The Pennsylvania State University

The Graduate School

Eberly College of Science

NEW INSIGHTS IN THE GAS-PHASE ION CHEMISTRY OF GROUP

IVB TRANSITION METAL OXIDES: CLUSTER MODELS FOR

CATALYSIS

A Dissertation in

Chemistry

by

Christopher L. Harmon

© 2016 Christopher L. Harmon

Submitted in Partial Fulfillment Of the Requirements For the Degree of

Doctor of Philosophy

August 2016

The dissertation of Christopher L. Harmon was reviewed and approved* by the following:

A. W. Castleman, Jr. Evan Pugh Professor of Chemistry and Physics Eberly Distinguished Chair in Science Dissertation Adviser Chair of Committee

Nicholas Winograd Evan Pugh Professor of Chemistry

Lasse Jensen Associate Professor of Chemistry

Robert M. Rioux Friedrich G. Helfferich Associate Professor of Chemical Engineering Professor of Chemistry

Kenneth S. Feldman Professor of Chemistry Graduate Program Chair

*Signatures are on file in the Graduate School.

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Abstract

The study of gas-phase cluster models has emerged as a useful tool to model catalytic active sites on surfaces. By observing how the reactivity of TMO clusters changes with cluster size, active site, and metal composition, we draw insights about the molecular factors governing reactivity and selectivity. The aim is to provide a conceptual framework to drive the development of improved catalysts with higher activity and selectivity.

As group IVB transition metal oxides (TMOs) are widely used as catalysts and supports, we have undertaken mass spectrometric reactivity studies of titanium, zirconium, and hafnium oxide clusters with small organic molecules of interest in catalysis. We particularly note the differences in reactivity observed as the identity of the

+ metal in the cluster changes. We report the reactivity of MxO2x (M = Ti, Zr) clusters that contain radical atomic oxygen, O•−, with methane, ethane, propane, ethylene, and propylene. We observe that in many cases the titanium clusters undergo a type of

“etching” reaction, where the cluster loses a TiO unit and associates the reactant gas.

Zirconium oxides strongly prefer the hydrogen atom abstraction pathway, and no evidence for an etching type of reaction is found for zirconium clusters. Next, we examine

+ the reactivity of TixO2x+1 clusters that are theoretically predicted to contain a superoxide

•− + active site, O2 , and find that the reactivity is quite different from ZrxO2x+1 . We also present one of the first studies of the reactivity of hafnium oxide clusters, and show that

+ + HfxO2x+1 acts very similarly to ZrxO2x+1 clusters, attributed to a superoxide active site.

+ However, Hf2O4 , which contains a radical oxygen atom, shows drastically different

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+ reactivity from Zr2O4 . Finally, we discuss these studies in the context of isoelectronic superatoms.

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Contents

List of Figures ...... vii List of Tables ...... x Acknowledgements ...... xi Introduction ...... 1 1.1 Catalysis ...... 1 1.2 Clusters: “Every Atom Counts” ...... 3 1.3 Clusters in Catalysis Research ...... 5 1.4 Outline of Dissertation ...... 10 Experimental Apparatus ...... 11 2.1 Overview ...... 11 2.2 Vacuum System ...... 12 2.3 Ion Creation...... 13 2.4 TQMS System: Quadrupoles, Octopoles and Ion Optics ...... 15 2.5 Ion Detection ...... 18 2.6 Data Analysis ...... 19 Differing Selectivity and Reactivity of Stoichiometric Titanium and Zirconium Oxide Cations with Small Hydrocarbons: Observation of a TiO Etching Reaction ..... 22 3.1 Introduction ...... 22 3.2 Methods ...... 24 3.2.1 Experimental Methods ...... 24 3.2.2 Computational Methods ...... 26 3.3 Results and Discussion ...... 27 3.3.1 Observation of a TiO Etching Reaction ...... 27 3.3.2 Reactions with Methane ...... 30 3.3.3 Reactions with Ethane ...... 33 3.3.4 Reactions with Propane ...... 39 3.3.5 Reactions with Ethylene ...... 43 3.3.6 Reactions with Propylene ...... 46 3.3.7 Overall Relative Rates ...... 49 3.4 Conclusion ...... 52 + Further Reactions of Titanium Oxide Clusters: Superoxide Behavior of TixO2x+1 ? ...... 54 4.1 Introduction ...... 54 4.2 Methods ...... 55 4.2.1 Experimental Methods ...... 55 4.2.2 Computational Methods ...... 55 4.3 Results and Discussion ...... 56 + 4.3.1 Calculated Structures of Ti2O2x+1 Clusters ...... 56 4.3.2 Revisiting Superoxide-Containing Zirconium Cluster Reactions: Correcting Assigned Reaction Products ...... 57 4.3.3 Titanium Superoxide Behavior ...... 60

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4.4 Conclusion ...... 66 Preliminary Studies on Hafnium Oxide Reactivity ...... 67 5.1 Introduction ...... 67 5.2 Experimental Methods ...... 69 5.3 Results and Discussion ...... 69 + 5.3.1 HfxO2x+1 Reactions ...... 69 + 5.3.2 Hf2O4 with Ethylene: Preference for the Oxidative Dehydrogenation Pathway...... 75 5.4 Conclusion ...... 78 Superatoms ...... 80 6.1 Development of the Concept of “Superatoms” ...... 80 6.2 Physical Explanations for the Phenomena ...... 84 Conclusion and Future Directions ...... 93 Appendix A. Theory of Quadrupole Operation ...... 95 A-1. The Mathieu Equations of Motion ...... 95 A-2. Applications to Quadrupole Operation ...... 102 Appendix B. Operating the Merlin Software ...... 104 B-1. How Mass Scanning Works ...... 104 B-2. Data Collection Macros for the Merlin Software ...... 105 B-1.1. Rxn ...... 106 B-1.2. Q1_scan ...... 110 B-1.3. Q3_scan ...... 113 Appendix C. Supplementary Rate Constant Plots for Stoichiometric Titanium and Zirconium Oxides ...... 117 References ...... 122

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List of Figures

Figure 1-1. Comparison of electronic structure for compounds of increasing size. From 22...... 4 Figure 2-1. Schematic of the triple-quadrupole mass spectrometer. Components not to scale...... 11 Figure 2-2. Diagram of the LaVa source...... 14 + Figure 2-3. Mass spectrum of Ti2O5 . Left: scan taken with newer equipment; right: scan taken with older, lower resolution equipment...... 17 Figure 3-1. Representative mass spectrum of cationic titanium oxide clusters...... 25 Figure 3-2. Representative mass spectrum of cationic zirconium oxide clusters...... 26 Figure 3-3. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions + of MxO2x (x=1-4) clusters with methane. A-D: titanium oxides; E-H: zirconium oxides...... 33 Figure 3-4. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions + of MxO2x (x=1-4) clusters with ethane. A-D: titanium oxides; E-H: zirconium oxides...... 37 + Figure 3-5. Potential energy surface for the reaction of Ti2O4 with ethane. Color code: yellow Ti, red O, gray C, white H...... 38 + Figure 3-6. Potential energy surface for the reaction of Zr2O4 with ethane. Color code: green Zr, red O, gray C, white H...... 39 Figure 3-7. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions + of MxO2x (x=1-4) clusters with propane. A-D: titanium oxides; E-H: zirconium oxides...... 42 + Figure 3-8. Potential energy surface for the reaction of Zr2O4 with propane. Color code: green Zr, red O, gray C, white H...... 43 Figure 3-9. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions + of MxO2x (x=1-4) clusters with ethylene. A-D: titanium oxides; E-H: zirconium oxides...... 46 Figure 3-10. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions + of MxO2x (x=1-4) clusters with propylene. A-D: titanium oxides; E-H: zirconium oxides...... 47 Figure 3-11. Representative example of the plot of ln[I]/[I]0 vs. [B]0 for the reactions + of TixO2x with ethane, where [I]/[I]0 is the percent intensity of the parent at [B]0, 3 and [B]0 is the concentration of reactant in number density form (molecules/cm )...... 49 Figure 3-12. The relative reaction rates (cm3/s) of each cluster with each hydrocarbon...... 51 Figure 3-13. C-H bond dissociation energies of methane, ethane, propane, ethylene and propylene...... 52 + Figure 4-1. Optimized structures of TixO2x+1 (x = 1-3) clusters with selected bond lengths given in Å...... 57

vii

+ Figure 4-2. Structures of TixO2x+1 (x = 1-3) clusters with positive spin density overlay. Spin density is concentrated on the superoxide unit of each cluster...... 57 + Figure 4-3. Comparison of the reaction of Zr2O5 with propylene A) using the low resolution equipment as explained in reference 28 and B) using the higher resolution equipment as described in Chapter 2...... 59 + Figure 4-4. Mass spectrum of the reaction between Zr3O7 and 0.309 mTorr propylene...... 60 + Figure 4-5. Mass spectrum of the reaction between Ti2O5 and 0.317 mTorr ethane...... 62 + Figure 4-6. Mass spectrum of the reaction between Ti3O7 and 0.317 mTorr ethane...... 62 + Figure 4-7. Mass spectrum of the reaction between Ti2O5 and 0.260 mTorr propane...... 63 + Figure 4-8. Mass spectrum of the reaction between Ti3O7 and 0.258 mTorr propane...... 64 + Figure 4-9. Mass spectrum of the reaction between Ti2O5 and 0.308 mTorr ethylene...... 65 + Figure 4-10. Mass spectrum of the reaction between Ti3O7 and 0.960 mTorr ethylene...... 65 + Figure 5-1. Mass spectrum of hafnium oxide cations HfxOy ...... 70 + Figure 5-2. Mass spectrum of the reaction of Hf2O5 with 0.420 mTorr propylene. The + major product is the 14 amu loss, similar to the reaction of Zr2O5 with propylene (see Figure 4-3)...... 71 Figure 5-3. Branching ratio (ion intensity vs. reactant gas pressure) for the reaction of + HfO3 with propylene...... 71 Figure 5-4. Branching ratio (ion intensity vs. reactant gas pressure) for the reaction of + Hf2O5 with propylene...... 72 + Figure 5-5. Rate plot for the reaction of HfO3 with propylene...... 72 + Figure 5-6. Rate plot for the reaction of Hf2O5 with propylene...... 73 Figure 5-7. Branching ratio (ion intensity vs. reactant gas pressure) for the reaction of + HfO3 with propane...... 75 + Figure 5-8. Rate plot for the reaction of HfO3 with propane...... 75 + Figure 5-9. Mass spectrum of the reaction of Hf2O4 with 0.366 mTorr C2H4...... 76 + Figure 5-10. Calculated ground state structures for M2O4 (M = Ti, Zr, Hf). From 65. 78 Figure 6-1. Electronic state comparisons between united atom pairs C with BH (left) and Si with AlH (right). Reprinted from Ref. 159...... 81 Figure 6-2. Orbital structure of compound XY2 as the X-Y bond distance r increases. At small r, the orbitals resemble the united atom; however, as r increases to the equilibrium bond distance, orbital structure begins to resemble that of the separated atoms X+2Y. Reprinted from 145...... 82 Figure 6-3. Mass spectra of the reactions of ZrO+ (upper) and Pd+ (lower) with approximately 2 mTorr propylene. The ZrO+ spectrum was obtained by this author on the higher resolution equipment, while the Pd+ spectrum was acquired by Eric Tyo with the lower resolution equipment...... 86

viii

- Figure 6-4. Mass spectrum of PdO2 with 0.398 mTorr CO. No products are observed...... 88 + Figure 6-5. Branching ratio for the reaction of PdO2 with ethylene...... 88 Figure A-1. Direction of x, y, and z axes relative to quadrupole orientation and propagation of the ion beam. Forward ion motion is in the z-axis along the long axis of the quadrupole...... 96 Figure A-2. Stability diagrams for a quadrupole mass analyzer. Regions marked with the numerals are stable in both the x and y axes. Taken from Ref. 189...... 101 Figure A-3. Close-up of the upper half of region I of the stability diagram. Taken from Ref. 189...... 103 + Figure C-1. Rate plots for the reactions of TixO2x with methane...... 117 + Figure C-2. Rate plots for the reactions of TixO2x with propane...... 118 + Figure C-3. Rate plots for the reactions of TixO2x with ethylene...... 118 + Figure C-4. Rate plots for the reactions of TixO2x with propylene...... 119 + Figure C-5. Rate plots for the reactions of ZrxO2x with methane...... 119 + Figure C-6. Rate plots for the reactions of ZrxO2x with ethane...... 120 + Figure C-7. Rate plots for the reactions of ZrxO2x with propane...... 120 + Figure C-8. Rate plots for the reactions of ZrxO2x with ethylene...... 121 + Figure C-9. Rate plots for the reactions of ZrxO2x with propylene...... 121

ix

List of Tables Table 1-1. Transition metal oxide cations with radical oxygen atom sites...... 9 + Table 3-1. Mass spectral peak shifts of observed product peaks in reactions of TixO2x (x = 2-4) with the indicated hydrocarbon...... 28 Table 3-2. Relative rates (cm3/s) for the reaction of each cluster discussed herein with each hydrocarbon...... 50 Table 5-1. Calculated dissociation energies for the loss of radical oxygen from group IVB transition metal oxides. Adapted from 65...... 30

x

Acknowledgements

This project would never have happened were it not for the support and guidance of a number of people. First, I would like to thank Prof. A. W. Castleman, Jr. for taking me into his group and giving me an opportunity to take on this research project. I am indebted to him for the experience I’ve had to grow as a scientist and researcher. Second, I thank my former coworkers, Dr. Eric Tyo and Dr. Don Gunaratne, for showing me the ropes in lab and teaching me the fundamentals of experimental physical chemistry. I’d also like to thank Dr. Jordan Smith for all his help in lab and in life; I don’t think I could have gotten through it all without Jordan. Of course, I am indebted to Connie Smith for her help on the logistics side of everything. She really doesn’t get enough praise for her work! I also thank all the other students, postdocs, staff, and collaborators I’ve had the pleasure of interacting with while at Penn State who are too numerous to name here. I would particularly like to thank my collaborators Marjan Krstic and Prof. Dr. Vlasta Bonačić-

Koutecký at the Humboldt University of Berlin as well as Dr. Cuneyt Berkdemir, former postdoc in our group, for their theoretical calculations.

On a more personal note, I am deeply grateful for the support my wife Micaela has given me the entire time I’ve known her. She has been my rock throughout this whole experience. I also am extremely grateful to my parents, Jeff and Melony, and brother,

Zach, for their moral support and encouragement. Thanks, Mom and Dad.

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Introduction

1.1 Catalysis

We live in an age where concerns regarding energy, fuels, and pollution, particularly with respect to climate change, are at an all-time high.1 These issues impact every aspect of society: economics, ecology and environment, and public health.

Consequently, finding ways to decrease energy usage, reduce the generation of pollutants, and develop environmentally-friendly energy sources is critically important.

Of the many technologies and methods that can be improved toward this end, catalysis is perhaps the field with the most wide-spread area of effect. Among the many benefits of catalysts, substances that increase the rate of a chemical reaction without being used up in the reaction, are reduced waste products due to higher selectivity (generation of desired reaction product), lower energy requirements, and reduced cost. Catalysts are so ubiquitous that they are used in an estimated 80 to 90% of industrial chemical processes, generating over a trillion dollars a year in revenue.2 They play an essential role in the production of pharmaceuticals, oil refining and the creation of oil-derived products, pollution control in automobiles, biological processes, and numerous other phenomena.

Clearly, any improvements with respect to chemical reactivity and selectivity in a field so embedded in so many different aspects of society will have far-reaching economic and environmental effects.

The potential global impact of catalysis has been recognized for decades. Even thirty years ago, the study of catalysis was identified as one of the top frontiers of chemistry, with the goal of improving air and water quality by improving selectivity.3

1

Despite the advancements that have been made since that statement, catalyst improvement still remains a challenge. Recently, improving catalyst selectivity was labelled the "frontier of surface-science research in the 21st century."2,4 Additionally, principle 9 of The US Environmental Protection Agency’s 12 principles of Green Chemistry encourages the use of catalytic reagents with high selectivity instead of stoichiometric reagents to reduce unwanted side products.5,6 A greater understanding of catalysis will lead to the design of new materials with economic and environmental benefits that surpass the materials we employ now.

Most catalysts are heterogeneous in nature and generally consist of metal nanoparticles embedded in a porous support material to reduce volume and maximize surface area (especially important for expensive metals such as Pt or Pd).7–9 These metals are usually transition metals, as they can adopt a number of different oxidation states, coordination modes, and bonding patterns due to their valence d orbitals.10 Among the many varied applications of transition metals in catalysis are iron for production of ammonia in the Haber-Bosch process and formation of liquid hydrocarbons from CO and

H2 in Fischer-Tropsch reactions, nickel for the hydrogenation of vegetable oils, vanadium oxides for production of sulfuric acid, titanium for the Ziegler-Natta polymerization of ethylene, and platinum group metals for the conversion of CO to CO2 in catalytic converters in automobiles.

