IDENTIFYING CO2 DISSOCIATION PATHWAYS ON STEPPED
AND KINKED COPPER SURFACES USING FIRST PRINCIPLES
CALCULATIONS
A Thesis
Presented to
The Academic Faculty
By
Alexander Ian Fergusson
In Partial fulfillment
Of the Requirements for the Degree
Master of Science in Chemical and Biomolecular Engineering
Georgia Institute of Technology
May, 2012
Identifying CO2 Dissociation Pathways on Stepped and Kinked Copper Surfaces Using
First Principles Calculations
Approved by:
Dr. David Sholl, Advisor
School of Chemical and Biomolecular
Engineering
Georgia Institute of Technology
Dr. Thomas Fuller
School of Chemical and Biomolecular
Engineering
Georgia Institute of Technology
Dr. Christopher Jones
School of Chemical and Biomolecular
Engineering
Georgia Institute of Technology
Date Approved: March 21, 2012
ACKNOWLEDGEMENTS
I would like to thank my advisor, Professor David Sholl. Without your guidance
and patience none of this would have been possible. You broke down complex concepts
in a way that made it possible for someone with no programming or computational
experience to excel. I would also like to thank my committee members for their time and
assistance.
All of the members of the Sholl group, I would like to thank you for your advice,
input, and friendship. Each one of you taught me something, and I would like to
acknowledge Emmanuel Haldoupis, Timmothy Van Heest, Taku Watanabe, Nita
Chandrasekhar, Liwei Li, Daniel Wei, and Xuerong Shi for your invaluable assistance.
I would like to thank all of my past teachers who inspired me to follow this path.
From Tom Dubic and Mona Hedrick who instilled a passion in science and engineering at
a young age, to my professors at the University of South Carolina, like Drs. Melissa
Moss, Christopher Williams, and Vincent Van Brunt, who pushed me to excel and
offered invaluable advise.
Finally I would like to thank my Family. My mother for her support and
unwavering belief in me, my father for encouraging my curiosity in science and
technology, and my sister for her friendship ad perspective.
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ........................................................................................................... iii
LIST OF TABLES .......................................................................................................................... v
LIST OF FIGURES ....................................................................................................................... vi
SUMMARY ................................................................................................................................... ix
CHAPTER 1: INTRODUCTION ................................................................................................... 1
CHAPTER 2: OVERVIEW ............................................................................................................ 4
2.1 Introduction ........................................................................................................................... 4
2.2 Brief introduction to DFT ..................................................................................................... 8
CHAPTER 3: METHODS ............................................................................................................ 11
CHAPTER 4: DFT RESULTS ..................................................................................................... 16
4.1 Identifying Reference states ................................................................................................ 16
4.2 Evaluation of CO2 dissociation on Cu(111) ........................................................................ 24
4.3 Evaluation of CO2 dissociation on Cu(211) ........................................................................ 28
4.4 Evaluation of CO2 dissociation on Cu(643) ........................................................................ 36
CHAPTER 5: KINETIC MODEL ................................................................................................ 44
CHAPTER 6: CONCLUSIONS ................................................................................................... 55
REFERENCES ............................................................................................................................. 59
iv
LIST OF TABLES
Table 1
Adsorption energy results for oxygen on Cu(111) comparing data from Xu
et al. to the computed values in this work.
18
Table 2
Results for oxygen adsorption on Cu(211) comparing published and
experimental results to the computed values in this work.
21
Table 3
Chemisorption energies of CO on Cu(111) from this work and literature
for the four adsorption sites on the Cu(111) surface
26
Table 4
BEP analysis results for Cu(643).
41
v
LIST OF FIGURES
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
The Cu(111) surface has four possible atomic adsorption sites, the top site,
the bridge site, the hcp site, and the fcc site.
Cu(211) has the same four adsorptions sites as the Cu(111) surface, however
there are three unique top, hcp, and fcc sites respectively, and five different
bridge sites.
Cu(643) has a significantly larger unit cell with fifty-three unique adsorption
sites. There are ten tops sites, ten hcp sites, ten fcc sites, and twenty-three
bridge sites.
Profile views of all three surfaces. Figures A, B, and C are the Cu(111),
Cu(211), and Cu(643) surfaces respectively.
Possible di-σ sites parallel to the surface for adsorption of O2 on Cu(111). For
brevity the names are shortened to their first letter, i.e. top-bridge-top is
abbreviated as t-b-t.
5
6
7
12
17
Figure 6
Adsorption distance comparison between this work and published results
from Xu et al. for oxygen on the Cu(111) surface.
19
Figure 7
Adsorption distance comparison between this work and published results
from Xu et al. for molecular oxygen on the Cu(211) surface.
22
Figure 8
Adsorption energy comparison between this work and published results from
Xu et al. for molecular oxygen on Cu(211).
23
Figure 9
Results for a three-image cNEB calculation for CO2 dissociation on the
Cu(111) surface.
27
Figure 10
Figure 11
Figure 12
Carbon monoxide adsorption energy on Cu(211).
Adsorption energy and interaction energy of CO+O on Cu(211).
Adsorption energy of CO2 on Cu(211).
29
30
32
Figure 13
NEB results for CO2 dissociation on Cu(211). The dashed lines are the singlepoint image approximations and the solid lines are the cNEB results.
33
Figure 14
BEP analysis of NEB results using the Universal BEP equation developed by
Wang and coworkers.
35
Figure 15
Adsorption energy of atomic oxygen on Cu(643).
vi
36
Figure 16
Figure 17
Figure 18
Figure 19
Adsorption energy of CO on Cu(643).
Adsorption energy and interaction energy of CO+O on Cu(643).
Adsorption energy of CO2 on Cu(643).
NEB results for CO2 dissociation on Cu(643).
37
38
40
42
Figure 20
Dissociation rate for the t1h3 pathway on Cu(211) in m-2 s-1 as a function of
pressure over 920-800 K using the NEB results
48
Figure 21
Dissociation rate for the t1h3 pathway on Cu(211) in m-2 s-1 as a function of
pressure over 530-480 K using the NEB results.
49
Figure 22
Dissociation rate for the t1h3 pathway on Cu(211) in m-2 s-1 as a function of
pressure over 530-480 K using the experimentally corrected results.
50
Figure 23
Dissociation rate for Cu(111) in m-2 s-1 as a function of pressure over 530-480
K using the experimentally corrected results.
51
Figure 24
Dissociation rate for the h4b9 pathway on Cu(643) in m-2 s-1 as a function of
pressure over 530-480 K using the experimentally corrected results.
52
Figure 25
Peak dissociation rate for Cu(111), blue, Cu(211), red, and Cu(643), green in
m-2 s-1 as a function of pressure over 480 - 530 K using the experimentally
corrected results.
vii
53
LIST OF SYMBOLS AND ABBREVIATIONS
DFT = Density Functional Theory
cNEB = Climbing Image Nudged Elastic Band
CCS = Carbon Capture and Sequestration
HREELS = High Resolution Electron Energy Loss Spectroscopy
HCP = Hexagonal Close Packed
FCC = Face-Centered Cubic
VASP = Vienna Ab-Initio Simulation Package
LDA = Local Density Approximation
PW91-GGA = Perdew-Wang Generalize Gradient Approximation (Published 1991)
viii
SUMMARY
Three Miller index surfaces of copper, Cu(111), Cu(211), and Cu(643) were
evaluated for spontaneous carbon dioxide dissociation. DFT (Density Functional Theory)
was used to characterize the initial and final adsorption states and Climbing Image
Nudged Elastic Band (cNEB) calculations were used to identify the dissociation
transition sites. A simple kinetic model was formulated and used to quantitatively
compare the three surfaces and determine which facilitated CO2 dissociation most
readily.
ix
CHAPTER 1: INTRODUCTION
Carbon dioxide production has become a more prevalent topic of discussion in the
past few years. Concerns about global warming have driven research to capture or use
CO2 as a chemical feedstock. Carbon capture and sequestration (CCS) is expensive and
wasteful. An interesting alternative is to utilize the waste as a feedstock and convert it to
a product of value. CO2 is a cheap source of carbon from both atmosphere and industrial
waste. If CCS legislation is passed, power utilities and chemical companies will give
away their captured CO2, or even pay a collaborator to accept the production waste,
rather than pay for the compression cycle for straight sequestration, never mind the
piping costs associated with plants that are not located in an area where sequestration can
be done on site. If carbon capture becomes more widespread, CO2 will be abundant and
cheap, with easy to access local sources globally.
CO2 can be used in a variety of accrued-value processes. It is vital in the watergas shift reaction and as well as methanol synthesis. Furthermore, it can be used as a
cheap C1 feedstock for low molecular weight alkanes and alkenes. CO2 conversion to
hydrocarbons has only been achieved in significant quantities on copper catalysts [1,2].
This is done via electrocatalysis, using a potential of 0.7 eV for methane and ethylene
across the copper substrate to drive the reaction. Hydrogen, carbon monoxide and formic
acid formed at if lower potentials are applied across the surface.
There is evidence that the potential barrier is lowered significantly by stepped
planes and defect sites [3,4]. Results indicate that there is no measurable adsorption or
dissociation of CO2 on Cu(110) under UHV conditions [5]. Significant production costs
1
can be saved if the potential required for the electrocatalysis can be minimized or
eliminated entirely. At high pressures, dissociation of CO2 was observed on the Cu(110)
surface, but with a reaction probability lower than ~10-9 per collision with the surface,
and at an apparent activation energy of -16 kcal/mole CO2 [5]. These results are
supported by equilibrium considerations based on a knowledge of the kinetics of the
reverse reaction (COa + Oa → CO2,g) and a thermochemical analysis of the system [5].
The Authors suggest that the reverse water-gas shift mechanism occurs via an absorbed
atomic oxygen (Oa) intermediate. The results also show that CO2/CO pressure ratios
greater than 100 are required to generate significant concentrations of Oa in the required
temperature range for the methanol synthesis reaction (<600 K), at least on pure copper
surfaces. [5].
The Cu(311) stepped surface is much more reactive toward CO-CO2 dissociation
than Cu(110) [6]. Cu(311) faces adsorb CO2, and D2, at low pressures (< 10-6 Torr). As a
point of comparison, there is no interaction on Cu(110) with either CO2 or D2 under low
pressures and temperatures (< 10-6 Torr and 150 K) [6]. Additionally, oxygen reacted
with a CO/H2 atmosphere two to five times faster from the Cu(311) surface than from the
low Miller index faces [6].
