CO oxidation at Pd(100): A first-principles constrained thermodynamics study

0.5 MB·English

by  Jutta Rogal

(submitted to Phys. Rev. B)
CO oxidation at Pd(100):
A first-principles constrained thermodynamics study
Jutta Rogal, Karsten Reuter, and Matthias Scheffler
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
7 (Received 30th January 2007)
0
0 The possible formation of oxides or thin oxide films (surface oxides) on late transition metal
2 surfacesisrecentlybeingrecognized asanessentialingredientwhenaimingtounderstandcatalytic
oxidation reactions undertechnologically relevant gas phaseconditions. UsingtheCO oxidation at
n
Pd(100)asexample,weinvestigatethecompositionandstructureofthismodelcatalystsurfaceover
a
a wide range of (T,p)-conditions within a multiscale modeling approach where density-functional
J
theory is linked to thermodynamics. The results show that under the catalytically most relevant
1
gasphaseconditionsathinsurfaceoxideisthemoststable“phase”andthatthesystemisactually
3
very close to a transition between this oxidic state and a reduced state in form of a CO covered

Pd(100) surface.
]
i
c
PACSnumbers: 82.65.+r,68.43.Bc,68.43.De,68.35.Md
s
-
l
r
t I. INTRODUCTION face mightbe formedunder the gasphase conditions ap-
m
plied in industrial oxidation catalysis. Using surface x-
. ray diffraction (SXRD) measurements a (T,p)-diagram
t
a Catalytic oxidation using transition metals (TM) as showing the detected structures in a pure oxygen atmo-
m theactivematerialisanimportanttechnologicalprocess,
sphere over a temperature range of T = 600 1000K
- of which we still have only limited microscopic insight. and pressures of p = 10 9 1atm could be i−nferred4.
d Muchvaluablemicroscopicinformationthathasbeenob- O2 − −
A thin surface oxide structure was measured over an ex-
n tainedunderultra-highvacuum(UHV) conditionsisnot
tended(T,p)-range,suggestingthat this structuremight
o
directlytransferabletotheconditionsofpracticalcataly-
c also appear under catalytic reaction conditions. In re-
sis (with pressures of severalbars and elevated tempera-
[ actorscanningtunnelingmicroscopy(STM)experiments
tures). And in-situ techniques that wouldoperate under by Hendriksen et al.5,6 the structure of the Pd(100) sur-
1 these conditions are still struggling to achieve atomic-
face could directly be monitoredduring the catalytic ox-
v
scalesurfacesensitiveinformation. Akeyfactorthathin-
7 idation of CO. Here, the surface was exposed to both
ders the direct transfer of the UHV insight is that under
7 oxygenand CO at a total pressure of p 1atm and a
tot
7 reaction conditions the entire structure and composition temperature of T 400K. The partial pr≈essures of the
1 ofthecatalystsurfacemightbechanged(oftencalledthe reactant gases CO≈and O , as well as the reaction prod-
2
0 “materialsgap”). Andifanewmaterialiscreatedduring
uct CO , were measured simultaneously with the STM
7 theinductionperiodofthecatalyticprocess,itwillobvi- 2
images. DependingonthepartialpressureofO andCO
0 ously exhibita verydifferent chemicalactivity; it willbe 2
theauthorsobservedachangeinthereactionrate,which
/
at quantitativelyandevenqualitativelydifferent. Underthe wasaccompaniedbyasignificantchangeinthemorphol-
oxygen-rich gas phase conditions and elevated tempera-
m ogy of the surface. This morphology change (albeit not
tures of oxidation catalysis the surface of the transition
atomicallyresolved)wasinterpretedasachangefromthe
-
metal catalyst might e.g. be oxidized, so that the actual
d adsorbate coveredPd(100) surface to an oxidic state.
n catalytically active state is not the pristine metal, but To address this problem from a theoretical point of
o rather the formed oxide. One example for this is the CO
viewweemployamultiscalemodelingapproachwherewe
c oxidation reaction over ruthenium. Here it was found,
use density-functionaltheory (DFT) to describe the sys-
:
v thatunderUHV conditionsthe Ru(0001)modelcatalyst temonanelectronic(microscopic)level. Bylinkingthese
Xi shows almost no catalytic activity, whereas under high results to thermodynamics7,8,9,10 it becomes possible to
oxygen pressures its catalytic activity exceeds even the
addressmuchlargersystemsizesandtocomparethesta-
r one of the frequently used palladium and platinum cata-
a bility of different surface structures in contact with the
lysts1. This increase in the catalytic activity was traced
surrounding gas phase11,12,13,14,15,16. We use in partic-
back to the formation of a RuO film at the surface2,3.
2 ular a constrained equilibrium approach15,16, where the
Forthe ruthenium catalystacleardistinctioncouldthus
surface is considered to be in full thermodynamic equi-
be made betweenthe differentstates, namelythe weakly
libriumwithtwoseparategasphasereservoirsofO and
catalyticallyactivemetalunderlowoxygenpressuresand 2
CO, and not allowing that O and CO can react. The
the highlyactiveoxidefilmunderhighoxygenpressures. 2
key result obtained is a surface “phase diagram”, which
Fortheherediscussedmodelsystem,theCOoxidation providesfirstinsightintopossiblesurfacestructuresover
at Pd(100), recent in-situ experimental measurements a wide range of temperature and pressure conditions of
alsoindicatethatanoxidicstructureatthePd(100)sur- the O and CO gas phase. Focusing on gas phase con-
2
2
ditions relevant for oxidation catalysis we find the sys- atoms are taken from/put into a bulk reservoir, repre-
temonthe vergeofeitherstabilizingathinsurfaceoxide sented by the chemical potential of the bulk solid phase,
structure or a CO covered Pd(100) surface. It is thus µbulk. Thechemicalpotentialsofthetwogasphasereser-
Pd
wellpossibleandevenlikelythatthesurfaceoxidestruc- voirsof oxygen,µ , and CO,µ , havebeen separated
O2 CO
turecontributestothe activestateofthe Pd(100)model into a total energy contribution and the remaining part
catalyst under reaction conditions. However, to verify containing all the temperature and pressure dependent
this,thekineticeffectsoftheon-goingcatalyticCO for- terms, i.e. µ = 1/2µ = 1/2Etot +∆µ (T,p), set-
2 O O2 O2 O
mation need to be considered. This is done in a second ting ∆µ (T,p) = 1/2∆µ (T,p), and µ = Etot +
O O2 CO CO
step of our hierarchical approach by performing kinetic ∆µ (T,p)13,16. In the last line of Eq. (2) the differ-
CO
Monte Carlo (kMC) simulations on the here identified enceoftheGibbsfreeenergiesofthecleanandadsorbate
surface structures, on which we report in a consecutive covered surfaces, and of the bulk system, has been ap-