In order to improve existing catalytic technology and develop new catalytic materials, a comprehensive understanding of the surface processes occurring on a molecular level is necessary. Thus attempting to model catalyst surfaces has been a topic

2

of interest since the 1960s. The first catalytic model systems were studies of chemisorption onto single crystals.11,12 This evolved into studies of clusters and nanoparticles on oxide supports to more closely mimic industrial systems that maximize surface area by using nanoparticles on porous supports.7,13 Despite the numerous studies in this field,11,12,14–18 there are still many facets about heterogeneous catalysis that remain to be understood.13 The composition of the support, for example, can have great effect on the catalyst through phenomena such as charge transfer, strong metal support interaction, and spillover.19 However, the roles of the catalyst, support and the interaction between the two are often difficult to pinpoint, and are still topics of great interest. The study of gas-phase clusters has emerged as a valuable tool to supplement bulk surface analytical methods by allowing for the facile examination of the effects of size, stoichiometry, composition, geometry, and charge state on the physical and chemical behavior of an atom or molecule.

1.2 Clusters: “Every Atom Counts”

The electronic structure of an atom consists of atomic orbitals at discrete energy levels. When two atoms bind to each other, we describe the resulting electronic structure in terms of molecular orbitals, a combination of atomic orbitals, also with discrete energy levels. As more atoms bond and share atomic orbitals, more molecular orbitals are formed, changing the electronic structure and increasing the density of these states.

Eventually there are so many molecular orbitals that their ordering becomes essentially continuous instead of consisting of a few discrete levels (see Figure 1-1). At intermediate

3

sizes, the addition or removal of just one atom, or even electron, is enough to change the physical and chemical properties of the cluster. We refer to molecules in this size regime as clusters. Here every atom counts. At such small scales a higher ratio of the atoms are surface atoms, with different bonding than interior atoms, changing the physical and chemical behavior of the cluster. Additionally, quantum confinement effects restrict the electrons in the cluster and they begin to resemble a particle in a box further altering electronic structure. This type of electronic structure is known as a band and the material is essentially a bulk material. In a bulk material, the addition or removal of one atom has little effect on the overall electronic structure, although the band structure can be disrupted at surfaces, interfaces or impurities. 20Thus, clusters lie intermediate in size between atoms and nanoparticles, bridging the properties of small molecules and bulk materials.21

Figure 1-1. Comparison of electronic structure for compounds of increasing size. From 22.

4

The term cluster as used in the field of cluster science is a little different from that used in inorganic chemistry, which defines them as “molecular compounds with metal- metal bonds that form triangular or larger cyclic structures.”23 Clusters as defined herein can consist of metals, non-metals, or a combination of the two, and can be bound covalently, ionically, or held together through Van der Waals forces.21 Clusters as used in this work are covalently bound ions, and we will focus on transition metal oxides.

One interesting facet of clusters is that some series of clusters may share a similar motif despite differing cluster size. For example, two series that will be discussed at length

+ + in this dissertation are the MxO2x and MxO2x+1 series, with M being a specific metal for each series. These have been referred to in the literature as “stoichiometric” and “non- stoichiometric,” respectively, as the latter series does not have a constant ratio of metal to cluster atoms. It has been shown that some clusters conforming to these formulas share a similar active site. For example, Castleman and coworkers demonstrated that

+ − + + different size clusters in the ZrxO2x , ZrxO2x+1 , TixO2x , and VxO2x series contain radical

+ 24– oxygen active sites, and clusters in the ZrxO2x+1 series contain a superoxide active site.

28 However, this is no guarantee of similar behavior, as in several cases reactivity has been shown to be dependent on the cluster size and geometry.

1.3 Clusters in Catalysis Research

Gas-phase cluster studies provide molecular-level insights into fundamental areas such as electronic structure and chemical reactivity by probing the effects of size, stoichiometry, composition, geometry, charge state and so on. Such information is

5

particularly useful in catalysis, where cluster experiments can be used effectively to model surface steps, edges, vacancies, and other structures frequently associated with catalytic activity.7,13,29 Gas-phase experimental methods prove advantageous in this regard, as gaseous ions are easily controlled, manipulated, and can generally be created reproducibly, a feat which can be difficult to achieve with bulk methods. Particularly, mass spectrometry is a technique used to great effect in the study of gas-phase clusters, as its ability to scan ions by mass offers a natural way to analyze clusters.30

Gas-phase cluster investigations have been shown to be quite useful for gaining insight into surface phenomena. For example, the vibrational spectrum of ethylidyne chemisorbed onto a rhodium surface has been shown to be nearly identical to the spectrum of ethylidyne attached to a three atom rhodium cluster.2 Our group has previously noted cases in which the bulk species shows comparable reactivity to the gas- phase clusters.31–34 For example, vanadium and niobium oxide cluster cations react with methanol to form formaldehyde, which is a major product formed from methanol by

+ + condensed phase vanadia surfaces. Additionally, V2O5 and V4O10 , shown to have an oxygen-centered radical active site, oxidize ethylene to produce acetaldehyde. Gas-phase cluster studies have even been used to gain insight into biochemical processes. Shaik,

Schwarz and coworkers invested the mechanism of hydroxylation of alkanes by cytochrome P-450 through gas-phase reactivity studies of FeO+, which is electronically similar to the iron-oxo species that serves as the active site on the enzyme.35–37

Understanding the details of how such reactions occur will play a significant role in the

6

future towards developing and improving catalysts, an increasingly important objective with promising energetic, economic, and industrial benefits.

One of the fascinating finds related to the changing behavior of matter at different size regimes was that nanoparticle gold was found to be highly active for the oxidation of

CO, while bulk gold is inert.38–43 This finding has led to an immense amount of research into the application of small particles as catalysts themselves instead of serving exclusively as model systems. A number of studies have demonstrated that small clusters, even single atoms, can be responsible for observed catalytic behavior, even in the presence of larger nanoparticles.38,44–53 This illustrates the potential for cluster-assembled materials with specifically tailored properties.54,55 Designing catalysts composed primarily of small clusters remains challenging, however, as methods of generating and depositing clusters onto real-world functional materials such that they retain structure and chemical reactivity remain elusive for the time being.

One of the major types of catalysts are oxides, with applications in such reactions as oxidation, hydrogenation, and dehydrogenation. Globally, more than one third of catalyst production is based on oxides, not including those used as supports, and around one quarter of the most important organic chemicals produced are made by selective oxidation processes.56 Generally, the role of oxide catalysts is providing oxygen in a useful state for reactants.29 One of the areas of focus in cluster catalysis is attempting to model this behavior on transition metals.57 Of the forms of activated oxygen on surfaces, three

•− 2− •− 58 are reactive: the superoxide radical O2 ; peroxide, O2 ; and atomic radical oxygen, O .

These species have been implicated in a number of surface reactions, such as selective

7

oxidation of alkanes,59–61 however it is often difficult to get precision information about such short-lived species on surfaces. Thus, a number of gas-phase studies have examined clusters identified to contain these types of active sites to try to understand the exact nature of their reactivity.

Atomic radical oxygen, O•−, is characterized by an elongated metal-oxygen bond, causing it to be more reactive than a typical metal-oxygen bond. This type of active site has been identified in a number of transition metal oxide clusters, as well as non-

+ + + + transition metal oxides, such as MgO , (Al2O3)n , P4O10 , and SO2 . He and coworkers have

q proposed a method for determining Δ, the degree of oxygen saturation of a cluster MxOy , to predict the existence of this active site (eq. 1-1).29,62–66

∆≡ 2푦 − 푛푥 + 푞 (1-1)

Here, n is the highest oxidation state of metal M. For unsaturated clusters, where ∆= 1, most compounds contain the oxygen-centered radical. Several examples are listed in

Table 1-1.

In many reactions, the radical oxygen has proven to be responsible for catalytic behavior such as oxidation (also referred to as oxygen atom transfer, OAT), hydrogen atom abstraction (HAA, or hydrogen atom transfer, HAT), and oxidative dehydrogenation

(ODH). Such processes are invaluable in the production of advanced chemicals. For example, the dehydrogenation of ethane to ethylene is highly important, as ethylene is used as a starting material for the production of other valuable chemicals such as ethylbenzene, styrene, ethanol, acetaldehyde, and acetic acid.67 As such, ethylene is the most produced organic chemical in the United States, followed by propylene.9

8

Compared to the radical oxygen active site, investigations on the superoxide

radical site are not as common. We have previously identified the superoxide site on

+ Zr2O2x+1 clusters and found it to be responsible for oxidation behavior of acetylene,

+ propylene, and butadiene by Zr2O5 .

Group IIIB Group IVB Group VB Group VIB Group VIIB Group VIIIB

+ + V2O5 , V4O10 , Row 3 + + + + + Sc2O3 (TiO2)n VO3 , V3O8 , MnO+ FeO + V5O13 + Row 4 + + + MoO3 Y2O3 (ZrO2)n Nb2O5 + Mo2O6 + + + Row 5 + (HfO2)n , (Ta2O5)x , + ReO3OH + La2O3 WO3 + OsO4 n = 1,2 x = 1-2 Re2O7 Table 1-1. Transition metal oxide cations with radical oxygen atom sites.

On account of the important of catalytic processes involving alkanes and alkenes,

such as HAA and ODH, we examine the reactivity of cationic group IVB transition metal

oxides containing these active sites with small hydrocarbons. Located in the same group,

Ti, Zr and Hf are isoelectronic with each other. Recently, the Castleman group has

proposed that a “correlation principle” exists where isoelectronic species have similar

electronic structures to each other. If isoelectronic species share similar electronic

structure, then we may reasonably expect them to share similar chemical properties as

well. Thus a large focus of this dissertation is comparing and contrasting the reactivity of

clusters with these different metals.

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1.4 Outline of Dissertation

This dissertation is laid out as follows. Chapter 2 describes the triple quadrupole mass spectrometer in detail and method of obtaining experimental results. Chapter 3

+ discusses the reactivity of titanium and zirconium clusters, MxO2x , with radical atomic oxygen active sites and the differences observed in the two metals. We observe that in many cases the titanium clusters undergo a type of “etching” reaction, where the cluster loses a TiO unit and associates the reactant gas. Zirconium oxides strongly prefer the hydrogen atom abstraction pathway, and no evidence for an etching type of reaction is found for zirconium clusters. Chapter 4 continues this comparison, looking at superoxide

+ clusters of Ti and Zr, MxO2x+1 . We find that DFT results show the superoxide to be present on the titanium clusters, but they demonstrate little to no oxidation, hydrogen atom abstraction, nor oxidative dehydrogenation behavior. Chapter 5 examines the behavior

+ + + of HfxO2x+1 and Hf2O4 in comparison to zirconium. We provide evidence that HfxO2x+1

+ clusters contain a superoxide radical that reacts very similarly to ZrxO2x+1 clusters. We

+ also demonstrate that the reactivity of Hf2O4 with ethylene, due to a radical oxygen

+ atom, is quite different from that of Zr2O4 . Chapter 6 discusses these studies in the context of isoelectronic superatoms.

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Experimental Apparatus

2.1 Overview

All experimental data presented in this dissertation were collected using a home- built triple quadrupole mass spectrometer (TQMS) in a quadrupole-octopole-quadrupole arrangement (QOQ). The purpose of the instrument is to examine the products of reactions of mass-selected cluster ions with reactant gases as a function of ion energy or gas pressure. Cluster ions are generated in a laser vaporization (LaVa) source and directed into the TQMS assembly where mass selection, reaction, and detection occur (see Figure

2-1). The instrument has the capability of manipulating cations or anions, depending on hardware settings. The current iteration of the instrument is similar in idea to previous versions of the instrument described elsewhere,68,69 although several components have been upgraded. Descriptions of the vacuum system, ion source, ion manipulation and optics, ion detection, and data analysis follow.

Q1 Q3 Channel Entrance Q1 Entrance Q3 Electron Skimmer Lens Q1 Exit Lens Octopole Lens Q3 Exit Lens Multiplier

Signal Out

Conversion Q1 Pre-filter Q1 Post-filter Reaction Cell Q3 Pre-filter Q3 Post-filter Lens Lens Lens Dynode Set 1 Set 2 Set 3 CEM Lens

Figure 2-1. Schematic of the triple-quadrupole mass spectrometer. Components not to scale.

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2.2 Vacuum System

The instrument is housed in three stainless steel vacuum chambers. The source region lies inside a stainless steel tee chamber, divided from the rest of the system by a 3 mm diameter skimmer. The source region is connected to the first vacuum chamber

(internal dimensions 23 cm wide × 19.5 cm long × 25.5 cm deep), which houses the first quadrupole, the octopole reaction cell, and their associated electrostatic lenses. It is connected by 8” flange to the second vacuum chamber (internal dimensions 46 cm wide

× 99 cm long × 20 cm deep), containing the second quadrupole, detector, and respective lenses. The source region is pumped by a 6” diffusion pump (Varian VHS-6), the first chamber is pumped by a 6” diffusion pump, and the second chamber is pumped by NRC

HS-10 10” and 6” diffusion pumps. Each diffusion pump is backed by a Welch Duoseal

1397 mechanical pump, roughing the pressure down to approximately 1 mTorr. Chamber pressure is measured by ion gauges (Fil-Tech G-100-P). The ultimate pressure of the system is 1 to 5 x 10-7 torr when only generating and detecting ions, but rises as high as 5 x 10-5 torr during reactions when gases are introduced into the reaction cell. Safety interlocks are set to turn off the quadrupole electronics should the pressure rise above approximately 5.5 x 10-5 torr, as pressures at that level are sufficient to cause arcing between the quad rods, damaging equipment. These interlocks were installed as part of the instrument upgrades and as a result, the limits of the reaction pressures we can safely obtain are only 0.6-0.7 mTorr, while previously we could go to up to approximately 10 mTorr.

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2.3 Ion Creation

Cluster ions are created in a standard LaVa source, which is an established method of generating thermalized cluster distributions.70 A rotating and translating metal rod is ablated with the 2nd harmonic (532 nm) of a Nd:YAG laser (Spectra-Physics, INDI-

50), while a backing gas is pulsed over the rod (see Figure 2-2). The laser and the pulse valve operate at 20 Hz, and the time delay between the two (General Valve, Series 9) is controlled via a pulse generator (Stanford Research Systems DG535). Generally, the pulse valve triggers 400-500 µs before the laser, depending on conditions in the source, such as the pressure of the backing gas tank. The optimal delay is the timing that results in the highest ion signal at the detector. The delay tends to get longer as the backing gas tank pressure decreases. The backing gas mixture consists primarily of a buffer gas and is seeded with a reactant gas to create clusters of a desired type: i.e. oxygen to make oxides, methane for carbides, etc. The buffer gas is usually an inert gas that serves to remove energy through collisions from growing molecules during cluster formation. In all experiments discussed here, the buffer gas is ultra-high purity helium and the reactant gas is ultra-high purity oxygen. The laser pulse atomizes the metal atoms on the surface of the rod and results in a plasma of metal and backing gas atoms. The plasma is confined to a small waiting room area where two- and three-body collisions occur. Cluster growth of cations, anions, and neutrals occurs as a result of three-body collisions in the plasma, whereas two-body collisions involving buffer gas remove energy. The plasma supersonically expands out a small orifice into a field-free region, further cooling the clusters. A skimmer at the end of the field-free region skims the cloud of clusters into a

13

molecular beam, which immediately enters the first set of electrostatic lenses in the

TQMS system.

Metal Rod Pulse Nozzle Expansion Nozzle Receptacle

Field-Free Backing Gas Region Cluster Supersonic Expansion

Laser Beam Path

Figure 2-2. Diagram of the LaVa source.

A conical expansion nozzle may be placed at the exit of the waiting room to enhance turbulence and encourage more varied distributions of clusters, however this usually reduces the total ion intensity significantly.71 In the experiments reported herein, no expansion nozzle is used, as titanium, zirconium, and hafnium oxide clusters are generated in sufficient quantities without it.

The ions are created at thermal energies, meaning that the ion source and octopole reaction cell and rods are kept at ground potential, and the reactant gas is at ambient temperature.72 Previous retarding potential analyses in our group have determined the ion energy to be around 1 eV.25,73–75

14

2.4 TQMS System: Quadrupoles, Octopoles and Ion Optics

The TQMS system is comprised mainly of three multipole elements in a QOQ arrangement, interspersed by electrostatic lenses that direct and focus the ion beam.

Lens voltages are controlled by a series of user-adjustable potentiometers and adjusted for maximum ion current at the mass of interest.

The operation of multipole elements as mass filters involves an RF voltage with a

DC offset applied to opposing poles, with opposite polarities applied to the alternating sets of poles. The ratio of RF to DC voltages determines which ions successfully translate the element without being ejected or striking an electrode. Ions of a certain mass to charge ratio (m/z) and energy are stable in this electric field at certain voltage ratios.

When the voltage ratio is ramped up, masses are scanned; alternatively, ions of specific mass can be selected by keeping the voltages constant (DC resolving mode). When only an RF voltage is applied with no DC voltage, the quadrupole allows all ions through (RF- only mode).

