲 due
to Becke23 and Perdew.24 The one-electron basis sets representing the electron density consist of both Herman–
Skillman numerical atomic orbitals 共NAOs兲 and Slater-type
orbitals 共STOs兲, with a frozen core. Scalar relativistic corrections have been included through the zeroth-order regular
approximation.25 Our slab calculations use two-dimensional
translational symmetry.
Table I shows the basis sets that were used in our calculations, together with a reference basis set for the convergence tests. The convergence of our calculations has been
checked by varying all important parameters, summarized in
Table II. Relative energies, like adsorption energies, are less
sensitive to basis set effects than cohesive properties, for
instance the cohesive energy 共as seen from Table II兲. We
have therefore used different basis sets to calculate adsorption energies and cohesive properties, respectively. The overall convergence is well within 0.1 eV in all our results, with
the GGA and the unit cell size 共including the number of
layers兲 as the only remaining approximations.
We use five different models to investigate a representative set of surface adsorption sites at the fcc 共111兲 alloy surface: pure silver and palladium slabs, a palladium slab coated
with a monolayer of silver 共Ag/Pd兲, a palladium slab coated
with a monolayer of 75% silver and 25% palladium
(Ag3 Pd/Pd), and a slab containing 75% palladium and 25%
silver (AgPd3 ). The alloy slabs are shown in Fig. 1. In the
calculation of adsorption energies we have used three fcc
stacked atom layers, and a 2⫻2 surface unit cell for all the
models. Several previous studies have shown that three layers are enough to describe adsorption reasonably well 共see
for instance Refs. 14, 26, 27兲, and we have also checked that
this is the case for the slabs with the surface layer being
different from the lower layers. A 2⫻2 surface unit cell
gives a hydrogen surface coverage of 25%, which should be
a reasonable approximation for the low-coverage region.
Surface energies were calculated using a 1⫻1 surface unit
cell for the pure metal slabs and for Ag/Pd.
The relaxed slabs were found by two different methods:
either by varying the lattice constant and the top layer relaxation independently, or simultaneously; by creating a twodimensional potential energy surface from the two coordinates. In the former case, the minimum was found using two
successive harmonic fits, while in the latter case it was found
from a two-dimensional spline fit.
We performed this test for both Ag, Pd, and Ag/Pd, using
three metal layers. The largest difference between the two
methods appeared for ⌬d on Ag, where the independent and
simultaneous variation gave 1.4% and 1.0% outwards relaxation of the upper metal layer, respectively. ⌬d on Ag/Pd
also varied slightly, the two methods giving 1.2% and 1.6%
relaxation, respectively. The other results gave differences
well within the numerical errors. We found this satisfactory,
and used the independent variation method to find a latt and
⌬d for the last two models.
The results in Table III show that our calculated lattice
constants are consistently 1%–2% above the experimental
ones, a familiar result for the GGA. All the results in Table
III are for three layer slabs. We have also increased the number of layers to 15, and found that the relaxed lattice constants of the metal slabs converge when the number of layers
reaches about eight. The converged values are about 0.02 Å
above those for three layers, but at the same time consistently about 0.01 Å lower than the bulk relaxed lattice
constant.7 The calculated top layer relaxation compares favorably with the experimental value for Pd, but the Ag result
is far off; we predict an outward relaxation, while experiment
shows inward relaxation.28 Other DFT studies have also
shown inwards relaxation,29,30 and we conclude that three
layers are not sufficient to give reliable results for the surface
relaxation.
B. Surface energy
A common way to calculate the surface energy ␴ is to
subtract the bulk cohesive energy E bulk from the slab cohesive energy E slab :
TABLE II. The most important error sources of the cohesive energy E coh
and the adsorption energy E ads in meV.
III. RESULTS
A. Cohesive properties
We have calculated the optimized lattice constant a latt
and the top layer relaxation ⌬d for our models, and the results are shown in Table III. All optimizations have been
done manually, since no forces are calculated by ADF-BAND.