paper. proximatedbytheDFT totalenergiesE13,16. Adetailed
discussion of the thereby neglected contributions to the
Gibbs free energy of adsorption and their influence on
II. THEORY the presented results will be given below.
In the constrained equilibrium approach leading to
A. Gibbs free energy of adsorption Eq. (2) the two gas phases are assumed to be non-
interacting16. TheGibbsfreeenergyofadsorption∆Gads
To determine the stability of a surface in contact with depends then linearly on the chemical potentials of both
agasphasereservoirweusethesurfacefreeenergyγ. For the oxygen and CO gas phase. The slope is respectively
a multi-component system in equilibrium with atomic determinedbythesurfacecoverageofoxygenand/orCO.
reservoirs(e.g. asurroundinggasorliquidphaseenviron- This is most apparent in the last line of Eq. (2), where
ment, or a macroscopicbulk phase) a general expression we haveintroduced the averagebinding energyof O and
for the surface free energy is given by CO as
Ebind = (3)
1 O,CO@Pd(100)
γ(T, p )= Gsurf N µ (T,p ) . (1)
i i i i
{ } A" − # = Etot Etot ∆N Etot
Xi e O,CO@Pd(100)− Pd(100)− Pd Pd
(cid:16) N
Here, Gsurf is the Gibbs free energy of the solid includ- OEtot N Etot .
ingthesurface,Aisthesurfaceareaandµ (T,p )arethe − 2 O2 − CO CO
i i (cid:17)
chemicalpotentialsofthevariousspeciesiinthesystem.
Since the most stable structure will be the one with
To compare the stability of different adsorption struc-
the lowest surface free energy, an adsorbate structure
turesofoxygenandCOonthePd(100)surfacedepending
will be stable with respect to the clean surface, if
onthe surroundinggasphase conditions one has to eval-
γ <γ ,i.e. if ∆Gads >0. Iftwostruc-
uatetheGibbsfreeenergyofadsorption,∆Gads.17,18 For O,CO@Pd(100) Pd(100)
tures contain an equivalent amount of oxygen and CO
this,thestabilityofthedifferentadsorptionstructuresis
they will also show the same dependence on ∆µ and
compared with respect to the clean metal surface. For a O
∆µ . The ratio of how these two structures contribute
Pd(100) surface in a constrained equilibrium with an O CO
2 tothestablestructuresisgovernedbythelawofmassac-
and CO gas phase ∆Gads is thus given by
tion,whichenablesustodirectlyexcludealessfavorable
∆Gads(∆µO,∆µCO)= (2) structure,if its binding energy,EObi,nCdO@Pd(100), differs by
muchmore thank T fromthe one ofthe mostfavorable
= γ γ B
Pd(100)− O,CO@Pd(100) structure. e
1
= Gsurf Gsurf ∆N µbulk FortheadsorptionofO/COonthePd(100)surfacethe
−A O,CO@Pd(100)− Pd(100)− Pd Pd averagebindingenergydefinedinEq.(3)isequivalentto
(cid:16)
N (1/2Etot+∆µ ) N (Etot +∆µ ) the commonly used binding energy, which is often given
− O O2 O − CO CO CO
per O atomrespectivelyCO molecule, e.g. in the caseof
1 N N (cid:17)
Ebind + O∆µ + CO∆µ , oxygen as
≈ −A O,CO@Pd(100) A O A CO
Ebind = (4)
where Gsurfe is the Gibbs free energy of the O@Pd(100)
O,CO@Pd(100)
1 N
Pd(100) surface with NO adsorbed O atoms and NCO = Etot Etot OEtot .
adsorbed CO molecules, and GsPudr(f100) is the Gibbs free NO (cid:18) O@Pd(100)− Pd(100)− 2 O2(cid:19)
energy of the clean palladium surface. If the number
of palladium atoms per surface area A in the adsorp- In the case of additional adsorption of O/CO on the re-
tion structure, N , and in the clean surface, N , are constructed √5 surface oxide (which will be introduced
Pd P′d
not equal (e.g. due to a surface reconstruction), i.e. below)the binding energyofthe atom/moleculewithre-
∆N = N N = 0, then the excess/deficiency spect to this √5 structure is then given by (here exem-
Pd Pd − P′d 6
3
plified for CO)
TABLE I: Computed heat of formation ∆Hf (0,0) and
PdO
Ebind = (5) binding energies of O2, CO and CO2 (see text). The quoted
CO@√5 experimentalvaluesareextrapolatedtoT =0Kandthezero
1
= Etot Etot N Etot , point vibration energy (ZPE) has been removed. All values
NCO CO@√5− √5− CO CO are in eV.
(cid:16) (cid:17)
where Etot is the total energy of the √5 surface oxide. PBE RPBE LDA Exp.20 ZPE
√5
We note that Ebind is in this case different to the above ∆Hf (0,0) -0.87 -0.62 -1.42 -0.97
PdO
defined Ebind in Eq. (3), since the latter also contains
the energetic changes due to the formation of the √5 EObi2nd -6.22 -5.75 -7.56 -5.30 (0.10)
surface oexide, i.e. it is referenced with respect to the ECbiOnd -11.65 -11.20 -12.93 -11.33 (0.13)
clean Pd(100) surface. ECbiOn2d -17.99 -17.09 -20.43 -16.98 (0.27)
∆Emol -3.24 -3.02 -3.72 -3.00
B. Bulk oxide stability
When considering a metal surface in contact with an translational free energy. The assumption that the CO2
O and CO gas phase complete conversion into an ex- formed at the surface is readily transported away, moti-
2
tended bulk oxide is also a thermodynamic possibility. vatesustodisregardthe translationalfreeenergycontri-
The stability of the corresponding bulk oxide has there- bution18. The vibrational free energy contribution will
fore to be evaluated with respect to the two gas phase be of the order of the ZPE for the temperature range
components and compared to the various stable struc- discussed here. As can be seen in Table I the ZPE value
turesforming atthe metalsurface18. Asufficientoxygen for CO2 is approximately 0.3eV. Variations of ∆Emol in
contentinthegasphasewillleadtotheformationofbulk Eq. (8) of this order of magnitude do not affect any of
palladium oxide, PdO, whereas a sufficient CO content theconclusionsdiscussedbelow,whichjustifiestherather
will favor the decomposition of PdO into CO and Pd crude approximation for the present purpose.
