The document provides background information on first-principles kinetic Monte Carlo simulations of NO oxidation on Pd(100) and PdO(101) surfaces. It discusses that Pd has shown better performance than Pt for NO oxidation in NOx storage reduction catalysts, but Pd may form an oxide under reaction conditions. Previous studies have suggested a thin film surface oxide, (√5×√5)R27°PdO(101), as an appropriate model. The document outlines the theory and computational setup for the first-principles kinetic Monte Carlo simulations, including the rate constants calculated using DFT for adsorption, desorption, diffusion, and reaction processes. Lattice models of Pd(100) and the P

1. 1 FIRST-PRINCIPLES KINETIC MONTE CARLO STUDY OF NO OXIDATION ON
Pd(100) AND PdO(101)(√5×√5)R27°-Pd(100)
1.1 Introduction
The development of diesel and lean-burn gasoline engines has been spurred by increasingly
stringent requirements for fuel economy since increased fuel efficiency can be achieved by combusting
hydrocarbons at high air/fuel ratios89,90
. However, toxic NOx exhaust gases dramatically increase as the
air/fuel ratio increases (>14.7:1), and these pollutants cannot be completely removed with conventional
three-way catalysts under oxygen-rich conditions. One of the strategies of handling the higher NOx
levels in lean burn automotive emissions is a NOx storage reduction (NSR) system91,92
. Noble metals like
platinum and palladium have been used as the active metal components in NSR catalysts due to their
performance at low temperature, and their thermal stability55-58
. Although Pd has been shown to
demonstrate even better performance at low temperature than Pt56
, Pd, unlike Pt, may form an oxide
under NO oxidation conditions93
. Ribeiro et al. suggested that formation of oxides on small Pt particles
was detrimental to their activity and resulted in poor performance.23
However, in their DFT based micro
kinetic modeling examination of Pt, Ir, Os and their oxides, Hu et al. reported that metal oxides may
exhibit comparable activity to metal surfaces for NO oxidation and, in fact, IrO2 out performs Ir26
.
Previously in the DFT based ab initio thermodynamics examination of Pd over a range of O2 and NO
partial pressures, Jelic and Meyer found that bulk PdO is thermodynamically stable under the typical NO
oxidation mode of a NSR catalyst (600 K, 1 atm O2, 0.001 atm NO).27
However, grazing incidence X-ray
diffraction results from Lungren et al. indicated that no bulk oxide was observed to form under 1 atm of
O2 (without the presence of NO) and 600 K after one hour due to kinetic limitations.28
From these
observations, it was suggested that a thin film surface oxide (√5×√5)R27°PdO(101) is an appropriate

2. model for the catalytic surface for NO oxidation in the NSR cycle.29, 30
We have used this model in DFT
based kinetic Monte Carlo simulations and found that, as in Hu et al.’s examination of the bulk oxide
terminations, the turnover frequency of the PdO(101)/Pd(100) surface oxide is on par with metal
surfaces.26, 29
The role of the surface oxide in NSR catalysis is of further interest due to the transient
nature of the process. When the surface cycles between the oxidizing regime and the reducing regime,
the surface oxide must be created and destroyed. Modeling this process explicitly is difficult given the
time scales involved. However, we can gain insight into this process by using a first principles kinetic
Monte Carlo technique. The role of surface oxides in CO oxidation has been previously debated by
Frenken et al., and Goodman et al.32-35
.While Frenken’s work with in situ STM and SXRD reactor of Pd
single crystals showed significant roughening with a concomitant increase in activity, the PM-IRAS and
reactivity data from work of Goodman suggest that the active phase is metallic. More recently
Rupprechter and co-workers examined CO oxidation on Pd, PdOx<1 and PdO nanoparticles on alumina
support and concluded that oxygen covered metallic palladium contributes the highest catalytic activity
based on the experimental results that Pd and PdOx<1 have almost equally high catalytic activity while
PdOx<1 can be reduced completely to Pd even under low partial pressure of CO36
. In a prior study of CO
oxidation, it was found that CO oxidation led to the formation of a region of meta-stability in which the
phase transformation (either from the surface oxide to the metal or from the metal to the surface oxide)
that is predicted thermodynamically is hindered kinetically.94
This result suggests that the answer to the
debate over the nature of the active surface is a combination of both surfaces rather than a single
surface. Now we will move this examination to determine how NO oxidation differs from CO oxidation
given that CO is a much stronger reductant than NO. We will also seek to determine if the nature of the
surface can be identifiedinNSRcatalysisanddetermine if orhow meta-stabilityplaysarole.