Experimental results indicate that CO2 dissociates on the stepped Cu(332) surface
[7]. No dissociation was observed on clean, defect-free, flat Cu surfaces [7]. According
to this study, spontaneous CO2 dissociation, that is without an applied potential to the
surface, has only been identified for a Cs promoted Cu(110) surface [8] and for a stepped
Cu (310) surface [9]. Studies have also been done on potassium promoted Cu(110)
surfaces. The adsorption of CO2 on the Cu(110)/K surface at a coverage of 0.75
2
monolayer (ML) at temperatures of 130 to 140 K leads to two different CO2 surface
species. The first is a highly reactive, bent CO2 species, which is formed already at low
exposures. The second is a weakly bonded, inactive, linear CO2 species, only observed
after high exposures [10]. The catalytic properties of Cu(110)/K at 130 to 140 K are
dominated by the interaction of potassium with CO2 [10]. At relatively high preadsorption of 0.75 ML potassium, the very different, specific properties of copper play at
most a secondary role to the potassium-CO2 interaction[10].
On a different low index Miller surface, Cu(100), molecularly adsorbed CO2 lies
parallel to the Cu(100) surface and closely resembles gas phase CO2.[11] The presence of
oxygen on the Cu ( 100) surface does not greatly alter the nature of molecularly adsorbed
CO2. [11] On clean Cu(100), CO2 adsorbs into a weakly bound physisorbed state with a
binding energy of approximately 25 kJ/mol, resembling the linear gas-phase molecule.
The HREELS (High Resolution Electron Energy Loss Spectroscopy) spectra for CO2 on
clean Cu(100) shows only the symmetric bending mode of linear CO2[12] indicating that
chemisorption has not occurred, as the surface would hinder the possible bending angle
and produce asymmetry.
3
CHAPTER 2: OVERVIEW
2.1 Introduction
When considering surface interaction and chemistry, it is important to evaluate
the fundamental variables governing the system. To do this, three characteristic surfaces
were chosen, and theoretical studies were performed using density functional theory
(DFT) to evaluate the effects of different topographical features. The goal was to quantify
what impact minute features have on the dissociation probability and rate. Miller
surfaces were chosen due to their features, or lack thereof.
The simplest surface chosen is Cu(111), a flat fcc surface with three-fold atomic
symmetry. There are no steps or cavities, which means this is a simple surface. One of
the useful qualities of the Cu(111) surface is the small unit cell, allowing for rapid
calculations. Another motivation to study this surface was the stepped and kinked
surfaces studied have terraces that have [111] geometry. As a result, the data generated
for Cu(111) provides bulk terrace values to evaluate the long-range edge effects of the
step-edges. Additionally, the 111 Miller surface is the closest packed fcc surface. It is
similar to hexagonal planar, however, fcc structures have a three-layer symmetry, rather
than the two-layer symmetry of hexagonal close-packed structures. Because of this, the
fcc structure has two different three-fold hollow sites. The hcp site is characterized by
having a nearest-neighbor atom directly below. The fcc site, on the other hand, is located
about the third substrate layer. As a result, the two sites have small, but significant
interaction differences. Adsorption is also possible on top of a surface atom in the top
site, as well as between two surface atoms in the bridge site. This is shown in Figure 1.
4
FCC
HCP
Top
Bridge
Figure 1: The Cu(111) surface has four possible atomic adsorption sites, the top site, located
directly above a copper atom, the bridge site, located between two adjacent atoms, the hcp site, a
threefold-hollow site with a copper atom directly below, and finally the fcc site, a threefold-hollow
site with a copper atom two layers below. The blue outline marks the 2x2 unit cell chosen for
these calculations.
The next phase is to introduce an atomic step to evaluate the impact of long
atomic ledges. Cu(211) was chosen since it is a simple stepped surface. Cu(211) has a
terrace three atoms deep before a single atomic step. The face of the step is Cu(100). This
provides 4-fold hollow sites along the foot of the step, while the terrace is Cu(111) so
comparison to the previous results is possible and appropriate. The step is perfectly
straight for the unblemished structure. Along the top of the step, there is less hindrance
by the surface, allowing for different adsorption angles for binding species. If an
5
adsorbing molecule has components that do not interact favorably with the surface, this
topography allows the binding elements to get close to the surface while allowing the
repulsive components as much distance from the surface as possible. Like Cu(111),
Cu(211) has a fairly small unit cell for quick calculations. Furthermore, there is data
available for oxygen and CO2 adsorption on Cu(211) to evaluate methodology and
compare results.
B5
B1
B4
B2
B3
F4
H5
T3
T2
H3
F0
H1
F2
T1
Figure 2: The Cu(211) surface shares the same four adsorptions sites as the Cu(111)
surface, however due to the geometry, there are three unique top, hcp, and fcc sites
respectively, and five different bridge sites.
Adding another layer of complexity leads to the Cu(643) surface. The fcc(643)
surface is an extensively studied index due to its kinked step. The terrace is Cu(111) three
atoms deep, just like the [211] surface. Continuing the uniformity, the long step is
6
Cu(100). The variation occurs after the third atom along the length of the step, where
there is a single Cu(110) kink in the step. The kink allows for additional degrees of
freedom in binding for adsorbates favoring the step-edge. It also means there is a highly
functionalized adsorption site at the foot of the kink at the intersection of the [111], [110],
and [100] planes. Computationally, a significantly larger unit cell is required for the
Cu(643) surface to account for the kink, which leads to larger computational cost. It also
means the number of unique binding sites is much larger as well. On the [111] surface
there are four unique binding sites, fourteen unique sites on the [211] surface, and fiftythree on the [643] structure.
B23
B22
F10
B21
F9
B20
B19
B17
T8
T9
T10 B18
H9
H8
B13 B12
B16 B15 B14
F6
F5
F7
T6
B10 T5
T7 B11
B9
T4
B8
F4
B3
H3
H6
B7
T3
B6
H5
B5
F3
B2
T2
B4
H1
H2
H7
H4
F2
B1
F8
F1
T1
H1a
Figure 3: Cu(643) has a significantly larger unit cell with fifty-three unique adsorption
sites. There are ten tops sites, ten hcp sites, ten fcc sites, and twenty-three bridge sites.
7
The surfaces are only half of the system. Five different adsorbed species are also
necessary for our calculations. We must consider carbon dioxide as well as all of its
derivatives. Calculations must be performed for atomic and molecular oxygen, carbon
monoxide, and the dissociated adsorbed state, carbon monoxide plus atomic oxygen.
Using energy minimization, favorable adsorption configurations for each of the species
are identified. Using the adsorption data, theoretical studies can be performed to predict
possible dissociation pathways, and from that the kinetic rates and probabilities
associated with those particular paths. In this work we evaluate the [111], [211] and [643]
surfaces. The transition states of multiple dissociation pathways are identified. Using
these data, a kinetic model is used to quantitatively compare the activity of the three
surfaces and identify the most promising candidate.
2.2 Brief introduction to DFT
The computational method chosen to carry out these calculations is density functional
theory (DFT). DFT is based on quantum chemistry. By assuming that the BornOppenheimer approximation is valid, that is that we can treat the atomic nucleus and the
associated electron cloud as two separate mathematical problems. This allows us to
calculate the minimum energy state of the electrons in the system to identify the ground
state of the species. This gives the potential energy of the surface in question, and more
importantly, the energy variation as other species interact with it [13].
Calculating the electron energy is accomplished using a form of the time independent
Schrodinger equation:
8
ℏ
∇ + ( ) + ( , ) = −
2
(1)
Within the brackets are the kinetic energy of each electron, the interaction energy
between each electron and the surrounding nuclei, and the interaction energy between
individual electrons. N is the number of electrons in the system. The solution of this
eigenproblem defines the electronic wave function, ψ, and E, the ground state energy of
the electrons.
Khon and Sham enabled DFT to exist via their first theorem that states, “the
ground-state energy from Schrodinger’s equation is a unique functional of the electron
density” [20]. This vastly simplifies the calculations necessary as it eliminates the
consideration of individual electrons, and instead focuses on the density of the electrons
within the system. While this first theorem demonstrated that electron density could be
used to solve the Schrodinger equation, it provided no information as to how to achieve
this goal: they didn’t define the functional of the electron density [13].
Kohn and Sham’s second theorem states that the electron density that minimizes
this functional is the true electron density which gives the full solution to the Schrodinger
equation. In practice this is impossible, the “true” form of the functional is simply not
known. However, there are many good approximations. If it were known, the electron
density could be varied until the energy was minimized. Using this approach, a selfconsistent solution of a set of single-particle equations can provide an approximation of
the ground state energy. To do this, an exchange-correlation functional must be defined.
Since the true form of this functional is not known, there are many approximations that
are tailored towards different systems and conditions. In this work the Perdew-Wang
9
generalized gradient approximation (GGA-PW91) will be used. This approach uses
information about the local electron density in conjunction with the gradient in this local
electron density to approximate the solution of the exchange-correlation functional. This
functional does a good job at describing metallic systems; however it will over-bind nonmetallic adsorbates, predicting slightly higher adsorption energy than would be found via
experiment [13].
There are several limitations to the application of DFT. The inherent error of
approximating the exchange-correlation functional gives a systematic error between the
calculated ground-state energies and the true energies from the Schrodinger equation
because the exact solution is simply not known. Having said that, if these approximations
are applied in a careful manner the results of DFT calculations provide physically
meaningful predictions for the ground-state energy of the system considered. DFT also
fails to give accurate results for systems that involve weak van der Waals interactions.
These interactions occur due to intermittent fluctuations in the electron density of one
molecule within the system and the energy of the electrons in the other molecule
responding to the perturbation. With calculations involving molecular adsorption on a
surface, van der Waals interactions are significant. Including these interactions would
lower the calculated adsorption energy. These energies will be considered in this work
and will be quantitatively discussed in the results.
10
CHAPTER 3: METHODS
The Vienna Ab Initio Simulation Package (VASP) packaged developed at Wien
University in Austria was used to conduct all DFT calculations for this work. The
Cu(111) surface was modeled with a 2x2 surface unit cell with four atomic layers. The
top two atomic layers allowed to relax, while the bottom two were locked into position
with a calculated bulk lattice constant for copper of 3.63 Å. This value is in good
agreement with the experimental value of 3.62 Å [14]. A vacuum spacing between slabs
of 12.7 Å was used.
The Cu(211) surface was modeled with a 1x2 surface unit cell with three layers.
However, due to the angle of the unit cell necessary for maintaining the step while using
periodic boundary conditions, nine discrete z-coordinates are necessary. This is better
illustrated in Figure 4. The top four layers were allowed to relax and a vacuum spacing of
10.4 Å was used.
11
C
A
B
Figure 4: Profile views of all three surfaces. Figures A, B, and C are the Cu(111),
Cu(211), and Cu(643) surfaces respectively. Cu(111) has four layers, Cu(211) has three
layers, and Cu(643) has four layers with an overlapping fifth layer. This extra layer, when
compared to Cu(211), was necessary for accurate surface energy calculations due to the
Cu(643) geometry.