2
metal. In a pure oxygen gas phase the thermodynamic
stability of the bulk oxide is given by
C. Computational Setup
µbulk <µbulk+µ , (6)
PdO Pd O
whereasinapureCOenvironmentthestabilitycondition With the approximations made in the last two sub-
for the oxide is sections, the crucial quantities determining the sta-
bility of surface structures are the total energies of
µbulk +µ <µbulk+µ . (7) the extended surfaces and of the involved gas phase
PdO CO Pd CO2
molecules. These total energies are obtained by DFT
IfweapproximatethechemicalpotentialofthefreeCO2 calculations which have been performed within the full-
molecule by its total energy only18, Eq. (6) and Eq. (7) potential (linearized) augmented plane wave + local or-
can be combined yielding the stability criterion for PdO bital (L)APW+lo method21,22 as implemented in the
in an oxygen and CO containing gas phase WIEN2k code23.
All surfaces are simulated within the supercell ap-
∆µ ∆µ . 2∆Hf (T =0K)+∆Emol . (8)
CO− O − PdO proach,usinginversionsymmetricslabsconsistingoffive
Pd(100) layers with adsorption of oxygen and/or CO or
Here,∆HPfdO ≈EPtodtO−EPtodt−1/2EOto2t istheheatoffor- thereconstructedsurfaceoxideplusadditionalO/COon
mationofPdOatT =0K,and∆Emol =Ebind Ebind both sides. The vacuum between consecutive slabs is
CO2− CO −
1/2Ebindisthedifferenceinbindingenergiesbetweenthe at least 14˚A. The adsorption layers and two outermost
O2
three gas phase molecules. Table I compiles these bind- palladium layers have been fully relaxed. The muffin-
ing energies, as well as the heat of formation of PdO, as tin radii have been set to RPd = 2.0bohr for palla-
MT
obtained by previously published highly converged DFT dium, RO = 1.0bohr for oxygen and RC = 1.0bohr
MT MT
calculations19 andusingthe computationalmethodology for carbon. Inside the muffin-tins the wave functions
describedbelow. Inadditionthe experimentalvaluesare are expanded up to lwf = 12 and the potential up to
max
quoted. These valueshavebeen extrapolatedto T =0K lpot =6. ForthePd(100)-(1 1)structurea[10 10 1]
max × × ×
and the zero point vibration energy (ZPE, also listed in Monkhorst-Pack (MP) grid has been used to integrate
Table I) has been removed. the Brillouin zone (BZ). For larger surface unit cells the
Substituting the chemical potential of CO , µ , by MP-gridhasbeenreducedaccordinglytoassureanequiv-
2 CO2
only the total energy term, Etot , in Eq. (7) is a rather alent sampling of the BZ. Since calculations with dif-
CO2
crudeapproximation. Themostimportantcontributions ferent MP-grids are not fully comparable, the energies
that have been neglected arise from the vibrational and of the clean metal surface, Etot , and of bulk palla-
Pd(100)
4
dium, Etot, needed to evaluate the Gibbs free energy of
Pd
adsorption as defined in Eq. (2), have been calculated
eachtime inthe same supercellas the correspondingad-
layers or surface oxide structure. The energy cutoff for
the expansion of the wave function in the interstitial is
Ewf =20Ry and for the potential Epot =196Ry. Us-
max max
ing these basis set parameters the average binding ener-
giesper oxygenatom/COmolecule areconvergedwithin
50meV,sothatthe Gibbsfreeenergiesofadsorptionare
convergedwithin 1-5meV/˚A2.
All molecular calculations are done in rectangular su-
FIG.1: (Color online) Top views of thethreeexperimentally
percells with side lengths of (13 14 15)bohr (atoms)
× × characterizedadlayerstructuresofCOonPd(100). Fromleft
or(13 14 20)bohr (molecules)using onlythe Γ-point
× × to right the coverage increases from Θ = 0.5 to Θ = 0.67
to sample the BZ. To obtain the binding energies of the andΘ=0.75ML.TheyellowsmallspheresrepresenttheCO
three gas phase molecules, O2, CO and CO2, very accu- molecules,thegreylargespheresthePd(100)surface(second
ratelythecutofffortheexpansionofthewavefunctionin layer atoms are darkened).
theinterstitialhasbeenincreasedtoEwf =37Ry. With
max
respect to this cutoff the binding energies are converged
within 10-20meV. (5 5) structure appears to be only of metastable char-
Theexchange-correlation(xc)energyistreatedwithin act×er andits formationwasfound to be verysensitive to
thegeneralizedgradientapproximation(GGA)usingthe the surface preparation and oxygen exposure range, so
PBE24 xc-functional. To assess the error introduced to that in the oxidation as well as in the reduction process
thetotalenergiesbytheapproximatexc-energy,themost the(5 5)structurecanbe bypassedgoingdirectlyfrom
importantcalculationshavealsobeenrepeatedusingan- a (2 ×2) to a √5 structure and vice versa30.
other gradient corrected xc-functional, the RPBE25, as ×
Thisleavesasorderedadlayersonlythep(2 2)at0.25
well as the local-density approximation,LDA26. The in- ×
monolayer (ML) coverage and the c(2 2) at 0.5ML.
fluenceofthesedifferentxc-functionalsontheresultswill ×
Computing the binding energy of O atoms in all high-
be discussed below.
symmetry sites offered by the (100) surface (bridge, top
and hollow), we find in both structures the fourfold hol-
low site to be the moststable adsorptionsite. The bind-
III. O AND/OR CO ADSORPTION AT Pd(100)
ing energies are calculated with respect to the O gas
2
phase molecule (cf. Eq. (4)) and the values of the bind-
In this section we discuss the different adlayer struc-
ingenergiesperoxygenatomarelistedinTableII. Itcan
tures of oxygen and/or CO on Pd(100) that will be
beseenthatthebindingenergydecreasesgoingfromthe
comparedwithintheconstrainedthermodynamicequilib-
p(2 2) to the higher coveragec(2 2) adlayer,indicat-
rium approach. In addition to the on-surface adsorption × ×
ing overall repulsive interactions between the adsorbed
of O/CO on Pd(100), the formation of a reconstructed
oxygen atoms.