Error 共meV兲
Test
E coh
E ads
Ag
Pd
H/Ag
H/Pd
KSPACE
ACCINT
7→9
15
9
20
10
4.5→5.0
1
1
8
5
Basis
1→2
345
470
66
29
2→3
52
43
31
62
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J. Chem. Phys., Vol. 118, No. 7, 15 February 2003
O. M. Løvvik and R. A. Olsen
␴ ⫽ 12 共 E slab⫺N layersE bulk兲 ,
共1兲
where N layers is the number of layers of the slab. This leads,
however, to a linear divergence in the surface energy as the
number of layers increases.31,32 In order to avoid this, the
bulk energy in the above-mentioned formula should be replaced by the increase in cohesive energy when increasing
the slab thickness by one layer.31 We have used a linear fit to
this energy as the slab thickness is varied:
E bulk⫽⌬Ē slab .
FIG. 1. Three of the models used in our calculations. We used three layers
on each slab when calculating the adsorption energy. The surface unit cell is
outlined by a solid line. The adsorption energy of hydrogen along the
straight line is plotted in Fig. 2, while the adsorption energy along the
suggested diffusion paths is plotted in Fig. 8.
共2兲
We have done this for silver slabs up to 15 layers, and
found that the surface energy is converged to about 0.03 eV
already after four layers. This was regardless of relaxing the
lattice constants or not. We used at least five layers to calculate the other surface energies. The surface energy of the
silver-coated palladium slab was calculated by comparing
the cohesive energies of slabs with a monolayer of silver on
each side of the slab, and an increasing number of palladium
layers between the silver layers 共up to five palladium layers
between兲. From this cohesive energy we subtracted 2⌬Ē slab
taken from the pure silver slab calculations, in addition to the
value found for the palladium atoms between the silver layers. The results are shown in Table III.
The ‘‘experimental’’ surface energies are 558 and 840
meV for Ag and Pd, respectively.33,34 They are derived from
the surface tension of liquid metals, and have unknown uncertainties. Other DFT studies have also calculated the surface energy of Ag共111兲 and Pd共111兲, using a full-potential
linear-muffin-tin-orbital 共LMTO兲 method,29 a full charge
density LMTO method,35 and a total energy pseudopotential
method.30 The former two studies both obtained significantly
higher values than the present study; respectively, 0.55 and
0.553 eV/atom for Ag, and 0.68 and 0.824 eV/atom for Pd.
The latter study reached almost the same result as ours;
0.357 eV/atom for Ag. All the mentioned studies compared
slab calculations to the bulk cohesive energy, which is
known to yield linear divergence. It is, however, unclear
whether the number of layers used in their calculations and
possible problems with linear divergences are sufficient to
explain the large differences.
To check whether our results could be an artifact due to
numerical problems, we performed extensive extra tests. We
TABLE III. The lattice constant a latt , the outwards relaxation of the upper metal layer ⌬d 共in % of the lattice
constant兲, and the surface energy ␴ for our five models. All our results are calculated using the BP GGA, except
the WIEN2K calculation, where the PBE GGA has been used 共see the text兲.
Slab
a latt 共Å兲
⌬d 共%兲
␴ 共meV/atom兲
This study
Expta
This study
Exptb
This study
WIEN2K
Exptc
Ag
Ag/Pd
Ag3 Pd/Pd
AgPd3
Pd
4.12
4.08
1.0
⫺2.5⫾0.5
325
373
558
4.00
3.99
3.98
1.6
1.5
1.0
3.93
3.88
1.1
2.0⫾2.0
560
625
840
303
516
a
Reference 49.
Ag: Ref. 28, Pd: Ref. 50.
c
Reference 33.
b
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J. Chem. Phys., Vol. 118, No. 7, 15 February 2003
Hydrogen adsorption on palladium–silver alloys
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TABLE IV. Adsorption energy in electron volts at the high coordination
adsorption sites on the various surfaces.