The quadrupoles are the main components that have been upgraded since the instrument has been described by Tyo et al.69 Formerly 9.5 mm (3/8”) diameter rods, the upgraded quadrupole rods (Extrel CMS) are 19 mm (¾”) in diameter and operate at 300

W and 880 KHz. The larger diameter rods increase mass resolution of the quadrupole and allow for higher ion throughput, with the downside of decreasing the available mass range of the system (from 1-4000 amu with 19 mm rods to 1-1000 amu with 9.5 mm rods).

Additionally, the larger quads come with pre- and post-filters (also known as Brubaker lenses), which are essentially shortened quadrupoles of the same rod diameter attached

15

collinearly to the entrance and exit of the main quadrupole. RF applied to the main poles leaks through the spatial gap to the filters, applying approximately 50% of the RF intensity.

These filters serve to decrease ion current loss by offsetting the defocusing fringing fields present at the ends of the quadrupoles.

The upgrade of the quadrupoles to the larger diameter rods increased the resolving power of the instrument. The old 9.5 mm rods could not resolve masses one amu apart, but the 19 mm rods allow us to do exactly that. This opens up the possibility for us to observe phenomena such as hydrogen atom abstraction (see Chapter 3). A

+ comparison of the resolution of the former and the newer equipment for a scan of Ti2O5 is given in Figure 2-3. The resolution of the two peaks is determined by the peak width definition from IUPAC76 given in eq. 2-1, where 푚 is the mass of the peak and ∆푚 is the full width at half max (FWHM). The resolution calculated for the spectra in Figure 2-3 is approximately 400 for the newer equipment (left) and 30 for the older equipment (right).

푚 푅 = (2-1) ∆푚

16

+ Figure 2-3. Mass spectrum of Ti2O5 . Left: scan taken with newer equipment; right: scan taken with older, lower

resolution equipment.

The two quadrupoles are powered by two 150-QC QMS Power Supplies, providing voltages to the rods via two copper RF lines going through a 2.75” CF flange vacuum feedthrough. The power supplies are controlled by a 5221 QMS Controller run by the

Merlin software (Extrel CMS, version 3.2). Through the Merlin software, all functionality of the quadrupoles is controlled, including defining scan modes (RF or DC resolving modes), scan mass ranges, resolution control via ΔR and ΔM, pole bias, and so on (see

Appendix A for details, particularly on mass resolution control).

The first quadrupole mass selects a cluster of interest in DC resolving mode. A reactant is introduced into the octopole ion guide and collision cell, and ionic products of a possible reaction are scanned by the second quadrupole. The octopole serves to move ions into the collision cell and then into the second quad. The octopole is operated in RF

17

mode as the eight pole arrangement is unsuitable for mass selection in DC resolving mode, yet offers RF-only ion transmission superior to that of quadrupoles. The octopole consists of 3.57 mm diameter rods that are 40.6 cm long. Surrounding the center of the octopole is the reaction cell, an enclosed cylinder 11.6 cm long with 5 cm internal diameter. A reactant gas is introduced into the cell via a ¼” Swagelok tube connection, which leads outside the chamber to a cylinder of gas. The pressure of reactant gas in the collision cell is controlled by a user-operated needle valve on this gas line. The octopole collects any ionic products of collisions between the ions and reactant gases and directs them into the remaining quad to be scanned. The pressure in the cell is measured by a

MKS baratron capacitance manometer connected via a separate ¼” fitting. The RF voltages applied to the octopole rods are applied by a home-built RF generator, the details of which can be found in elsewhere.68 Additionally, a DC float voltage can be applied equally to the rods on top of the RF voltage. The actual ion energy seen by the octopole is the kinetic energy of the ions minus this DC float voltage; thus the energy of the ions can be controlled.

Switching between cations and anions is accomplished by switching the polarity of the ion lens power supplies, the DC float voltage power supply, and the conversion dynode power supply.

2.5 Ion Detection

Ions are detected by a Detech XP-2145 channel electron multiplier (CEM) attached directly to the end of the last quadrupole. A conversion dynode with a high voltage

18

applied (±5000 V; polarity depending on whether cations or anions are detected) attracts the ion beam and emits electrons when struck. These electrons are attracted by a positive potential applied to the cone of the electron multiplier, and pulled into the CEM tube, which is covered with a material that emits secondary electrons when struck. This process occurs several times in the CEM, creating a cascade of electrons that eventually grows large enough to be detected.

Output from the detector goes through an Advanced Research Instruments Corp.

F-100T amplifier-discriminator, which amplifies the signal and cuts off anything below a user-adjustable threshold to reduce noise. The result is a TTL signal sent to the QMS controller and on to the Merlin software, where ion intensity is displayed to the end user in counts/kilocounts per second (cps/kcps) or mV. Mass scanning is performed by dwelling at each mass, taking an intensity reading, and stepping to the next mass (see

Appendix B for why this is necessary). Merlin macros for the collection of data are also found in Appendix B.

2.6 Data Analysis

Reactivity of a cluster is examined by mass selecting one isotope of a species of interest with Q1, allowing it to react with a reactant molecule in the octopole reaction cell, and scanning the ionic products with Q3. The resulting mass spectra at each pressure are then normalized, Gaussian smoothed, and baseline adjusted. Each peak area is then integrated to find the relative intensity with respect to the largest peak in the spectrum.

Plotting the relative intensities of all the peaks observed in the spectra as a function of

19

reactant gas pressure results in a branching ratio (see Section 3.3 for examples). For a reactive ion, a decrease in the intensity of the parent peak is simultaneous with the increase in the intensity of products. Identity of observed peaks is confirmed with isotope labeling experiments, usually using deuterated reactant gases.

The relative intensities of a product give us an estimate of the relative rate constant for that reaction. It is very difficult to get absolute rate constants from a multipole device, so any discussion of rates is relative to specific conditions of our experiment.77–79 Previous experiments in our lab have quantified the relative rate of a reaction (eq. 2-1) with the branching ratio data applied to a pseudofirst order approximation using eq. 2-2, which was originally used to describe the rates of reactions in flow tube reactors.73,79,80

퐴 + 퐵 → 퐶 + 퐷 (2-1)

[퐴] ln = −푘푟푒푙[퐵]0푡 (2-2) [퐴]0

Here [퐴] is the concentration of species A, [퐴]0 is the initial concentration of A, [퐵]0 is the initial concentration of B, 푘 is the rate constant, and 푡 is the reaction time. The reaction time is estimated from the velocity of the ions from the supersonic expansion as determined by the equations of Anderson and Finn (eq. 2-3), where 푀푇 is the mach number, 훾 is the specific heat capacity, 푚 is the cluster mass, 푅 is the gas constant, and

푇 the temperature. The specific heat capacity of helium is used, as it comprises the majority of the backing gas. The time is then calculated by dividing the distance traveled by the ion in the reaction cell (estimated by a trapezoidal fall-off approximation to be 12.9

20

cm)71 by the velocity. We note that this determination of the reaction time is not exact, as the motion of an ion through the octopole is not linear.

1 ⁄2 훾푅푇 푣 = 푀푇 ( ) 훾 − 1 2 푚 (1 + 2 ) 푀푇

Plotting the natural logarithm of the ratio of [퐴] to its initial concentration versus

[퐵]0 yields a line with the slope equal to −푘푟푒푙푡. We note that most interactions of metal clusters with hydrocarbons we present herein result in multiple reactions occurring simultaneously. Thus using the concentration information of a reactant A gives you a rate for all the reactions occurring instead of just one. Still, this method provides a means to compare the overall reactivity of a cluster with another.

21

Differing Selectivity and Reactivity of Stoichiometric

Titanium and Zirconium Oxide Cations with Small Hydrocarbons:

Observation of a TiO Etching Reaction

3.1 Introduction

Transition metal oxides (TMOs) see wide use in chemical processes as catalysts and supports,15 although a detailed understanding of the roles of the cluster catalyst, support material, and the interaction between the two are still a topic of debate.19,38,81–

84 Studies of gas-phase clusters have emerged as good methods to model surface active sites to address this issue and a significant amount of research has been poured in to this undertaking.7,13,29

One category of materials receiving a lot of attention in the catalysis field are

TMOs with oxygen-centered radical sites. The oxygen-centered radical, O⋅− , is characterized by an oxygen atom with unpaired spin density and a longer than usual metal-oxygen bond length, allowing it to be highly reactive in certain types of reactions.

Its behavior has been implicated in a number of catalytic surface reactions, yet active site characterization on these surfaces is often difficult. Thus studies of gas-phase clusters with oxygen-centered radicals can help elucidate the mechanisms and physical chemistry of important processes. Additionally, behavior present in clusters that is not observed in surfaces may lead to the development of cluster-assembled materials with properties tailored for specific applications.54,55,85,86

22

Recently, numerous TMO oxide clusters have been identified containing oxygen- centered radicals, including the group IVB metals Ti, Zr, and Hf, which are widely used as catalysts and supports. Clusters with this active site have been shown to be active for the oxidation of CO and alkenes, and in C-H bond activation in hydrocarbons, important processes in the creation of fine chemicals from feedstocks.24–26,29,62–65,87–94 C-H activation in particular is a challenge due to the difficulty of breaking these bond in alkanes.

Activation of alkanes by transition metal catalysts has been a hot topic in the past two decades.29,64,65,91,95–99 Particularly, methane activation has been widely studied as it is a greenhouse gas and the most inert alkane, so its conversion is both difficult to achieve and environmentally important.100 Direct conversion of methane to methanol is one of the prime goals in this area.

Only in the past few years have investigations on Group IVB radical oxygen- containing TMOs begun to elucidate hydrogen abstraction behavior from small hydrocarbons. One review from 2010 stated that there was “no example of C-H bond activation” by group IVB oxide compounds.101 About that time, reports were published that demonstrated that TMO clusters containing the oxygen-centered radical were active for hydrogen atom abstraction from such small hydrocarbons as methane and ethylene.96,102 The behavior of activated oxygen on transition metal oxides will enable the development of more refined catalysts for a variety of chemical reactions of great importance.

Here we report on mass-selected cluster studies of the reactivity of stoichiometric

+ titanium and zirconium oxide cations MxO2x with the small hydrocarbons methane,

23

ethane, propane, ethylene, and propylene. We report the observation of an “etching” reaction present only in reactions of the titanium clusters. Additionally, our studies reveal large differences in the reactivity and selectivity of these clusters, particularly in regards to hydrogen atom abstraction and the etching product. This behavior is unexpected, although not unprecedented, as previous studies have noted certain situations where the

103 reactivity of congeners differed. For example, Trunschke et al. have shown that TiO2 and ZrO2 materials have different selectivities for n-alkane aromatization, and Wu et al.

94 + + examined the differences in reactivity between V2O5 and Nb2O5 clusters.

3.2 Methods

3.2.1 Experimental Methods

Gas-phase cluster reactivity experiments are performed on a custom-built triple quadrupole mass spectrometer (TQMS) as described in Chapter 2. In short, clusters are created by laser ablation of a rotating and translating 1/8” diameter Ti or Zr rod while a backing gas consisting of approximately 10% O2 in He is pulsed over. Resultant clusters are cooled via supersonic expansion, skimmed into a beam by a skimmer, and focused into the TQMS by a series of ion optics. The first quadrupole mass selects a cluster of interest, which reacts with a reactant gas presented into the octopole reaction cell. Ionic reaction products are then scanned by the second quadrupole and detected by a channel electron multiplier, generating a mass spectrum. Branching ratios are obtained by plotting the intensities of each product versus the pressure of reactant gas. Product identifications are confirmed by reactions with deuterated species. Representative mass spectra of

24

cationic titanium and zirconium oxides are given in Figure 3-2 and Figure 3-2, respectively.

Reaction rates are calculated with the pseudofirst order approximation as described in

Section 2.6.

+ Ti2O5 + Ti3O7 + Ti4O7 Ti O + 2 3 + Ti3O5

+ Ti3O6

+ Ti4O8 Ti O + 2 4 Ti O + + 4 9 Ti2O6 + Ti5O10

+ Ti5O9 Ti O + 5 11 + TiO+ Ti6O11

+ Ti O + TiO3 6 12 + TiO2

Figure 3-1. Representative mass spectrum of cationic titanium oxide clusters.

25

+ + Zr2O5 Zr3O7

+ Zr3O6

+ Zr3O5

+ + Zr2O4 Zr4O8 Zr O + 2 3 + + Zr4O7 Zr4O9

+ Zr5O10

+ Zr5O11 + Zr5O9

Figure 3-2. Representative mass spectrum of cationic zirconium oxide clusters.

3.2.2 Computational Methods

Theoretical calculations were performed by our collaborators Marjan Krstic and

+ Vlasta Bonacic-Koutecky. The structural properties of the cationic (TiO2)x (x = 2) and

+ (ZrO2)x (x = 2) clusters and their reactivity toward C2H6 and C3H8 were studied using DFT method with the hybrid B3LYP functional.104–106 For the titanium and zirconium atoms a triple-ζ-valence-plus-polarization (TZVP) atomic basis set combined with the Stuttgart group 12-electron relativistic effective core potential (12e-RECP) was employed.107–110 For the carbon, oxygen and hydrogen atoms the TZVP basis sets were used.109 Our previous studies of the reactivity of transition metal oxides have shown that such a combination of hybrid density functionals with triple zeta quality basis sets allow reliable prediction of

26

the reaction energetics and mechanisms.24,25,27,90,111 All structures presented were fully optimized using gradient minimization techniques and stationary points were characterized as minima or transition states by calculating the frequencies. Moreover, the reaction mechanisms were determined by calculating the energy profiles based on DFT energies.

3.3 Results and Discussion

3.3.1 Observation of a TiO Etching Reaction

Interestingly, we observe a product peak in the hydrocarbon reactions with the titanium oxides that, to the best of our knowledge, has not been discussed previously. It is present to some extent in every reaction of clusters with 2 or more titanium atoms and

+ each hydrocarbon, except Ti4O8 with methane. This product peak shifts depending on the hydrocarbon reactant used, indicating that the product contains all or part of the reactant gas (see Table 3-1). Experiments using deuterated forms of these reactants confirm the presence of the hydrocarbon in the product. Subtracting the mass of the hydrocarbon from the mass of the peak results in a mass of -64. The peak shifts plus isotopically labelled results indicate that this product is the result of a 64 amu loss plus reactant gas association, in a type of etching or replacement reaction. It is unlikely that the 64 amu loss is a loss of four oxygen atoms, as the number of bonds broken in that reaction would require an exceedingly complex mechanism. Additionally, several titanium oxide reactions that show the TiO loss plus reactant gas product also show a minor TiO loss product. Other studies have shown TiO loss in collision induced dissociation

27

experiments, however our CID experiments demonstrate no TiO loss for our reaction conditions, indicating the observed peak is a reaction product, not a collisional loss.

+ + Reactions of the hydrocarbons with Tix−1O2x−1 clusters, simulating TiO loss from TixO2x , demonstrated little to no addition product (see the following sections for more discussion

+ on TixO2x reactivity). This leads us to conclude that the product is the result of a reaction, and not a collisional loss plus gas association.

Reactant Gas Peak Position Relative to Parent (amu)

CH4 -48 C2H6 -34 C3H8 -20 C2H4 -36 C3H6 -22

+ Table 3-1. Mass spectral peak shifts of observed product peaks in reactions of TixO2x (x = 2-4) with the indicated

hydrocarbon.

Therefore, we propose that this product is a neutral TiO loss plus reactant gas

+ association (eq. 3-1). No evidence for this type of product is found in reactions of TiO2 with any of the hydrocarbons. We note that etching reactions have been observed previously in cluster studies; for example, anionic aluminum oxide clusters undergo Al2O loss when exposed to molecular oxygen.112,113 We also observe this product in the

+ + reactions of superoxide-containing clusters Ti2O5 and Ti3O7 with ethane and propane

+ (see Section 4.3.3), and in reactions of Ti2O3 with ethane and propane. This suggests that the reaction mechanism does not require a radical oxygen active site (either atomic or superoxide) to proceed; therefore, it’s most likely that the reaction proceeds by attachment of a carbon atom in the gas to a metal atom in the cluster. The presence of

+ the etching product in the reactions of Ti2O3 with ethane and propane also rules out

28

losing four O atoms, as the cluster does not have four O atoms to lose. As will be discussed in the following sections, this peak is the major product in many reactions of titanium oxides with hydrocarbons.

+ + Ti푥O2푥 + C푚H푛 → Ti푥−1O2푥−1C푚H푛 + TiO (3-1)

No evidence of neutral ZrO loss plus gas addition is observed in any of the reactions of zirconium oxide cluster cations with the hydrocarbons reported herein.