(√5 √5)R27 (abbreviated with √5 in the following)
◦
×
surfaceoxidehasexperimentallybeenobservedathigher
oxygenexposure27,28,29,30. Since the structure of the √5
2. Pure CO adsorption
surface oxide is quite different from the clean Pd(100)
surface,alsoexhibiting different adsorptionsites,we will
discuss the two surfaces separately. TheadsorptionofCOonPd(100)hasbeenstudiedin-
tensively32,33,34,35,36,37,38,39. In all experimental studies
it is found that CO binds upright in the bridge position
A. Adlayers on Pd(100) viatheCatom. AtacoverageofΘ=0.50MLanordered
(2√2 √2)R45 adlayer is formed, which is compressed
◦
×
1. Pure oxygen adsorption to a (3√2 √2)R45◦ structure at Θ = 0.67ML and a
×
(4√2 √2)R45 at Θ = 0.75ML (cf. Fig. 1). The for-
◦
×
Experimentally, four different adsorption structures mation of the (2√2 √2)R45◦ adlayer rather than a
×
have been observed when exposing the Pd(100) surface simple c(2 2) structure is assumed to be mainly due
×
to oxygen27,28,29,30,31. These are a p(2 2), a c(2 2), to overall strongly repulsive interactions among the ad-
a (5 5) and the √5 surface oxide str×ucture. Th×e √5 sorbedCOmolecules40. Inthec(2 2)eachCOmolecule
surfa×ce oxide will be discussed in detail in the next sec- has four nearest neighbors at a d×istance of √2a, where
tion. The (5 5) structure will not been considered in a is the length of the (1 1) surface unit cell. In the
× ×
this study, since the structure and state of the oxygen (2√2 √2)R45 structure, however, the CO molecules
◦
×
atoms has not been well established so far, i.e. there ex- formadistortedhexagonaloverlayerwithonlytwonear-
ists no well defined structural model. In addition, the est neighbors at a distance of √2a and four neighbors
5
TABLEII:Calculatedbindingenergiesofon-surfaceadlayers
of O/CO on Pd(100). For the pure adlayer structures the
binding energies are given per O atom resp. CO molecule.
Forthemixedstructuresthetotalbindingenergiesaregiven.
All values are in eV.
Coverage Θ Ebind
Pure O structures:
p(2 2)-Ohol 0.25 -1.35 FIG. 2: (Color online) Top views of the considered co-
c(2×2)-Ohol 0.50 -1.10 adsorbed overlayer structuresof oxygen and CO on Pd(100).
× The small red (dark) spheres correspond to oxygen atoms,
the small yellow (light) spheres represent the CO molecules
Pure CO structures:
and the large grey spheres the Pd(100) surface (second layer
p(2 2)-CObr 0.25 -1.92
c(2×2)-CObr 0.50 -1.92 atoms are darkened).
(2√×2 √2)R45◦-CObr 0.50 -1.92
×
(3√2 √2)R45◦-CObr 0.67 -1.73
×
(4√2 √2)R45◦-CObr 0.75 -1.63
(1 1×)-CObr 1.00 -1.31
× is rather unlikely that the adsorbedoxygenreacted with
the CO at this low temperature. The disappearance of
Mixed O/CO structures:
the LEED signal was thus interpreted as a CO induced
(2 2)-Ohol-CObr 0.50 -2.95
(2×2)-2Ohol-CObr 0.75 -2.93 disorderingoftheoxygenislands. Toneverthelessobtain
(2×2)-Ohol-2CObr 0.75 -3.96 an idea about the simultaneous adsorption of O and CO
(2×2)-2Ohol-2CObr 1.00 -3.64 onPd(100)wesetupdifferentmodelsformixedoverlayer
× structures that seemed to be most obvious from a com-
binatorialpoint of view. For this we used(2 2) surface
×
unit cells placing 1 to 2 O atoms and CO molecules in
slightly further away at a distance of 5/2a. theirfavoriteadsorptionsites,i.e. OinhollowandCOin
Inadditiontotheseexperimentallyobservedstructures bridge sites. Excluding any structures where O and CO
p
also simple (1 1) and (2 2) adlayers with CO in top, are closer to each other than the length a of the (1 1)
bridge and hol×low sites are×considered in this work. The surface unit cell we obtain the four different struct×ures
adsorptionin bridge sites is found to be energetically fa- shown in Fig. 2. The corresponding average binding en-
voredatallcomputedcoverages. TableIIcompilesthere- ergies calculated using Eq. (3) are listed in Table II.
fore only the results for bridge-bonded CO. Looking at
the values in Table II it can be seen that the binding Similar to the pure adlayer structures of O or CO on
energy per CO molecule is almost constant up to a cov- Pd(100),thebindingenergyperadsorbatedecreaseswith
erage of Θ = 0.50ML. For higher coverages the binding increasingcoverageintheconsideredco-adsorptionstruc-
energydecreasesdue tooverallrepulsiveinteractionsbe- tures. This trend in binding energies reflects the afore
tween the adsorbed CO molecules. Comparing the two mentioned repulsive interactions among the adsorbed O
discussed structures with a coverage of Θ = 0.50ML we atomsandCOmolecules. ForacoverageofΘ=0.50ML
in fact find them to be degenerate within our computa- the binding energy of the mixed O/CO overlayer is less
tional accuracy (the (2√2 √2)R45◦ is only favored by favorableby70meVthanthesumofthebindingenergies
×
a few meV). These results are also fully consistent with oftherespectivec(2 2)pureadlayersofOandCO.This
previous DFT pseudopotential studies25,40. indicatesthatthe re×pulsiveinteractionsamongadsorbed
O and CO are even stronger than between O and O, re-
spectively CO and CO in the pure adlayer structures.
3. Mixed O/CO adsorption The adsorption of both O and CO in hollow sites in a
c(2 2) structure further decreases the binding strength
×
AstotheadsorptionofoxygenandCOonthePd(100) of the adsorbates.
surface, experimentally no ordered overlayers have been
reportedsofar. IfthePd(100)surfaceisexposedtoboth Theevenstrongerrepulsiveinteractionsinthesemixed
oxygen and CO, the two adsorbed species tend to form adsorbatestructureswillthusfavortheseparationofoxy-
separate domains instead31. In their low energy electron gen and CO into separate domains. The adsorption of
diffraction(LEED)measurementsStuveetal.31 observed COintoap(2 2)-Ostructurecantheninduceademixing
×
that for a fully developed p(2 2)-O/Pd(100) structure ofthetwospeciesanddestroythelong-rangeorder,which
×
the p(2 2) LEED pattern vanished after exposure to is consistent with the disappearance of the LEED spot
×
CO ata temperature ofT =80K.Assuming a barrierof intensitiesintheaforementionedexperimentbyStuveet
1.0eVforthereactionofOandCOtoformCO 41,42 it al.31.
