AND KINKED COPPER SURFACES USING FIRST PRINCIPLES CALCULATIONS

Transcription

1 IDENTIFYING CO 2 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

2 Identifying CO 2 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

3 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

4 TABLE OF CONTENTS ACKNOWLEDGEMENTS... iii LIST OF TABLES... v LIST OF FIGURES... vi SUMMARY... ix CHAPTER 1: INTRODUCTION... 1 CHAPTER 2: OVERVIEW Introduction Brief introduction to DFT... 8 CHAPTER 3: METHODS CHAPTER 4: DFT RESULTS Identifying Reference states Evaluation of CO 2 dissociation on Cu(111) Evaluation of CO 2 dissociation on Cu(211) Evaluation of CO 2 dissociation on Cu(643) CHAPTER 5: KINETIC MODEL CHAPTER 6: CONCLUSIONS REFERENCES iv

5 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

6 LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 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. Adsorption distance comparison between this work and published results from Xu et al. for oxygen on the Cu(111) surface. Adsorption distance comparison between this work and published results from Xu et al. for molecular oxygen on the Cu(211) surface. Adsorption energy comparison between this work and published results from Xu et al. for molecular oxygen on Cu(211). Results for a three-image cneb calculation for CO 2 dissociation on the Cu(111) surface. Carbon monoxide adsorption energy on Cu(211) Figure 11 Adsorption energy and interaction energy of CO+O on Cu(211). 30 Figure 12 Adsorption energy of CO 2 on Cu(211). 32 Figure 13 Figure 14 Figure 15 NEB results for CO 2 dissociation on Cu(211). The dashed lines are the singlepoint image approximations and the solid lines are the cneb results. BEP analysis of NEB results using the Universal BEP equation developed by Wang and coworkers. Adsorption energy of atomic oxygen on Cu(643) vi

7 Figure 16 Adsorption energy of CO on Cu(643). 37 Figure 17 Adsorption energy and interaction energy of CO+O on Cu(643). 38 Figure 18 Adsorption energy of CO 2 on Cu(643). 40 Figure 19 NEB results for CO 2 dissociation on Cu(643). 42 Figure 20 Figure 21 Figure 22 Dissociation rate for the t1h3 pathway on Cu(211) in m -2 s -1 as a function of pressure over K using the NEB results Dissociation rate for the t1h3 pathway on Cu(211) in m -2 s -1 as a function of pressure over K using the NEB results. Dissociation rate for the t1h3 pathway on Cu(211) in m -2 s -1 as a function of pressure over K using the experimentally corrected results Figure 23 Dissociation rate for Cu(111) in m -2 s -1 as a function of pressure over K using the experimentally corrected results. 51 Figure 24 Figure 25 Dissociation rate for the h4b9 pathway on Cu(643) in m-2 s-1 as a function of pressure over K using the experimentally corrected results. 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 K using the experimentally corrected results vii

8 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

9 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 CO 2 dissociation most readily. ix

10 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 CO 2 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. CO 2 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 CO 2, 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, CO 2 will be abundant and cheap, with easy to access local sources globally. CO 2 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 C 1 feedstock for low molecular weight alkanes and alkenes. CO 2 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 CO 2 on Cu(110) under UHV conditions [5]. Significant production costs 1

11 can be saved if the potential required for the electrocatalysis can be minimized or eliminated entirely. At high pressures, dissociation of CO 2 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 CO 2 [5]. These results are supported by equilibrium considerations based on a knowledge of the kinetics of the reverse reaction (CO a + O a CO 2,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 (O a ) intermediate. The results also show that CO 2 /CO pressure ratios greater than 100 are required to generate significant concentrations of O a 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-CO 2 dissociation than Cu(110) [6]. Cu(311) faces adsorb CO 2, and D 2, at low pressures (< 10-6 Torr). As a point of comparison, there is no interaction on Cu(110) with either CO 2 or D 2 under low pressures and temperatures (< 10-6 Torr and 150 K) [6]. Additionally, oxygen reacted with a CO/H 2 atmosphere two to five times faster from the Cu(311) surface than from the low Miller index faces [6]. Experimental results indicate that CO 2 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 CO 2 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 CO 2 on the Cu(110)/K surface at a coverage of