Castleman and coworkers invoked two ideas to explain the differences in reactivity of V,

Nb, and Ta clusters: the difference in preference of oxidation states of the metals and differences in bond dissociation energies of the metal-radical oxygen bond.114,115 Wu et

+ + al. used the same ideas to explain differences in reactivity between V2O5 and Nb2O5 clusters with ethane.94 The same ideas may be used to explain the observation of the etching reaction with titanium clusters and not with zirconium clusters. Titanium, while usually in the +3 or +4 oxidation state, is found in the +2 oxidation state fairly commonly, while zirconium strongly prefers the +4 oxidation state. This would favor the production of TiO and hinder the production of ZrO. Additionally, calculated bond dissociation energies65 demonstrate that the Ti-radical O bond is weaker than that for Zr-O, making it more reactive (see Table 3-2). Since that bond is harder to break in zirconium oxide clusters, the hydrogen atom abstraction is preferred.

29

Cluster ∆푯ퟎ푲 (eV) + + TiOퟐ → TiO + O 3.21 + + ZrOퟐ → ZrO + O 4.28 + + HfOퟐ → HfO + O 4.12 + + TiퟐOퟒ → TiퟐOퟑ + O 3.40 + + ZrퟐOퟒ → ZrퟐOퟑ + O 4.08 + + HfퟐOퟒ → HfퟐOퟑ + O 4.15 + + TiퟑOퟔ → TiퟑOퟓ + O 3.49 + + ZrퟑOퟔ → ZrퟑOퟓ + O 4.40 + + HfퟑOퟔ → HfퟑOퟓ + O 4.64 Table 3-2. Calculated dissociation energies for the loss of radical oxygen from group IVB transition metal oxides.

Adapted from 65.

3.3.2 Reactions with Methane

Of perhaps greatest interest is the potential of a cluster to activate the C-H bonds in methane, as it is the most inert alkane and a greenhouse gas. As methane emissions from vehicles are expected to be regulated in the future, low-temperature methods of methane oxidation are sought.116 Considerable effort has been invested in looking at thermal methane activation with the prize being an efficient catalyst for the creation of methanol or formaldehyde from methane.117 The gas-phase conversion of methane to methanol by strong oxidants is overall exothermic, however activation energy barriers for the breaking of the C-H bond slow this reaction down.118 Thus, studies on the activation of C-H bonds by gas-phase transition metal catalysts may shed light on new methods to achieve this “holy grail” of chemistry.

Thermal hydrogen atom abstraction from methane by several TMO clusters,

+ + including (TiO2)x and (ZrO2)x , has already been identified and examined, however not in

30

branching ratio form.10,119 We present our results for comparison with reactions with other hydrocarbons.

+ The branching ratios for the reactions of MxO2x (M = Ti, Zr; x = 1-4) with methane are given in Figure 3-3. The top row (A-D) shows results for the titanium oxide reactions, while the bottom row (E-H) shows the results for the zirconium oxide reactions. In these reactions, up to four products are observed: three being reactions and the fourth a minor

O2 loss due to collisions (see eqs. 3-1 and 3-2). Equation 3-1, as mentioned in the previous section, is only observed in the titanium reactions.

+ + M푥O2푥 + CH4 → M푥O2푥H + ⋅CH3 (3-2)

+ + M푥O2푥 + CH4 → M푥O2푥−1 + CH3O (3-3)

+ In all of these experiments, the hydrogen atom abstraction species M푥O2푥H (eq.

3-2) is the major product, although the relative intensity at the highest methane pressures measured varies. The relative ion intensities at highest measure pressures are 4.2%,

19.3%, 15.5%, and 7.9% for clusters with one to four titanium atoms, respectively. For the counterpart zirconium clusters, the intensities at max pressures are 3.8%, 28.2%, 17.3%, and 10.0%. The clusters with the highest activity for HAA are those containing 2 or 3 metal

+ + + + atoms. The observed reactivity trend is M2O4 > M3O6 > M4O8 > MO2 .

As mentioned before, HAA has been observed previously and attributed to the radical oxygen active site.120 Although potential energy profiles have not been calculated

+ + for the TixO2x or ZrxO2x reactions with methane, the mechanism has been investigated

+ 91 + 121 + for other radical oxygen-containing species such as V4O10 , MgO , and Al8O12 .

31

+ In reactions with methane, the etching product is Tix−1O2x−1CH4 . In reactions with

+ Ti3O6 it is the second most intense product behind hydrogen atom abstraction, and only

+ a small side product in reactions with Ti2O4 with approximately the same intensity as the

+ + + oxidation product Ti2O3 . This product is not observed for the reactions of TiO2 and Ti4O8 with methane.

+ The nature of the oxygen-centered radical on MO2 clusters is slightly different than on the larger clusters, as the unpaired spin density is split evenly between both oxygen atoms, rather than being focused on one atom. This makes it relatively less reactive than the larger clusters, where the spin density is primarily concentrated on one oxygen atom, and explains the observed reactivity trend.26

A minor product (less than 3% relative ion intensity at highest pressures of

+ methane) observed in a few of the reactions is the product MxO2x−1 (eq. 3-2). Collisional experiments with He and Ar indicate this product is not collisional. This product is a result of oxidation, creating formaldehyde or methanol. Although it appears promising that a few clusters are able to demonstrate this type of reactivity, even if only in small quantities, these clusters are much more active for the formation of the HAA product. This demonstrates one of the major challenges in catalysis: finding catalysts that are selective for one desired reaction with minimal side products.17

32

+ Figure 3-3. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions of MxO2x (x=1-4) clusters with

methane. A-D: titanium oxides; E-H: zirconium oxides.

3.3.3 Reactions with Ethane

+ The reactions of MxO2x (M = Ti, Zr; x = 1-4) with ethane, C2H6, are given in Figure

3-4. Again, the top row (A-D) shows results for the titanium oxide reactions, while the bottom row (E-H) shows the results for the zirconium oxide reactions. There are five reaction products observed; four products correspond to the reactions listed in eq. 3-4 to

+ 3-7, with the fifth being O2 loss. We note that Ti4O8 with ethane actually results in a significant amount of O2 loss, up to 18% of the total ion intensity at highest measured pressures of reactant (see Figure 3-4D).

33

+ + M푥O2푥 + C2H6 → M푥O2푥H + ⋅C2H5 (3-4)

+ + M푥O2푥 + C2H6 → M푥O2푥H2 + C2H4 (3-5)

+ + Ti푥O2푥 + C2H6 → Ti푥−1O2푥−1C2H6 (3-6)

+ + Ti푥O2푥 + C2H6 → Ti푥−1O2푥−1 (3-7)

+ + Only the reaction of TiO2 with ethane showed any trace of the oxidation product TiO (A) so it will not be discussed.

In all the zirconium oxide reactions, hydrogen atom abstraction is the major product (eq. 3-4), with only very minor quantities of other products (less than 2% relative intensity at highest pressures measured), just as in the methane reactions. However, the zirconium series is much more reactive to ethane than methane. The intensities of the

HAA products at highest reaction gas pressures are 17%, 72%, 58%, and 41% for clusters with one to four zirconium atoms, respectively. The reactivity trend is the same as the

+ + + + methane reactions, that is, Zr2O4 > Zr3O6 > Zr4O8 > ZrO2 , although the intensities for

+ ZrxO2xH from ethane are much higher. We attribute this to the lower C-H bond strength in ethane and the fact that the radical oxygen in clusters of 2 or more metal atoms has the spin density concentrated on one oxygen, leading to it being more reactive.

In contrast, the titanium oxides show a different reactivity pattern. The hydrogen

+ atom abstraction product is the major product only for TiO2 , about equal to the TiO

+ loss/CH4 association in Ti2O4 , the second product behind hydrogen atom abstraction in

+ + Ti3O6 , and the third most intense product with Ti4O8 (intensities of 25%, 30%, 24%, and

+ 8%, respectively). The major product in the larger TixO2x reactions is the etching product

34

+ Tix−1O2x−1C2H6 with intensities of 40%, 39% and 24% for clusters with two to four titanium atoms, respectively.

We also observe a small (less than 5% relative ion intensity) oxidative

+ + + + dehydrogenation (ODH) peak, MxO2xH2 , in the TiO2 and M2O4 and TiO2 reactions (eq.

3-5). ODH is of particular interest, as it is actively being researched as a potential replacement for present methods of alkene production.52,122–127 In reactions with ethane, the ODH product is ethylene, C2H4. This product appears in reactions with other hydrocarbons at larger intensities (see the following sections).

To gain more insight into the mechanisms involved in the observed reactions, computations were performed by the Bonacic-Koutecky group. The calculated reaction

+ + profiles for the reactions of Ti2O4 and Zr2O4 with ethane resulting in hydrogen atom abstraction are given in Figure 3-5 and Figure 3-6, respectively. Both proceed in a similar manner; the major difference being the energies of the first intermediate and transition state. Initially, ethane binds through both carbon atoms to the metal atom attached to the radical oxygen, leading to an intermediate 0.96/0.73 eV (Ti/Zr) lower than the reactants. Then the radical oxygen binds to a hydrogen atom and the metal-carbon bonds break, leading to a transition state 0.30/0.32 eV higher than the intermediate. A second intermediate is formed as the hydrogen is pulled off the hydrocarbon at 1.48/1.41 eV lower than the reactants. The final products are 1.09/1.12 eV lower than the starting species. Our findings agree mechanistically with the calculated potential energy profile of

+ 96 Wu et al. for the reaction of Zr2O4 with C2H4. For more discussion on the reactions of zirconium and titanium oxides with ethylene, see Section 3.3.5.

35

We note that hydrogen abstraction from ethane and butane has been observed

− − 97 by the radical oxygen-containing anionic counterparts Zr2O5 and Zr3O7 . The lowest

− energy reaction pathway calculated for the reaction of Zr2O5 with ethane does not

+ involve metal-carbon bonds as we have shown with Zr2O4 ; instead the first intermediate is a direct attachment of the ethane to the radical oxygen through a hydrogen. This is

− + attributed to the molecular electrostatic potential difference between Zr2O5 and Zr2O4 ; the charge around the cation is mostly positive, as expected, while the charge around the anion is mostly negative except for a single region of slightly positive charge on the zirconium atom not directly bound to the radical oxygen.25 This prevents nucleophilic hydrocarbons from binding to the anion via the titanium with the radical oxygen, so the interaction between the radical oxygen and hydrogen cannot be facilitated easily and must proceed by a hydrogen attaching directly to the radical oxygen. Breaking the carbon- hydrogen bond in this manner requires overcoming a large energy barrier 0.06 eV above the energy of starting molecules.

36

+ Figure 3-4. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions of MxO2x (x=1-4) clusters with

ethane. A-D: titanium oxides; E-H: zirconium oxides.

37

+ Figure 3-5. Potential energy surface for the reaction of Ti2O4 with ethane. Color code: yellow Ti, red O, gray C,

white H.

38

+ Figure 3-6. Potential energy surface for the reaction of Zr2O4 with ethane. Color code: green Zr, red O, gray C,

white H.

3.3.4 Reactions with Propane

+ The reactions of MxO2x (M = Ti, Zr; x = 1-4) with propane, C3H8, are given in Figure

3-7 with the top row (A-D) showing results for the titanium oxide reactions and the bottom row (E-H) showing the results for the zirconium oxide reactions. The five products observed are similar to those observed in reactions with ethane; four products correspond to the reactions listed in eqs. 3-8 to 3-11, with the fifth being O2 loss. As with

+ + ethane, only larger clusters (in this case Ti3O6 and Ti4O8 in Figure 3-7 C and D) show significant amount of O2 loss. When observed in reactions with other clusters, the O2 loss product is minor at only a few percent of the total ion intensity.

+ + M푥O2푥 + C3H8 → M푥O2푥H + ⋅C3H7 (3-8)

39

+ + M푥O2푥 + C3H8 → M푥O2푥H2 + C3H6 (3-9)

+ + Ti푥O2푥 + C3H8 → Ti푥−1O2푥−1C3H8 (3-10)

+ + Ti푥O2푥 + C3H8 → Ti푥−1O2푥−1 (3-11)

+ High intensities of the MxO2xH product demonstrate that the stoichiometric zirconium oxide clusters are highly active for hydrogen atom abstraction from propane, as with ethane (eq. 3-8). The intensities for the HAA product are 27%, 81%, 61%, and 55% for clusters with one to four zirconium atoms, respectively, continuing the reactivity trend

+ + + + of Zr2O4 > Zr3O6 > Zr4O8 > ZrO2 . Only small amounts of other products are found in a

+ few of the zirconium reactions; namely the ODH product Zr2O4H2 in Figure 3-7F.

+ The calculated reaction profile for Zr2O4 with propane is given in Figure 3-8. It is

+ similar both qualitatively and quantitatively to the HAA of Zr2O4 with ethane (see Figure

3-6). Although we might expect the abstracted hydrogen to come from the middle carbon in propane due to the lower C-H bond energy of this type of hydrogen (410.5 vs. 420.5 kJ/mol for ethane and the middle bond in propane, respectively; see Figure 3-13) and the increased stability of a carbon radical due to two substituted ligands, the calculations demonstrates that a terminal hydrogen is pulled off instead, resulting in a terminal radical. This is because the initial favored interaction between the oxide cluster and the organic is a bond connecting the middle carbon to the metal attached to the radical oxygen. This leaves only a terminal hydrogen available for the radical oxygen to grab.

Comparison of the C-H bond energies in ethane and terminal atoms in propane are quite close (420.5 vs. 422.2 kJ/mol), explaining the similarities found in the potential energy profiles between the two reactions.

40

Hydrogen atom abstraction is also observed for the titanium series, albeit at significantly lower activity than the zirconium series demonstrates, with intensities of

21%, 5%, 14%, and 16% for clusters of one to four titanium atoms. For the larger titanium

+ clusters (x = 2-4), the HAA product is secondary to the etching product Tix−1O2x−1C3H8 , which is present at 44%, 31%, and 23% at highest pressures measured for propane.

Interestingly, the relationship between the HAA product and the etching product for these larger clusters is opposite the trend observed for reactions with ethane; that is, the

+ relative difference in intensities between the two products is largest for Ti2O4 , where

+ there is almost no HAA product observed, and approximately equal for Ti4O8 .

+ + Another minor product observed is a TiO loss for Ti3O6 and Ti4O8 (eq. 13, see

Figure 3-7 C and D). Presence of this product supports the assignment of the peak 30 amu

+ below the parent as the etching product Tix−1O2x−1C3H8 , as it may be an intermediate or the result of the etching product undergoing collisional loss of C3H8. Additionally, the

+ + secondary product in the TiO2 reaction is the ODH species TiO2H2 at approximately 10% of the total ion intensity, half the intensity of the HAA product (Figure 3-7A).

41

+ Figure 3-7. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions of MxO2x (x=1-4) clusters with

propane. A-D: titanium oxides; E-H: zirconium oxides.

42

+ Figure 3-8. Potential energy surface for the reaction of Zr2O4 with propane. Color code: green Zr, red O, gray C,

white H.

3.3.5 Reactions with Ethylene

+ The reactions of MxO2x (M = Ti, Zr; x = 1-4) with ethylene, C2H4, are given in Figure

3-9 with the top row (A-D) showing results for the titanium oxide reactions and the

+ bottom row (E-G) showing the results for the zirconium oxide reactions. Zr4O8 with ethylene is not presented, as the mass spectrum of the reaction is so littered with products at similar low intensities (at least 14 resolved peaks) that little conclusions can be drawn except by noting the differences from smaller zirconium clusters. For the other clusters, six different products are observed, corresponding to the reactions in eq. 3-12 to 3-14. Again, O2 loss is observed in several reactions but it is a collisional product and not discussed further.

43

+ + M푥O2푥 + C2H4 → M푥O2푥−1 + C2H4O (3-12)

+ + M푥O2푥 + C2H4 → M푥O2푥H + ⋅C2H3 (3-13)

+ + M푥O2푥 + C2H4 → M푥O2푥H2 + C2H2 (3-14)

+ + Ti푥O2푥 + C2H4 → Ti푥−1O2푥−1C2H4 (3-15)

+ + Zr푥O2푥 + C2H4 → Zr푥O2푥C2H3 (3-16)

+ Present in all of the product spectra is the oxidation product MxO2x−1 (eq. 3-12).

Oxidation behavior of stoichiometric titanium26 and zirconium24 oxide cations has already been examined at length by other authors and will not be addressed here except in relation to other reaction products.

The hydrogen atom abstraction product (eq. 3-13) is again the major product for the zirconium series reactions. HAA behavior from ethylene by stoichiometric zirconium oxide clusters has been observed previously, however not via mass-selected reactivity

96 + experiments. The relative ion intensities for Zr2O2xH (x = 1-3) at highest measured pressures of ethylene are 12%, 38%, and 24%, respectively. The same reactivity trend for

+ + + HAA found for reactions with hydrocarbons applies here: Zr2O4 > Zr3O6 > ZrO2 .

+ + While Zr2O2xH is almost exclusively the product in reactions of ZrxO2x−1 with saturated hydrocarbons, in reactions with ethylene a number of other products in

+ + significant quantities are found. For ZrO2 and Zr2O4 , the oxidation product is secondary to the HAA product at 6% and 23% relative ion intensity, respectively. It is a minor product

+ + at 3% relative ion intensity for Zr3O6 . Another minor product observed is ZrxO2xC2H3 (eq.

