This document summarizes a first-principles constrained thermodynamics study of H2 oxidation at Pd(100). It examines various surface structures and compositions using DFT calculations linked to ab initio thermodynamics to build a thermodynamic map of surface termination under different O2 and H2 partial pressures. Key findings include: 1) For O adsorption on Pd(100), binding energy decreases with increasing coverage from 0.25 to 1 ML due to repulsive interactions between adsorbed O atoms. Above 0.5 ML coverage, surface oxide formation is favored. 2) For H adsorption, maximum binding energy occurs at 0.5 ML coverage in a c(2×2) structure

1. 1 H2 OXIDATION AT Pd(100): A FIRST-PRINCIPLES CONSTRAINED
THERMODYNAMICS STUDY
1.1 Introduction
Oxidation reactions are ubiquitous in heterogeneous catalysis. The nature of the active metal surface
under steady state conditions for oxidation reactions of different species has been intensively studied.22,
27, 30, 34, 35, 70, 72, 115, 116, 119, 127-129, 131-145
For example, CO oxidation over Pd(100) has been well studied by
Reuter and co-workers using a constrained ab initio thermodynamics approach.72
In those studies it was
found that a monolayer thick surface oxide of PdO(101) supported above Pd(100) was the most stable
surface for a large portion of the phase diagram, particularly in the range of partial pressures of CO and
O2 and at temperatures representative of technological operation. This work demonstrated that the
proper surface termination (which may be predicted from thermodynamics) must be considered when
trying to use density functional theory calculations to evaluate the kinetics of the catalytic mechanism,
and that the proper surface termination may be an oxide when considering oxidation reactions over d-
bandtransitionmetal catalysts.
More recently, we have attempted to expand this approach to examine the oxidation of NO over
Pd(100) and Pd(111).27
In contrast to the CO oxidation case, we found that the bulk oxide, i.e. thick bulk-
like oxidic overlayers, dominates the phase diagram when NO is the reducing agent. This stems from the
fact that NO is a weak reductant compared to CO, and therefore the reaction equilibrium for NO +
PdObulk ↔ Pdbulk + NO2 is shifted to higher NO partial pressures compared to an analogous reaction
statementfor CO oxidation. Furthermore, the product, NO2, is not volatile as in the case of CO oxidation.
This complicates the analysis of the proper surface termination because NO2 cannot be assumed to
desorb.

2. Another common reductant is hydrogen. Due to its important role in heterogeneous catalysis, metal
corrosion and surface electrochemistry, hydrogen oxidation has been well studied over Pd surfaces by
several groups ever since Langmuir’s early work in 1922.146, 147, 148, 149, 150, 151, 152, 153, 154, 155
A palladium
oxide thin film above pristine metal has been investigated as a potential active surface for hydrogen
oxidation, but only under ultra-high vacuum conditions or using density-functional theory (DFT).135,
48
However, experiments on palladium methane oxidation catalysts suggest that the surface may be
covered with hydroxyl groups under reaction conditions.116
Although, Blanco Rey et al. did examine the
stability of the oxide in mixture atmospheres of H2 and O2,48
a complete surface termination map across
a wide range of conditions has not been developed, and in particular a map that would rationalize the
appearance of hydroxylatedsurfaces.
Therefore, DFT calculations linked to ab initio thermodynamics52, 53
have been employed herein to
examine a variety of surface structures and compositions on Pd(100) and to build a thermodynamic map
of surface termination under different partial pressure of O2 and H2. Using this method, we can
determine whatthe mostappropriate surface terminationtoconsiderforaparticularapplication.
1.2 Computational Methodology
DFT calculations were performed using the Vienna Ab Initio Simulation Package (VASP).99, 100A
plane wave basis set with a cutoff energy of 500 eV and the projector-augmented wave (PAW)101
pseudopotentials were used, and all calculations have been done using the Perdew-Burke-
Ernzerhof (PBE)102 exchange-correlation functional.
Pure palladium metal surface models used in this work are inversion-symmetric slabs
consisting of five Pd(100) layers with the adsorbate (H, O etc) on each side and with the middle