The Cu(643) surface was modeled with a 1x1 surface unit cell with 40 layers.
There are four layers perpendicular to the terrace plane, see Figure 4 for a profile view of
the Cu(643) surface. The atoms in the top 2.57 Å were allowed to relax. Between each
slab there was a vacuum spacing of 13.07 Å.
The Brillouin zone was sampled at a 4x4x1 set of Monkhorst-Pack k-points for all
surfaces with a cutoff energy of 400 eV and a cutoff criteria of -0.3 eV/ Å. Preliminary
calculations indicated that this sampling of reciprocal space gave well converged results.
The exchange-correlation functional used is the Perdew-Wang generalized gradient
approximation (GGA-PW91). All total energies were extrapolated to kBT=0 eV.
Molecular oxygen in a vacuum was found to have a bond energy of 9.77 eV, compared to
an experimental value of 5.25 eV [15]. The bond energy is from calculations using spin
polarization effects. The bond length calculated for Xu et al. was 1.24 Å, the same as this
12
work and very close to the experimental value of 1.21 Å [15]. CO2 has a bond energy of
23.02 eV. Binding energies were determined by:
= − !#$
− %#&$
(')
where is the total energy of the surface plus the adsorbed species, (2)
!#$
energy of the relaxed surface without any adsorbate in the system, and %#&$
is the
(')
is
the bond energy of the adsorbate calculated in a vacuum. The value used for atomic
oxygen is half the bond energy of molecular oxygen in the vacuum.
To calculate transition states and dissociation pathways, a method known as the
nudged elastic band (NEB) was used. This method is a way to find saddle points
(transitions sites) and minimum energy pathways between the adsorbed state and
dissociated state, or more simply, between reactants and products on a potential energy
surface. In an NEB calculation, intermediate images between the initial and final states
are optimized to the lowest possible energy while maintaining distance between each
image to prevent them from converging to local minima. This is done via constrained
optimization where spring forces are added along band images to counter the forces of
the potential perpendicular to the band. Since these images are not in an energy minima
on the surface, they are inclined to move towards the local minima. NEB introduces a
force to counteract the energy minimization so the energy along the path can be
computed [13]. These calculations are much more computationally expensive. Unlike the
energy minimization calculations used to identify the initial and final states, an NEB
calculation must minimize the energy of all the images, while also calculating a spring
interaction between images necessary to counteract the minimization [16].
13
A modification of NEB that is more often used is climbing image NEB (cNEB). It
is designed to more rigorously identify the saddle point on a potential energy surface than
NEB. This means that if the images chosen by the user do not include the saddle point,
the images will be moved to include the transition site. While it may be possible to
predict the transition site for simple molecules on simple surfaces, when complex
molecules or surfaces are introduced, predicting a transition site with certainty is
impossible [16].
In this work we used a five-step cNEB calculation: three images were used to
identify minimum energy pathways between the initial state CO2 and the dissociated
state, (CO +O)a plus the initial and final states themselves. The heat of reaction is
calculated from the binding energy difference between the final dissociated state and the
starting molecular state. To maintain internal consistency, all steps were calculated with
gas phase CO2 as reference state. The transition states are identified from highest value
result from cNEB images. Activation energies were calculated from = $,() − $,*)
where TS is the transition state and IS is the initial state (adsorbed CO2).
Once the cNEB calculations were finished for the Cu(211) surface the universal
Bronsted-Evans-Polanyi (BEP) developed by Wang and coworkers [17]. They developed
a simple method to predict the transition state energy from the dissociation energy for
multiple broken bonds, including C-C, C-O, C-N, N-O, N-N, and O-O. They studied the
transition states on many different stepped transition metal surfaces such as Co, Ni, Cu,
Ru, Rh, Pd, Ag, Ir, Pt, and Au. This simple method linearly relates the transition state
energy with the dissociative adsorption energy, where the transition state energy is
calculated using:
14
() = ()/#$ − #$ − '#
(3)
where ()/#$ is the total energy of the slab with transition states, #$ is the total
energy of the clean slab, and '# is the energy of the gas phase reference state. The
dissociative adsorption energy is calculated using:
∆%## = -/#$ + /#$ − 2 ∗ #$ − '#
(4)
where -/#$ and/#$ are the total energies of the slabs with adsorbates A or B.
after performing DFT calculations for a wide variety of molecules on a range of
different stepped metal surfaces, Wang and coworkers arrived at a simple linear relation
to describe the relationship between transitions states and reaction energies where
# = 2 ∗ ∆%## + 3
(5)
The variables 2 and 3 are fitting parameters with values of 0.84 and 1.92 eV respectively.
The mean absolute error for the equation is 0.35 eV. Equation 5 was applied to the cNEB
results for the Cu(211) surface, and after confirming good agreement, was used to predict
the most favorable dissociated sites on the Cu(643) surface.
15
CHAPTER 4: DFT RESULTS
4.1 Identifying Reference states
To understand the relation of DFT to physical results the work of Xu et al. was
extensively studied [18]. Xu et al. performed DFT calculations for atomic adsorption on
Cu(111) and Cu(211) using the PW91-GGA functional. This exercise was also used to
ensure that our DFT calculations had good numerical convergence and repeatability. For
uniformity, the same inputs were used when repeating the work of Xu et al. whenever
possible. Thus, we used an ideal bulk-truncated Cu(111) slab to model the flat copper
surfaces and a Cu(211) slab to model the steps. The Cu(111) slab consisted of a 2x2
surface unit cell with four layers and a vacuum spacing equivalent to six copper layers.
The Cu(211) surface has a 1x2 surface unit cell with nine copper layers with a terrace
three atoms deep and two atoms wide. The vacuum separation is 10.4 Å. The first 2
layers of the Cu(111) surface and the top 4 layers of the Cu(211) surfaces were allowed
to relax. GGA-PW91 was used for the Exchange-correlation functional. DFT calculations
were performed with DACAPO in the work by Xu et al. In this work VASP was used.
The work by Feibelman et al. [19] demonstrates that “DFT calculations cannot yet be
viewed as a ‘black box’ simulation tool.” They found that for a given functional, the
binding energy of CO on Pt(111) could vary by 0.10 eV depending on the software
package and functional used.
Experimental data shows that the preferred adsorption site for oxygen on the
Cu(111) surface is the threefold hollow site [20-22]. At low temperatures both atomic and
16
molecular oxygen are chemisorbed on the surface [20-22]. Oxygen dissociates on
Cu(111) at 170 K. Above 170 K only atomic oxygen is found [23-25].
t-f-b
t-b-t
b-h-b
t-h-b
Figure 5: Possible di-σ sites parallel to the surface for adsorption of O2 on Cu(111). For
brevity the names are shortened to their first letter, i.e. top-bridge-top is abbreviated as tb-t.
Molecular oxygen adsorbs with its molecular bond approximately parallel to the
Cu(111) surface, with the two O atoms occupying more than one adsorption site. These
sites are illustrated in Figure 5. These adsorption locations are known as di-σ sites. The
continued use of the full names of each site, like bridge-hcp-bridge, is cumbersome. For
convenience, they have been truncated, in the case of bridge-hcp-bridge, to b-h-b.
17
Table 1: Adsorption energy results for oxygen on Cu(111) comparing data from Xu et al.
to the computed values in this work. Three reference states were considered, DFT
calculated molecular oxygen in a vacuum, DFT calculated molecular oxygen in a vacuum
accounting for spin polarization effects, and atomic oxygen in a vacuum with spin
polarization.
Atomic Oxygen
Site
Hcp (eV)
Xu et al. [18]
-4.17
With spin
-1.54
Without spin
-2.03
atomic spin
-4.91
Molecular Oxygen
Site
t-b-t (eV)
Xu et al. [18]
-0.45
With spin
-0.62
Without spin
-1.60
Fcc (eV)
-4.29
-1.66
-2.15
-5.03
t-f-b (eV)
-0.79
-0.84
-1.83
Several methods for calculating the reference state energy were considered to
generate matching data. Table 1 compares the results for the most favorable atomic and
molecular binding sites on the Cu(111) surface. Calculations were conducted with a
variety of inputs to get the most physically accurate result. These inputs included
considering the spin polarization of the oxygen. The results demonstrated that spin
polarization had a large contribution and was necessary to get results not only similar to
Xu et al. but also results that were physically relevant. Without including the spin, the
atomic results under-bind by a large amount while the molecular results over
-bind. For the atomic case, the reference state was a single oxygen atom in the gas
phase. Using half of the energy of molecular oxygen in the gas phase resulted in a
significant under prediction of the binding energy. From these data, it is clear that spin
polarization is not negligible, and must be included for physically accurate results. It is
interesting to note that while the magnitude of the adsorption energies are different
18
between this work and the work of Xu and coworkers, the difference between sites are
approximately the same. This further indicates that the differences seen in these
calculations are due to the difference in energy of the reference states.
Spin polarization was used for all subsequent adsorption and NEB calculations
involving oxygen in the remainder of this work since spin polarization contributes even
in the adsorbed state. With carbon dioxide there are not any spin issues. Because this
work is internally consistent comparing several different surfaces, the difference in
reference state energies between this work and the work of Xu et al. is not a critical
concern.
2.5
Angstrom
2
1.5
1
Z Calculated
Z Paper
D Calculated
D Paper
0.5
0
hcp
fcc
t-b-t
t-h-b
t-f-b
b-h-b
b-f-b
Figure 6: Adsorption distance comparison between this work and published results from
Xu et al. for oxygen on the Cu(111) surface. The distance from the surface plane, z, and
the copper-oxygen distance, D, are shown. The hcp and fcc data are atomic oxygen
distances, the subsequent data are molecular oxygen data.
19
The distances from the plane, z, and the distance between oxygen and copper
atoms, D, from this work were compared to the results from Xu and coworkers. The z
results were approximately the same for both molecular and atomic oxygen in both sets
of calculations. There is a marked difference, however, between the previous results and
our calculations for D for molecular oxygen. In the reference work the molecular oxygen
adsorbs much closer to the surface than the atomic oxygen. In our calculations, the
adsorption distance is similar for both molecular and atomic oxygen on Cu(111).
Molecular oxygen is a physisorbed species. DFT calculations without dispersion force
corrections describe physisorption poorly, leading to imprecision in the adsorption
distances [13]. The results for the adsorption distance from the surface plane, on the other
hand, are similar for both sets of data. The measurements were taken from the center of
mass of the oxygen molecule to the center of mass of the first layer of copper atoms on
the surface. If the angle of the molecule to the surface is different between this work and
Xu et al., the Cu-O distance would be different while the z distance remained about the
same.