18; see Figure 3-9 F, G). This is the result of association of the radical hydrocarbon product from HAA to the metal cluster, providing additional evidence of HAA behavior.

44

+ Also observed is the ODH product MxO2xH2 peak (eq. 3-14). This product is

+ + present in significant quantities in the reactions of Zr2O4 (13%) and Zr3O6 (15%), yet only

+ present in very small amounts in the reaction of Ti2O4 and absent in the other Ti cluster reactions.

The titanium series shows almost completely different behavior to the zirconium

+ + series. The oxidation product is TixO2x-1 is the major product in the reaction with TiO2 , but present in only very small quantities in reactions with larger clusters. Instead, the

+ etching product Tix−1O2x−1C2H4 (eq. 17) dominates at larger sizes with x=2-4 relative ion intensities of 21%, 49%, and 25%, respectively. Minor products for these reactions include

+ oxidation, as mentioned previously, and O2 loss. The preferences for oxidation by TiO2

+ and HAA by ZrO2 may be explained by the dissociation energy of losing an oxygen atom

65 + + as calculated by Zhao et al. This dissociation energy for TiO2 is 3.21 eV, while for ZrO2

+ it is 4.28 eV, indicating that the bond is easier to break in TiO2 .

The difference in reactivity between the titanium series and the zirconium series is striking. Whereas reactions with the zirconium clusters demonstrate primarily HAA related products with some oxidation, reactions with titanium clusters demonstrate almost no HAA.

45

+ Figure 3-9. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions of MxO2x (x=1-4) clusters with

ethylene. A-D: titanium oxides; E-H: zirconium oxides.

3.3.6 Reactions with Propylene

+ The reactions of MxO2x (M = Ti, Zr; x = 1-4) with propylene, C3H6, are given in

Figure 3-9 with the top row (A-D) showing results for the titanium oxide reactions and the bottom row (E-G) showing the results for the zirconium oxide reactions. As with ethylene,

+ the Zr4O8 reaction with propylene is not presented as the signal to noise ratio was quite low when it was performed so no conclusions could be drawn. A number of different

46

products corresponding to the reactions given in eq. 3-17 to 3-22 are observed. Again, O2 loss is observed in several reactions but it is a collisional product.

+ + M푥O2푥 + C3H6 → M푥O2푥−1 + C3H6O (3-17)

+ + M푥O2푥 + C3H6 → M푥O2푥H + ⋅C3H5 (3-18)

+ + M푥O2푥 + C3H6 → M푥O2푥H2 + C3H4 (3-19)

+ + Ti푥O2푥 + C3H6 → Ti푥−1O2푥−1C3H6 (3-20)

+ + Zr푥O2푥 + C3H6 → Zr푥O2푥C2H3 (3-21)

+ + Zr푥O2푥 + C3H6 → Zr푥O2푥C3H5 (3-22)

+ Figure 3-10. Branching ratios (ion intensity vs. reactant gas pressure) for the reactions of MxO2x (x=1-4) clusters

with propylene. A-D: titanium oxides; E-H: zirconium oxides. 47

HAA (eq. 3-18) is again the major product in reactions with the zirconium series

(28%, 71%, 45%, and 19%), with minor products making up only a few percent of the total

+ ion intensity. The minor products include the oxidation product ZrxO2x−1 (eq. 3-17), the

+ ODH product ZrxO2xH2 (eq. 3-19), the association of the radical hydrocarbon product of

+ + HAA ZrxO2xC3H5 (eq. 3-22), and even evidence of C-C bond breaking with ZrxO2xC2H3 (eq.

3-21). The intensities of the HAA product and the strong preference for it over other products are features more similar to the zirconium reactions with propane than ethylene. This suggests that association of the hydrocarbon to the zirconium atoms to initiate the reaction occurs through the binding of the sp3 carbons rather than the sp2 carbons.

Interestingly, the major product in the reactions of the titanium series with propylene is not the etching product, as it is with the larger clusters of ethane, propane and ethylene. Rather, HAA is predominant at relative ion intensities of 24%, 36%, 30%,

+ and 31% for clusters of one to four titanium atoms, respectively. For TiO2 , the oxidation product is present in approximately the same yield as the HAA product, and is secondary to HAA for the larger clusters with x = 2-4 relative ion intensities of 28%, 12%, and 14%.

+ The etching product Tix−1O2x−1C3H6 (eq. 3-20) is present in only fairly small quantities, with

+ + + relative ion intensities in reactions with Ti2O4 , Ti3O6 , and Ti4O8 of 5%, 12%, and 3%,

+ respectively. Also present is the ODH product TixO2xH2 (eq. 3-19) in similar quantities as

+ + the etching product. That the TixO2x clusters oxidize propylene more than ZrxO2x do is again correlated to the dissociation energies of these clusters losing atomic oxygen as calculated by Zhao et al.65

48

3.3.7 Overall Relative Rates

Relative rates were calculated for the reaction of each cluster with each hydrocarbons as described in Section 2.6. We note that in many cases several reactions are occurring at once, and because the parent intensity is used for the rate determination, the relative rates discussed here are rates of all the reactions each cluster undergoes with a specific reactant. However, examining these rates still gives us insight into the patterns of reactivity in the clusters. An example of the natural log plots for the rate determination are given in Figure 3-11, all others are shown in Appendix C. The slopes of these plots are then divided by −푡 to find 푘푟푒푙.

+ Figure 3-11. Representative example of the plot of ln[I]/[I]0 vs. [B]0 for the reactions of TixO2x with ethane, where [I]/[I]0 is the percent intensity of the parent at [B]0, and [B]0 is the concentration of reactant in number density form (molecules/cm3).

The calculated relative rates for the reactions of each cluster with each hydrocarbon are given in Table 3-3. This data is visualized in Figure 3-12. The rate of reaction of each cluster

49

with methane is drastically lower than the rates of each cluster with larger hydrocarbons.

This is expected, as methane has the strongest C-H bonds. Reactivity tends to increase with larger cluster size, as propane and propylene tend to have the highest rates of reaction. This again correlates to C-H bond strength, as propane and propylene have the weakest C-H bonds of the reported alkanes and alkenes, respectively (see Figure 3-13).

+ As for differences in clusters, Zr2O4 has the highest overall reactivity with the hydrocarbons, being much higher than the other Zr clusters. Ti clusters, however, are

+ much closer to each other, with Ti3O6 having the highest rates out of the four. Some

+ differences in selectivity are apparent. For example, the rate of reaction for Ti3O6 with

+ ethylene is twice that of Ti2O4 with ethylene. However, care needs to be taken when comparing rates of a cluster with multiple hydrocarbons. For example, the reaction rate

+ for Ti2O4 with propylene is twice its rate with ethylene, but the reactions occurring with each alkene are very different. The ethylene reaction primarily results in the etching product, while the propylene reaction primarily results in hydrogen atom abstraction and oxidation.

+ + + + + + + + TiO2 Ti2O4 Ti3O6 Ti4O8 ZrO2 Zr2O4 Zr3O6 Zr4O8

Methane 7.8E-14 3.6E-13 4.1E-13 9.9E-14 6.1E-14 3.9E-13 1.7E-13 7.3E-14 Ethane 7.8E-13 1.3E-12 1.3E-12 8.8E-13 2.9E-13 1.6E-12 5.4E-13 3.2E-13 Propane 1.0E-12 1.2E-12 1.4E-12 6.7E-13 4.8E-13 2.0E-12 7.9E-13 5.8E-13 Ethylene 1.1E-12 6.4E-13 1.2E-12 8.1E-13 2.6E-13 1.6E-12 7.2E-13 Propylene 1.2E-12 1.5E-12 1.8E-12 1.1E-12 5.7E-13 1.9E-12 1.1E-12 Table 3-3. Relative rates (cm3/s) for the reaction of each cluster discussed herein with each hydrocarbon.

50

+ Relative Rates for the Reactions of MxO2x with Small Hydrocarbons 2E-12

2E-12

2E-12

1E-12

1E-12

3 1E-12 krel (cm /s) 8E-13

6E-13

4E-13

2E-13

1E-14 TiO2+ Ti2O4+ Ti3O6+ Ti4O8+ ZrO2+ Zr2O4+ Zr3O6+ Zr4O8+ Cluster

Methane Ethane Propane Ethylene Propylene

Figure 3-12. The relative reaction rates (cm3/s) of each cluster with each hydrocarbon.

51

C-H Bond Dissociation Energies in Small Alkanes and Alkenes 500

480 464.2 464.8 460 439.35 440 420.5 422.2 420 410.5

400

(kJ/mol) 0

H 380 369 Δ 360 340 320 300 Middle Terminal sp2 sp3 Methane Ethane Propane Ethylene Propylene Alkanes Alkenes

Figure 3-13. C-H bond dissociation energies of methane, ethane, propane, ethylene and propylene.

3.4 Conclusion

Our results demonstrate that the stoichiometric oxide clusters of congeners Ti and

Zr demonstrate surprisingly different reactivity towards the small hydrocarbons methane,

+ ethane, propane, ethylene, and propylene. ZrxO2x clusters show a strong preference for

+ hydrogen atom abstraction in all cases while the reactivity of TixO2x clusters is more nuanced, the reactivity and selectivity depending on both the size of the cluster and the

+ reactant gas. A prominent product in the reactions of TixO2x clusters with multiple metal

+ atoms is the etching product Tix-1O2x-1R where R is the reactant gas. We do not attribute

+ this behavior to the radical oxygen site, as reactions with Ti2O5+ and Ti2O3 also

52

demonstrate this behavior. If this behavior can be translated to surfaces or bulk materials, it may be a way of generating TiO, or trapping hydrocarbons for further reactions. Beware of poisoning the material with hydrocarbons. Additionally, these results may be used as a guide to understand the design of cluster-assembled materials for selective reactions with desired reactants.

53

Further Reactions of Titanium Oxide Clusters: Superoxide

+ Behavior of TixO2x+1 ?

4.1 Introduction

The first step in reoxidation of a metal oxide catalyst by molecular oxygen is thought to produce a bound radical O2 unit by electron transfer from a reduced metal site.58,66,128 This type of oxygen species has an elongated O-O bond at 1.33 Å and is known as a superoxide, which can then participate in chemical reactions.129,130 For example, it has been shown to enhance the reactivity of gold cluster anions producing CO2 from

CO.131 In attempts to model the activation of oxygen on metal species, superoxides have been identified and characterized in a number of gas-phase clusters, including

132 − − 53,128 − 66 + 71,133 − monomagnesium oxides, W2O8 and W3O11 , La3O7 , VxO2x+2 , and HfOx (x

= 4-6).134

However, comparatively few studies have examined the reactivity of clusters containing isolated superoxide units. Among the first reports to do so was our recent

+ demonstration that the zirconium oxide series ZrxO2x+1 contains a superoxide unit. The

+ behavior of this superoxide depends on the size of the cluster; Zr2O5 oxidizes acetylene,

+ + propylene, and butadiene, while ZrO3 only oxidizes butadiene and Zr3O7 primarily

+ associates the reactants. Studies in our lab have demonstrated that both TixO2x and

+ ZrxO2x cluster series contain radical oxygen atoms responsible for reactivity with small organic molecules,24,26 although the reactivity can vary greatly (see Chapter 3). Therefore,

+ we have undertaken reactions of TixO2x+1 clusters with small hydrocarbons to ascertain

54

whether the same superoxide is present on these clusters, and if so, if there are possible

+ differences from ZrxO2x+1 in terms of reactivity. In doing so, we have revisited reactions

+ + of Zr2O5 and Zr3O7 with propylene with equipment capable of higher mass resolution and updated our findings accordingly.

4.2 Methods

4.2.1 Experimental Methods

Gas-phase cluster reactivity experiments are performed on a custom-built triple quadrupole mass spectrometer (TQMS) as described in Chapter 2. In short, clusters are created by laser ablation of a rotating and translating 1/8” diameter Ti (Alfa Aesar) or Zr rod while a backing gas consisting of approximately 10% O2 in He is pulsed over. Resultant clusters are cooled via supersonic expansion, skimmed into a beam by a skimmer, and focused into the TQMS by a series of ion optics. The first quadrupole mass selects a cluster of interest, which reacts with a reactant gas presented into the octopole reaction cell.

Ionic reaction products are then scanned by the second quadrupole and detected by a channel electron multiplier, generating a mass spectrum. Branching ratios were not obtained. Product identifications are confirmed by reactions with deuterated species. As

+ very low intensities of TiO3 are produced, no reactions with this cluster were performed.

4.2.2 Computational Methods

Calculations presented in this chapter were performed by Dr. Cuneyt Berkdemir.

Calculations were performed using the GAUSSIAN 09 program package. The singlet, triplet and quintet spin multiplicity states of neutral TixOy (x=1,2 and y=1-5) and the doublet,

55

quartet and sextet spin multiplicity states of anion and cation TixOy clusters were treated using density functional theory (DFT) calculation as implemented in GAUSSIAN 09.

Different initial structures were considered and the ground state structures of clusters were assigned as final optimized geometries that were obtained from the lowest-energy spin multiplicity states. Becke’s three-parameter hybrid functional was employed by incorporating the correlation functional of Lee, Yang, and Parr (B3LYP). In many computational problems related to DFT calculations, the B3LYP method has been shown to be remarkably accurate and is considered the best compromise between speed and efficiency for relatively large systems. Moreover, the use of B3LYP method has been found well-suited to deal with oxygen bonded systems. The 6-311++G(3d,3p) basis set was selected for Ti and O atoms. The zero-point vibrational energy corrections were included in the total energy results of clusters.

4.3 Results and Discussion

+ 4.3.1 Calculated Structures of Ti2O2x+1 Clusters

+ The DFT calculated structures of TixO2x+1 (x = 1-3) clusters are displayed in Figure

4-1, with the spin densities shown in Figure 4-2. The optimized structures show the presence of an O2 radical unit with approximate O-O bond length of 1.3 Å on each cluster.

•− Most of the spin density in each cluster resides on this O2 unit. These structures are indicative a superoxide active site. These structures are quite similar to those calculated

+ 28 for ZrxO2x+1 (x = 1-3) clusters.

56

1.585

1.314 1.951 1.562 1.300 1.962 2.021 1.581 1.983 1.992 1.316

+ Figure 4-1. Optimized structures of TixO2x+1 (x = 1-3) clusters with selected bond lengths given in Å.

+ + + TiO3 Ti2O5 Ti3O7

+ Figure 4-2. Structures of TixO2x+1 (x = 1-3) clusters with positive spin density overlay. Spin density is concentrated

on the superoxide unit of each cluster.

4.3.2 Revisiting Superoxide-Containing Zirconium Cluster Reactions: Correcting Assigned

Reaction Products

+ As part of our investigations into TixOy reactivity, we repeated certain reactions

+ + of Zr2O5 and Zr3O7 for comparison purposes, as the equipment we used for previous

+ 28 investigations of superoxide units on ZrxO2x+1 clusters did not have mass unit resolution.

The low resolution equipment had no ability to select one isotope of a cluster due to the limitations of the quadrupoles used, so each peak present in the resulting mass spectrum could stretch to almost 10 amu wide. This made it impossible to discern different reaction

57

products within a few amu of each other, and in some cases, caused the incorrect identification of product identities. A comparison of the mass spectra obtained via the

+ previous and current equipment is given in Figure 4-3 for the reaction of Zr2O5 with propylene. Using the low resolution equipment, we had previously identified the major

+ product in the Zr2O5 with propylene reaction as the oxidation product propanal, C3H6O

(eq. 4-1). However, the new results demonstrate the large peak attributed to the O loss is actually comprised of multiple products at 14 and 15 amu below the parent, with a small peak at 13 amu below the parent. Wu et al. also found a 14 amu loss product in the

+ + reaction of V2O5 with ethane and identified it as V2O5H2 , concluding the neutral product

94 to be acetaldehyde, C2H4O. Additionally, Wang et al. calculated the formation of acrolein (propenal) from the reaction of VO3 with propylene to be the most thermodynamically favorable product of the seven possible products they examined.135

Labeling experiments confirm the product peak to contain two hydrogens; therefore we propose that the major product is actually acrolein, C3H4O (eq. 4-2). This is an interesting difference, as acrolein is an important intermediate in industrial processes, and is formed by oxidation of propylene over supported vanadium oxide surfaces.135–137

The 15 amu loss product was found to have one hydrogen atom, so we conclude

+ the product to be oxygen loss plus hydrogen atom transfer, Zr2O4H (eq. 4-3). Also present are a small hydrogen atom abstraction product (eq. 4-4) and addition of C-C cracking products (eq. 4-5, 4-6).

58

+ Zr2O5

+ Zr2O4

+ Zr2O5

+ Zr2O4H2

+ Zr2O4H + + + Zr2O5H2 Zr2O5C Zr2O5C3H6

+ Figure 4-3. Comparison of the reaction of Zr2O5 with propylene A) using the low resolution equipment as explained

in reference 28 and B) using the higher resolution equipment as described in Chapter 2.

