The Pennsylvania State University

The Graduate School

Department of Mechanical and Nuclear Engineering

PREDICTING STABILITY OF MODIFIED OXIDE SURFACES WITH FUNCTIONAL

ATOMIC-LAYERS FOR NANO-ENGINEERED CATALYSTS THROUGH FIRST

PRINCIPLES CALCULATIONS AND STATISTICAL LEARNING

A Dissertation in

Mechanical Engineering

by

A S M Jonayat

 2018 A S M Jonayat

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2018

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The dissertation of A S M Jonayat was reviewed and approved* by the following:

Adri C.T. van Duin Professor of the Department of Mechanical and Nuclear Engineering Dissertation Advisor Chair of Committee

Michael J. Janik Professor of the Department of Chemical Engineering Dissertation Co-adviser

Richard Yetter Professor of the Department of Mechanical and Nuclear Engineering

Lasse Jensen Professor of the Department of Chemistry

Karen A. Thole Professor of the Department of Mechanical and Nuclear Engineering Head of the Department of Mechanical and Nuclear Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

Multicomponent metal oxides (MMOs) are of significant interest because of their tunable catalytic properties. They can form different structures – core shell particles, coatings on substrate, or bulk mixtures. Two specific types of MMOs – monolayer metal oxides and surface confined mixed metal oxides - are the focus of this work.

Despite the growing interest in MMOs, our understanding of their stability to date has been limited; only a few experiments have been undertaken of such systems. To date, discovery of these systems has mainly been through empirical procedures. The large number of possible combination makes it very difficult to discover stable MMOs and systems of interest may be

metastable, making experimental discovery more difficult.

In this dissertation, Density Functional Theory was used along with ab initio

thermodynamics to find possible descriptors of (meta)stable monolayer metal oxides and surface

confined mixed oxides. A thermodynamic framework is developed to predict phase diagrams of

monolayer metal oxide stability with respect to oxide particles of different sizes and pressures- temperatures. Finally, we show that statistical and Machine Learning algorithms can be useful to not only predict, but also discover underlying physical rules that dictate the stability of the monolayer coating/oxide support combinations.

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TABLE OF CONTENTS

List of Figures………………………………………………………………………vii

List of Tables……………………………………………………………………….xi

Acknowledgements…………………………………………………………………xii

Chapter 1 Introduction ...... 1

1.1 Background ...... 2 1.2 Research Questions and Hypotheses ...... 6 1.3 Computational Methods ...... 8 1.3.1 Density Functional Theory (DFT) ...... 8 1.3.2 Ab initio thermodynamics ...... 9 1.3.3 Shrinkage Method, LASSO+lo ...... 11 1.4 Summary of Chapters ...... 12 1.5 References ...... 12

Chapter 2 A first-principles study of stability of surface confined mixed metal oxides with a corundum structure (Fe2O3, Cr2O3, V2O3) ...... 16

2.1 Introduction ...... 16 2.2 Method ...... 18 2.2.1. Bulk Structures ...... 20 2.2.2 The (0001) Surface of (TM)2O3 Corundum Oxides ...... 23 2.2.3 Reducibility of the Fe/V2O3 (0001) Surface ...... 24 2.2.4. Pure Oxide Surface Energy ...... 25 2.2.5. Stable Structures of Surface-confined Mixed TM Oxides ...... 27 2.3. Results and Discussion ...... 29 2.3.1 Bulk Structures ...... 29 2.3.2. Predicted Surface Segregation from Pure Oxide Surface Energies ...... 29 2.3.3. Reducibility of the Fe/V2O3 (0001) Surface ...... 31 2.3.4. Surface/Subsurface Segregation of Substituted TM2 in (TM1)2O3 (0001) .... 32 2.4. Conclusions ...... 37 2.5 Acknowledgements ...... 38 2.6 References ...... 38 Supplementary information ...... 42

Chapter 3 Predicting monolayer oxide stability over low-index surfaces of TiO2 polymorphs using ab initio thermodynamics ...... 55

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3.1 Introduction ...... 55 3.2 Computational methods ...... 57 3.2.1 Electronic structure calculations ...... 57 3.2.2 Surface energy for TiO2 supports ...... 58 3.2.3 Monolayer oxide formation energy: ...... 58 3.2.4 Correction for particle reference: ...... 59 3.2.5 Bulk structures...... 60 3.2.6 Surfaces ...... 61 3.3 Results ...... 65 3.3.1 Surface energies of bare surfaces ...... 65 3.3.2 Monolayer formation energy ...... 65 3.3.3 Decomposition of monolayer formation energy ...... 66 3.4 Discussion ...... 70 3.4.1 Stoichiometric coating oxides (MO2) ...... 71 3.4.2 Coating oxides with +3 reference state (M2O3/M3O4) ...... 72 3.4.3 Coating oxides with +2 reference state (MO) ...... 72 3.4.4 Metal reference state (M) ...... 73 3.4.5 Temperature and pressure effect ...... 73 3.4.6 Particle reference: ...... 74 3.5 Conclusions ...... 76 3.6 Acknowledgements ...... 77 3.7 References ...... 77 Supporting information ...... 81

Chapter 4 An ab initio thermodynamic investigation of monolayer stability of multi- component metal oxides: MxOy/ZnO (0001) and MxOy/TiO2 (110) (M=Pd, Ru, Ni, Pt, Au, Zn) ...... 86

4.1 Introduction ...... 86 4.2 Methods ...... 89 4.2.1 Thermodynamic Model for Testing Monolayer Stability ...... 89 4.2.2 Electronic Structure Calculation Method and Structural Models ...... 92 4.3 Results and Discussions ...... 98 4.3.1 Reference Particle Energy ...... 98 4.3.2 ZnO (0001) Substrate ...... 100 4.3. Rutile TiO2 (110) Substrate ...... 106 4.3.3.1 Monolayer Stability ...... 106 4.4 Conclusions ...... 110 4.5 Acknowledgements ...... 110 4.6 References ...... 111 Supplementary information ...... 115

Chapter 5 Interaction trends between single metal atoms and oxide supports identified with density functional theory and statistical learning ...... 120

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5.1 Introduction ...... 120 5.2 Results ...... 122 5.2.1 Trends in Strong Metal-Support Adsorption Energies ...... 122 5.2.2 Electronic Structure Analysis ...... 129 5.3 Physical Descriptors for the Prediction of Binding Energy ...... 133 5.3.1 Feature Space ...... 134 5.3.2 LASSO+lo Analysis ...... 136 5.4 Conclusions ...... 141 5.5 Methods ...... 141 5.5.1 DFT specifications ...... 141 5.5.2 Calculation of adsorption energies and correlation parameters ...... 143 5.6 Acknowledgement ...... 144 5.7 References ...... 144 Supplementary information ...... 148

Chapter 6 Discovery of descriptors for stable monolayer oxide coatings through machine learning...... 163

6.1 Introduction ...... 163 6.2 MMO Computational Model ...... 166 6.2.1 Electronic structure calculations ...... 166 6.2.2 Descriptor/Feature Space ...... 170 6.2.3 Shrinkage Method/Feature Selection (LASSO+lo) ...... 175 6.3 Results and Discussion ...... 176 6.3.1 LASSO+lo analysis ...... 176 6.3.2 Validation ...... 182 6.3.3 Sensitivity Analysis ...... 183 6.4 Conclusions ...... 185 6.5 Acknowledgements ...... 186 6.6 References ...... 186 Supplementary Information ...... 191

Chapter 7 Conclusions and recommendations for future work ...... 197

7.1 Summary of conclusions ...... 197 7.2 Future work ...... 199 7.3 References ...... 202

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LIST OF FIGURES

Figure 1-1. Some possible types of MMOs. M1 and M2 represent metal atom of support and coating, respectively. (a) Supported M2 or M1xOy species (b) M2 or M2xOy species at edges/defects (c) Monolayer M2xOy on M1xOy (d) Substituted or “doped” .... 3

Figure 2-1. (a) Rhombohedral unit cell of Cr2O3 with magnetic ordering. (b) Hexagonal unit cell used in this study for different TM oxides. a, b, c represents the lattice vector directions...... 20

Figure 2-2. (a) (√3×√3) R30° mirror slab model for V2O3 with 1/3 ML Fe and 2/3 ML O coverage. Schematic without subsurface oxygens in inset. (b) Top schematic view of V in top 3 layers (shown without oxygens for simplicity). Index indicate the layer of V atom where 1 is the highest layer. With 1/3 ML Fe coverage, one of the three V atoms at the topmost layer, indicated by 1, is replaced by Fe...... 24

Figure 2-3. Structures used for stability check of Fe on V2O3 (0001) at very reducing environment. Subsurface oxygens are not shown for simplicity...... 27

Figure 2-4. Structures used for stability check of Fe on V2O3 (0001) with 1/3 ML oxygen coverage. Subsurface oxygens are not shown for simplicity...... 28

Figure 2-5. Surface energies of metal and metal-oxide termination of studied (TM)2O3 (0001) surfaces...... 30

Figure 2-6. Effect of Fe and O coverage on ADE of oxygen on V2O3 (0001) (AF1 spin configuration)...... 31

Figure 2-7. 1/3 ML Fe and 0 ML O coverage becomes 1/3 ML O coverage after oxidation pulling V to the Fe2O3 (0001) surface. Subsurface oxygens are not shown for simplicity ...... 34

Figure 2-8. Δε for reaction shown in Fig. 2.7 and Fig. 2.9 with varying oxygen chemical potential ...... 35

Figure 2-9. 1/3 ML Fe and 2/3 ML O coverage becomes 1 ML O coverage after oxidation. Of V2O3 (0001) Subsurface oxygens are not shown for simplicity...... 36

Figure 3-1. Unit cells of (a) anatase (b) brookite (c) rutile TiO2 bulk oxides. Blue and red spheres represent Ti and O atoms, respectively...... 60

Figure 3-2. Optimized surface structures for (a) anatase (b) brookite (c) rutile TiO2 terminations. Blue and red spheres represent Ti and O atom, respectively. Outermost Ti atom and its nearest neighbors are labeled. Dotted line represents unit cell and

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solid lines represents Ti-O bonds. Ti-O distances are reported in Table 2. Ti` indicates the second Ti atom exposed with different coordination than Ti...... 63

Figure 3-3. Monolayer formation energies at 300 K and 1 atm. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy. All coatings were given the MO2 stoichiometry when on TiO2 surface...... 66

Figure 3-4. Monolayer formation (ΔGML) in three-step thermodynamic process- bulk transformation (ΔG1), monolayer creation (ΔG2) and adhesion (ΔG3)...... 67

Figure 3-5. Bulk transformation energy per functional unit of TiO2 at 300 K and 1 atm. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy...... 68

Figure 3-6. Monolayer Creation Energies per functional unit for different coating oxides. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy...... 69

Figure 3-7. Adhesion Energies per functional unit for coating metal oxides. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy...... 70

Figure 3-8. Predicted Particle radius required for RuO2 monolayer stability on various termination of TiO2 phases. a,b and r in legends represents anatase, brookite and rutile, respectively. Only results for radius greater than 10 Å at O-poor limit are shown...... 74

Figure 4-1. Lowest surface energies of different metal oxides as a function of chemical potential...... 95

Figure 4-2. 9 bilayer ZnO (0001) with M2O adsorbed on one side (5×5 expanded) (a) side (b) top view. TiO2 (110) slab with M2O2 adsorbed as a tri-layer (c) side view (d) top view. Black line shows the unit cell used for calculation...... 97

Figure 4-3. Wulff construction of RuO2 at (a) 300 K, 1 atm (b) 573 K, 0.1 atm (c) 1073 K, 1 atm...... 98

Figure 4-4. Formation energy comparison between GCMC (ReaxFF) predicted and approximated method...... 99

Figure 4-5. (a) Reaction for testing stability of PdO over ZnO (0001) (b) Graphical respresentation of the test reaction...... 100

Figure 4-6. PdO monolayer formation at three different chemical potentials of O atom...... 101

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Figure 4-7. Stability region of PdO over ZnO (0001)-Zn surface...... 102

Figure 4-8. Maximum particle radius for PdO, RuO2 and Au as a function of o for monolayer stability over ZnO (0001)...... 103 𝜇𝜇 Figure 4-9. Stability of bi-layer oxide on ZnO (0001) ...... 105

Figure 4-10. Maximum particle size for different oxides for monolayer stability on TiO2 (110)...... 106

Figure 4-11. ZnO stability on TiO2(110) with different coverages of Zn and O...... 109

Figure 5-1. Adsorption geometries of metals on CeO2 (111) and MgO (100). Top view of adsorbed late transition metals on the CeO2 (111) surface at the a) 3-fold hollow site (Ag), b) 2-fold oxygen bridge site (Ir), or c) oxygen side-bridge site (Pd). Adsorbed metals on MgO (100) all prefer the d) anionic oxygen site. The black rectangle represents the unit cell used in the study...... 123

Figure 5-2. Correlation between metal/support adsorption energies and metal adatom’s oxide formation enthalpy. Adsorption energies of transition metals on MgO (100), CeO2 (111), CeO2 (110), TiO2 (011), ZnO (100), TbO2 (111) and α-Al2O3 (0001) plotted against the formation enthalpy of the metal adatom’s most stable oxide. TbO2 (111) adsorption energies are plotted on the right (blue) y-axis while the remaining data are plotted on the left y-axis (due to scale difference). Dotted lines represent the best linear fit to the data for each support, with fit equations and quality given in Supplementary Table 5. Vertical lines (grey) are label guides...... 124

Figure 5-3. Correlation between slopes from Figure 5.2 and support’s oxygen vacancy formation energy. Slopes from the lines of best fit for adsorption energy vs. metal adatom’s oxide formation enthalpy for each surface are plotted against the surface’s oxygen vacancy formation energy...... 126

Figure 5-4. Correlation between metal/support adsorption energies and the support’s oxygen vacancy formation energy. Adsorption energies of Ag, Ir, and Pd atoms to TbO2 (111), α-Al2O3 (0001), CeO2 (111), CeO2 (110), TiO2 (011), ZnO (100), and MgO (100) supports plotted against the corresponding oxygen vacancy formation energies of the support. Vertical grey lines are label guides...... 127

Figure 5-5. Density of states plots of Ir/CeO2 (111) and Ag/CeO2 (111). Projected DOS of 2+ 3+ metal adsorption on CeO2 (111) showing a) the d states of Ir , all states of Ce , and p states of O in the Ir-O-Ce bond on the surface and b) the d states of Ag+, all states of Ce3+, and p states of O on the surface...... 131

Figure 5-6. Metal-support interactions on CeO2 (111) and MgO (100) supports. Isostructural charge density difference plots of a) Ir/CeO2 (111) b) Ag/CeO2 (111)

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and c) Ir/MgO (100). Blue denotes depletion of electron density while green represents accumulation. The isosurface level is ±0.005 e bohr-3. d) DOS plot of Ir/CeO2 (111) and an orbital density image of the peak indicated with an arrow...... 132

Figure 5-7. Comparison between descriptor predicted and DFT binding energies. Results shown for (a) feature space 1 (b) feature space 2. ‘n’ in nD represents the number of terms in the descriptor...... 137

Figure 6-1. RMSE for 1D-5D descriptors for (a) 95 percentile of the training data for the three feature spaces (a) Stoichiometric coat/support oxide dataset (b) Non- stoichiometric coat/support oxide dataset...... 177

Figure 6-2. Cross-correlation of descriptors (a) correlation between the two descriptor terms that multiplies surface energy in stoichiometric coating/oxide dataset. (b) Correlation between Zunger (s+d) orbital Radii and row in Periodic table...... 180

Figure 6-3. DFT and descriptor predicted monolayer formation energy for (a) stoichiometric (b) non-stoichiometric data set...... 181

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LIST OF TABLES

Table 2-1. Stability of TM2 on TM1 oxide in the absence of surface oxygen (very reducing environment). L1, L2 and L3 indicate position of substituted TM2 as shown in Fig. 2.2 ...... 33

Table 3-1. Bulk oxide parameters of TiO2 phases and coating metal oxides...... 61

Table 3-2. Surface energy, Ti-O atomic distances at the outermost layer and DFT parameters for low index facets of TiO2. O1-O5` represents nearest neighbor O atoms as shown in Fig 3.2...... 62

Table 4-1. Computational Details and Bulk Lattice Constants of Metal/Metal Oxides Used in Current Study...... 94

Table 5-1. Bader charge differences (in e-, positive difference indicates the accumulation of negative charge) and total magnetic moments (in μB) after Ir and Ag adsorption on CeO2 (111) and MgO (100) surfaces. Atom labels correspond to labels shown in Supplementary Figures 1-13...... 130

Table 5-2. Equations for binding energy (eV) prediction based on LASSO+lo analysis using feature space 2. ΔHf,Ox, ΔEvac, EA, L and IE are in eV and 13 is in (density 1/3 48 unit) ...... 139 Δ𝜂𝜂 Table 6-1. Bulk oxide parameters of coating metal oxides...... 169

Table 6-2. Descriptor set using LASSO+lo analysis of Ω3 feature space...... 177

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ACKNOWLEDGEMENTS

I would like to express my gratitude to my advisors, Dr. Adri van Duin and Dr. Michael

J. Janik, for their mentorship, guidance and patience. They gave me ample support and time to catch up with the world of computational chemistry when I switched research field after my

Masters. They were never frustrated with me when I asked the simplest questions. Their continued support and mentorship over the years and the freedom to work on projects and numerical methods I found interesting, have been the best part of my graduate life. I am truly grateful to be able to work with both of them.

I would also like to thank my committee members, Dr. Richard Yetter and Dr. Lasse

Jensen. I would also like to thank faculties and graduate students affiliated with the NRT CoMET program. Dr. Jensen’s Quantum Chemistry course, the DFT café, CoMET seminars and Dr. Jorge

Sofo and Dr. Vincent Crespi’s passionate discussions and feedback from the NRT faculties, have been a great learning experience.

I am grateful to all of my lab mates both in Dr. van Duin’s and Dr. Janik’s research group. Special thanks to Sriram, Mahbub, Chowdhury, Ian, Gaurav, Joel and Haoran for helping me out and answering my questions even during their busiest times.

I am also grateful for the support I have got from my family. There have been weeks when I did not call back home and my parents never complained and motivated me for my graduate studies never letting me know of their hardships. Here at Penn State, far away from my family, BSA at Penn State never made me feel alone. I am thankful to every member of the

Bangladeshi community. Special thanks to Sarthok and Tareq for their time and support during the last part of my graduate life.

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Finally, I am grateful to my wife, Syeda Sabrina, who supported me throughout my Ph.D. journey. Even though she had to leave State College for her job, she kept me motivated however she could. We spent countless hours discussing my presentation slides/figures and sadly never made it to the acknowledgements. So, I dedicate this work to her.

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Chapter 1

Introduction

Metal oxides have a wide range of industrial applications that include amongst others, high-temperature coatings and chemical functional materials. As chemical functional materials, they are used in fuel cells1–4, gas sensors5–7, or as heterogeneous catalysts8–10. Since they are exposed to high temperature and various gas phase environments during their application, an effective oxide design requires consideration of stability, surface reconstruction, and in situ oxidation state. Multi component metal oxides (MMO) can offer tunable structure and chemical reactivity. Due to incorporation of more than one metal and possible number of different morphologies, their stability is more complex than single metal oxides. Most MMOs so far have been developed by an empirical approach. Due to recent advancement in synthesis and surface characterization techniques, it is possible to create catalysts with atomic level precision.

Computational methods like Density Functional Theory (DFT), which solves the electronic structure of a material, and statistical and Machine Learning algorithms can be used in

conjunction as predictive tools for designing atomic-scale catalysts.

The objective of this dissertation is to develop a fundamental understanding of the

stability of MMOs to accelerate the discovery of these systems using computational methods.

DFT works as the main computational method for calculating accurate relative energies while ab

initio thermodynamics is used to extrapolate 0 K DFT energies to meaningful properties at higher

temperatures and different pressures. Statistical learning algorithms are utilized to analyze DFT

2 predicted energies and properties to find underlying physical principles that correlate to the stability of these systems.

The organization of this introductory chapter is as follows – first, a brief review is presented on multicomponent metal oxides and studies that have looked at the stability of such systems in Section 1.1. In Section 1.2 a general overview of the research objects of this dissertation is presented. Section 1.3 gives a brief introduction to the computational methods used in this work and Section 1.4 gives an overview of the organization of each chapter.

1.1 Background

Among metal oxides catalysts, multicomponent metal catalysts have gained interest in recent years due to their tunable characteristics and chemical reactivity. These can be bulk mixed oxides11 – where two or more oxides are mixed completely in bulk phase. Other possible

structures include a metal oxide supported on top of another metal12–14 or metal/metal cluster on

top of a metal oxide10. There are also core-shell structures, with a metal/metal oxide as core and another metal oxide/metal as the outer shell15,16. Some of these are categorized as Strong Metal

Support Interactions (SMSI) where properties of metal oxide catalysts are altered by functional

perturbations due to the oxide support.17 Among the many possible combinations (Fig 1.1), two classes have been identified as having the potential for designing oxide surfaces with unique chemical properties. These are (1) monolayer of oxidized transition metals overlayer on another oxide support18–21 and (2) surface-confined mixed oxides.22

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Figure 1-1. Some possible types of MMOs. M1 and M2 represent metal atom of support and coating, respectively. (a) Supported M2 or M1xOy species (b) M2 or M2xOy species at edges/defects (c) Monolayer M2xOy on M1xOy (d) Substituted or “doped”

The growth behavior of thin metal oxide films is usually categorized in three modes: 3D islanding (“Volmer-Weber”) where the overlayer does not wet the substrate, growth in a layer-by- layer like fashion (“Franck-van der Merwe”) and complete wetting of the first monolayer followed by growth in three-dimensional islands (“Stranski- Krastanov”). The growth of oxides can also be a combination of these methods. For monolayer overlayer, we are specifically interested in the layer-by-layer growth of monolayer MMOs (Fig 1.1(c)). Some work on layer-by- layer monolayer oxide growth on metal oxide supports exists in the literature. Thin homostructural epitaxial growth (where the overlayer conforms to the underlying support lattice)

23 of RuO2 on rutile TiO2 (110) have been studied experimentally by Xiang et al. by varying RuO2 particle size. They observed that when the particle sizes were sub ~2nm in diameter, epitaxial

RuO2 islands (3 monolayers thick) were formed. Particle size larger than that remained unchanged in shape. Similar epitaxial growth was also reported by He et al.24 using physical

vapor deposition of Ru in an oxygen atmosphere (600 K, 10-6 mbar) at low coverages. Dulub et

al.18 observed 2D growth of Cu over ZnO (0001) at very low coverages in different oxidation

4 states. Warschkow et al.19 calculated the 2D phase diagram for stability of different surface

structures in oxidation and reduction conditions using ab initio thermodynamics and tried to

relate to experimental observations of such systems. Vanadia overlayers on different support

21 materials (SiO2, Al2O3, ZrO2, TiO2 and CeO2) was used by Israel Wachs to compare turnover for methanol oxidation to formaldehyde which indicated that the oxide support may play an active role in changing the chemical reactivity of the vanadia surface. Novell-Leruth et al.25 used

DFT calculated adhesion energy to predict relative stability of monolayers of rutile MO2 (M= Ir,

Ru, Sn and Ti) on each other.

Surface-confined mixed metal oxides are metal oxides where one or more of the metals

of the surface layer are replaced by another metal oxide. They are also termed as “substitutional

doping” or just “doping”. Fig 1.1(d) shows one single metal (M1) substituted by another metal

(M2) in a large unit cell. The degree to which support metals (M1) is substituted by (M2) can

control the catalytic properties. In literature this substitutional doping is sometimes termed as n

ML coverage of M2 on M1xOy, indicating monolayer coverage when n equals 1. Eric McFarland and Horia Metiu published a detailed review on such meal oxide surfaces26 and other previous

works are present on how surface chemical properties are changed by doping some of the support

oxide metals.27–29 One of the recent works by Colussi et al.22 reported that Pd-O-Ce surface- confined mixed metal oxides on CeO2 (110) surface have a higher activity for methane oxidation than Pd metal particles supported on CeO2 (110). The common theme here is that, by choosing the right support that stabilizes a MMO structure, the chemical activity can be tuned to create oxidation catalysts with desirable properties.

In terms of chemical reactivity of the above-mentioned classes of oxides, there have been numerous studies using DFT. However, a key thing about these multicomponent metal oxides is that they might be metastable, meaning they are only stable under certain pressure and

5 temperature. The majority of the DFT reactivity studies do not directly evaluate the stability of the mixed oxide surface model used. We also observe that MMO stability depends on coating/support oxide combination, preference for surface terminations, and dependence on precursor size (particle size). Thus, even though DFT predicts desirable chemical properties of a material it might not be stable at the application pressure and temperature conditions. This meta- stability makes the materials experimentally harder to synthesize leaving an empirical, trial and

error method of experimentally developing these materials a daunting task. Warchkow et al.’s19

pioneering work on CuxOy stability on ZnO (0001) surface as a function of chemical potential of

oxygen and copper gives a hint that ab initio thermodynamics can be used as a predictive tool for

stability of such oxides. This suggests DFT approaches can be used to filter out possible

(meta)stable combinations of metals oxides. However, a thermodynamic framework that

systematically defines stability for these classes of materials is needed.

With the increase of computational power and decrease in expense, quantum calculations

are now widely utilized for solving various problems in many brunches of scientific research.

Recent efforts to standardize and centralize the quantum calculations into big databases have

given rise to databases such as Materials Project,30 NOMAD,31 OQMD,32 AFLOW33 etc.

Statistical/machine learning algorithms, a tool now useful to computational chemists due to the

vast amount of quantum calculations available, have been widely successful in making sense out

of these large datasets. They have been used to predict materials properties such as band gap,34

vibrational free energy and entropies,35 possible 2D materials,36,37 and even new materials.38

Ghiringhelli et al.39 successfully used Machine Learning to predict zincblend and rocksalt

structure energies of 82 octet binary metal systems. Such analysis is able to identify physical

properties of the system that correlates to the desired property being modeled. To the best of our

6 knowledge, these statistical tools has not been used to discover properties and underlying physical rules that correlate with the stability of the monolayer MMOs.

1.2 Research Questions and Hypotheses

This dissertation aims at developing a basic understanding and guiding principle for

predicting the formation and stability of monolayer and surface-confined mixed metal oxides

using electronic structure calculations (DFT) and machine learning. To achieve this goal the

following research questions and hypothesis are investigated -

1) For the most ideal case, when all the oxides have the same crystal structure and small

lattice differences – is there a property that can predict the stability of monolayer and

surface-confined mixed metal oxides on similar termination? How does the stability

change with change in pressure/temperature?

Hypothesis: Surface energy represents stability of the atoms on the surface. Since they

have similar crystal structure, pure oxide surface energy may be correlated to their mixed

state stability as well. Changes in surface energy with pressure/temperature might also

capture their mixed state change.

2) For the same support oxide with different phases and termination, how does the

monolayer stability change for different stoichiometric non-stoichiometric coating

oxides?

Hypothesis: Oxides that have similar polymorph as the support oxide are likely to be

more stable. Surfaces terminations with high surface energies are probably going to show

stronger bound monolayers. By decomposing the process of monolayer formation into

three-thermodynamic sub-processes, a better understanding can be achieved.

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3) Is there a more relevant reference state (computationally tractable) for the coating process

than the bulk state for coating oxides? Is this possible to calculate in DFT?

Hypothesis: finite particles with the oxidation level depending on pressure/temperature.

This is likely too expensive for DFT with too many possibilities for structure – but it may

be possible to approximate.

4) Can ab initio thermodynamics be used to develop criteria to predict stable monolayer

coatings under varying pressure/temperature?

Hypothesis: Using the more reasonable finite particle as reference state for coating oxide,

ab initio thermodynamics enables calculation of particle energy at different conditions.

This should enable us to develop a criterion for particle size for monolayer stability at

each pressure/temperature combination.

5) What statistical/machine learning algorithm can predict descriptors for surface

interactions for a large number of possibilities?

Hypothesis: Supervised machine learning algorithms are probably the best choice for

finding the right descriptors from many possibilities. Previous studies have shown that by

using shrinkage methods, metal-metal and metal-oxide interactions are correctly modeled

using only a few parameters. Surface adsorption of metal/metal oxide overlayers are also

mostly an interaction between metal-metal and metal-oxygen on metal oxide surface.

6) What are the properties that makes a coating oxide/support combination stable?

Hypothesis: Surface energy, oxidation state, coating oxides similarity with support oxides

are possible descriptors but the actual relationship is likely to be nonlinear.

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1.3 Computational Methods

1.3.1 Density Functional Theory (DFT)

DFT is used as the main calculation method for evaluation of total energies of a system of

nuclei and electrons. Using DFT, one can calculate the ground state energy given an atomic

nuclei arrangement. Here, only a brief description of the formulation is presented. The principle

equation of quantum mechanics, the Schrödinger equation, in its time independent nonrelativistic

form can be represented as –

( , ) = ( , ) (1.1)

𝑖𝑖 𝐴𝐴 𝑖𝑖 𝐴𝐴 where E is the energy of the system,𝐻𝐻� ΨΨ is𝑟𝑟 the𝑅𝑅 wavefunction𝐸𝐸Ψ 𝑟𝑟 𝑅𝑅 expressed as a function of electronic coordinates, ri and ionic coordinates RA. is the Hamiltonian operator of the system. Under

Born–Oppenheimer approximation (velocity𝐻𝐻� of electrons are too high, and the move

instantaneously compared to ions) we can treat the electron and ions separately –

( , ) = ( ) ( ; ) (1.2)

𝑖𝑖 𝐴𝐴 𝐴𝐴 𝑖𝑖 𝐴𝐴 and the Hamiltonian can be expressedΨ 𝑟𝑟 as𝑅𝑅- Φ 𝑅𝑅 𝜓𝜓 𝑟𝑟 𝑅𝑅

1 1 + ( ; ) = ( ; ) (1.3) 2 2 , 𝐴𝐴 𝑖𝑖 𝑍𝑍 𝑖𝑖 𝐴𝐴 𝑒𝑒𝑒𝑒 𝑖𝑖 𝐴𝐴 �− � ∇ − � 𝐴𝐴𝐴𝐴 � 𝑖𝑖𝑖𝑖� 𝜓𝜓 𝑟𝑟 𝑅𝑅 𝐸𝐸 𝜓𝜓 𝑟𝑟 𝑅𝑅 𝑖𝑖 𝐴𝐴 𝑖𝑖 𝑟𝑟 𝑖𝑖>𝑗𝑗 𝑟𝑟 1 1 ( ) = ( ) (1.4) 2 2 𝐴𝐴 𝐵𝐵 𝐴𝐴 𝑍𝑍 𝑍𝑍 𝐴𝐴 𝑛𝑛𝑛𝑛𝑛𝑛 𝐴𝐴 �− � 𝐴𝐴 ∇ − � 𝐴𝐴𝐴𝐴 � Φ 𝑅𝑅 𝐸𝐸 Φ 𝑅𝑅 𝐴𝐴 𝑀𝑀 𝐴𝐴>𝐵𝐵 𝑅𝑅 where the Hamiltonian of the electron system consists of three terms: the kinetic term, the

external potential term resultant from electrostatic interaction between electrons and atomic

nuclei with charge A, and the electron-electron electrostatic interaction term. The Hamiltonian for the ions contains𝑍𝑍 a kinetic term and ion-ion interaction term. Hohenherg-Kohn theorem40 proved that there is one-to-one mapping between wavefunction of electrons and electron density

9

distribution. This enables the Hamiltonian to be represented as a functional of the electron

density. Currently the most used formulation of DFT is based on the Kohn-Sham (KS) equations

where electrons are treated as non-interacting particles in a fictitious potential that gives the same ground state density as the interacting system and expressed as –

1 ( ) ( ) [ ( )] = [ ( )] + + [ ( )] + ( ) ( ) (1.5) 2 | |′ 𝜌𝜌 𝑟𝑟 𝜌𝜌 𝑟𝑟 ′ 𝐸𝐸 𝜌𝜌 𝑟𝑟 𝑇𝑇𝑆𝑆 𝜌𝜌 𝑟𝑟 � ′ 𝑑𝑑𝑑𝑑𝑑𝑑𝑟𝑟 𝐸𝐸𝑥𝑥𝑥𝑥 𝜌𝜌 𝑟𝑟 � 𝜌𝜌 𝑟𝑟 𝑣𝑣𝑒𝑒𝑒𝑒𝑒𝑒 𝑟𝑟 𝑑𝑑𝑑𝑑 𝑟𝑟 − 𝑟𝑟 ( ) = 𝑁𝑁 | ( )| (1.6) 2 𝜌𝜌 𝑟𝑟 � 𝜑𝜑𝑖𝑖 𝑟𝑟 [ ( )] = ( [ ( )] [ 𝑖𝑖( )]) + ( [ ( )] [ ( )]) (1.7)

𝑥𝑥𝑥𝑥 𝑠𝑠 𝑒𝑒𝑒𝑒 where ( ) is single𝐸𝐸 electron𝜌𝜌 𝑟𝑟 wavefunction,𝑇𝑇 𝜌𝜌 𝑟𝑟 − 𝑇𝑇 Ts𝜌𝜌 is𝑟𝑟 the kinetic𝑉𝑉 energy𝜌𝜌 𝑟𝑟 − of𝐽𝐽 election𝜌𝜌 𝑟𝑟 in non-interacting

𝑖𝑖 environment,𝜑𝜑 𝑟𝑟 the second term in the electron-electron interaction ( [ ( )]) and the last term is the

electrostatic interactions. Exc is the exchange correlation term and includes𝐽𝐽 𝜌𝜌 𝑟𝑟 the error due to

approximating the kinetic energy term in fictitious non-interacting system and non-classical part of the electron-electron interactions. The actual mathematical expression for Exc is unknown and

approximated based on theory of an ideal electron gas and physical constraints with empirical

tunable parameters. The KS formalism drastically reduces the computational requirements for the

approximate solution of Schrödinger equation by remapping the problem in terms of electron

density and single electron wavefunctions. Thus, solutions to the KS equations provide the total

ground state energy as a function of ionic positions.

1.3.2 Ab initio thermodynamics

DFT predicts total energies at zero temperature and pressure thus yielding the zero-

Kelvin potential energy surface (PES). Actual operating conditions are never at zero temperature/pressure conditions. Ab initio thermodynamics allows to account for temperature and

10 pressure effects, bridging the information on the PES with statistical thermodynamics. A system in finite temperature (T), pressure (p) and volume (V), minimizes the Gibbs free energy (G) which can be expressed as-

( , ) = ( , ) + (1.8) where F is the Helmholtz energy. Decomposing𝐺𝐺 𝑇𝑇 𝑝𝑝 𝐹𝐹 Helmholtz𝑇𝑇 𝑝𝑝 𝑝𝑝 free𝑝𝑝 energy to internal energy (E) and temperature entropy (S) term-

( , ) = + = + + 𝐺𝐺 𝑇𝑇 𝑝𝑝 𝐸𝐸 − 𝑇𝑇𝑇𝑇 𝑝𝑝𝑝𝑝 = +𝑡𝑡𝑡𝑡𝑡𝑡 𝑣𝑣𝑣𝑣𝑣𝑣 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + (1.9) 𝑡𝑡𝑡𝑡𝑡𝑡 𝐸𝐸 𝑍𝑍𝑍𝑍𝑍𝑍𝐹𝐹 −𝑣𝑣𝑣𝑣𝑇𝑇𝑣𝑣𝑆𝑆 𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝑐𝑐𝑝𝑝 where Etot is the DFT calculated𝐸𝐸 energy,𝐸𝐸 EZPE− is𝑇𝑇 zero𝑆𝑆 -point− 𝑇𝑇𝑆𝑆 energy, 𝑝𝑝S𝑝𝑝vib and Sconf are the vibrational

and configurational entropy. For this work, use of ab initio thermodynamics is limited to

calculations of surface free energy and gas phase chemical potential. For a multi-component system in equilibrium with surrounding gas or liquid phase the general expression41 for surface

energy is –

1 ( , ) = ( , ) (1.10) 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝛾𝛾 𝑇𝑇 𝑝𝑝𝑖𝑖 �𝐺𝐺 − � 𝑁𝑁𝑖𝑖𝜇𝜇𝑖𝑖 𝑇𝑇 𝑝𝑝𝑖𝑖 � 𝐴𝐴 𝑖𝑖 where Gsurf is the Gibbs free energy of the surface, ( , ) is the chemical potential of the species i in the system and N is its number. In most𝜇𝜇 cases,𝑖𝑖 𝑇𝑇 𝑝𝑝 𝑖𝑖the Gibbs free energy of the surface

~DFT total energy assuming all the other contributions are small for a fixed surface (Fvib can be large in some cases). For a gas phase ideal gas, chemical potential is given by –

( , ) = + + ( , ) (1.11) 𝐷𝐷𝐷𝐷𝐷𝐷 𝑍𝑍𝑍𝑍𝑍𝑍 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 The value of ( , 𝜇𝜇) can𝑇𝑇 𝑝𝑝either𝐸𝐸 be calculated𝐸𝐸 usingΔ𝜇𝜇 statistical𝑇𝑇 𝑝𝑝 thermodynamics or using thermochemical tablesΔ42𝜇𝜇 𝑖𝑖as𝑇𝑇 –𝑝𝑝

( , ) = ( , ) ( , ) + (1.12) 𝑜𝑜 𝑜𝑜 𝑜𝑜 𝑝𝑝 Δ𝜇𝜇𝑖𝑖 𝑇𝑇 𝑝𝑝 𝜇𝜇𝑖𝑖 𝑇𝑇 𝑝𝑝 − 𝜇𝜇𝑖𝑖 𝑇𝑇 𝑝𝑝 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 � 𝑜𝑜� 𝑝𝑝

11

1.3.3 Shrinkage Method, LASSO+lo

For the statistical learning part, we want to select the best n descriptors that best describes a property from a large number for possible descriptors. LASSO (least absolute shrinkage and selection operator) is a shrinkage method that reduces the number of descriptors using l1 penalty –

or in other words, it penalizes the number of coefficients. LASSO minimizes the residual sum of

squares of the expression given in Eqn 1.13 and is similar to least squares methods except for the

important regularization term at the end.