3. layer fixed. A uniform (7×7×1) k-point grid is used for the Brillouin zone integration within a 2×2 unit
cell.
The thin film surface oxide model was based upon the (√5×√5)R27°PdO(101)-Pd(100) structure
previously employed by Reuter et al.27, 29, 30, 72, 86, 87
For the structure optimization calculation, a
‘mirror’ structure with five-layers of Pd(100) and one-layer of PdO(101) on both sides has been
created in order to cancel the polarity from the oxide. All atoms are set to relax except the three
center layers of palladium metal. The slabs are separated by approximately 11 Å, equivalent to the
thickness of five layers of Pd(100). A uniform (5×5×1) k-point grid is used for the Brillouin zone
integrations.104
Geometries will be considered to be optimized once all residual forces fall below 0.02
eV/Å.
A four-atom fcc unit cell was adopted to calculate the energy of bulk Pd by sampling in a (9×9×9) k-
point grid. The optimized DFT result for the lattice constant is 3.95 Å in good agreement with
experimental data (3.89 Å)156
and previous calculation result157
. Bulk PdO is a simple tetragonal structure
with lattice constants a = 3.03 Å and c = 5.33 Å at ambient conditions.158, 159, 160
PdO was calculated by
samplingin a (9×9×7) k-point grid and the optimized DFT result gave lattice constants of a = 3.05 Å and c
= 5.48 Å, in good agreement with experimental data. Calculation of energies of molecules (O2, H2, H2O)
were performedina10 Å cubicsupercell withGamma k-pointgridsampling.
For the determination of the surface termination we follow the surface ab initio thermodynamics
approach established by Scheffler and co-workers.72, 27, 52, 28, 161, 162, 163
The underlying principle for this
approach is that the observed termination for a given gas-phase of defined (T, Pi) is the one with lowest
surface free energy, where T is temperature and Pi are the partial pressures of species i. Specifically
considered is a constrained equilibrium, in which the surface is separately in equilibrium with i gas
reservoirs of the i gas phase species, and therefore no provision exists for gas-phase reactions (and

4. concomitant equilibration between the different gas reservoirs). The normalized surface free energy Ω
of a given surface termination at the given gas-phase conditions is then obtained by the following
expression
Ω(T, Pi) = [ Gslab(T, Ni, Pi) – ΣiNiμi(T, Pi)] / 2A , (1.1)
where Gslab denotes the Gibbs free energy of the specific surface slab, μi(T,Pi) are the chemical potentials
of species i for a given temperature T and partial pressure Pi, and Niis the number of atoms (or
molecules) of species i present in the system. The surface free energy is normalized by the surface area,
2A, where A is the area of the surface unit-cell, and the factor of 2 accounts for the fact that all slabs are
modeledasmirrorstructureswithtwoequivalentsurfaces.
The chemical potential of gas-phase species ican be obtainedbythe followingequation:
μi(T, P) = ΔH(T, Pº) + Egas – TΔS(T,Pº) + kBT ln(P/Pº), (1.2)
where Egas is the total energy of the isolated gas phase molecule i, ΔH and ΔS represent the changes in
enthalpy and entropy associated with the temperature of the system at standard pressure P°, and the
final term describes the free energy change with respect to the actual partial pressure of the gas phase
species. In practice ΔH and ΔS were calculated by the Shomate equation using the data from the NIST
database.164,165
Rigorously,Gslab can be expressedas
Gslab = Etotal + Fvib- T Sconf + pV, (1.3)
where Etotal
is the total energy of the slab, Fvib
is the vibrational free energy, and Sconf
is the
configurational entropy. As previously discussed in detail by Reuter and Scheffler,72
Equation (3.1) may
be simplified greatly by recognizing that the difference in the Gibbs free energy between the slab and