+ + Zr2O5 + C3H6 → Zr2O4 + C3H6O (4-1)

+ + Zr2O5 + C3H6 → Zr2O4H2 + C3H4O (4-2)

+ + Zr2O5 + C3H6 → Zr2O4H + C3H5O (4-3)

+ + Zr2O5 + C3H6 → Zr2O5H + ⋅C3H5 (4-4)

+ + Zr2O5 + C3H6 → Zr2O5C + C2H6 (4-5)

+ + Zr2O5 + C3H6 → Zr2O5C2H3 + CH3 (4-6)

+ The reaction of Zr3O7 and propylene is given in Figure 4-4. Again, the product peak that was formerly labeled by Tyo et al. as an O loss (16 amu loss) is found at 14 amu below

+ the parent, and we also identify it as Zr3O6H2 . However, this product is not the major

+ product observed in the reaction; instead we see more intense peaks of Zr3O7H (HAA),

59

+ and Zr3O7C3H6 (propylene association). As explained in the previous study, while overall the reaction is exothermic, the barrier for OAT in this reaction is 0.36 eV higher than the

+ starting materials, while for Zr2O5 it is lower in energy than the starting materials. This

+ deters production of Zr3O6H2 .

+ Zr3O7

+ + Zr3O7H Zr3O6C3H6

+ Zr3O6H2

+ Figure 4-4. Mass spectrum of the reaction between Zr3O7 and 0.309 mTorr propylene.

4.3.3 Titanium Superoxide Behavior

+ + We reacted Ti2O5 and Ti3O7 with ethane, propane, ethylene, propylene, acetylene, and carbon monoxide. Branching ratios were not obtained, only product mass spectra. Both clusters were found to be unreactive with propylene, acetylene, and CO and only slightly reactive with ethane, propane, and ethylene. Overall, the reactivity of the superoxide-containing clusters is less than that of the clusters with oxygen-centered radical.

60

+ + The product mass spectra of the reactions between Ti2O5 and Ti3O7 with ethane are given in Figure 4-5 and Figure 4-6, respectively. While several products are observed, no product is more than 2% of the total ion intensity. The observed products include the

+ + etching product Tix-1O2x-1C2H6 (eq. 4-1), the HAA product TixO2xH (eq. 4-3), the

+ association of ethane product TixO2xC2H6 (eq. 4-4), and collisional O2 loss. Presence of the etching product in these product spectra indicate that this reaction is not unique to

+ species with the atomic radical oxygen active site. Interestingly, in the reaction of Ti2O5

+ with ethane, we also observe a peak consistent with TiO3 loss plus gas addition, TiO2C2H6

(eq. 4-2). Investigating further to observe which species could undergo the etching

+ + reaction, reactions of Ti2O3 with ethane and propane show this product, while Ti2O3 with ethylene and propylene do not. Therefore, this reaction mechanism is not dependent on an oxidative active site. Again, no evidence for this type of reaction is observed in the

+ ZrxO2x+1 reactions.

61

+ Ti2O5

+ Ti2O3

+ + TiO4C2H6 + TiO2C2H6 + Ti2O5C2H6 Ti2O5H

+ Figure 4-5. Mass spectrum of the reaction between Ti2O5 and 0.317 mTorr ethane.

+ Ti3O7

+ Ti3O5

+ + Ti2O6C2H6 + Ti O C H Ti3O7H 3 7 2 6

+ Figure 4-6. Mass spectrum of the reaction between Ti3O7 and 0.317 mTorr ethane.

62

+ + Ti푥O2푥+1 + C2H6 → Ti푥−1O2푥C2H6 + TiO (4-1)

+ + Ti푥O2푥+1 + C2H6 → Ti푥−1O2푥−2C2H6 + TiO3 (4-2)

+ + Ti푥O2푥+1 + C2H6 → Ti푥O2푥+1H + ⋅C2H5 (4-3)

+ + Ti푥O2푥+1 + C2H6 → Ti푥O2푥+1C2H6 (4-4)

+ + The product mass spectra for the reactions between Ti2O5 and Ti3O7 with propane are given in Figure 4-7 and Figure 4-8, respectively. The major product for the

+ + Ti2O5 reaction is the TiO3 etching product TiO2C3H8 (eq. 4-5). Also present is some

+ collisional O2 loss, and small amounts of the TiO etching product TiO3C3H8 (eq. 4-6), HAA

+ + product Ti2O5H (eq. 4-7), and addition product Ti2O5C3H8 (eq. 4-8). The products of the

+ Ti3O7 reaction are similar, with the major product being O2 loss and almost no HAA

+ + + observed. Zr2O5 , Zr3O7 and Zr4O9 are not reactive with propane.

+ Ti2O5

TiO C H + 2 3 8 + Ti2O3 + + Ti O C H + TiO4C2H6 Ti2O5H 2 5 3 8

+ Figure 4-7. Mass spectrum of the reaction between Ti2O5 and 0.260 mTorr propane.

63

+ Ti3O7

+ Ti3O5 + Ti2O6C3H8 + + Ti3O7C Ti3O7C3H8

+ Figure 4-8. Mass spectrum of the reaction between Ti3O7 and 0.258 mTorr propane.

+ + Ti푥O2푥+1 + C3H8 → Ti푥−1O2푥−2C3H8 + TiO3 (4-5)

+ + Ti푥O2푥+1 + C3H8 → Ti푥−1O2푥C3H8 + TiO (4-6)

+ + Ti푥O2푥+1 + C3H8 → Ti푥O2푥+1H + ⋅C3H7 (4-7)

+ + Ti푥O2푥+1 + C3H8 → Ti푥O2푥+1C3H8 (4-8)

+ + The product mass spectra for the reactions between Ti2O5 and Ti3O7 with

+ ethylene are given in Figure 4-9 and Figure 4-10, respectively. While Ti3O7 displays almost

+ + no reactivity toward ethylene, Ti2O5 results in the TiO3 etching product TiO2C2H4 (7%,

+ eq. 4-9), the TiO etching product TiO4C2H4 (3.5%, eq. 4-10), one and two ethylene

+ addition (4.4% and 0.8%, eqs. 4-11 and 4-12), and O2 loss. Zr2O5 is unreactive with

+ ethylene. As observed in the ZrxO2x+1 reactions with alkenes (see Section 4.3.2), the size of the cluster greatly affects observed products.

64

+ Ti2O5

+ TiO2C2H4 + TiO C H + Ti2O5C2H4 4 2 4 + + Ti2O5(C2H4)2 Ti2O3

+ Figure 4-9. Mass spectrum of the reaction between Ti2O5 and 0.308 mTorr ethylene.

+ Figure 4-10. Mass spectrum of the reaction between Ti3O7 and 0.960 mTorr ethylene.

65

+ + Ti2O5 + C2H4 → TiO2C2H4 + TiO3 (4-9)

+ + Ti2O5 + C2H4 → TiO4C2H4 + TiO (4-10)

+ + Ti2O5 + C2H4 → Ti2O5C2H4 (4-11)

+ + Ti2O5 + C2H4 → Ti2O5(C2H4)2 (4-12)

4.4 Conclusion

As observed in our comparisons of the stoichiometric titanium and zirconium oxide series with radical oxygen atoms, we find large differences in the reactivity with

+ + small hydrocarbons between the two series TixO2x+1 and ZrxO2x+1 . The titanium series is not reactive toward acetylene, propylene, and carbon monoxide, and only slightly reactive with ethane, propylene, and ethylene. However, its reactivity with the latter three shows no evidence of oxidation nor oxidative dehydrogenation, only the two types of etching reactions and gas association. As we have demonstrated, a radical oxygen moiety is not a requirement for the etching reaction to occur; therefore, it is surprising to

+ find no evidence of superoxide behavior in the reactions of TixO2x+1 despite computation results demonstrating their presence. Further theoretical work is needed to reveal why

+ the superoxide unit does not appear to cause reactivity in TixO2x+1 clusters. Additional,

+ we suspect that gas-phase cluster studies of V2O5 with propylene will result in acrolein, which may shed light onto similar industrial processes.

66

Preliminary Studies on Hafnium Oxide Reactivity

5.1 Introduction

Traditionally, hafnium-based materials have been used more for their physical properties than chemical ones; for example, its primary uses are as control rods in nuclear reactors due to high neutron cross-section and as the gate oxide in 45 nm integrated circuits due to its high dielectric constant. Hafnium’s high cost and chemical similarity to its congener zirconium frequently make zirconium the preferable choice in matters where chemical reactivity is the primary concern. Cotton has stated “The chemistries of hafnium and zirconium are more nearly identical than for any other two congeneric elements.”138,139 This has led to relatively few studies on hafnium and hafnium oxide based materials.

Recently, however, interest in the chemical properties of hafnium-based materials has grown. De Roo et al. used reagents as ligands to enable colloidal HfO2 nanocrystals to catalyze transesterifications,140 while Trunschke et al. showed that hafnia nanoparticles embedded in a carbon composite catalyze aromatization of n-alkanes.103 Perhaps the most activity in this subject has come in the area of hafnium-based metal organic frameworks (MOFs) for heterogeneous catalysis and chemical separations as Hf has a higher Brønsted acidity than Zr, causing it to be a more efficient catalyst in acid-catalyzed systems.134,141–148 With increasing focus on hafnium catalysis, studies of gas-phase ion chemistry of hafnium oxides can shed light on the behavior of hafnium-based materials or lead to the development of materials with specifically tailored properties.

67

The dearth of studies on hafnium oxides also applies to cluster studies. Compared to the amount of studies on titanium and zirconium oxide clusters, hafnium materials seem relatively unexplored. Relatively few structural, spectroscopic, and reactivity investigations have been undertaken on gas-phase hafnium atoms and clusters compared to elements such as titanium and vanadium. The Castleman group found that hafnium

+ 149 was able to form metallocarbohedrenes, Hf8C12 . Merritt et al. used the pulsed field ionization zero electron kinetic energy (PFI-ZEKE) technique of photoelectron spectroscopy to determine the ionization energy of HfO and vibrational frequencies of

HfO+.150 Bowen and coworkers have found significant differences in the electronic

− − − − structures of isoelectronic pairs ZrO /HfO and ZrO2 /HfO2 through anion photoelectron spectroscopy (PES).139,151 Zhai et al. used anion PES to examine the electronic and

0/− 134 geometric structure of HfO1-6 . Gong et al. used matrix isolation infrared spectroscopy

152 + to study group IVB neutral clusters M2O2 and M2O4. The reactions of Hf with O2 and

CO153 and Hf with water154 have been examined, as well as the reactivity of the dication

2+ 2+ 2+ 155,156 + + clusters Hf , HfO , and HfO2 . Recently, the reactivity of HfO and XHfO (X = F, Cl,

Br, I) toward methane was probed by Zhou et al.157

+ More relevantly, Ding et al. determined that (HfO2)1-2 has a radical oxygen atom

+ + 119 responsible for HAA from methane, similar to (TiO2)1-2 and (ZrO2)1-2 . As demonstrated with the reactions of stoichiometric titanium and zirconium oxide cations with small hydrocarbons (see Chapter 3), elements in the same group can show remarkably different reactivity patterns. As we have also demonstrated through experiment and calculations

+ that the series ZrxO2x+1 contains a superoxide active site, an investigation into the nature

68

+ + of HfxO2x and HfxO2x+1 clusters is in order. Therefore, we have undergone reactivity studies of cationic hafnium oxide clusters to compare to previous studies of zirconium

+ oxide clusters. Our findings indicate that the HfxO2x series contains a radical oxygen active

+ site and the HfxO2x+1 series contains a superoxide active site, keeping with the behavior of the other group IVB metals, albeit with different selectivity.

5.2 Experimental Methods

Gas-phase cluster reactivity experiments are performed on a custom-built triple quadrupole mass spectrometer (TQMS) as described in Chapter 2. In short, clusters are created by laser ablation of a rotating and translating 1/8” diameter Hf rod while a backing gas consisting of approximately 10% O2 in He is pulsed over. Resultant clusters are cooled via supersonic expansion, skimmed into a beam by a skimmer, and focused into the TQMS by a series of ion optics. The first quadrupole mass selects a cluster of interest, which reacts with a reactant gas introduced into the octopole reaction cell. Ionic reaction products are then scanned by the second quadrupole and detected by a channel electron multiplier. Branching ratios are obtained by plotting the intensities of each product versus the pressure of reactant gas. Due to the difficulty of obtaining absolute rate constants, only relative ones can be determined, and are done so according to Section 2.6.

5.3 Results and Discussion

+ 5.3.1 HfxO2x+1 Reactions

69

+ The mass spectrum of hafnium oxide cations, HfxOy , is given in Figure 5-1. Just as titanium and zirconium, hafnium readily forms oxide clusters with a variety of stoichiometries.

HfO+

+ Hf2O5

+ Hf2O4

+ Hf2O3

+ Hf2O6 + + HfO3 HfO7 HfO + + + 8 Hf2O7 HfO6 + + HfO2 HfO + 5 Hf2O9 + HfO4

+ Figure 5-1. Mass spectrum of hafnium oxide cations HfxOy .

+ The product spectrum of the reaction Hf2O5 with propylene is given in Figure 5-2,

+ + with the branching ratios for the reactions of HfO3 and Hf2O5 given in Figure 5-3 and

Figure 5-4, respectively, with the rate plots for each cluster given in Figure 5-5 and Figure

-13 3 + 5-6. The relative rates are determined from the rate plots to be 7.9 x 10 cm /s for HfO3

-13 3 + and 3.5 x 10 cm /s for Hf2O5 . The observed reactions are listed in eq. 5-3 to 5-6.

+ + Hf푥O2푥+1 + C3H6 → Hf푥O2푥H + C3H5O (5-3)

+ + Hf푥O2푥+1 + C3H6 → Hf푥O2푥H2 + C3H4O (5-4)

+ + Hf푥O2푥+1 + C3H6 → Hf푥O2푥+1H + ⋅C3H5 (5-5)

+ + Hf푥O2푥+1 + C3H6 → Hf푥O2푥+1CH3 + C2H4 (5-6) 70

+ Hf2O5

+ Hf2O4H2

Hf O H+ 2 4 + + Hf2O4H3 Hf2O5H

+ Figure 5-2. Mass spectrum of the reaction of Hf2O5 with 0.420 mTorr propylene. The major product is the 14 amu

+ loss, similar to the reaction of Zr2O5 with propylene (see Figure 4-3).

+ Figure 5-3. Branching ratio (ion intensity vs. reactant gas pressure) for the reaction of HfO3 with propylene.

71

+ Figure 5-4. Branching ratio (ion intensity vs. reactant gas pressure) for the reaction of Hf2O5 with propylene.

+ Figure 5-5. Rate plot for the reaction of HfO3 with propylene.

72

+ Figure 5-6. Rate plot for the reaction of Hf2O5 with propylene.

+ The similarity of the product distribution of Hf2O5 with that of the reaction of

+ + Zr2O5 with propylene in Figure 4-3 is readily apparent, and HfO3 has an almost identical

+ branching ratio. The major product for reactions of both clusters is the MxO2xH2 peak discussed in the previous section. The branching ratios shows that this product is 19% of

+ the total ion intensity at the highest pressures measured of propylene for the HfO3

+ reaction and 21% for Hf2O5 . Minor products (4% of the total ion intensity or less) include

+ hydrogen atom abstraction (eq. 5-5), a product most likely similar to M2O4H2 with one less hydrogen (eq. 5-3), and addition of a C-C cracking fragment (eq. 5-6). Not shown on the branching ratios are additions of other various C-C cracking fragments, as they are numerous and each only accounts for a small percentage of the total ion intensity.

+ The resemblance of the reactivity of the hafnium species to that of Zr2O5 strongly

+ suggests that the HfxO2x+1 series contains a superoxide active site, as would be expected

73

from the general chemical similarity between hafnium and zirconium. The question is: what is the mode of attack of the superoxide on the propylene? Does it attack through the terminal sp2 hybridized carbon, as the DFT calculations from reference 28 suggest, although this ends up in more steps to create acrolein? Or does it attack the terminal sp3

+ carbon, in analogy with V2O5 and ethane? Further DFT calculations are required to find out.

+ For comparison purposes with propylene, we studied the reaction of HfO3 with propane. The branching ratio for this reaction is given in Figure 5-7 and the rate plot is given in Figure 5-8. The relative rate for the reaction as determined from the rate plot is

2.80 x 10-13 cm3/s. The major products for this reaction are given in eq. 5-7 to 5-10. The

+ + primary products are the additions of C-C cracking products HfO3CH4 and HfO3C2H5 (eqs.

+ + 5-9 and 5-10), with only small amounts of the HAA product HfO3H (eq. 5-8) and HfO2H2

(eq. 5-7).

+ + HfO3 + C3H8 → HfO2H2 + C3H6O (5-7)

+ + HfO3 + C3H8 → HfO3H + ⋅C3H7 (5-8)

+ + HfO3 + C3H8 → HfO3CH4 + C2H4 (5-9)

+ + HfO3 + C3H8 → HfO3C2H5 + ⋅CH3 (5-10)

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+ Figure 5-7. Branching ratio (ion intensity vs. reactant gas pressure) for the reaction of HfO3 with propane.