1 argmin 𝑝𝑝 2 + 𝑝𝑝 (1.13) 2 𝑁𝑁 𝑖𝑖 𝑖𝑖𝑖𝑖 𝑗𝑗 𝑗𝑗 𝛽𝛽 � � �𝑦𝑦 − � 𝑥𝑥 𝛽𝛽 � 𝜆𝜆 ��𝛽𝛽 �� 𝑁𝑁 𝑖𝑖=1 𝑗𝑗=1 𝑗𝑗=1 Here y is a column vector of responses which has been centered (i.e., some DFT

calculated property we want to fit to), x is a (N×p) dimensional design matrix (N is the total

number of observations and p is the total number of descriptors) of descriptors (scaled and

centered), and β is the column vector of coefficients that is to be determined. λ is a penalty

parameter that, when increased, decreases the number of non-zero components of vector β. For a

maximum value of λ ( = | , |), all elements of the β will be zero, and as λ is 1 𝑚𝑚𝑚𝑚𝑚𝑚 𝑙𝑙 𝑙𝑙 decreased, more elements𝜆𝜆 will 𝑁𝑁take𝑚𝑚𝑚𝑚 non𝑚𝑚 〈-𝑥𝑥zero𝑦𝑦〉 values. Since LASSO is not scale invariant, we

standardized36 the descriptor matrix, x, to have a zero-mean and unit-variance by subtracting from each column its mean and normalizing by its standard deviation. This normalization puts all the descriptors on a common scale to render the penalty parameter, λ, meaningful. After enforcing a cutoff value of λ, a subsequent exhaustive search using least squares method over all possible subsets of descriptors with non-zero β values is completed. Due to the linear correlation between descriptors, the best results may not be achieved solely by employing LASSO. Details of this

39 method (LASSO+lo) can be found elsewhere.

12

1.4 Summary of Chapters

Each chapter in the dissertation tests one or more of the hypotheses listed in section 1.2.

In terms of computational methods, DFT, ab initio thermodynamics and a statistical learning method (LASSO+lo) are used. The layout of the following chapters are as follows- Chapter 2

investigates monolayer and surface-confined mixed metal-oxide stability of oxides with the

corundum structure (V2O3, Cr2O3 and Fe2O3) and presents correlation with their pure oxide

surface energy. Chapter 3 reports the monolayer formation energy of different coating oxides on

several low-index surfaces of three phases of TiO2 and decomposes the process into a three-step thermodynamic process to investigate relative importance of each step. In Chapter 4 we present a

thermodynamic framework to predict stable monolayers with respect to coating oxide particles of

different size at different pressure temperature conditions. An approximate method based on DFT

calculated surface energy and spherical approximation for the oxide particle in presented to

model the particle energy. Chapter 5 explores the idea of using statistical learning method

(LASSO+ lo) to find the best descriptors that predict stability of metal adatoms on metal oxide

surfaces using DFT calculated binding energy to the surface as the indicator. In Chapter 6,

LASSO+ lo method is used to find correlation between physical properties of stable coat oxide/

support combinations from a feature space with ~1×106 descriptors using DFT calculated

monolayer formation energies of 506 coat/support oxide combinations. Chapter 7 reports the

conclusion and discusses future works.

1.5 References

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19 O. Warschkow, K. Chuasiripattana, M. J. Lyle, B. Delley and C. Stampfl, Cu/ZnO(0001) under oxidating and reducing conditions: A first-principles survey of surface structures, Phys. Rev. B, 2011, 84, 125311. 20 N. Nilius, T. Risse, S. Schauermann, S. Shaikhutdinov, M. Sterrer and H.-J. Freund, Model Studies in Catalysis, Top. Catal., 2011, 54, 4–12. 21 I. E. Wachs, Recent conceptual advances in the catalysis science of mixed metal oxide catalytic materials, Catal. Today, 2005, 100, 79–94. 22 S. Colussi, A. Gayen, M. Farnesi Camellone, M. Boaro, J. Llorca, S. Fabris and A. Trovarelli, Nanofaceted Pd-O Sites in Pd-Ce Surface Superstructures: Enhanced Activity in Catalytic Combustion of Methane, Angew. Chem. Int. Ed., 2009, 48, 8481–8484. 23 G. Xiang, X. Shi, Y. Wu, J. Zhuang and X. Wang, Size effects in Atomic-Level Epitaxial Redistribution Process of RuO2 over TiO2, Sci. Rep., 2012, 2, 801. 24 Y. He, D. Langsdorf, L. Li and H. Over, Versatile Model System for Studying Processes Ranging from Heterogeneous to Photocatalysis: Epitaxial RuO2(110) on TiO2(110), J. Phys. Chem. C, 2015, 119, 2692–2702. 25 G. Novell-Leruth, G. Carchini and N. López, On the properties of binary rutile MO2 compounds, M = Ir, Ru, Sn, and Ti: A DFT study, J. Chem. Phys., 2013, 138, 194706. 26 E. W. McFarland and H. Metiu, Catalysis by Doped Oxides, Chem. Rev., 2013, 113, 4391– 4427. 27 S. Chrétien and H. Metiu, Density Functional Study of the CO Oxidation on a Doped Rutile TiO2(110): Effect of Ionic Au in Catalysis, Catal. Lett., 2006, 107, 143–147. 28 R. G. S. Pala and H. Metiu, Modification of the Oxidative Power of ZnO(101̄0) Surface by Substituting Some Surface Zn Atoms with Other Metals, J. Phys. Chem. C, 2007, 111, 8617–8622. 29 H. Y. Kim, H. M. Lee, R. G. S. Pala, V. Shapovalov and H. Metiu, CO Oxidation by Rutile TiO2(110) Doped with V, W, Cr, Mo, and Mn, J. Phys. Chem. C, 2008, 112, 12398–12408. 30 A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder and K. a. Persson, The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater., 2013, 1, 011002. 31 NOMAD Repository, . 32 Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD) | SpringerLink, https://link.springer.com/article/10.1007%2Fs11837-013-0755-4, (accessed May 19, 2018). 33 S. Curtarolo, W. Setyawan, G. L. W. Hart, M. Jahnatek, R. V. Chepulskii, R. H. Taylor, S. Wang, J. Xue, K. Yang, O. Levy, M. J. Mehl, H. T. Stokes, D. O. Demchenko and D. Morgan, AFLOW: An automatic framework for high-throughput materials discovery, Comput. Mater. Sci., 2012, 58, 218–226. 34 G. Pilania, A. Mannodi-Kanakkithodi, B. P. Uberuaga, R. Ramprasad, J. E. Gubernatis and T. Lookman, Machine learning bandgaps of double perovskites, Sci. Rep., 2016, 6, srep19375. 35 F. Legrain, J. Carrete, A. van Roekeghem, S. Curtarolo and N. Mingo, How the Chemical Composition Alone Can Predict Vibrational Free Energies and Entropies of Solids, ArXiv170302309 Cond-Mat.

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36 K. Choudhary, I. Kalish, R. Beams and F. Tavazza, High-throughput Identification and Characterization of Two-dimensional Materials using Density functional theory, Sci. Rep., 2017, 7, 5179. 37 A. K. Singh, K. Mathew, A. V. Davydov, R. G. Hennig and F. Tavazza, eds. N. P. Kobayashi, A. A. Talin, M. S. Islam and A. V. Davydov, 2015, p. 955316. 38 F. Ren, L. Ward, T. Williams, K. J. Laws, C. Wolverton, J. Hattrick-Simpers and A. Mehta, Accelerated discovery of metallic glasses through iteration of machine learning and high- throughput experiments, Sci. Adv., 2018, 4, eaaq1566. 39 L. M. Ghiringhelli, J. Vybiral, E. Ahmetcik, R. Ouyang, S. V. Levchenko, C. Draxl and M. Scheffler, Learning physical descriptors for materials science by compressed sensing, ArXiv Prepr. ArXiv161204285. 40 P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Phys. Rev., 1964, 136, B864– B871. 41 K. Reuter and M. Scheffler, First-Principles Atomistic Thermodynamics for Oxidation Catalysis: Surface Phase Diagrams and Catalytically Interesting Regions, Phys. Rev. Lett., 2003, 90, 046103. 42 D. R. Stull and H. Prophet, JANAF thermochemical tables, DTIC Document, 1971.

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Chapter 2

A first-principles study of stability of surface confined mixed metal oxides with a corundum structure (Fe2O3, Cr2O3, V2O3)

[This chapter is published as: A. S. M. Jonayat, A. Kramer, L. Bignardi, P. Lacovig, S. Lizzit, A. C. T. van Duin, M. Batzill and M. J. Janik, Physical Chemistry Chemical Physics, 2018, 20, 7073–7081. All DFT calculations and their analysis were done by A S M Jonayat. The experimental part of the paper and corresponding analysis presented in supplementary information were done by A. Kramer]

2.1 Introduction

Recent literature has showed a great interest in multicomponent metal oxide (MMO)

catalysts.1 These multicomponent catalysts offer a range of advantages over the traditional, single-component oxide materials – in particular, tunable structure and chemical reactivity. In addition, surface confined MMOs limit the mixing to the surface region and provide chemical properties that can be different from the host oxide. Transition metal (TM) oxides are the primary candidate for MMO-based catalysts, and electronic structure calculations can be used to predict their stability2–4 – thus identifying promising candidates for material synthesis. Most of the

current electronic structure based studies, however, focused on predicting catalytic characteristics

of the surface assuming the desired surface oxide composition is formed and stable. Less work

has been done to predict the stability of such surface-confined mixed metal oxides. Such work is

essential to connect with experimental material synthesis efforts.

17

The catalytic properties of corundum phase TM oxides (e.g. Al2O3, Fe2O3, Cr2O3, V2O3)

and their (0001) termination have widely been investigated.5–8 The surface terminations of these

TM oxides can vary widely depending on the temperature and pressure, from metal terminated to a full monolayer coverage of oxygen.9–11 These surfaces are known to catalyze oxidation reactions by transferring surface oxygen atoms.12 Romanyshyn et al.7 studied oxy- dehydrogenation of methanol to form formaldehyde on V2O3 (0001) with different surface

oxidation states. Such surfaces were studied by Gobke et al.8 as well. Both studies reported a relationship between oxygen vacancy formation and the amount of methoxy intermediate formation, as well as the importance of vanadyl (-V=O) oxygen vacancy formation energy.

Mixing other metal atoms in the surface may allow tuning of the vanadyl oxygen vacancy formation energy. Such surface-confined mixed oxide must also be stable to enable the desired change in catalytic properties.

Surface terminations of pure V2O3 with different oxidation states and their relative

stability have been examined by surface science and Density Functional Theory (DFT) studies.9–

11,13,14 In these works, the stable oxidation state of the surface at a given temperature-pressure was

predicted using DFT calculated surface energies at different oxygen chemical potentials and used

15–17 to explain observations from experiments. The same approach has been applied for Fe2O3 and

17,18 Cr2O3 (0001) terminations. A number of DFT studies have investigated bulk and surface properties of corundum and mixed/doped corundum structures. Above the Néel temperature,

V2O3, which is paramagnetic metal at ambient conditions, changes to a paramagnetic insulator

upon doping with Cr or a pressure decrease. The behavior of Cr-doped V2O3, has motivated both

experiments and electronic structure calculations to investigate the metal to insulator transition

(MIT).19–22 Other mixed corundum oxide structures have received less attention. Baltrusaitis et

23 al. studied the electronic structure and chemical reactivity of the Fe and Cr substituted α-Al2O3

18

(0001) surface, but did not explicitly evaluate the stability of such surfaces. The design of mixed corundum oxides for enhanced catalytic properties can be improved if we are able to predict their stability theoretically before expensive synthesis processes are undertaken. Does the knowledge of pure oxide surface energy at different pressure-temperature conditions and oxidation states help us understand what will happen in their mixed oxides? This is a question that has not been addressed.

Herein, we use DFT to examine the stability of mixed Fe2O3, Cr2O3 and V2O3 corundum

oxide (0001) surfaces under varying chemical potential of oxygen. The reducibility of the mixed

metal oxide surface is investigated by calculating the Associative Desorption Energy (ADE) of an oxygen atom. We examine if substituting different amounts of Fe in the V2O3 (0001) surface

increases its reducibility compared to pure V2O3 (0001). After observing increased reducibility,

the stability of Fe on the V2O3 (0001) surface, versus segregating to the bulk, is investigated as a function of a varying oxygen chemical potential (µo). Stability of substituted Fe/ Cr/ V onto

Fe2O3/ Cr2O3/ V2O3 (0001) surfaces and subsurfaces are studied at different oxidation states and coverages. Pure TM oxide surface energies are shown to be an indicator of the calculated mixed surface stabilities. Finally, experimental observations for chromia/V2O3 (0001) and vanadia/Cr2O3

(0001) systems that partially verify our DFT predicted surface stability are briefly discussed, and detailed in the Supplementary Information (SI).

2.2 Method

First-principles Electronic structures were evaluated using DFT with a plane wave basis set as implemented in the Vienna ab initio simulation package (VASP).24 The interaction between the ionic cores and valence electrons is described by the projector augmented wave

19

(PAW)25 method. For vanadium, chromium, iron and oxygen, the outer 11, 12, 14 and 6 electrons are treated as valence electrons, respectively. Energy was converged to 3 meV with respect to k- point sampling and plane-wave basis set energy cut-off. The k-point grids are generated using the

Monkhorst-Pack scheme.26 Vosko-Wilk-Nusair interpolation27 for the correlation part of the exchange correlation functional is used. Structures were optimized until forces on each atom was less than 0.05 eV/ Å.

TM oxides that are not fully oxidized have localized d or f electrons that are strongly correlated systems. Conventional DFT methods with the generalized gradient approximation

(GGA) for exchange and correlation suffers from inaccuracies in representing strongly correlated systems. The intra-atomic exchange and Coulomb terms are not properly cancelled leading to a well-known problem of self-interaction over-repulsion also known as the ‘delocalization error’ in

DFT. This inaccurate delocalized description often leads to a wrong electronic structure description and causes unreliable changes in total energy during change of oxidation state. To correct this error, the DFT+U method28 is used here which adds a Hubbard U correction term to

these localized states and can provide accurate band gaps and reduction energetics. The accuracy

of this approach relies on the choice of parameters U and J, which can be tuned to match an

experimental band gap29–31 or reduction energy.32 Here, the formulation introduced by Dudarev et al.33 is used for which only U-J values are meaningful. PBE34 exchange correlation functional is

35 used for all electronic structure calculations. For V2O3 bulk structures, the PW91 functional was used in addition to PBE34 for comparison. The U-J values used for the calculations are

mentioned in the appropriate section.

20

2.2.1. Bulk Structures

Bulk structure evaluation is necessary to construct surface models for calculating surface energy and stability evaluation. A brief description of the bulk corundum structures is given in the following section.

Figure 2-1. (a) Rhombohedral unit cell of Cr2O3 with magnetic ordering. (b) Hexagonal unit cell used in this study for different TM oxides. a, b, c represents the lattice vector directions.

2.2.1.1. Cr2O3

Lattice optimization of Cr2O3 was performed using a hexagonal unit cell (18 O and 12 Cr atoms). The structure consists of alternating oxygen layers and chromium bilayers stacked along the c-axis of the hexagonal lattice.18 The PBE functional with a 720 eV plane-wave basis set

energy cut-off and 6×6×2 k-point grid was used. The magnetic order of Cr atoms was initialized using the experimentally observed distribution17,36 which is antiferromagnetic (AF). Figure 2.1(a)

shows the magnetic order of a rhombohedral unit cell where there are four Cr atoms in the

diagonal direction. These can be subdivided in terms of distances from each other – short and

long. For Cr2O3, the Cr atom pairs that are located at short and long distance from each other are

all arranged in AF alignment. This magnetic order is shown in Figure 2.1(a) along with the

hexagonal unit cell used in this calculation (Figure 2.1 (b)). The magnetic ordering of the

21 rhombohedral unit cell is converted to the hexagonal unit cell to model the experimental magnetic order. Each atom in the rhombohedral unit cell has three corresponding atoms in the hexagonal unit cell. The U-J value of 4 is used for Cr d-orbitals.17

2.2.1.2. Fe2O3

Similar to Cr2O3, a hexagonal unit cell was used for Fe2O3. The PBE functional with a

725 eV plane-wave basis set energy cutoff and a 4×4×2 k-point grid was used for calculations.

16,17 The magnetic order in Fe2O3 was initialized to AF as observed experimentally. The short

distance Fe atom pairs are in AF alignment and the long-distance ones are in ferromagnetic (FM)

arrangement - in the diagonal direction of the rhombohedral unit cell. The U-J for Fe atoms was

4.3.37

2.2.1.3 V2O3

V2O3 is a paramagnetic (PM) metal in ambient conditions. However, spin polarized calculations in the DFT framework give a density of states (DOS) which shows a nonmetallic

9,10 structure. Most calculations available in the literature avoid calculating the V2O3 structure with

spin polarization. If spin polarization is important, the majority of the published works do not

provide the spin order that was used to initialize or found after convergence7 while Nilius et al.38

mention using an AF arrangement. Following Kresse et al.9 and Ezhov et al.39,40 three possible AF and one FM alignments were calculated for the bulk.

For AF, in one possible alignment (AF1), the order is such that each V atom is AF to its nearest neighbors in its basal plane and FM to the nearest neighbor in the c-axis, similar to the AF

22 alignment mentioned by Kresse et at.9, Grieger et al.39 and Ezhov et al. 40. Another AF alignment

(AF2) is similar to AF1 except it is AF to the nearest neighbor along the c-axis. In the last

considered alignment (AF3) - the two V atoms of the V bilayer in the hexagonal unit cell are in

FM alignment and each bilayer is AF to another bilayer. Henceforth, only AF1 alignment results

are presented for comparison and results for other alignments are given in SI. The PBE functional

were used both with and without spin polarization. Some of the calculations are repeated with the

PW91 functional to check the functional dependency of the results. A 720 eV plane-wave basis

set energy cut-off and 6×6×2 k-point grid are used for these calculations. A U-J value of 3.15 was used for V d-orbitals.41

In DFT+U framework, we have used U-J values previously reported in literature that

match the experimental lattice parameters, volume, bulk electronic structure or oxidation

enthalpy. The validity is not well established for using bulk-parameterized U-J values to represent

surface metal atoms or different oxidation states not considered in the bulk. Methods like

DFT+U(R)42 where U is also a function of atomic distance (R), work by Huang et al.43 where U

for each metal atom in different termination of Fe2O3 (0001) are evaluated using linear response theory from perturbation of Fe-d and O-p orbitals, or using hybrid functionals with Fock exchange,10 exist to partially alleviate the unknown validity of constant U-J values. We have

checked qualitative conclusions on surface segregation tendencies with different U-J values, and

compared our results to literature studies of the Fe2O3 (0001) surface using the surface specific U

43 10 values and to a V2O3 (0001) study using hybrid functionals. These comparisons confirm that

the qualitative conclusions we report are robust versus the choice of U-J value, though the exact oxygen chemical potential at which redox transition occur will vary with the choice of U-J value.

The use of hybrid functionals is too computationally expensive for our purposes. Hence, we have

23 used constant U-J values for bulk and surface metal atoms assuming these can predict the oxidation state change with acceptable accuracy.

2.2.2 The (0001) Surface of (TM)2O3 Corundum Oxides

In the corundum structure of (TM)2O3, O layers and TM bilayers are stacked along the c- axis of the hexagonal lattice. The (0001) surface is made by cleaving the bulk structure along the c-axis. When a (√3×√3) R30° unit cell is used, the exposed surface has three TM atoms on the surface with two more TM layers below the first oxygen layer. For a V2O3 (0001) surface, this

enabled calculations at coverages of 0, 1/3, 2/3 and 1 ML for O and substituted Fe on the surface.

Here, 2/3 ML O and 1/3 ML Fe coverage means two out of the three surface metal atoms are

oxidized (-TM=O) and one of the surface V atoms has been substituted by an Fe atom,

respectively. A mirror slab model of this coverage with 18 atomic layers and 4 atomic layers

fixed at the center is shown in Figure 2.2(a). Figure 2.2(b) shows the top three V layers and

atomic positions as 1, 2, 3 from top to subsurface. At least 15 Å vacuum is kept in the surface

normal direction to avoid interactions between periodic images for all calculations. No significant

surface reconstructions were observed for any of the mixed oxide surfaces.

24

Figure 2-2. (a) (√3×√3) R30° mirror slab model for V2O3 with 1/3 ML Fe and 2/3 ML O coverage. Schematic without subsurface oxygens in inset. (b) Top schematic view of V in top 3 layers (shown without oxygens for simplicity). Index indicate the layer of V atom where 1 is the highest layer. With 1/3 ML Fe coverage, one of the three V atoms at the topmost layer, indicated by 1, is replaced by Fe.

2.2.3 Reducibility of the Fe/V2O3 (0001) Surface

Given the importance of oxygen vacancy formation/binding energy in certain catalytic reactions like formaldehyde formation,7,8 the associative dissociation energy (ADE) was calculated for different amount of Fe coverage on the V2O3 (0001) surface. Here, we define ADE

as the energy needed to remove one O atom from a X=O (X=Fe or V) surface species to vacuum.

Without any Fe coverage, the reaction simplifies to –

= + 1 2 (2.1)

2 3 2 3 2 The ADE energy is ∙then∙∙ 𝑉𝑉 𝑂𝑂 – − 𝑉𝑉 𝑂𝑂 →∙∙∙ 𝑉𝑉 𝑂𝑂 − 𝑉𝑉 ⁄ 𝑂𝑂

= ( ) + ( ) ( ) (2.2)

𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸 ∙∙∙𝑉𝑉2𝑂𝑂3−𝑉𝑉 𝐸𝐸 1⁄2 𝑂𝑂2 − 𝐸𝐸 ∙∙∙𝑉𝑉2𝑂𝑂3−𝑉𝑉=𝑂𝑂

25

This serves as an indicator of surface reducibility. A mirror slab model of the V2O3

(0001) surface as described in section 2.2.2 was used. The PBE+U functional with U-J values of

3.15 and 4.3 for V and Fe, respectively, were used.

2.2.4. Pure Oxide Surface Energy

To investigate the relationship between mixed oxide surface stability and pure oxide surface energies, the surface energies of pure oxides were calculated using bulk structures of each

TM oxide cleaved along the c-axis to make the (0001) surface. A (1×1) mirror slab model was used with 18 atomic layers and 4 atomic layers were kept fixed at the center. A 6×6×1 k-point grid with 500 eV energy cut-off were used for these calculations. Surface energies of both metal terminated and oxygen terminated surfaces were calculated. For the oxygen terminated surface, the ab initio thermodynamics approach has been used here, which takes into account the addition of oxygen on the surface referencing the chemical potential of gas phase oxygen.44,45 The surface

energy (γ) is defined as-

1 ( , ) = [ ( , , , ) ( , ) ( , )] (2.3)

𝛾𝛾 𝑇𝑇 𝑝𝑝 𝐺𝐺 𝑇𝑇 𝑝𝑝 𝑁𝑁𝑇𝑇𝑇𝑇 𝑁𝑁𝑂𝑂 − 𝑁𝑁𝑇𝑇𝑇𝑇𝜇𝜇𝑇𝑇𝑇𝑇 𝑇𝑇 𝑝𝑝 − 𝑁𝑁𝑂𝑂𝜇𝜇𝑂𝑂 𝑇𝑇 𝑝𝑝 The subscript, TM and O represent𝐴𝐴 transition metal and oxygen, respectively. T, p, N, A, µ, G are

temperature, pressure, number of atoms, surface area of the cleaved surfaces, chemical potential

and Gibbs free energy respectively. For a pressure below 100 atm, relating the Gibbs free energy

to the Helmholtz free energy and assuming vibrational energy contribution to surface energy is

small, it can be approximated that –

( , , , ) ( , , ) (2.4) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝐺𝐺 𝑇𝑇 𝑝𝑝 𝑁𝑁𝑇𝑇𝑇𝑇 𝑁𝑁𝑂𝑂 ≈ 𝐸𝐸 𝑉𝑉 𝑁𝑁𝑇𝑇𝑇𝑇 𝑁𝑁𝑂𝑂

26 where ETotal is the DFT calculated total energy of the structure and V is the volume. The chemical potential of TM and O are related by the Gibbs free energy of the bulk oxide (if there is enough bulk material to act as a thermodynamic reservoir).

2 ( , ) + 3 ( , ) = ( ) ( , ) (2.5) 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝜇𝜇𝑇𝑇𝑇𝑇 𝑇𝑇 𝑝𝑝 𝜇𝜇𝑂𝑂 𝑇𝑇 𝑝𝑝 𝑔𝑔 𝑇𝑇𝑇𝑇2 2𝑂𝑂3 𝑇𝑇 𝑝𝑝 here g represents the per unit (TM)2O3 Gibbs free energy. Using Eqn 2.4 and Eqn 2.5 and

assuming per unit (TM)2O3 Gibbs free energy ≈ DFT calculated total energy then Eqn 2.3 can be rewritten as –

1 3 × ( , ) = ( , , ) ( ) ( , ) (2.6) 2 ( ) 2 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑁𝑁𝑇𝑇𝑇𝑇 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑁𝑁𝑇𝑇𝑇𝑇 𝛾𝛾 𝑇𝑇 𝑝𝑝 �𝐸𝐸 𝑉𝑉 𝑁𝑁𝑇𝑇𝑇𝑇 𝑁𝑁𝑂𝑂 − 𝐸𝐸 𝑇𝑇𝑇𝑇2 2𝑂𝑂3 − 𝑁𝑁𝑂𝑂 − 𝜇𝜇𝑂𝑂 𝑇𝑇 𝑝𝑝 � Since the mirror𝐴𝐴 surface model has two surfaces, A = 2 × slab surface area.

The chemical potential of oxygen, µo, is the only term that is a function of temperature

and pressure in Eqn (2.6) due to the assumptions mentioned above. The ideal gas oxygen

chemical potential is given as –

1 ( , ) = ( , ) + (2.7) 2 𝑜𝑜 𝑝𝑝 𝜇𝜇𝑜𝑜 𝑇𝑇 𝑝𝑝 𝜇𝜇𝑜𝑜 𝑇𝑇 𝑝𝑝 𝑘𝑘𝑘𝑘 � 𝑜𝑜� Eqn (2.7) gives the chemical potential of oxygen at certain𝑝𝑝 temperature and pressure

o (µo(T, p)) given that the chemical potential as a function of temperature (µo(T, p )) is known at a

o reference pressure, p . Taking the zero reference state of µo(T, p) to be half of the DFT energy of

o 46 an isolated oxygen molecule, the µo(T,p ) values can be calculated from thermodynamic tables

(po=1 atm). Inserting the values of µo(T, po) in Eqn (2.7) then gives chemical potential at any

temperature and pressure. Table S1 in SI provides chemical potential of oxygen with varying

temperature at five different pressures.

27

Figure 2-3. Structures used for stability check of Fe on V2O3 (0001) at very reducing environment. Subsurface oxygens are not shown for simplicity.

2.2.5. Stable Structures of Surface-confined Mixed TM Oxides

Different reducing environments (decreasing µo) are considered to check the stability of

surface-confined mixed TM oxides. First, an extremely reducing environment (Set 1) is

considered at which there is no oxygen on the surface and one of the TM (TM1) atoms (L1 in

Figure 2.2(a)) is substituted with another TM (TM2) (Figure 2.3 with TM2=Fe and TM1=V). The

stability of this structure is compared with two other structures where the substitutions are done in

one of the subsurface TM1 bilayer location (L2, L3 in Figure 2.2(a)) as shown Figure 2.3(a, b) for

Fe/V2O3 (0001). If Δε is negative for the reactions shown in Figure 2.3(a, b), it can be concluded that TM2 prefers to segregate to subsurface when substituted into (TM1)2O3.

28

Figure 2-4. Structures used for stability check of Fe on V2O3 (0001) with 1/3 ML oxygen coverage. Subsurface oxygens are not shown for simplicity.

A more reducing environment (Set 2) is also considered where one oxygen atoms binds to one of the surface TMs. The more stable configuration between O binding to TM1 or TM2 when TM2 is surface segregated is evaluated. The stability of this structure is then compared with two other structures where the substitution of TM1 with TM2 is done in one of the subsurface

TM1 bilayers as shown in Figure 2.4 (a, b). Finally, similar calculations were done for two and three O atoms binding to the surface TMs. Mirror slab models, as described in section 2.2.2, were used for these calculations. We restrict our calculations to 1/3 ML TM2 coverage, as our goal is to represent the mixed oxide surface and this is the lowest coverage possible with a (√3×√3) R30° unit cell.

29

2.3. Results and Discussion

2.3.1 Bulk Structures

The bulk lattice parameters of Cr2O3 were found to be a=b=5.0659 Å and c =13.8865 Å

for the hexagonal unit cell. These are similar to those reported before using GGA(PW91)+U17

17,18 and experimentally measured. For Fe2O3, the calculated values were a=b=5.0992 Å,

c=13.8950 Å and c/a=2.7249. The experimentally measured value for c/a is reported to be 2.73017

which is similar to the value reported here. Previous works using GGA(PW91)+U17,47 and

PBE+U6 also give similar values of lattice parameters to those reported here.

For the bulk lattice parameters of V2O3, negligible difference between the lattice parameters with/without spin polarization was observed irrespective of the functional

(PBE/PW91) used. This is similar to previous studies by Kresse et al.9 From the results with

PBE+U, even with different magnetic alignments (FM/ AF1/ AF2/ AF3), the lattice parameters

were similar (Table S2). AF1 and AF2 results are energetically similar to those reported by

Ezhov et al.40 The calculated lattice parameters with PBE+U (U-J=3.15) were a=b=5.07923 and

c=14.37606, which are close to experimental values9 and previously reported calculated values using LDA+U40 and PW91.9 Detailed results of the bulk values are provided in the SI.

2.3.2. Predicted Surface Segregation from Pure Oxide Surface Energies

Surface energies for TM and TM=O terminated (0001) surfaces (AF1 for V2O3) are shown in Figure 2.5 with varying oxygen chemical potential (µo). The stoichiometric TM terminated surface energy is constant with µo, while the TM=O surface energy increases in a

more reducing environment (decreasing µo). For V2O3, the non-polarized calculation of V

30 termination (not shown in Figure 2.5) predicts a surface energy of 69.0 meV/Å2. This is somewhat less stable than the PBE value (~58 meV/Å2) reported by Feiten et al.10. The discrepancy between the PBE value found here and that from Feiten et al.10 reported values may

be due to our use of the U-correction. The reported values with non-polarized hybrid functional calculations10 are even lower (~50 meV/Å2). For spin-polarized calculations, the surface energy

was predicted to be 86.0 meV/ Å2 for V and -40.6 meV/Å2 for the V=O terminated surface (at zero oxygen chemical potential). Table S3 in SI reports values for other spin alignments.

Figure 2-5. Surface energies of metal and metal-oxide termination of studied (TM)2O3 (0001) surfaces.

The surface energies for TM terminated Cr2O3 and Fe2O3 (0001) surfaces were 103.1 and

72.2 meV/Å2 respectively. These values are very close to those calculated by others with DFT+U.

6,47 However, the Cr2O3 surface energy is high compared to GGA(PW91)+U results by Rohrbach

et al.17 (~82meV/ Å2). The TM=O termination values are also reported in Figure 2.5 as a function of oxygen chemical potential.

31

From our PBE+U results, among the TM surface terminations, Fe and Cr has the lowest and highest surface energy, respectively. We might, therefore, expect a mixed (Fe/Cr or V)2O3

structure to expose Fe atoms on the surface under reducing environment. For the TM=O

terminated surface, the V=O is much more stable than Fe/Cr=O termination. We might then

expect V atoms to be surface exposed and form V=O species under an oxidizing environment in

mixture of (V/Cr or Fe)2O3. The use of pure oxide surface energy to predict mixed oxide segregation is considered in section 2.3.4.

Figure 2-6. Effect of Fe and O coverage on ADE of oxygen on V2O3 (0001) (AF1 spin configuration).

2.3.3. Reducibility of the Fe/V2O3 (0001) Surface

Twenty different structural optimizations were performed using (√3×√3) R30° unit cells

(section 2.2.2) with combinations 0, 1/3, 2/3 and 1 ML coverage of Fe and O. We have chosen

the Fe substituted onto V2O3 (0001) surface to probe the dopants effects on reducibility because of the contrast between Fe2O3 (0001) having the most stable metal termination and V2O3 (0001)

32 forming the most stable X=O (X=Fe, Cr, V) termination. We expect the variation in the ADE of the mixed oxide of these two to be more significant.

Figure 2.6 shows the results of all ADE calculations for AF1 spin configuration.

Although there are some variations in magnitude using different magnetic alignments, qualitatively they are similar. For 1/3 and 2/3 ML Fe coverage, the O dissociation starts from available Fe=O surface species then from V=O. The ADE values reduce with increasing Fe coverage for the same O coverage (Figure 2.6). For 1 ML O coverage, in the pure V2O3 (0001) surface (0 ML Fe), the ADE value is ~2.4 eV greater for breaking the V=O bond then the ~-0.1 eV value for Fe=O bond with 1 ML Fe coverage. Clearly, the Fe=O is significantly more reducible than V=O.

Above results of ADE energies show that Fe substitution on the V2O3 (0001) surface can

make the surface more reducible, providing a stronger oxidant. Also, substituting Fe on the

surface lowers the V=O dissociation energy compared to a pure V2O3 (0001) surface (Figure 2.6).

Therefore, Fe may be a suitable TM oxide to mix in the surface layer of V2O3 (0001) to make a

catalyst with stronger oxidizing properties. The ADE trend matches that of the surface energies.

The relative surface energies of the oxidized and reduced surfaces suggest Fe to be more

reducible than V, in agreement with the lower ADE of Fe=O.

2.3.4. Surface/Subsurface Segregation of Substituted TM2 in (TM1)2O3 (0001)

To predict stable surface confined mixed TM oxides at different oxidizing environments,

we evaluated the most stable configuration with different O coverage and 1/3 ML of TM2

coverage of (TM1)2O3 (0001) surface. Using these structures, we studied the surface/subsurface segregation of the substituted TM2 with change of oxygen coverage. Our analysis considers only

33 the thermodynamics of the surface exchange reactions, and does not consider the kinetics

(activation barriers) of the exchange process. The results of this analysis are described below.

Table 2-1. Stability of TM2 on TM1 oxide in the absence of surface oxygen (very reducing environment). L1, L2 and L3 indicate position of substituted TM2 as shown in Fig. 2.2 Support V2O3 Cr2O3 Fe2O3 ((TM1)2O3) Dopant (TM2) Fe Cr Fe V Cr V Δε (eV) L1 0 0 0 0 0 0 L2 0.4096 -0.1659 0.7226 0.0823 -0.7895 -0.5634 L3 0.4097 -0.1210 0.7799 0.2626 -0.7204 -0.5325

2.3.4.1. 0 ML O coverage

Table 2.1 reports the difference in energies between surface (L1) and subsurface segregated TM2 structures (L2 and L3 positions) with 1/3 ML TM2 and 0 ML O coverage on

(TM1)2O3 (0001) (Set 1-Figure 2.3(a,b)). The energy differences (Δε) indicate that Fe substituted onto V2O3 (0001) prefers to segregate to the surface (positive Δε) whereas Cr prefers to go to the subsurface V2O3 (0001) (negative Δε). For Cr2O3 (0001), both substituted Fe and V prefer to be on

the surface. For Fe2O3, both Cr and V prefer to segregate to the subsurface. The

surface/subsurface segregation tendencies for these reduced surfaces correlate with their surface

energy of the pure metal terminated oxide. Fe2O3 (0001) has the lowest metal terminated surface

energy and prefers the surface position when doped into V2O3 (0001) and Cr2O3 (0001).

Similarly, V and Cr will segregate to subsurface to leave Fe atoms on the surface of doped Fe2O3

(0001).

34

2.3.4.2. 1/3 ML O Coverage

For 1/3 ML O coverage, O preferentially binds to a V atom on V2O3 (0001) when either

Fe or Cr is substituted. Any Fe atoms in the surface remain reduced and prefer to surface

segregate while Cr prefers to segregate to subsurface. For Fe\Cr2O3 (0001), Fe surface

segregation is favorable with the surface O atom binding with Cr rather than Fe (3.7 eV more

stable). For V\Cr2O3 (0001), O preferentially binds to surface V atom rather than Cr (3.7 eV more

stable). Similarly, O prefers binding to Cr and V on the Fe2O3 (0001) surface (3.92 and 5.65 eV

more stable, respectively) and cause both to surface segregate, reversing the Cr and V subsurface

tendency when no O atoms are on the surface. The tendencies of surface oxidation to pull V or Cr

to the surface in Fe2O3 (0001) is illustrated in Figure 2.7 for V. Below some value of µo, Δε will

be positive for the reaction in Figure 2.7 and V or Cr dopants would prefer subsurface. As the µo

is increased, surface oxidation will pull V or Cr to the surface. The µo to pull V to the surface was calculated to be -2.45 eV (Figure 2.8). At 1 atm oxygen pressure, this corresponds to extremely high temperatures. At very low pressures (1.32×10-9 atm/10-6 Torr) this corresponds to ~1200 K,

suggesting V will be present in the surface of Fe2O3 (0001) as V=O species under most relevant

conditions. Similarly, for Cr\Fe2O3 (0001), Cr will segregate to the subsurface if µo is decreased below -0.44 eV. At 1 atm oxygen pressure this is around 450 K.

Figure 2-7. 1/3 ML Fe and 0 ML O coverage becomes 1/3 ML O coverage after oxidation pulling V to the Fe2O3 (0001) surface. Subsurface oxygens are not shown for simplicity

35

2.3.4.3. 2/3 and 1 ML O Coverage

As the oxygen coverage is increased from 1/3 ML to 2/3 ML, a second O atom binds to an available surface TM, then a third for 1ML. For Fe doping in V2O3 and Cr2O3 (0001), Fe will be driven to the subsurface due to preference for V=O or Cr=O termination. This reaction is shown graphically for Fe in V2O3 (0001) in Figure 2.9. The transition will occur below µo = -2.26 and -0.27 eV for Fe on V2O3 (0001) and Cr2O3 (0001) respectively (Figure 2.8). At very low pressures (1.32×10-9 atm/10-6 Torr), -2.26 eV corresponds to ~1125 K and at 1 atm oxygen

pressure, -0.27 eV is around 300 K. Dependence of the transition point for Fe/V2O3 (0001) on the

initial spin alignment of the support is reported in Table S7. Although substitutional doping of Fe

in V2O3 (0001) will make it a stronger oxidant, the stability calculations show that Fe is only stable on the surface at very low pressure and high temperatures. However, the surface Fe atom weakens the remaining two V=O bonds making the surface more reducible than pure V2O3

(0001).

Figure 2-8. Δε for reaction shown in Fig. 2.7 and Fig. 2.9 with varying oxygen chemical potential

For 0 ML oxygen coverage (all surface TM atoms in 3+ state) the surface segregation preference of TM2 on (TM1)2O3 directly follows its pure oxide TM termination surface energy

36 trend (Fe > V > Cr). Whenever there is a possibility of binding to an O on the surface (5+ state of surface TM atoms), then the surface segregation preference is V=O > Cr=O > Fe=O which correlates with the sequence of TM=O termination surface energies. Therefore, for Fe2O3 (0001),

V2O3 (0001) and Cr2O3 (0001), the surface segregation tendencies of the mixed metal oxide surfaces can be directly predicted by their pure oxide surface termination energies. Experimental evidence of agreement with these DFT predictions are discussed below and detailed in the SI.

Figure 2-9. 1/3 ML Fe and 2/3 ML O coverage becomes 1 ML O coverage after oxidation. Of V2O3 (0001) Subsurface oxygens are not shown for simplicity.