3. 1.2 Theory
1.2.1 First-principles kinetic Monte Carlo simulations
A first-principles kinetic Monte Carlo method is used herein to examine the surface stability under
reaction conditions by analyzing the steady-state coverage of NO and O in micro-kinetic models as a
function of thermodynamic conditions (T, PNO, PO2, PNO2). However, unlike mean field micro-kinetic
models, the spatial distribution of the surface species is explicitly determined and accounted for.
Furthermore, kinetic Monte Carlo simulations allow one to follow the time evolution of the catalytic
surface by coarse graining rare-event dynamics80, 95-97
. It has been previously used successfully to
improve understanding of the activity and stability of specific structures under particular
thermodynamicconditions84, 86, 94
.
Without accounting for the short-time dynamics of the system in between states, one kinetic Monte
Carlo step corresponds to the execution of a single rare event and each state is independent as the
system retains no knowledge of the preceding step. A complete list of relevant elementary processes
with their corresponding rate constants, kp,is required to create for a kMC model where kp characterizes
the probability of transition from the current state by the process p. The mathematic algorithm is
detailed in a review by Reuter80
and will be briefly described here. First a total rate constant, ktot, is
calculated by summing all possible rate constants for individual processes kp for a given initial
configuration:ktot = ∑pkp.The executedprocessisthenchosenbythe followinginequality:
p
q
ptotp
q
p kkk 1
111

   ，(1.1)
where ρ is a random number between 0 (not including 0) and 1. The configuration is updated by
executingthe chosenprocess iandtime evolutioncanbe obtainedby

4. t→t – ln(ρ2)/ ktot ， (1.2)
herein, ρ2∈(0,1] isasecondrandomnumber98
.
The above mentioned rate constants are essential to a meaningful kinetic Monte Carlo simulation
and they can be obtained from DFT based transition-state theory (TST) calculations. Based on our
models for NO oxidation over Pd(100) and (√5×√5)R27°PdO(101) four different types of elemental
processhave beenincluded:adsorption,desorption,diffusion,andreaction.
1.2.2 Rate Constants
1.2.2.1 Adsorption
The rate constant of adsorption ),(, i
ads
sti pTk of species i with partial pressure ip on a surface site of
type stis a function of the impingement rate and the local sticking coefficient stiS ,
~
as shown in equation
(2.3):
Tkm
Ap
TSpTk
Bi
i
stii
ads
sti
2
)(
~
),( ,,  . (1.3)
Herein A is the surface area of the unit cell; im is the mass of species i; Bk is the Boltzmann constant,
and T is the temperature of the system. The sticking coefficient gives a statistical average fraction of
the impinging particles that stick to a given free site of the specified site st at temperatureT as
describedinfollowingequation:
)exp()(
~ ,,,
,,
Tk
E
A
A
fTS
B
jstiistads
stisti

 .(1.4)

5. In equation (2.4), istA , is the active area such that the ratio of Ast,i/A represents a geometric factor of the
fractional surface area which is available for the molecules for adsorption when impinging on the
surface and jstiE ,, is the adsorption barrier (if any) along the minimum energy pathway (MEP).
ads
stif , is
an efficiency factor which describes the fraction of impinging gas phase molecules that travel along the
MEP as opposed to those which do not and therefore experience a higher barrier. Herein, as in previous
work,it issimplifiedto1 since mostof the moleculesdofollow the MEP84, 86, 87, 94
.
1.2.2.2 Desorption
The desorption process is the time-reversed process of adsorption, therefore the desorption rate
constantis relative tothe adsorptionrate constantbyequation(2.5):
)
),(
exp(),(),( ,
,,
Tk
pTG
pTkpTk
B
isti
i
ads
stii
des
sti

 .(1.5)
The change in the Gibbs free energy, ),(, isti pTG can be approximated by the difference between the
chemical potential of the species i in the gas phase and the binding energy of species i in the adsorbed
state:
bind
istiigasisti EpTpTG ,,, ),(),(   .
1.2.2.3 Diffusion
Once adsorbed on the surface, species i can diffuse to other surface sites with a barrier
obtained by transition state theory identifying the saddle point along the diffusion pathway. The
diffusion rate constant for species i from site st to site st’ can be written as
)exp())(()(
'
''
,,
,,
Tk
E
h
Tk
TfTk
B
diff
ststiBTSTdiff
ststi
diff
ststi



 .(1.6)

6. In equation (2.6), TSTdiff
ststi
f ,
, '

is the ratio of the vibrational partition functions in the transition state and
that in the initial state, which is generally smaller than but very close to 1. Considering the error from
DFT, using 1 instead of the real value of TSTdiff
ststi
f ,
, '

is an acceptable approximation. Therefore in our work,
the diffusionrate constantissimplifiedas:
)exp()()(
'
'
,
,
Tk
E
h
Tk
Tk
B
diff
ststiBdiff
ststi



 .(1.7)
1.2.2.4 Reaction
Finally, species on the surface can react with each other. The barrier for reaction can be determined
by using transition state theory if a suitable reaction coordinate can be identified that contains a saddle
point.The rate constantcan be calculatedas writteninequation(2.8):
)exp())(()( ,
Tk
E
h
Tk
TfTk
B
reac
fiBTSTreac
fi
reac
fi