2
≈
6
top2f
topI4f topI2f br II hoIl IhIoIl
toIpI4f II br I hIoIl IhVol
top−sites bridge−sites hollow−sites
Pd(100) FIG. 4: (Color online) Top views of high-symmetry adsorp-
surface oxide tionsitesonthe(√5 √5)R27◦ surfaceoxidestructure. Red
×
small spheres represent thelattice oxygen atoms, large light-
FIG.3: (Coloronline)Topviewofthe(√5 √5)R27◦surface blue ones the reconstructed Pd atoms and large dark-blue
×
oxide structure (left part) and the Pd(100) substrate (right spheresPdatomsbelongtotheunderlyingPd(100)substrate.
part) and their corresponding surface unit cells (black lines).
Red small spheres represent the lattice oxygen atoms, large
light-blue ones the reconstructed Pd atoms and large dark-
TABLE III: Calculated binding energies of CO on the √5
bluespheresPdatomsbelongtotheunderlyingPd(100)sub-
surfaceoxidestructurecalculatedusingEq.(5). 2COdenotes
strate. The arrow indicates the easy shift direction of the
that two CO molecules are adsorbed in the √5 surface unit
surface oxidetrilayer along thePd(100) substrate.
cell. TheadsorptionoftwoCOmoleculesintop4fsitesorone
CO in bridge and a second in a top2f site does not lead to a
stable structure. All values are per CO molecule and in eV.
B. O and CO on the surface oxide
Ebind Ebind Ebind
CO@√5 CO@√5 CO@√5
At a coverage of Θ = 0.80ML, the adsorbed oxygen CObr -0.93 2CObr -0.75 2CObr,top2f —
induces a reconstruction of the Pd(100) surface forming COtop2f -0.62 2COtop2f -0.51 2CObr,top4f -0.45
the √5 surface oxide structure. An atomistic model for COtop4f -0.13 2COtop4f — 2COtop2f,top4f -0.29
the surface oxide (cf. Fig. 3) was proposed in a detailed
experimental and theoretical study, revealing that the
structure can actually be described as a PdO(101) tri-
layer on Pd(100)43. The surface unit cell contains four responding Pd atom is twofold or fourfold coordinated
palladium and four oxygen atoms. Two Pd atoms are by oxygen. As yet there is no experimental information
fourfold and the other two are twofold coordinated by available for the additional adsorption of O or CO on
oxygen. There are also two kinds of O atoms. Two O the √5 surface oxide. Therefore, we performed a sys-
atomssiton-topofthereconstructedPdlayerandtwoat tematic investigation of possible overlayer structures of
the interface to the Pd(100) substrate forming the afore O and CO involving the reconstructed √5 surface oxide
mentioned trilayer structure. andstartingwith the adsorptionsites depicted inFig. 4.
In addition to the previous discussion on this surface In a first step only one CO molecule is adsorbed in
oxide structure43, we note that the potential energy sur- any of the ten adsorption sites. We find that the four
faceforaregistryshiftoftheentiresurfaceoxidetrilayer different hollow sites are not stable, i.e. upon relax-
overthePd(100)substrateisveryshallow. Inparticular, ation the adsorbed CO molecule always moves to the
shiftsofupto 0.5˚A alongthedirectionasindicatedby respective neighboring bridge site. The binding energies
∼
thearrowinFig.3andparalleltothesurfaceleadonlyto of the two bridge (br I and br II) sites are almost de-
energyvariationsoflessthan50meVper√5surfaceunit generate as expected from the only slight structural dif-
cell. Without anchoring by e.g. defects, the lateral posi- ferences, i.e. the binding energies as defined in Eq. (5)
tionoftheidealsurfaceoxideoverthe Pd(100)surfaceis differ by less than 0.1eV. Similarly, the two top sites at
thus not well defined. In extended test calculations, we the two twofold (top2f I and top2f II) oxygen coordi-
verified that this uncertainty in the lateral position has nated Pd atoms exhibit nearly equivalent binding ener-
no consequences on the adsorption energetics discussed gies (∆Ebind < 50meV). The same is also found for the
here and therefore simply use in the present work the two top sites at the two fourfold (top4f I and top4f II)
lateral position determined in Ref. 43. oxygen coordinated Pd atoms. In the following we will
Fortheadditionaladsorptionofoxygenand/orCOon thus treat these correspondinglyvery similar sites as be-
the surfaceoxidestructure thereareseveralpossibilities. ing identical. The bridge site is the most stable adsorp-
As can be seen in Fig. 4 the surface oxide exhibits top, tion site followed by the top2f site, and on the top4f site
bridge andhollowhigh-symmetry sites. Due to the sym- the CO molecule is already only weakly bound (cf. Ta-
metry of the underlying Pd(100) substrate multiple ad- ble III).
sorptionsitesofthesametype(top,bridgeorhollow)are It is also possible to adsorb two CO molecules in the
not fully equivalent, but still very similar. Only the top √5 surface unit cell, andagainwe find the adsorptionin
sites differ substantially depending on whether the cor- the two bridge sites most stable. Mixing the adsorption
7
sites, i.e. placing e.g. one CO in a bridge site and a Even if we leave out the four unstable hollow sites in
second one in a top2f site does always yield less stable Fig.4thereisfinallystillahugeamountofpossibleover-
structuresthantheadsorptioninlikesites(cf. TableIII). layer structures that can be created by combinatorially
It also becomes energetically very unfavorable to place placing an arbitrary number of O and CO per surface
morethantwoCOmoleculesinthe√5surfaceunitcellas unit cell into any of the available sites. Since there is
deducedfromtestcalculationswithupto4COmolecules only little known about the adsorption on the surface
per surface unit cell. oxide none of these structures can a priori be excluded.