5. clean metal, the free energy contributions cancel to a large degree. Therefore equation (3.1) can be
approximatedasfollows:
Ω = [Etotal – ΣNi μi(T, Pi)] / 2A, (1.4)
where Etotal
is given by the DFTcalculations. Utilizing Equation (3.4), surface energies for different
structuresat variousthermodynamicconditions(T,PO2,PH2) are obtained.
In this study a large number of candidate surfaces were evaluated and a comparison of their
stability was examined over a large range of partial pressures of both O2 and H2 for a given temperature,
following the previousexamples of Reuter et al. and Jelic and Meyer.72, 27
As will be shown, only a certain
sub-set of these candidate structures were actually found to be most stable in the range of chemical
potentials examined. However, as always, we are limited here by our need to calculate ordered
structures with defined stoichiometry in unit cells of finite size, and it is certainly possible that there are
stable structureswhichwe didnotconsider.
Finally, the stability of an adsorption structure can also be expressed through its binding energy72
.
For example, for gas-phase species i adsorbed at the Pd(100) surface its binding energy ∆Ei@Pd(100) is
givenby
(1.5)
Where Etotal
Pdi )100(@ is the total energy with species i at the Pd(100) surface, Etotal
Pd )100( is the total
energy of the clean Pd(100) surface, and Etotal is the total energy of an isolatedmolecule i. ni is the
numberof species ion one surface unitcell.
)/( @ (100)@ (100) (100) i
total total totalE NE E E iii Pdi Pd Pd N   

6. 1.3 Results and Discussion
First, different adsorption structures of oxygen were examined for Pd(100) within the constrained
thermodynamic equilibrium approach. In this work, three different ordered adsorption structures
containing dissociated O in a p(2×2), c(2×2), (3√2×√2) R45°, (1×1) arrangement, as well as the
(√5×√5)R27°PdO(101)-Pd(100) surface oxide have been calculated. The p(2×2), c(2×2), (3√2×√2) R45°,
(1×1) structures are the expected structures for coverage of O on Pd(100) at 0.25 monolayer
(ML), 0.50 ML, 0.67 ML and 1.00 ML, respectively. The binding energies were calculated by eq. (5)
with respect to the O2 gas phase molecule. Previous studies115, 52
indicated the adsorption of oxygen on
the fourfold hollow site as most stable one and based on these results, only O adsorption at the fourfold
hollow site of Pd(100) was considered in this work. All adsorption energies calculated by above methods
are shown in Table 3.1 and the corresponding structures are shown in Figure 3.1. The calculated
adsorption energies for the p(2×2) and c(2×2) structure agree with the data from previous
calculations.72 Itis obvious that the adsorption energy decreases as the O coverage increases from 0.25
ML to 1.00 ML. This decrease is associated with repulsive interactions between adsorbed O atoms108
. A
closer look at the side view in Figure 3.1 shows that the Pd(100) surface structure with 1.00 ML
adsorbed O restructures in response to the adsorbate. The palladium atoms have been pulled out from
the (100) surface by the surrounding oxygen, which is indicative of the formation of a surface oxide. In
fact experimentally, coverages of O above 0.5 ML are not found to be stable as Low Energy Electron
Diffraction and Scanning Tunneling Microscopy experiments indeed indicate the formation of surface
oxidesstartingatan O coverage of ~ 0.5 ML.115,106
Coverage Θ Ebind
(eV)

7. Pure O structures
p(2×2)-Ohol
0.25 -1.26
c(2×2)-Ohol
0.50 -1.06
(1×1)- Ohol 1.00 -0.88
Pure H structures
p(2×2)-Hbr
0.25 -0.34
p(2×2)-Hhol
0.25 -0.41
c(2×2)-Hhol
0.50 -0.47
(3√2×√2) R45°- Hhol
0.67 -0.45
(1×1)- Hhol 1.00 -0.45
MixedO/Hstructures
(2×2)-Ohol
-Hhol
0.50 -1.73
Table 1.1: Adsorption energies (per atom) of O/H atom on Pd(100). For the mixed adsorption structure,
energies are given by one surface.