Slab
Ag
Ag/Pd
Top
Bridge
fcc
hcp
0.64
0.27
0.20
0.23
0.69
0.33
0.25
0.28
Ag3 Pd/Pd
⫺0.02
⫺0.06
⫺0.05
0.00
0.79
0.40
0.36
0.39
AgPd3
0.04
⫺0.33
⫺0.49
⫺0.38
E ads⫽E coh共 PdH兲 ⫺E coh共 Pd兲 ⫺ 21 E H2 ⫺E H ,
FIG. 2. The adsorption energy 共as defined in the text兲 along the straight lines
depicted in Fig. 1. The lines between the calculated points are only a guide
to the eye.
calculated the surface energy using the largest basis set in
Table I, which should give results very close to the basis set
limit, giving no significant difference. The same results were
also obtained when including spin–orbit interactions. We
checked three different GGAs 关Becke23 and Perdew,24
Perdew and Wang,36 and Perdew, Burke, and Ernzerhof
共PBE兲兴,37 which all gave the same results within 0.03 eV.
To check whether it could be a result of the atomic orbital basises used in the ADF-BAND program, we also calculated the same surface energies using the WIEN2K program,
which is a full-potential linear augmented plane wave code.38
This does not rely on pseudo-potentials, and should be able
to give results quite close to the GGA limit, just like ADFBAND. The k-space integration parameter was set to give results converged to within 1 meV, and we employed the PBE
GGA. The resulting surface energies are shown in Table III,
as we see in good correspondence with our results using
ADF-BAND. Further investigations are clearly needed to resolve the discrepancy between our results and those presented by Vitos et al.,35 but that is beyond the scope of this
paper.
The surface energy of silver is in either case much lower
than that of palladium, while we have calculated that the
surface energy of Ag/Pd is slightly lower than that of silver.
We have also calculated the surface energy of a palladium
coated silver slab 共not shown in Table III兲, and found that
␴ ⫽566 meV for this slab; slightly higher than that of a pure
palladium slab. We also note that the surface energy of the
AgPd3 alloy is considerably higher, almost just as high as
that of Pd. All these findings are consistent with the excess of
silver atoms that is found on the surface of palladium–silver
alloys; the silver atom is more stable at the surface than a
palladium atom on these surfaces.
C. Site preference
The four high-symmetry sites on the fcc共111兲 surface lie
on the straight lines depicted in Fig. 1. We have calculated
the adsorption energy of a single hydrogen atom at these
sites, and the results are shown in Fig. 2 and Table IV. The
adsorption energy is defined as
0.84
⫺0.27
⫺0.22
⫺0.22
Pd
⫺0.07
⫺0.37
⫺0.49
⫺0.45
共3兲
where E coh is the cohesive energy of the slabs, while E H2
⫽⫺4.80 eV and E H⫽⫺0.93 eV are the calculated GGA energy of the hydrogen molecule and the energy difference
between a spin-restricted and spin-unrestricted hydrogen
atom, respectively. This means that a negative adsorption
energy is stable compared to free hydrogen molecules. The
coordinates of the hydrogen atoms at the various sites are
taken as the equilibrium coordinates of hydrogen on the pure
palladium and silver slabs 共they are practically the same兲. We
have not tried to find local minima outside the high coordination site.
We first note the similarities between hydrogen adsorption on Pd and Ag, the main difference being that adsorption
is about 0.7 eV more stable on the Pd surface. The threefold
hollow sites are most stable on both surfaces, with the fcc
site being slightly more stable than the hcp site.
We further see that sites with the same nearest surroundings may have significantly different adsorption energies; as
an example, top sites above a silver atom vary from 0.64 eV
共on Ag兲 to 0.84 eV 共on AgPd3 ). Since the type of atom to
which H bonds is unchanged for these surfaces, this effect is
purely electronic, and we are thus able to extract the electronic contribution to the adsorption energy from the data in
Fig. 2. It has become common to relate this kind of contribution to the center of mass of the electronic density of states
projected on the atomic d orbitals of the metal before adsorption 共the d-band center兲, see for instance Refs. 17, 39– 41.