Table S4-S7 in SI reports energy differences for the other two magnetic alignment for

V2O3 at the conditions discussed above. A brief study of the effect of U-J values has also been

performed. The oxidation reaction energies (Figure 2.7 and Figure 2.9) are highly dependent on

the U-J values. Lower values of U-J make the oxidation step more favorable (Table S9). Details

of these calculations are given in the SI.

Two experimental analyses of corundum oxide surfaces have been conducted to support

theoretical predictions surface behavior of mixed-corundum oxides. The two systems,

chromia/V2O3 (0001) and vanadia/Cr2O3 (0001), have been studied by scanning tunneling microscopy (STM) and synchrotron soft x-ray photoemission spectroscopy (SXPS), respectively.

The STM studies of the V2O3 (0001) surface after being exposed to sub-monolayer amounts of

chromia (7×10-8 mbar oxygen, room temperature) and subsequent annealing show evidence of

37 chromia diffusing to the subsurface, as predicted by the DFT analysis. The integrated peak

intensities of Cr-3s and V-3s from SXPS studies after vanadium oxide deposition on Cr2O3

(0001) and subsequent annealing to higher temperature (720 K) show no significant change. This

is further confirmed by photon-energy dependent studies, indicating vanadia remains at the

surface and there is negligible diffusion of vanadium into the subsurface region. This also agrees

with DFT predictions. Details of the experimental procedure and results are provided in the SI

(section 2.6) and some more detailed study of the surfaces are reported by Kramer et al.48 While these experimental observations provide support for our DFT calculated predictions, they consider a subset of systems and environmental conditions, such that the DFT work provides predictions beyond what was considered experimentally.

2.4. Conclusions

We have used DFT and ab initio thermodynamics calculations to predict the stability of surface confined mixed corundum oxides (V2O3, Fe2O3, Cr2O3). Our calculations predict that, for these oxides with similar lattice parameters, surface-segregated mixed metal oxides on their

(0001) surface follows the stability of their pure oxide termination. For 3+ (TM terminated) and

5+ state (TM=O terminated) the surface segregation preferences are Fe > V > Cr and V=O >

Cr=O > Fe=O respectively. Experimental observations of subsurface segregation of chromia on

V2O3 (0001) and surface segregation of vanadia on Cr2O3 (0001) match the DFT predictions.

Transition points in oxygen chemical potential are identified, across which surface and subsurface

segregation preference switches due to the surface oxidation. While decreasing from 1/3 to 0 ML

O coverage, surface Cr and V will exchange location with a subsurface Fe in Fe2O3 (0001) below an oxygen chemical potential of -0.44 and -2.45 eV, respectively. Decreasing from 1 ML to 2/3

ML O coverage, subsurface Fe in V2O3 (0001) and Cr2O3 (0001) exchanges location with surface

38

V/Cr below -2.26 and -0.27 eV, respectively. The Fe=O bond is weaker than the V=O bond, and is therefore more reducible, if present on surface. However, only Fe metal (3+ state) termination is stable on the V2O3 (0001) surface under practically relevant oxygen chemical potentials. The

reduced surface Fe atoms can work as active sites for oxy-hydrogenation of methanol in formaldehyde formation and require less energy to form than V species in pure V2O3 surface

(0001). The surface Fe species do increase the reducibility of the V=O species on the V2O3 (0001)

surface which can help with the H2O formation step as well. Similarly, substitution of surface Fe with V in Fe2O3 (0001) surface increases its oxygen storage capacity and can potentially increase the redox rate of hydrocarbon oxidation in chemical looping combustion technology.

2.5 Acknowledgements

The authors gratefully acknowledge funding for this research from the National Science

Foundation, Grant #1505607 and #1505609. Training provided by the Computational Materials

Education and Training (CoMET) NSF Research Traineeship (Grant # DGE-1449785) is

acknowledged. This work used the Extreme Science and Engineering Discovery Environment

(XSEDE),49 which is supported by National Science Foundation grant number ACI-1548562.

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43 X. Huang, S. K. Ramadugu and S. E. Mason, Surface-Specific DFT + U Approach Applied to α-Fe 2 O 3 (0001), J. Phys. Chem. C, 2016, 120, 4919–4930. 44 K. Reuter and M. Scheffler, Composition, structure, and stability of RuO2(110) as a function of oxygen pressure, Phys. Rev. B, 2001, 65, 035406. 45 J. Rogal, K. Reuter and M. Scheffler, Thermodynamic stability of PdO surfaces, Phys. Rev. B, 2004, 69, 075421. 46 D. R. Stull and H. Prophet, JANAF thermochemical tables, DTIC Document, 1971. 47 A. Kiejna and T. Pabisiak, Surface properties of clean and Au or Pd covered hematite (α- Fe 2O3) (0001), J. Phys. Condens. Matter, 2012, 24, 095003. 48 A. R. Kramer, L. Bignardi, P. Lacovig, silvano lizzit and M. Batzill, Comparison of surface structures of corundum Cr2O3(0001) and V2O3(0001) ultrathin films by x-ray photoelectron diffraction, J. Phys. Condens. Matter. 49 J. Towns, T. Cockerill, M. Dahan, I. Foster, K. Gaither, A. Grimshaw, V. Hazlewood, S. Lathrop, D. Lifka, G. D. Peterson, R. Roskies, J. R. Scott and N. Wilkins-Diehr, Comput. Sci. Eng., 2014, 16, 62–74

42

Supplementary information

1. Oxygen Chemical Potential at Different Relevant Pressure and Temperatures

Table S1: Oxygen chemical potential, µo (O atom at Oxygen molecule at 0 K as reference) at different pressures and temperatures.

43

2. Bulk Lattice Parameters for V2O3

For the bulk lattice parameters of V2O3, both PBE and PW91 functional gave similar values under DFT+U framework (Table S2). Varying U-J values slightly (3.15 vs. 3.25), very small change in the lattice parameters were observed. Negligible difference between the lattice parameters with/without spin polarization was observed. All the lattice parameters are very close to experimentally measured lattice parameters. Also, similar to previous studies by Kresse et al.1, introducing spin polarization did not make the internal structure any better. From the results with

PBE+U, it is observed with even with different magnetic alignments (FM/AF1/AF2/AF3) the lattice parameters were almost the same. AF1 and AF2 results are energetically almost similar as reported by Ezhov et al.2 who reported a 5K (4.31 meV) difference between the arrangements.

Table S2: Lattice parameters of optimized V2O3 hexagonal unit cell.

Lattice Parameters

Mag. Method Functional U-J a c a/c Order DFT+U PBE 3.15 -- 4.96127 14.04220 0.35331

DFT+U (Spin. Pol) PBE 3.15 FM 5.08141 14.38223 0.35331

DFT+U (Spin. Pol) PBE 3.15 AF1 5.07923 14.37606 0.35331

DFT+U (Spin. Pol) PBE 3.15 AF2 5.07746 4.37105 0.35331

DFT+U (Spin. Pol) PBE 3.15 AF3 5.07787 14.37222 0.35331

DFT PW91 0 -- 0.35331 4.90410 13.88050 DFT (Spin. Pol) PW91 0 FM 0.35331 4.93130 13.95740 DFT+U PW91 3.25 -- 0.35331 4.94780 14.00420 DFT+U (Spin. Pol) PW91 3.25 FM 0.35331 5.07890 14.37520

Exp 1 4.94000 13.97000 0.35361

Exp 2 4.51000 14.00200 0.32210

44

3. Effect of magnetic arrangement on surface energy of V2O3 (0001)

Table S3: Surface energies of V2O3 with different termination and magnetic arrangement. Surface Termination FM AF1 AF2 AF3 V Termination 101.59933 85.91425 89.3825 98.27945 V=O Termination* 31.49121 40.63948 39.25028 40.43035 *at zero oxygen chemical potential

4. Effect of magnetic arrangement on surface/subsurface segregation of substituted TM in V2O3 (0001)

4.1. 0 ML O coverage 1/3 ML Fe

Table S4: Energy difference wrt. 1/3 ML Fe on surface in TM terminated surface (very reducing environment). L1, L2 and L3 indicates atomic layers as shown in Fig 2.1 Substituted Fe position AF3 AF1 AF2 L1 0 0 0 L3 0.44763 0.40958 0.71676 L2 0.44302 0.40972 0.45891 Diff. with Most Stable Fe Top 0.44902 0.17138 0

4.2. 0 ML O coverage 1/3 ML Cr

Table S5: Energy difference wrt. 1/3 ML Cr on surface in TM terminated surface. L1, L2 and L3 indicates atomic layers as shown in Fig 2.2 Substituted Cr position AF3 AF1 AF2 L1 0 0 0 L3 0.05936 0.12103 0.09073 L2 0.06283 0.16592 0.20691 Diff. with Most Stable Cr Top 0.14135 0 0.05484

45

4.3. ML O Coverage 1/3 ML Fe 𝟏𝟏 Table S6: Energy𝟑𝟑 difference wrt. 1/3 ML Fe on surface with 1/3 ML O coverage. L1, L2 and L3 indicates atomic layers as shown in Fig 2.2 TM Positions AF3 AF1 AF2 Fe, V, VO on surface 0 0 0 2×V, VO surface (L1), Fe subsurface (L3) 0.39920 0.41048 0.60642 2×V, VO surface (L1), Fe 0.3610 0.3843 0.4780 subsurface (L2) 4 8 8 0.7265 0.3106 Diff with Most Stable Fe top 1 2 0

4.4. ML O Coverage 1/3 ML Cr 𝟏𝟏 Table S7: Energy𝟑𝟑 difference wrt. 1/3 ML Cr on surface with 1/3 ML O coverage. L1, L2 and L3 indicates atomic layers as shown in Fig 2.2 TM Positions AF3 AF1 AF2 Cr, V, VO on surface (L1) 0 0 0 2×V, VO surface (L1), Cr subsurface (L3) 0.12018 0.05533 0.06539 2×V, VO surface (L1), Cr subsurface (L2) 0.02566 0.14413 0.14429 Diff with Most Stable Cr Top 0.20257 0.00598 0

4.5. Transition oxygen chemical potential for Fe subsurface segregation during oxidation of 2/3 ML O coverage to 1 ML O coverage

Table S8: Chemical potential for which Δε becomes zero for the reaction shown in Figure 9. L2 and L3 indicates atomic layers as shown in Fig 2.2 AF3 AF1 AF2 L3 -1.91943 -2.10534 -1.92397 L2 -2.01474 -2.26753 -2.09882

46

5. Effect U-J Value:

Figure 11: Reaction shown in Figure 9 in two steps. The U-J values used here might introduce another uncertainty in the predicted value. To

show this, the reaction in Figure 10 was broken down in to two steps. In step 1, the Fe goes from

surface to the subsurface. In step 2, the V on the surface becomes oxidized (Figure S1). The Δε of

the reactions are given in Table S. The step of oxidation is dependent highly on U-J value. A 0.85

eV increase in U-J for V, increases the Δεb of oxidation step by 0.64 eV while the Δεb increases by

0.14 eV. However, at this point this uncertainty associated with U-J variation has not been

quantified.

Table S9: Δε for 2 step reaction shown in Figure S1 U-J Δεa Δεb 2.5 0.6315 -10.6207 3.15 0.7305 -10.1941 4 0.8702 -9.5524

The uncertainty of U-J value can somewhat be solved by using hybrid functional like

HSE06 or PBE0. However, this includes a choice of extent of the mixing of exact exchange.

6. Experimental Study

6.1. Methods

Two experimental analyses of corundum oxide surfaces have been conducted to verify theoretical predictions of the stability of oxidized corundum-forming transition metals at the surface of dissimilar corundum oxide substrates. The two systems, chromia/V2O3 (0001) and

47 vanadia/Cr2O3 (0001), have been studied by scanning tunneling microscopy (STM) and

synchrotron soft x-ray photoemission spectroscopy (SXPS), respectively. A short description of

the methods is given in the following section.

6.1.1. STM of Chromia on V2O3 (0001)

STM studies were performed in an ultra-high vacuum (UHV) chamber with a base

-10 pressure in the low 10 mbar range. An ~10 nm thick V2O3 (0001) film was grown on a W (110)

single crystal by pulsed laser deposition. A V2O5 ceramic target was ablated using a solid state

Nd:YAG laser (430 mJ power at wavelength of 355 nm and 5 Hz repetition frequency). The film

-6 was deposited in 1×10 mbar O2 at room temperature. We have previously shown that this

3 procedure results in the growth of V2O3 films and may be compared to vapor deposition

4–6 4,7 procedures of V2O3 films on various metal single crystal substrates including W (110). The

V2O3 film grown by PLD was transferred to a UHV STM with help of a vacuum suitcase that

maintained a pressure of ~10-8 mbar during transfer. Subsequently the sample was annealed at

850 K for 30 min within the UHV STM chamber. Such prepared V2O3 thin films are exposed to small (sub-monolayer) amounts of chromia, by vapor deposition of chromium in 7×10-8 mbar oxygen, with the sample held at room temperature. To study the surface stability of these chromia deposits the sample is subsequently annealed to 720 K and 820 K.

6.1.2. SXPS of Vanadia on Cr2O3 (0001)

SXPS studies were performed at the Elettra-synchrotron in Italy at the SuperESCA UHV- endstation.8 By tuning the photon energy to emit photoelectrons with a kinetic energy that falls close to the minimum of the energy-dependent inelastic mean free path length, extreme surface sensitivity can be obtained. This makes SXPS an ideal tool for characterizing the stability of atomic species at the surface.

48

Cr2O3 films were prepared by oxidation of a Cr (110) single-crystal. The preparation procedure for formation of the Cr2O3 film followed the procedure previously described by Bender

et al.9. Briefly, the Cr (110) crystal was cleaned by cycles of sputtering and annealing to 1000 K.

This procedure could not remove C and N contamination completely, which are known as major contaminants in Cr-crystals. However, these contaminants did not affect the subsequent oxidation

-6 and formation of a Cr2O3 (0001) film. Oxidation was performed by leaking 1×10 mbar of O2 into

the UHV chamber and annealing of the sample at 800 K for 3 min. Subsequently the sample was

flash-annealed to 1000 K in UHV. No metallic Cr signal was detected in XPS and the low energy

electron diffraction (LEED) pattern exhibited the hexagonal structure of Cr2O3 (0001). The Cr-3s

core-level of the Cr2O3 monolayer shows a peak at 74.78 eV binding energy and a satellite peak

10 at 78.87 eV. This is consistent with previous reports for Cr2O3. Vanadium oxide was then

-8 deposited on the Cr2O3 surface by vapor deposition of vanadium in 1×10 mbar O2 with the sample at room temperature. The vanadium oxide deposition was monitored with fast SXPS by sweeping the kinetic energy corresponding to the Cr-3s and V-3s region using a photon energy of

-8 190 eV. Subsequent annealing in 1×10 mbar O2 was done to a temperature of 720 K to study

surface stability.

Our DFT calculations, as well as the pure surface energies, predict that Cr will segregate

to subsurface in V2O3 (0001) and V will be stable in Cr2O3 (0001) surface for any temperature-

pressure conditions. Experimental observations of these predictions are described in this section.

6.2. Experimental Results

Our DFT calculations, as well as the pure surface energies, predict that Cr will

segregate to subsurface in V2O3 (0001) and V will be stable in Cr2O3 (0001) surface for any

temperature-pressure conditions. Experimental observations of these predictions are described in

this section.

49

6.2.1. Chromia on V2O3 (0001)

After annealing of a V2O3 film grown by PLD in UHV STM chamber, STM imaging of the sample revealed flat terraces and some deeper ‘trenches’ suggesting an island growth with the

‘trenches’ indicating grain (or island) boundaries. In this study, we focus on the morphology of the terraces. Figure 10(a) shows STM images of the V2O3 (0001) surface. The terraces exhibit a

domain structure, which we attribute to areas terminated by vanadyl-oxygen and areas where the

terminating oxygen has been removed. Such clustering of vanadyl-oxygen in nano-domains has

11–17 been previously observed in partially reduced V2O3 (0001) surface by STM. This gives the

V2O3 surface a characteristic appearance that helps in identifying the surface termination.

Figure S2: Scanning tunneling microscopy observations of chromia deposition on V2O3 (0001) thin films. The as grown V2O3 (0001) film is shown in (a) [scan area: (a1) 40×40 nm and (a2)20×20 nm]. STM images after chromia deposition at room temperature is shown in (b), and after annealing to 720 K in (c) [scan areas: 40×40 nm]. STM images after further annealing to 820 K are shown in (d) [scan area: (d1) 40×40 nm and (d2)20×20 nm]. Tunneling bias voltages and tunneling currents for the subfigures were: (a1) 1.0V, 1.0nA, (a2) 1.5V, 1.0nA,(b) 1.2V, 0.2nA, (c) 1.1V, 0.2nA, (d1) 1.1V, 0.15nA, (d2) 1.1V, 0.5nA.

50

Exposure to sub-monolayer amounts of chromia (7×10-8 mbar oxygen, room temperature)

of this surface causes a disordering of the surface and formation of small clusters that are

associated with chromia shown in Figure 10(b). After subsequent annealing to 720 K, larger

clusters are formed at the surface as shown in Figure 10(c). It is not possible to unambiguously

identify the composition of these clusters from STM images. They may consist of chromia or

vanadia. The latter would form if chromium cations diffuse into the vanadia forming a solid

solution. This process would require site exchange of vanadium ions with chromium ions and

thus expelling vanadium cations to the surface where they could rearrange into small vanadia ad-

islands on top of the vanadia terraces. Evidence for this process becomes clearer at higher

annealing temperatures of 820 K, shown in Figure 10(d). At this annealing temperature, the small

islands aggregated into larger well-defined islands at the surface. These islands are of atomic- layer height and exhibit triangular shapes, as expected from the hexagonal structure of the corundum (0001) terraces. Importantly, the same nanostructure is observed on the islands and the lower terraces that we attributed to vanadyl-terminated domains as for the as-prepared V2O3 film.

Atomic corrugation consistent with vanadyl termination can also be discerned which is

highlighted in the inset of Figure 10(d). This demonstrates that this surface has the same

termination as pure V2O3 and consequently strongly suggests that chromia has diffused subsurface, as predicted in the DFT simulations.

6.2.2. Vanadia on Cr2O3 (0001)

The integrated peak intensities of Cr-3s and V-3s during vanadium oxide deposition on

Cr2O3 (0001) are plotted in Figure 11(a). It indicates linear decrease and increase of the peak intensity with deposition time for Cr-3s and V-3s, respectively. Linear dependence of the peak intensities indicates that the vanadia amount deposited was sub-monolayer. Subsequent annealing

-8 in 1×10 mbar O2 shows no significant change in either the Cr-3s or the V-3s intensities up to

51 annealing temperature of 720 K, as shown in Figure 11(b). This suggests that vanadia remains at the surface and there is negligible diffusion of vanadium into the subsurface region. This is further confirmed by photon-energy dependent studies. Figure 11(c) reports the Cr-3s and V-3s core levels after annealing, measured with 160 eV and 190 eV photon-energies. The inelastic mean free paths lengths of the corresponding photoelectrons are estimated18 to be ~0.5 and ~0.6

nm, respectively. Thus 160 eV photon energy is more surface sensitive than 190 eV. Figure 11(c)

shows an increased V-3s/Cr-3s peak ratio at 160 eV, demonstrating that V is at the surface.

Figure S3: Soft x-ray photoemission spectroscopy (SXPS) investigation of vanadia deposition and thermal stability on a Cr2O3 thin film. a) Fast SXPS spectra (hν= 190eV) during deposition of V and total peak area of V and Cr 3s as a function of deposition time (inset). b) Monitoring of the surface composition by fast SXPS (hν= 190eV) as a function of annealing temperature. The inset shows the V-3s and Cr-3s peak area during annealing and cooling of the sample plotted as a function of temperature.

52

While the total peak intensity for V-3s core level does not change with annealing, the peak shape undergoes some variation with annealing, which is shown more clearly in Figure

11(d). In all cases the V-3s peak can be fitted with two components, whose binding energy does not vary significantly but their relative intensity changes. The low binding energy component has an energy of 67.71 eV and the separation between the two components is ~ 2.3eV. This is consistent with the V-3s spectra for V2O3, for which it was argued that the coupling of the spin of

the 3s photo-hole with total spin of the partially filled 3d band in V2O3 gives rise to an exchange splitting of the 3s core-level19. The magnitude of the measured splitting is also consistent with

20 that measured previously for V2O3. The intensity ratio of the exchange split band is given by

spin states and should be 0.5 in the case of pure V2O3. The ratio observed in the studies reported here diverge from that of pure V2O3 which may be expected for different coordination and the

possible substitution of cations in the Cr2O3 surface. The relative intensity variations of the two

components with annealing is likely an indication of local rearrangement and reordering of the V-

cations at the surface. The proximity of the Cr-3s peak with the V-3s also complicates the subtraction of an appropriate background which may significantly affect the ratio of the two V-3s components. Important for this study is, however, that despite the mobility of the vanadium cations that enables local rearrangements, the vanadium remains at the surface indicating that it is the energetically favorable location. This observation is consistent with the DFT simulations that

V will surface segregate to the Cr2O3 (0001) surface.

53

References

1 G. Kresse, S. Surnev, J. Schoiswohl and F. P. Netzer, V2O3(0001) surface terminations: a density functional study, Surf. Sci., 2004, 555, 118–134. 2 S. Y. Ezhov, V. I. Anisimov, D. I. Khomskii and G. A. Sawatzky, Orbital Occupation, Local Spin, and Exchange Interactions in V 2 O 3, Phys. Rev. Lett., 1999, 83, 4136. 3 A. Kramer, E. Sutter, D. Su and M. Batzill, Epitaxial corundum-VTiO3 thin films grown on c-cut sapphire, Thin Solid Films, 2017, 631, 85–92. 4 A. C. Dupuis, M. Abu Haija, B. Richter, H. Kuhlenbeck and H. J. Freund, V2O3(0001) on Au(111) and W(110): growth, termination and electronic structure, Surf. Sci., 2003, 539, 99–112. 5 A. K. Kundua and K. S. R. Menon, in International Conference on Condensed Matter and Applied Physics, eds. M. S. Shekhawat, S. Bhardwaj and B. Suthar, 2016, vol. 1728. 6 H. Niehus, R. P. Blum and D. Ahlbehrendt, Structure of vanadium oxide (V2O3) grown on Cu3Au(100), Surf. Rev. Lett., 2003, 10, 353–359. 7 M. Abu Haija, S. Guimond, Y. Romanyshyn, A. Uhl, H. Kuhlenbeck, T. K. Todorova, M. V. Ganduglia-Pirovano, J. Dobler, J. Sauer and H. J. Freund, Low temperature adsorption of oxygen on reduced V2O3(0001) surfaces, Surf. Sci., 2006, 600, 1497–1503. 8 W. Jark, Soft x-ray monochromator configurations for the ELETTRA undulators: A stigmatic SX700, Rev. Sci. Instrum., 1992, 63, 1241–1246. 9 M. Bender, D. Ehrlich, I. N. Yakovkin, F. Rohr, M. Baumer, H. Kuhlenbeck, H. J. Freund and V. Staemmler, Structural rearrangement and surface magnetism on oxide surfaces: a temperature-dependent low-energy electron diffraction-electron energy loss spectroscopy study of Cr2O3 (111)/Cr (110), J. Phys.-Condens. Matter, 1995, 7, 5289– 5301. 10 E. Agostinelli, C. Battistoni, D. Fiorani and G. Mattogno, An XPS study of the electronic structure of the ZnxCd1- xCr2 (X= S, Se) spinel system, J. Phys. Chem. Solids, 1989, 50, 269–272. 11 F. E. Feiten, H. Kuhlenbeck and H. J. Freund, Reducing the V2O3(0001) surface through electron bombardment - a quantitative structure determination with I/V-LEED, Phys. Chem. Chem. Phys., 2016, 18, 3124–3130. 12 F. Pfuner, J. Schoiswohl, M. Sock, S. Surnev, M. G. Ramsey and F. P. Netzer, The metal- insulator transition in V2O3(0001) thin films: surface termination effects, J. Phys.- Condens. Matter, 2005, 17, 4035–4047. 13 J. Schoiswohl, M. Sock, S. Surnev, M. G. Ramsey, F. P. Netzer, G. Kresse and J. N. Andersen, V2O3(0001) surface terminations: from oxygen- to vanadium-rich, Surf. Sci., 2004, 555, 101–117. 14 A. J. Window, A. Hentz, D. C. Sheppard, G. S. Parkinson, D. P. Woodruff, W. Unterberger, T. C. Q. Noakes, P. Bailey, M. V. Ganduglia-Pirovano and J. Sauer, The structure of epitaxial V2O3 films and their surfaces: A medium energy ion scattering study, Surf. Sci., 2012, 606, 1716–1727. 15 F. P. Leisenberger, S. Surnev, L. Vitali, M. G. Ramsey and F. P. Netzer, Nature, growth, and stability of vanadium oxides on Pd(111), J. Vac. Sci. Technol. -Vac. Surf. Films, 1999, 17, 1743–1749. 16 F. E. Feiten, H. Kuhlenbeck and H.-J. Freund, Surface Structure of V2O3(0001): A Combined I/V-LEED and STM Study, J. Phys. Chem. C, 2015, 119, 22961–22969.

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17 F. E. Feiten, J. Seifert, J. Paier, H. Kuhlenbeck, H. Winter, J. Sauer and H.-J. Freund, Surface Structure of V2O3(0001) Revisited, Phys. Rev. Lett., 2015, 114, 216101. 18 S. Tanuma, C. J. Powell and D. R. Penn, Calculations of electron inelastic mean free paths (IMFPS). IV. Evaluation of calculated IMFPs and of the predictive IMFP formula TPP-2 for electron energies between 50 and 2000 eV, Surf. Interface Anal., 1993, 20, 77–89. 19 R. Zimmermann, R. Claessen, F. Reinert, P. Steiner and S. Hufner, Strong hybridization in vanadium oxides: evidence from photoemission and absorption spectroscopy, J. Phys.- Condens. Matter, 1998, 10, 5697–5716. 20 S. Shin, Y. Tezuka, T. Kinoshita, A. Kakizaki, T. Ishii, Y. Ueda, W. Jang, H. Takei, Y. Chiba and M. Ishigame, Observation of local magnetic moments in the Mott transition of V2O3 by means of 3s photoemission, Phys. Rev. B, 1992, 46, 9224–9227.

55

Chapter 3

Predicting monolayer oxide stability over low-index surfaces of TiO2 polymorphs using ab initio thermodynamics

[Manuscript in preparation]

3.1 Introduction

Titania (TiO2) is used as a white pigment in paint industry, as photocatalyst for removal of organic contaminations and production of hydrogen1 Its industrial use also includes as gas

sensor and heterogeneous catalyst. TiO2 is a common low cost oxide support for metal in

2 heterogeneous catalysis. Metals are typically well dispersed on the TiO2 support either as metal/metal cluster or oxide film dependent on pressure/temperature. When deposited on the surface, the supported metals/metal oxides can have a catalytic property that is completely different than the support or the metals bulk phase. For example, while a clean rutile TiO2(110)

surface2,3 is inactive for methanol oxidation to formaldehyde, a vanadium oxide monolayer on

2 TiO2(110) catalyzes this reaction. The catalytic reactivity of these systems also depend on the phase of the support oxide. For example, Au on anatase TiO2 was found to have almost two

3 orders of magnitude higher H2 production rate than on rutile TiO2.

Systems in which there are more than one oxide either as bulk mixed, substituted, in a core-shell structure or as thin film can be referred to as Multi-component metal oxides (MMOs).

In supported monolayer MMO films, the added monolayer oxide conforms to the crystal lattice of the support oxide. For example, RuO2/TiO2(110) surface was shown to have 3 conformal layers

56

4 of rutile RuO2 on the rutile TiO2(110) termination of P25 Titania powder. This catalyst is used in industrial deacon process where Cl is recovered from HCl by oxidation. For monolayer MMOs, the ideal thickness would be one monolayer. Ultra-thin oxides are already known to have different interactions with metals than their thick counterpart.5,6 By using different combinations

of oxides as monolayer and support, the catalytic properties of the combination can be tuned.

7–9 TiO2 supported metal catalysts have been investigated both experimentally and computationally.10,11 However, few works are available on supported monolayer MMOs of

4,12 TiO2. The number of combinations of possible monolayer metal oxides on TiO2 support is

quite large due to its three stable polymorphs. In addition to that, the monolayers can be

metastable, which makes synthesis of such systems and experimental discovery of stable

combinations more difficult. We have previously shown that for oxides with similar crystal

structure and lattice parameters, stability of their mixed and monolayer combinations are directly

correlated to their pure oxide surface energy.13 It is not well understood if such correlations hold for different terminations and phases of the same support oxide. In addition to its widespread use

1,14 as support in heterogeneous catalysis, TiO2 with its three different stable polymorphs (rutile, anatase, brookite) and well-studied surface terminations of each1,2,15–19 makes it the perfect

candidate for such investigation. Here, we present as systematic investigation of stability of

monolayers of transitions oxides over different stoichiometric terminations of anatase, brookite

and rutile TiO2 using density functional theory (DFT). We investigate if the surface energy is

correlated with monolayer stability for these systems and look for other possible properties that

might be have some correlation. Finally, we apply a correction20 to the bulk reference state of the

coating oxides to predict stability compared to coating oxide particles.

57

3.2 Computational methods

3.2.1 Electronic structure calculations

Electronic structure calculations were performed using DFT with a plane wave basis set and the Perdew–Burke–Ernzerhof (PBE) exchange correlation21 potential as implemented in the

Vienna Ab initio Simulation Package (VASP)22,23. The interaction between the ionic cores and valence electrons is described by the projector augmented wave (PAW) method24. All

calculations are spin polarized. The k-point grids, generated using the Monkhorst-Pack scheme25, are given in Table 1 for bulk calculations. Vosko-Wilk-Nusair interpolation26 for the correlation

part of the exchange correlation functional is used. Energy was converged to 3 meV with respect

to k-point sampling and plane-wave basis set energy cut-off. Structures were optimized until forces on each atom were less than 0.05 eVÅ-1. For asymmetric slab models, a dipole correction27

was used to correct the unphysical interaction between dipoles in adjacent images along the

surface normal.

Transition metal oxides that are not fully oxidized have strongly-correlated localized d or f electrons. Conventional DFT methods with the generalized gradient approximation (GGA) for exchange and correlation suffer from inaccuracies in representing strongly correlated systems.

The intra-atomic exchange and Coulomb terms are not properly cancelled, leading to a well- known problem of self-interaction over-repulsion also known as ‘delocalization error’. This inaccurate delocalized description can cause unreliable changes in total energy during change of oxidation state. To correct this error, the DFT+U method28 is used, which adds a Hubbard U correction term to these localized states and can provide accurate band gaps or reduction energetics. The accuracy of this approach relies on the choice of U value, which can be tuned to match an experimental band gap29–31 or reduction energy32, however, this empiricism limits

58 predictive ability and transferability to other structures. Despite this limitation, a vast literature now exists parameterizing U values for various metal oxides and matches experimental observations.33,34 Here, the formulation introduced by Dudarev et al.35 is used and values for U-J

used for f-electrons of Ce and d-electron of all other metals are reported in Table 1.

3.2.2 Surface energy for TiO2 supports

Surface energy is defined as the energy needed to cleave a surface from the bulk, expressed per area. For “stoichiometric surfaces” studied here the surface termination maintains the same stoichiometry as the bulk oxide and thus the surface energy (γ) can be calculated as–

1 = × {[ ] × [ ] } (3.1) 2 𝛾𝛾 𝑇𝑇𝑇𝑇𝑂𝑂2 𝑡𝑡 − 𝑡𝑡 𝑇𝑇𝑇𝑇𝑂𝑂2 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 where A is the surface area of𝐴𝐴 one side of the slab, t is the number of functional units in

the slab, subscript bulk in [TiO2]bulk represents the per functional unit energy of TiO2 in the bulk

oxide in the same phase as the support.

3.2.3 Monolayer oxide formation energy:

The monolayer oxide formation energy (ΔGML) is defined as the energy to transform a layer of bulk oxide to a conformal monolayer coating on TiO2 surface and can be calculated as-

[ ] , + [ ] + (3.2) 𝛥𝛥𝛥𝛥𝑀𝑀𝑀𝑀 2 𝛿𝛿 𝑇𝑇𝑇𝑇𝑂𝑂2 𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑣𝑣�𝑀𝑀𝑝𝑝𝑂𝑂𝑞𝑞�𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏−𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 �⎯⎯� �𝑀𝑀𝑝𝑝𝑂𝑂𝑞𝑞−𝛿𝛿�𝑣𝑣𝑜𝑜𝑜𝑜 𝑇𝑇𝑇𝑇𝑂𝑂2 𝑡𝑡 𝑣𝑣 𝑂𝑂2 where t represents the number of functional units in the TiO2 slab model, v is the number

functional units of M oxide needed to form a conformal stoichiometric monolayer, and (p, q)

represents the stoichiometry of metal and oxygen in the M coating oxide. δ accounts for the

potential change in monolayer oxidation state relative to the reference bulk oxide and can be

59

positive or negative. The energies of all condensed phases are approximated as DFT calculated

total energies. With this approximation, all temperature and pressure dependence is due to oxygen

chemical potential, µo. Under the ideal gas approximation, µo(T,p) can be calculated as –

1 ( , ) = ( , ) + (3.3) 2 𝑜𝑜 𝑝𝑝 𝑜𝑜 𝑜𝑜 𝑜𝑜 o 𝜇𝜇 𝑇𝑇 𝑝𝑝 𝜇𝜇 𝑇𝑇 𝑝𝑝 𝑘𝑘𝑘𝑘 � � where p is a reference pressure and k is the Boltzmann𝑝𝑝 constant. We can obtain

( , )from thermodynamic tables,36 and put values on the relevant DFT scale by using the 𝑜𝑜 𝜇𝜇DFT𝑜𝑜 𝑇𝑇 calculated𝑝𝑝 energy of isolated oxygen molecule as our reference state.

3.2.4 Correction for particle reference:

Eqn 3.2 gives the energy to form a monolayer coating with reference to the pure bulk oxide.

In an actual physical process, the coating would compete for stability with a particle of some finite size, which itself would have a surface energy. As, particles can have different shapes and include a large number of atoms, we cannot simply use DFT to directly calculate a reference particle energy.

As we have done previously20 (Chapter 4 for details on this method) we reference a spherical particle of radius, r, with its surface energy approximated as that of the lowest energy single crystal facet of the bulk oxide. For a particle radius of r, the per functional unit particle energy can be calculated as-

× + 4 × , , = 2 (3.4) 𝑛𝑛 𝐸𝐸�𝑀𝑀𝑝𝑝𝑂𝑂𝑞𝑞� 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝜋𝜋𝑟𝑟 𝛾𝛾𝑚𝑚𝑚𝑚𝑚𝑚 𝐸𝐸�𝑀𝑀𝑝𝑝𝑂𝑂𝑞𝑞� 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 where n is the number of functional units present in the 𝑛𝑛particle and γmin is the surface energy of the lowest energy surface termination of the coating oxide. The value of γmin can be a function of the oxygen chemical potential.20

60

3.2.5 Bulk structures

Figure 3-1. Unit cells of (a) anatase (b) brookite (c) rutile TiO2 bulk oxides. Blue and red spheres represent Ti and O atoms, respectively.

3.2.5.1 TiO2 phases

Optimized unit cells of anatase, rutile, and brookite are shown in Fig 3.1. Rutile and

anatase have tetragonal crystal structure while brookite has an orthorhombic crystal structure. In

all three structures, Ti forms TiO6 octahedra. For anatase and rutile, the short (4-bonds) and long

(2-bonds) Ti-O bonds in each phase have the same bond length, while for brookite this is not

true17. Our calculated lattice parameters compare well previously reported values in literature and are given in Table 3.1 with references. Our DFT calculation predicts anatase to be 5.7 meV more stable than rutile and brookite to be the least stable. Relative stability of rutile and anatase TiO2

compared to experimental observation is a well-known issue of DFT1,17,18 but DFT has been successful at predicting surface structure and relative surface energies.

61

3.2.5.1 Coating metal oxides

Reference state bulk oxides include CoO, NiO, CuO, ZnO, PdO, Mn3O4, V2O3, Cr2O3,

Fe2O3, α-ZrO2, MoO2, RuO2, CeO2, IrO2 and α-PtO2. Calculated lattice parameters for each oxide are given in Table 3.1 which are in agreement with available literature and experimental values.

We chose reference oxide states that are stable over a wide range of pressure and temperature that

Cutoff Lattice Parameters ( Å, degree) k-point Function Oxide U-J Energy Ref grid a b c α β γ al Units (eV) 1 2,3 a-TiO2 4.2 6×6×3 500 3.873 3.873 9.731 90 90 90 4 1 2,4 b-TiO2 4.2 8×8×4 500 9.38 5.571 5.253 90 90 90 8 1 3,5,6 r-TiO2 4.2 4×4×7 500 4.689 4.689 3.02 90 90 90 2 Ag 0 9×9×9 600 2.937 2.937 2.937 60 60 60 1 7 Au 0 9×9×9 450 4.172 4.172 4.172 90 90 90 4 8 CoO 3.39 5×5×5 650 8.523 8.523 8.523 90 90 90 32 10 NiO 5.31 12×12×12 490 4.238 4.238 4.238 90 90 90 4 11 CuO 0 5×6×4 650 4.684 3.423 5.129 90 99.54 90 4 12 ZnO 0 7×7×7 450 3.294 3.294 5.277 90 90 120 2 13 PdO 0 12×12×12 450 3.102 3.102 5.439 90 90 90 2 14 15 15,16 Mn3O4 4 4×4×2 650 5.882 5.882 9.597 90 90 90 4 17 18 V2O3 3.15 6×6×2 720 5.078 5.078 14.372 90 90 120 6 17 19 Cr2O3 4 6×6×2 720 5.066 5.066 13.886 90 90 120 6 17 20 Fe2O3 4.3 6×6×2 720 5.100 5.100 13.895 90 90 120 6 21 α-ZrO2 0 6×6×6 650 5.203 5.266 5.375 90 99.25 90 4 22 MoO2 0 5×5×7 650 5.662 4.902 5.679 90 120.92 90 4 23 RuO2 0 6×6×9 475 4.542 4.542 3.141 90 90 90 2 24 24 CeO2 5 5×5×5 700 5.481 5.481 5.481 90 90 90 4 25 IrO2 0 6×6×9 650 4.543 4.543 3.19 90 90 90 2 26 α-PtO2 0 8×8×6 520 3.164 3.164 4.728 90 90 120 1 are relevant to practical catalysis conditions.20 For Ag and Au, we choose the metal state as reference since thus is the stable oxidation state over most relevant conditions.

Table 3-1. Bulk oxide parameters of TiO2 phases and coating metal oxides.