8. Figure 1.1: View of different O adsorption on Pd(100) structure; (a) top view of p(2×2), representing 0.25
ML coverage; (b)top view of c(2×2),representing 0.50 ML coverage; (c) top view of (1×1), representing
1.00 ML coverage; (d) side view of p(2×2) ; (e)side view of c(2×2); (f) side view of (1×1). Red (dark
gray) spheres indicate the oxygen atoms while blue (light gray)spheres are the palladium atoms.
For H adsorbed at Pd(100), we first compared the stability of H on atop sites, bridge sites and hollow
sites within a p(2×2) arrangement. The obtained energetic preference for the four–fold hollow site
agrees with Hennig and Lober’s previous results.166
Results for higher coverage of H on Pd(100) including
c(2×2), (3√2×√2)R45° and (1×1) arrangements with H always in hollow sites were consequently
obtained. Calculated adsorption energies are listed in Table 3.1 and corresponding structures
are shown in Figure 3.2. The adsorption energy of H reaches a maximum at 0.50 ML. This is in
agreement with the experimental observation that hydrogen islands with the c(2×2) structure
are formed at the coverage near 0.5 ML indicating attractive lateral interactions are present at
this coverage.167
Figure 1.2: Top view of different H adsorption structures on Pd(100) ; (a) top view of p(2×2),
representing 0.25 ML coverage; (b)top view of c(2×2),representing 0.50 ML coverage; (c) top view of
(1×1) ; (d) top view of (3√2×√2) R45°, representing 0.67 ML coverage. White (white) spheres are
hydrogen atoms while blue (light gray) spheres are palladium atoms.
Co-adsorption of H and O on Pd(111) has been previously studied with scanning tunneling microscopy,
indicating repulsion between H and O leading to formation of O islands and H islands on the surface.149,

9. 150, 151, 152, 153
However, Pd(100) has seen considerably less study. Co-adsorption of ordered H and O on
the Pd(100) surface has been calculated in our work. Adsorption energies of H and O co-adsorption are
lower than sum of the adsorption energies of the respective pure ad-layers of O and H except in the case
of 0.25 ML of H and 0.25 ML O co-adsorption. In this case, the adsorption energy is slightly higher due to
the low density of adsorbates on the surface. However, with increasing coverage, the surface becomes
more crowded and repulsive lateral interactions lead to decreasing adsorption energies, which shows H
and O have similar behavior on Pd(100) as on Pd(111) though Pd(100) is more open. Previous work by
Nyberg and Tengstal indicates that O and H will form an ordered structure when co-adsorbed at low T
and annealedto275 K withp(2×2) symmetry.147
Once the O coverage has reached 0.5 ML, a surface oxide will be the thermodynamically favored phase.
The oxide thin film model structure (√5×√5)R27°PdO(101)-Pd(100) has multiple high-symmetry sites, top,
bridge and hollow as discussed in Reuter et al. (all sites are shown in Figure 3.4).30
Adsorption of O on
the monolayer oxide film has previously been addressed. It has been determined that adsorption on the
bridge sites on the √5 surface has been found to be -0.04 eV at 0.20 ML O coverage. At higher coverage
(0.40 ML O coverage) where O is adsorbed on both bridge sites of the unit cell at the same time, O
adsorptionisthermodynamicallyunfavorable.
Ohol
-Hhol
2Ohol
-Hhol
Ohol
-2Hhol
2Ohol
-2Hhol

10. Figure 1.3: Top view of considered coadsorbed overlayer structures of O and H on Pd(100). White
(white) spheres are hydrogen atoms, red (dark gray) spheres are oxygen atoms and blue (light gray)
spheres are palladium atoms.
Figure 1.4: Top view of high-symmetry adsorption sites on the (√5×√5)R27°PdO(101)-Pd(100) surface
oxide structure. Red (dark gray) spheres are oxygen atoms while blue (light gray) spheres are palladium
atoms.
Although hydrogen and oxygen adsorption has been well studied on Pd metal surfaces, only UHV
studies have examined co-adsorption on the oxide. Hakanoglu et al. observed H2 adsorption and
dissociation (via water formation) on their four-layer of PdO(101) thin film model grown above
Pd(111).135
However, in this case, the oxide film is multi-layer as opposed to the single layer oxide thin
film. Previous X-ray diffraction results indicate that monolayer of PdO is stable under 600 K and 1 atm O2
over one hour but that the bulk oxide will not form under these conditions.28
Using DFT calculations,
Blanco-Rey et al. found that H2 is unable to adsorb on to the monolayer oxide surface because of the
repulsive electrostatic force on H2 caused by charge accumulation.48
However, dissociative adsorption of
H2 whereby H atoms bond atop to O in the PdO film to form hydroxyl groups is favored. Results from our
calculation confirmed that no molecular adsorption of H2 on the monolayer oxide model can occur while
the molecular adsorption of H2 on the four-layer model is possible.151
In a similar fashion, the adsorption
of H atoms has been examined on all sites. H adsorption on the bridge sites is possible though it is also