+ Figure 5-8. Rate plot for the reaction of HfO3 with propane.

+ 5.3.2 Hf2O4 with Ethylene: Preference for the Oxidative Dehydrogenation Pathway

75

Although a full branching ratio was not taken, the product spectrum of the

+ reaction of Hf2O4 and 0.366 mTorr ethylene is given in Figure 5-9. Five products are visible, corresponding to the reactions given in eq. 5-7 to 5-11.

+ + Hf2O4 + C2H4 → Hf2O3 + C2H4O (5-7)

+ + Hf2O4 + C2H4 → Hf2O3H2 + C2H2O (5-8)

+ + Hf2O4 + C2H4 → Hf2O4H + ⋅C2H3 (5-9)

+ + Hf2O4 + C2H4 → Hf2O4H2 + C2H2 (5-10)

+ + Hf2O4 + C2H4 → Hf2O4C2H3 (5-11)

+ Hf2O4

+ Hf2O4H

+ Hf2O4H2

+ Hf2O4C2H3 + + Hf2O3H2 Hf2O3

+ Figure 5-9. Mass spectrum of the reaction of Hf2O4 with 0.366 mTorr C2H4.

+ The major product is the oxidative dehydrogenation (ODH) product Hf2O4H2 (eq.

5-10) at 16% of the total ion intensity, twice the intensity of the secondary products of

HAA (7%, eq. 5-9) and C-C bond breaking (8%, eq. 5-11). This is approximately the same

+ ODH intensity as observed in the reaction of Zr2O4 with ethylene at similar pressures (see

76

+ Section 3.3.5), however the HAA and OAT products of the Zr2O4 reaction are higher in

+ abundance, HAA being much more so. Minor products in the Hf2O4 reaction are OAT (3%,

+ + eq. 5-7) and the Hf2O3H2 product (3%, eq. 5-8). The relative lack of OAT from Hf2O4

+ compared to Zr2O4 is again correlated to the dissociation energy of radical oxygen (∆퐻0퐾) from the two species as calculated by Zhao et al. (see Table 3-2).65 A higher dissociation energy represents a stronger bond; therefore, we expect those clusters with lower dissociation energies for the radical oxygen to be more prone to reactions involving

+ oxygen loss. In this case the dissociation energy for the loss of the radical oxygen on Hf2O4

+ is 4.15 eV, compared to 4.08 eV Zr2O4 . The difference between the two is quite small at

0.07 eV, and ultimately may not account for the observed differences in selectivity. While the energy differences between typical Hf-O and Zr-O bonds is greater (8.31 vs. 8.04 eV),148 the aforementioned dissociation energies are calculated specifically for the radical type oxygen atoms, which have a lower bond strength than normal metal-oxygen bonds.

One aspect that likely affects the observed reactivity patterns is the difference in

+ + calculated ground state structures between Hf2O4 and Zr2O4 (see Figure 5-10). In the same report detailing the computational dissociation energies for radical oxygens, Zhao

+ 65 + et al. calculated the lowest energy geometries for the M2O4 clusters. Both Ti2O4 and

+ Zr2O4 have similar structures of two terminal oxygen atoms with two bridging oxygen atoms between the metal atoms, with the titanium cluster having generally shorter M−O bond lengths. The radical oxygen center is the terminal oxygen with elongated M−O bond

+ length. Hf2O4 , on the other hand, has only one terminal oxygen, the radical, with three bridging oxygen atoms. The difference in structure undoubtedly causes differences in

77

orbital location, affecting the transition states and intermediates available to the cluster as it undergoes a reaction with ethylene, possibly explaining the experimentally observed

+ difference in reactivity from Zr2O4 . However, the details of the reaction mechanism remain to be examined by DFT calculations.

+ Figure 5-10. Calculated ground state structures for M2O4 (M = Ti, Zr, Hf). From 65.

5.4 Conclusion

+ Our investigations demonstrate that HfxO2x+1 clusters contain a superoxide active

+ site with similar reactivity to ZrxO2x+1 in reactions with propylene. As shown in Chapter 3, the reactivity of a cluster with different hydrocarbons can vary widely; thus, more experimental data of the reactions of superoxide-containing hafnium clusters with more hydrocarbons is needed. Additionally, we have shown additional experimental evidence

+ toward the radical oxygen nature of Hf2O4 clusters. Interestingly, we find this cluster to

+ demonstrate different selectivity when reacted with ethylene than Zr2O4 , showing a preference for ODH. Further computations are required to determine the cause of this

78

phenomenon. Understanding this may allow us to predict or design hafnium oxide-based materials with tailored characteristics to fill pressing needs in catalysis.

79

Superatoms

6.1 Development of the Concept of “Superatoms”

The idea that elements with the same number of valence electrons share similar chemical behavior is fundamental to the whole idea of the periodic table, as elements are placed in the same column as those that have similar properties. One of the advances made by Mendeleev was to switch the old ordering of tellurium and iodine so that they fit better chemically in their respective groups, despite the ordering of atomic mass that had guided previous attempts at creating a periodic table (tellurium, element 52, actually has a higher average atomic weight than iodine, element 53). Once the role of electrons in chemical behavior became known, group behavior was explained by Niels Bohr with the filling of electron shells.

The prototypical idea/genesis of the idea of superatoms was the unified atom theory, an attempt by Robert Mulliken to describe the electronic states of a diatomic molecule by comparison with an isoelectronic atom (see Figure 6-1). Although this model had limited use for some situations where one atom is much larger than the other (for example, in hydrides), it was otherwise unsuccessful and applied only at very small bond lengths. In fact, in the cases where it failed, the molecular orbital structure was generally more similar to the separate atoms than the isoelectronic analog (see Figure 6-2).158 As

Mulliken himself said, “In most molecules, the relation to the united-atom is too remote to be of direct interest except in a few respects, relations to the separated atoms being much closer.”159

80

Figure 6-1. Electronic state comparisons between united atom pairs C with BH (left) and Si with AlH (right).

Reprinted from Ref. 159.

81

Figure 6-2. Orbital structure of compound XY2 as the X-Y bond distance r increases. At small r, the orbitals resemble

the united atom; however, as r increases to the equilibrium bond distance, orbital structure begins to resemble

that of the separated atoms X+2Y. Reprinted from 145.

The idea of a group of atoms mimicking behavior of an atom again gained traction in the 1980s with the development of jellium theory and subsequent use in describing experimental cluster phenomena.160–163 Compounds adhering to jellium theory are perhaps superatoms in the truest sense of the term, as the theory describes spherical

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metal clusters as a valence electron cloud smeared around a positive core like jelly (hence the name jellium) in a structure not unlike an atom. The valence electron structure of jellium species form orbitals and shells similar to those of atoms, and particular stability is conferred by having a closed shell. Thus, jellium molecules tend to react in attempts to

− complete a shell. Al13 , perhaps the most well-known jellium cluster, has 40 valence electrons, coinciding with a jellium shell closing, and displays particular resistance to

112 etching by O2 compared with aluminum clusters that do not have closed jellium shells.

The neutral form of this cluster, Al13, has one less valence electron at 39, and attempts to react with other compounds to fill that shell in the same way halogens react to complete an octet. The resulting halogen-like reactivity has been demonstrated experimentally by

− observation of the ionic complex KAl13 and triiodide-like behavior of Al13I2 . Jellium theory and its modifications have had great success in explaining the stability and reactivity of a number of clusters and continues to be an area of focus in cluster science. Particularly interesting is the possibility of using these principles to design cluster-assembled materials, in effect creating a “3D periodic table” of element mimics.55,164 In fact, it was this concept that lead to Khanna and Jena coining the term “superatom.”165

Apart from jellium compounds, a number of other types of superatoms have been identified, including magnetic,166 aromatic,167 and Wade-Mingos168 types. Additionally, an

“isoelectronic” type of superatom has been proposed, where species with the same number of valence electrons as another element have similar electronic structure and/or chemical behavior to that element. It is this type of superatom that will be the focus of this chapter.

83

6.2 Physical Explanations for the Phenomena

Peppernick et al. used velocity map imaging photoelectron spectroscopy (VMI

PES) to correlate the electronic states of transition metal diatomic anions with isoelectronic elements: TiO− with Ni−, ZrO− with Pd−, and WC− with Pt−, finding a number of similarities in electronic states and energy spacings between the counterparts and proposing that a “correlation principle” connected the electronic structure of isoelectronic species.169,170

If the electronic structure of two atoms or clusters is similar, then we might reasonably expect the two to react similarly. This led Tyo et al. to examine the reactivity of ZrO+ with ethane at high kinetic energies, finding similar C-C cracking behavior to that of Pd+ with the same, whereas Zr+ does not exhibit this behavior.171 They proposed that the addition of the oxygen atom caused the Zr 4d orbital to more closely resemble those

+ + + of Pd . Extending to larger clusters, we examined the isoelectronic pairs ZrO2 /PdO and

+ + 172 TiO2 /NiO and found similar behavior between them with ethylene and CO.

However, the comparisons made between the isoelectronic pairs in the studies reported above are not without discrepancies. We note that the behavior of ZrO+ is not universally similar to that of Pd+. For example, it is known that late transition metal ions are unreactive with ethylene and propylene,173 yet ZrO+ demonstrates strong association and even polymerization channels with both reactants. A comparison of the mass spectra of the aforementioned reactions is given in Figure 6-3; the difference in reactivity between the two species is immediately apparent. Behavior of each ion with ethylene is

84

quite similar to that of its reaction with propylene. For the study of larger clusters,

+ + + discrepancies are also present. While both ZrO2 and PdO display an OAT pathway, PdO

+ demonstrates an equal intensity of O loss/gas association to form the product PdC2H4 .

+ No such product is observed in the ZrO2 reaction; instead, a minor C2H4 association product is observed. Even in the calculated reaction profiles of OAT, which is found in both reactions, there are large differences in energy of forming the oxidized product. The oxidation product Pd+ is 2.73 eV below the lowest energy starting materials, with a spin- crossover occurring, while the ZrO+ oxidation product is 0.52 eV below the starting materials, with energetic barriers much higher than those in the PdO+ reaction. This isn’t a total negative; indeed, it may even be seen as a good thing. Finding a material that displays a similarity to an isoelectronic compound in one property but not another can lead to the development of a new catalyst with improved selectivity, which, as mentioned in Chapter 1, is of particular interest in environmental chemistry.

85

+ ZrO(C3H6)3

ZrO+ + C5H9 + + + ZrO(C3H6)2 C6H13 C7H15 + + + ZrOC3H6 C3H3 C4H9

Figure 6-3. Mass spectra of the reactions of ZrO+ (upper) and Pd+ (lower) with approximately 2 mTorr propylene.

The ZrO+ spectrum was obtained by this author on the higher resolution equipment, while the Pd+ spectrum was

acquired by Eric Tyo with the lower resolution equipment.

In the initial proposal of this idea of isovalent superatoms by Peppernick et al., they raised the question on if similarities could be found for larger clusters. Behera et al.

174 performed DFT studies on neutral and ionic (ZrO)n and Pdn (n = 1-5) clusters, comparing the two series by determining ionization potentials, electron affinities, binding energies, hardness, and reactivity with H2, O2 and CO. Despite some similarities in the bonding patterns of H2 to the cationic clusters, significant differences were found between the zirconium oxide and palladium series for both the electronic structure and the reactivity

− − − results. Additionally, consider the isoelectronic pair ZrO3 /PdO2 . ZrO3 belongs to the

− 25 MxO2x+1 series and contains a radical oxygen. Johnson et al. showed that this radical

− oxygen site oxidizes CO, whereas we demonstrate that PdO2 does not react with CO (See

+ + Figure 6-4). The cationic counterparts, ZrO3 and PdO2 , also show drastically different

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reactivity with ethylene. The zirconium cluster in this case contains a superoxide active

+ site. Despite this, it demonstrates no reactivity toward C2H4, while PdO2 loses an O atom and associates the gas as well as oxidizes ethylene (see Figure 6-5).

Let us also consider the differences found in the reactivity of titanium, zirconium, and hafnium oxides as discussed in this dissertation. We have presented many cases

+ where the reactivity of clusters containing different metals is vastly different. TixO2x (x =

2-4) preferentially undergoes the etching reaction with ethane, propane, and ethylene,

+ + whereas ZrxO2x (x = 1-4) strongly prefers hydrogen atom abstraction. TixO2x+1 (x = 2-3), despite being determined by theory to contain a superoxide, shows no oxidation behavior

+ + with propylene, unlike Zr2O5 . Hf2O4 strongly prefers the oxidative dehydrogenation

+ reaction with ethylene, while Zr2O4 shows more intense hydrogen atom abstraction and oxidation channels. Clearly, even elements in the same group do not always show similar chemical behavior.

87

- Figure 6-4. Mass spectrum of PdO2 with 0.398 mTorr CO. No products are observed.

+ Figure 6-5. Branching ratio for the reaction of PdO2 with ethylene.

88

The ultimate test of the usefulness of a theory is its predictive power. Does the idea of isovalency allow us to predict new superatoms? The idea would suggest that just about any molecule with the same number of valence electrons will act like any other; however, this seems to contradict chemical intuition. If there are similarities, what is their extent? Does this principle scale up with the size of the clusters? Attempts to answer these questions have since been addressed by a number of studies.

Bowen and coworkers used PES to compare oxide clusters of congeners Zr and Hf, finding “significant differences” in the electronic structures of isoelectronic pairs ZrO/HfO

139,151 and ZrO2/HfO2. These differences are attributed to a relativistic mass-velocity effect, which stabilizes the σ orbital and destabilizes the δ orbital in ZrO and HfO. This effect is much stronger in Hf because of its larger weight, thus causing even larger orbital energy shifts. Stabilization of 4d orbitals across a row causes NbN− and MoC− to fill orbitals in a

2 1 2 4 − 2 1 different order, resulting in different ground states ∆ (1δ 3σ ) and Σ (1δ 3σ ), respectively.175 The photoelectron spectra for these two species are quite different, exacerbated by the fact that MoC− has several low lying excited electronic states, so its spectrum is more complex with vibrational hot bands.

Further, invoking the idea of isovalency to make assumptions about the electronic structure of a molecule can lead to incorrect conclusions. For example, Wu and Wang proposed electronic ground states for a series of early transition metal oxide diatomic anions based on the known ground states of isoelectronic neutral oxide diatomics that later experimental and theoretical investigations, including work from our lab and this

3 − author, invalidated. For example, they proposed a ∆ ground state for ScO based on the

89

176 4 − − 177 5 ground state of isoelectronic TiO, a Σ ground state for TiO based on VO, and a Π ground state for VO− based on CrO.178 Later studies would demonstrate the ground states

1 − 179 2 169 3 − 180 of these three anions to be Σ , Δ3/2, and Σ , respectively. This analogy to isoelectronic counterparts caused incorrect identification of the HOMOs and SOMOs. The

5 − Π proposed ground state of VO was due to a hypothetical electron configuration of

3휋48휎29휎11훿24휋1, however our velocity map imaging photoelectron spectroscopy

3 − experiments revealed the true state to be Σ with corresponding electron configuration

3휋48휎29휎21훿2, confirming various theoretical calculations181–183 that agreed on this state.

The importance of the HOMOs in chemical reactivity was emphasized by Ma et al. in examinations of the reactions of HNbN− and the Pt atom with methane and ethane.184

Although HNbN− is not strictly isoelectronic with Pt (12 valence electrons vs. 10), the authors considered the two electrons of the Nb-H bond to not contribute much to the orbitals directly involved in bonding. Both species insert into a C-H bond of methane, resulting in addition of CH4, and dehydrogenate C2H6 to form ethylene. DFT results show that that the Pt orbital governing reactivity with methane is the 5푑푧2 orbital, while the

− HOMO of HNbN is a hybrid orbital consisting of 58% Nb 5s and 25% Nb 4푑푧2 with similar shape to the Pt 5푑푧2.

We are then left with a question: are the examples already demonstrated in the literature of element mimics merely coincidence, or is there a more complicated explanation underlying this phenomenon? Recent work by Sahoo et al. has attempted to address this issue.185 Their calculations on the C-C bond activation behavior of row 5

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transition metal-carbon diatomics with ethane demonstrates that it is not simply the filling of 4d states in the transition metal that controls the reactivity of the molecule, as would be implied by invoking the idea of isovalency. The controlling factors are the filling

2 of the 5s orbital and the position of the 4dz orbital. If this idea about the detailed properties of the molecular orbitals can be generalized to explain the behavior of other element mimics, then it is indeed the specifics of the electronic structure that determine

“superatom” behavior, and not the general electronic structure as described by isovalency.