 .(1.8)
In equation (2.8),
reac
fiE is the reaction process barrier, the energy difference in the transition and
initial state and
TSTreac
fif ,
 is ratio of the partition functions in the transition and initial states. Again, in
our work we artificially assign
TSTreac
fif ,
 equal to 1. Of course both forward and reverse reaction rates
mustbe considered.
1.2.2.5 Computational setup
The Vienna Ab Initio Simulation Package (VASP) utilizing a plane wave basis set with a
cutoff energy of 500 eV has been employed to perform the DFT calculations99, 100.The projector-
augmented wave (PAW)101 pseudopotentials were adopted in this work and all calculations have

7. been done using the Perdew-Burke-Ernzerhof (PBE)102 exchange-correlation functional. The
Climbing Nudged Elastic Band (NEB) method has been used to determine the reaction paths and
barriers103. Calculation of the energies of molecules (O2, NO, NO2) was done in a 10Å cube with
a 1×1×1 k-point grid sampling.
For Pd(100), pure palladium metal surface models used in this work are inversion-symmetric slabs consisting of five Pd(100) layers with
potential adsorbates (NO, O etc) on both sides, withthe middle layer fixed. A uniform 7×7×1 k-point grid is employed for the
Brillouin zone104 with a (2×2) unit cell.
The surface oxide will use the previous employed model of Todorova et al a
(√5×√5)R27°PdO(101) structure above Pd(100). 30
A 1×1 unit cell of the √5 surface is used with a 5 layers
Pd(100) slab beneath a single oxide layer. All atoms are set to relax except the very three center layers
of palladium metal. The slabs are separated by approximately five layers of vacuum. A uniform 7×7×1 k-
point grid is used for the Brillouin zone. Lattice constants are consistent with the experimental values.
Geometriesare consideredtobe optimizedonce aforce lessthan0.02eV/Å is achieved.
1.2.3 Kinetic Monte Carlo model
Appropriate lattice models are required to perform kinetic Monte Carlo simulations. Herein a
(1x1) Pd(100) surface shown in Figure 2.1 is adopted as a model for the clean metal surface
while a monolayer of PdO(101) above the Pd(100) surface (known as the √5 structure shown in
Figure 2.2) is applied as the model of ultra-thin surfaceoxide30.
1.2.3.1 Pd(100)
Considering strong lateral interactions between surface species105 and the morphology
transformation caused by high coverages of O (≥0.5 monolayer (ML)106, the coverage has been
limited to a range of 0-0.5 ML. Previous experimental107 and theoretical108 studies both indicate

8. that O preferably adsorbs on the fourfold hollow sites at Pd(100) for O coverages of 0-0.5 ML.
However, for NO, the evolution of coverage is more complicated. Core level photoemission and
LEED data from Jaworowsk and co-workers109 shown that NO prefers fourfold hollow site at
coverage up to 0.25-0.30 ML, while NO only occupies bridge sites when the NO coverage rises
to 0.5 ML. Based on above observations, in our kMC model for Pd(100) O is fixed to exclusively
adsorb on fourfold hollow sites while NO can adsorb on either hollow sites or bridge sites.
Nearest-neighbor positions have been blocked for oxygen adsorption and diffusion processes
since the lateral interactions between nearest-neighbor sites are very strong (up to 1.0
eV)according to Zhang and coworkers108. Occupation of second-nearest-neighbor sites is
allowed despite the fact that moderately repulsive interaction exists108. Therefore O2 dissociative
adsorption requires an ensemble of eight empty sites known as the 8-site rule110-113. The nearest-
neighbor sites are also blocked for NO adsorption and diffusion due to lateral interactions.
For NO oxidation on Pd(100), there are 18 possible processes including adsorption,
desorption, diffusion, and reaction events included in the model. The data for the event list are
given in Table 2.1.
Figure 1.1: Top view of the Pd(100) surface. The white square area is for one unit cell of 1×1 Pd(100)
surface.