11. very weakly bound (binding energies in two bridge sites are -0.05 eV and -0.02 eV referenced to gas
phase H2). H adsorption is unstable on any of the atop sites or hollow sites and when performing
geometry optimizations starting in configurations with adsorption on those sites, upon relaxation the
adsorbed H atom always moves to the respective neighboring bridge site. As in the case of O, the
adsorption of two H on neighboring bridge sites on the √5 surface is thermodynamically unfavorable.
From kinetic studies of CO oxidation, it is known that reduction of the oxide surface may result in
removal of a fraction of the oxygen atoms and surface restructuring.86
As shown above, H adsorption on
the pristine metal Pd(100) surface is stronger than on any site of PdO(101). Based on the idea of
“reducing” the surface oxide, the upper oxygen atoms were removed and H atom adsorption was
examined at the hollow sites left by O. Results show that H atoms are more stable on this hollow site (-
0.38 eV) than on the bridge site (-0.05 eV/-0.02 eV). However, the adsorption energy of H to the hollow
site is much weaker than for O (-1.81 eV) to the same site, whichimplies O will preferentially occupy the
hollowsiteswhenthe twoadsorbatescompete forthissite.
Comparing aforementioned structures by applying Equation (4) at various partial pressures of H2 and
O2, a phase diagram under different thermodynamic condition (T, pO2, pH2) has been constructed to
reflect the stable region of a particular surface termination and the diagram is shown in Figure 3.5. The
phase diagram as presented can be translated from chemical potential to T, P by setting the
temperature constant and viewing the changes in chemical potential as changes in the partial pressures
of the gas species. As indicated in Figure 3.5, if the temperature is assumed to be 600 K then the partial
pressure of H2 can be varied from ultra-high vacuum conditions to pressures well exceeding normal
reaction conditions along the y-axis. Similarly, following the x-axis across from the left to the right, one
can follow the increase in oxygen pressure. Starting in the lower left corner at low partial pressure for
both species, and moving from the left to right, one can examine the change from pristine Pd (100) to,
p(2×2)-O/Pd(100) and ultimately to(√5×√5)R27°PdO(101)-Pd(100) as the O2 pressure is increased. The

12. disappearance of c(2×2) from the phase diagram indicates this is a metastable surface produced
by the exposure kinetics according to Scheffler and co-workers.72Alternatively, when
maintaining an extremely low chemical potential (partial pressure) of O2 and increasing the H2
pressure (chemical potential), the surface will change from pristine Pd(100) to c(2×2)-H/Pd(100),
then to (1×1)-H/Pd(100).
Figure 1.5: Phase diagram for Pd (100) system in contact with gas reservoirs of H2 and O2 at T = 600 K
assumingconsideringco-adsorptionof Hand O only.

13. In addition to these stable phases involving one of the adsorbates, there are also stable
phases that involve both oxygen and hydrogen. Without considering formation of OH on the
surface, co-adsorbed hydrogen and oxygen on Pd(100) at 0.25 ML coverage appears on the
phase diagram. Co-adsorbed O and H is only stabilized in a narrow area then disappears as
increasing O coverage results in the formation of the surface oxide. Phases involving H
adsorbed oxide surfaces are possible when the partial pressures of H2 and O2 both extremely
high (107 atm). For the primary conditions of interest however, around 1 atm for both H2 and O2,
for example, the phase diagram indicates the surface oxide will be present (but without any
adsorbed H). This result gives yet another example of the stability of thin oxide films even
under a significant reductant partial pressure.
In addition to the stable surfaces, one must consider the formation of bulk phases (oxides,
hydrides). For example, in extreme oxidizing conditions, bulk PdO would form. In our case, PdO
will form when
oEbulk
PdEbulk
PdO
 , (1.6)
which defines the transition from the Pd to PdO at increasing oxygen pressure indicated by the vertical
line at ∆μO = - 0.96 eV. Similarly, this bulk oxide will decompose due to reduction by H2 once the
followingconditionismet
 OHEbulk
PdHEbulk
PdO 22
 (1.7)