We have calculated the d-band center from the density of
states of these surfaces, and the result is shown in Fig. 3.
Here the adsorption energy is given as a function of the
distance of the d-band center from the Fermi level for all the
high coordination sites with only one kind of neighbor. There
is a clear correlation between the adsorption energy and the
d-band center at all the sites, and we see that all the sites
show the same behavior: as the center of the d band moves
toward the Fermi level, the adsorption gets less stable. But
this is the opposite trend that has been reported from previous theoretical studies, which all have seen that adsorption
gets more stable when the center of the d band moves toward
the Fermi level.
It is not surprising that the center of the d band moves
toward the Fermi level as we mix more Pd together with the
Ag atoms. But why is this in our case followed by a decrease
in reactivity, rather than an increase, as in other systems? In
our previous study on hydrogen in bulk palladium–silver
alloys, we found that an increased lattice constant was important to explain more stable absorption of hydrogen when
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J. Chem. Phys., Vol. 118, No. 7, 15 February 2003
O. M. Løvvik and R. A. Olsen
FIG. 3. The adsorption energy at sites
with only one kind of metal neighbors
as a function of the center of the silver
d band, illustrating the contribution
from electronic effects to the adsorption energy.
silver was added to the alloy.7 Mavrikakis et al. also found
that the lattice constant was important to the reactivity of
various metal surfaces.40 We have checked the influence of
the lattice constant on some sites, and found only small
changes. As an example, we calculated the adsorption energy
at top sites above a silver atom, and found that it changed by
less than 20 meV when we changed the lattice constant from
the alloy optimized lattice constant to the silver lattice con-
stant. The difference in adsorption energy between these sites
remained, or even increased.
We thus have to look more closely at the details of the
electron density, and have calculated the local density of
states 共LDOS兲 and the crystal orbital overlap population
共COOP兲 of the relevant sites 共see, e.g., Ref. 42兲. We have
plotted the LDOS both with and without hydrogen at the hcp
site in Fig. 4 共the fcc site looks quite similar兲. We see that the
FIG. 4. LDOS of a top layer silver
atom for pure and hydrogen-covered
slabs with hydrogen adsorbed at the
hcp site. The upper and lower panels
show the DOS projected on the silver
sp and d bands, respectively. The dotted and solid curves show the LDOS
of the silver atom before and after adsorption of a hydrogen atom, respectively. The energy is measured relative
to the Fermi level.
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J. Chem. Phys., Vol. 118, No. 7, 15 February 2003
Hydrogen adsorption on palladium–silver alloys
3273
FIG. 5. COOP 共solid curves兲 and integrated COOP 共dotted curves兲 between
a top layer silver atom and an adsorbed hydrogen atom located at the
hcp site. The COOP is between silver
sp bands and hydrogen in the upper
panels, and between silver d bands and
hydrogen in the lower panels. The energy is measured relative to the Fermi
level.