9. add
holholOE  ,2 = 0.00
add
holNOE , = 0.00
add
brNOE , = 0.00
add
brNOE ,2 = 0.00
des
holholOE  ,2
= -2.51
des
holNOE , = -2.08
des
brNOE , = -2.08
des
holNOE ,2
 = -1.42
diff
holholOE  , = 0.28
diff
holholNOE  , = 0.28
diff
brbrNOE  , = 0.56
diff
holbrNOE  , = 0.09
diff
brholNOE  , = 0.10
diff
holholNOE  ,2
=0.37
reac
OholNOholE  = 0.75
reac
OholNObrE  = 0.81
diss
OholNOholNOE  2
= 0.42
diss
OholNObrNOE  2
= 0.62
Table 1.1: Summary of DFT binding energies, diffusion and reaction barriers on Pd(100). All values are
in eV.
1.2.3.2 √5 surface oxide
The monolayer surface oxide structure (√5×√5)R27°PdO(101)-Pd(100), described in detail
by Todorova and coworkers23 has been previously adopted as a model for an ultra-thin surface
oxide30, 72, 86, 87. Previously, the unit cell of the √5 surface oxide in the kMC model has been
constructed to be half the size of the true unit cell of the √5 oxide film to simplify the structure.
Since differences in the adsorption energies of species on the two different “upper” (hollow) sites
are often smaller than 0.05 eV, these two sites herein can be considered as equivalent. Similarly,
the difference in adsorption energies of O or NO on the two different bridge sites are less than
0.1 eV and therefore the two bridge sites are also considered as equivalent. The surface structure
is shown in Figure 2.2.
For the kMC model of√5 surface oxide, the available adsorption sites for oxygen and NO are
Pd atop sites, bridge, and hollow sites (which are produced by removing the top O from the
surface). However, the binding energies of NO on Pd atop sites (0.9 eV and 0.5 eV respectively

10. for atop 2f site and atop 4f site (site designations are shown in Figure 2.2)) are much lower than
that on bridge sites (1.55 eV) and hollow sites (2.31 eV). Such a small NO adsorption energy on
the Pd atop site implies that NO would diffuse to the bridge or hollow site before any reaction
can occur at the atop sites at steady state. O atoms are extremely stable on the hollow site with a
-1.97 eV binding energy, which seems logical since it will make the surface stoichiometrically
complete. Comparing to the binding energy of O on to the surface at hollow and bridge sites, O
on atop sites (0.4 eV and 0.2 eV respectively for atop 2f site and atop 4f site) are very weak,
which leads to the need to consider only O on the bridge and hollow sites being considered in our
model.
The coverage of the higher position oxygen is an indicator of the stability of the monolayer
of surface oxide and the simulation specifically allows for their occupancy to change. However,
we do not explicitly calculate the reconstruction of the PdO(101) surface. Therefore in this kMC
model, positions of all Pd atoms and lower position oxygen atoms are fixed. When the
simulation is initialized, the upper oxygen atoms are removed and oxygen atoms, NO and NO2
molecules as well as empty sites are randomly assigned to these locations to give a starting
configuration for the system.
In this NO oxidation model, there are 38 possible elementary processes including adsorption,
desorption, diffusion, and reaction events. The values for each elementary processes were
calculated by the same method introduced in Rogal et al.’s work87. For NO oxidation, there are
seven adsorption processes in total: non-dissociative adsorption of NO on the bridge sites and
hollow sites, non-dissociative adsorption of NO2 on the bridge sites and hollow sites and
dissociative adsorption of O2 to hollow-hollow sites, hollow-bridge sites and bridge-bridge sites.
From the adsorption data shown in Table 2.2, it is obvious that only O2 dissociative adsorption

11. onto bridge-bridge sites has a barrier. Desorption from the surface was also calculated using the
adsorption energies shown in Table 2.3. From the data, we can easily conclude that all species
prefer adsorbing on hollow sites created by removing the higher position oxygen. Diffusion of
species on the surface can take place between bridge and bridge sites, bridge and hollow sites,
and hollow and hollow sites as shown in Table 2.4. Table 2.5 lists the four pathways of NO2
formation that have been calculated in our work, with varying locations for NO and O:
holhol ONO  , brhol ONO  , holbr ONO  , brbr ONO  . Each NO2 formation reaction has a corresponding
reverse reaction of NO2 dissociation into NO + O, also shown in Table 2.5.
Figure 1.2: (a) Top view of the PdO(101)/Pd(100) surface oxide structure; (b) Side view of the
PdO(101)/Pd(100) surface oxide structure. The oxygens with black circles are the higher position
oxygens, which can be removed during the kMC simulation leaving a hollow site. The white square area
represents one unit cell of the √5 surface oxide, which is split by the dashed line in the middle.
add
holholOE  ,2 = 0.00
add
brholOE  ,2 = 0.00
add
brbrOE  ,2 =1.90
add
holNOE , = 0.00
add
brNOE , = 0.00
add
holNOE ,2 = 0.00
add
brNOE ,2 = 0.00
Table 1.2: Adsorption barriers of NO, O2 and NO2 on the √5 surface oxide.