14. and 
2
H is sufficiently high. Since and and under the
assumption of no reaction between H2 and O2 in gas phase for this so called “constrained equilibrium”
approach,expression(3.6) and(3.7) can be writtenrespectivelyinEquation(3.8) and(3.9)
total
O
EEbulk
PdEbulk
PdOo
2
 (1.8)
bind
O
Ebind
H
Ebind
OH
Etotal
O
EEbulk
PdEbulk
PdOH
22
1
222
 (1.9)
Conversely, in extreme reducing conditions, bulk PdH would form. There are two palladium
hydride phases: α and β168. In our calculation, only β palladium hydride has been considered.
The structure of β palladium hydride adopted herein is PdH. PdH will form when
 HEbulk
PdEbulk
PdH
 . (1.10)
Equation (3.10) defines the transition from the Pd to PdH at increasing hydrogen pressure indicated by
the vertical line at ∆μH = - 0.14 eV. Similarly, this bulk hydride will decompose due to oxidation by O2
once the followingconditionismet
 5.0
2
5.0 OHEbulk
PdOEbulk
PdH
 (1.11)
Etotal
O2
  Etotal
HHH 2
 

15. As discussed,Etotal
O
2
, Etotal
H
2
,Ebind
O
2
, Ebind
H
2
are obtained by DFT calculation of the molecules in
vacuum. Previous work shows that palladium hydride can be formed at very low H2 partial pressure and
the start forming pressure is increasing with the ratio of H and temperature.168-170
Formation of β PdHx
starts at around P(H2) = 0.01 atm at 300 K according to the phase-diagram obtained by Lewis while
Schogl found β PdHxformed at 1 mbar at 320 K.168,171
Obviously H/Pd ratio x and temperature affect the
formation pressure dramatically. Our result indicates formation of bulk PdH starts at P(H2) = 102.2
atm at
300 K while at 600 K, required pressure of H2 is about 104.8
atm. Over-binding of H2 as calculated by GGA
functionals leads to PdHX formation pressures that are much higher compared to experimental data,
which also observed in a ReaxFF investigation of hydride formation in Pd nanoclusters from Senftle and
co-workers.172
Overall, the basic shape of the H2-O2 phase diagram of Pd(100) is very close to the CO-O2
phase diagram.72 The partial pressure of H2 required to decompose the bulk oxide at 600 K and
PO2 = 1 atm is only 0.0001 atm indicating that H2 is strong reductant like CO which requires an
even lower partial pressure of about 10-7 atm to decompose the bulk oxide under the same
conditions. This is in sharp contrast to NO which required a pressure of 1010 atm at 600 K and 1
atm O2 to decompose bulk PdO. However, compared to CO or NO adsorption, H adsorption on both
Pd(100) and the PdO surface is very weak and therefore the portion of the phase diagram that involves
adsorptionof the reducinggasis small.
In either CO oxidation or NO oxidation, there is no intermediate produced, but for H2 oxidation, the
intermediate OH was observed as a stable species on the Pd (100) surface147
by EELS under 215 K. DFT
calculation results show the binding energy of OH to surface is up to 1.98 eV. Therefore in our work, we
also examined surface structures with OH to determine how the phase diagram would change. Table 3.2

16. shows the calculated adsorption energies of OH with different coverage on the surface and detailed
structures are shown in Figure 3.6 at various OH coverage, 0.25 ML, 0.50 ML, and 1.00 ML. Obviously
repulsive interactions between OH groups become stronger as the coverage increases, which is
indicated by the decreasing binding energies for increasing coverage. For H adsorption on the surface
oxide, there are additional sites, atop the four O atoms on the surface, which are not available for CO.
Results show that the oxide thin film structure is stable when the H binds to the higher O atom, which is
not true when H binds to the lower O atom. The binding energy is~0.5 eV for both cases. As shown in
Figure 3.7, inclusion of OH terminated structures, dramatically changes the phase diagram in the region
of medium to high chemical potentials of both O2 and H2,where the formation of OH becomes available.
In either the low O2 pressure area or low H2 pressure zone, the phase diagram is essentially unchanged
since either the low chemical potential of H2 or O2 makes the formation of OH unlikely. However, the
predominant surface in the primary region of interest is no longer the bare surface oxide but one which
is covered by OH groups at the bridge sites. The formation of OH on Pd(100) has been previously studied
by Nyberg and Tengstal.155
They found that no reaction occurs between O and H below 275 K under
ultrahigh vacuum conditions. At 300 K O and H will react, but did not form stable OH groups on the
surface, and instead formed H2O directly which then desorbs. In contrast, the reaction of O and H2O on
the Pd(100) surface at 110 K formed OH which was then stable up to 300 K. This result indicates that OH
formation from O and H on Pd(100) is kinetically limited. While our diagram shows a vast region
dominated by OH groups, there are kinetic limitations which may prevent its observation under reaction
conditions. OH groups have been observed previously on the surface of Pd nanoparticles under CH4
oxidationconditionsbyCiuparu etal..173
Coverage Θ Ebind
(eV)