20
Table 2: Results for oxygen adsorption on Cu(211) comparing published and
experimental results to the computed values in this work. The reference state used in this
work is DFT calculated molecular oxygen in a vacuum accounting for spin polarization
effects calculated using Equation 2.
Atomic Oxygen
Site
f0 (eV)
Xu et al. [18]
-4.00
This work
-5.27
Edge of Step
Site
Xu et al. [18]
This work
t-b-t (eV)
-0.92
-1.42
Foot of Step
Site
Xu et al. [18]
This work
t-b-t (eV)
-1.16
-1.37
h3 (eV)
-3.96
-4.93
T-f-b
(eV)
-0.79
-1.34
t-f-b
(eV)
-0.8
-1.34
We established with the Cu(111) surface that the atomic spin was necessary and
as a result that is the reference state used for all the oxygen calculations described in the
remainder of this section. On the Cu(211) surface, the difference between different
adsorption site energies between the Xu et al. data and the data from this work are more
pronounced. For atomic adsorption, the results of Xu et al. and this work agree that f0 is
the most favorable site, however the results from this work found a difference of 0.34 eV
between the two sites compared to 0.04 eV for Xu and coworkers. For molecular
adsorption, the t-b-t site on the step-edge was found to be the most favorable site for this
work, while the t-b-t site at the foot of the step was the most favorable site according to
the results of Xu et al. These differences are a result of adsorption distance differences
between the results from our work and the reference, shown in Figure 7.
21
2.5
Angstrom
2
1.5
1
Z Calculated: Molecular
Z Paper: Molecular
D Calculated: Molecular
D Paper: Molecular
0.5
0
t-b-t
t-h-b
t-f-b
b-h-b
b-f-b
Figure 7: Adsorption distance comparison between this work and published results from
Xu et al. for molecular oxygen on the Cu(211) surface. The distance from the surface
plane, z, and the copper-oxygen distance, D, are shown.
The atomic distance from the plane, z, and the distance from the nearest copper
atom, D, calculated for this work does not correlate well with the work of Xu et al. The
adsorption distances for the molecular oxygen on Cu(211) are about 0.5 Å further away
from a surface copper atom, while the distance from the plane varies from 0.01 Å to 0.39
Å. There is no obvious correlation with the variation in adsorption distance and the
variation the adsorption energy in Table 2. The copper-oxygen distance for the t-f-b site
is larger than the published value, and there is a noticeable difference in the adsorption
energy. However for the t-b-t and b-h-b sites, D is the same for this work and the
published results, however the binding energy is much more favorable in the t-b-t case,
but only marginable more favorable in the b-h-b case. This disparity is most likely due to
the fact that the distance measurements only measure the closest oxygen-copper distance
or center of mass-surface plane position. The second oxygen contributes to the energy
22
and geometry of the system, however the location isn’t given in the published work. As a
result, the most favorable positions found in this work may differ from those identified by
Xu et al.
0
Eb (eV)
-0.2
t-b-t
t-h-b
t-f-b
b-h-b
b-f-b
-0.4
Calculated: Molecular step-edge
-0.6
Paper: Molecular step-edge
-0.8
-1
-1.2
-1.4
-1.6
-1.8
Figure 8: Adsorption energy comparison between this work and published results from
Xu et al. for molecular oxygen on the Cu(211) surface at di-σ binding sites at the step
edge.
There is more variation in the molecular results, with this work demonstrating
more favorable adsorption for the t-h-b and t-f-b adsorption sites. This is due to the more
complicated surface, and the role of dispersion forces for this physisorbed species.
Overall there is a systematic error between these results and the published work. We
found that the binding energy on Cu(211) was, on average, 1.0 eV more favorable than
the results from Xu et al. This is slightly more than the 0.75 eV more favorable found on
the Cu(111) surface. For Cu(111), the geometry for this work and the reference material
23
was negligible, indicating a difference in reference states. It is necessary to include the
spin potential of oxygen to calculate accurate results. The results presented from this
work were confirmed by other members of our research group. The data from this work
identified more favorable adsorption energies for both atomic and molecular binding. The
results for molecular physisorption have some inherent error because dispersion forces
were not accounted for; however, we identified a more stable binding for physisorption at
a larger distance from the surface than the results presented by Xu et al.
It is important to note that the largest discrepancies between our calculations and
those of Xu et al. are associated with the choice of a reference state for oxygen in the gas
phase. In the remainder of this thesis, this reference state is not needed; all calculations
are defined using gas phase CO2 as a reference state unless otherwise noted.
4.2 Evaluation of CO2 dissociation on Cu(111)
Having presented initial data for oxygen adsorption on Cu(111) and Cu(211), we
can begin to evaluate CO2 adsorption and dissociation on these surfaces. To do this we
must generate data for carbon dioxide, carbon monoxide, and the dissociated product CO
+ O. We must consider this dissociated state as a separate calculation due to interaction
effects between the two molecules on the same surface. It is not enough to combine the
results of the atomic oxygen and carbon monoxide calculations to define the dissociated
state energy since the two molecules will interact when they are close, changing their net
energy.
Zhang et al. [26] examined CO2 dissociation on Cu(111) with DFT using the
PW91-GGA functional and compared the results to Pt(111) and Cu3Pt(111). They were
24
looking to create a catalyst with properties similar to pure platinum, but significantly
cheaper. The solution they identified was to use an alloy of Cu3Pt with long range order
with one platinum atom per layer at alternating acute corners of the unit cell
parallelogram. Their data demonstrated that this alloy had almost identical chemisorption
values as pure platinum, at -1.50 eV, versus the value of pure copper, -0.66 eV (although,
as mentioned below, this is for a metastable adsorption site). The transition state energy
for the alloy was between the values for copper, -0.68 eV, and platinum,- 0.87 eV, with a
value of -0.80 eV when considering dissociation along the long axis of the parallelogram
using the two three-fold hollow sites.
Hammer and coworkers also looked at CO adsorption on Cu(111) [27]. They
calculated the adsorption energy using ab-initio DFT with the PW91-GGA functional.
They also calculated the adsorption energy for platinum and Pt3Cu and found them to be 1.51 eV and -1.45 eV respectively which is in good agreement with the results of Zhang
et al. Experimentally, Ishi and coworkers used Infrared Reflection Absorption
Spectroscopy (IRAS) and Electron Energy-Loss Spectroscopy (EELS) to identify the
vibrational modes of adsorbed CO adsorbed on Cu(111) [28]. They found CO to have an
adsorbed C-O bond with an EELS frequency of 2078 cm-1 which corresponds to top-site
adsorption.
25
Table 3: Chemisorption energies of CO on Cu(111) from this work and literature for the
four adsorption sites on the Cu(111) surface. Zhang [23] stated that the adsorption value
for the fcc site was 0.1-0.2 eV higher than the reported top-site value, but an exact result
was not reported.
Literature
Site
hcp
fcc
bridge
top
This Work
(eV)
-0.76
-0.85
-0.81
-0.70
Zhang
[26]
(eV)
N/A
N/A
N/A
-0.66
Hammer
[27] (eV)
N/A
N/A
N/A
-0.62
Experimental
[28] (eV)
N/A
N/A
N/A
-0.52
The CO binding energies for various possible sites on Cu(111) from our
calculations are listed in Table 3. It is interesting to note that carbon monoxide prefers the
three-fold hollow site by about 0.1 eV. Zhang et al. [26] saw the same results, although
they did not report the exact data values they calculated. They argued that the binding
energy in the metastable top site was relevant for their situation because had a much
higher binding affinity to the fcc site, and in practice very little CO would be found in the
fcc site. This argument, however, is specific to the situation when a large coverage of O
exists on the surface. For us to consider the initial reaction rate of CO2 dissociation on
Cu(111), it is the energetically preferred sites for each species that are the most relevant.
For all four sites the adsorption energy for CO2 ranged from 0.22 eV for the fcc
site to 0.09 eV for the top site. These are positive values, meaning the system is at a
lower total energy with CO2 in the gas phase and a clean surface than it does in the
physisorbed phase. For the dissociated phase with CO on the top site and O on the fcc
site, an adsorption energy of 0.95 eV was calculated. These relative locations can be seen
in Figure 1. This adsorption energy is very unfavorable, however it is important to note
26
that the reference state for this calculation is carbon dioxide in a vacuum, which is has a
bond energy 3.5 eV greater than the sum of the bond energy of carbon monoxide and one
half O2.For the previous results for CO and O on the surface individually, the reference
state was CO and atomic oxygen value respectively.
2.5
higher res
2
Energy (eV)
NEB HR
1.5
1
0.5
0
0
CO+O
1
2
Images
3
CO42
Figure 9: Results for a three-image cNEB calculation for CO2 dissociation on the
Cu(111) surface. The red line is the results for limiting the images to freedom of
movement in only the z-axis. The green line is the fully relaxed cNEB result.
To maintain uniformity for the NEB calculation a constant reference state of
gaseous CO2 in a vacuum is required. Using the figures from the work of Zhang et al.
[26] as a reference, the transition site was approximated and then allowed to relax only in
the z-axis. A single-image NEB calculation was done from this result, relaxing all
degrees of freedom. With these results, two additional images were interpolated to
increase the resolution. The interpolated coordinates were then modified by hand to
prevent atomic overlap and ensure a good approximation. These coordinates were then
27
relaxed in the z-axis before the full cNEB calculation was conducted. A transition state
energy of 2.11 eV was found from the cNEB calculation. The transition site energy is
approximately 2 eV higher in energy than the adsorption energy of CO2. Due to such a
high transition site energy, it is very unlikely that the dissociation process to occur on
Cu(111). This value is larger than the data from Zhang et al., but they used a constrained
optimization scheme to identify the transition site. The important similarities are that the
initial state, final state, and transition state geometries were the same for this work and
the figures presented in the work by Zhang and coworkers.
4.3 Evaluation of CO2 dissociation on Cu(211)
As discussed in previous sections, Cu(211) has many more binding sites than
Cu(111) due to the geometry of the surface. This leads to higher computational cost due
to the additional time required to explore all sites. The additional sites and geometry also
requires more careful molecular placement and data analysis. While carbon monoxide
and carbon dioxide are simple molecules, they introduce another level of complexity
when compared with molecular oxygen.
28
0
f0
h1
f2
h3
f4
h5
t1
t2
t3
b1
b2
b3
b4
b5
Adsorption Energy (eV)
-0.2
-0.4
-0.6
-0.8
-1
-1.2
-1.4
Figure 10: Carbon monoxide adsorption energy on Cu(211). Overall, the sites along the
top of the step are favored over those on the terrace or the foot of the step with the
exception of the b4 site which is stabilized by the proximity of the step.