3.2.6 Surfaces

Support oxide surfaces for anatase, rutile and brookite are created by cleaving the unit cell in (hkl) directions where h,k,l are Miller indices. We examine monolayer metal oxide

62 coatings on a series of low index TiO2 surfaces. Symmetric slab models are used for all the

surface termination except the rutile (110) surface. Slab thickness was chosen so that surface

energy is converged within 0.3 meV/Å2. The k-point grid, total number of functional units and number of fixed layers in middle (bottom for rutile (110)) are reported in Table 3.2. Below is a brief description of these support surfaces. Henceforth, they are referred to as “p-hkl” where p is the phase of the bulk TiO2 crystal phase from which they are created.

Table 3-2. Surface energy, Ti-O atomic distances at the outermost layer and DFT parameters for low index facets of TiO2. O1-O5` represents nearest neighbor O atoms as shown in Fig 3.2. % Change in distance to nearest oxygen Surface Total laye Phase- atom from initial distance Fixed energy Coordi funct r k-point Terminat functiona (meV/Å2 nation O2/ O3/ O4/ O5/ O6/ ional fixe grid ion O1 l units ) O2' O3' O4' O5' O6' units d a-110 81.5 4f 7.0 7.0 7.0 7.0 24 8 4 6×6×1 - 5f -1.7 7.8 -1.6 6.8 1.6 a-101 43.2 24 8 4 6×6×1 - 6f 0.0 3.6 -4.0 -0.1 -5.9 1.2 - a-100 49.4 5f -1.4 -1.4 8.4 6.4 24 8 4 6×6×1 4.3 a-001 73.8 5f -0.7 -0.7 0.4 0.4 2.6 12 2 2 6×6×1 - b-210 51.8 5f -4.1 3.4 6.3 8.3 48 8 4 6×2×1 0.3 b-010 69.0 4f 5.6 7.5 6.1 5.0 24 4 2 8×8×1 b-001 89.6 4f 8.2 5.5 3.6 9.5 32 8 4 8×8×1 5f 0.9 0.9 0.9 0.9 6.3 r-110 50.0 6 2 1 4×4×1 6f -3.2 5.7 -3.2 5.7 -5.7 -5.7 - r-101 80.5 5f 5.3 6.2 -6.3 4.8 12 4 2 5×5×1 3.2 - r-100 63.7 5f 5.0 5.1 -4.2 5.6 16 4 4 5×5×1 4.2 r-001 103.8 4f 5.4 5.4 7.1 7.2 16 4 4 5×5×1

3.2.6.1 Anatase

We studied the (001), (100), (101) and (110) terminations of anatase. Fig 3.2(a) shows

the surfaces terminations after ionic relaxation. a-(101), a-(001) and a-(100) terminations have 5-

fold Ti atoms exposed. They also have 2-fold and 3-fold O atoms at the outermost atomic layers.

63 a-(101) has a saw-tooth profile that also exposes a 6-fold coordinated Ti atoms. a-(100) is quite similar to a-(101) in that it also has fully coordinated Ti atoms exposed in the narrow channels that are formed in the (010) direction. A more stable reconstructed surface of a-(001) has been proposed1,37 but has not been considered in this study. The a-(110) termination has a 4-fold Ti and a 2-fold O atom exposed in the surface. Atomic distances between exposed Ti and O atoms are reported in Table 3.2. The surface relaxations observed are similar to DFT calculate values available in literature.1,2

Figure 3-2. Optimized surface structures for (a) anatase (b) brookite (c) rutile TiO2 terminations. Blue and red spheres represent Ti and O atom, respectively. Outermost Ti atom and its nearest neighbors are labeled. Dotted line represents unit cell and solid lines represents Ti-O bonds. Ti-O distances are reported in Table 2. Ti` indicates the second Ti atom exposed with different coordination than Ti.

64

3.2.6.2 Brookite

For brookite, the b-(001), b-(010) and b-(210) surface terminations are modeled. As shown in Fig 3.2(b), b-(001) and b-(010) both have 4-fold Ti and 2-fold O atoms exposed. For the b-(010) termination, Gong and Selloni17 observed that the outermost 6-fold Ti atom became 5-

fold coordinated with a Ti-O distance of 2.41 Å. However, we found this distance to be 2.23 Å

after ionic relaxation. The b-(210) surface has a 5-fold Ti, 2-fold and 3-fold O atoms exposed on

the outer most layers. Atomic distances for unsaturated Ti and O atoms are reported in Table 3.2

which agrees well with previously reported values in literature.1,17,38

3.2.6.3 Rutile

The r-(001), r-(100), r-(101) and r-(110) surface terminations are studied for rutile and optimized structures are shown in Fig 3.2(c). 5-fold Ti and 2-fold O atoms are found in the outer surface after cleaving the r-(100), r-(101) and r-(110) surface. A 6-fold coordinated Ti atom and

3-fold O atom are also present on the outer layer of the r-(110) surface. The r-(001) surface, has

4-fold coordinated Ti and 2-fold O atoms that make it very reactive. Atomic distances after relaxation are reported in Table 3.2 for the outermost Ti and O atoms. Our observed surface relaxations are similar to the ones reported by Perron et al.18 and Morgan and Watson.15

65

3.3 Results

3.3.1 Surface energies of bare surfaces

Surfaces energy for each surface were calculated based on Eqn 3.1 and compared well with previously reported surface energies1,2,17,18. According to the calculated surface energies, the

stabilities of surfaces: r-(110) > r-(100) > r-(101) > r-(001), a-(101) > a-(100) > a-(001) > a-(110) and b-(210) > b-(010) > b-(001). For each phase, the most stable surface has 5-fold coordinated

Ti atoms and experiences the greatest deformation (Table 3.2). Surfaces with 4-fold coordinated

Ti atom exposed are least stable. The overall sequence of surface stability across all phases is then a-101>a-100>r-110>b-210>r-100>b-010>a-001>r-101>a-110>b-001>r-001.

3.3.2 Monolayer formation energy

Monolayer formation energy (ΔGML) of coating metal oxides of – Ag, Au, Co, Ni, Cu, Zn,

Pd, Mn, V, Cr, Fe, Zr, Mo, Ru, Ce, Ir and Pt on all the TiO2 terminations has been calculated using Eqn. 3.2. Fig 3.3 presents the monolayer formation energies at 300 K, 1 atm pressure. The formation energies at 0 K are reported in Fig S1 in the supplementary information (SI). The vertical axis is sorted according to the surface energy with the a-(101) being the most stable. The horizontal axis is sorted according to first the oxidation states, of the reference metal oxide then their atomic number. A lower value of ΔGML represents a higher probability of the oxide wetting

the TiO2 surface.

66

Figure 3-3. Monolayer formation energies at 300 K and 1 atm. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy. All coatings were given the MO2 stoichiometry when on TiO2 surface.

3.3.3 Decomposition of monolayer formation energy

We can decompose the monolayer formation energy into a three-step thermodynamic cycle. Fig 3.4 shows this three-step process, using NiO as an example. In the first step, the bulk of the coating metal oxide transforms from its stable crystal structure to that of the support metal oxide (bulk transformation energy, ΔG1). In the next step, the coating oxide in support metal oxide phase is cleaved to form a monolayer that conforms to the surface termination (monolayer creation energy, ΔG2). And finally, the monolayer is placed on to the TiO2 surface and gains stability (adhesion energy, ΔG3). To calculate the adhesion energy, we separated the monolayer

67 from the support and performed a single point DFT calculation of the monolayer and took the difference of the monolayer energy and bare surface with respect to the coated support. Thus, any energy for reconstruction of the surface are included in the adhesion energy. Similarly, any energy associated with the deformation of the monolayer is included in the monolayer creation energy.

Figure 3-4. Monolayer formation (ΔGML) in three-step thermodynamic process- bulk transformation (ΔG1), monolayer creation (ΔG2) and adhesion (ΔG3).

For bulk formation energy of oxides that have different stoichiometry than TiO2, O atoms

are added or removed from atmosphere. The bulk transformation energy is normalized by per

MO2 unit. The general reaction representing the bulk transformation energy (ΔG1)-

1 + 1 (5) 2 ∆𝐺𝐺1 𝑞𝑞 𝑀𝑀𝑝𝑝𝑂𝑂𝑞𝑞 � − � 𝑂𝑂2 �� 𝑀𝑀𝑂𝑂2 The bulk transformation energy (𝑝𝑝ΔG1) per MO2 unit𝑝𝑝 is then -

1 = × + 1 × 2 × (6) 2 𝑞𝑞 ∆𝐺𝐺1 𝐸𝐸𝑀𝑀𝑂𝑂2 − � 𝐸𝐸𝑀𝑀𝑝𝑝𝑂𝑂𝑞𝑞 � − � 𝜇𝜇𝑂𝑂� 𝑝𝑝 𝑝𝑝

68

where represents the energy of the coating oxides in the anatase, brookite or rutile

𝑀𝑀𝑀𝑀2 structure and 𝐸𝐸 is the energy in their stable oxide structure. The effect of temperature and

𝐸𝐸𝑀𝑀𝑝𝑝𝑂𝑂𝑞𝑞 pressure is included in the oxygen chemical potential, µO. Fig 3.5 represents these energies at 300

K and 1atm condition (0 K results are provided in Fig S2).

The monolayer creation and adhesion energy is also normalized by the number of functional units in the monolayer and given in Fig 3.6 and 3.7. For adhesion energy, a surface area normalized value could be of interest and is reported in Fig S3.

Figure 3-5. Bulk transformation energy per functional unit of TiO2 at 300 K and 1 atm. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy.

69

Figure 3-6. Monolayer Creation Energies per functional unit for different coating oxides. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy.

70

Figure 3-7. Adhesion Energies per functional unit for coating metal oxides. Horizontal axis sorted by the oxidation state of the reference oxide and vertical axis by surface energy.

3.4 Discussion

The monolayer formation energies (ΔGML) calculated using Eqn 3.2 for 300 K and 1 atm are given in Fig 3.3. The Bulk transformation energies (ΔG1) at 300 K and 1 atom are reported in

Fig 3.5 calculated using Eqn 3.6. Monolayer creation (ΔG2) and adhesion (ΔG3) energies are reported in Fig 3.6 and 3.7 respectively. Below we discuss how ΔGML varies for coating oxides with similar/dissimilar oxidation states and how ΔG1, ΔG2 and ΔG3 relate ΔGML as part of the three-step thermodynamic process.

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3.4.1 Stoichiometric coating oxides (MO2)

For Stoichiometric coating oxides, assuming a cutoff value of ~0.45 eV for stability for

this discussion (Fig S4), RuO2 and PtO2 has the higher possibility to coat the r-(001), r-(101), b-

(001), r-(100) and r-(110) surfaces. MoO2 has the lowest monolayer formation energy on the b-

(001) surface and ZrO2 on the a-(001) surface. They also have low ΔGML for r-(001) and r-(101) surfaces. From Fig 3.5, we observe that both RuO2 and PtO2 oxides have low bulk transformation

39 energy for rutile and anatase phases. RuO2 has stable rutile phase and the β-PtO2 phase has a distorted rutile structure,40,41 consequently they show the lowest bulk transformation energy for

rutile phase. MoO2 also has a distorted rutile structure and lattice optimized MoO2 in rutile and

brookite phases show that the rutile phase is 0.11 eV/per formula unit more stable than brookite.42

However, since we have fixed the lattice parameters to that of TiO2, we observed that the brookite

43 phase is 0.08 eV more stable. ZrO2 has a brookite polymorph at high pressures thus shows low

ΔG1 for brookite phase. In Fig 3.5, the vertical axis is sorted by surface energy and we observe that r-(110), a-(100), a-(101), r-(100), and a-(001) have low monolayer creation energy. In general, the low energy surface terminations are easier to create. One exception is b-(210) surface which has surprisingly high values for all the oxides. Based on ΔG2, CeO2 might seem to be becoming very stable as monolayer but this is a direct result of the CeO2 bulk transformation energies being too high. From adhesion energies in Fig 3.7, the common conception that stable surfaces do not bind monolayer/adatoms strongly, holds. The high negative adhesion energy for b-(210) surface and PtO2 on r-(001) are in line with the highly positive ΔG2 for these surface terminations. For RuO2 and PtO2, the low ΔGML occurs at rutile phases – thus the low values of

ΔG1 for rutile along with low ΔG2 and ΔG3 makes the monolayers stable. For MoO2, low values of

ΔG1 for brookite, stronger adhesion to the support that compensates the high value of ΔG2 makes

72 it likely to be stable on b-(001). For ZrO2, even though ΔG1 was lowest for brookite phase, it

binds to the a-(001) surface so strongly that ΔGML become negative.

3.4.2 Coating oxides with +3 reference state (M2O3/M3O4)

Among coating oxides with +3 states, V2O3 is predicted to have a stable monolayer on all

the terminations. Cr3O4 and Mn3O4 oxides are stable on the same surfaces as stoichiometric

oxides. In addition, they also have low ΔGML for the a-(110) and b-(010) surfaces. Most of these

surfaces are rutile. V, Cr and Mn(β-MnO2) all have rutile phases. The lattice difference is lowest

44,45 for VO2 and highest for MnO2. That is the same sequence as our calculated bulk

transformation energy (Fig 3.5). V and Ti has a large number of polymorphs in common46 so it’s

not surprising to see the bulk transformation energy to be negative meaning V2O3 is less stable than VO2 structures at 0 K. Cr shows similar behavior as V but the phases are less stable for Cr.

The lower value of ΔGML and low energy surfaces of rutile (low ΔG2) helps to stabilize the monolayer. However, stable monolayers are also formed on the brookite phases because of the strong binding to the brookite surfaces as observed in the adhesion energies (ΔG3). Oxides with

+3 state, shows higher addition energy than oxides in +2 state and metals. This is most likely due

to the fact that in monolayer MO2 state in vacuum they are further from their stable oxidation state than as MO2 monolayer on TiO2 surfaces.

3.4.3 Coating oxides with +2 reference state (MO)

Among coating oxides with +2 oxidation state, our calculations predict CoO and PdO to

be stable on the r-(001), r-(101), b-(001), r-(100) and r-(110) surface, similar to the stable stoichiometric and +3 state oxides. The most stable monolayer is predicted on b-(001) for CoO

73 and r-(001)/(110) for PdO. The rutile phase of PdO2 which has the lowest bulk formation energy

was claimed to be observed experimentally47 although it has very low thermal stability. Co has the lowest ΔG1 value for rutile but the strong adhesion energy makes it more stable on b-(001).

3.4.4 Metal reference state (M)

Ag and Au, Au prefers their metal state and shows high bulk transformation energy. They predicted to be unstable on all surfaces of TiO2. Their monolayer creation energy is very low (-ve for some surfaces) and binds less strongly to the surface probably because they don’t prefer the

+2-state bulk crystal of TiO2 (high ΔG1).

3.4.5 Temperature and pressure effect

For stoichiometric coating oxide, there is no change in ΔGML, since there is no adsorption

or desorption of oxygen to/from the system. For non-stoichiometric oxides studied here, increase

in temperature (decreasing µo) will decreases the stability of the coating monolayer. From Eqn

3.2, the change in ΔGML is equal to -2×Δµo, -Δµo and -0.5×Δµo for +0, +2 and +3 states oxides,

respectively. This means, regardless of the surface termination, monolayers of Co, Pd, Mn, Cr

and V will become less stable and more difficult to form with increase of temperature.

We observed a general relationship that if the coating oxide had stable phase similar to

the surface in the same stoichiometry, then the bulk transformation energy is generally low and

the monolayer formation energy is low as well. This is true for Ru, V, Cr, Mn, Pd and Pt. The

higher formation energy for Ir, which has stable rutile oxide phase, might be due to the higher

percentage of lattice mismatch with TiO2. We also observe that even though brookite phase does not exist for all the coating oxides, the most unstable brookite surface is easier to coat and

74 generally high energy surfaces have lower monolayer formation energy – which shows surface energy does play a role in the stability.

Figure 3-8. Predicted Particle radius required for RuO2 monolayer stability on various termination of TiO2 phases. a,b and r in legends represents anatase, brookite and rutile, respectively. Only results for radius greater than 10 Å at O-poor limit are shown.

3.4.6 Particle reference:

The discussion above shows that bulk transformation/monolayer creation/adhesion energy cannot be used individually to predict the monolayer stability. Previous work is literature48 has shown to use adhesion energy as an indicator for monolayer stability. While we observe some correlation, they do not give a direct indication of stability. On top of that, bulk reference state is too restrictive since in an actual physical system the reference state is most likely to be a finite oxide particle as we have discussed in Chapter 4.20 The bulk reference state can be corrected to a particle reference state by using a correction for the surface energy and particle size per functional unit bulk oxide energy using Eqn 3.4. We can predict the particle sizes for which the formation energy is negative over a wide oxygen chemical potential and generate a phase diagram

75 for monolayer stability. For example, from results for RuO2 over all the surface terminations studied here, we observe that the most stable RuO2 monolayer is formed on r-(001) and then on r-

(101). This is shown in Fig 3.8 for surface terminations for which RuO2 monolayer is stable against particle sizes of 10 Å or higher at their O-poor limit (oxygen chemical potential below which Ru metal is more stable than RuO2). Since the same correction is applied for all the surfaces, the particle size requirement follows the same trend as their monolayer formation energy with respect to the bulk oxide reference. However, if we reference the bulk oxide, due to

the positive formation energies, we would conclude that none of the RuO2 monolayer is stable on

TiO2 supports. Surface energy of the coating metal oxide play a large role in the stability of monolayer oxide. For PtO2, we observed similar magnitude of formation energy, however, the

(0001) α-PtO2 is so stable (2 – 0.7 meV/ Å2) that monolayer stability requires extremely small particles of PtO2. PdO is stable as monolayer on r-(001) and r-(110) at very low temperatures

(low oxygen chemical potentials) which may not be useful for practical purposes (Fig S5).

Similar correction can be applied for ZrO2, CoO, Mn3O4 and Cr2O3.

While the three-step decomposition and calculation of monolayer formation energy is useful for insight into the thermodynamic process, it is very difficult to identify indicators that predicts the stability of the monolayer. We have tried to analyze their correlation using simple atomic, oxides and surface properties (full list of properties are given in the SI) using 2D cluster plots and Pearson coefficient between the individual properties and monolayer formation energies. However, they do not show any clear trend and none of the properties have a Pearson coefficient greater than 0.4. The possible number of descriptors are too many to analyze visually in 2D plots and this method is not capable of indicating complex non-linear correlations.

Recently, there has been a wide application of feature engineering in Machine learning.

76

Supervised machine learning methods are specifically useful when we have some knowledge of the properties. Recent development in the use of compact sensing49 and introducing

linear/nonlinear relationship between properties50,51 have been found to be successful in

predicting material properties.52–55 We expect such methods will be useful for getting further insights and general descriptors for monolayer stability.

3.5 Conclusions

Stability of monolayer metal oxides over three different phases and stoichiometric terminations of TiO2 has been studied. Our analysis shows that r-(001), r-(101), r-(100), r-(110) and b-001 surfaces of TiO2 have the tendency to stabilize oxide monolayers of Co, Pd, Mn, Zr,

Ru and Pt. However, for oxides with different stoichiometry than the support, the stability of the monolayer decreases with increase of temperature due to its dependency on oxygen chemical potential. The monolayer formation process was further broken down into a three-step thermos dynamic process to find possible correlations. We find that in general, coating metal oxides that have similar polymorph as the support oxide are more stable as monolayer but it is not the only factor that describes the stability. Similarly, surface energy of the support does play a role, with less stable surfaces producing more stable monolayers, however, it can be influenced by other factors as well. Using a bulk oxide reference is more restrictive and an approximate particle reference state enables us to predict the higher limit of the particle sizes required for monolayer stability. Besides particle size, surface energies of the coating oxide also influence the stability of the monolayer. A particle with highly stable surface is unlikely to coat its oxide support. Further analysis should focus on the complex correlations between metal/metal oxide/support properties and monolayer stability.

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3.6 Acknowledgements

This material is based upon work supported by the National Science Foundation under

Grant No. 1505607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the National Science

Foundation. This work used the Extreme Science and Engineering Discovery Environment

(XSEDE), which is supported by the National Science Foundation under Grant No. ACI-

1548562.

3.7 References

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32. Lutfalla, S., Shapovalov, V. & Bell, A. T. Calibration of the DFT/GGA+U Method for Determination of Reduction Energies for Transition and Rare Earth Metal Oxides of Ti, V, Mo, and Ce. J. Chem. Theory Comput. 7, 2218–2223 (2011). 33. Colussi, S. et al. Nanofaceted Pd-O Sites in Pd-Ce Surface Superstructures: Enhanced Activity in Catalytic Combustion of Methane. Angew. Chem. Int. Ed. 48, 8481–8484 (2009). 34. Mayernick, A. D. & Janik, M. J. Methane Activation and Oxygen Vacancy Formation over CeO2 and Zr, Pd Substituted CeO2 Surfaces. J. Phys. Chem. C 112, 14955–14964 (2008). 35. Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron- energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998). 36. Stull, D. R. & Prophet, H. JANAF thermochemical tables. (DTIC Document, 1971). 37. Yuan, W. et al. In Situ STEM Determination of the Atomic Structure and Reconstruction Mechanism of the TiO2 (001) (1 × 4) Surface. Chem. Mater. 29, 3189–3194 (2017). 38. Esch, T. R., Gadaczek, I. & Bredow, T. Surface structures and thermodynamics of low- index of rutile, brookite and anatase – A comparative DFT study. Appl. Surf. Sci. 288, 275– 287 (2014). 39. Grillo, M. E. Stability of corundum- versus rutile-type structures of ruthenium and rhodium oxides. Phys. Rev. B 70, 184115 (2004). 40. Nomiyama, R. K., Piotrowski, M. J. & Da Silva, J. L. F. Bulk structures of PtO and PtO 2 from density functional calculations. Phys. Rev. B 84, (2011). 41. Siegel, S., Hoekstra, H. R. & Tani, B. S. The crystal structure of beta-platinum dioxide. J. Inorg. Nucl. Chem. 31, 3803–3807 (1969). 42. Becker, N. & Dronskowski, R. A first-principles study on new high-pressure metastable polymorphs of MoO2. J. Solid State Chem. 237, 404–410 (2016). 43. Terki, R., Bertrand, G., Aourag, H. & Coddet, C. Structural and electronic properties of zirconia phases: A FP-LAPW investigations. Mater. Sci. Semicond. Process. 9, 1006–1013 (2006). 44. Seehra, M. S. & Wijn, H. P. J. 6.1.3.1 Simple dioxides MO2. in Various Other Oxides (ed. Wijn, H. P. J.) 38–44 (Springer Berlin Heidelberg, 1992). doi:10.1007/10057685_9 45. McWhan, D. B., Marezio, M., Remeika, J. P. & Dernier, P. D. X-ray diffraction study of metallic VO2. Phys. Rev. B 10, 490–495 (1974). 46. Ding, H. et al. Computational Approach for Epitaxial Polymorph Stabilization through Substrate Selection. ACS Appl. Mater. Interfaces 8, 13086–13093 (2016). 47. Matar, S. F., Demazeau, G., Möller, M. H. & Pöttgen, R. Electronic structure and equation of state of PdO2 from ab initio. Chem. Phys. Lett. 508, 215–218 (2011). 48. Novell-Leruth, G., Carchini, G. & López, N. On the properties of binary rutile MO2 compounds, M = Ir, Ru, Sn, and Ti: A DFT study. J. Chem. Phys. 138, 194706 (2013). 49. Nelson, L. J., Hart, G. L. W., Zhou, F. & Ozoliņš, V. Compressive sensing as a paradigm for building physics models. Phys. Rev. B 87, 035125 (2013). 50. Ghiringhelli, L. M. et al. Learning physical descriptors for materials science by compressed sensing. New J. Phys. 19, 023017 (2017). 51. Goldsmith, B. R., Boley, M., Vreeken, J., Scheffler, M. & Ghiringhelli, L. M. Uncovering structure-property relationships of materials by subgroup discovery. New J. Phys. 19, 013031 (2017).

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Supporting information

1. Monolayer Formation Energies at 0 K

Figure S1: Monolayer formation energies at 0 K. Horizontal axis sorted according to oxidation state of reference oxide, then atomic number. Vertical axis sorted by surface energy.

2. Bulk formation energies at 0 K

Figure S2: Bulk formation energies at 0 K. Horizontal axis sorted according to oxidation state of reference oxide, then atomic number.

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3. Adhesion energies normalized by surface area

Figure S3: Adhesion energies (eV) normalized by surface area (Å2). Horizontal axis sorted according to oxidation state of reference oxide, then atomic number. Vertical axis sorted by surface energy.

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4. Monolayer formation energies at 300 K, 1 atm with a 0.45 eV cutoff for heatmap max value

Figure S4: Monolayer formation energies with a cutoff of 0.45eV. Horizontal axis sorted according to oxidation state of reference oxide, then atomic number. Vertical axis is sorted using Euclidian distances between points for clustering similar values together. Dendrograms for clustering are shown in the left.

5. Particle radius requirement for PdO2 for monolayer stability over surface of polymorphs of TiO2

Figure S5: Predicted Particle radius required for PdO2 monolayer stability on various termination of TiO2 phases. r in legends represents rutile. Only surfaces with highest particle size greater than 5 Å are plotted.

84

6. Properties used in Pearson correlation check:

Values for the properties can be found in supplementary information of Chapter 6

6.1 Atomic Properties:

atomic number, Pauling electronegativity, ionization energy (IEn;

n=1,2,3,4), electron affinity, total number of valance electrons, atomic weight, number of valance

elections in s, p, d, f orbital, space group and type presented as numeric values, row and column

number in periodic table, covalent radius, HOMO and LUMO energies and Zunger1 orbital radii

2 (rs, rp, rd). Two parameters introduced by Meidema et al. that represent the chemical potential of electrons in the metal (φ*) and are combined with parameters that represent the discontinuity in electron density between the two binding metals (η1/3).

6.2 Oxide Properties:

Oxidation state of metal and cohesive energy, coordination number (CN)

of metal and oxygen, next nearest neighbor distance, bond valance (BV),3 density (ρ), packing

factor (pf), volume per atom (Vpa), space group and type, enthalpy of formation4,5 per metal atom

for bulk oxides and heat of sublimation for metal4,5 shear modulus (SM) and bulk modulus (BM)6

of the oxides.

6.3 Support Properties:

DFT calculated surface energy, CN of metal and oxygen, and next nearest neighbor

distance in the outer most layers of the surface.

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References

1. Zunger, A. Systematization of the stable crystal structure of all AB-type binary compounds: A pseudopotential orbital-radii approach. Phys. Rev. B 22, 5839 (1980). 2. Miedema, A. R., de Châtel, P. F. & de Boer, F. R. Cohesion in alloys — fundamentals of a semi-empirical model. Phys. BC 100, 1–28 (1980). 3. Brown, I. D. The Bond Valence Model as a Tool for Teaching Inorganic Chemistry: The Ionic Model Revisited. J. Chem. Educ. 77, 1070 (2000). 4. Kubaschewski, O., Kubaschewski, O., Alcock, C. B. & Spencer, P. J. Materials Thermochemistry. (Pergamon Press, 1993). 5. Lide, D. R. CRC handbook of chemistry and physics. (CRC press, 2004). 6. Jong, M. de et al. Charting the complete elastic properties of inorganic crystalline compounds. Sci. Data 2, 150009 (2015).

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Chapter 4

An ab initio thermodynamic investigation of monolayer stability of multi- component metal oxides: MxOy/ZnO (0001) and MxOy/TiO2 (110) (M=Pd, Ru, Ni, Pt, Au, Zn)

[This chapter has been published as: A. S. M. Jonayat, A. C. T. van Duin and M. J. Janik, J. Phys.

Chem. C, 2017, 121, 21439–21448.]

4.1 Introduction

Metal oxides have a wide range of industrial applications that range from high-

temperature coatings to chemical functional materials. As chemical functional materials, they are

used in fuel cells1–4, gas sensors5–7, and as heterogeneous catalysts8–10. Since they are exposed to high temperature and various gas phase environments during their application, an effective oxide design requires consideration of stability, surface reconstruction, and in situ oxidation state.

Multicomponent metal oxide catalysts can offer tunable structure and chemical reactivity. So far, most multicomponent oxides have been developed using an empirical approach. Due to recent advances in synthesis and surface characterization techniques, it is now possible to create catalysts with atomic level precision11,12. However, nanostructured catalysts are inherently metastable13–15. This metastability makes experimental discovery of such catalysts a very time

consuming and difficult task. Computational screening methods based on ab initio calculations

has been utilized for solving similar “needle-in-a-haystack” problems16. Density Functional

87

Theory (DFT) calculations can be used as predictive tools for accelerating the discovery of

(meta)stable multicomponent metal oxides.

Multicomponent metal oxide catalysts can be classified into a variety of structure types.

Bulk mixed oxides17 occur when two or more oxides are mixed completely in the bulk phase. One metal oxide can be supported on top of another metal18–20 or metal oxide10. Core-shell structures can use metal/metal oxides as the core and another metal oxide/metal as the outer shell21,22.

When a small cluster or small number of layers of metal oxide is exposed above a substrate, its properties are altered relative to its single component system. These systems offer catalytic properties that vary with the choice of support23. In this work, we apply DFT methods to identify

metastable monolayers of oxidized transition metals over another metal oxide support, systems

with potential as multi-component oxide surfaces with unique chemical properties.

Oxide growth on metal oxide supports has been previously examined. Dulub et al.11

observed 2D growth of Cu over ZnO (0001) at very low coverages in different oxidation states. In

their studies of Cu/ZnO-based catalysis, Warschkow et al.15 used ab initio thermodynamics to

calculate the 2D phase diagram of CuxOy over ZnO (0001) at different oxygen and copper

potentials and related this to experimental observations. They evaluated the electronic structure of

more than 400 configurations with varying amounts of Cu and O on the surface as well as Zn

vacancies and substitutional Cu. They predicted three copper-oxide monolayer structures that are stable over a broad range of oxygen and copper chemical potentials. Two of them, Cu4O3-ZnO

(0001) and Cu12O13-ZnO (0001), were found to be stable over a wider range of oxygen chemical

potential. Vanadia overlayers on different support oxides (SiO2, Al2O3, ZrO2, TiO2 and CeO2)

have been examined for methanol oxidation to formaldehyde, demonstrating that the oxide

support plays an active role in changing the chemical reactivity of the vanadia surface24. A

88 common theme is that the support can tune chemical activity to create oxidation catalysts with desirable properties.

Though DFT has been applied to look at the chemical reactivity or stability of particular systems, its application to predictively discover stable multicomponent oxides is less common.

25 Tripković et al. looked at the stability and reactivity for Pt layers over MO2 (M=Ti, Sn, Ta, Nb,

Hf and Zr). They found that a three monolayer Pt coating is the most stable, however, it was the least reactive for oxygen reduction reaction. Mayernick and Janik26 used ab initio thermodynamics to predict the stability of Pd atoms, PdOx species and small Pd particles on different terminations of CeO2 with varying oxygen chemical potential. However, similar DFT

work for predicting stability of monolayer metal oxides is rare in literature. Warchkow et al.’s15 examination of CuxOy stability on the ZnO (0001) surface as a function of oxygen and copper chemical potentials demonstrates that ab initio thermodynamics can be used as a predictive tool for stability of such oxides. As seen for the CuxOy/ZnO system, specific multicomponent oxide combinations are metastable under certain oxygen pressures and temperatures. This metastability not only makes it experimentally difficult to synthesize such catalysts, but also makes the empirical method of discovering these multicomponent metal oxide catalysts a daunting task.

DFT can be used to screen possible combinations of metals oxides for potential synthesis targets, thus providing a systematic thermodynamic framework to identify metastable multicomponent metal oxide catalysts, which can accelerate material discovery.

Here, we develop a basic approach for predicting the stability of surface confined monolayer oxides using electronic structure calculations. An ab initio thermodynamic framework is presented to predict the stability of a monolayer metal oxide on top of another metal oxide under varying gas phase oxidation potential. This method is applied to examine the metastability

89 of monolayer oxide systems, namely - MxOy/ZnO (0001), and MxOy /rutile TiO2 (110) (M=Pd,

Ru, Au, Pt, Ni, Zn) at different temperatures and pressures.

4.2 Methods

4.2.1 Thermodynamic Model for Testing Monolayer Stability

A thermodynamic framework is developed to evaluate the stability of a substrate metal

(M1) oxide coated by a monolayer of another metal (M2) oxide. M2 to oxygen ratio of the surface layer is considered both at the same value as the substrate and other stoichiometries. In this framework, we compare the stability of a coating metal (M2) oxide with respect to a completely dewetted particle. This reference state is not unique or necessarily sufficient to demonstrate the stability of the 2D monolayer, as it does not consider stability relative to a bulk mixed oxide, supported 3D growth of small clusters, a mixed oxide surface, or other possible structures. Our goal is to identify possible metastable 2D systems, which then can be subjected to further computational study or experimental evaluation. A detailed description of this framework is given in this section.

4.2.1.1 Particle Reference Structure

For the coating/wetting metal (M2) oxide over a substrate metal (M1) oxide, the

reference state to which stability is compared is a M2 oxide or M2 metal particle. The M2 oxygen

stoichiometry of the reference state is chosen as the most stable phase at a given oxygen chemical

potential (µo). The energy of a metal or metal oxide particle can be calculated from the bulk M2

90

(oxide) energy and the surface energies of all possible terminations using a Wulff construction.

The energy of a MxOy particle can be divided into two parts as shown in Eqn. (4.1).

k E=×+× nE Aγ ()MOx y bulk ∑ i i (4.1) (M xyO ) Particle i=1

Here, n is the number of MxOy units in the particle, and Ai and γ i represent the surface area and energy per unit surface area of the ith facet of the particle. The first term on the right-

hand side represents the energy of n MxOy units if they were in their bulk phase. The second term represents the total surface energy of the particle. Since the atoms on the surface are not in their most stable condition (bulk), the particle energy will be higher than the bulk energy of the same number of atoms. A facet with a much lower surface energy than others will be the most exposed and will dominate the surface energy of the particle. Since it is computationally difficult to predict and calculate all possible surface terminations, an approximate method, using only the most stable surface’s energy, is used for calculating the particle energy. This approximated energy is then compared with the Wulff construction value for a subset of species.

We approximate the particle surface area as that of a spherical particle and presume a constant surface energy of the most stable termination. Under these approximations, Eqn. (4.1) becomes-

E=×+× nE4πγ r2 (4.2) MO ()MOx y bulk min ( xy)Particle

where, r is the radius of the particle and γ min is the lowest surface energy. The value of

γ min can change with oxygen chemical potential, µo, and allow for non-stoichiometric

terminations. This spherical approximation gives accurate particle energies relative to a Wulff

construction when one of the surface energies are much smaller than others. Since a spherical

91 surface area is the smallest surface area for a given volume and the surface energy of a real particle is greater than that of the most stable facet, the particle reference energies used from Eqn.

(4.2) will overpredict the particle stability. This is also true for Wulff constructions of particles

which are not dominated by their lowest energy surface termination (e.g., HCP crystals). The

stability of the monolayer oxide will, therefore, be underpredicted. The particle reference state

energy is dependent on µo as the surface oxidation state can change with pressure and temperature. From Eqn.(4.2), the radius of the particle also alters the reference state energy, smaller particles being less stable. We will therefore examine the stability of a monolayer coating relative to a spherical particle as a function of both the µo and particle radius, r.

4.2.1.2 Monolayer Stability Relative to Particle Reference State

Taking the particle energy of a given radius and at a specific µo as reference state, the stability of a layer of M2 oxide on top of a M1 oxide surface can be predicted by calculating the change in Gibbs free energy (ΔG) of the following reaction –

δ + ∆ →G + (MM1)ipOj v( 2) Oq{(M2) p Oqj−δ } on ( MO1)i vO2 ts, urfa ce particle v t 2

(4.3)

here, t represents the number of atomic layers in the slab, v is the number of M2 oxide units adsorbed in forming the monolayer and ( ij, ), ( pq, ) represents the stoichiometry of metal and oxygen in the M1 substrate and M2 coating oxide respectively. δ accounts for the

potential change in monolayer oxidation state relative to the particle reference and can be positive

or negative. The energies of all condensed phases are approximated as DFT calculated total

92 energies. With this approximation, all temperature and pressure dependence is due to oxygen chemical potential, µo.

For a given particle radius and µo, if ΔG is negative, the monolayer is stable relative to a

M2pOq particle and an uncoated M1iOj surface. A positive ΔG suggests the M2pOq monolayer

would prefer 3D growth (not necessarily following the same atomic structure of the substrate) to

a particle instead of a 2D coating of the M1iOj surface. We, therefore, use DFT calculations to

search for combinations of M1iOj substrates and M2pOq coatings with varying δ that are stable

over broad ranges of µo and relative to as large of particles (r) as possible.

4.2.2 Electronic Structure Calculation Method and Structural Models

DFT has been widely used for evaluation of electronic structure and total energies of metal oxide systems. We use total energies of different structures as input to the stability analysis. ab initio electronic structure calculations are done using DFT with the Perdew–Burke–Ernzerhof

(PBE) exchange correlation27 potential as implemented in the Vienna Ab initio Simulation

Package (VASP)28,29. The interaction between the ionic cores and valence electrons is described

by the projector augmented wave (PAW) method30. All calculations are spin polarized. The k-

point grids, generated using the Monkhorst-Pack scheme31, are given in Error! Reference source not found. for bulk calculations. Vosko-Wilk-Nusair interpolation32 for the correlation part of the

exchange correlation functional is used. The total energy was converged to 0.003 eV with respect

to k-point sampling and energy cut-off for the plane-wave basis set. Structures were optimized

until forces on each atom were less than 0.05 eVÅ-1. Some of the calculations were redone using a 0.02 eVÅ-1 convergence criteria to confirm that total energies were not impacted significantly by the looser convergence criteria. For asymmetric slab models, a dipole correction33 was used to correct the unphysical interaction between dipoles in adjacent images along the surface normal.

93

Transition metal oxides that are not fully oxidized have strongly-correlated localized d or f electrons. Conventional DFT methods with the generalized gradient approximation (GGA) for exchange and correlation suffer from inaccuracies in representing strongly correlated systems.

The intra-atomic exchange and Coulomb terms are not properly cancelled, leading to a well- known problem of self-interaction over-repulsion also known as ‘delocalization error’. This inaccurate delocalized description can cause unreliable changes in total energy during change of oxidation state. To correct this error, the DFT+U method34 is used, which adds a Hubbard U correction term to these localized states and can provide accurate band gaps or reduction energetics. The accuracy of this approach relies on the choice of U value, which can be tuned to match an experimental band gap35–37 or reduction energy38, however, this empiricism limits predictive ability and transferability to other structures. Despite this limitation, a vast literature now exists parameterizing U values for various metal oxides. For example, Mayernick et al.26,39

have demonstrated the use of DFT+U to predict the behavior of a Pd-ceria mixed surface oxide

for methane catalytic combustion and these predictions were later realized experimentally12. Our group has also shown that U parameters for Ce and Mn, calibrated for the individual oxides, predict mixed phase behavior matching XANES characterization40.