17. Pure OH structures
p(2×2)-OHhol
0.25 -1.98
c(2×2)-OHhol
0.50 -1.79
(1×1)- OHhol 1.00 -1.20
Pure H2O structures
p(2×2)- H2Ohol
0.25 -0.18
c(2×2)- H2Ohol
0.50 -0.24
Table 1.2: Adsorption energies (per OH group) of OH atom on Pd(100) and adsorption energies of H2O
on Pd(100).
Ebind
(eV) Ebind
(eV)
Hbr
-0.05(-0.03) Obr
-0.04(-0.01)
OHbr
-1.86
H2Obr
-0.13 2OHbr
-3.08
Table 1.3: Calculated binding energies of different species (H, O, OH) at bridge sites on the √5 surface.
Figure 1.6 Top view of different OH adsorption on Pd(100) structure; (a) top view of p(2×2), representing
0.25 ML coverage; (b)top view of c(2×2),representing 0.50 ML coverage; (c) top view of (1×1),
representing 1.00 ML coverage. White (white) spheres are hydrogen atoms while blue (light gray) spheres
are palladium atoms and Red (dark gray) spheres are oxygen atom.

18. Figure 1.7: Phase diagram for Pd (100) system at T = 600 K considering the possible formation of OH
intermediates.
In the cases for CO oxidation and NO oxidation, the formed product on the surface, either CO2 or NO2
has been assumed to be readily transported away.72, 27
Water adsorption may be stabilized on metal
surfaces154, 174
and on oxide surfaces like PdO(101)146
as well. Therefore structures with molecular water
have also been considered in our work. Formation of a hydrogen bond between the surface and the
water molecule makes the higher coverage on Pd(100) favored when the coverage of H2O goes from
0.25 ML to 0.50 ML, the binding energy changes from -0.18 to -0.24 eV per water molecule. According to
Nyberg and Tengstal, an intermolecular hydrogen bond forms with increasing coverage of H2O and an
ice-like two-dimentional adsorption layer may form on Pd(100).147
The binding energy of H2O in the
bridge site on the √5 surface is -0.13 eV. Calculation of various coverages of OH/H2O done by Weaver et
al. indicated a combination of HO-H2O at a coverage of 0.5 ML is most stable for the four layer PdO(101)
surface.116
Most of the phase-diagram is dominated by H2O termination, if one does not consider its
desorption. However, under typical reaction conditions (600 K, 1 bar), the free energy gain through

19. removal of H2O from the surface to the gas phase would outweigh the adsorption energy by 1.10 eV at
600 K and 1 atm. Note that the approach presented here is a constrained thermodynamic approach as it
does not connect the H2 and O2 reservoirs in the gas phase with a corresponding H2O reservoir.
Obviously given the highly exothermic formation of water from H2 and O2, relaxing that constraint would
leadto a trivial result.
1.4 Conclusions
Density functional theory calculations linked to thermodynamic methods have been applied to explore
the stability of different surface structures under various thermodynamic conditions (T, PO2, PH2). A
complete surface phase diagram has been constructed. H2 is a strong reductant, like CO, and therefore
the bulk oxide formation region is small compared to NO oxidation. In contrast to NO and CO oxidation,
the phase diagram of H2 oxidation is dominated by surfaces involving the presence of a surface
intermediate, OH. Under typical reaction conditions, the favored surface termination will be a
hydroxylated monolayer oxide film. This result seems to be in agreement with previous experimental
resultsof Pdmethane oxidationcatalysts.