12. des
holholOE  ,2 = -3.94
des
brholOE  ,2 = -2.66
des
brbrOE  ,2 = -1.38
des
holNOE , = -2.31
des
brNOE , = -1.55
des
holNOE ,2 = -1.27
des
brNOE ,2 = -1.15
Table 1.3: Desorption energies of NO, O2 and NO2 on the √5 surface oxide
diff
brbrOE  , = 1.17
diff
holbrOE  , = 0.41
diff
brholOE  , = 1.69
diff
holholOE  , = 1.92
diff
brbrNOE  , = 0.44
diff
holbrNOE  , = 0.51
diff
brholNOE  , = 1.27
diff
holholNOE  , = 1.16
diff
brbrNOE  ,2
= 0.80
diff
holbrNOE  ,2
= 0.40
diff
brholNOE  ,2
= 0.52
diff
brbrNOE  ,2
= 0.90
Table 1.4 Diffusion barriers of NO, O2 and NO2 on the √5 surface oxide
reac
holNOOholNObrE 2 = 1.08 reac
brNOObrNObrE 2 = 1.31 reac
holNOOholNOholE 2 =1.75 reac
brNOObrNOholE 2 = 0.54
diss
OholNObrholNOE  2
= 0.6 diss
OholNOholholNOE  2
= 0.48 diss
ObrNObrbrNOE  2
= 2.06 diss
ObrNOholbrNOE  2
= 1.03
Table 1.5 Reaction barriers of NO + O → NO2 and dissociation barriers of NO2→ NO + O on √5 surface
oxide
1.2.4 Simulation setup
The Pd(100) kinetic Monte Carlo simulations are performed through the kmos framework114
while reported results for √5 surface oxide work are obtained by our internally developed fortran
based kMC code and verified by kmos framework for √5 surface oxide. All simulations were
performed in (20×20) unit cells employing a periodic boundary condition. The grid size has been
confirmed large enough since no differences were observed in the steady state occupancies or

13. reaction rates when the cell size was increased to 40×40. The goal for this simulation is to
determine the average surface occupations sti, of species i on site st, and TOFs under steady-
state condition for a given thermodynamic condition ),,,( 22 NOONO pppT . The average surface
occupations sti, of nth step of kinetic Monte Carlo simulation in the time step of nt can be
obtained through following equation:





n n
n nnsti
sti
t
t,,
,

 .(1.9)
In Equation (2.9), nsti ,, is the coverage of species i at site st at nth
kMC step after steady state has been
reached. Different initial configurations (clean surface, O-fully-covered surface and random-filled-
surface) have beentestedandnomultiplesteady-statephenomenahave beenobserved.
1.3 Results and Discussion
The stability of two surface structures, Pd(100) and (√5×√5)R27°PdO(101)-Pd(100) surface oxide,
under reaction conditions has been evaluated by monitoring the oxygen occupancy in the kMC
simulations.
1.3.1 Pd(100)
In our Pd(100) model, dynamic formation of surface oxide from pristine metal surface
Pd(100) cannot be observed with changes in partial pressure of O2 since the surface structure has
been fixed. Instead we applied an easy to observe indicator to determine whether the surface
oxide has been formed or not. The Pd(100) surface is expected to be stable when the coverage of
O on the surface is smaller than 0.25 ML which is representative for the experimentally

14. characterized p(2×2) overlayer28, 11328, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528, 11528,
11528, 115(Zheng and Altman, 2002a, Lundgren et al., 2004), 115In other words, the pristine metal
surface Pd(100) is considered stable only when coverage of O holO, is no larger than 0.25 ML
(0.25 ML is shown as a dotted line in Figure 2.3(a)). Based on the above assumption, a map of
coverage of O has been constructed for NO partial pressures ranging from 10-7to 1 atm and O
partial pressures from 10-7to 1 atm at 600 K. The oxygen coverage varies as a function of NO
and O2 partial pressures in an intuitively expected distribution. For a fixed NO partial pressure,
when the partial pressure of O2 increases, the coverage of O on the surface gradually increases.
As Figure 2.4 (a) shown at a fixed partial pressure of O2 (P(O2) = 1.0 atm), and P(NO2) = 10-13
atm, the reaction order of NO is close to 1 when 10-5 ≤ P(NO) ≤ 0.1 atm. When P(NO) exceeds
0.1 atm, the reaction order decreases. When P(NO) is fixed at 1 atm and P(NO2) = 10-13 atm, the
reaction order of O2 is close to 1 in the O2 pressure range 0.1 ≤ P(NO) ≤ 1.0 atm as shown in
Figure 2.4 (b).
(a) (b)
Figure 1.3: (a) O coverage on Pd(100) as a function of partial pressure of NO and O2 at 600 K. The
dotted black line between pink region and red region is the starting point of decomposition of surface
holO,