1s split-off state at about 7 eV below the Fermi level is
clearly larger on Ag and Ag/Pd than on Ag3 Pd/Pd, being
consistent with a smaller reactivity between Ag and H on
Ag3 Pd/Pd (E ads⫽0.39 eV) than on Ag and Ag/Pd (E ads
⫽0.23 and 0.28 eV, respectively兲. The same trend can also
be seen in a plot of the COOP between hydrogen and silver
at the same site, shown in Fig. 5. We can here clearly see
how the overlap between the silver 4d and the hydrogen 1s
band is much smaller at Ag3 Pd/Pd than at the other alloys. In
addition, we see that the overlap between the Ag sp band and
hydrogen is smallest at Ag3 Pd/Pd. The integrated COOP up
to the Fermi level is also shown in each plot, giving support
to the above-given description. This means that inclusion of
more Pd not only affects the d electrons, but also the sp
electrons of Ag. This is different from the common assumptions of previous studies, that the interaction with sp electrons remains constant.17,40
Geometric 共‘‘ensemble’’兲 contributions to the adsorption
energy have in other systems been found to depend on the
center of the d band in the same way as electronic 共‘‘ligand’’兲
contributions to the adsorption energy, only stronger.17,40
That is, the adsorption gets stronger when the d-band center
moves toward the Fermi level. We are not able to separate
the electronic and geometric effects fully in this study, since
we have not included enough different surfaces to calculate
all possible electronic surroundings for each geometric configuration. But we are able to find the total effect
(geometric⫹electronic), since we have calculated all possible geometric configurations. This is shown in Fig. 6,
where the adsorption energy is plotted as a function of the
fraction of silver atoms at the different sites. It is evident that
the total effect is working the same way here as in other
systems, with the adsorption strength decreasing as the fraction of silver atoms at the site increases, and thus as the
d-band center moves away from the Fermi level. Since the
ligand effect works the opposite way 共see above兲, we conclude that the ensemble effect is the largest, and responsible
for the direction of the total effect. It is also quite straightforward to understand the direction of the ensemble effect by
studying the COOP between hydrogen and the metal d electrons when hydrogen is adsorbed on a hollow site at the pure
metal slabs, as shown in Fig. 7. We see there that the effect
FIG. 6. The adsorption energy at fcc sites as a function of the fraction of
silver atoms at the site. The symbols refer to the same surfaces as in Fig. 2.
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3274
J. Chem. Phys., Vol. 118, No. 7, 15 February 2003
O. M. Løvvik and R. A. Olsen
FIG. 8. The adsorption energy along possible surface diffusion paths as
lined out in Fig. 1.
FIG. 7. The crystal orbital overlap population between the hydrogen s electrons and metal d electrons when hydrogen is adsorbed at the fcc site on the
pure silver and palladium surfaces. The energy is measured relative to the
Fermi level.
of moving from the Pd to the Ag site is twofold: the large
bonding peak at the bottom of the overlap is moved away
from the Fermi level, while a broad antibonding peak is
moved from above the Fermi level to below. This means that,
as we include more silver atoms at a site, more antibonding
orbitals are occupied, and the reactivity decreases.
The correlation between the presence of silver and the
adsorption energy in Fig. 6 means that, at the crudest level,
the adsorption energy at a particular site can be estimated as
the interpolation between the ‘‘pure’’ sites, only taking the
nearest neighbors into account. Deviations from this approximation are due to the combination of geometric and electronic effects, and must be calculated directly in each case.
D. Diffusion paths
There are numerous possible surface diffusion paths on
real alloy surfaces, and in order to model some typical possible paths, we have chosen a representative diffusion path
on each slab, shown in Fig. 1. The resulting adsorption energy is plotted in Fig. 8. We see that the adsorption energy of
hydrogen is so much lower at sites with at least one palladium atom, that palladium atoms at the surface would act as
hydrogen traps. At low palladium concentrations in the surface this should not be important, since after the first hydrogen atoms have been trapped by palladium, new hydrogen
atoms should be able to diffuse between the pure silver sites.