Energy minimization calculations were performed for all adsorption sites on
Cu(211). These sites are illustrated in Figure 2. Overall, carbon monoxide favored the
step-edge over the foot. The h1 and b1 sites are the most favorable with both having an
adsorption energy of -1.21 eV. The b4 site energy is close to h1 and b4 with an
adsorption energy of -1.19 eV. This is an interesting outlier that does not appear to follow
the observed trends of favoring the step-edge. The proximity of the foot of the step
stabilizes the carbon monoxide in the b4 site. The adsorption distance for CO at the b4
site was 2.38 Å from the terrace surface and the step, while the distance at other bridge
sites was approximately 1.5 Å. Additionally the t1 site has a fairly favorable binding
energy of -1.12 eV. Furthermore, the top site on the Cu(111) surface had an adsorption
energy of -0.70 eV, which is close to the t2 and t3 values of -0.81 eV and -0.73 eV
29
respectively. The adsorption of CO on Cu(211) is favored by approximately 0.4 eV
relative to Cu(111). This is consistent with the general trend on many metal surfaces that
less coordinated surface sites bind molecules more strongly than more highly coordinated
sites.
Now that data is available for CO and O on the Cu(211) surface, we must
consider the system where CO and O are both bound to the same surface to explore any
interaction effects. The interaction is calculated using 4 = 5(,6 + (,76 8 −
5(,7696 + ) 8, where ET is the total energy of the system and the O, CO, and CO+O
subscripts indicate the system where O, CO, and CO+O are adsorbed to the surfaces. ES
is the energy of the clean slab.
2
Energy (eV)
1.8
1.6
Eb
1.4
Interaction
Energy
1.2
1
0.8
0.6
0.4
0.2
0
f0f4
f0b5 h1h5 h1b4 h1b5 t1h3 t1f4
t1t3 t1b4 t1b5 b1h3 b1f4 b1b4
Figure 11: Adsorption energy and interaction energy of CO+O on Cu(211). The
configurations are defined by a name that combines the CO location first with the O
position second.
30
To examine a range of different dissociated states, four different CO adsorption
sites were chosen: f0, h1, t1 and b1 and six O sites were chosen: h3, f4, h5, t3, b4, and
b5. The 24 possible combinations were constructed and the energy was minimized. The
naming convention of the labels combines the location of the CO with the location of the
O. For example, with the first configuration, f0f4, the CO is in the f0 site, and the O is in
the f4 site. In the cases where the CO or O moved to a different site, or where they
recombined into CO2, the combination of sites was eliminated from consideration. This
left the thirteen sites shown in Figure 11.
The reference state for the system was CO2 in a vacuum. At first glance, the data
does not appear to agree with the data reported for the CO on Cu(211) and O on Cu(211)
systems discussed earlier, however this is because those calculations had a different
reference state. Across the various sites considered the overall adsorption energy ranged
from 0.22 eV to 1.72 eV. These positive values mean that the states considered are less
favorable energetically than a clean surface with gaseous CO2. These states are, however,
local minima. Those states with very high adsorption energy like t1t3 with an adsorption
energy of 1.72 eV it is very unlikely that dissociated CO2 would settle into this
configuration. For other states with more favorable energies, the transition state energies
between the CO2 and CO+O configurations are high enough to allow these dissociated
states to be locally stable.
The interaction energy for the sites examined ranged from 0.01 eV to 1.29 eV. A
positive interaction energy value indicates that the overall energy of the combined system
is higher than the isolated cases, indicating the presence of both destabilize each other.
There appears to be no correlation between interaction energy and adsorption energy.
31
0.15
Adsorption Energy (eV)
0.1
0.05
0
f0
h1
f2
h3
f4
h5
t1
t2
t3
b1
b2
b3
b4
b5
-0.05
-0.1
-0.15
Figure 12: Adsorption energy of CO2 on Cu(211). The site was identified by where the
center of the CO2 molecule was located, with the molecular axis approximately
perpendicular to the plane of the step.
Unlike carbon monoxide, CO2 did not favor the step edge over the foot. Overall,
CO2 had a much larger binding distance, measured from the center of mass to the nearest
Cu surface atom, than CO or O ranging from 2.0 Å to 3.5 Å. The molecules bound at a
larger distance actually exhibit a more favorable adsorption energy. CO2 molecules
favored adsorbing at a slight angle from parallel to the terrace, perpendicular to the plane
of the step.
The f0, h5, and b1 sites all exhibited unfavorable adsorption energies for CO2.
Adsorption in the h5 position could be considered to be in the f0 or b1 site since the CO2
could not fit in the adsorption site at the foot of the step. The most favorable site for
adsorption was the f4 site, with an energy of -0.10 eV. The range of values is fairly small.
When considering the accepted error for DFT is approximately 0.05 eV, it is difficult to
32
draw any conclusive results as to which site is favored. This is not unexpected, since CO2
is physisorbed on this surface.
t1h3
t1h3 NEB
h1h5
h1h5 NEB
t1b4
t1b4 NEB
2.5
2
Energy (eV)
1.5
1
0.5
0
-0.5
0
CO+O
1
2
Images
3
CO4
Figure 13: NEB results for CO2 dissociation on Cu(211). The dashed lines are the singlepoint image approximations and the solid lines are the cNEB results. The naming
convention is defined by the dissociated state, where the first site is the CO location and
the second site is the O location.
Considering the CO2 adsorption and CO+O adsorption results, three pathways
were chosen for NEB calculations. The criteria considered the viability of the initial and
final states. Sites were selected based on the adsorption energy as well as interaction
energy. We assumed that the most probable reaction would favor the most favorable
sites. For simplicity, we also assumed that the CO would move in orientation only, it
would not translate from one site to another. That is, only the dissociated oxygen atom
would move. Because the CO is not moving, the possible sites for the final position of
33
CO2 are limited to those where CO was stable in the CO+O calculations. Those sites are
f0, h1, t1 and b1. Comparing these sites with the CO2 data, the list is further truncated to
the h1 and t1 sites since the adsorption energy of CO2 at the f0 and b1 sites are positive
values. The t1h3 system was chosen because it has an interaction energy of almost zero.
On the other hand, the t1b4 and h1h5 have significant interaction energies of at least 0.5
eV.
The stepwise calculations were designed to establish an initial guess for the
dissociation pathways. The x and y coordinates for the adsorbed species were locked and
only allowed to relax in the z direction. Because of this, it is unlikely that these positions
would identify the transition state location. As a result, the values for the stepwise
calculations are typically lower than the full cNEB results, as the molecules are able to
relax in all three directions to find the saddle point in those calculations. By performing
the stepwise calculations first, the pathway can be evaluated for viability, and also
provides a more accurate input for the cNEB calculation. Without these initial
calculations, it is difficult to generate the initial positions for the images.
The t1h3, h1h5, and t1b4 systems have a transition site energy of 1.83 eV, 1.91
eV, and 1.94 eV respectively and an activation energy of 1.92 eV, 1.96 eV, and 2.04 eV.
These values are all lower than the transition site energy on the Cu(111) surface of 2.11
eV. When considering the activation energy, the differences are less pronounced. The
activation energy on the Cu(111) surface is 2.10 eV.
BEP analysis of the dissociation pathways was performed on Cu(211) and
Cu(111) to assess its application to this work. The results from the cNEB calculations
34
from both surfaces were plotted against the universal BEP equations developed by Wang
and coworkers [17]. The dissociation energy of the three different Cu(211) pathways and
the one pathway on Cu(111) were plotted against the universal BEP equation, Equation 5
in the methodology section. The results can be seen in Figure 14, below.
cNEB
4
Universal BEP
3
MAE
Ets (eV)
2
1
0
-4
-3
-2
-1
0
1
-1
Ediss (eV)
-2
Figure 14: BEP analysis of NEB results using the Universal BEP equation developed by
Wang and coworkers [17]. The data generated from the cNEB calculations were plotted
against the universal BEP equation (Equation 5) to evaluate its use as a predictive
mechanism for identifying favorable dissociated states.
Overall, the universal BEP (red line) under predicts the transition state energy. The
cNEB data lies on or just above the mean average error (MAE) determined by Wang and
coworkers [17], shown as a green line in Figure 14. The correlation is close enough that
we are comfortable using the universal BEP relation to predict what pathways to consider
for the Cu(643) surface. This approach should be more rigorous than the approach used
for the Cu(211) surface. It was retroactively applied to the Cu(211) surface, and the only
pathway that was predicted to have a significantly lower transition site energy is t1t3.
35
Unfortunately, this site has a prohibitively high dissociated state energy of 1.72 eV,
which indicates that, while useful, the BEP analysis cannot be blindly followed.
4.4 Evaluation of CO2 dissociation on Cu(643)
The inclusion of a step edge makes for a larger and more interesting unit cell.
There are fifty three unique adsorption sites on the Cu(643) surface. Each of these sites
must be evaluated for adsorption of O, CO, and CO2. Due to the size of the unit cell and
the quantity of sites, this is computationally expensive. The placement of the different
adsorbates is much the same as how it was done with the Cu(211) surface. Care was
taken to ensure that the CO molecules were perpendicular to the surface and the CO2
molecules were aligned in the most energetically favorable position.
-4.60
t4 t10 h1 h2 h3 h4 h5 h6 h8 f2 f3 f5 f6 f7 f8 f9 b3 b9 b16 b21 b22
Adsprption Energy (eV)
-4.80
-5.00
-5.20
-5.40
-5.60
-5.80
-6.00
Figure 15: Adsorption energy of atomic oxygen on Cu(643). The sites shown are those
that have stable oxygen adsorption. If the oxygen moved to a different adsorption site
during energy minimization, then the initial position was removed as a candidate. The top
site data are shown in blue, the hcp data in green, the fcc data in purple and the bridge
data in red.
36
The most favorable adsorption sites for atomic oxygen on Cu(643) were the
h1,h8,f2, and b16 sites with energies of -5.71 eV, -5.74 eV, -5.81 eV, and -5.64 eV
respectively. The favorable three-fold sites are along the top of the step, the bridge site is
stabilized by the [110] four-fold site at the foot of the step. The least favorable sites were
the t10 and b22 sites with adsorption energies of -4.89 eV and -5.01 eV respectively.
These binding energies are more favorable than the Cu(111) surface, which had
adsorption energies for atomic oxygen as high as -5.03 eV for the Cu(111) fcc site and
comparable to the Cu(211) surface which had a binding energy of -5.77 for the h1 threefold site.
-0.20
b22
b21
b20
b19
b18
b17
b16
b14
b13
b12
b11
b10
b6
b5
b2
b1
f9
f6
f5
f3
f2
f1
h8
h5
h4
h2
h1
t10
t9
t7
t6
t5
t3
t1
-0.40
Adsorption enrgy (eV)
-0.60
-0.80
-1.00
-1.20
-1.40
-1.60
-1.80
Figure 16: Adsorption energy of CO on Cu(643). The sites shown are those that are stable
local minima. There were thirty-four stable sites out of the possible fifty-three, compared
to twenty-one for atomic oxygen. The top site data are shown in blue, the hcp data in
green, the fcc data in purple and the bridge data in red.