15. oxide; (b) O coverage on the √5 surface oxide as a function of partial pressure of NO and O2 at
600 K and the dotted black line between pink region and red region is the starting point of formation of
surface oxide.
(a) (b)
-4 -2
0
1
2
TOF[site-1
s-1
]
log (P(NO) atm)
-1.0 -0.8 -0.6 -0.4 -0.2 0.0
0
1
2
TOF[site-1
s-1
]
log (P(O2
) atm)
Figure 1.4: (a) The NO oxidation rate on Pd(100) as a function of the partial pressure of NO with fixed
P(NO2) = 10-13
atm and P(O2) = 1.0 atm at T = 600 K; (b) The NO oxidation rate on Pd(100) as a
function of the partial pressure of O2 with fixed P(NO) = 1.0 atm and P(NO2) = 10-13
atm atT = 600 K.
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0
0.0
0.2
0.4
0.6
0.8
1.0
original DFT data
reduced reaction barriers
CoverageofO
log (P(NO) atm)
Figure 1.5: Average coverage of O on hollow sites as a function of the partial pressure of NO with fixed
P(O2) = 0.2 atm and P(NO2) = 10-13
atm at 600 K. Black squares indicate the results of simulations with
the reaction barriers obtained from DFT calculations(
reac
holNOOholNObrE 2 =1.08 eV,
reac
brNOObrNOholE 2 =0.54
eV); Red diamonds represent the results of simulations with reduced reaction barriers(
reac
holNOOholNObrE 2
=0.98 eV,
reac
brNOObrNOholE 2 =0.44 eV).
holO,

16. Figure 1.6: O coverage on the √5 surface oxide as a function of the partial pressures of NO and O2
at 600 K (a) and at 450 K (b).
(a) (b)
200 400 600 800 1000 1200 1400 1600 1800 2000 2200
0.0
0.2
0.4
0.6
0.8
1.0
coverageofO
Temperature / K
P(O2
) = 0.2 atm
P(O2
) = 0.00001 atm
-6 -4 -2 0
400
600
800
1000
log (P(O2
) atm)
Temperature/K
0.2000
0.4000
0.6000
0.8000
1.000
Figure 1.7: Average coverage of O as a function of temperature and oxygen pressure on the √5 surface
oxide model. (a)Average coverage of O as a function of temperature at P(O2) = 0.2 atm (black squares)
and P(O2) = 0.00001 atm (red diamonds); (b) Average coverage of O as function of temperature and
oxygen pressure.
holO,

17. 1.3.2 √5 surface oxide
Just as in the case of Pd(100), we cannot explicitly observe the reconstruction of the surface
oxide as the film decomposes. Instead, we use a fixed lattice and apply a decomposition criteria
to mark the transition from the oxide to the metal 27. We set the decomposition condition to
match previous studies of CO oxidation87 whereby decomposition of surface oxide occurs when
the average coverage of O in the hollow site holO, falls below 90%. Following this criteria, if
holO, ≥ 90%, the √5 surface oxide is considered as stable under the thermodynamic conditions,
but if the holO, drops below 90% then the transition to the metal surface is considered to have
occurred (0.90 ML is shown as a dotted line in Figure 2.3 (b)). The value for holO, chosen here
is not critical, the quantitative numbers for the transition pressures almost remain in the same
magnitude even when we set the 70% as the value for holO, in the O2 rich region (70% coverage
is shown in a dashed line in Figure 2.3 (b)). When we manually decrease the barriers of two most
important reactions holNOOholNObr 2
 and brNOObrNOhol 2

( holNOOholNObr 2
 is dominant because the strong preference for O to the hollow
sites29) by 0.1 eV, the surface decomposes faster but will remain stable at P(NO) = 10-3 atm
shown as Figure 2.5. From the ab initio thermodynamics based phase-diagram, the region of √5
surface oxide is found to be very small because of the ample stability of bulk PdO27. Our kMC
model focuses on the region where both Pd(100) and the √5 surface oxide could appear, which
spans from NO partial pressures of 10-7 to 1 atm and oxygen partial pressures of 10-7 to 1 atm.
Again, the oxygen coverage intuitively reflects the coverage variations with partial pressures.

18. Starting from an intact surface oxide, when the partial pressure of O2 decreases, the coverage of
O on the surface gradually decreases as well with fixed NO pressure. Simulation results show
that the region of a stable √5 surface oxide ties well with the results from thermodynamic
prediction27 and the surface oxide is stable under a typical operating condition ( T = 600 K, PNO =
0.001 atm, PO2 =1 atm) as shown in Figure 2.3 (b). In order to understand the effect of
temperature on the stability of the surface oxide, simulations at 450 K also have been performed.
Results show that across a range of reaction temperatures , a higher partial pressure of NO is
required in order to reduce the surface oxide at a higher temperature as shown in Figure 2.6,
which is consistent with previous observations of CO oxidation on the √5 surface that higher
temperature stabilized the surface oxide.87 This is likely due to the shorter lifetime of the
reductant on the surface as the temperature increases. A screening of the stability of the
palladium thin film oxide at various temperature under a pure oxygen environment P(O2) =0.2
atm indicates that the palladium thin film oxide starts decomposing at T = 1100 K while when
oxygen pressure decrease to P(O2) =0.00001 atm, the thin film oxide starts decomposing at T =
950 K as indicated in Figure 2.7(a). Weaver and coworkers found their PdO(101) thin films
which grew on Pd(111) decomposed completely at T = 923 K under UHV condition116. As
reported by Wang and coworkers, a higher oxygen partial pressure would require a higher
temperature to decompose palladium oxide as they observed the decomposition temperature of
PdO increased from 750 to 810 ⁰C as the oxygenpartial pressure increased from 5 to 20 kPa117.
This is further confirmed by our calculation results shown in Figure 2.7 (b) that higher
temperature is required in order to decompose the oxide under higher oxygen pressure. The
reaction orders of NO and O2 have been examined at various partial pressures excluding the
presence of NO2 in the gas phase (a discussion of NO2 will follow below). Previous work from