12 monolayer (ML) at temperatures of 130 to 140 K leads to two different CO 2 surface species. The first is a highly reactive, bent CO 2 species, which is formed already at low exposures. The second is a weakly bonded, inactive, linear CO 2 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 CO 2 [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-co 2 interaction[10]. On a different low index Miller surface, Cu(100), molecularly adsorbed CO 2 lies parallel to the Cu(100) surface and closely resembles gas phase CO 2.[11] The presence of oxygen on the Cu ( 100) surface does not greatly alter the nature of molecularly adsorbed CO 2. [11] On clean Cu(100), CO 2 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 CO 2 on clean Cu(100) shows only the symmetric bending mode of linear CO 2 [12] indicating that chemisorption has not occurred, as the surface would hinder the possible bending angle and produce asymmetry. 3

13 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

14 FCC HCP Bridge Top 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

15 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 CO 2 adsorption on Cu(211) to evaluate methodology and compare results. B5 B4 B3 B2 B1 H5 F4 T2 H1 F0 T3 H3 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

16 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. T4 B9 B23 B22 B21 B20 B19 F10 F9 F8 T10 B18 T9 B17 T8 H9 H8 H7 B16 B15 B14 B13 B12 F7 F6 F5 T7 B11 T6 B10 T5 H6 H5 H4 B8 B7 B6 B5 B4 F4 F3 F2 F1 B3 T3 B2 T2 B1 T1 H3 H2 H1 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

17 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 Born- Oppenheimer 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

18 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

19 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

20 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

21 A B C 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 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 k B T=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

22 work and very close to the experimental value of 1.21 Å [15]. CO 2 has a bond energy of ev. Binding energies were determined by: = ( ) (2) where is the total energy of the surface plus the adsorbed species, is the energy of the relaxed surface without any adsorbate in the system, and ( ) 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

23 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 CO 2 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 CO 2 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 CO 2 ). 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

24 = / (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 = + (5) The variables and 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

25 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

26 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-b-t t-f-b b-h-b t-h-b Figure 5: Possible di-σ sites parallel to the surface for adsorption of O 2 on Cu(111). For brevity the names are shortened to their first letter, i.e. top-bridge-top is abbreviated as t- b-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

27 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) Fcc (ev) Xu et al. [18] With spin Without spin atomic spin Molecular Oxygen Site t-b-t (ev) t-f-b (ev) Xu et al. [18] With spin Without spin 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

28 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 Angstrom Z Calculated Z Paper D Calculated D Paper 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

29 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

30 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) h3 (ev) Xu et al. [18] This work Edge of Step Site t-b-t (ev) T-f-b (ev) Xu et al. [18] This work Foot of Step Site t-b-t (ev) t-f-b (ev) Xu et al. [18] This work 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

31 2.5 2 Angstrom Z Calculated: Molecular Z Paper: Molecular D Calculated: Molecular D Paper: Molecular 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

32 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 t-b-t t-h-b t-f-b b-h-b b-f-b Calculated: Molecular step-edge Paper: Molecular step-edge E b (ev) 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

33 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 CO 2 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 CO 2 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 CO 2 dissociation on Cu(111) with DFT using the PW91-GGA functional and compared the results to Pt(111) and Cu 3 Pt(111). They were 24

34 looking to create a catalyst with properties similar to pure platinum, but significantly cheaper. The solution they identified was to use an alloy of Cu 3 Pt 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 ev, versus the value of pure copper, 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, ev, and platinum, ev, with a value of 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 Pt 3 Cu and found them to be ev and 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

35 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 ev higher than the reported top-site value, but an exact result was not reported. Site This Work (ev) Zhang [26] (ev) Literature Experimental [28] (ev) Hammer [27](eV) hcp N/A N/A N/A fcc N/A N/A N/A bridge N/A N/A N/A top 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 CO 2 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 CO 2 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 CO 2 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

36 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 O 2.For the previous results for CO and O on the surface individually, the reference state was CO and atomic oxygen value respectively. 2.5 Energy (ev) higher res NEB HR CO+O CO4 2 Images Figure 9: Results for a three-image cneb calculation for CO 2 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 CO 2 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

37 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 CO 2. 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

38 0 f0 h1 f2 h3 f4 h5 t1 t2 t3 b1 b2 b3 b4 b5-0.2 Adsorption Energy (ev) 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 ev. The b4 site energy is close to h1 and b4 with an adsorption energy of 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 ev. Furthermore, the top site on the Cu(111) surface had an adsorption energy of ev, which is close to the t2 and t3 values of ev and ev 29

39 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 =, +,, +, where E T 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. E S is the energy of the clean slab. 2 Energy (ev) Eb Interaction Energy 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

40 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 CO 2, the combination of sites was eliminated from consideration. This left the thirteen sites shown in Figure 11. The reference state for the system was CO 2 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 CO 2. 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 CO 2 would settle into this configuration. For other states with more favorable energies, the transition state energies between the CO 2 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