The adsorption of oxygen in the high-symmetry sites Motivated by the strong repulsive interactions seen in
of the √5 surface oxide gives similar results. Again, the our calculations with one or two adsorbates per surface
bridge site is the most stable site (Ebind = 0.14eV) unitcell,weneverthelessdiscardquiteanumberofthese
O@√5 −
and the hollow sites are unstable upon relaxation. How- structureswiththe criterionthatnotwoadsorbatesmay
ever, it is now not possible to adsorb any oxygen in the sit in directly neighboring sites (i.e. at a distance of less
top2f and top4f sites in the √5 unit cell. If one CO than 1/4 of the length of √5 surface unit cell). This
molecule and one O atom are adsorbed simultaneously, still leaves 92 “plausible” structures and DFT calcula-
likewise the adsorptionin two bridge sites is found to be tions were performed for all of them (for more details on
favored. the calculated overlayer structures see Ref. 44). Out of
Our calculations with one and two adsorbates per √5 these only 55 are stable upon relaxation and are then
surfaceunitcellthusindicatenoticeableoverallrepulsive considered in our constrained “phase diagram”.
lateral interactions. We correspondingly extended our
calculations also to more sparse adlayers in (2 1) and
×
(1 2) √5 surface unit cells, but did not find significant IV. STABILITY IN A CONSTRAINED
×
lateral interactions extending across the √5 surface unit EQUILIBRIUM WITH AN O2 AND CO GAS
cell. Theobtainedbindingenergieswerealwaystowithin PHASE
25meV per adsorbate of those calculated for the same
adsorption site in a (1 1) cell. UsingtheGibbsfreeenergyofadsorptionasdefinedin
×
Toincreasetheconfigurationspaceofconsideredover- Eq.(2)itispossibletocomparethestabilityofallcalcu-
layers based on the √5 surface oxide, we also considered lated adsorption structures in a constrained equilibrium
structures, in which the original surface oxide structure with an O andCO gas phase. In this approachthe sur-
2
is slightly modified. In a first step, one of the upper face is consideredto be in equilibrium with two separate
hollow site oxygen atoms is removed, and CO and O gas phase reservoirs of O and CO, i.e. the formation
2
are again placed in the afore described sites. Also in of CO is neglected in the gas phase as well as on the
2
this modified structure the bridge site results as the pre- surface16. In the gas phase this assumption seems quite
ferred adsorption site. If both upper oxygen atoms are justified, since the direct reaction of O and CO is ki-
2
removed from the √5 surface oxide, we find the struc- netically hindered by a huge free energy barrier. On the
ture already to some extend destabilized. Due to the surface,though,thereactionisactuallysupposedtotake
lower palladium density in the reconstructedlayer (4 Pd place at the working catalyst. Here, the assumption of
atoms on 5 Pd(100) substrate atoms per unit cell) the aconstrainedequilibrium is thus onlyreasonableas long
structure is rather open, and the structural relaxation as the O and CO adsorption and desorption events are
2
showed that the Pd atoms can now move quite easily in much more frequent than the reaction, so that the sur-
lateral direction on the surface. It is still possible to ad- face canmaintainits equilibrium with the twogas phase
sorb O/CO in any of the other adsorption sites, but we components. In other words, the approach amounts to
foundthesestructureseitherunstableuponrelaxationor assumingthatthekineticsoftheon-goingcatalyticreac-
ingeneralmuchlessstablethanthecorrespondingstruc- tionsdoesnotchangethesurfacestructureandcomposi-
tures, where the original O hollow vacancy is refilled. tion. The resulting constrainedsurface “phase diagram”
In addition to simply removing the upper oxygen canthus onlyprovideafirstidea ofthe possiblyrelevant
atomsfromthe√5surfaceoxidestructureandfillingad- surface structures, which needs to be scrutinized explic-
ditional on-surface adsorption sites, we also substituted itly treating the surface kinetics. On the other hand the
the topmost O atoms by CO molecules, and placed ad- constrainedequilibriumapproachallowstorapidlyscreen
ditional O atoms and/or CO molecules in top2f, top4f a huge number of (structurally quite different) surface
and bridge sites. In the substituted hollow site the CO configurations and compare their stability over a wide
binds quite strongly. However, since the O atoms bind (T,p)-range of possible gas phase conditions. By using
evenstrongerto this site by 0.6eV, O willalwaysprefer- ab initio thermodynamics we are thus able to identify
entially occupythe hollowsites whenthe twoadsorbates those regions in (T,p)-space that are likely catalytically
compete for this sites. The situation is reversed for ad- active and where we then zoom in with more sophisti-
sorption in the bridge sites. Regardless of whether O or cated methods. This second, refining step explicitly in-
CO occupies the threefold hollow sites, we always find a cludes the effect of the reaction kinetics on the average
strongerbinding byatleast0.7eVofCOcomparedto O surface composition (using kinetic Monte Carlo simula-
at these bridge sites. tions) and the results of these simulations, which are re-
8
stricted to the most relevant surface structural models ing both the oxygen and CO content in the gas phase.
identified here, are discussed in a second paper. This Intuitively, one would expect co-adsorptionstructures of
will then also bring us into a position to scrutinize the O and CO on Pd(100) to become favorable. But none
validityoftheassumptionofthe constrainedequilibrium of the above discussed ordered co-adsorption structures
approach employed here. (cf. Fig. 2) are found to be a most stable “phase” under
any gas phase conditions. This is consistent with the al-
ready mentioned experimental findings, that O and CO
A. Surface Phase Diagram prefer to form separate domains rather than ordered co-
adsorbedoverlayers31. The lowerstability of such mixed
Theresultsoftheabovedescribecalculationsconcern- structures can be explained by the strongly repulsive in-
ing the afore discussed overlayers of oxygen and CO on teractions between adsorbed O and CO, which lead to
Pd(100), also including the (modified) √5 surface ox- a significant decrease in binding energies (cf. Table II).
ide structure,are summarizedin Fig.5, whichshowsthe However, we can of course not exclude that ordered ar-
moststable“phases”(i.e. theonesthatmaximize∆Gads rangements with different periodicities than those con-
as defined in Eq.(2)) for any givenchemical potentialof sideredherewouldnotleadtoaloweringintherepulsive
the oxygen and CO gas phase. The dependence on the interactions. To take a reasonablepart in the “phase di-
chemical potentials has also been converted into more agram”, though, the binding energies would have to in-
intuitive pressures scales for temperatures of T = 300K creasebyasmuchas0.3–0.5eVperOatom/COmolecule
and T = 600K in the top two x-axes for oxygen and compared to the now proposed structures. Compared
the right two y-axes for CO. As expected from the to the pure overlayer structures this would even imply
Gibbs phase rule, stable “phases” cover volumes in the the necessity of attractive interactions between the two
3-dimensionalspace spannedby (T,p ,p ), andcoex- species.