4.2.2.1 Bulk Calculations

For calculating reference particle energy using Eqn.(4.2), we first need to calculate the bulk reference energy of the M2pOq structure. Bulk energy calculations were carried out for Au,

PdO, α- PtO2, ZnO, NiO and RuO2. The optimized lattice constants are reported in Table 4.1, and

match well with experimental values and previously reported DFT values. The metal-oxygen

stoichiometries of these oxides are based on their most stable oxidation state in an oxygen

chemical potential range of practical relevance (discussed below).

94

Table 4-1. Computational Details and Bulk Lattice Constants of Metal/Metal Oxides Used in Current Study. Metal/ U-J k-point Cutoff Lattice Constants Functional Crystal Metal (eV) grid Energy Units Structure Oxide (eV) This work (Å) Experiment (Å) a c a c Tetragonal PdO 0 12×12×12 450 3.1020 5.4391 3.0434[41] 5.3363[41] 2 PdO (P44/mmc)

[42] [42] Tetragonal RuO2 0 6×6×9 475 4.5419 3.1414 4.492 3.106 2 RuO2 (P42/mnm) Rocksalt NiO 5.3 12×12×12 490 4.2135 4.1743 4 NiO (Fm-3m)

44 44 Hexagonal -PtO2 0 8×8×6 520 3.1641 4.7278 3.10 4.8 1 PtO2 α (P-3m1) FCC Au 0 9×9×9 450 4.1717 4.0845 4 Au (Fm-3m) Wurtzite ZnO 0 7×7×7 450 3.2938 5.2767 3.25046 5.20746 2 ZnO (P63mc) 47 47 Tetragonal TiO2 4.2 4×4×7 500 4.6891 3.0202 4.593 2.958 2 TiO2 (P42/mnm)

For NiO, there is a strong Coulomb-repulsion force amongst the electrons in local Ni 3d orbitals. To correct this effect, the DFT+U method introduce by Dudarev et al.48 has been used.

43 Here, U-J equals 5.3 following Rohrbach et al. . Among possible oxides of Pd, both PdO2 and

Pd2O3 are unstable and decompose to PdO. PdO has been used as the reference state in this work.

Similarly, for Ru, the most stable oxide, RuO2, is used as reference. For platinum oxides, the thermodynamically stable phase at low temperature is α − PtO2. At high temperature, it converts

to Pt3O4 and then finally to Pt. The temperature for these transitions were reported to be 910 K and 1070 K when oxidized nanoparticles were subjected to annealing49. For this study, the α −

PtO2 is taken to be the most stable phase in the considered oxygen chemical potential range.

Finally, for Au, the metal phase is the most stable oxidation state over a wide range of temperature and oxygen pressure. Results are only reported over oxygen chemical potential ranges for which the reference M2pOq state is stable. Table 1 reports the computational parameters used for each reference metal/ metal oxide.

95

4.2.2.2 Most Stable Surface Energies

Figure 4-1. Lowest surface energies of different metal oxides as a function of chemical potential.

To approximate the metal particle energy using Eqn.(4.2), the surface energy of the

lowest energy termination is needed. For convenience, we have restricted our M2pOq

structures to those with reliable DFT surface energies in the literature, calculated with DFT

approaches similar to that used here. All reported values of µo in this work, uses the zero

kelvin isolated oxygen molecule energy as the reference. A comprehensive explanation with derivation of this referencing system can be found elsewhere50. Figure 4.1 reports the most stable termination surface energy of different oxides43,45,51–56, reported only over the oxygen chemical potential ranges where the reference bulk oxidation state is stable. The

50 lowest value of µo for which metal oxide is stable is termed as “O-poor” . Below this value

the metal oxide would reduce to its metal phase. The highest value of µo, 0 eV in Figure

4.1, represent that energy of the ½ O2 at 0 K. This is termed as the “O-rich” limit, neglecting the possibility of forming higher oxidation states. The specific surface terminations that are

96

most stable for each metal oxide, at varying µo values, are discussed in the supplementary information.

4.2.2.3 Supports/ Substrates

Possible stable monolayer oxides over two supports are examined in this work –

ZnO (0001) and rutile TiO2 (110). These are typical oxide support structures and surface

terminations, have been widely studied both computationally and experimentally, and

offer different oxygen stoichiometry for our analysis. A brief description of their

structural models is given below.

4.2.2.3.1 ZnO (0001)/ ZnO (0001)

The computational parameters and bulk lattice structure used for ZnO are given in Table

1. In a stoichiometric slab of ZnO (0001), each layer of Zn and O form a bilayer. This surface is a

Tasker Type 357 polar surface that, in a stoichiometric slab model, has one end terminated with

Zn and the other end terminated with O. For the current study, monolayer M2 oxide is

constructed on top of a Zn terminated model because it was found to be more stable from DFT

predicted energies. The monolayer coated oxide is taken to form a conformal metal oxide layer on

top of ZnO, maintaining the crystal order of the ZnO (0001) surface to model a pseudomorphic

heteroepitaxial growth in a (1×1) surface cell. Henceforth the ZnO (0001) – Zn terminated surface is termed as ZnO (0001). A larger surface cell could allow for reconstruction that would stabilize

97 the monolayer, therefore, the requirement of a (1×1) conformal oxide is a more stringent requirement for stable system discovery.

Figure 4-2. 9 bilayer ZnO (0001) with M2O adsorbed on one side (5×5 expanded) (a) side (b) top view. TiO2 (110) slab with M2O2 adsorbed as a tri-layer (c) side view (d) top view. Black line shows the unit cell used for calculation.

Due to inherent polar instability of the Type 3 surface, a ZnO (0001) surface requires a

thick slab46. A 9-bilayer (18 atomic layers) asymmetric slab model was found to be sufficient for converging the adsorption energy of PdO. Figure 4.2 (a, b) shows the slab model. All layers were allowed to relax in the reported calculations, and we confirmed that fixing 2, 3 or 5 layers did not

make any significant difference in the total energy of the structure.

4.2.2.3.2 Rutile TiO2 (110)

Rutile TiO2 has a tetragonal crystal structure. Details of computational parameters and obtained lattice parameters for unit cell are given in Table 1. DFT+U was used with a U-J value of 4.2 eV, which is the commonly used value for Ti 3d states58–60. The lattice parameters obtained compare well with previous DFT calculated values58–61 and experimental values47.

62 The (110) surface is the most stable of the low-index surfaces of rutile TiO2 . This

63 surface has a repeating O-Ti2O2-O tri-layer structure. Perron et al. reported that convergence for surface energy is reached within 10~12 layers for a completely relaxed system. For constrained systems, five-layer models with their most inner layer frozen to bulk positions were found to be a

98 good compromise. In our study, a 9-atomic layer slab (3 tri-layers) was used with the bottom 3 atomic layers fixed. Figure 4.2 (c, d) show the surface with a monolayer of M2O2 coating.

4.3 Results and Discussions

4.3.1 Reference Particle Energy

To compare the difference between the energy of a particle using the spherical

64 approximation and Wulff construction, we have calculated the particle energies of RuO2 at three

different pressure and temperature combinations. The Wulff constructions, shown in Figure 4.3,

were generated using surface energies of the five low-index surfaces using reported values by

Wang et al.52. For the same volume of the Wulff construction, a hypothetical spherical particle terminated by the most stable surface will have a lower surface area. For the three particles studied, the spherical particle approximation gave particle energies ~15, ~15 and ~13% more stable than that of the Wulff construction. The degree of error is acceptable for our qualitative purpose of identifying possible stable monolayer oxides surfaces as the approximation will cause us to slightly underpredict the monolayer stability.

Figure 4-3. Wulff construction of RuO2 at (a) 300 K, 1 atm (b) 573 K, 0.1 atm (c) 1073 K, 1 atm.

99

Figure 4-4. Formation energy comparison between GCMC (ReaxFF) predicted and approximated method.

We further test the spherical particle approximation by comparing to a ReaxFF65 calculation of PdO particle energies. Senftle et al.66 studied the oxidation of Pd particles with a

ReaxFF force field under varying µo using GCMC simulations. The formation energy per Pd

atom of each 3-nm diameter particle at different µo are compared with the formation energy of similar sized particles using our spherical approximation. To compare the spherical approximation and ReaxFF GCMC results, we need a common reference state. The following reaction is used to calculate the formation energies taking Pd atom in bulk metal and O atom in an

O2 molecule in the atmosphere as reference –

11∆ε a×× Pd+ a OO  → (Pd O )+ ()ab− × (4.4) bulk 2222a b particle

Here, a and b are the number of Pd and O atoms in the particle respectively. For the

spherical approximation, a is equal to b, whereas non-stoichiometric particles are possible in

66 GCMC results . The formation energy per Pd atom, Δε, is shown in Figure 4.4 with varying µo.

The spherical approximation method predicts the PdO particle to be more stable than the GCMC

results for most of the PdO stable region. The two particle models vary by a maximum of 0.10 eV

100 per Pd atom. We conclude the two methods are in general agreement. One reason of discrepancy between the values may be due to a 0.13 eV per Pd atom difference in oxidation enthalpy of PdO in ReaxFF compared to DFT.

For small particle sizes, the particle energy will not be well approximated as a combination of bulk and surface energy. Our stability test, which neglects a particle support interaction, also becomes less realistic when comparing to very small particles. Though our approximations for the energy of vary small particles will be unrealistic, we allow our stability test to consider very small particles. The particle energy increases as the radius decreases, allowing the radius to also serve as a surrogate metric for the relative stability of different compositions of monolayer oxides.

4.3.2 ZnO (0001) Substrate

4.3.2.1 Monolayer Stability

Figure 4-5. (a) Reaction for testing stability of PdO over ZnO (0001) (b) Graphical respresentation of the test reaction.

As described in Section 2 and Eqn. (4.3), the stability of a M2pOq monolayer oxide is predicted relative to a particle of the most stable M2 oxide at a varying oxygen chemical

101 potential. For example, for a PdO monolayer on ZnO (0001), the stability criterion is illustrated in

Figure 4.5. For this monolayer system, the Eqn. (4.3) values are, t = 9 and v,i,j,p,q = 1. For a monolayer coating of RuO on ZnO (0001) with a RuO2 reference state, v,i,j = 1, p = 1, q = 2 with

Eqn. (4.3) written as

∆ 1 ()()ZnO+ RuO  →G Ru − O −()ZnO + O (4.5) n 2 particle n 2 2

For a PdO monolayer, the ΔG depends on µo due to the particle surface energy’s µo

dependence for non-stoichiometric terminations. For the RuO monolayer, or, more generally, metal oxides that have a different reference metal-oxygen stoichiometry than the support, the energy of the O atom released/adsorbed to/from atmosphere also depends on µo.

Figure 4-6. PdO monolayer formation at three different chemical potentials of O atom.

Figure 4.6 shows the ΔG for the formation of the PdO/ZnO (0001) monolayer with varying particle radius and at 3 different µo values, O-rich and O-poor limits and atmospheric conditions (µo=-0.27 eV). Under the O-poor condition, PdO particles of radius less than 7.8 Å

(~76 PdO units) would be more stable as an extended monolayer on ZnO (0001), suggesting a

102 monolayer of PdO could be metastable on this surface. As the oxygen chemical potential increases, monolayer formation becomes less favorable. This is due to the decrease in reference particle surface energy with increasing µo as an oxidized PdO surface becomes more favorable.

Under the O-rich condition, a 1.6 Å particle would be favorable to extend to a monolayer. As this requires less than one PdO unit in the particle, we conclude the PdO/ZnO (0001) monolayer would not be stable relative to a PdO particle under O-rich conditions.

Figure 4.7 shows the same analysis in the form of a “phase diagram”, showing the µo and

particle radius ranges over which the monolayer would be metastable. The monolayer stability

region is bound by µo ranges where Pd metal (low µo) or condensed phase O2 (high µo) would form, and the extreme O-rich and O-poor limits in Figure 4.6 are labeled by open and closed dot points respectively in Figure 4.7. Similar analysis is carried out for other M2Oq systems over ZnO

(0001) and rutile TiO2 (110), and we use these “phase diagrams” moving forward to determine

whether the monolayer oxide is metastable over a physically significant µo and particle radius

range.

Figure 4-7. Stability region of PdO over ZnO (0001)-Zn surface.

103

Figure 4.8 shows the particle radius as a function of µo for PdO, RuO, NiO and AuO monolayer stability on ZnO (0001). In the range of µo where PtO2 is stable, the ∆G for a

monolayer of PtO on ZnO (0001) to form is always positive. Hence, a PtO monolayer is unlikely

to form on top of ZnO (0001) surface.

The particle radius relative to which a NiO monolayer is metastable on a ZnO (0001) is

not a function of µo, as NiO shares the same oxidation state in its reference state and as a monolayer, and the most stable reference NiO surface termination is also stoichiometric. The model predicts particles with radius below ~16 Å prefer to extend to a monolayer. If a U correction is not used for Ni 3d states, our analysis would predict the monolayer to be stable relative to all particle radii.

Figure 4-8. Maximum particle radius for PdO, RuO2 and Au as a function of o for monolayer stability over ZnO (0001). 𝜇𝜇

A RuO monolayer on ZnO (0001) is more favorable than its reference state RuO2 particle at very low µo, which corresponds to very low pressure and high temperature. As µo increases, the reference state surface energy decreases and causes the particle to be more stable. The RuO2

104 particle has to release oxygen to form a RuO monolayer. As µo increases, stability of O2 (gas)

decreases, which makes releasing an O atom less favorable. Because of these two effects working

in the same direction, RuO monolayer becomes less stable relative to a RuO2 particle with increasing µo, requiring smaller particle radii to favor monolayer formation.

The µo, r phase diagram for AuO monolayer stability on ZnO (0001) is shown in Figure

4.8 inset. As expected, AuO is difficult to form, requiring an unphysically small 3.65 Å particle

(~11 Au) or smaller depending on µo. However, the AuO monolayer is an interesting example of

how surface energy and O atom adsorption/desorption favorability impact the stability region

when the coating oxide has a different metal-oxygen stoichiometry than the support. The

reference state is a Au metal particle, requiring an O atom to be absorbed from the atmosphere to

form the AuO monolayer. In the low µo region, a constant surface energy of the most stable termination of Au, combined with the increasing ease of adsorbing an O atom from the atmosphere with increasing µo, predicts a Au monolayer to be more favorable. However, starting at µo = -0.4 eV, the most stable surface termination of Au changes from the Au (111) metal termination to an O-adsorbed termination45. These two competing effects lead to a non-monotonic trend in AuO monolayer stability with µo.

We also examined the stability of oxidized monolayers, with another layer of oxygen on top of the monolayer oxides to form a M2O2 monolayer. This corresponds to a O-M2-O-ZnO

(0001) surface termination. Except for RuO2, the M2-O-ZnO (0001) is more stable for all M2

oxides in the µo ranges considered. For RuO2, the RuO2 monolayer is more stable in the high µo

region (µo > 1.5 eV), as shown in Figure 4.8.

We conclude that there are µo ranges where NiO, RuO, RuO2, or PdO monolayers may be

metastable over the ZnO (0001) substrate. NiO has the greatest potential for stability, whereas

RuO, RuO2, and PdO all show stability relative to much smaller particle reference sizes.

105

4.3.2.2 Subsurface and Bi-layer Stability of Oxide

Since PdO, RuO2 and NiO particles are predicted to have some tendency to extend to a monolayer, we consider additional stability test for these systems. We consider whether the surface monolayer would preferably exchange with a subsurface layer. This stability test is carried out by comparing the energy of a structure with the same number of atoms as the monolayer structure, except, the outer most bi-layer is formed by Zn and O, and a PdO/ RuO/

NiO bi-layer sits just below. This subsurface stability is considering exchange of a full (1×1) unit cell isomorphic layer. This is a computationally simple and fast check to confirm surface segregation on the mixed oxide structure. Further tests might consider segregation of the surface layer to form a bulk mixed oxide, or formation of a mixed monolayer. The specific test for surface segregation tendencies might depend on whether the experimental procedure could result in bulk mixed oxides (i.e., when both oxide pre-cursors are simultaneously deposited/condensed) or a surface mixture (i.e., deposition of M2pOq on already prepared M1iOj).

Figure 4-9. Stability of bi-layer oxide on ZnO (0001) A second criterion, bi-layer stability, is also considered to examine if growth of 2D epitaxial multi-layers is preferred over the monolayer. The bi-layer formation reaction for a RuO2

particle is given as-

106

∆ 1 Ru−−+ O()() ZnO RuO →−−+G (Ru O )() Zn O O (4.6) n 2 particle 2 n 2 2

Figure 4.9 shows the predicted particle radius for stability of a bi-layer oxide on top of

ZnO (0001). For the monolayer of NiO and PdO, the particle size required for bi-layer stability is smaller than that for monolayer stability, indicating a greater preference for 2D monolayer growth. Contrarily, for a RuO bi-layer, the particle size requirements for bilayer growth are similar to that for monolayer stability at high µo. At low µo, bi-layer formation becomes more

favorable. This indicates that RuO2 has a slight tendency to prefer 2D multi-layer epitaxial growth. Our growth criterion ignores the effect of edges and reconstructions of the first monolayer, as we considered an infinitely long monolayer or bilayer with a (1×1) unit cell.

4.3. Rutile TiO2 (110) Substrate

4.3.3.1 Monolayer Stability

Figure 4-10. Maximum particle size for different oxides for monolayer stability on TiO2 (110).

107

The stabilities of monolayer coatings of M2O2 (M2=Pd, Ni, Au, Ru, Pt, Zn) on a rutile

TiO2 (11O) surface were evaluated. The TiO2 (110) surface has an O-Ti2O2-O tri-layer repeating

unit in the surface normal direction, with the uncoated surface model consisting of two tri-layers

[(TiO2)6]. An additional O-M22O2-O tri-layer is added to form monolayer coated structures. For

example:

∆G ()2()TiO226 + × PdOparticle + O2  → OPdOOTiO − 22 − − ()6 (4.7)

A µo, r stability phase diagram is shown in Figure 4.10 for coatings on the TiO2 (110)

substrate. Only RuO2 shows a physically significant stability range, and Ni, Au, Pt, and Zn results

are included in the inset figure due to extremely small radii needed to allow monolayer stability.

PdO monolayer become stable at high µo, though this range is not physically significant as PdO2

rather than PdO would be the proper particle reference state at such a high oxygen chemical

potential.

The RuO2 monolayer shows stability against particles with radius as large as 19

Å, suggesting possibility for RuO2 to form a monolayer coating on TiO2 (110). As Ru was the

only metal stable in a 4+ oxide in the studied µo range, and RuO2 has the same crystal structure as

67 rutile TiO2 with a lattice mismatch < 5%, its greater stability is expected . Thus, the O-Ru2O2-O monolayer is relatively more stable at lower µo conditions and becomes less stable with increasing

µo, following its surface energy versus µo curve. Partially reduced monolayers are studied in the

following section.

The surface segregation tendency of the RuO2 monolayer was considered by

swapping the monolayer with subsurface tri-layer. The RuO2 monolayer oxide on the TiO2 (110)

surface is 1.0 eV more stable (per 1×1 cell) than the corresponding subsurface structure. Thus,

RuO2 has a tendency to surface segregate on the TiO2 (110) substrate, further suggesting the potential for RuO2 monolayer oxide formation. To evaluate the preference for 2D multi-layer

108 growth, we checked the stability of two, three and four epitaxial monolayers over the first RuO2 monolayer. Our stability check, similar to Eqn. (4.6), predicts the second monolayer to be stable for any particle size while the third and fourth monolayer required ~8 to 9 nm radius particles respectively (details in supplementary information). This indicates that RuO2 has a high preference for 2D multi-layer epitaxial growth after forming the first heteroepitaxial monolayer.

The 2D multi-layer growth would presumably begin with growth of a small 2D monolayer that would terminate and form edges after reaching a critical dimension, due to the multi-layer growth preference. Consideration of the edge energies would be needed to further clarify the size to which 2D growth might be stable, and the size of epitaxial 2D multi-layer RuO2 islands that might form.

Thin epitaxial growth of RuO2 on rutile TiO2 (110) have been studied

68 experimentally by Xiang et al. by varying RuO2 particle size. They observed that when the particle sizes were sub ~2nm in diameter, epitaxial RuO2 islands (3 monolayers thick) were formed. Particle size larger than that remained unchanged in shape. Similar epitaxial growth was also reported by He et al.69 using physical vapor deposition of Ru in an oxygen atmosphere (600

K, 10-6 mbar) at low coverages. As mentioned earlier, due to the limitations of our current model,

we are not able to predict the lateral growth and coalesce of RuO2 islands at higher coverages as

69 70 observed by He et al. A RuO2/TiO2 (110) catalyst is also commercially available for

Hydrogen chloride oxidation which reports having a 0.3 nm thick and 0.9 nm long coating of

RuO2. These experimental observations provide qualitative validation of the potential of our screening procedure to provide possible stable systems that are physically realizable.

109

4.3.3.2 Stability of Non-Stoichiometric Monolayers

Figure 4-11. ZnO stability on TiO2(110) with different coverages of Zn and O.

Stability of monolayers with partial oxygen coverage of the O-M22O2-O tri-layer have

been considered. We refer to these as partial monolayer coatings with compositions M22O2-O,

M22O-O, M22-O, M22, M2-O, M2 denoted as (1, ¾), (1, ½), (1, ¼), (1, 0), (½, ¼) and (½, 0) ML respectively. For all M2 oxides (M2= Ru, Pd, Ni, Au, Pt) except ZnO, the partial coating required smaller, unphysical particle sizes for stability. For the ZnO partial monolayers, the (1, ½) ML

(Figure 4.11) is stable relative to a reference particle radius that is larger than the monolayer. The

µO, r stability diagrams for partial ZnO monolayers are reported in Figure 4.11.

Based on our analysis, NiO, PdO and RuO2 monolayers are potentially (meta)stable on the ZnO (0001) substrate. ZnO partial monolayer coating are (meta)stable on the rutile TiO2 (110) surface. The RuO2 monolayer is stable relative to particles 2 nm or smaller, however, it also has

a preference for 2D multi-layer growth, indicating a tendency to form epitaxial islands.

110

4.4 Conclusions

An ab initio thermodynamic framework has been developed that predicts the stability of a monolayer metal oxide on another metal oxide substrate. Density functional theory is used to calculate the electronic structures of the coated / uncoated surfaces. Reference state particle energies are approximated from the lowest surface energy terminations. This approximation was validated, within acceptable error limits, for a PdO particle against results from Wulff constructions and GCMC ReaxFF simulations. Phase diagrams for stability were constructed as a function of reference particle radius and oxygen chemical potential, giving the maximum particle size against which, the monolayer is stable at any oxygen chemical potential. Using this framework, we conclude that NiO has the highest potential to form monolayer coatings over the

ZnO (0001) surface whereas PdO and RuO2 require much smaller particles. For rutile TiO2 (110) substrate, a RuO2 coating showed reasonable stability but also a preference for growing as 2D multilayer epitaxial islands. Partial ZnO monolayer coatings were found to be stable over the

TiO2 (110) substrate. The framework presented can be used to provide an initial screen for potentially stable monolayer oxide coatings.

4.5 Acknowledgements

The authors gratefully acknowledge funding for this research from the National Science

Foundation, Grant # 1505607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the

National Science Foundation. This work used the Extreme Science and Engineering Discovery

Environment (XSEDE)71, which is supported by National Science Foundation grant number ACI-

1548562.

111

4.6 References

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Supplementary information

1 Surface energies of most stable surface termination

The most stable surface energies for different oxides at varying chemical potential

(Figure 1) used in calculation is discussed briefly in the following section.

1.1 PdO

Rogan el al1 reported that among the (1×1) surface terminations, PdO(100)-PdO surface has the lowest surface energy. The range of chemical potential between which this surface is stable is predicted to be from 0 to -0.88 eV (experimental value -0.96 eV). The surface energy

1 linearly increases with decrease of µo (see Figure 2 of Ref ). Following Eqn. (2), this means the

energy of a fixed radius PdO particle will decrease with decrease of µo.

1.2 RuO2

For RuO2, Wulff Construction for RuO2 Nanoparticles under different oxidizing

conditions has been reported using ab initio calculations2. Like the PdO analysis, all (1×1) terminations have been considered. For RuO2, the possible low-index surfaces have three possible

terminations named as O-poor, stoichiometric and O-rich. For (111) surface, there is another

possible termination with more oxygen. This termination is termed as “super-rich” by the

2 authors . In this case, the lowest surface energy changes from RuO2 (001) to (110) with decrease of µo. Initially when µo decreases there is an increase is surface energy because the most stable surface is RuO2 (001) O-super-rich surface but becomes constant when the most stable surface is

2 (110) stoichiometric (see Figure 2 of Ref ). The range between which RuO2 is calculated to be stable is 0 to -1.86 eV 2.

1.3 NiO

Among NiO (1×1) terminations reported by previous works3,4 (100) surface has the

lowest surface energy and it varies from 41 to 713 meV/ Å2 based on methods used. For this

116

2 study, the surface energy was taken to be 49 meV/ Å following the reported value of Rohrbach et

3 al which used SGGA+U (U-J=5.3) and assumed to be constant for different values of µo.

1.4 α -PtO2

α -PtO2 (0001) has the lowest surface energy among other terminations. The reported value in literature varies from 25 to 0.76 meV/ Å2. This value is so low compared to other

terminations that it will dominate the particle surface energy and hence is used as a constant value

with varying µo.

1.5 Au

For Au, Shi and Stampfl7 reported how nanoparticle morphology changes with chemical potential based on surface energy of different terminations. They found that at low chemical potential the Au (111) has the lowest surface energy but between -0.4 to -0.18 eV. O-Au structures forms on all low index surfaces, however, Au (111) remains the dominating surface.

While Au (111) energy is constant, O-Au surface energies increases with decrease of µo. At -0.26 to -0.18 eV, the lowest surface energy switches to Au (110) with a (2×1)-2O structure. The surface energies reported by Shi and Stampfl7 are used here for calculating the particle energy.

1.6 ZnO

The polar surfaces of ZnO, (0001)-Zn and (0001)-O are reported to have the lower

8 surface energy among the ones studies by Tang et al. . At low µo, (0001)-Zn has the lower surface energy but increases with increasing µo and at ~-1.6 eV switches to (0001)-O surface which

decreases with increasing µo.

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2 Growth mode of RuO2 over TiO2 (110)

Figure S1: First (1 ML), second (2 ML), third (3 ML) and fourth (4 ML) monolayer stability test of RuO2 on rutile TiO2 (110). Maximum particle size at each step is shown in Figure S2.

2D multilayer growth preference for RuO2 over TiO2 (110) has been evaluated by

comparing the particle size requirement for monolayer layer stability over the first, second, third

and fourth layer. For each monolayer, the following stability criteria has been calculated.

( ) ( ) , + 2 × ( ) ( ) ( ) , [

2 𝑛𝑛 2 6 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 2 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 2 𝑛𝑛+2 2 6 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑅𝑅𝑅𝑅𝑂𝑂 − 𝑇𝑇𝑇𝑇=𝑂𝑂 0,2,4,6] 𝑅𝑅𝑅𝑅𝑂𝑂 → 𝑅𝑅𝑅𝑅𝑂𝑂 − 𝑇𝑇𝑇𝑇𝑂𝑂 𝑛𝑛

118

Figure S1 shows the 2D multilayer growth preference test process graphically and Figure

S2 reports the maximum particle size for each monolayer layer of RuO2. As seen in Figure S2, maximum particle radius is around ~8 to 9 nm for third and fourth monolayer stability. The second monolayer has not been shown in the figure because it was predicted to be stable for any particle size in the oxygen chemical potential range where RuO2 is stable. These calculations were redone with a TiO2 (110) mirror slab model with seven tri-layers and the results were same. From these results, we conclude that RuO2 shows high preference for 2D multilayer growth after the first monolayer is formed.

Figure S2: Maximum particle size for different monolayer stability of RuO2 on TiO2 (110). The second monolayer is not shown because it is stable for any particle size.

119

References:

(1) Rogal, J.; Reuter, K.; Scheffler, M. Thermodynamic Stability of PdO Surfaces. Phys. Rev. B 2004, 69 (7), 075421. (2) Wang, T.; Jelic, J.; Rosenthal, D.; Reuter, K. Exploring Pretreatment-Morphology Relationships: Ab Initio Wulff Construction for RuO2 Nanoparticles under Oxidising Conditions. ChemCatChem 2013, 5 (11), 3398–3403. (3) Rohrbach, A.; Hafner, J.; Kresse, G. Molecular Adsorption on the Surface of Strongly Correlated Transition-Metal Oxides: A Case Study for CO/NiO(100). Phys. Rev. B 2004, 69 (7), 075413. (4) Su, D.; Ford, M.; Wang, G. Mesoporous NiO Crystals with Dominantly Exposed {110} Reactive Facets for Ultrafast Lithium Storage. Sci. Rep. 2012, 2. (5) Seriani, N.; Jin, Z.; Pompe, W.; Ciacchi, L. C. Density Functional Theory Study of Platinum Oxides: From Infinite Crystals to Nanoscopic Particles. Phys. Rev. B 2007, 76 (15), 155421. (6) Pedersen, T. M.; Xue Li, W.; Hammer, B. Structure and Activity of Oxidized Pt(110) and α- PtO2. Phys. Chem. Chem. Phys. 2006, 8 (13), 1566. (7) Shi, H.; Stampfl, C. Shape and Surface Structure of Gold Nanoparticles under Oxidizing Conditions. Phys. Rev. B 2008, 77 (9), 094127. (8) Tang, C.; Spencer, M. J. S.; Barnard, A. S. Activity of ZnO Polar Surfaces: An Insight from Surface Energies. Phys. Chem. Chem. Phys. 2014, 16 (40), 22139–22144.

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Chapter 5

Interaction trends between single metal atoms and oxide supports identified with density functional theory and statistical learning

[This chapter has been accepted for publication: Nolan J. O’Connor, A S M Jonayat, Michael J.

Janik, Thomas P. Senftle, Nature Catalysis, 2018. The DFT binding energies and corresponding analysis were done by Nolan O’Connor. The Statistical Learning part was done by A S M Jonayat]

5.1 Introduction

The stability and activity of supported metal catalysts can be significantly influenced by interactions between the metal and the support.1,2 For single metal atom catalysts supported on metal-oxide surfaces, support interactions impact both the metal’s catalytic properties and its resistance to sintering.3 The nature of active sites exposed on the metal surface can be affected by the size, shape, and dispersion of the metal clusters.1,2,3 Therefore, understanding metal-support interactions is essential for tuning the activity, selectivity, and stability of oxide-supported metal catalysts. Despite the large number of studies investigating metal-support interactions,1,2,4,5,6,7,8,9,10 trends that predict interaction strengths between metal/support pairs are relatively unexplored.

Sintering compromises the reactivity of a catalyst by reducing available catalytic surface area.7,8,9 Typically governed by Ostwald ripening,11 sintering of metal catalyst particles has been

shown to decrease reactivity for a number of important reactions, including the water gas shift

121 reaction, methane oxidation, and the selective hydrogenation of nitroarenes.12,13,14 Single atoms anchored to supports, however, can exhibit strong resistance to sintering, and make for longer- lasting, highly active catalysts.8 The degree to which a metal is anchored to a support is governed by the metal atom’s binding energy — metals that exhibit strong exothermic binding to a support are less likely to diffuse across the support and agglomerate.9

Due to their influence over catalytic performance, strong metal-support interactions

(SMSIs) have long been studied, even before Tauster first coined the term when describing

15,16 chemisorption loss over TiO2-supported Pt sites. Recently, SMSIs have taken on a new

meaning,4,7,17,18 with numerous studies investigating metal/oxide adsorption energies as a method for improving catalytic performance.4,5,7,8,9,18,19,20,21 The activity and selectivity of many metal/oxide systems are governed by effects linked to SMSIs.1,2 In particular, metal/oxide systems that can stabilize single atom catalysts (SACs) have proven to be effective in many applications.22,23 The well-defined active site of a SAC system can also provide high selectivity if one can achieve well-controlled uniformity across the catalyst surface.6 As such, the strength of

metal interaction on an oxide support can significantly impact overall stability and activity of the

SAC.

Several notable studies have investigated SMSIs using both experimental and

computational techniques, most examining the interactions between one particular metal/oxide

pair,19 and some studying trends across different metals5,8,20,21 and supports. Understanding such

trends is critical for screening combinations of metals and supports that can work in conjunction to produce sinter-resistant catalysts. Considering their well-defined morphology as supported metal catalysts, SACs frequently serve as useful experimental model systems for studying strong metal-support interactions, even if the technologically relevant catalysts feature metal clusters as opposed to single atoms.24 Density functional theory (DFT) has also proven to be a powerful tool

122 for investigating the energetic properties of metal/oxide systems, and has complemented experimental efforts in many studies.4,19,20

Campbell and co-workers demonstrated that a metal adatom’s oxide formation enthalpy can be used to effectively predict a metal’s adsorption energy to an oxide support8—an approach

that has been further validated in recent experimental and computational work.20 They have also

suggested some correlation between a metal atom’s adsorption energy and a support’s oxide

reduction energy.10,25

Herein, we expand these correlations for a range of early and late transition metals and oxide supports. We employ DFT to investigate the properties of single adatoms and oxide supports that influence SMSIs, as well as investigate periodic trends and electronic interactions of metal/oxide systems. Finally, we analyze different analytical forms of these properties using statistical learning based on least absolute shrinkage and selection operator (LASSO)26

regression, which is employed to identify physical descriptors that significantly influence

metal/oxide binding energy. Based on this analysis, we propose a predictor equation for

metal/oxide binding energy by evaluating error predictions characteristic of all possible subsets of

various analytical forms of descriptor combinations.

5.2 Results

5.2.1 Trends in Strong Metal-Support Adsorption Energies

A range of transition metals (Cu, Ag, Au, Ni, Pd, Pt, Co, Rh, Ir, Fe, Ru, Mn, and V) were

adsorbed on several reducible and irreducible oxide supports (CeO2 (111), MgO (100), CeO2

(110), TbO2 (111), ZnO (100), TiO2 (011), and α-Al2O3 (0001) surfaces) to investigate trends in

metal adsorption energy among metals and supports. On each support surface, a single metal

123 atom was adsorbed to several high symmetry sites corresponding to energetically favorable configurations. For example, Ag favorably adsorbs at a 3-fold hollow site (Figure 5.1(a)),

5 consistent with previous DFT studies, while Ir favorably adsorbs to CeO2 (111) at an oxygen

bridge location (Figure 5.1(b)). Conversely, all atoms adsorb above the anionic oxygen on the

MgO (100) surface, which is a well-documented property of this surface.27 The full range of

adsorption sites and energies for each metal atom on all oxide surfaces are reported in

Supplementary Table 3, and adsorbed configurations are shown in Supplementary Figures 1-13.

The adsorption sites for all previously studied metal/oxide systems were validated against

existing literature when possible.21,28,29,30 Specifications of DFT method and calculation procedures for adsorption energies ( ) are provided in the Methods section.

∆𝐸𝐸𝑎𝑎𝑎𝑎𝑎𝑎

Figure 5-1. Adsorption geometries of metals on CeO2 (111) and MgO (100). Top view of adsorbed late transition metals on the CeO2 (111) surface at the a) 3-fold hollow site (Ag), b) 2-fold oxygen bridge site (Ir), or c) oxygen side-bridge site (Pd). Adsorbed metals on MgO (100) all prefer the d) anionic oxygen site. The black rectangle represents the unit cell used in the study. Campbell and colleagues first proposed the correlation between the binding energy of

metal nanoparticles on oxide supports and the oxide formation enthalpy ( , ) of the metal

𝑓𝑓 𝑂𝑂𝑂𝑂 adatoms.8 This descriptor determines the interaction strength between a gas∆𝐻𝐻-phase metal atom and oxygen, and is determined from experimental reference data using the relation presented in the

124

Methods section. This oxide formation enthalpy reflects the metal adatom’s affinity for oxygen, and therefore it is intuitive that it is correlated to the metal adatom’s interaction strength with an oxide surface. Previous work by Hosokawa et al.31 has confirmed the presence of M-O-M bonds formed during single-atom adsorption on oxides, further demonstrating the importance of metal- oxygen interactions that dictate metal adsorption. However, this descriptor is not independently sufficient to predict metal atom adsorption energy, in part due to possible metal-metal interactions between the adatom metal and the support metal (see below).

Figure 5-2. Correlation between metal/support adsorption energies and metal adatom’s oxide formation enthalpy. Adsorption energies of transition metals on MgO (100), CeO2 (111), CeO2 (110), TiO2 (011), ZnO (100), TbO2 (111) and α-Al2O3 (0001) plotted against the formation enthalpy of the metal adatom’s most stable oxide. TbO2 (111) adsorption energies are plotted on the right (blue) y-axis while the remaining data are plotted on the left y-axis (due to scale difference). Dotted lines represent the best linear fit to the data for each support, with fit equations and quality given in Supplementary Table 5. Vertical lines (grey) are label guides.

In Figure 5.2, the adsorption energy of a metal onto an oxide surface is plotted against the

adsorbed metal’s oxide formation enthalpy. A linear trend for each support suggests that the

metal adatom’s interactions with surface oxygen atoms have a considerable effect on the strength

125 of its interfacial bond to the oxide. Metals with a weaker affinity for oxygen, such as Ag, bind to any oxide significantly weaker than those with high oxygen affinity, such as V. Thus, the oxide formation enthalpy of the metal is an effective predictor of that metal’s relative binding strength to an oxide support. The slopes, y-intercepts, R2 values, and mean absolute errors (MAEs)

corresponding to each oxide surface are reported in Supplementary Table 5. The R2 values confirm a reasonable degree of correlation for each support, except for MgO (100), which experiences a poor correlation because it binds all metals so weakly that oxidation enthalpy becomes a poor descriptor. The MAE values range from 0.20 to 0.68 eV, and are higher for supports that bind metals more strongly, such as TbO2 (111).

The trend of metal adsorption strength on each support surface is described by a unique slope, suggesting that characteristics of the support itself also play a role in determining the overall metal binding strength. Indeed, properties of oxide supports, such as nanocrystal shape and exposed facet, have been shown to strongly influence the catalytic activity of oxide-supported catalysts.1,32 In particular, the reducibility of a support has been shown to affect the strength with

which it adorbs metal atoms.10,33 Support reducibility is quantified by the oxygen vacancy

formation energy ( ) of the oxide (see Methods for details regarding the computation of

𝑣𝑣𝑣𝑣𝑣𝑣 ). Typically, 𝛥𝛥reducible𝛥𝛥 supports with less endothermic oxygen vacancy formation energies are𝛥𝛥𝛥𝛥𝑣𝑣 formed𝑣𝑣𝑣𝑣 from parent metals with unoccupied low energy states that can readily accept transferred electrons following the formation of an oxygen vacancy. The ability of the surface to accept donated electrons influences the adsorption of metal atoms, which in many cases have been shown to oxidize upon adsorption and, accordingly, reduce the metal atoms in the support itself.34

126

Figure 5-3. Correlation between slopes from Figure 5.2 and support’s oxygen vacancy formation energy. Slopes from the lines of best fit for adsorption energy vs. metal adatom’s oxide formation enthalpy for each surface are plotted against the surface’s oxygen vacancy formation energy.