37
For carbon monoxide, the most stable sites were the h4, f2, f5, b12, and b19 sites
with binding energies of -1.53 eV, -1.54 eV, -1.57 eV, -1.54 eV, and -1.50eV. The bridge
sites were stabilized by their proximity to the step edge, allowing for an increase in
binding energy of approximately 0.4eV when compared to the remainder of the bridge
sites. As discussed in the Cu(111) section, The top sites are typically favored by CO
experimentally on flat surfaces [26]. On the flat Cu(111) surface, these sites were only
0.1eV less favorable when compared to the hollow sites. On the Cu(643) surface, the top
sites were anywhere from 0.1 eV to 0.8 eV less favorable.
1.00
Adsorption Energy (eV)
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
Carbon Monoxide + Oxygen
0.10
Interaction Energy
0.00
Figure 17: Adsorption energy and interaction energy of CO+O on Cu(643). Like Cu(211)
the configurations are defined by a name that combines the CO location first with the O
position second.
Eight different CO adsorption sites were chosen for possible dissociated states: b12,
b19, f2, f5, h1, h4, t1, and t5 . Due to the size of the unit cell, the selection of the oxygen
38
adsorption sites were chosen by selecting sites close to the CO adsorption site location to
ensure the dissociation move was an elementary step. This gave twenty-four possible
sites to consider, and after eliminating the ones that re-associated or were otherwise
unfavorable, we were left with seventeen dissociated configurations. Like the Cu(211)
surface, the naming convention of the labels combines the location of the CO with the
location of the O. Across the various sites considered the overall adsorption energy
ranged from 0.10 eV to 0.62 eV which is more favorable than the data from the Cu(211)
surface, which ranged from 0.22 eV to 1.72 eV.
The interaction energy between the CO and O ranged from 0.43 eV to 0.94 eV,
significantly higher than most of the Cu(211) results of 0.01 eV to 1.29 eV. The
interaction energy is the difference in energy between the isolated adsorbates and both
adsorbates in the same unit cell. A positive interaction energy value indicates that the
overall energy of the combined system is higher than the isolated cases, indicating the
presence of both mutually destabilize each other. Unlike the Cu(211) there appears to be
some correlation between interaction energy and adsorption energy with the dissociated
states chosen.
39
0.20
Adsorption Energy (eV)
0.10
0.00
b1
b4 b12 b19
f1
f2
f5
f8
t1
t5
t8
h1
h4
h7
h1a
-0.10
-0.20
-0.30
-0.40
-0.50
Figure 18: Adsorption energy of CO2 on Cu(643). The site was identified by where the
center of the CO2 molecule was located, with the molecular axis approximately
perpendicular to the plane of the step.
A clean trend like the one seen for carbon monoxide was not observed for CO2 on
Cu(211). Again, CO2 had a much larger binding distance ranging from 2.2 Å to 3.5 Å.
The molecules bound at a larger distance actually exhibit a more favorable adsorption
energy. The CO2 molecules favored adsorbing at a slight angle from parallel to the
terrace, perpendicular to the plane of the step. The f2, t8, and h1 sites all exhibited
unfavorable adsorption energies. These adsorption sites all had adsorption distances of
2.30 Å or less. The most favorable site for adsorption was the t5 site, with an adsorption
energy of -0.38 eV and an adsorption distance of 2.92 Å. A very close second is the b1
site, with an adsorption energy of -0.36 eV and an adsorption distance of 3.07 Å.
40
Table4: BEP analysis results for Cu(643). The transition state energy was calculated
using the universal BEP, Equation 5. The four systems chosen are highlighted in yellow.
Three were chosen due to the lowest predicated transition site energy, h4h3 was chosen
because of the more favorable final state. The cell color scheme assigns the smallest
values red and the larges values blue, the numbers in bold are for the systems where CO
does not move.
CO+O
b12b9
b19b16
b19h8
f2b9
f2h1
f2h3
f2h5
f5b16
f5b9
h1b16
h1h3
h4b9
h4h3
t1b9
t1f2
t1h3
t5b9
CO2 b1 b4 b12 b19 f1
f2
f5
f8
t1
t5
h1 h4 h7
-0.36 -0.32 -0.01 -0.01 -0.35 0.11 -0.35 -0.33 -0.30 -0.38 0.10 -0.24 -0.29
0.59 1.61 1.62 1.71 1.71 1.62 1.75 1.61 1.62 1.63 1.61 1.74 1.65 1.63
0.38 1.67 1.68 1.77 1.77 1.68 1.81 1.67 1.68 1.69 1.67 1.80 1.70 1.69
0.14 1.74 1.75 1.84 1.84 1.74 1.87 1.74 1.75 1.76 1.73 1.87 1.77 1.76
0.45 1.65 1.66 1.75 1.75 1.65 1.79 1.65 1.66 1.67 1.65 1.78 1.68 1.67
0.10 1.75 1.76 1.85 1.85 1.76 1.89 1.75 1.76 1.77 1.75 1.88 1.79 1.77
0.15 1.74 1.75 1.84 1.84 1.74 1.87 1.74 1.74 1.75 1.73 1.87 1.77 1.76
0.51 1.63 1.64 1.73 1.73 1.64 1.77 1.63 1.64 1.65 1.63 1.76 1.67 1.65
0.12 1.75 1.76 1.85 1.85 1.75 1.88 1.75 1.75 1.76 1.74 1.88 1.78 1.77
0.55 1.62 1.63 1.72 1.72 1.63 1.76 1.63 1.63 1.64 1.62 1.75 1.66 1.64
0.28 1.70 1.71 1.80 1.80 1.70 1.83 1.70 1.71 1.72 1.69 1.83 1.73 1.72
0.21 1.72 1.73 1.82 1.82 1.72 1.86 1.72 1.73 1.74 1.71 1.85 1.75 1.74
0.62 1.60 1.61 1.70 1.70 1.61 1.74 1.60 1.61 1.62 1.60 1.73 1.64 1.62
0.22 1.72 1.73 1.82 1.82 1.72 1.85 1.72 1.72 1.73 1.71 1.85 1.75 1.74
0.37 1.67 1.68 1.77 1.77 1.68 1.81 1.68 1.68 1.69 1.67 1.80 1.71 1.69
0.47 1.65 1.66 1.75 1.75 1.65 1.78 1.65 1.65 1.66 1.64 1.78 1.68 1.67
0.36 1.68 1.69 1.78 1.78 1.68 1.81 1.68 1.68 1.69 1.67 1.81 1.71 1.70
0.57 1.62 1.63 1.72 1.72 1.62 1.75 1.62 1.62 1.63 1.61 1.75 1.65 1.64
h1a
-0.23
1.65
1.71
1.77
1.69
1.79
1.77
1.67
1.78
1.66
1.73
1.76
1.64
1.75
1.71
1.68
1.71
1.65
A BEP analysis was conducted using the results from the CO2 and CO+O
adsorption calculations to determine which NEB calculations should be conducted. Once
all of the data for CO2 and CO+O were gathered, Equation 5 was used to predict the
transition state energies for all combinations of initial and final states. To keep the cNEB
calculations simple, the binding site for CO and CO2 are the same, with only the oxygen
atom moving. The results that meet this criterion are shown in bold in Table 4. The f5b9,
h4b9, and t5b9 systems were chosen because they have the lowest predicted transition
site energies where the CO does not move. Additionally, the h4h3 site was chosen as a
41
control using the same selection criteria that was used for the Cu(211) cNEB calculations
although it has a higher predicted transition site energy.
h4b9
t5b9
f5b9
h4h3
3
h4b9 neb
t5b9 neb
f5b9 neb
h4h3 neb
2.5
Energy (eV)
2
1.5
1
0.5
0
-0.5
-1
CO+
0
1
2
Image
3
42
CO
Figure 19: NEB results for CO2 dissociation on Cu(643). The dissociated state is at step 0
and CO2 is at step 4. The dashed lines are the single-point image approximations and the
solid lines are the cNEB results.
Three pathways were chosen from the BEP predictions and one pathway from the
criteria established for selecting the Cu(211) pathways for cNEB calculations. These are
the h4b9, t5b9, f5b9, and h4h3 paths. Again, stepwise calculations were performed to get
an estimate for the cNEB images. The results can be seen in Figure 19, the single-point
image approximations are shown as dashed lines for each of the four pathways. In these
initial calculations the peaks for the curves range from 1.50 eV for the f5b9 path, to 1.85
eV for the t5b9 path. These peaks may not be the actual transition state, since they are
only a guess and are limited to relaxing in the z-direction only.
42
The results for the full cNEB calculations are shown as solid lines in Figure 19.
The results for the h4b9 path followed the stepwise results fairly closely. One curiosity is
that the energy calculated for the first image is 0.4 eV lower than the stepwise result. This
is due to the fact that the cNEB calculations are able to relax in all three dimensions
allowing the image to settle into a more stable path. The transition state energy for the
h4b9 path is 1.76 eV, approximately 0.1 eV higher than the predicted transition site
energy for the BEP calculations. This pathway has the lowest transition site energy out of
the four considered on the Cu(643) surface. The f5b9 path also followed the stepwise
prediction fairly closely. It has a transition site energy of 1.83 eV, 0.2 eV greater than the
BEP prediction. The t5b9 pathway had a surprisingly high transition site energy. The
stepwise prediction for the t5b9 path was the highest of the four at 1.85 eV, however, the
cNEB results found a transition site energy of 2.48 eV. This value is higher than the
results on any of the other surfaces, and as a result, it is doubtful that this dissociation
path would be favored. The h4h3 pathway also had a fairly high transition site energy of
2.07 eV. Even though the dissociated state has a more favorable adsorption energy, the
transition site barrier is probably too high for this path to be followed. It is important to
note that while the h4b9 dissociation path is the most favorable path out of those
considered; only a small number of pathways have been considered. With using the BEP
analysis, we hope to have identified the most favorable dissociation pathways, however,
unless calculations are done for all possible dissociation paths, we cannot state that this
path is the best for the Cu(643) surface, only that it is the best out of the ones we
considered. Among the paths examined with cNEB, the lowest activation energy for CO2
dissociation was 2.01 eV for the h4b9 pathway.
43
CHAPTER 5: KINETIC MODEL
The previous results demonstrated that the transition site energy of the h4b9 pathway
on Cu(643) is the lowest out of all the dissociation pathways considered on all three
surfaces. While this is an interesting result, it would be more interesting to quantify the
rate of reaction and be able to directly compare the rates of reaction of different surfaces.