19. Weiss and Iglesia have shown that the orders for NO, O2 and NO2 are 1, 1, and -1 respectively93.
kMC simulation results (Figure 2.8 (1)) show that reaction order of NO is 1 up to P(NO) = 1000
Pa with constant P(O2) = 5000 Pa and the reaction order of O2 is 1 up to P(O2) = 1000 Pa with
constant P(NO) = 112 Pa when we applied original data from DFT calculation, which is
consistent with previous experimental result. However, the data also show that when partial
pressure of O2 exceeds 1 kPa, the reaction order gradually decreases and is zero order for P(O2) ≥
0.1 atm. This deviation from the experimental results of Weiss and Iglesia likely results from
over prediction of the adsorption energy from DFT. Using RPBE instead of PBE, for example,
has been recommended by Norskov and co-workers for a more accurate assessment of the
binding energy of oxygen on d-band transition metal surfaces (although one may argue RPBE is
guilty of under prediction of adsorption energies)118. The adsorption energy of O on hollow site
decreases to 3.67 eV when using RPBE compared to 3.84 eV using PBE. However by using this
data, deviation from experimental results still exits. To address this issue, we artificially decrease
the adsorption energy to determine, to what extent our results must be perturbed to reproduce the
1st order dependence in oxygen observed by Weiss and Iglesia. By decreasing the adsorption
energy of O on hollow site by 0.3 eV, the oxygen pressure region that indicates first order
dependence of O2 could be extended to 1 kPa and completely re-produce Iglesia and coworker’s
data93 as shown in Figure 2.8 (2).
(1)
(a) (b)

20. (2)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
0
200
400
600
800
1000
1200
TOF/s-1
site-1
O2 pressure / Pa
Figure 1.8: (1)(a) The NO oxidation rate on the √5 surface oxide as a function of the partial pressure of
NO with fixed P(NO2) = 56 Pa and P(O2) = 5000 Pa at T = 600 K; (b) The NO oxidation rate on the √5
surface oxide as a function of the partial pressure of O2 with fixed P(NO) = 112 Pa and P(NO2) = 56 Pa
atT = 600 K; (2) The NO oxidation rate dependence on O2 partial pressure on the √5 surface oxide with
fixed P(NO) = 112 Pa and P(NO2) = 56 Pa at T = 600 K using a lower adsorption energy for O (see text).
1.3.3 Combining the result from Pd(100) and the √5 surface oxide
It is obvious that at given oxygen partial pressure, a much higher NO pressure is required to
decompose a formed surface oxide than the pressure observed for which a surface oxide may
start to form. This phenomena is also observed experimentally and theoretically for CO
oxidation94, 119, 120. Pd(100) is considered stable only when coverage of O does not exceed 0.25

21. ML which corresponds to a coverage regime representative for a p(2×2) over-layer28, 115. The
dotted line between 0.2 ML and 0.3 ML coverage of O in Figure 2.3 (a) indicates a 0.25 ML
coverage of O. Hence any gas-phase conditions to the upper left of this line are expected to result
in a stable Pd(100) surface. As stated previously, the √5 surface oxide is considered to begin its
decomposition when the coverage of O is smaller than 0.9 ML. The dashed line indicating 0.9
ML O coverage is drawn in the red area of Figure 2.3 (b) and any gas-phase conditions to the
down-right of this line are expected to result in a stable surface oxide. By combing Figure 2.3 (a)
and Figure 2.3 (b), we obtain an area of bistability where both Pd(100) and the surface oxide are
predicted to be stable depending upon which surface is initially considered, as shown in Figure
2.9. This type of hysteresis phenomena has been previously observed in CO oxidation49, 51-53.
Similar observations of hysteresis in the rate have been made by Frenken and coworkers for CO
oxidation on Pd and Pt when the conditions allowed both oxide and metal surface to co-exit.88, 119,
121, 122 In the low-pressure region, atomic-scale restructuring of the catalyst surface could cause
spontaneous and self-sustained oscillations in the rate while spontaneous and periodic switching
from metal surface to oxide surface is the reason for the oscillations at atmospheric pressure
region121, 122. Compared to the previous work on CO oxidation, a larger bi-stability region exists
for NO oxidation. Despite the apparent simplicity of the reaction, NO oxidation itself still has
several intrinsic differences from CO oxidation. First NO2 can bond to surface much stronger
than CO2and it is actually endothermic to form NO2 on the surface for a typical NSR operating
condition (P(O2) = 0.2 atm, P(NO) = 0.001 atm and T = 600 K) when P(NO2) > 10-4 atm. Such
an effect has been artificially suppressed removing gas phase NO2 from the simulation27, 29. The
kMC simulations did not reveal obvious differences in the oxide surface stability up to P(NO2) =
10-3 atm. However, by setting P(NO2) to more realistic pressures, we do observe an effect of