In Figure 5.3, the slope of each surface’s trend line in Figure 5.2 is correlated with the

surface oxygen vacancy formation energies of each support. This reflects a general trend in which

reducible supports (i.e., supports with less endothermic vacancy formation energies) will tend to

have a steep slope featuring more variation in metal atom binding across transition metals. The

linear correlation in Figure 5.2 over a large range of oxygen vacancy formation energies indicates

that the reducibility of each surface is a viable indicator that each support’s reducibility reflects

its capacity to strongly adsorb metal atoms. MgO (100), an irreducible surface, does not interact

strongly with Ag or V, which are the atoms with the lowest and highest oxide formation enthalpy,

respectively. Thus, the slope of MgO (100) is much shallower than that of TbO2 (111), the most

reducible surface, which strongly adsorbs the metal atoms that readily oxidize, such as Ir, Ru, and

V. The notion that the surface’s reducibility measures its capacity to strongly adsorb metal atoms

also explains the larger variations in V adsorption energies compared to Ag adsorption energies.

127

Figure 5-4. Correlation between metal/support adsorption energies and the support’s oxygen vacancy formation energy. Adsorption energies of Ag, Ir, and Pd atoms to TbO2 (111), α-Al2O3 (0001), CeO2 (111), CeO2 (110), TiO2 (011), ZnO (100), and MgO (100) supports plotted against the corresponding oxygen vacancy formation energies of the support. Vertical grey lines are label guides.

If surface reducibility, as measured by the oxygen vacancy formation energy (ΔEvac),

serves as a reasonable descriptor for the varying slopes in Figure 5.2, then oxygen vacancy

formation energy in a support should correlate to the adsorption energy of a specific metal. In

Figure 5.4, the surface adsorption energies of Ag, Ir, and Pd atoms are plotted against each oxide

support’s reducibility. As shown in Figure 5.4, a linear trend emerges, this time for each metal

across varying supports. These linear trends indicate a relationship between ΔEvac of a support and the strength to which that support can bind a metal atom. Whereas Figure 5.2 shows the characteristics of the metal adatom that influence strong adsorption energies to an oxide support,

Figure 5.4 shows the characteristics of the oxide support that influence its ability to strongly bind metal atoms. That is, metal atoms with a higher affinity for oxygen bind strongly to oxide supports and supports that readily release oxygen bind metals more strongly. The equations and

128 mean average errors for the best fit lines shown in Figure 5.4 are reported in Supplementary

Table 6.

The adsorption energy and oxygen vacancy formation energy correlations obtained in this study are stronger than those recently reported by Campbell and co-workers when attempting to compare experimental adsorption energies to computationally-derived oxygen vacancy formation energies.10 It is likely that the lack of an apparent trend between experimental metal adsorption energies and computational oxygen vacancy energies results from the difficulty in ensuring that the DFT data and experimental data are properly normalized with respect to metal coverage and oxygen vacancy concentration on the surface. The concentration of surface oxygen vacancies is known to significantly influence oxygen vacancy formation energy.35 Oxygen vacancy formation

energy is highly dependent on the size and shape of the simulation cell, as well as the local

configuration of vacancies—making it difficult to cross-compare the experimental and

computational data. In this study, the oxygen vacancy formation energy and metal adsorption

energy are always computed with simulation cells that are the same size, thus enforcing the

proper normalization between metal adatom coverage and oxygen vacancy concentration. The

oxygen vacancy data and metal adsorption data are therefore directly comparable, leading to the

strong correlations seen in Figures 2 and 4.

While the trends between adsorption energy and oxygen vacancy formation energy hold

for supports over a long range of surface reducibilities, they do not accurately describe the

adsorption energy differences between surfaces with similar oxygen vacancy formation energies

(e.g., CeO2 (110), CeO2 (111) and TiO2 (011) surfaces). As discussed below, metal-metal binding can also contribute to differences in metal atom adsorption energies and can partially explain differences among supports. Specific binding geometries, as well as surface reconstruction and relaxation, will inevitably contribute noise to the presented correlations. It is also important to

129 consider that DFT has well-known deficiencies when describing highly-correlated rare earth oxides like CeO2 and TbO2, even with the inclusion of the U correction. Despite such

deficiencies, we have included analyses of these systems due to their industrial relevance and

importance to the catalysis community—particularly CeO2. Within the context of this study, inaccuracies inherent to DFT likely result in total formation energies and oxygen vacancy formation energies that are over-estimated in magnitude on the CeO2 and TbO2 facets considered

here. However, we anticipate that the overall trends are still meaningful, as they agree with trends

related to oxides for which DFT and DFT+U are known to perform better for these types of

analyses.

5.2.2 Electronic Structure Analysis

This section provides an electronic structure analysis of trends identified in the

previous section, which serve to elucidate the electronic mechanism behind strong metal-support

interactions. We focus on two metal atoms and two oxide supports: Ag and Ir (representing

metals with low and high oxide formation enthalpies, respectively) and CeO2 (111) and MgO

(100) surfaces (representing low and high oxygen vacancy formation energies, respectively).

These metal atoms and oxide supports are also technologically relevant in many industrial

applications, and have been the subject of many studies.4,5,21,27

The binding energies of Ag to CeO2 (111) and MgO (100) are -1.74 and -0.44 eV

respectively. For Ir, the binding energies are -4.26 and -2.00 eV, in the same order. These

adsorption energy values follow the trends described in the previous section: Ag binds weakly to

each surface because it has a low affinity for oxygen and MgO (100) binds both atoms weakly

because its oxygen vacancy formation enthalpy is endothermic. The density of states (DOS) plots

in Figure 5.5 demonstrate clear differences in the adsorption of Ag and Ir on the CeO2 (111)

130 surface. The many overlapping states between Ce3+, O2-, and Irδ+ below the Fermi level in Figure

5.5(a) suggest hybridization between Ir, Ce, and O orbitals, reflecting the formation of surface bonds responsible for the strong adsorption of Ir on CeO2 (111). Conversely, the overlap in Figure

5.5(b) of only one state between Ce3+, O2-, and Agδ+ below the Fermi level demonstrates weaker

Ag adsorption to the CeO2 (111) surface.

Table 5-1. Bader charge differences (in e-, positive difference indicates the accumulation of negative charge) and total magnetic moments (in μB) after Ir and Ag adsorption on CeO2 (111) and MgO (100) surfaces. Atom labels correspond to labels shown in Supplementary Figures 1-13.

CeO2 (111) Ag Ir Bader Total Bader Total charge magnetic charge magnetic difference moment difference moment Ce1 0.25 0.84 0.07 0.02 Ce2 0.06 0.00 0.28 0.96 Ce3 0.06 0.00 0.13 0.02 Ce4 0.06 0.00 0.26 0.93 O1 0.02 0.00 -0.09 -0.14 O2 0.01 0.00 -0.1 -0.14 O3 0.01 0.00 0.00 -0.01 Metal -0.55 0.00 -0.84 -0.65

MgO (100) O1 -0.16 0.12 -0.34 -0.01 Metal 0.15 0.72 0.39 0.94

A visual representation of charge transfer upon metal adsorption on CeO2 (111) is shown

in the isostructural charge density difference plots presented in Figure 5.6(a,b). Figure 5.6(a)

demonstrates that upon Ir adsorption on CeO2 (111) significant charge transfer occurs between the

Ir adatom and the surface oxygen and Ce atoms. Charge initially surrounding the Ir adatom

redistributes toward neighboring O and Ce atoms, where two Ce atoms are reduced by the

131 formation of an Ir2+ state. This reduction is evident in the charge density difference’s distinct resemblance to f orbitals localized on adjacent Ce atoms, and by Bader charge differences and site-projected magnetic moments reported in Table 5.1. Positive Bader charge differences indicate reduction while negative differences correspond to oxidation. Ce atoms with a total magnetic moment approaching one represent Ce3+ ions. Indeed, the formation of interfacial Ce3+

ions has been reported in several computational and experimental studies.5,34,36 In Figure 5.6(b),

Ag exchanges significantly less charge with CeO2 (111), reducing only one Ce atom forming an

Ag+ state. Bader charges are used here to qualitatively compare charge transfer between different

metal adatoms and oxide supports, which is adequate for determining physically relevant trends.

Figure 5-5. Density of states plots of Ir/CeO2 (111) and Ag/CeO2 (111). Projected DOS of metal 2+ 3+ adsorption on CeO2 (111) showing a) the d states of Ir , all states of Ce , and p states of O in the Ir-O-Ce bond on the surface and b) the d states of Ag+, all states of Ce3+, and p states of O on the surface.

132

While the reduction of surface Ce atoms in both Ir/CeO2 (111) and Ag/CeO2 (111) may be

interpreted as stemming from the metal atoms’ interaction with oxygen atoms, the adsorbed metal

does, in both cases, interact with surface Ce atoms directly. Examination of the charge density

difference plot of Ir/CeO2 (111) in Figure 5.6(a) reveals the presence of metal-metal binding

between the Ir and Ce atoms (labeled Ce2). The green band linking the two atoms indicates a

charge accumulation in a metal-metal hybrid orbital, which corresponds to the peak just above the

Ce-O band on the Ir/CeO2 (111) DOS plot in Figure 5.6(d), as indicated by the image of charge density associated with that peak (also showing a band of electron density linking the Ir and Ce atoms). Metal-metal binding between metal adatoms and metal oxides has previously been reported,15,20 but has never been considered influential in strong metal-support interactions. This

possibility is examined in the following sections.

Figure 5-6. Metal-support interactions on CeO2 (111) and MgO (100) supports. Isostructural charge density difference plots of a) Ir/CeO2 (111) b) Ag/CeO2 (111) and c) Ir/MgO (100). Blue denotes depletion of electron density while green represents accumulation. The isosurface level is ±0.005 e -3 bohr . d) DOS plot of Ir/CeO2 (111) and an orbital density image of the peak indicated with an arrow.

133

Electronic structure analyses can also explain the energy differences between CeO2 (111) and MgO (100) in the binding of metal adatoms. Since MgO (100) is irreducible, it is unable to readily accept electron density donated by a metal adatom, and instead reduces the metal adatom, as indicated by a positive Bader charge difference on the metal adatom (Table 5.1). Whereas the adsorption of Ir onto CeO2 involves the interaction between neighboring O and Ce atoms, the metal-support interactions from the adsorption of Ir onto MgO (100) are localized onto one surface O atom. This transfer of electron density from the support to the adsorbed Ir atom is evident in the isostructural charge density difference of Ir/MgO (100) shown in Figure 5.6(c).

5.3 Physical Descriptors for the Prediction of Binding Energy

Our DFT results have shown correlations between the binding energy of a metal adatom, its oxide formation enthalpy, and the support’s oxygen vacancy formation energy. Metal-metal binding is also evident from DOS and Bader charge analyses. Though the above trends suggest linear correlations, these primary descriptors can be used (and combined) in various other functional forms to predict the adatom binding energy. We therefore have performed a systematic analysis to identify the most important analytical form for each descriptor set. In statistical learning, various shrinkage methods, such as ridge regression (RR), least absolute shrinkage and selection operator (LASSO), and least angle regression (LAR)26 can be used to

identify within a feature space a subset of descriptors that minimize deviation between the

predicted and actual values. These methods are also used in machine learning (ML) applications.

Our objective is to determine the descriptors that will yield the best prediction for the

binding energy, considering those suggested by the DFT analysis in the previous sections as well

as other available descriptors of structural and electronic properties. This problem is readily

addressed using statistical learning based on compressed sensing (CS).37 Here, we adopt a

134 systematic analysis method based on CS described by Ghiringhelli et al.,38,39 where a feature space is generated by combining primary descriptors using analytical formulas. LASSO is then used to identify the most important descriptors via Equation 5.1,

argmin 𝑁𝑁 𝑀𝑀 , 2 + 𝑀𝑀 | | (5.1)

𝑀𝑀 𝑗𝑗 𝑗𝑗 𝑘𝑘 𝑘𝑘 𝑘𝑘 𝑐𝑐∈𝑅𝑅 � �𝑃𝑃 − � 𝑑𝑑 𝑐𝑐 � 𝜆𝜆 � 𝑐𝑐 𝑗𝑗=1 𝑘𝑘=1 𝑘𝑘=1 where P is a column vector of responses (i.e., DFT binding energies), d is a (N×M) dimensional design matrix of descriptors, and c is the column vector of coefficients that is to be determined. λ is a penalty parameter that, when increased, decreases the number of non-zero components of vector c. For a maximum value of λ, all elements of c will be zero, and as λ is

decreased more elements will take non-zero values. Since LASSO is not scale invariant, we

standardized26 the descriptor matrix, d, to have zero-mean and unit-variance by subtracting from each column its mean and normalizing by its standard deviation. This normalization renders all descriptors in the common scale and makes the penalty parameter, λ, meaningful. After enforcing a cutoff value of λ, a subsequent exhaustive search using l2 norm minimization over all possible

subsets of descriptors with non-zero c values is completed. Due to the linear correlation between

descriptors, the best results may not be achieved solely by employing LASSO. Details of this

38,39 composite method (LASSO+lo) can be found elsewhere, and examples of the application of

LASSO for material-science problems can be found in References 40,41.

5.3.1 Feature Space

We have completed two analyses with varying numbers of primary descriptors. For the

first analysis we used a minimal feature space based on the DFT analysis presented above. This

first feature space included only the oxide formation enthalpy of the metal adatom (ΔHf,Ox = ΔHsub

135

- ΔHf,Ox,bulk) and the oxygen vacancy energy of the oxide support (ΔEvac) as the two primary descriptors. The secondary descriptors include ratios, differences, summations, and squares of the primary descriptors, as well as absolute differences and squares of absolute differences. This generates a total of ten descriptors in the first feature space (Supplementary Table 7).

For the second analysis, the primary feature space was expanded to also include atomic properties of the adatom and support. The chosen properties have been proposed in the literature to have some correlation to metal-metal/metal-oxide interactions and have been previously used in machine learning approaches.39,40,41,42,43,44 Atomic properties of the metal adatom (m) and the support (s) include electronegativity of the metal in Pauling ( ) and Martynov-Batsanov ( )

𝑃𝑃 𝑀𝑀𝑀𝑀 scales, (n-1)th and nth ionization energies ( ) with the bulk metal𝜒𝜒 in the n+ oxidation state𝜒𝜒,

electron affinity (EA), HOMO (H) and LUMO𝐼𝐼𝐼𝐼𝑛𝑛 (L) of single metal atoms relative to vacuum calculated with DFT, s ( ) and p ( ) orbital radii245 (Zunger46 and Weber-Cremer47), number of

𝑠𝑠 𝑝𝑝 valance electrons (Nval), 𝑟𝑟and atomic𝑟𝑟 number (Z). Two parameters derived from a previously

reported semi-empirical method for predicting metal-metal binding enthalpies were also

included.48 These two parameters, first introduced by Miedema et al.,48 represent the chemical

potential of the electrons in the metal (ϕ) and are combined with parameters that represent the

discontinuity in electron density between the two binding metals (η1/3). Heat of sublimation

(ΔHsub) and oxidation energy of the bulk metal (ΔHf,Ox,bulk) of each metal adatom are also included

as individual descriptors. For oxide surface properties, the descriptor set includes oxygen vacancy

formation energy (ΔEvac), workfunction (WF), and surface energy (γ) of the support. Coordination

number of the metal (CNs) and the oxygen (CNO) in the support and bond valance49 (BV) of the

metal in the support are also included. Values used for these primary descriptors, calculation

methods, and data sources are provided in the Supplementary Information.

136

The secondary descriptors for this feature space are populated with the absolute value of ratios, differences, summations, and multiplications of primary descriptors, followed by taking the inverse, square, and square root of all of generated descriptors, where we only allow analytical functions (summation and subtraction) between descriptors with consistent units. Since the number of features grows rapidly during this process, in some cases we have used physical intuition to remove unphysical (e.g. ( + )) and unimportant (e.g. ( + )) analytical 𝑚𝑚 𝑠𝑠 𝑚𝑚 𝑠𝑠 forms. In the final step, all primary and𝐻𝐻 secondary𝐻𝐻 descriptors are combined,𝐸𝐸𝐸𝐸 and𝐸𝐸 another𝐸𝐸 set of descriptors is generated by multiplying each descriptor of this set with the remaining descriptors

(avoiding repetition). The combination of these two sets yields a final feature space with 333,932 descriptors. The full list of analytical formations applied to generate the secondary feature space is provided in the SI. While a simple least squares regression is adequate for screening out the best of the ten descriptors in the first feature space, it is computationally intractable for screening the second feature space. Therefore, application of LASSO+lo is necessary with such a large feature set.

5.3.2 LASSO+lo Analysis

The first feature space contains no metal-metal binding parameters. The penalty term, λ, is logarithmically decreased from λmax = 2.363 to λmin = 0.001×λmax following the procedure

39 50 described in Reference in which all ck values are zero at = , . The 1 𝑚𝑚𝑚𝑚𝑚𝑚 𝑗𝑗 𝑗𝑗 𝜆𝜆 𝑁𝑁 𝑚𝑚𝑚𝑚𝑚𝑚 �〈𝑑𝑑 𝑃𝑃〉� 2 descriptors with non-zero coefficients in sequence with decreasing λ are: (1) (ΔHf,Ox - ΔEvac) , (2)

2 ΔEvac, (3) ΔHf,Ox/ΔEvac, (4) ΔHf,Ox - ΔEvac, and (5) ΔEvac , where the employed cutoff is λ = 0.0044.

To check the consistency of these descriptors, we conducted several trials in which we randomly left out 10% of the DFT predicted binding energies from the analysis. The same descriptors

137 appeared in the same sequence for all trials. Next, an exhaustive search using l2 norm minimization with all possible combinations of descriptors with one (1D) to five (5D) elements was performed with all data points. The descriptor combinations with the lowest root mean square error (RMSE) for 1D to 5D are 1.65, 1.16, 1.03, 0.96 and 0.91 eV, respectively. The predictor equations are given in Supplementary Table 8. Figure 5.7(a) demonstrates that, intuitively, the prediction improves with increasing numbers of descriptors, where five descriptors (5D) yields the lowest RMSE. Even at 5D the RMSE remains high (0.91 eV), suggesting our descriptor set is incomplete. With such a small feature space, we could have reached the same predictor equations using direct l2 norm minimization over the ten descriptors,

but have detailed the complete procedure used here as it was repeated for the larger second

feature space.

Figure 5-7. Comparison between descriptor predicted and DFT binding energies. Results shown for (a) feature space 1 (b) feature space 2. ‘n’ in nD represents the number of terms in the descriptor.

138

For the second feature space, all 333,932 descriptors were screened using LASSO, with λ logarithmically decreased from λmax = 2.7921 to λmin = 0.001×λmax. A total of 75 descriptors were identified with the cutoff value reduced to λ = 0.0602. An exhaustive search using l2 norm minimization yields 1D to 5D sets that have significantly lower RMSE values compared to feature space 1. The 1D descriptor set of the second feature set outperforms the 5D descriptor set of the first feature space (Figure 5.7(b)). Table 5.2 reports the 1D-3D descriptor equations with

RMSE, and Figure 5.7(b) shows the comparison between predicted and DFT binding energies.

Here, all data points were used for training. The 4D and 5D descriptors are reported in

Supplementary Table 9. The optimal 5D descriptor set reduces the RMSE to 0.4096 eV. To check the robustness of these descriptors, we left out 10% of data (randomly selected) and used the remaining data for our LASSO+lo analysis. We repeated the procedure 50 times, standardizing

the remaining 90% of the training data each time before the LASSO step. This confirmed that no

information from the test set was transferred to the randomly selected training data. For 1D and

2D, the same descriptors were predicted in 74% and 68% of the trials, respectively. For 3D-5D,

the variations in the selected descriptor set were larger. However, similar RMSE values for

different trials indicates that in higher dimensions there are more combinations of similar primary

descriptors that can equally describe the randomly selected training data. For example, when all

data points are used for training, the RMSE varies by 0.03 eV within the top five 1D descriptors

and for 3D it only varies by 0.006 eV. For the reported coefficients in Table 5.2 we have used all

data points available and have not kept a separate set of data for testing due to the limited

availability of data (91 points). However, for 50 repeated ‘leave 10% out’ analyses, the average

RMSE when applying the 1D and 2D descriptors to predict the test set with the left-out data were

0.6969±0.2473 eV and 0.5948±0.1632 eV, respectively, which supports their applicability to external data points.

139

Table 5-2. Equations for binding energy (eV) prediction based on LASSO+lo analysis using feature 1/3 48 space 2. ΔHf,Ox, ΔEvac, EA, L and IE are in eV and 1 is in (density unit) . 3 RMSE Binding EnergyΔ𝜂𝜂 Predicting Equation (eV) 1D 0.1507 × × , 0.3962 0.6873 𝑚𝑚 ∆𝐻𝐻𝑓𝑓 𝑜𝑜𝑜𝑜 − �𝐶𝐶𝐶𝐶𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 � ∆𝐸𝐸𝑣𝑣𝑣𝑣𝑣𝑣 �� − 0.4839 × × , 1.1756 × × , 0.0770 2D 𝑠𝑠 0.5586 ∆𝐻𝐻𝑓𝑓 𝑜𝑜𝑜𝑜 ∆𝐻𝐻𝑓𝑓 𝑜𝑜𝑜𝑜 𝑚𝑚 𝐿𝐿 𝑚𝑚 − �√𝐸𝐸𝐸𝐸 � ∆𝐸𝐸𝑣𝑣𝑣𝑣𝑣𝑣 �� − ��𝐿𝐿 � � ∆𝐸𝐸𝑣𝑣𝑣𝑣𝑣𝑣 �� − 0.3206 × × , 1.0850 × × , 𝑠𝑠 𝑚𝑚 ∆𝐻𝐻𝑓𝑓 𝑜𝑜𝑜𝑜 𝐿𝐿 ∆𝐻𝐻𝑓𝑓 𝑜𝑜𝑜𝑜 − �√𝐸𝐸𝐸𝐸 � �� − �� 𝑚𝑚� � �� 3D ∆𝐸𝐸𝑣𝑣𝑎𝑎𝑎𝑎 𝐿𝐿 ∆𝐸𝐸𝑣𝑣𝑣𝑣𝑣𝑣 0.5028 2.1228 × × 0.3279 𝑚𝑚 𝑠𝑠 2 𝑛𝑛 𝑛𝑛 1 𝐼𝐼𝐼𝐼 − 𝐼𝐼𝐼𝐼 3 𝑚𝑚 − �� 𝑛𝑛 � �Δ𝜂𝜂 � � − 𝐼𝐼𝐼𝐼

In agreement with our DFT results, the top five 1D descriptors contain both the metal adatom’s oxidation enthalpy and the support’s oxygen vacancy formation energy (Supplementary

Table 10). The ratio of these values (ΔHf,Ox/ΔEvac) always appears in the 1D descriptor multiplied by a second term. Metal atom binds more strongly to surfaces when they have increased oxide formation enthalpies (i.e., when they form more stable oxide) and bind less strongly to surfaces that have increased surface oxygen vacancy formation energies (i.e., surfaces that are less reducible). The ratio between these two properties, (|ΔHf,Ox/ΔEvac|), captures this trend. TbO2(111)

is the only surface with a negative oxygen vacancy formation energy (-1.1 eV). Although the

absolute value of the ratio does not capture the negative ΔEvac, we are still able to model this

surface since the oxygen vacancy formation energy of TbO2 (111) is much smaller than all other surfaces.

The lowest RMSE is obtained when the second term is the coordination number of the surface metal atom in the bulk phase ( ), suggesting again that the surface metal’s ability to 𝑚𝑚 form bonds plays an important role in 𝐶𝐶metal/support𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 binding. A similar RMSE is obtained with

140 this second term in the 1D descriptor replaced by the LUMO energy (or √LUMO) of the surface metal atom, or difference of nth ionization energy of the adatom and surface metal atom weighted

by the nth ionization energy of the surface metal. A term involving (p+s) orbital radius (Zunger) also gives similar RMSE. These descriptors are all highly correlated, as demonstrated by the calculated Pearson correlation coefficient (Supplementary Table 10). The additional term in the

1D descriptors is either a characteristic of the support metal atom or a combined property of both the adatom and the support metal, suggesting that properties related to metal-metal interactions are required to better predict adatom binding. For a 2D descriptor set, both elements of the top five descriptor pairs (Supplementary Table 11) contain the |ΔHf,Ox/ΔEvac| term. Among the top five descriptor pairs, at least one of the multiplication terms is a combined property of the adatom and surface metal atom. These terms involve ratios of their LUMO/HOMO, electron affinity (EA), ionization energy (IE), or multiplication of (p+s) orbital radius terms. This indicates that the

metal-metal interaction is of secondary importance compared to the metal-oxygen parameters yet must be included for better prediction of the binding energy. Similar terms are also present in the

3D descriptor set. The first term includes -(Δη1/3)2 which is a known form of the Miedema

parameters48 that represents metal-metal interaction. In 4D and 5D, we find that surface properties are introduced, but our ‘leave 10% out’ analysis shows that the possible combinations with lowest

RMSE will greatly vary. Hence, 1D and 2D descriptors are more robust.

Our LASSO+lo analysis agrees well with our DFT analyses indicating that neither ΔHf,Ox

nor Evac can alone predict the binding energy. We conclude that their ratio is a better predictor

when multiplied by either a surface metal property or combined property of both the adatom and

the surface metal atom. Higher accuracy in binding energy prediction is achieved when metal-

metal interactions are captured in descriptor terms that include properties of both the adatom and

the surface metal in the ≥2D descriptor sets.

141

5.4 Conclusions

Adsorption energies obtained by DFT were reported for a range of early and late transition metals when adsorbed onto several reducible and irreducible oxide supports. These adsorption energies are correlated with properties of both the metal and the support; namely, metal oxidation enthalpy, support reducibility, and enthalpy of metal-metal interactions. To explain the trends in strong metal-support interactions, electronic structures for metal/oxide systems that exhibit both strong and weak interactions were analyzed. Metal-metal interactions between adatom and support were observed for every metal/oxide system except for those supported on MgO (100). The parameters that influence strong-metal support interactions were used in conjunction with LASSO+lo to develop a predictive model for screening metal/support

combinations that produce strongly adsorbed single atom catalysts.

5.5 Methods

5.5.1 DFT specifications

Spin-polarized DFT calculations were employed to investigate the adsorption of single

transition metal atoms on oxide supports. The calculations were performed using the Vienna ab

initio simulation package (VASP),51 using the Perdew-Wang (PW91)52 version of the generalized gradient approximation (GGA) as the exchange correlation functional, with the projector augmented wave (PAW)53 approximation representing the atomic core regions. An atomic force

convergence criterion of 0.05 eV Å-1 was used to identify optimized geometries. Plane wave basis sets were truncated at a kinetic energy cutoff of 450 eV. Valences for each atom type are reported in Supplementary Table 1.

142

A range of nonreducible and reducible low-index oxide supports, including MgO (100),

CeO2 (111), CeO2 (110), TbO2 (111), ZnO (100), rutile-TiO2 (011) (referred to as TiO2(011) in

this paper), and α-Al2O3 (0001), were studied in their stoichiometric states. Each surface facet was cleaved from an optimized bulk unit cell and was then expanded such that each surface had at least four oxygen atoms in the outermost oxygen layer, except for α-Al2O3(0001) which had three oxygen atoms. A surface normal lattice vector of 30 Å gave ample vacuum space between periodic slabs. The lattice constants for optimized surface structures and Monkhorst-Pack54 k-

point sampling used for each facet are reported in Supplementary Table 2. DFT fails to accurately

represent localized d and f orbitals, and as such we employed the Dudarev DFT+U55 formalism to treat the f states of TbO2 and CeO2 and the d states of TiO2, using literature-derived U values of 6 eV,56 5 eV,57 and 4.2 eV,19 respectively. DFT+U with the PW91 functional yields charge transfer

and adsorption energy values comparable to the hybrid functional HSE06 for metal/oxide systems

(e.g., see reference 58, and references therein), verifying that it is appropriate for studying the

metal/metal-oxide systems investigated here. Various single metal atoms were adsorbed on the surface models, including both late transition metals (Cu, Ag, Au, Ni, Pd, Pt, Co, Rh, and Ir) and early transition metals (Fe, Ru, Mn, and V). All high symmetry adsorption sites of each surface

(e.g., hollow, bridge, and atop) were tested to identify the most favorable adsorption geometry for each metal/oxide pair. A dipole correction59 was used to correct the unphysical interaction between dipoles in adjacent images along the surface normal for asymmetric slab models. Viable adsorption sites for CeO2 (111) and MgO (100), which are the primary focus in the later sections in this work, are shown in Figure 5.1. Detailed descriptions of all adsorption sites can be found in

Supplementary Table 3.

143

5.5.2 Calculation of adsorption energies and correlation parameters

Adsorption energies were calculated using Equation 5.2, where ( ) is the total

𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚− 𝑔𝑔 DFT energy of the metal atom in the gas phase, is the energy of𝐸𝐸 the stoichiometric oxide

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 support, and / is the energy of the 𝐸𝐸total metal/support system.

𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = / – – ( ) (5.2)

𝑎𝑎𝑎𝑎𝑎𝑎 𝑚𝑚𝑒𝑒𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚− 𝑔𝑔 The∆ 𝐸𝐸reducibilit𝐸𝐸 y of each oxide 𝐸𝐸support, quantified𝐸𝐸 by the support’s surface oxygen vacancy formation energy, was investigated as a descriptor for the strength of metal/support interaction. Oxygen vacancy formation energy was calculated using Equation 5.3,

= + (5.3) 2 𝐸𝐸𝑂𝑂2 𝛥𝛥𝛥𝛥𝑣𝑣𝑣𝑣𝑣𝑣 𝐸𝐸𝑀𝑀𝑛𝑛𝑂𝑂𝑥𝑥−1 − 𝐸𝐸𝑀𝑀𝑛𝑛𝑂𝑂𝑥𝑥 where is the energy of the reduced support, is the energy of gas phase

𝑀𝑀𝑛𝑛𝑂𝑂𝑥𝑥−1 𝑂𝑂2 molecular oxygen,𝐸𝐸 and is the energy of the stoichiometric𝐸𝐸 support. Note that the vibrational

𝑀𝑀𝑛𝑛𝑂𝑂𝑥𝑥 energy and entropy of gas𝐸𝐸 phase O2 are not included, as these corrections will be uniform across

all oxides and therefore will not impact relative trends between supports.

To predict the binding strength of single metal atoms, we use the metal atom’s oxide

8 formation enthalpy ( , ), a descriptor first proposed by Campbell and Sellers. This oxide

𝑓𝑓 𝑂𝑂𝑂𝑂 formation enthalpy is∆ determined𝐻𝐻 from experimental reference data using the relation presented in

Equation 5.4,

, = , , (5.4)

𝑓𝑓 𝑂𝑂𝑂𝑂 𝑠𝑠𝑠𝑠𝑠𝑠 𝑓𝑓 𝑂𝑂𝑂𝑂 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 where is the sublimation∆𝐻𝐻 ∆ 𝐻𝐻energy− of∆𝐻𝐻 the metal atom (i.e., the experimentally

𝑠𝑠𝑠𝑠𝑠𝑠 determined cohesion∆𝐻𝐻 energy of the bulk metal) and , , is the formation enthalpy of the

𝑓𝑓 𝑂𝑂𝑂𝑂 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 metal’s most stable oxide relative to the bulk metal ∆and𝐻𝐻 O2 (per metal atom). With the inclusion of , , is related to the energy of a single atom rather than the bulk metal phase.

∆𝐻𝐻𝑠𝑠𝑠𝑠𝑠𝑠 ∆𝐻𝐻𝑓𝑓 𝑂𝑂𝑂𝑂

144

Experimental and , , values used for each metal type are provided in

𝑠𝑠𝑠𝑠𝑠𝑠 𝑓𝑓 𝑂𝑂𝑂𝑂 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 Supplementary∆ 𝐻𝐻Table 4. ∆𝐻𝐻

5.6 Acknowledgement

This work was supported by the National Science Foundation under Grant No. CHE-

1505607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the National Science Foundation.

5.7 References

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Supplementary information

1. Supplementary Figures

CeO2 (111)

Supplementary Figure 1. Side and top views of the CeO2 (111) “hollow” binding site.

Supplementary Figure 2. Side and top views of the CeO2 (111) “bridge” binding site.

149

Supplementary Figure 3. Side and top views of the CeO2 (111) “side bridge” binding site.

CeO2 (110)

Supplementary Figure 4. Side and top views of the CeO2 (110) “hollow” binding site.

Supplementary Figure 5. Side and top views of the CeO2 (110) “bridge” binding site.

150

MgO (100)

Supplementary Figure 6. Side and top views of the MgO (100) “O-top” binding site.

ZnO (100)

Supplementary Figure 7. Side and top views of the ZnO (100) “O-top” binding site.

α-Al2O3 (0001)-Al terminated

Supplementary Figure 8. Two binding sites of the α-Al2O3 (0001)-Al terminated surface. Al4 and O2 indicate that the adatom is adsorbed on top of atoms in each atomic layer (not atomic positions in surface normal direction). The outer most Al and oxygen layers are very close to each other (0.16 Å distance) with Al on top.

151

TiO2 (011)

Supplementary Figure 9. Side and top views of the TiO2 (011) “hollow 1” binding site.

Supplementary Figure 10. Side and top views of the TiO2 (011) “hollow 1” binding site.

Supplementary Figure 11. Side and top views of the TiO2 (011) “hollow 2” binding site.

152

TbO2 (111)

Supplementary Figure 12. Side and top views of the TbO2 (011) “hollow 2” binding site.

Supplementary Figure 13. Alternate side and top views of the TbO2 (011) “hollow” binding site, with surface-level atomic shifting induced by the adsorbed Ir atom.

153

2. Supplementary Tables

Supplementary Table 1. The valence configurations are given for each metal adatom and oxide included in this study.

Supplementary Table 2. The cell configuration, size, and layers are reported along with the lattice constants for the DFT-optimized surface, as well as the exchange-correlation functional, k-points, and U correction used to optimize the surface.

154

Supplementary Table 3. Adsorption energies and sites are reported for each adatom/oxide combination included in this study (in eV).

Supplementary Table 4. The oxide formation enthalpies [ΔHsub-ΔHf,ox,bulk] for each metal adatom are reported (in eV). Values obtained from Reference 1.

155

Supplementary Table 5. The slopes, y-intercepts, and R2 values corresponding to the best fit lines from the oxide formation enthalpy versus adsorption energy relationship plotted in Figure 2.

Supplementary Table 6. The slopes, y-intercepts, R2 values, and mean absolute error (MAE) values for each metal adatom in Figure 4 are reported.

Supplementary Table 7. Feature Space 1 for LASSO analysis.

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Supplementary Table 8. Predictor equation for binding energy (eV) prediction based on LASSO+lo analysis using feature space 1. ΔHf,Ox and ΔEvac have units of eV.

2. Supplementary Methods

2.1 Feature Space 2: Primary Features

Electronegativity of the metal in Pauling ( )3 scale, (n-1)th and nth ionization energy

𝑃𝑃 ( ), and electron affinity (EA) were collected from𝜒𝜒 the mendeleev4 python module.

𝑛𝑛 Electronegativity𝐼𝐼𝐼𝐼 in Martynov-Batsanov ( )5 scale was collected from Villars.6 HUMO and

𝑀𝑀𝑀𝑀 LUMO of single metal atoms with respect to𝜒𝜒 vacuum were calculated using VASP in 9×9.5×10 box with spin polarized, gamma point calculations, where each the atom was in its lowest energyÅ spin orientation. s and p orbital radii from Zunger et al.7 and Waber and Cromer8 were used.

Work function and surface energy was calculated using VASP with the same parameters and surface model that were used for calculating the binding energy. Coordination numbers were identified from the converged surface models. Bond valances were calculated using metal-oxygen distances from the converged surface models and bond valance parameters9 corresponded to

oxidation states in bulk state. The complete dataset is provided as an excel file in the

supplementary online repository.

157

2.2 Feature Space 2: Secondary Feature Generation

Secondary Features were generated by using analytical formulas on the primary descriptors. As mentioned earlier, we have used physical intuition for some of the analytical forms to keep the total number of descriptors computationally manageable. Below the full procedure is described.

In the procedure that follows, m and s superscripts indicate adatom and surface metal, respectively. ‘[x,y,z]’ represents of a set of descriptors- x,y,z and represents the union set operation between two descriptor sets. C≡ {B} [A] represents a mathematical∪ operation where, B is a set of analytical functions (|-|, |+| etc.), A is a descriptor set and C is the set of descriptors which is obtained when each of the analytical functions of B operates on two elements of A.

Identity operation is indicated by ‘I’.