We consider the following reaction:
kads
CO 2 + *
kdiss
CO 2*
CO* + O*
(6)
kdes
The asterisk represents an adsorption site, where it is used as a superscript, it denotes and
adsorbed species. In this reaction, we assume that the carbon dioxide is free to adsorb and
desorb from the surface. We consider only the initial reaction of CO2 on the surface, so
we can assume that the coverage of CO* and O* are small. As a result, the implications
of nonzero coverage of these species on the overall reaction are not considered below.
The basic reaction rate can be formulated as:
=
:;<∗
∗
∗
= >%# ? ∗ − >% # ?
− >%## ? ∗ ?
@
@
:=
(7)
where θ is the coverage, either vacant site or CO2, and kads, kdes, and kdiss are the rate
constants of adsorption, desorption and dissociation, respectively. With the assumptions
described above, then CO2 coverage is defined as:
∗
?
= (1 − ? ∗ )
@
44
(8)
Substituting this assumption into Equation (7) gives:
=
:;<∗
= >%# ? ∗ − >% # (1 − ? ∗ ) − >%## ? ∗ (1 − ? ∗ )
:=
(9)
Assuming steady state:
:;<∗
= >%# ? ∗ − >% # (1 − ? ∗ ) − >%## ? ∗ (1 − ? ∗ ) = 0
:=
(10)
Now the rate constants must be defined. The adsorption rate is defined as,
>%# =
C∗D
E2F>$ G
∗H
(11)
where P is pressure, S is a sticking constant (assumed to be 1), m is the mass of the
adsorbed molecule, kb is the Boltzmann constant, T is temperature, and L is the number of
unit sites per square meter of surface [29]. The desorption rate follows Arrhenius kinetics
[29], defined as,
>%
#
−
= I ∗ JKL M
N
>$ G
(12)
where I ≅ 10P Q R. This is a fairly common assumption that is independent of surface
structure. Ea is the activation energy. Finally the dissociation rate also follows Arrhenius
kinetics [29],
−
>%## = I ∗ JKL M
N
>$ G
(13)
In the case of dissociation, the value of A is different for each path on the surface. The
value of the prefactor was found using transition state theory,
45
I=
∑! T76,
∑!R U#
(14)
where n is the number of vibrational modes for adsorbed CO2 and ν is the vibrational
frequency. Because the transition site is a saddle point there is one fewer real vibrational
modes. Using this method gives a more accurate result than assuming a dissociation
prefactor of I ≅ 10 Q R [13]. The corrected values are 9.86x1011 s-1, 3.05x1011 s-1, and
8.93x1011 s-1 for Cu(111), Cu(211) and Cu(643) respectively. The vibrational frequencies
for the initial state and the transition state were all calculated using DFT. The harmonic
oscillator approximation was used to determine the vibrational frequencies. The
optimized adsorbate structure on the relaxed surface was displaced in a series of static
calculations by 0.01 Å – 0.1 Å from the equilibrium position. The data can then be
plotted as a parabola of vibrational frequency vs displacement and the calculated
vibrational frequency is found at the minima.
Compared to >% # VW:>%# , >%## is very small. As a result we can make the
assumption that the contribution associated with >%## . In Eq. (10) is negligible.
Applying this assumption gives:
:;<∗
= >%# ? ∗ − >% # (1 − ? ∗ ) = 0
:=
(15)
Rearranging Equation (15) results in,
Solving explicitly for ? ∗:
>% #
?∗
=X=
(1 − ? ∗ )
>%#
46
(16)
∗
And solving for ?
yields,
@
?∗ =
X
1+X
∗
?
= (1 − ? ∗ ) =
@
(17)
1
1+X
(18)
If we assume that CO2 dissociation on the surface is an elementary reaction then for first
order kinetics the overall rate of dissociation for CO2 on crystalline copper is:
∗
%## = >%## ? ∗ ?
=
@
X ∗ >%##
(1 + X)
(19)
Now it is useful to consider the limiting behaviors of this expression. As the value
of K increases, the vacant site coverage goes to 1, i.e. there is no CO2 on the surface. As a
result the dissociation rate goes to zero since there is nothing on the surface to dissociate.
As pressure is increased, the value of K decreases. As K gets smaller, the denominator of
Equation (17) approaches 1, and ? ∗ = X. In this case, the dissociation rate also goes to
zero because the surface is completely covered in CO2 and too sterically hindered for
dissociation to take place. This approach is somewhat simplistic since it assumes all sites
on the surface are the same, and they are the most favored site, however it gives some
idea of the relative dissociation rates of the various surfaces. We have assumes that all
three sites have the same site density for this analysis.
47
3.5E+18
Dissociation rate (m-2s-1)
3E+18
2.5E+18
920 K
900 K
2E+18
880 K
860 K
1.5E+18
840 K
1E+18
820 K
800 K
5E+17
0
0.0001
0.001
0.01
0.1
1
10
100
Pressure (Pa)
Figure 20: Dissociation rate for the t1h3 pathway on Cu(211) in m-2 s-1 as a function of
pressure over 920-800 K using the NEB results.
The magnitudes of the peaks in Figure 20 are a result of the Arrhenius
contribution to the desorption term continually increasing with increasing temperature.
When the pressure is too low there is very little CO2 coverage on the surface, resulting in
a small dissociation rate. For these temperatures, the pressure is about 0.001 Pa. When
the pressure is high the surface is sterically hindered by too much CO2 adsorption and the
dissociation cannot occur. As the temperature is increased this value shifts to the right.
The pressure at which this occurs ranges from 0.5 Pa for 800K to 20 Pa for 920 K.
48
7.E+10
6.E+10
530 K
Dissociation rate (m-2s-1)
525 K
5.E+10
520 K
515 K
4.E+10
510 K
505 K
3.E+10
500 K
2.E+10
495 K
490 K
1.E+10
0.E+00
1.E-12
485 K
480 K
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
Pressure (Pa)
Figure 21: Dissociation rate for the t1h3 pathway on Cu(211) in m-2 s-1 as a function of
pressure over 530-480 K using the NEB results.
When the temperature is reduced by 400 K the pressure the pressure range over
which the reaction occurs shifts from ~0.01 Pa to ~10-9 Pa. As would be expected the
dissociation rate also drops considerably at lower temperatures. This reveals that there is
a region of reactivity that increases rapidly in pressure as temperature is increased. This
relationship between reactivity and temperature is a result of the exponential term in the
Arrhenius contributions of desorption and dissociation.
In order to assess the physical relevance of this model we corrected the CO2
adsorption energy using experimental data from Rasmussen and coworkers [30]. Because
DFT does a poor job of accounting for dispersion effects a correction is necessary to
achieve more physically accurate calculation results. Rasmussen et al. used temperature-
49
programmed desorption (TPD) to find the binding energy of CO2 on Cu(100) of 25-30 kJ
mol-1 (approximately 0.29 eV). Cu(100) is not a surface that has been considered in this
work, however it gives us a good estimate of adsorption energy on copper. We corrected
for dispersion interactions by assuming that the Cu(100) and the three Cu surfaces we
examined have approximately the same contribution to adsorption energy of CO2 from
dispersion. Moreover, we assume that the dispersion correct for coadsorbed CO+O is the
same as for CO2. With this assumption, the minimum energy paths computed with DFT
as described above are shifted uniformly by 0.29 eV. This correction leaves the
dissociation activation energies unchanged, but alters the adsorption/desorption
equilibrium.
1.E+08
1.E+08
530 K
525 K
520 K
515 K
510 K
505 K
500 K
495 K
490 K
485 K
480 K
Dissociation rate (m-2s-1)
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
1E-14
1E-13
1E-12
1E-11
Pressure (Pa)
1E-10
1E-09
1E-08
Figure 22: Dissociation rate for the t1h3 pathway on Cu(211) in m-2 s-1 as a function of
pressure over 530-480 K using the experimentally corrected results.
50
Implementing the experimental correction shifts the pressure peak for 530 K from
approximately 10-9 Pa to approximately 10-11 Pa. The reaction rate decreases
significantly, from 6.0x1010 m-2 s-1 to 1x108 m-2 s-1 at 530 K. Because the adsorption
energy value is more favorable using this correction the pressure term contributes less to
the value of K. Since K is larger, the lower limit of → 0asX → ∞ is achieved slightly
faster, shifting the peak left. The upper limit shifts by approximately the same amount.
6.E+06
530 K
525 K
520 K
515 K
510 K
505 K
500 K
495 K
490 K
485 K
480 K
5.E+06
Dissociation rate (m-2s-1)
4.E+06
3.E+06
2.E+06
1.E+06
0.E+00
1E-14
1E-13
1E-12
1E-11
Pressure (Pa)
1E-10
1E-09
1E-08
Figure 23: Dissociation rate for Cu(111) in m-2 s-1 as a function of pressure over 530-480
K using the experimentally corrected results.
The dissociation rate on the Cu(111) surface is significantly smaller than the rate
on Cu(211). The corrected data, rather than the data from cNEB, was used because the
correction used applies a systematic shift of the peak location and no further information
51
is gained from comparing the non-corrected data for the two surfaces. The rate was
reduced by approximately 1.5 orders of magnitude between the two surfaces for 530 K.
The reduction in dissociation rate is to be expected since the activation energy of the
Cu(111) surface is higher than the Cu(211) surface and the adsorption energy of CO2 on
Cu(111) is 0.2 eV smaller. The peak pressure for 530 K is at approximately 10-11 Pa, the
same pressure as Cu(211). The peaks for Cu(211) and Cu(111) are very similar, the
Cu(111) data are just shifted to a smaller magnitude.
6.00E+07
530 K
525 K
520 K
515 K
510 K
505 K
500 K
495 K
490 K
485 K
480 K
Dissociation rate (m-2s-1)
5.00E+07
4.00E+07
3.00E+07
2.00E+07
1.00E+07
0.00E+00
1.E-13
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
Pressure (Pa)
Figure 24: Dissociation rate for the h4b9 pathway on Cu(643) in m-2 s-1 as a function of
pressure over 530-480 K using the experimentally corrected results.
The peak pressure of 10-10 Pa for Cu(643) is about an order of magnitude greater
than the results for Cu(211) or Cu(111). The peak shape mimics the Cu(211) peaks very
52
closely. The rate at 530 K is approximately half the rate for Cu(211). This indicates that
there is a difference between the stepped and kinked surface, and having a kink does not
necessarily increase the rate of dissociation. This reduction in rate is due to the higher
activation energy on the Cu(643) surface. Although the transition site energy is smallest
for Cu(643), because the adsorption energy is much more favorable than Cu(211), the
activation energy is actually larger for Cu(643) than it is for Cu(211). The result is a
smaller dissociation rate for the h4b9 pathway than expected.