O2 CO
istence regions between two “phases” cover areas. Cor- ForhighoxygenandCO contentinthe gasphase(up-
respondingly in the 2-dimensional sectional plane shown per right part of Fig. 5) we find instead co-adsorbed
in Fig. 5 this leads to areas and lines for the two cases, structures involving the √5 surface oxide (two orange-
respectively. Out of the set of 191 tested structures only white hatched regions) to become stable. These two
11 turn out to be “phases” appearing in Fig. 5. mixed structures correspond to the surface oxide with
Wewillstartthediscussionoftheobtainedconstrained one and two CO molecules adsorbed in bridge sites, re-
surface“phasediagram”inFig.5inthelowerleftcorner. spectively. In a small range of very oxygen-rich and in-
Here, both the chemical potential of oxygen and CO are termediateCOgasphaseconditionsadditionalOadsorp-
very low, i.e. the oxygen/COcontent in the gas phase is tion in the bridge sites of the √5 structure leads also to
insignificant and consequently the clean Pd(100) surface a stable “phase” (dark red-white hatched region).
results as the most stable system state. If we now move Lookingagainatthewholesurface“phasediagram”in
alongthe x-axis inFig.5 to the rightwereachmore and Fig. 5 the 11 “phases” can be divided into three groups:
moreoxygen-richconditions,whiletheCOcontentinthe on-surface adlayer structures of O or CO on Pd(100),
gasphaseis keptlow. The increaseinthe oxygenchemi- phases involving the √5 surface oxide structure, and the
calpotentialleadstoastabilizationofoxygencontaining
stability region of the bulk oxide as discussed in sec-
structureswithincreasingcoverage: First,thep(2 2)-O
tion IIB. Focusing on these three different groups of
×
overlayer on Pd(100)45, then the √5 surface oxide and phasestwoimportantconclusionswithrespecttotherel-
finally the PdO bulk oxide representing thick bulk-like evance of oxide formation under catalytic reaction con-
oxidefilms onthe surface. This sequence ofstable struc- ditions can be drawn. First, the formation of a thick,
tureswasalsoconfirmedby in situ surfaceX-raydiffrac- bulk-like oxide (grey cross-hatched area) at the surface
tionmeasurements4. Interestingly,the c(2 2)structure undertechnologicallyrelevantgasphaseconditionsofO
observedunder UHV conditions27,28,29,30,31×does not ap- andCO(blackbarinFig.5,p 1atm,T 300 600K2)
i
pear in the surface “phase diagram”. Thus we conclude can be ruled out. This is thus ∼in marked c∼ontras−t to the
that the c(2 2) structure is most likely a meta-stable muchwiderstabilityrangeofbulkRuO , whichdoesex-
× 2
state produced by the exposure kinetics. tendtotheseconditions18. Second,thestabilityregionof
If the oxygencontent is kept low in the gas phase and the √5 surface oxide (hatched area)does extend to such
the CO content is gradually increased, i.e. moving from conditions. Infact,itiseitherthismonolayerthinsurface
thelowerleftcorneralongthey-axistothetopinFig.5, oxide or CO adlayers on Pd(100),which are neighboring
aseriesoforderedCOadlayerstructureswithincreasing “phases”aroundthe catalytically active regionin (T,p)-
coverage is stabilized on Pd(100). At first we find the space. As can be seen in Fig. 5 the catalytically relevant
also experimentally observed (2√2 √2)R45◦, (3√2 conditionsareactuallyrightattheboundarybetweenthe
× ×
√2)R45 and(4√2 √2)R45 structures,andfinallyfor √5 surface oxide structures and the CO overlayerstruc-
◦ ◦
×
averyhighCOcontentinthegasphasea(1 1)structure tures on Pd(100). Small changes in the Gibbs free en-
×
with 1ML CO in bridge sites. ergyofadsorptioncausingashift inthis boundarycould
StartingagaininthelowerleftcornerofFig.5wenow thus well affect the conclusion as to which is the most
move along the diagonal, which corresponds to increas- stable “phase” under these conditions. Apart from the
9
−CO bridge/
Pd(100) 600 K
300 K
surface oxide
+2CO bridge
CO/Pd(100)
surface oxide
CO/Pd(100) +CO bridge
CO/Pd(100)
surface oxide
+O bridge
clean Pd(100)
PdO bulk
surface oxide
−O/Pd(100)
FIG. 5: (Color online) Surface “phase diagram” of thePd(100) surface in constrained thermodynamicequilibrium with an O2
andCOgasphase. Theatomicstructuresunderlyingthevariousstable(co-)adsorptionstructuresonthemetalandthesurface
oxide, as well as a thick bulk-like oxide film (indicated by the bulk unit cell) are also shown (Pd = large blue spheres, O =
smallredspheresandC=smallyellowspheres). Theblackbarmarksgasphaseconditionsrepresentativeoftechnological CO
oxidation catalysis, i.e. partial pressuresof1atmandtemperaturesof 300 600K.Thedependenceof thechemicalpotentials
−
of the two gas phases is translated into pressure scales for T =300K and T =600K (upperx-axesand right y-axes).
assumptionofaconstrained thermodynamicequilibrium, influenced by considering all contributions to the Gibbs
the mainuncertainties,whichmaycausesuchchangesin freeenergy,therespectivetermshavetobecalculatedex-
∆Gads are the approximate DFT total energies and the plicitly. However,theorderofmagnitudeestimatecanbe
neglectedfree energy contributions. We verifiedthat the obtainedveryeasilyandisthushelpfultodecidewhether
uncertaintiesintheDFTtotalenergiesduetothenumer- or not it becomes necessary to evaluate the entire Gibbs
ical approximations (supercell setup, finite basis set) are free energy.
not significant in this respect. What needs to be scruti- Following the discussion in Refs. 13 and 16 the con-
nized are therefore the uncertainties due to the approx- tributions to the Gibbs free energy of adsorption arising
imate xc-functional underlying the DFT total energies from the pV-term and the configurational entropy are
and the neglected free energy contributions to ∆Gads. rather small for systems like the one presented here. We
This will be done in the next two subsections. will thus only discuss the most crucial approximation,
namely the neglect of the vibrational free energy contri-
bution,∆Fads,vib totheGibbs freeenergyofadsorption.