Pauling Electronegativity, :

𝑃𝑃 A≡ [ , , | |] 𝜒𝜒 𝑚𝑚 𝑠𝑠 𝑚𝑚 𝑠𝑠 𝑃𝑃 𝑃𝑃 𝑃𝑃 𝑃𝑃 B≡ {𝜒𝜒|÷|}[A]𝜒𝜒 𝜒𝜒 −𝜒𝜒

C≡ , , , [A B] 2 −1 Ionization�𝐼𝐼 √ Energy,� IE: ∪

[ , , , ] 𝑚𝑚 𝑚𝑚 𝑠𝑠 𝑠𝑠 𝑛𝑛 𝑛𝑛 𝐴𝐴 ≡ [𝐼𝐼| 𝐼𝐼𝑛𝑛−1 𝐼𝐼𝐼𝐼+ 𝐼𝐼𝐼𝐼𝑛𝑛|− ,1 |𝐼𝐼 𝐼𝐼 |] 𝑚𝑚 𝑚𝑚 𝑠𝑠 𝑠𝑠 𝑛𝑛 𝑛𝑛 C𝐵𝐵 ≡ {| 𝐼𝐼𝐼𝐼|}𝑛𝑛 −[A]1 𝐼𝐼{𝐼𝐼| |} [B]𝐼𝐼𝐼𝐼 𝑛𝑛−1 − 𝐼𝐼𝐼𝐼

D ≡ {|÷−|}[ [A ∪ B − C]

E ≡ , , , ∪ ∪ [A B C D] 2 −1 �𝐼𝐼 √ � ∪ ∪ ∪

Electron Affinity, EA:

A ≡[EA(m), EA(s), |EA(m)-EA(s)|]

158

B ≡ {| |, |÷|}[ [A]

C ≡ −, , , [A B] 2 −1 �𝐼𝐼 √ � ∪

HOMO (H) and LUMO (L) Energy:

A ≡ [Hm, Lm, Hs, Ls]

B ≡ {| |, |÷|} [A]

C ≡ {|÷−|} [A B];

D ≡ , , ,∪ [A B C] 2 −1 �𝐼𝐼 √ � ∪ ∪

Zunger Orbital Radius, r:

, 𝑚𝑚 𝑚𝑚 𝑠𝑠 𝑝𝑝 𝐴𝐴 ≡ �𝑟𝑟 , 𝑟𝑟 � 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑝𝑝 𝐵𝐵C ≡ {�|𝑟𝑟+|,𝑟𝑟| �|} [A] {|+|, | |} [B]

D ≡ {|+|, |−|, |×|, |÷∪|} [C] −

E ≡ {|+|, |−|, |×|, |÷|} [C D]

F ≡ , , − , [C D∪ E] 2 −1 �𝐼𝐼 √ � ∪ ∪

Atomic Number, Z:

A ≡ [Zm, Zs ]

B ≡ {|+|, | |, |÷|} [A]

C ≡ {|+|, |−|, |×|, |÷|} [B]

D ≡ , , − , [B C] 2 −1 �𝐼𝐼 √ � ∪

159

Meidema Parameters for metal atoms:

/ , / , , 1 3 𝑚𝑚 1 3 𝑠𝑠 𝑚𝑚 𝑠𝑠 𝐴𝐴 ≡ ��𝜂𝜂 � �𝜂𝜂 � 𝜑𝜑 𝜑𝜑 � / / , | |, 1 3 𝑚𝑚 1 3 𝑠𝑠 𝑚𝑚 𝑠𝑠 𝐵𝐵 ≡ ���𝜂𝜂 � − �𝜂𝜂 � � 𝜑𝜑 − 𝜑𝜑 � C ≡ { , } [A B] 2 𝐼𝐼 ∪

Valance Electron, Nval:

[ , , | |] 𝑚𝑚 𝑠𝑠 𝑚𝑚 𝑠𝑠 𝑣𝑣𝑣𝑣𝑣𝑣 𝑣𝑣𝑣𝑣𝑣𝑣 𝑣𝑣𝑣𝑣𝑣𝑣 𝑣𝑣𝑣𝑣𝑣𝑣 B𝐴𝐴 ≡ 𝑁𝑁, , 𝑁𝑁, 𝑁𝑁 [A]− 𝑁𝑁 2 −1 �𝐼𝐼 √ �

Oxygen Vacancy Energy (ΔEvac) and Workfunction (WF) of Surface:

A ≡ {ΔEvac, WF}

B ≡ {|+|, | |, |×|, |÷|} [A]

C ≡ , , − , [A B] 2 −1 �𝐼𝐼 √ � ∪

Surface Energy, γ:

A ≡ { γ }

B ≡ , , , [A] 2 −1 �𝐼𝐼 √ �

Coordination Number, CN:

, 𝑠𝑠 𝑠𝑠 𝑜𝑜 𝑜𝑜 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝐴𝐴B ≡ �{�|𝐶𝐶+𝐶𝐶|, | |,−|÷𝐶𝐶|}𝐶𝐶 [A] � �𝐶𝐶𝐶𝐶 − 𝐶𝐶𝐶𝐶 ��

C ≡ , , − , [A B] 2 −1 �𝐼𝐼 √ � ∪

160

Bond Valence of surface metal atom, BV:

, 𝑚𝑚 𝑚𝑚 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝐴𝐴B ≡ {�|𝐵𝐵𝐵𝐵|} [A]𝐵𝐵 𝐵𝐵 �

C ≡ −, , , [A B] 2 −1 �𝐼𝐼 √ � ∪

In the last step, the final derived descriptors from each group is collected and each descriptor is multiplied with all other descriptors generating a total of 333,932 descriptors.

Martynov-Batsanov Electronegativity and Waber and Cromer orbitals follow the same procedure of Pauling Electronegativity and Zunger orbital radii, respectively. None of these two were selected in the LASSO screened descriptor set. So, we removed them from our repeated ‘leave

10% out’ analysis.

Supplementary Table 9. LASSO+lo analysis results for Feature Space 2. Units are same as the ones provided in SI.

161

Supplementary Table 10: Top five 1D descriptors in Feature Space 2. Units are same as above.

Supplementary Table 11: Top five 2D descriptors in Feature Space 2. Units are same as above.

162

References 1 Rumble, J. R. & Rumble, J. CRC Handbook of Chemistry and Physics, 98th Edition. (CRC Press LLC, 2017). 2 Strayer, M. E. et al. Charge transfer stabilization of late transition metal oxide nanoparticles on a layered niobate support. J. Am. Chem. Soc. 137, 16216-16224, (2015). 3 Pauling, L. The nature of the chemical bond. IV. The energy of single bonds and the relative electronegativity of atoms. J. Am. Chem. Soc. 54, 3570-3582, (1932). 4 mendeleev – A Python resource for properties of chemical elements, ions and isotopes v. 0.3.6 (2014). 5 Stepan, S. B. Dielectric methods of studying the chemical bond and the concept of electronegativity. Russ. Chem. Rev. 51, 684, (1982). 6 Villars, P. A three-dimensional structural stability diagram for 998 binary AB intermetallic compounds. Journal of the Less Common Metals 92, 215-238, (1983). 7 Zunger, A. Systematization of the stable crystal structure of all AB-type binary compounds: A pseudopotential orbital-radii approach. Phys. Rev. B 22, 5839, (1980). 8 Waber, J. T. & Cromer, D. T. Orbital radii of atoms and ions. J. Chem. Phys. 42, 4116-4123, (1965). 9 Brown, I. D. The Chemical Bond in Inorganic Chemistry: The Bond Valence Model. (Oxford University Press, 2002).

163

Chapter 6

Discovery of descriptors for stable monolayer oxide coatings through machine learning

[Manuscript in preparation]

6.1 Introduction

Recent developments in synthesis techniques have made it possible to create unique combinations of metal oxides in different configurations (bulk mixed,1 core-shell, 2,3 coated4 etc.).

Multicomponent transition metal oxides demonstrate tunable catalytic properties.5 Advanced surface sciences techniques along with first principles based computational models have confirmed the existence dispersed metal oxide phases under some of the reaction conditions.6–8

Monolayer metal oxides (MMOs), in which a coating oxide forms a monolayer on a different metal oxide support, are a specific mixed monolayer structure for which a homostructural epitaxial layer can offer tunable chemical properties that differ from the bulk metal oxide or the support. These MMOs can enhance catalytic performance8 or provide emergent catalytic

characteristics not offered by the support or coating oxide.9 While there is an increasing interest to synthesize these unique multicomponent metal oxides, empirical evaluation of the broad range of possible coating/support combinations is daunting, especially given that only a subset of

combinations will offer sufficient stability to be realized. MMOs are typically metastable relative

to bulk mixing or phase separation, and often only under certain temperature and/or gas phase

164 pressure ranges. Computational models using density functional theory (DFT) can predict the stability of similar systems, and have used coating/substrate adhesion energy as a predictor of stability.10,11 The stability of monolayers are compared to their most stable bulk oxide state12 or a

nanoparticle reference13. Though these studies provide a DFT framework to screen possible stable

MMO combinations, these DFT calculations can still be expensive for a first screening process.

We, therefore, seek to identify descriptors that can predict the stability of monolayer oxides, and do so using machine learning algorithms to identify descriptors for a DFT training database of

MMO structures and possible descriptors.

Statistical/machine learning methods have been gaining popularity in materials and surface science due to availability of a vast amount of data and efforts to centralize this data

(Materials Project,14 NOMAD,15 OQMD,16 AFLOW17 etc.). Machine learning algorithms can

discover underlying physical principles from these data for predictive purposes. They have been

used to predict materials properties such as bang gap,18 vibrational free energy and entropies,19

stable 2D materials,20,21 synthetically reachable new materials,22 and complex system total

energies23 that can have ~3meV/atom accuracy. Broadly, there are two major approaches that depend on the final objectives. The first uses more accurate first principles calculations to train artificial neural networks (ANN) to predict either total energies24,25 or material/surface

properties.26,27 In the second approach, logistic or linear regression methods are trained using

physical properties of the material system to either classify or to predict desired properties.18,28,29

These physical properties are called ‘descriptors’ or ‘features’. Logistic and linear regression

methods are quite useful to filter out important properties that predict certain characteristics of a

system. Methods based on decision trees and shrinkage methods30 (Ridge, LARS, LASSO and

SIS31) are popular for this purpose. In most cases, the final target property does not depend on one

single descriptor of the system, rather it can be dependent on a complex form of multiple

165 descriptors, and the mathematical form of this dependence is challenging to predict. Various algebraic operations (+,-,/,×,exp, log, xn etc.) can be applied to the primary descriptors to include nonlinear relationships, effectively adding additional possible descriptors to the data set.32

Multiple iterations of the algebraic operations (physically meaningful) can be performed until a desired cutoff value for accuracy is achieved using one of the shrinkage methods. Ghiringhelli et

33 al. proposed a modified LASSO approach (LASSO+lo) using LASSO as a primary selection

method followed by secondary search with linear regression of all possible combinations of n

dimensional descriptors. This supervised machine learning approach was reported to successfully

find important descriptors for predicting zincblend and rocksalt structure energies of 82 octet

binary metal systems.28 We have used this same method to find important descriptors for

predicting binding energies of single atoms to different metal oxide supports.

Herein, the LASSO+lo serves as a central tool for predicting the stability of MMOs. We first present the construction of our DFT database of monolayer formation energies. This database references monolayer stability to the bulk oxide phase, and we then present a suggested correction to reference nanoparticles of the coating oxide. We construct a property database and apply the LASSO+lo method against the DFT database to find descriptors of the monolayer

formation energies, uncovering physical properties that impact monolayer stability. Development

of descriptors then enables prediction of MMO stability with acceptable error for screening

purposes and without having to run a DFT calculation, by using material properties available

either in databases or previously published literature.

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6.2 MMO Computational Model

6.2.1 Electronic structure calculations

Electronic structure calculations were performed using DFT with plane wave basis sets and the Perdew–Burke–Ernzerhof (PBE)34 exchange correlation potential as implemented in the

Vienna Ab initio Simulation Package (VASP).35,36 The interaction between the ionic cores and

valence electrons is described by the projector augmented wave (PAW) method37. All

calculations are spin polarized. The k-point grids, generated using the Monkhorst-Pack scheme38, are given in Table 6.1 for 3D bulk calculations. Vosko-Wilk-Nusair interpolation39 for the

correlation part of the exchange correlation functional is used. Energies were converged to 3 meV

with respect to k-point sampling and plane-wave basis set energy cut-off. Structures were optimized until forces on each atom were less than 0.05 eVÅ-1. For asymmetric slab models, a dipole correction40 was used to correct the unphysical interaction between dipoles in adjacent images along the surface normal.

Transition metal oxides that are not fully oxidized have strongly-correlated localized d or f electrons. Conventional DFT methods with the generalized gradient approximation (GGA) for exchange and correlation suffer from inaccuracies in representing strongly correlated systems.

The intra-atomic exchange and Coulomb terms are not properly cancelled, leading to a well- known problem of self-interaction over-repulsion also known as ‘delocalization error’. This inaccurate delocalized description can cause unreliable changes in total energy during change of oxidation state. To correct this error, the DFT+U method41 is used, which adds a Hubbard U correction term to these localized states and can provide accurate band gaps or reduction energetics. The accuracy of this approach relies on the choice of U value, which can be tuned to match an experimental band gap42–44 or reduction energy45, however, this empiricism limits

167 predictive ability and transferability to other structures. Despite this limitation, a vast literature now exists parameterizing U values for various metal oxides and matches experimental observations.8,46 Here, the formulation introduced by Dudarev et al.47 is used for which only U-J values are meaningful.

6.2.1.1 Monolayer oxide formation energy

We reference the stability of the MMO to an uncoated substrate and the coating oxide in

its bulk oxide form, though this reference state is one of multiple choices such as stability relative

to dissolution in the substrate and 3D growth of many possible structures. The MMO Gibbs

formation energy (ΔGML) is defined as the reaction energy of

( 1) + ( 2) ( 2) ( 1) + (6.1) , 𝛥𝛥𝐺𝐺𝑀𝑀𝑀𝑀 2 𝛿𝛿 � 𝑀𝑀 𝑖𝑖𝑂𝑂𝑗𝑗�𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑣𝑣� 𝑀𝑀 𝑝𝑝𝑂𝑂𝑞𝑞�𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏−𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 �⎯⎯� � 𝑀𝑀 𝑝𝑝𝑂𝑂𝑞𝑞−𝛿𝛿�𝑣𝑣𝑜𝑜𝑜𝑜� 𝑀𝑀 𝑖𝑖𝑂𝑂𝑗𝑗�𝑡𝑡 𝑣𝑣 𝑂𝑂2 where, t represents the number of functional units in the support oxide slab model, v is the number functional units of M2 oxide needed to form a conformal stoichiometric monolayer.

(i,j) and (p,q) represents the stoichiometry of metal and oxygen in the support (M1) and coating

(M2) oxide respectively. δ accounts for the potential change in monolayer oxidation state relative to the reference bulk oxide and can be positive or negative. The free energies of all condensed phases are approximated as DFT calculated total energies. With this approximation, temperature and pressure dependence is due to only oxygen chemical potential, µo. Under the ideal gas approximation, µo(T,p) can be calculated as

1 ( , ) = ( , ) + (6.2) 2 𝑜𝑜 𝑝𝑝 𝜇𝜇𝑜𝑜 𝑇𝑇 𝑝𝑝 𝜇𝜇𝑜𝑜 𝑇𝑇 𝑝𝑝 𝑘𝑘𝑘𝑘 � 𝑜𝑜� 𝑝𝑝

168

o where p is a reference pressure and k is the Boltzmann constant. We obtain ( , ) 𝑜𝑜 from thermodynamic tables48 and put on the relevant VASP DFT scale by setting the𝜇𝜇 0K𝑜𝑜 𝑇𝑇 𝑝𝑝

reference state as half of the DFT calculated energy of isolated oxygen molecule.

Judging stability versus the bulk reference state of the oxide is quite restrictive, as this

state is much more stable than the small 3D particles that would form were a monolayer oxide to

convert to a more stable form. A more relevant reference state to examine whether a MMO might

form during a deposition procedure would be a small oxide nanoparticle. As particles can have

different shapes based on the environment and will include a large number of atoms, it is not

practical to use DFT calculated particle energies as the reference energy. An approximate method

to correct the bulk oxide energy for particle reference assumes13 that the particle can be modeled as a sphere with the surface energy of its lowest surface energy termination. For a particle radius of r, the per functional unit particle energy is calculated from the bulk oxide energy as-

× + 4 × ( ) , ( ) , = 2 (6.3) 𝑛𝑛 𝐸𝐸� 𝑀𝑀2 𝑝𝑝𝑂𝑂𝑞𝑞� 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝜋𝜋𝑟𝑟 𝛾𝛾𝑚𝑚𝑚𝑚𝑚𝑚 𝐸𝐸� 𝑀𝑀2 𝑝𝑝𝑂𝑂𝑞𝑞� 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 where p,q represents the stoichiometry of the metal and oxygen𝑛𝑛 of the coating oxide, n is the

number for functional units present in the particle, and γmin is the surface energy of the lowest

energy surface termination of the coating oxide, which can be a function of the oxygen chemical

13 potential, µo. The number of functional units of the oxide in the particle is calculated using the bulk oxide unit volume. While using Eqn 6.1 gives the MMO formation energy with respect to the bulk oxide, replacing the bulk oxide energy using Eqn 6.3 gives the MMO formation energy with respect to a particle oxide.

169

6.2.1.2 Bulk oxides

DFT lattice optimizations of bulk lattice parameters of coating and support oxides were performed for AgO, Au2O3, MgO, RhO2, SnO2. Experimental lattice parameters were

used for Nb2O5 and Y2O3. Optimized structure information and DFT parameters are provided in

Table 6.1. Previously reported bulk optimized structures and DFT parameters including U-J values described in Chapter 2 are used for CoO, NiO, CuO, ZnO, PdO, Mn3O4, V2O3, Cr2O3,

Fe2O3, α-ZrO2, MoO2, RuO2, CeO2, IrO2. For TiO2, rutile, anatase and brookite phases were used for support oxides. For TiO2 MMOs on other oxide supports, the most stable rutile TiO2 phase

49 was used as the bulk reference. Magnetic arrangements were important for CoO, Fe2O3, Cr2O3

50 and V2O3 to get the lowest energy structure. GGA based DFT fails to predict the lattice

parameters and multi-oxidation states of Ag atoms in AgO compared to hybrid functionals.51

However, to be consistent with the rest of the dataset, we have used DFT for calculating the bulk

AgO energy.

Table 6-1. Bulk oxide parameters of coating metal oxides.

Cutoff k-point Lattice Parameters ( Å, degree) Functional Oxide U-J Energy Ref. grid Units (eV) a b c α β γ AgO 0 5×5×4 650 4.42 4.89 5.62 90 90 90 4 1 2 Au2O3 0 6×2×1 650 4.06 10.66 13.05 90 90 90 8 MgO 0 5×5×5 500 4.26 4.26 4.26 90 90 90 4 3 4 RhO2 0 5×5×8 650 4.56 4.56 3.13 90 90 90 2 5 SnO2 0 8×8×10 750 4.83 4.83 3.25 90 90 90 2 6 Nb2O5 0 2×6×2 520 21.16 3.82 16.79 90 90 90 14 7 Y2O3 0 2×2×2 650 10.7 10.7 10.7 90 90 90 16

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6.2.1.3 Support structures

Metal oxide support structures are created by cleaving different low index

surface facets of ZnO, MgO, NiO, SnO2, Cr2O3, Fe2O3, V2O3 and anatase (a-), brookite (b-) and rutile (r-) TiO2. All 25-surface terminations studied here are stoichiometric surface terminations.

We have previously reported MMO formation energies for a-TiO2 [(001), (100), (101), (110)], b-

TiO2 [(001), (010), (210)] and r-TiO2 [(001), (100), (101), (110)], (0001) surface terminations of

V2O3, Fe2O3 and Cr2O3, and the ZnO (0001)-Zn terminated surface. In this study, we add to this data set MMOs with substrates of ZnO [(100), (110)], MgO [(110), (100)], NiO [(001), (110)] and SnO2 [(001), (101), (100), (110)]. Fig S1-4 in supplementary information (SI) shows these surface terminations.

We calculated the DFT energies of support oxides each coated with a conformal

monolayer oxide of metals of all possible combinations of support and bulk oxides mentioned

above. Using the DFT energies of support oxides and bulk references states, monolayer formation

energies following Eqn 6.1 were calculated for a total of 506 pairs of coating metal oxide and

support oxide surfaces. All values are reported in Table S1.

6.2.2 Descriptor/Feature Space

We search for descriptors to predict the MMO formation energy, the values are

calculated for our training set using Eqn 6.1. We choose to look for descriptors for the bulk-oxide referenced formation energy, as we know how to then add the “correction” to reference the stability relative to the oxide nanoparticle given the oxide’s most stable surface energy (γmin) and the oxygen chemical potential (µo). Descriptors/features are physical properties of the system that

are correlated to the final target property. In supervised machine learning methods, we start with a

171 hypothesized list of primary descriptors, and search within this list for those that best describe the final target property. In most cases, the descriptors will not correlate with the target property linearly, so non-linearity is added by applying different algebraic operations (+,-,/,×,exp, log, xn

etc.) to the descriptors, with increasing complexity of mathematical operation added iteratively

until a desired accuracy for the predicted property is reached. We start from just the primary set

of descriptors and increase the number of derivative (secondary) descriptors with each iteration.

6.2.2.1 Primary Descriptors

The primary descriptors included in this study are chosen as properties we

hypothesize might have some correlation with monolayer formation energy or have been used

previously to describe metal-metal or metal-oxygen interactions.18,29,32,52–56 These can be divided

into three different categories.

6.2.2.1.1 Atomistic Properties

For atomistic properties, we have included atomic number (N), Pauling electronegativity

( ), ionization energy (IEn; n=1,2,3,4), electron affinity (EA), total number of valence electrons

𝑃𝑃 (𝜒𝜒NV), atomic weight (Ar), number of valance elections in s, p, d, or f orbitals (NVn; n=s, p, d, f),

space group (SG) and type (SGT) presented as numeric values, periodic table row (PR) and

57 column (PC), covalent radius (rc), HOMO (H) and LUMO (L) energies, and Zunger orbital radii

58 (rs, rp, rd). We have also included two parameters introduced by Meidema et al. that account for metal-metal binding derived from a previously reported semi-empirical method for predicting metal-metal binding enthalpies. These parameters represent the chemical potential of electrons in the metal (φ*) and are combined with parameters that represent the discontinuity in electron

172 density between the two binding metals (η1/3). These 25 properties are included for both the

support oxide metal (M1) and coating metal (M2) and reported in Table S2.

6.2.2.1.2 Oxide properties

For oxide properties, we have included HOMO and LUMO energies, band center (BC),

oxidation state of the metal (OxM), and cohesive energy (CE). Structural parameters include

coordination number (CN) of metal and oxygen, next nearest neighbor absolute (NNa) and

relative (NNr) distance, bond valence (BV),59 density (ρ), packing factor (pf), volume per atom

(Vpa), SG and SGT. These were obtained using composition information and DFT optimized bulk

60 61,62 oxide structures in python package matminer. The enthalpy of formation (ΔHf) per metal

61,62 atom for bulk oxides and heat of sublimation for metals (ΔHsub) are also included. Shear modulus (SM) and bulk modulus (BM)63 of the oxides are included as well. A total of 20

descriptors are included as oxide properties and values are given in Table S3.

6.2.2.1.3 Support properties

As properties of the support oxide structure, DFT calculated surface energy (γsurf) and

work function (WF) are included. Surface energies for stoichiometric surfaces were calculated as

–

1 = ( 1) ( 1) (6.4) , , 𝛾𝛾𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 �� 𝑀𝑀 𝑖𝑖𝑂𝑂𝑗𝑗�𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − � 𝑀𝑀 𝑖𝑖𝑂𝑂𝑗𝑗�𝑡𝑡 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏� where A is the total surface𝐴𝐴 area exposed. For the polar surface ZnO (0001)-Zn, the surface slab’s top and bottom terminations (Zn terminated and O terminated) are different and using Eqn 6.4 gives the cleavage energy of the surface as an average of the two types of surface terminations. We have used this value in our descriptor dataset. Workfunction of the surface is the energy required to move an electron from the surface to vacuum and is an indicator of the reductive property of the surface.64 We calculate these values by correcting the VASP calculated

fermi energy to the potential at the center of the vacuum region. Calculated surface energy and

173 workfunction values are provided in Table S3 of the SI. From optimized DFT structures of the surface, the NNa and BV for metals, and CN of metal and oxygen in the outer most layers of the surface are included. These properties can be found/calculated using values reported in literature as well. All values used here as support surface properties are reported in Table S4.

6.2.2.1.4 Coating-Support oxide properties

Some of the properties included in the primary descriptors depend on both the oxide of the coating and the support oxide. We calculated the similarity index (SMI) between the bulk oxides of the coating and support using an algorithm proposed by Zimmermann et al.65 that compares two structures based on the local coordination information from all sites. The implementation of this algorithm in the matminer python package60 was used to calculate the SMI between all coating-support oxide pairs. We have also included the NNa for coating metals after ionic relaxation in the bulk structure of the support oxide (Table S5). Two more ionization energies are added as separate primary descriptors (IEn and IEnp) – for a coating oxide with +n and support with +m oxidation state. If n>m, we included the n and n-1 ionization energies for the coating metal and m+1 and m+2 ionization energy for the support oxide. For n

For the coating oxide, we also included the total ionization energy (IEs) required to go from +n to

+m state. The change in ionization energy to go from n to n+1 is considered positive.

Henceforth, we use SM and CM superscripts to indicate properties of support and coating metal and SMO and CMO for support and coating metal oxide properties. SUP superscript is used for support oxide property if required.

174

6.2.2.2 Feature Spaces (Ω1, Ω2, Ω3)

Secondary descriptors are generated by applying algebraic operations on the primary descriptors. We have generated three different feature spaces from the primary descriptors mentioned above. The procedure followed to create these feature spaces are described below.

6.2.2.2.1 Feature Space 1, Ω1

In feature space 1 (Ω1), in addition to the primary descriptors, we included the

addition and subtraction for atomic HOMO and LUMO, summation of all possible combinations

th n of 1-4 ionization energies ( Cr; n=4, r=2,3,4), summation of possible combinations of valence

n electrons in s, p, d, and f orbitals ( Cr; n=4,r=2,3), and addition and absolute subtraction of all

n possible combinations of atomic radius ( Cr; n=3, r=2) for each metal atom. The addition and subtraction for oxide HOMO, LUMO, and (ΔHsub-ΔHf) are also included in this feature space. A total of 169 descriptors are present in Ω1.

6.2.2.2.2 Feature Space 2, Ω2

For feature space 2, we apply the algebraic unary operations {exp(x), log(x),

2 sqrt(x), 1/x, x } where x represents the set of all descriptors of Ω1. Next, binary {+,-,|-|} operations

between all similar descriptors (with same units) between the coating and support metal and metal

oxide are added. Binary {+,-,|-|} operations on the CN of the metal and oxygen, NND (absolute) and BV of support and coating oxide (bulk) and support and support oxide (bulk) are performed.

Ω2 also includes all descriptors of Ω1. Any descriptor involving infinity/-infinity, constant values for all coat/oxide support pairs and operations that are not defined are discarded. The total number of descriptors in Ω2 is 1,114.

6.2.2.2.3 Feature Space 3, Ω3

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For feature space 3, we first apply the algebraic operations {exp(x), log(x),

2 sqrt(x), 1/x, x } to the descriptors in Ω2 that were generated by the binary operations. Next, binary

operations {×,÷} are applied on all possible combinations of two descriptors from Ω2. For

division operation we take into consideration the order of the elements (i.e. x1/x2 and x2/x1 are

considered as separate descriptors). Similar to Ω2 generation, any descriptor involving infinity/- infinity, constants values for all coat/oxide support pairs and operations that are not defined are discarded. Ω3 also includes all descriptors of Ω2 and the total number of descriptors is 1,708,803.

6.2.3 Shrinkage Method/Feature Selection (LASSO+lo)

From our generated feature spaces, we select the best n descriptors that describes the formation energy of the monolayer using the LASSO+lo approach. LASSO (least absolute shrinkage and selection operator) is a shrinkage method that reduces the number of descriptors

using a l1 penalty, or, in other words, it penalizes for having a larger number of coefficients.

LASSO minimizes the residual sum of squares of the expression given in Eqn 6.5 and is similar to the least squares methods except for the important regularization term.

1 argmin 𝑝𝑝 2 + 𝑝𝑝 (6.5) 2 𝑁𝑁 𝑖𝑖 𝑖𝑖𝑖𝑖 𝑗𝑗 𝑗𝑗 𝛽𝛽 � � �𝑦𝑦 − � 𝑥𝑥 𝛽𝛽 � 𝜆𝜆 ��𝛽𝛽 �� 𝑁𝑁 𝑖𝑖=1 𝑗𝑗=1 𝑗𝑗=1 where y is a column vector of responses that has been centered (i.e., the DFT calculated monolayer formation energies), x is a (N×p) dimensional design matrix of scaled and centered descriptors (N is the total number of observations, i.e, the number of total monolayer formation energy calculations and p is the total number of descriptors), and β is the column vector of coefficients that is to be determined. λ is a penalty parameter that, when increased, decreases the

176

number of non-zero components of vector β. For a maximum value of λ ( =

𝑚𝑚𝑚𝑚𝑚𝑚 | , |), all elements of β will be zero, and as λ is decreased, more𝜆𝜆 elements will take 1 𝑙𝑙 𝑙𝑙 𝑁𝑁non𝑚𝑚𝑚𝑚-zero𝑚𝑚 〈 𝑥𝑥values.𝑦𝑦〉 Since LASSO is not scale invariant, we standardized36 the descriptor matrix, x, to have a zero-mean and unit-variance by subtracting from each column its mean and normalizing by its standard deviation. This normalization puts all the descriptors on a common scale to render the penalty parameter, λ, meaningful. After enforcing a cutoff value of λ, a subsequent exhaustive search using least squares method over all possible subsets of descriptors with non-zero β values is completed. Due to the linear correlation between descriptors, the best results may not be achieved solely by employing LASSO. Details of this method (LASSO+lo) can be found

elsewhere.33

6.3 Results and Discussion

6.3.1 LASSO+lo analysis

Out of the 506 DFT calculated monolayer formation energies, 95 percent of the values

(481 data points) fall below 5.3 eV. These 95 percentile points are close to a normal distribution, though the distribution is somewhat skewed negative. Though these is not a clear physical reasoning for having a normal distribution, including very high positive monolayer formation energies in the training set is not useful as descriptor determination becomes biased towards explaining these outlier points that represent highly unstable systems. We therefore utilize the reduced 481 point data set. We also separate this data set into two sub-data sets, a

“stoichiometric” data set representing only combinations of coating oxides and supports for

177 which the coating’s bulk oxide stoichiometry matches that of the support, and a second for which these do not match.

Figure 6-1. RMSE for 1D-5D descriptors for (a) 95 percentile of the training data for the three feature spaces (a) Stoichiometric coat/support oxide dataset (b) Non-stoichiometric coat/support oxide dataset.

Table 6-2. Descriptor set using LASSO+lo analysis of Ω3 feature space. Descriptors Sign of RMSE coefficient (eV) All data points 1D H , exp ( ) + 0.72 2D 𝐶𝐶𝐶𝐶𝐶𝐶 2 𝑆𝑆𝑆𝑆𝑆𝑆 H exp + � Δ 𝑓𝑓,𝑜𝑜𝑜𝑜� � 𝑂𝑂𝑂𝑂𝑂𝑂 0.58 ( 𝐶𝐶𝐶𝐶𝐶𝐶 ×2 𝑆𝑆𝑆𝑆𝑆𝑆 ) + 𝑓𝑓 𝑜𝑜𝑜𝑜 Stoichiometric 1D 𝑆𝑆𝑆𝑆� Δ𝐶𝐶𝐶𝐶 � �𝑆𝑆𝑆𝑆𝑆𝑆� 𝑂𝑂𝐶𝐶𝑂𝑂𝑂𝑂𝐶𝐶𝐶𝐶� 𝑑𝑑 𝑑𝑑 × log ( ) - 0.33 2D � 𝑟𝑟 −𝐶𝐶𝐶𝐶 𝑟𝑟 � � 𝐵𝐵𝐵𝐵 − 𝐵𝐵𝐵𝐵� × log - 𝑟𝑟𝑠𝑠+𝑑𝑑 𝛾𝛾𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 0.28 exp 𝐶𝐶𝐶𝐶 × - 𝑠𝑠+𝑑𝑑 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 Non- 1D 𝐶𝐶𝐶𝐶𝐶𝐶 𝑟𝑟 𝑆𝑆𝑆𝑆 �𝛾𝛾 �𝐶𝐶𝐶𝐶 H exp𝑛𝑛−𝑛𝑛 (𝑛𝑛 ) 𝑛𝑛−𝑛𝑛𝑛𝑛 + 0.78 stoichiometric � 𝑣𝑣𝑣𝑣𝑣𝑣� , � 𝐼𝐼𝐼𝐼 − 𝐼𝐼𝐼𝐼 � 𝐶𝐶𝐶𝐶𝐶𝐶 2 𝑆𝑆𝑆𝑆𝑆𝑆 2D log ( ) - � Δ 𝑓𝑓 𝑜𝑜𝑜𝑜� � 𝐵𝐵𝐵𝐵 0.62 𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶 + 𝑆𝑆𝑆𝑆𝑂𝑂 𝐻𝐻�𝐶𝐶𝐶𝐶𝐶𝐶 𝑁𝑁𝑁𝑁𝐶𝐶𝐶𝐶 � 𝐵𝐵𝐵𝐵 − 𝐵𝐵𝐵𝐵�� 𝐼𝐼𝐼𝐼𝑛𝑛𝑛𝑛

Following the LASSO+lo approach, we decrease the penalty term, λ, logarithmically from

λmax to λmin = 0.001×λmax. A λcutoff value is chosen for each feature space so that ~100 descriptors

are chosen in the LASSO step. Next, an exhaustive search using least squares method is

performed with all possible combinations of descriptors selected in the LASSO step with one

(1D) to five (5D) descriptors. The root mean squared error (RMSE) for each feature space and 1D

178 to 5D descriptors are shown in Fig 6.1(a). We clearly observe the decrease of RMSE with increasing number of terms in the descriptors as well as with increasing complexity/size of the feature space. The lowest RMSE is observed for 5D descriptors in Ω3 with a value of 0.44 eV.

The 1D and 2D descriptors for Ω3 are given in Table 6.2 and for Ω2 and Ω1 they are provided in the Table S6.

Lower dimensional descriptors (1D~3D) give physical insight as to what controls MMO stability, whereas it becomes increasingly difficult to extract physical meanings from higher dimensional descriptors. The first descriptor, H , exp ( ), has a positive 𝐶𝐶𝐶𝐶𝐶𝐶 2 𝑆𝑆𝑆𝑆𝑆𝑆 Δ 𝑓𝑓 𝑜𝑜𝑜𝑜 � 𝑂𝑂𝑂𝑂𝑂𝑂 coefficient. The term H , = ,� represents the� energy for a metal oxide to

𝑓𝑓 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠 𝑓𝑓 decompose to its metalΔ atom and∆ 𝐻𝐻oxygen.− ∆ This𝐻𝐻 indicates that a metal with a less stable metal oxide reference state is more likely to form a MMO. This property is scaled in the first descriptor by the exponent of the oxidation state of the support oxide metal. Thus, supports with higher oxidation state are more likely to stabilize the monolayer, though the effect decays exponentially.

For the 2D descriptor set, the first descriptor is same as the 1D descriptor. The second descriptor indicates that support and coating oxides with similar oxidation states (BV is a measure of oxidation state) and d-orbital radii favor monolayer formation. Going beyond 2D, the RSME decreased to 0.44 eV (5D) and we observe the surface energy of the support also becomes an important descriptor. As the RMSE of 0.44 eV is quite high given the range of formation energies, we examine the two data subsets to illustrate that it is specifically challenging to find descriptors that simultaneously predict stoichiometric and non-stoichiometric coatings.

We again removed outlier data points in the subsets by including 95 percentiles of the data for non-stoichiometric dataset (328 data points). We only discarded 4 points (>4 eV) from the stoichiometric dataset (157 data points). We follow the same procedure of LASSO+lo

that was previously described for the full dataset and observed similar decreased of RMSE with

179 increase of descriptors in the three feature spaces (Fig 6.1(b-c)). For the stoichiometric dataset, with a 5D descriptor the RMSE was a relatively low value of 0.22 eV. The 1D and 2D descriptors are given in Table 6.2. For the 1D descriptor set, the descriptor consists of the log of surface energy multiplied by the summation of s and p orbital radii of the coating oxide. The coefficient for this descriptor is negative. This can be interpreted as indicating that support surfaces with higher surface energy are more likely to stabilize a MMO. The term that multiplies the surface energy term, (summation of s and d orbital radii of the coating oxide), switches to the 𝐶𝐶𝐶𝐶 𝑠𝑠+𝑑𝑑 periodic table row𝑟𝑟 number ( ) in higher dimensional descriptors. The Pearson coefficient is 𝐶𝐶𝐶𝐶 0.89 between these two descriptors𝑃𝑃𝑃𝑃 of the coating metal oxides and these descriptors show an almost linear relationship with one another (Fig 6.2(a)). clearly has a different range of 𝐶𝐶𝐶𝐶 𝑠𝑠+𝑑𝑑 values for rows 4 and 5, though row 6 values overlap with values𝑟𝑟 of row 5 in Fig 6.2(b). Our 1D and higher descriptors therefore both indicate that a decrease of row number of the coating gives a more stable MMO. Oxides of Ti, V, Cr, Fe, Ni, Zn, Co and Cu have higher tendency to form monolayers on support oxides with the same stoichiometry. Physically, this might arise from the greater oxygen affinity of 3D metals or their generally smaller size, though direct descriptors of these properties were also included in the database. For 2D descriptors, the second descriptor includes the volume per atom (Vpa) of the coating oxide multiplied by ionization energy (IE)

differences between the support and coating oxide, with a negative coefficient. This term is

relatively complex; while we expect an oxide with higher Vpa might not prefer to coat a support

oxide (unless Vpa is similar), the second term ( ), can be both positive and 𝑆𝑆𝑆𝑆 𝐶𝐶𝐶𝐶 𝑛𝑛−𝑛𝑛𝑛𝑛 𝑛𝑛−𝑛𝑛𝑛𝑛 negative based on the coating/support combination.𝐼𝐼𝐼𝐼 According− 𝐼𝐼to𝐼𝐼 our definition, if coating and

support oxide both have the same oxidation state, m, then based on their m+1 ionization energy

we assigned IEn and IEn+p to either m and m-1 or m+1 and m+2, assuming the lower ionization energy metal’s oxidation state will increase and vice versa. For coating/support oxide pairs in the

180 m oxidation sate, the net effect of this term is, if support m+1th IE is greater than coating oxides

th m+1 IE, ( ) is positive (except for Ce, Ir and Zn on TiO2 surfaces), thus, 𝑆𝑆𝑆𝑆 𝐶𝐶𝐶𝐶 𝑛𝑛−𝑛𝑛𝑛𝑛 𝑛𝑛−𝑛𝑛𝑛𝑛 increases the stability𝐼𝐼𝐼𝐼 −of the𝐼𝐼 𝐼𝐼monolayer due to the negative coefficient. In the opposite case, the

monolayer stability is decreased. For both, the effect is scaled by the exponent Vpa term of the

coating oxide. Going to higher dimensional descriptors, support oxide structural and difference of

atomic properties are introduced.

Figure 6-2. Cross-correlation of descriptors (a) correlation between the two descriptor terms that multiplies surface energy in stoichiometric coating/oxide dataset. (b) Correlation between Zunger (s+d) orbital Radii and row in Periodic table.

For the non-stoichiometric dataset, the RMSE compared to the full dataset is

always higher. This might be expected as the structural and chemical properties of the coating

differ more from their bulk form, and the energy of adding or subtracting oxygen is included. The

1D and 2D descriptors are reported in Table 6.2. With 5D descriptors, the lowest RMSE is 0.46

eV. For 1D, the descriptor set is similar to that of the full dataset (BV and oxidation state are

correlated, Pearson correlation coefficient of 0.9973). In the 2D descriptor set, the first descriptor

log ( ) , has a negative coefficient. The value of total valence electron for coating 𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶 𝐻𝐻� 𝑁𝑁𝑁𝑁

181 oxides varies from 2 to 12, such that 1 log ( ) decays with increase of NV. Since the HOMO 𝐶𝐶𝐶𝐶 energy is negative, and this descriptor ⁄has a negative𝑁𝑁𝑁𝑁 coefficient, it indicates that coating metals with lower HOMO energy and a higher number of valence electrons have a higher stability as

MMOs for non-stoichiometric cases. The second descriptor of 2D, is always positive and signifies that coating oxides with larger differences in oxidation with support are likely to be less stable. Higher dimensional descriptors include ∆Hf , ∆Hf,ox and BG of the coating oxide and support structural information.