The opposite is the case at high palladium concentrations;
then hydrogen should be able to diffuse between sites containing palladium. At intermediate concentrations, however,
we should expect that surface diffusion is effectively inhibited by the palladium atoms acting as hydrogen traps. This is
in line with the results of Ref. 43, where the diffusion constant through bulk palladium silver alloys was found as a
function of the silver content. They found that the diffusion
constant was constant from 0 to 25% silver content, then
dropped by three orders of magnitude from 25% to 60%, and
after that increased back to the diffusion constant of silver
again, which is about the same as that of palladium. We are
not aware of any studies measuring the surface diffusion
constant of hydrogen on a PdAg共111兲 surface, but note that
the untreated 共111兲 and 共100兲 surfaces of Pd67Ag33 contain
only 5.2% and less than 0.05% palladium, respectively.6 This
is clearly not enough to inhibit surface diffusion, but we
would expect that hydrogen sticks to the palladium sites
when possible. This is exactly what has been observed in a
STM study of oxygen on a PdAg surface, where oxygen is
found to occupy palladium sites only, and oxygen diffusion
takes place between the Pd sites.44
On real PdAg membranes containing around 25% silver,
the hydrogen transport is very effective,4,45,46 even with a
pure silver surface added.47 This is apparently in conflict
with our results, where all sites with only silver atoms have
E ads⭓0.20 eV. This could be because of real membrane surfaces differing from the perfect 共111兲 surface, possibly with
different surface plane orientations, polycrystallinity, or defects. It could also be that we obtain too high adsorption
energies in this study, because of high hydrogen coverage
共25%兲 and uncomplete relaxation. The relatively high hydrogen coverage could possibly be a problem, since the solubility of hydrogen in silver is very low. We have calculated the
adsorption energy of hydrogen on a pure silver 共111兲 surface,
and found that it decreases from 0.36 to 0.20 eV when the
coverage decreases from 1 to 0.25. This is much more than
on Pd, where E ads decreases from ⫺0.39 to ⫺0.44 eV with
the same coverage variation.48 We thus expect that calculated
adsorption energies of hydrogen on silver at very low coverage should be lower than the present results.
IV. CONCLUSIONS
We have calculated properties of various pure and hydrogen covered 共111兲 surfaces of palladium silver alloys
through DFT within the GGAs employing a slab representation of the surface. Our calculated lattice constants are in
good agreement with known experimental data, but we find a
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J. Chem. Phys., Vol. 118, No. 7, 15 February 2003
substantially lower surface energy for Ag共111兲 and Pd共111兲
than experiments33,34 and some previous theoretical
studies.29,35 Our results are, however, in line with the results
of a total energy pseudopotential study,30 and we also get the
same result when employing two different accurate DFT
schemes.
The potential energy surface of hydrogen on the pure
Ag共111兲 and Pd共111兲 surfaces are quite similar 共with the
threefold hollow sites being the most stable兲, except that adsorption is about 0.7 eV less stable on the Ag surface. On the
alloyed surfaces we found that threefold hollow sites with as
many palladium neighbors as possible are preferred.
We assumed that the adsorption energy consists of geometric 共‘‘ensemble’’兲 and electronic 共‘‘ligand’’兲 contributions, and found the geometric contribution 共the type of atoms to which H bonds兲 to dominate. The adsorption on the
alloy surfaces can therefore in the crudest approximation be
found by interpolation between the ‘‘pure’’ adsorption sites,
where the fraction of Ag atoms at the adsorption site is the
most important parameter in determining the adsorption energy. For the geometric contribution it is seen that the binding strength increases as the d-band center moves toward the
Fermi level, a result also found by a number of other theoretical studies.
Considering adsorption sites with the same geometric
constitution 共the type of atoms to which H bonds兲, but with
different surroundings, we could isolate the electronic
共‘‘ligand’’兲 contributions to the adsorption energy 共as also
done by others兲. We find that hydrogen adsorption gets less
stable when the d-band center moves toward the Fermi level.
This is contrary to previous studies, where the opposite trend
has been found. We suggest that this can partly be attributed
to a large variation of the overlap between the hydrogen 1s
state and the metal sp band, which is assumed to be constant
in other studies.
We have also found that hydrogen binds much more
strongly to palladium than to silver, so that palladium atoms
work as an effective hydrogen trap. We expect that this
should make surface diffusion difficult when the fraction of
palladium atoms at the surface is too small to make diffusion
between palladium atoms possible, and large enough to inhibit diffusion at silver sites only. At real membrane surfaces,
however, the palladium content is probably too low for this
to become a problem.
ACKNOWLEDGMENTS
Financial support and computer time from the Norwegian Research Council 共OML兲 is acknowledged. R.A.O. acknowledges financial support from the Dutch National Research Council-Chemical sciences 共NWO-CW兲 and the
National Research School Combination ‘‘Catalysis Controlled by Chemical Design’’ 共NRSC-Catalysis兲.
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