B. Evaluating the Gibbs Free Energy Inordertoestimatethesizeof∆Fads,vib weapproximate
the phonon density of states (DOS) within the Einstein
TocalculatetheGibbsfreeenergyofadsorption∆Gads modelby one characteristicfrequency. Followingthe ap-
theGibbsfreeenergiesofthedifferentcomponentsenter- proach outlined in Ref. 13 the vibrational contribution
ing Eq. (2) have to be evaluated. The Gibbs free energy to the Gibbs free energy of adsorption for the p(2 2)-
×
O/Pd(100)structure can then be estimated as
G(T,p)=Etot+Fvib TSconf +pV (9)
− ∆Fads,vib(T) (10)
≈
comprises contributions from the total energy Etot, the 1 1
Fvib(T,ω¯surf ) Fvib,ZPE(ω¯gas) ,
vibrational free energy Fvib including the zero point en- ≈ −A O−Pd − 2 O2
ergy (ZPE), the configurational entropy Sconf and the (cid:18) (cid:19)
pV-term. In Eq. (2) we substituted the Gibbs free en- where Fvib(T,ω) is the frequency dependent function
ergydifferencebyonlytheleadingterm,thetotalenergy
1
differences, which can be directly obtained from DFT Fvib(T,ω)= ~ω+kBT ln(1 e−β~ω) (11)
2 −
calculations. We assess the uncertainty introduced by
this approximation by an order of magnitude estimate with β =1/k T. ω¯surf is the characteristic vibrational
B O Pd
of the remaining contributions to ∆Gads. If this first frequency of an oxyg−en atom adsorbed in a fourfold hol-
approximation reveals that the results are significantly low site on Pd(100), and ω¯gas is the stretch frequency
O2
10
1100. contribution are included. There are some small shifts
inthe boundariesbetweenstablephases,butnoneofthe
ωOsu−rfPd= 24 meV stable structures disappearsfromand none of the unsta-
ωsurf = 48 meV
O−Pd ble ones appears in the “phase diagram”. Furthermore,
ωsurf = 72 meV
O−Pd the boundary between the surface oxide structures and
5
5. the CO adlayers on Pd(100) is only marginally affected
and consequently remains in the vicinity of the catalytic
active region in (T,p)-space. We are thus confident that
for the here discussed results the approximation of the
Gibbs free energy differences by only the total energy
0
0. 200. 400. 600. 800. 1000.
0 200 400 600 800 1000 terms in Eq. (2) is justified.
Temperature (K)
FIG. 6: (Color online) Vibrational contribution to theGibbs C. Influence of the xc-functional
free energy of adsorption for the p(2 2)-O adlayer on
×
Pd(100), within the Einstein approximation using different
To obtain an estimate of the uncertainty in Fig. 5 due
characteristic frequencies (see “inset” and text).
to the choice of the PBE-GGA xc-functional we reeval-
uate the constrained surface “phase diagram” using the
RPBE25 and LDA26 xc-functionals. The corresponding
of the O2 gas phase molecule. The change in the vibra- surface “phase diagrams”are shown in Fig. 7 and are to
tionalcontributionofthePdatomsinthecleanandoxy- becomparedwithFig.5. The“phasediagram”obtained
gencoveredPd(100)is neglected, sothat the vibrational byusingtheRPBEapproximationforthexc-energy(top
contribution to ∆Gads is given by the difference in the graph, Fig. 7(a)) looks in fact very similar to the previ-
vibrational energy of the O2 molecule in the gas phase ously discussed one. There are some shifts in the ac-
and the oxygen atom on the surface. For the oxygen tual phase boundaries, and the stability regions of the
molecule only the ZPE (not included in the presented high coverage phases of oxygen and CO, the √5+Obr
DFT total energies) has to be considered, since all re- and(1 1)-CObr/Pd(100)structures,areshiftedoutside
maining contributions to Fvib are already contained in the sho×wn range of chemical potentials. Yet, the overall
∆µO (cf. Eq. (2)). In Fig. 6 the resulting vibrational topology is fully conserved. In agreement with the PBE
contribution ∆Fads,vib(T) is shown for a characteristic results the bulk oxide is not a stable “phase” anywhere
frequency of ω¯surf = 48meV for the Pd-O stretch fre- near ambient gas phase conditions. Due to the smaller
O Pd
quencyofanads−orbedOatom46 andanO-Ovibrational heatofformation(cf. Table.I),thestabilityregionofthe
frequency of ω¯gas = 196meV47. We find that for the bulk oxide is in fact much further awayfromthis region.
O2
p(2 2)-O/Pd(100) structure the vibrational contribu- Mostimportantly,theboundarybetweenthesimpleover-
tion×to∆Gads staysbelow 3meV/˚A2 fortemperatures layerstructures on Pd(100)and the phases based on the
∼
up to T = 1000K (black-solid line in Fig. 6). Since the √5 surface oxide structure (hatched area) is only very
chosen ω¯surf is only a rough guess, we also allow for a little influenced, so that the most interesting region for
O Pd
50% cha−nge of this value, but even then the contribu- oxidationcatalysis (black bar)is againrightat the tran-
±
tion does not increase considerably (red-dashed, 50% sitionbetweenaCO coveredPd(100)surfaceandphases
−
and blue-dotted, +50%, lines in Fig. 6). involving the surface oxide.
Similarestimateshavebeenperformedforeverystruc- EveniftheLDAisusedasxc-functional(bottomplot,
tureconsideredforthesurface“phasediagram”inFig.5. Fig. 7(b)) the stability region of the bulk oxide does not
For CO containing structures ∆Fads,vib comprises two extendtothe catalyticallyrelevantgasphaseconditions.
different contributions when comparing the gas phase Itcoversamuchlargerrangecomparedtothe“phasedi-
and the adsorbed state, namely the change of the C- agrams”obtainedwiththetwoGGAfunctionalsthough.
O stretch vibration due to the adsorption and an addi- ItshouldalsobenotedthatintheshownLDA“phasedi-
tional Pd-C vibration. For structures involving the √5 agram”therangeofOandCOchemicalpotentialsisen-
surface oxide an additional contribution arises from the largedtolowervaluestoincludethestabilityregionofthe
change in the vibrational energy between bulk and sur- clean metal surface, which in the LDA appears at much
face Pd atoms. The √5 structure contains one surface lower gas phase concentrations. This is a consequence
atom less than the corresponding Pd(100) surface per of the strong overbinding in the LDA, which stabilizes
unitcellwhichalsohastobe balancedbythe bulkreser- any adsorbate structure at much lower pressures at the
voir (∆N = 1 in Eq. (2)). surface. Nevertheless, the range of technologically rele-
Pd
−
With this procedure we find that for all structures vantcatalyticgas phaseconditions (black bar)lies again
∆Fads,vib stays always below 10meV/˚A2 for tempera- right at the boundary between the CO covered Pd(100)
turesuptoT =600K.Thesurface“phasediagram”dis- surface and √5 surface oxide structures.
cussedintheprevioussectionisnotsignificantlychanged, From these results, we conclude that the choice of the
if these estimated, maximum values for the vibrational xc-functional does have a strong influence on the abso-