Figure 6-3. DFT and descriptor predicted monolayer formation energy for (a) stoichiometric (b) non-stoichiometric data set.

182

Fig 6.3 shows the DFT calculated vs descriptor predicted values for 1D and 5D for both stoichiometric and non-stoichiometric dataset. We can clearly observe the improvement in prediction as we use higher dimensional descriptors for prediction.

6.3.2 Validation

To check the robustness of the developed descriptors, we left out 10% of data (randomly selected) and used the remaining data for LASSO+lo analysis. We repeated the procedure 50 times, standardizing the remaining 90% of the training data each time before the LASSO step.

Re-normalization assured that no information from the test set was transferred to the randomly selected training data. Using this method, for the stoichiometric data set, we found similar 1D descriptors 92% of the time. All of them contained the log of surface energy multiplied by a

second term which was either sum of s and p orbital radii (or exponent of the sum) or sum of p

and d orbital radii (or log of their sum). The Pearson correlation coefficient between them is

~0.98, so they can be regarded as the same descriptor. For 2D descriptors, we found various sets

of descriptors out of the 50 trials. The same descriptors with all stoichiometric data points were

repeated 54% of the time. The other most repeated set was found 12% of the time. They all

include at least one descriptor with the surface energy (either log or ) multiplied by another

term, either the orbital radius or NND (relative). For the non-stoichiometric√ dataset 1D descriptor, we get the descriptor, H , exp ( ), 60% of the time and the descriptor, 𝐶𝐶𝐶𝐶𝐶𝐶 2 𝑆𝑆𝑆𝑆𝑆𝑆 � Δ 𝑓𝑓 𝑜𝑜𝑜𝑜� � 𝐵𝐵𝐵𝐵 H , exp ( ), 40% of the time. Since BV and oxidation state are highly correlated, 𝐶𝐶𝐶𝐶𝐶𝐶 2 𝑆𝑆𝑆𝑆𝑂𝑂 𝑓𝑓 𝑜𝑜𝑜𝑜 we� essentiallyΔ � �get the same𝐵𝐵𝐵𝐵 descriptor 100% of the time. For the 2D descriptor, the same descriptors as the full non-stoichiometric dataset are repeated 66% of the time. The second most repeated descriptor set is similar to the full dataset 2D descriptor. For the non-stoichiometric

183 dataset, even though the RMSE is high, the descriptors are robust with random selection of data points. Beyond 2D, both for stoichiometric and non-stoichiometric datasets, the number of possible combinations is large and the descriptor sets change with the random selection. This has been observed before for similar studies involving large descriptor sets28 indicating the possibility

of different sets giving the same order of error.

The purpose of the LASSO+lo analysis was to predict and gain insight to the underlying

physical properties that effects the monolayer stability. From the LASSO+lo analysis of all data points, we observed that coating metals with less stable metal oxides and support metals with higher oxidation state are more preferable for monolayer formation. In stoichiometric combinations of coating/support oxide, besides a high surface energy, metal oxides with low s+p orbital radii or oxides in earlier rows in the periodic table are favorable combinations for monolayer formation. Non-stoichiometric combinations show the same behavior as the full data set. 2D descriptors show that lower HOMO energy, higher number of valence electrons and small difference between oxidation state of coating and support oxide lowers the monolayer formation energy.

6.3.3 Sensitivity Analysis

Sensitivity analysis gives us a measure of uncertainty of the output due to the possible uncertainty in the inputs. In this study, we focus on the uncertainty of the descriptors due to errors or imprecision in the DFT-calculated monolayer formation energies. Errors may arise from numerical approximations (for example, the use of finite convergence criteria) or inaccuracies in the DFT representation of the electronic structure (for example, the self-interaction errors in highly localized systems). The optimal descriptors arrived at can also be sensitive to errors in the primary descriptors. However, we only examine sensitivity to the objective monolayer formation

184 energies. This analysis allows us to assess whether the accuracy of the DFT methods is sufficient to reach conclusions as to useful descriptors, and whether lower accuracy methods (for example, force-field based methods) would be sufficient to more rapidly consider monolayer stability.

To examine sensitivity of the developed descriptors to error in the monolayer formation energies, we added uniformly distributed random values between ±δ eV as noise to our calculated values. We used 11 different values of δ (0.003, 0.01. 0.03, 0.06, 0.1, 0.2, 0.3, 0.5, 0.6, 0.7 and

0.8 eV) and repeated the LASSO+lo procedure 25 times for each of them. If the same descriptors are arrived at despite variation up to a certain value of δ, we would conclude that these descriptors are robust in predicting monolayer formation energies despite error up to that value.

For stoichiometric dataset, we found that the 1D and 2D descriptors were relatively robust with errors as large as 0.1 eV in the training data set. For variation up to δ=0.03 eV, the same 1D and 2D descriptors were predicted 100% of the time. For δ up to 0.1 eV, the 1D descriptor presented was either the same as that without error produced, or a second descriptor that had a Pearson correlation coefficient ~0.98 (p<0.001) with the original 1D descriptor. We conclude that the 1D descriptor is robust up to an error of 0.1 eV, with larger errors leading to different 1D descriptors. For 2D, with δ=0.06 eV, the no-error descriptors were predicted 92% of the time, and at δ=0.1 eV the repetition decreased to 72%. For 3D, with δ=0.01 eV, 88% of the time the 3D δ=0 eV descriptor set was predicted. Increasing δ to 0.03 eV decreased the repetition to 60%. Overall, for the stoichiometric dataset, the 1D and 2D descriptors were less sensitive to uniform random errors that did not exceed ±0.1 eV, whereas 3D descriptor set is more sensitive to errors.

For the non-stoichiometric case, the descriptors were less sensitive to inaccuracies in the monolayer formation energies. 1D descriptors were repeated 100% of the times for all δ values tested. For 2D, as δ increased to 0.06/0.1/0.2 eV, the repetition rates dropped to 88% from 100%.

185

Surprisingly, the 3D descriptors were less sensitive and only dropped below 100% at δ=0.2 eV

(96%). Our analysis indicated that non-stoichiometric dataset is less sensitive to the uniform random error in monolayer formation energy than stoichiometric dataset descriptors.

The sensitivity analysis results show that the predicted 1D-2D descriptors are not sensitive to changes in the monolayer formation energy within ±0.1 eV or 2.31 kcal/mol. This indicates, within our chosen functional (PBE) and numerical convergence criteria, the predictors are robust. However, DFT results for monolayer formation energies are not robust to this accuracy among changes in exchange-correlation functional (i.e., on switching to other GGA or hybrid functionals), and we do not know to what extent trends among the systems would be robust to functional. Experimental monolayer formation energies are not available to assess accuracy relative to, but an error of greater than 0.1 eV would be expected. We conclude that the machine learning approach applied here is robust in descriptor formation with respect to the numerical accuracy used in our approach, but subject to the choice of exchange-correlation functional used.

6.4 Conclusions

A descriptor search to predict the stability of conformal monolayer metal oxides on support metal oxides has been presented. Using the LASSO+lo, a supervised machine learning

algorithm, we have gained insight into the underlying physical properties that effect monolayer

stability. We find the stoichiometric and non-stoichiometric surfaces have different rules for stability. Stoichiometric monolayer stability is enhanced on higher surface energy substrates, and when containing metals with small s+d orbital radii (i.e., 3d metals). Differences in support versus coating metal ionization energies are also important for stoichiometric coatings. For non-

186 stoichiometric coating/support oxide pairs, a more stable bulk oxide of the coating decreases monolayer stability and using supports with higher oxidation state increases monolayer stability.

The low dimensional descriptors found in this study were robust in the “leave 10% out” analysis, making their physical interpretation meaningful. Sensitivity analysis also showed low dimensional descriptors are not very sensitive to changes in monolayer formation energies within

±0.1 eV, but may be subject to choice of exchange-correlation functional and preclude the use of empirical force-fields. Higher dimensional descriptors may be useful for first screening of possible stable monolayer systems, depending on the cost associated with subsequent computational or experimental materials discovery steps.

6.5 Acknowledgements

This material is based upon work supported by the National Science Foundation under

Grant No. 1505607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the National Science

Foundation. This work used the Extreme Science and Engineering Discovery Environment

(XSEDE), which is supported by the National Science Foundation under Grant No. ACI-

1548562.

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Supplementary Information

1. Supplementary Figures

Figure S1: ZnO surface terminations.

Figure S2: MgO surface terminations.

Fig S3: NiO surface terminations.

Fig S4: SnO2 surface terminations.

192

2. Supplementary Tables

Table S1: Formation energy per coating metal atom (eV) Surface/Coat Metal Ag Au Ce Co Cr Cu Fe Ir Mn Mo Nb Ni Pd Pt Rh Ru Ti V Y Zn Zr ZnO_100 0.306 0.820 4.775 0.052 2.355 0.064 1.232 2.925 0.780 4.418 6.362 0.350 0.780 1.431 2.183 3.063 4.606 2.449 3.783 0.000 6.008 ZnO_110 0.099 0.816 4.038 0.037 2.217 0.029 1.056 2.414 0.739 3.804 7.368 0.198 0.628 2.026 1.981 2.568 4.549 2.411 3.348 0.000 5.614 ZnO_001 -0.440 0.324 5.670 0.123 2.388 -0.667 1.382 2.963 0.897 5.285 6.978 0.223 0.336 1.681 1.749 3.042 4.971 2.753 4.576 0.000 6.568 MgO_110 8.612 3.161 6.697 -0.299 1.417 13.952 2.282 2.996 0.070 4.366 6.054 -0.171 5.898 5.804 1.777 8.484 3.857 1.940 3.084 16.821 5.339 MgO_100 -0.088 0.639 5.560 -0.034 1.525 0.151 5.416 3.920 0.462 4.724 6.786 0.002 0.727 2.243 2.373 6.774 4.568 2.103 4.062 0.093 12.692 NiO_001 -0.056 0.782 4.845 0.031 2.341 0.161 1.698 3.975 2.833 4.941 6.731 0.000 0.710 2.218 2.457 3.515 4.329 2.337 3.349 0.076 5.390 NiO_110 -0.965 -0.498 3.737 -0.161 2.022 0.181 1.646 2.888 1.501 4.464 6.210 0.000 0.160 1.328 1.834 2.948 3.986 2.318 3.380 -0.150 5.520 SnO2_001 0.433 0.412 0.055 -0.860 -0.088 0.361 -0.053 1.012 -0.198 -0.126 1.479 0.124 0.064 0.681 0.447 0.329 -0.046 -1.561 0.484 0.887 0.596 SnO2_101 0.717 0.304 0.390 0.201 0.314 0.833 0.562 0.442 0.289 0.420 1.407 0.991 0.167 0.365 0.215 0.216 0.021 -0.930 0.787 1.345 0.228 SnO2_100 0.774 0.271 0.830 2.122 0.593 0.958 0.645 1.054 0.345 0.741 1.559 0.815 0.375 0.649 0.643 0.782 0.113 -0.681 1.341 1.456 0.183 SnO2_110 0.789 0.311 1.022 0.644 0.710 1.071 0.909 0.642 1.159 0.620 1.467 1.256 0.114 0.297 0.452 0.534 0.180 -0.506 1.151 1.698 0.167 V2O3_001 -1.084 0.529 2.642 -0.717 0.172 -1.120 -0.225 1.797 -0.419 2.391 3.810 -0.967 -0.192 0.863 0.600 1.244 1.626 0.000 1.385 -0.870 2.875 Cr2O3_001 0.139 0.497 2.435 -0.841 0.000 -0.371 -0.234 1.498 -0.503 2.388 3.678 -0.253 -0.090 0.802 0.621 1.284 1.717 0.137 1.413 0.163 3.215 Fe2O3_001 0.469 0.788 2.075 -0.640 0.364 0.024 0.000 1.718 -0.185 2.337 3.473 0.055 0.224 1.064 0.925 1.432 1.544 0.248 1.605 0.623 2.702 CeO2_111 0.000 1.620 0.000 19.337 1.807 19.872 1.879 20.616 0.000 20.182 20.281 0.715 1.801 2.398 21.749 2.503 19.825 -0.465 20.574 2.506 19.825 A-TiO2_001 0.945 0.692 0.572 0.286 0.487 0.965 0.619 0.973 0.244 0.634 1.430 1.241 0.475 0.851 0.660 0.539 0.000 -0.973 1.026 1.587 -0.040 A-TiO2_100 1.189 0.741 1.344 0.429 0.481 1.125 0.742 1.076 0.273 0.917 1.706 1.439 0.527 0.812 0.723 0.732 0.000 -0.821 0.941 2.002 0.519 A-TiO2_101 1.298 0.846 0.995 0.424 0.548 1.120 0.746 1.089 0.261 0.640 1.779 1.485 0.536 0.851 0.713 0.774 0.000 -0.844 0.879 2.045 0.479 A-TiO2_110 0.777 0.861 1.176 0.321 0.472 0.756 0.528 1.221 0.064 0.862 1.683 1.177 0.426 0.816 0.860 0.911 0.000 -0.760 1.375 1.698 0.588 B-TiO2_001 0.954 0.553 0.755 -0.120 0.133 0.716 0.438 0.640 -0.055 0.234 1.578 0.867 0.192 0.399 0.411 0.354 0.000 -1.017 1.108 1.514 0.675 B-TiO2_010 1.189 0.731 1.111 0.208 0.096 0.929 0.636 1.048 0.124 0.790 1.711 1.247 0.402 0.749 0.728 0.696 0.000 -0.949 1.447 1.681 0.607 B-TiO2_210 1.758 1.433 0.886 0.759 0.975 1.555 1.175 1.694 0.556 1.173 1.713 1.796 1.187 1.569 1.277 1.304 0.000 -0.496 1.409 2.037 0.584 R-TiO2_001 0.952 0.552 0.716 0.226 -0.022 0.950 0.600 0.452 0.122 0.556 1.665 1.166 0.011 0.285 0.160 0.035 0.000 -1.032 0.994 1.634 0.429 R-TiO2_100 1.034 0.373 1.906 0.208 0.311 0.828 0.701 0.545 0.030 0.600 1.663 1.005 0.108 0.310 0.287 0.279 0.000 -0.887 1.950 1.845 0.637 R-TiO2_101 0.660 0.192 0.637 0.084 0.267 0.866 0.590 0.469 0.153 0.499 1.156 1.001 0.161 0.349 0.214 0.203 0.000 -0.927 0.948 1.465 0.384 R-TiO2_110 0.962 0.450 1.820 0.073 0.273 0.760 0.419 0.516 -0.035 0.568 1.482 0.950 0.014 0.253 0.239 0.348 0.000 -0.927 1.964 1.636 0.664

193

Table S2: Atomic Properties metal N Chi IE1 IE2 IE3 IE4 EA NV Ar NVS NVP NVD NVF NVT SG SGT PC PR rc HOMO LUM O rs rp rd nws phi Ag 47 1.93 7.58 21.48 34.83 49.00 1.30 11 107.87 1 0 10 0 11 225 1 11 5 1.45 -4.564 -3.792 1.045 1.330 0.385 1.39 4.45 Au 79 2.4 9.23 20.20 30.00 45.00 2.31 11 196.97 1 0 10 14 25 225 1 11 6 1.36 -5.839 -5.129 1.210 1.450 0.488 1.57 5.15 Ce 58 1.12 5.54 10.85 20.20 36.91 0.65 2 140.12 2 0 1 1 4 194 2 3 6 2.04 -2.019 -1.770 2.000 2.500 0.000 1.34 3.25 Co 27 1.88 7.88 17.08 33.50 51.27 0.66 9 58.93 2 0 7 0 9 194 2 9 4 1.26 -3.964 -3.264 0.920 1.100 0.210 1.75 5.1 Cr 24 1.66 6.77 16.49 30.96 49.16 0.67 6 52.00 1 0 5 0 6 229 1 6 4 1.39 -4.054 -1.028 1.070 1.370 0.250 4.65 1.73 Cu 29 1.9 7.73 20.29 36.84 57.38 1.24 11 63.55 1 0 10 0 11 225 1 11 4 1.32 -4.775 -3.946 0.880 1.160 0.185 1.47 4.55 Fe 26 1.83 7.90 16.20 30.65 54.91 0.15 8 55.85 2 0 6 0 8 229 1 8 4 1.32 -4.565 -3.135 0.950 1.160 0.220 1.77 4.93 Ir 77 2.2 8.97 17.00 28.00 40.00 1.56 9 192.22 2 0 7 14 23 225 1 9 6 1.41 -4.707 -4.601 1.160 1.468 0.526 1.83 5.55 Mg 12 1.31 7.65 15.04 80.14 109.27 -0.42 2 24.31 2 0 0 0 2 194 2 2 3 1.41 -4.515 -1.095 0.900 1.130 0.000 1.17 3.45 Mn 25 1.55 7.43 15.64 33.67 51.20 -0.52 7 54.94 2 0 5 0 7 217 1 7 4 1.39 -4.205 -1.813 0.990 1.230 0.230 1.61 4.45 Mo 42 2.16 7.09 16.16 27.13 40.33 0.75 6 95.95 1 0 5 0 6 229 1 6 5 1.54 -4.340 -1.483 1.220 1.500 0.490 4.65 1.77 Nb 41 1.6 6.76 14.32 25.00 37.61 0.92 5 92.91 1 0 4 0 5 229 1 5 5 1.64 -3.329 -3.319 1.230 1.530 0.510 4 1.62 Ni 28 1.91 7.64 18.17 35.19 54.90 1.16 10 58.69 2 0 8 0 10 225 1 10 4 1.24 -4.476 -3.392 0.960 1.220 0.195 1.75 5.2 Pd 46 2.2 8.34 19.43 32.93 46.00 0.56 12 106.42 0 0 10 0 10 225 1 10 5 1.39 -3.865 -3.206 1.080 1.370 0.400 1.65 5.45 Pt 78 2.2 8.96 18.56 29.00 43.00 2.13 10 195.08 1 0 9 14 24 225 1 10 6 1.36 -5.147 -4.997 1.240 1.460 0.510 1.78 5.65 Rh 45 2.28 7.46 18.08 31.06 42.00 1.14 9 102.91 1 0 8 0 9 225 1 9 5 1.42 -4.524 -4.227 1.110 1.410 0.420 1.76 5.4 Ru 44 2.2 7.36 16.76 28.47 45.00 1.05 8 101.07 1 0 7 0 8 194 2 8 5 1.46 -3.994 -3.184 1.145 1.460 0.450 1.83 5.4 Sn 50 1.96 7.34 14.63 30.50 40.74 1.11 4 118.71 2 2 10 0 14 141 4 14 5 1.39 -3.693 -3.610 0.880 1.000 0.345 1.24 4.15 Ti 22 1.54 6.83 13.58 27.49 43.27 0.08 4 47.87 2 0 2 0 4 194 4 4 4 1.6 -3.857 -2.237 1.150 1.430 0.280 1.47 3.65 V 23 1.63 6.75 14.62 29.31 46.71 0.53 5 50.94 2 0 3 0 5 229 1 5 4 1.53 -3.054 -1.190 1.090 1.340 0.260 1.64 4.25 Y 39 1.22 6.22 12.22 20.52 60.61 0.31 3 88.91 2 0 1 0 3 194 4 3 5 1.9 -2.729 -2.151 1.320 1.620 0.580 3.2 1.21 Zn 30 1.65 9.39 17.96 39.72 59.57 -0.62 12 65.38 2 0 10 0 12 194 4 12 4 1.22 -5.843 -0.961 0.820 1.060 0.175 1.32 4.1 Zr 40 1.33 6.63 13.13 23.17 34.42 0.43 4 91.22 2 0 2 0 4 194 4 4 5 1.75 -3.761 -3.530 1.265 1.56 0.54 3.4 1.39

N Atomic Number Chi Electronegativity IEn nth Ionization Energy EA Electron affinity NV # Valance electrons Ar Atomic Weight NVn Number of valance in n orbital SG Space group SGT Space group type PC Periodic Table column PR Periodic Table row rc Covalent radius HOMO Highest occupied orbital energy LUMO Lowest unoccupied orbital energy rn Zunger radii of n orbital nws Meidema Parameters phi Meidema Parameters

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Table S3: Oxide Properties oxide HOMO LUMO BC OxM CE SM BM BG Hf Hsub CNM CNO NNDr NNDa BV rho vpa pf SG SGT AgO -0.299 -0.299 -2.577 2 3.229 13 103 0 -0.252 2.953 4 4 0.802 2.165 1.67 6.775 15.181 0.595 66 5 Au2O3 -0.305 -0.305 -3.047 3 3.550 38 81 0.82 -0.018 3.816 4 3 0.877 1.991 2.578 10.407 14.103 0.331 43 5 CeO2 -0.338 -0.337 -2.367 4 7.119 72 177 1.865 -11.284 4.384 8 4 0.993 2.373 3.145 6.942 13.724 0.688 225 1 CoO -0.322 -0.322 -2.543 2 4.825 31 129 0.588 -2.466 4.402 6 6 0.913 2.125 1.828 6.432 9.673 0.579 139 1 Cr2O3 -0.118 -0.118 -2.570 3 5.549 113 203 2.437 -5.906 4.110 6 4 0.987 2.009 2.617 4.907 10.288 0.500 167 3 CuO -0.202 -0.202 -2.557 2 3.999 25 143 0 -1.678 3.497 4 4 0.902 1.939 1.797 6.205 10.643 0.527 15 6 Fe2O3 -0.295 -0.295 -2.672 3 5.158 86 192 1.528 -4.271 4.315 6 4 0.897 2.129 2.78 5.085 10.430 0.493 167 3 IrO2 -0.335 -0.335 -2.964 4 5.306 104 270 0 -2.585 6.938 6 3 0.970 1.983 4.186 11.311 10.973 0.368 136 4 MgO -0.338 -0.175 -2.123 2 5.126 119 151 4.445 -6.235 1.525 6 6 1.004 2.128 1.851 3.472 9.639 0.780 225 1 Mn3O4 -0.267 -0.267 -2.444 3 4.801 47 127 0.693 -4.795 2.909 6 4 0.868 2.003 2.421 4.578 11.857 0.459 141 4 MoO2 -0.153 -0.153 -2.946 4 6.157 89 219 0 -6.104 6.821 6 3 0.962 1.991 4.089 6.284 11.270 0.431 14 6 Nb2O5 -0.338 -0.144 -2.764 5 7.072 68.73 139.37 1.614 -9.843 7.523 6 4 0.862 1.827 5.176 4.552 13.853 0.310 10 6 NiO -0.338 -0.338 -2.563 2 4.454 98 184 2.318 -2.484 4.454 6 6 1.014 2.107 1.868 6.517 9.516 0.589 225 1 PdO -0.161 -0.161 -2.751 2 4.047 34 159 0 -1.197 3.907 4 4 0.905 2.063 1.925 7.768 13.084 0.474 131 4 PtO2 -0.274 -0.274 -2.999 4 4.621 87 202 0.642 -0.563 5.859 6 3 1.055 2.058 3.699 9.199 13.664 0.296 164 3 RhO2 -0.239 -0.239 -2.999 4 4.888 94 234 0 -1.843 5.732 6 3 0.979 1.977 3.503 6.894 10.831 0.373 136 4 RuO2 -0.210 -0.210 -2.964 4 5.453 93 252 0 -3.161 6.751 6 3 0.963 1.965 3.921 6.819 10.801 0.340 136 4 SnO2 -0.338 -0.338 -2.852 4 4.905 87 172 0.652 -5.986 3.122 6 3 0.938 2.092 3.616 6.619 12.603 0.386 136 4 R-TiO2 -0.338 -0.170 -2.632 4 6.868 110 209 1.781 -9.784 4.902 6 3 0.920 1.988 3.649 3.996 11.062 0.401 136 4 V2O3 -0.205 -0.205 -2.552 3 6.218 80 202 0.476 -6.316 5.329 6 4 0.979 2.106 2.557 4.653 10.698 0.436 167 3 Y2O3 -0.338 -0.151 -2.272 3 7.294 61 138 4.053 -9.874 4.366 6 4 0.909 2.268 2.795 4.898 15.310 0.674 206 1 ZnO -0.338 -0.223 -2.382 2 3.773 41 130 0.732 -3.633 1.352 4 4 0.863 2.002 1.775 5.453 12.394 0.452 186 2 ZrO2 -0.338 -0.162 -2.506 4 7.649 85 183 3.474 -11.409 6.231 7 4 0.899 2.077 3.602 5.631 12.113 0.479 14 6 A-TiO2 -0.338 -0.170 -2.632 4 6.868 55 179 2.052 -9.757 4.902 6 3 0.978 1.981 3.714 3.633 12.167 0.364 141 4 B-TiO2 -0.338 -0.170 -2.632 4 6.868 78 191 2.298 -9.777 4.902 6 3 0.962 1.949 3.668 3.865 11.438 0.388 61 5

BC Bond Center OxM Oxidation State CE Cohesive Energy SM Shear Modulus BM Bulk Modulus BG Band Gap Hf Enthalpy of formation (eV) Hsub Heat of sublimation (eV) CNM Coordination No. of Metal CNO Coordination No. of Oxygen NNDr Next Nearest Neighbor (relative) NNDa Next Nearest Neighbor (absolute) BV Bond Valance rho Density vpa Volume per atom pf Packing factor

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Table S4: Support properties

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Table S5: Next nearest neighbor distance – coat metal in support oxide bulk lattice (Å) Surface OxidAg Au Ce Co Cr Cu Fe Ir Mg Mn Mo Nb Ni Pd Pt Rh Ru Sn Ti V Y Zn Zr ZnO 0.848 1.030 0.817 0.863 0.916 0.931 0.855 1.030 0.867 0.841 0.949 0.935 0.949 0.878 0.902 1.030 0.953 0.898 0.878 0.906 0.834 0.863 0.867 MgO 0.909 1.090 0.813 1.010 0.983 0.999 1.060 1.090 1.000 1.030 1.020 1.000 1.020 0.942 0.967 1.090 1.020 1.020 0.942 0.972 0.836 0.994 1.000 NiO 0.931 1.080 0.805 1.000 0.973 0.989 1.050 1.080 0.994 1.020 1.010 0.994 1.010 0.932 0.958 1.080 1.010 1.010 0.932 0.962 0.828 0.984 0.994 A-TiO2 0.913 1.020 0.809 0.935 1.010 0.921 0.988 0.969 0.943 1.020 0.957 0.943 0.939 0.973 1.020 0.981 0.971 0.939 0.978 0.990 0.825 0.917 0.926 B-TiO2 0.898 0.999 0.795 0.999 0.989 0.906 0.974 0.953 0.928 0.999 0.941 0.928 1.030 0.957 0.999 0.964 0.955 0.898 0.962 0.974 0.812 0.902 0.886 R-TiO2 0.916 1.020 0.812 0.857 1.010 0.925 0.994 0.972 0.947 1.020 0.960 0.900 0.942 0.977 1.020 0.984 0.975 0.892 0.920 0.929 0.828 0.857 0.861 SnO2 0.964 1.070 0.840 0.902 0.957 0.973 0.894 1.020 0.906 0.879 1.010 0.947 0.991 0.917 1.070 1.040 1.030 0.938 0.968 0.947 0.872 0.902 0.906 V2O3 0.929 0.888 0.755 1.010 0.991 1.030 0.916 0.960 0.956 0.992 0.955 0.942 1.010 0.925 1.030 0.967 0.960 0.904 0.965 0.979 0.808 0.869 0.873 Fe2O3 0.910 0.870 0.715 0.988 0.970 1.010 0.897 0.940 0.940 0.971 0.936 0.922 0.987 0.906 1.010 0.947 0.940 0.963 0.945 0.958 0.791 0.851 0.855 Cr2O3 0.926 0.885 0.728 1.010 0.987 1.020 0.913 0.956 0.907 0.988 0.952 0.939 1.000 0.921 1.010 0.963 0.956 0.939 0.961 0.975 0.805 0.866 0.870 CeO2 1.010 1.220 0.993 1.020 1.090 1.100 1.010 1.160 1.030 0.997 1.150 1.110 1.120 1.040 1.220 1.170 1.130 1.060 1.040 1.070 0.973 1.020 1.050

Table S6: Descriptor of for full dataset for feature space 1 and 2 using LASSO+lo

Table S7: 3D-5D descriptors of for full dataset for feature space 3 using LASSO+lo

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Chapter 7

Conclusions and recommendations for future work

This dissertation aimed at developing a fundamental understanding of monolayer and surface-confined mixed metal oxide stability through ab initio calculations and statistical learning and finding some guidelines for predicting stable monolayer/oxide support pairs. In Section 7.1 a brief summary of the conclusions reached in each Chapter is presented along with the related hypothesis put forward in Chapter 1. In Section 7.2 future work related to this study is discussed.

7.1 Summary of conclusions

In Chapter 2 the stability of monolayer and surface-confined mixed metal oxides was investigated for corundum oxides -V2O3, Cr2O3 and Fe2O3.The hypothesis was relative surface stability of pure oxides for these oxides with similar lattice parameters should correlate to their stability in the monolayer/mixed state. Ab inito thermodynamics showed that surface- segregated mixed metal oxides on their (0001) surface follows the stability of their pure oxide termination. For 3+ (TM terminated) and 5+ state (TM=O terminated) the surface segregation preferences are Fe > V > Cr and V=O > Cr=O > Fe=O respectively. Experimental observations of subsurface segregation of chromia on V2O3 (0001) and surface segregation of vanadia on Cr2O3

(0001) matched the DFT predictions. Transition points in oxygen chemical potential were identified, across which surface and subsurface segregation preference switches due to the surface

198 oxidation. The Fe substitute doping in surface level was considered. Although a better oxidant, Fe surface segregates in an oxidizing environment in vanadia.

In Chapter 3, the support oxides were low index facets of TiO2 in its three different polymorphs (anatase, brookite and rutile). The coating formation was decomposed into three-step thermodynamic process. From this thermodynamic decomposition, it was observed that coating metal oxides that have similar polymorphs as the support oxide are more stable as monolayer but this is not the only factor that describes the stability. It was also found that while supports surface energy do affect the stability of the monolayer coating oxide due to less strong binding to more stable support surface, it alone cannot predict the monolayer stability either. A better analysis method was required to find the underlying relationships between properties and the monolayer stability.

Chapter 4 presented a thermodynamic framework to calculate 2D phase diagram showing the stability region of monolayers and particles. Hypotheses 3 and 4 were addressed in this chapter. To better model the reference state, a spherical particle was proposed. The available possible structures for a particle are too high and are too computationally expensive. An approximate method that assumes the particle to be spherical with its lowest surface energy termination is proposed. This particle is then used as reference for stability. On rutile (110), RuO2

showed preference for monolayer coating while ZnO was only found to be stable with ½

monolayer coverage. NiO had the highest probability of coating ZnO(0001) surface.

In Chapter 5, a statistical learning method (LASSO+lo) was used to predict the stability of metals on oxide surfaces. Out of 333,932 descriptors 1-5D descriptors are selected with RMSE as low as 0.5 eV. The LASSO+lo predicted that neither ΔHf,Ox nor Evac can alone predict the binding energy and their ratio is the better predictor, which means that metals that form a stable oxide and surfaces that are easily reducible are likely to be more stable due to high binding energy. The

199 surfaces capability to form bonds is also important it shows up as the term scaling the enthalpy of formation and surface vacancy energy ratio.

Chapter 6 applies the LASSO+lo analysis to a dataset containing 506 calculations of monolayer formation energy. Two separate analysis were done for stoichiometric and non- stoichiometric combinations. Besides high energy surfaces, metals with small s+d orbital radii are favorable for monolayer stability for stoichiometric cases. These are generally metals in row 4 of the periodic table. Differences in metal ionization energies are also important for stoichiometric coatings. For non-stoichiometric coating/support oxide pairs, a more stable bulk oxide of the coating decreases monolayer stability while supports with higher oxidation state increases monolayer stability. The low dimensional descriptors found in this study were robust in the

“leave 10% out” analysis, making their physical interpretation meaningful. Higher dimensional descriptors can be used for predicting monolayer formation.

Overall, in this dissertation a thermodynamic framework was presented to predict particle sizes required for monolayer stability on metal oxide support at different temperatures and pressures. Since the particle reference state is a correction to the bulk reference state, LASSO+lo

was applied on the 0 K monolayer formation energies to understand the underlying physical rules

for stability. High dimensional descriptors from this trained model can be used to predict stability

of other coat/support oxide pairs that can be further corrected with particle reference if required.

7.2 Future work

In this section, some of the potential future studies related to this dissertation work are discussed

- DFT is a very accurate computational modeling tool, but it is also quite computationally

intensive – restricting applications to relatively small systems. Since, the particle

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reference state thermodynamic framework is ultimately being used as a screening tool it

might be worthwhile to investigate how computationally efficient empirical force fields

such as ReaxFF1 perform for this screening process. At the time of preparation of this

work, the full set of metal/metal and metal/oxygen parameters were not available in

ReaxFF framework. However, this is likely to change in future and with the rise of neural

network base forcefields2–5 the development in force field is likely to accelerate. This also

enables looking into coating layers with edges, defects and 3D clusters.

- The monolayer stability was focused mainly on stoichiometric surface terminations. At

changing pressure-temperature conditions surfaces are likely to be oxidized or reduced.

In terms of possible choices, the possibilities are many and may be too expensive for

DFT. This work as already produced 506 sample DFT data points that can be used to

train an artificial neural network along with few other new surfaces. It would be

computationally inexpensive to only model interaction in the surface layers instead of the

whole slab which has less effect on the monolayer formation energy. Such an DFT

trained artificial neural network-based force field was shown to be successful in

predicting adhesion energies of molecules over a large number of surface terminations

and adsorption sites.6

- This work has solely focused on homostructural epitaxy where the overlayer has the same

lattice structure of the surface. Another possible structure is heterostructual epitaxy where

the overlayer has a different structure than the support oxide. The possibilities for this

kind of structure are much higher. Although, high throughput calculations and some

physical rules has been applied to predict growth of such overlayers these methods only

focus on the physical/structural aspect of the overlayer/support interface7 and clearly

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chemical interactions will play a role in their stability. This work can be extended to such

surface along with the physical constrains as new descriptors.

- The shrinkage method LASSO+lo will reach its limit when number of descriptor reaches

~1010. Algorithms such as SISSO8 was proposed to successful in those cases and will

have to be implemented if the level of complexity is increases from what is presented in

this work.

- For the machine learning part using LASSO+lo, a sensitivity analysis could help to

estimate how sensitive the n dimensional descriptors are to the level of accuracy of the

descriptors.9 Such sensitivity analysis could also provide information on the level of

accuracy required and if different functionals or level of theory can be used while

calculating or collecting the primary descriptors.

- One of the uses of the training set generated in this work can be to predict a “correct”

starting point for empirical force field training (for example, ReaxFF). For training

interfaces, the amount of angle strain and bond stretch/compression can be provided from

a prediction equation based on a similar LASSO+lo method, to the ReaxFF framework so

that the initial force field starts with a good guess for the first few cycles of training

which is often computationally expensive to reach.

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7.3 References

1. Chenoweth, K. et al. Development and Application of a ReaxFF Reactive Force Field for Oxidative Dehydrogenation on Vanadium Oxide Catalysts. J. Phys. Chem. C 112, 14645– 14654 (2008). 2. Kolb, B., Lentz, L. C. & Kolpak, A. M. Discovering charge density functionals and structure- property relationships with PROPhet: A general framework for coupling machine learning and first-principles methods. Scientific Reports 7, 1192 (2017). 3. Khorshidi, A. & Peterson, A. A. Amp: A modular approach to machine learning in atomistic simulations. Computer Physics Communications 207, 310–324 (2016). 4. Cubuk, E. D., Malone, B. D., Onat, B., Waterland, A. & Kaxiras, E. Representations in neural network based empirical potentials. The Journal of Chemical Physics 147, 024104 (2017). 5. Hutchinson, M. L. et al. Overcoming data scarcity with transfer learning. arXiv:1711.05099 [cond-mat, stat] (2017). 6. Ulissi, Z. W. et al. Machine-Learning Methods Enable Exhaustive Searches for Active Bimetallic Facets and Reveal Active Site Motifs for CO 2 Reduction. ACS Catalysis 7, 6600– 6608 (2017). 7. Ding, H. et al. Computational Approach for Epitaxial Polymorph Stabilization through Substrate Selection. ACS Appl. Mater. Interfaces 8, 13086–13093 (2016). 8. Ouyang, R., Curtarolo, S., Ahmetcik, E., Scheffler, M. & Ghiringhelli, L. M. SISSO: a compressed-sensing method for systematically identifying efficient physical models of materials properties. arXiv:1710.03319 [cond-mat] (2017). 9. Ghiringhelli, L. M. et al. Learning physical descriptors for materials science by compressed sensing. New Journal of Physics 19, 023017 (2017).

VITA A S M Jonayat 265 Blue Course Dr. Apt 20D State College, PA-16803 email: [email protected]

Education

The Pennsylvania State University, PA Aug 2018 Ph.D. Candidate, Mechanical Engineering Minor: Computational Materials

University of Illinois at Urbana-Champaign, IL May 2014 Master of Science in Mechanical Engineering Graduate Concentration: Computational Science and Engineering (CSE)

Research Experience

Research Assistant Jan 2015- Department of Mechanical and Nuclear Engineering, PSU Present Adviser: Dr. Adri C. T. van Duin Co-adviser: Dr. Michael J. Janik

Published Publications

1. O’Connor, Nolan J., A. S. M. Jonayat, Michael J. Janik, Thomas P. Senftle. Interaction trends between single metal atoms and oxide supports identified with density functional theory and statistical learning. (equal contribution paper, accepted in Nature Catalysis, 2018) 2. Jonayat, A. S. M., Adri CT van Duin, and Michael J. Janik. Ab Initio Thermodynamic Investigation of Monolayer Stability of Multicomponent Metal Oxides: Mx Oy/ZnO (0001) and MxOy/TiO2 (110)(M= Pd, Ru, Ni, Pt, Au, Zn). The Journal of Physical Chemistry C (2017). DOI: 10.1021/acs.jpcc.7b06521 3. Jonayat, A. S. M., Alan Kramer, Luca Bignardi, Paolo Lacovig, Silvano Lizzit, Adri C.T. van Duin, Matthias Batzill, Michael J. Janik. A First-principles Study of Stability of Surface Confined Mixed Metal Oxides with Corundum Structure (Fe2O3, Cr2O3, V2O3). Physical Chemistry Chemical Physics, 2018,20, 7073-7081. DOI: 10.1039/C8CP00154E 4. Lotfi, Roghayyeh, A. S. M. Jonayat, Adri CT van Duin, Mousumi M. Biswas, and Robert Hempstead. A Reactive Force Field Study on the Interaction of Lubricant with Diamond-Like Carbon Structures. The Journal of Physical Chemistry C 120, no. 48 (2016): 27443-27451. DOI: 10.1021/acs.jpcc.6b09729