Peak Dissociation rate (m-2s-1)
1.2E+08
Cu(111)
1.0E+08
Cu(211)
8.0E+07
Cu(643)
6.0E+07
4.0E+07
2.0E+07
0.0E+00
480
490
500
510
520
530
Temperature (K)
Figure 25: Peak dissociation rate for Cu(111), blue, Cu(211), red, and Cu(643), green in
m-2 s-1 as a function of pressure over 480 - 530 K using the experimentally corrected
results.
For high temperature the peak dissociation rate is approximately the same for both
the Cu(211) surface and the Cu(643) surface at 920 K. As the temperature decreases the
ratio of peak rates becomes more significant. At 530 K the peak reaction rate is 1.87
53
times greater for the t1h3 pathway on the Cu(211) surface than the h4b9 pathway on the
Cu(643) surface. Once the temperature is down to 480 K the peak reaction rate is 2.22
times greater on Cu(211). This means, for our calculations, the presence of a kink
actually makes the dissociation less probable at experimental temperatures. Due to the
surface geometry of Cu(643), the t1h3 pathway calculated on Cu(211) exists on the
Cu(643) surface, so there are paths on the Cu(643) surface that are as favorable as the
stepped Cu(211) surface. These results demonstrate the kink may actually hinder the
dissociation, or the path between site t5 and site b9 on the Cu(643) surface chosen was
not the lowest energy pathway between the two sites.
The Cu(643) surface is 3.2 times more reactive at 920 K than Cu(111) and
Cu(211) is 2.9 times more reactive. At 480 K Cu(643) is 9.3 times more reactive, but
Cu(211) is 20.6 times more reactive than Cu(111). This indicates that there is little gained
benefit between the stepped and kinked surfaces and the results for a much simpler step
edge calculation can be used to predict the results for both stepped and kinked surfaces
with a decent level of accuracy.
54
CHAPTER 6: CONCLUSIONS
In this work we theoretically examined three crystalline copper surfaces using
DFT. The purpose of these calculations was to identify which surface geometry was most
conducive to spontaneous CO2 dissociation. This was done by first identifying physically
correct reference states. Second, favorable adsorption sites for each of the three
adsorbates, CO, CO2, and O were identified. Third, cNEB calculations were performed to
identify the transition state energy. Finally, a simple kinetic model was used to compute
the dissociation rate for each of the three surfaces.
We evaluated the possible reference states of oxygen using the work of Xu et al.
as a reference [18]. It was found that spin polarization was necessary for calculations
involving oxygen to accurately predict adsorption energies. Without these corrections,
adsorption results varied significantly, yielding good results for one surface, or adsorbate,
but not the others. Once the most physically appropriate reference state for oxygen was
identified, calculations for CO and CO2 were performed. CO and CO2 did not need the
spin correction. Since the calculations involving CO and CO2 were compared internally,
the reference state was only required to be self-consistent across all calculations.
Next, we systematically probed the three surfaces for favorable adsorption sites.
Cu(111), having such a small unit cell, had only one viable dissociated state, with O
adsorbed in the fcc hollow site and the CO adsorbed in the top site. For the Cu(211),
there were fourteen possible adsorption sites. Four favorable CO adsorption sites and six
favorable O adsorption sites were identified via single adsorbate energy minimization
calculations. After calculating the associated adsorption and interaction energies of the
55
twenty-four possible combinations, three dissociated states were identified as candidates
for cNEB. The adsorption energies of CO2 at these locations was also taken into account.
To have an elementary reaction, it was assumed that the dissociated O was the only
product to move to a different adsorption site. The final surface examines was Cu(643).
Because of the kink in the Cu(643) surface, a much larger unit cell with fifty-three unique
adsorption sites. All of these sites were evaluated for CO, CO2, and O adsorption. With
the addition of BEP analysis confirmed with the Cu(211) results, four possible
dissociated states were identified.
The third step was to perform cNEB calculations for the identified dissociation
pathways on the three surfaces. An activation energy of 2.10 eV was calculated for the
Cu(111) surface. On Cu(211) three possible dissociated states were considered: t1h3,
h1h5, and t1b4. These have an activation energy of 1.92 eV, 1.96 eV, and 2.04 eV. Based
on these results, the t1h3 dissociated state was selected as the most probable, even though
the results for all three are extremely close. BEP analysis was performed to identify
whether there were more favorable dissociation pathways, but the only one identified as
significantly better, t1t3, had already been eliminated due to instability. The BEP analysis
was used to select dissociated states on Cu(643). From this analysis, three states were
chosen for cNEB. F5b9, h4b9, and t5b9 were all identified as favorable candidates. H4h3
was also chosen as a possibility using the criteria used for Cu(211). H4b9 had the lowest
activation energy at 2.01 eV. The activation energy was higher than expected when
compared to Cu(211), however this was due to the much more stable CO2 adsorption on
Cu(643). Interestingly, the presence of the step did not have a significant effect on the
56
activation energy. There is only a 0.2 eV difference between the activation energy of
Cu(111) and Cu(211).
Finally, these cNEB results were used to construct a simple kinetic model to
compare the relative reactivities of the three surfaces. An elementary, first order reaction
was chosen to describe the dissociation. This method assumed that all sites on the surface
had the activation energy of the most favorable site identified in the NEB calculations
and all three surfaces had the same site density. The dissociation rate had an upper
pressure bound, where at high enough pressure there is total CO2 coverage covering the
sites necessary for dissociation, and a lower bound, where there were no CO2 molecules
adsorbed to the surface. Comparing these results directly, we found that the stepped
Cu(211) surface exhibited more favorable reaction rates. Although the Cu(643) surface
bound CO2 more strongly, the transition state energy was about the same as the Cu(211)
surface, resulting in a higher activation energy.
Because DFT does not accurately account for dispersion forces, an experimental
correction term of 0.29 eV was applied to the CO2 adsorption energies on all three
surfaces. This correction alters the absolute reaction rate predicted at any chosen set of
conditions, but it does not change our overall conclusions about the relative reactivity of
the surfaces. We assumed that the correction would be approximately the same for all
surfaces. This correction systematically shifted all peak adsorption rates down by
anywhere from one to four orders of magnitude, depending on the temperature.
When comparing the surfaces directly, the t1h3 path on Cu(211) was the most
favorable dissociation pathway at experimentally relevant temperatures. This was due to
57
the similar transition state energies between Cu(643) and Cu(211), both being 1.83 eV for
the chosen dissociation paths. The CO2 adsorption energy was much more favorable on
Cu(643) and as a result the activation energy was higher. As a result the kink does not
appear to facilitate a more probable dissociation. From these results, the dissociation rate
for a stepped and kinked surface could be determined through analysis of the step alone,
which is computationally much cheaper. Furthermore, the step does not provide a
significantly easier dissociation path for CO2. We expected the activation energy to be
substantially lower for the stepped surface; however this was not the case
It is important to reiterate that there may be a more favorable pathway on any of
these surfaces that was not considered in this work. The BEP analysis was used to
mitigate this possibility. All of the other possible pathways had very similar predicted
transition state energies within approximately 0.1 eV. Even with this additional analysis,
there may be other dissociation paths that are more favorable which can only be ruled out
by performing a cNEB calculation on every possible pathway. The computational cost to
do this is prohibitively expensive. Further work is necessary to identify if the kink is less
favorable on other transition metal surfaces. Physical experiments are needed to verify
the accuracy of these claims.
58
REFERENCES
[1] Y. Hori, K. Kikuchi, S. Suzuki, Chemistry Letters 14 (11) (1985) 1695.
[2] Y. Hori, K. Kikuchi, S. Suzuki, Chemistry Letters 15 (6) (1986) 897.
[3] S.S. Fu, G.A. Somorjai, surf. Sci. 262 (1992) 68, 76.
[4] T Schneider, W Hirschwald, Catal. Lett. 16 (1992) 459, 460.
[5] Nakamura, J.; Rodriguez, J. A.; Campbell, C. T. Journal of Physics: Condensed
Matter 1989, 1, SB149-SB160.
[6] Fu, S. S.; Somorjai, G. A. Surface Science 262 1992, 68-76.
[7] Copperthwaite et al. Catalysis Letters 11-20, 1, 1988.
[8] Ernst et al. 1992, 134, 66-74
[9] Bonicke, I.; Kirstein, W.; Thieme, F. Surface Science 1994, 307-309, 177-181.
[10] Krause et al. Surface Science 1996, 347, 1-10.
[11] Taylor, P. A.; Rasmussen, P. B.; Chorkendorff, I. Journal of Vacuum Science and
Technology A 1992, 2570-2575.
[12] Chorkendorff et al. Surface Science 1993, 287/288, 208-211.
[13] Sholl, David S., and Janice A. Steckel. Density Functional Theory: A Practical
Introduction. Hoboken, NJ: Wiley, 2009. Print
[14] R.W.G. Wyckoff, in: Crystal Structures, vol 1, Wiley, New York 1963.
[15] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.
[16] G. Henkelman, B. P. Uberuaga, and H. Jonsson. J. Chem. Phys. 113 (2000) 9901.
[17] S. Wang et al. Catal. Lettl (2011) 141:370-373.
[18] Y. Xu, M. Mavrikakis, Surf. Sci. 538 (2003) 219-232.
[19] P. J. Feibelman et al. J. Phys. Chem. B.105 (18) (2001) 4018.
[20] A. Spitzer, H. Luth, Surf. Sci. 118 (1982) 136.
59
[21] K. Prabhakaran, P. Sen, C.N.R. Rao, Surf. Sci. 177 (1986) L971.
[22] M.K. Rajumon, K. Prabhakaran, C.N.R. Rao, Surf. Sci. 365 (1996) 310.
[23] J. Haase, H.J. Huhr, Surf. Sci. 203 (1988) L695.
[24] H. Niehus, Surf. Sci. 119 (192) 399.
[25] F.H.P.M. Habraken, E.P. Kieffer, G.A. Bootsma, Surf. Sci. 83 (1979) 45.
[26] C.J. Zhang et al. J. Chem. Phys. 115 (11) (2001) 5272.
[27] B. Hammer, Y. Morikawa, and J.K. Norskov, Phys. Rev. Lett. 76 (1996) 2141.
[28] S. Ishi, Y. Ohno, B. Viswannathan, Surf. Sci. 162 (1985) 349.
[29] Vannice, M. Albert. Kinetics of Catalytic Reactions. New York: Springer, 2005.
Print
[30] P.B. Rasmussen, P.A. Taylor and I. Chorkendorff. Surf. Sci. 269 (1992) 352.
[31] P.A. Redhead, Vacuum 12, 203 (1963)
60