22. NO2 on the TOF. As Figure 2.10 shows at P(NO) = 0.1 atm, the presence of NO2 lowers the TOF
on the thin film surface oxide. The decrease in the TOF can be attributed to the reverse reactions
of holNOOholNObr 2
 and brNOObrNOhol 2
 , as the barriers for dissociation of
NO2 are much lower than the barriers to form NO2. (as listed in Table 2.5). A higher P(NO2) will
lower the total TOF for NO oxidation. However, our model failed to predict the experimentally
observed reaction order for NO2 of -1 determined by Weiss and Iglesia when we search in the
pressure region of 10-7≤P(NO2) ≤ 10-3 atm with fixed P(NO) and P(O2). Our results show NO2
has a slightly negative order while previous experimental data shows a much stronger inversely
proportional relationship. The work of Weiss and Iglesia suggests that the NO2 pressure is
critical since NO2 determines the concentration of the vacancies required for O2 activation25, 93,
123. From Table 2.3 we can see that NO2 bonding strength on the surface is weaker than either of
O and NO. In the kMC model, the chance for a process to be selected depends on the rate
constant of the elementary step80 (in addition to the concentrations of surface species and their
arrangements). This implies that the NO2 desorption step has a high chance of selection if NO2 is
on the surface. Therefore for the typical simulation times that we employ, NO2 adsorbs and
desorbs many times before any dissociation reaction occurs. The reaction barriers of NO
oxidation are higher than that of CO oxidation, which indicates kinetically, it is more difficult to
reduce a surface oxide. The TOF on both surfaces at P(O2) = 0.2 atm indicates that both surfaces
are active for NO oxidation at ambient pressure as shown in Figure 2.11 and similar to CO
oxidation case. In the low P(NO) regime, the metal surface is more active than surface oxide
while in the oxygen rich region surface oxide is superior124. From our results showing a large bi-
stability region and the comparable TOFs at the relevant environmental pressures, we may
conclude that both the surface oxide and the pristine metal could be the active surface for NO

23. oxidation. However, due to the error associated with the DFT calculation, the exact region for
this bistability cannot be located. At this point there is no detailed experimental work for NO
oxidation on Pd catalysts which identifies the nature of surface during NSR process to further
support our simulation data as there is for CO oxidation32-35, 88, 119, 123, 125-129. Nevertheless, we
can conclude that the surface oxide plays an important role during NO oxidation and oscillation
between these two surfaces may be the real condition when NO oxidation is carried out over Pd
catalysts.
Figure 1.9: Surface structure map as a function of the partial pressures of O2 and NO at 600 K. The Pink
region is the possible region of bi-stability.
Pd(100)
√5 oxide surface

24. -5 -4 -3 -2 -1 0
0
20
40
60
80
100
120
TOF/s-1
site-1
log (P(O2
) atm)
P(NO2
) = 10-3
atm
P(NO2
) = 10-13
atm
Figure 1.10: NO oxidation TOF on the √5 surface oxide as a function of oxygen partial pressure at a fixed
P(NO) = 0.1 atm. Reddots indicate the TOF at P(NO2) = 10-13
atm; Black square indicate the TOF at
P(NO2) = 10-3
atm.
-5 -4 -3 -2 -1 0
12
14
16
18
20
22
log(TOF/s-1
m-2
)
log (P(NO) atm)
sqrt 5 surface oxide
Pd(100)
Figure 1.11: Comparison of the intrinsic TOFs of Pd(100) surface and the √5 oxide surface with fixed
P(O2) = 0.1 atm at T = 600 K.

25. 1.4 CONCLUSIONS
First-principles kinetic Monte Carlo simulations have been applied to examine the coverage of O on
Pd(100) and the (√5×√5)R27°PdO(101)-Pd(100) surface oxide in the steady state NO oxidation reaction.
The decomposition pressure of the surface oxide matches well with phase-diagram constructed by
thermodynamic methods27
. Fixing the partial pressure of oxygen, the NO pressure for surface oxide
decomposition is much higher than that when the surface oxide starts forming, which indicates a kinetic
limitation for the formation the surface oxide. By examining the partial pressures of NO and O from 10-7
to 1 atm at temperature of 450 K and 600 K, higher temperatures were found to stabilize the thin film
surface oxide. Comparing the average coverage of oxygen on Pd(100) and the √5 surface oxide, a
bistability region was found to exist in which both Pd(100) and PdO(101) could be the active surface for
reactionNO+ O → NO2 inthe practical operation.