All of this evidence points toward the conclusion that the fact that two molecules share the same number of valence electrons is no guarantee of similar electronic structure nor chemical reactivity. To state otherwise would represent a gross oversimplification of the elements that go in to defining electronic structure. It takes into account almost no information regarding orbitals nor orbital energies. As the several studies previously mentioned show, the controlling factor is similarity in specific orbitals involved in a reaction, which generally cannot be predicted simply by counting valence electrons. It appears that theoretical calculations are required to determine if

The above discussion is centered on wholesale replacement of an entity by an isoelectronic counterpart. However, single atom substitutions in larger clusters to create isoelectronic species with different charge are promising. Zhao et al. showed that the

+ − bonding properties of TiVO5 and CrVO6 are similar to those of V2O5 and V2O6 ,

65 + respectively. Nössler et al. demonstrated that atom substitution into Zr2O4 to make

91

− ZrScO4 or Zr2O5 to make ZrNbO5 also result in radical oxygen active sites with similar reactivity.90

92

Conclusion and Future Directions

Mass spectrometric methods for the examination of gas-phase clusters have produced a wealth of information about these systems, particularly the effects of charge, geometry, stoichiometry, oxidation state, etc. on chemical and physical properties.30 We

+ presented the reactivity of MxO2x (M = Ti, Zr) clusters that contain radical atomic oxygen,

O•−, with methane, ethane, propane, ethylene, and propylene. We observe that in many cases the titanium clusters undergo a type of “etching” reaction, where the cluster loses a TiO unit and associates the reactant gas. Zirconium oxides strongly prefer the hydrogen atom abstraction pathway, and no evidence for an etching type of reaction is found for

+ zirconium clusters. Next, we examined the reactivity of TixO2x+1 clusters that are

•− theoretically predicted to contain a superoxide active site, O2 , and find that the

+ reactivity is quite different from ZrxO2x+1 . We also presented one of the first studies of

+ the reactivity of hafnium oxide clusters, and show that HfxO2x+1 acts very similarly to

+ + ZrxO2x+1 clusters, attributed to a superoxide active site. However, Hf2O4 , which contains

+ a radical oxygen atom, shows drastically different reactivity from Zr2O4 . Finally, we discussed these studies in the context of isoelectronic superatoms, and concluded that predicting similar electronic structure or chemical behavior by simply counting valence electrons is insufficient, that the underlying cause of similar reactivity is due to the

+ similarity of a specific orbital or set of orbitals. Our studies of the reactions of MxO2x and

+ MxO2x+1 (M = Ti, Zr, Hf) demonstrate that there is significant difference in the reactivity of clusters with different metal atoms, despite all three belonging to the same group of the periodic table. Effects such as cluster geometry, metal-oxygen bond strengths, and

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relativistic effects alter the electronic structure of the cluster, causing observed activity and selectivity of different clusters to vary.

The hope of this author is that findings in cluster science can be used to direct the development of cluster-assembled and improved catalytic materials. There is a good deal of interest in the development of new materials by deposition of small, size-selected clusters onto surfaces, and this has evolved into its own subdiscipline of cluster science.14

However, attempts to soft land a cluster without significantly changing its behavior from that in the gas-phase is difficult, as landing on a surface tends to destroy or alter the cluster. Further, should the landing not damage the molecule, studies have shown that clusters tend to deform onto the surface, or diffuse until binding to a defect or active site, ultimately disturbing the electronic structure.186 Attempts to study clusters on surfaces or in matrices without interaction from other species are ongoing.22

Toward this end, there are many opportunities for advancing our knowledge in this area. As hafnium oxides are still relative newcomers to the field, further research into their behavior is in order, particularly DFT studies to complement the reactivity studies presented herein. Additionally, relatively few gas-phase studies have probed palladium oxide and iridium oxide cluster behavior, two important materials in catalysis. Attempts by this author to generate clean mass spectra of palladium and iridium oxide clusters failed due to a contaminant that could not be removed. To model cluster-support interactions, mixed-metal clusters are of particular interest, although they prove an experimental challenge to generate.

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Appendix A. Theory of Quadrupole Operation

A-1. The Mathieu Equations of Motion

This appendix describes the derivation of the Mathieu equations of motion for ions in a quadrupolar electric field187–191 and the implications the results have on the operation of quadrupole devices, particularly regarding mass resolution.

Before we begin the derivation, we note that if the quadrupole rods are hyperbolic, the equations of motion in each coordinate are independent, i.e. they do not depend on the position of the particle in any of the other two coordinates. This simplifies some math later on. Because it is very difficult to machine a hyperbolic rod with the precision required to maintain stable and precise DC and RF voltages, hyperbolic fields are approximated by using spherical rods of diameter 1.148 times the radius of the circle inscribed by the electrodes.

In a quadrupolar device, the potential at any point in terms of rectangular coordinates is given in eq. A-1, where A is the electric potential applied between the electrodes of opposing polarity (either an RF alone or RF with DC), C is a fixed potential applied to all the rods (also RF only or RF and DC), and λ, σ, γ are weighting constants for x, y, and z, respectively.189

ퟐ ퟐ ퟐ 흓풙,풚,풛 = 푨(흀풙 + 흈풚 + 휸풛 ) + 푪 (A-1)

Conceptual drawings for the orientation of the x, y, and z axes compared to the orientation of the quadrupole and the propagation of the ion beam are given in Figure

A-1.

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Figure A-1. Direction of x, y, and z axes relative to quadrupole orientation and propagation of the ion beam.

Forward ion motion is in the z-axis along the long axis of the quadrupole.

Since we are dealing with electric fields, the potential must satisfy Laplace’s equation given in eq. A-2.

2 ∇ 휙푥,푦,푧 = 0 (A-2)

Splitting each part of the potential into the respective coordinates yields eq. A-3.

휕2휙 휕2휙 휕2휙 ∇2휙 = + + = 0 (A-3) 휕푥2 휕푦2 휕푧2

In a real system, the potential distribution ϕ at time t is given by eq. A-4, where U is the

DC potential (+U applied to x electrodes, -U applied to the y electrodes), V is the magnitude of the RF potential, and ω is the angular frequency of the RF (equal to 2πf, f being frequency).

휙 = 2(푈 + 푉푐표푠휔푡) (A-4)

Since the electric field is the negative gradient of the potential (퐸 = −훻휙), then the x, y, and z components of the electric field are given in eq. A-5 to A-7, respectively.

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휕휙 2푥 퐸푥 = − = −[푈 + 푉 cos 휔푡] 2 (A-5) 휕푥 푟0

휕휙 2푦 2푦 퐸푦 = − = −[−푈 + 푉 cos 휔푡] 2 = [푈 − 푉 cos 휔푡] 2 (A-6) 휕푦 푟0 푟0

휕휙 퐸 = − = 0 (A-7) 푧 휕푧

Here 푟0 is the distance from the z axis to the surface of any of the four electrodes (the radius of the inscribed circle of the electrodes). The force a charged particle feels in these fields is related by 퐹⃑ = 퐸⃑⃑ ⋅ 푒, where e is the charge on the particle. Thus the components of force in the three coordinates are given in A-8 to A-10.

2푒푥 퐹푥 = −[푈 + 푉 cos 휔푡] 2 (A-8) 푟0

2푒푦 퐹푦 = [푈 − 푉 cos 휔푡] 2 (A-9) 푟0

퐹푧 = 0 (A-10)

According to Newton’s second law, 퐹 = 푚푎, and the definition of acceleration (the second time derivative of position), we get a set of differential equations (eq. A-11 to A-

13) that, when solved, yield ion trajectories in their respective coordinates.

푑2푥 푞푥 2 + 2 [푈 + 푉 cos 휔푡] = 0 (A-11) 푑푡 푚푟0

푑2푦 푞푦 2 − 2 [푈 − 푉 cos 휔푡] = 0 (A-12) 푑푡 푚푟0

푑2푧 = 0 (A-13) 푑푡2

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Simplifying things, we may define two parameters, aU and qU (a and q in the x or y coordinate), given in eq. A-14 and A-15.

8푒푈 ( ) 푎푥 = 2 2 A-14 휔 푟0 푚

−4푒푉 ( ) 푞푦 = 2 2 A-15 휔 푟0 푚 where m is the mass of the particle, and 푎푥 = −푎푦 and 푞푥 = −푞푦. Substituting into our equations for the second derivatives, we obtain eq. A-16 and A-17.

푑2푥 휔2 + [푎 + 2푞 cos 휔푡]푥 = 0 (A-16) 푑푡2 4 푥 푥

푑2푦 휔2 − [푎 − 2푞 cos 휔푡]푦 = 0 (A-17) 푑푡2 4 푦 푦

And of course the z-component of the electric field is still zero so the trajectory along that axis remains as it was before the ion entered the quadrupole. These equations can lead us to a generalized form for Mathieu’s equations of motion by the change in variables 휉 =

2 휔푡 and calculating 푑 푢, where u is either the coordinate x or y. This is accomplished by the 2 푑휉2 chain rule for the first (eq. A-18) and second (eq. A-19) derivative.

푑푢 푑푡 푑푡 = ⋅ (A-18) 푑휉 푑푡 푑휉 and the second derivative is

푑2푢 푑푡 푑푢 푑푡 = [ ⋅ ] (A-19) 푑휉2 푑휉 푑푡 푑휉

Applying the product rule yields eq. A-20, with first and second derivatives of 푑푢/푑t with respect to 휉 given in eq. A-21 and A-22 and the first and second derivatives of t with respect to 휉 given in eq. A-23 and A-24.

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푑2푢 푑2푡 푑푢 푑 푑푢 푑푡 = ⋅ + [ ] ⋅ (A-20) 푑휉2 푑휉2 푑푡 푑푡 푑푡 푑휉

푑 푑푢 푑2푢 푑푡 [ ] = ⋅ (A-21) 푑휉 푑푡 푑푡2 푑휉

푑2푢 푑2푡 푑푢 푑2푢 푑푡 2 = ⋅ + ⋅ [ ] (A-22) 푑휉2 푑휉2 푑푡 푑푡2 푑휉

푑푡 2 = (A-23) 푑휉 휔

푑2푡 = 0 (A-24) 푑휉2

Making these substitutions and factoring out 4/ω2 leaves us with the canonical form of

Mathieu’s equation in eq. A-25.

푑2푢 + [푎 − 2푞 cos 휔푡]푢 = 0 (A-25) 푑휉2 푢 푢

The results of the Mathieu equations are given by Floquet’s theorem, which is simply a way of dealing with a certain type of linear differential equations (the case where the time derivative of a coordinate is equal to a piecewise continuous periodic function times t).

The solutions take the form

∞ ∞ 휇휉 2푖푛휉 −휇휉 −2푖푛휉 푢 = 훼′푒 ∑ 퐶2푛푒 + 훼′′푒 ∑ 퐶2푛푒 푛=−∞ 푛=−∞ where 푖 is the imaginary unit, 훼’ and 훼’’ are integration constants that depend on the initial conditions only (푢0, 푑푢0/푑푡, and 휉0, representing initial position along the x or y coordinate, velocity in that coordinate, and initial time, respectively), and 푐2푛 (expansion coefficients) and 휇 (a complex number) depend on the parameters a and q only, not the initial coordinates. This second part leads to an important point: the periodicity of motion

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of an ion depends on a and q, not the initial conditions; thus, all ions with the same values of a and q have the same periodicity of motion, regardless of initial velocity or position when entering the quadrupole.

For our purposes it is not important to look at the specifics of the solutions, but rather general ideas. In these solutions there are two competing parts. The sums as given in eq. A-27 are simply Fourier series, which means that they are simply many (in this case infinite) different oscillations that add up to construct a separate periodic function.

∞ ±2푖푛휉 ∑ 퐶2푛푒 (A-27) 푛=−∞

The other term, 푒휇휉, is either an oscillating or an exponentially growing term, depending on the value of 휇. This term ultimately determines the stability of a specific ion trajectory.

If the entire expression results in a periodic function that does not increase over time, the result is generally a stable trajectory (bounded solutions). A solution that does increase over time generally yields unstable trajectories (unbounded solutions), since ions will continuously increase their position along the x or y axis until they strike an electrode or miss the detector.

Since 휇 is a complex, real, or imaginary number, it contains a real part and/or an imaginary part (eq. A-28), leading to eq. A-29.

휇 = Re(휇) + 푖 ⋅ im(휇) (A-28)

푒휇휉 = 푒[Re(휇)+푖⋅im(휇)]휉 = 푒[Re(휇)]휉푒[푖⋅im(휇)]휉 (A-29)

If 휇 contains any real component at all, then as time increases (remember 휉 is directly proportional to time) the term 푒휇휉 is, of course, an exponentially increasing term

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multiplied by an oscillating term. [If Re(휇) is positive, then the positive form of eq. A-27 increases with time and the negative form approaches a limit as n approaches infinity. If

Re(휇) is negative, then the negative form becomes the exponential growth term while its complex conjugate counterpart approaches a limit.] The end result is that 휇 continuously increases over time, to the point that ions crash into the electrodes. This is an unstable solution. The other possibility for 휇 is that it is strictly imaginary. If Im(휇) is not a whole number, then the solutions are periodic stable trajectories. Otherwise, the solutions are periodic but unstable. These solutions are called functions of integral order and form bounds on the resulting regions of stability in graphs of a vs. q (see Error! Reference s ource not found.2).

Figure A-2. Stability diagrams for a quadrupole mass analyzer. Regions marked with the numerals are stable in both

the x and y axes. Taken from Ref. 189.

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A-2. Applications to Quadrupole Operation

All that was a really complicated way of saying that the stability of a trajectory for a certain ion mass is dependent on the ratio between a and q, or, more simply, U and V (DC and RF potentials). Certain values of a/q will yield stable trajectories in either the x or the y plane. For mass filter operation, we need to operate the quadrupole in regions in which both x and y trajectories are stable. Generally, this occurs in region I. Scanning the quadrupole consists of increasing the magnitudes of U and V while keeping the ratio between them constant. In U, V space, each ion with different mass has a different stability diagram (see Error! Reference source not found.A-3). The line formed by keeping U

and V at a constant ratio but increasing magnitudes is called a scan line or operating line.

Operating the quadrupole in RF-only mode, where U=0, means the scan line lies on the V axis, allowing all ions through. When U is nonzero, the quadrupole operates in DC resolving mode.

By adjusting the slope and the V intercept of the scan line in DC resolving mode, the resolution can be controlled. Adjusting the slope changes the resolution more for higher masses than lower ones, so it is known as high mass resolution. In Merlin, this is controlled via the Delta R variable. Adjusting the V intercept changes the resolution of lower masses more than higher ones, so it is low mass resolution. In Merlin, this is adjusted via the Delta M variable. Adjusting the resolution comes with a drawback, however. Increasing the resolution leads to decreased ion signal. Thus, care has to be taken to not set the resolution too high, where not enough signal comes through, or too low, where separate masses cannot be resolved from one another.

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Figure A-3. Close-up of the upper half of region I of the stability diagram. Taken from Ref. 189.

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Appendix B. Operating the Merlin Software

B-1. How Mass Scanning Works

In my opinion, the operation of the Merlin software has a rather steep learning curve, and the documentation is lacking, particularly for understanding how the whole system works. Therefore, I include here some notes about the operation of the software that I’ve spent years teasing out.

Since we use a pulsed source and the Merlin software was designed for continuous ion sources, minor modification of the Merlin data collection routine is necessary. Data collection in Merlin occurs by sampling once every 80 μs. This is a hardware specification and cannot be changed in the software. In normal operation of the system as designed by

Extrel, a mass range, target scan time, and target samples per amu (named ADC_SPM in

Merlin) are set for the quadrupole(s) by the user. The software attempts to reconcile all three of these parameters together by getting as close as it can to the target scan time by adjusting ADC_SPM. Getting the correct scan parameters is actually fairly difficult. For some reason it’s really difficult to set a high ADC_SPM with a decent-sized mass range as the system likes to start introducing “microscans” to hit the target scan time. What ends up happening in our system is most samples end up returning zero ion current because they sample during the large amounts of time in-between ion packets, which are only a few ms wide and 50 ms apart when operating at 20 Hz. This causes any spectra measured this way to not have reliable intensities, even when averaged over many scans.

The way around this when mass selecting is to define a mass range that is smaller than the minimum DAC step the hardware is able to make. This means that the voltage

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command increment to go from one mass to the other is so small that the hardware is unable to do it, so it can’t compute the number of samples it needs to perform the scan in the mass range. However, it’s possible to change the software variable

ADC_SAMPLES_MIN, which tells the software what to do in this situation by giving it a default number of samples. In our system, ADC_SAMPLES_MIN is set to the time between ion packets. This guarantees that each scan operated this way results in a scan of such length that we expect exactly one ion packet to arrive. If not operated this way, you run the risk of reading an ion intensity of zero because the scan timing was not synchronized with the staggered arrival of ion packets. So when operating at 10 Hz, we set

ADC_SAMPLES_MIN to 1250 (with 80 μs samples this results in a 100 ms scan), 625 at 20

Hz (50 ms scan), and 417 at 30 Hz (33.3 ms scan). Thus to collect a mass spectrum, the system dwells at each mass long enough for an ion packet to come through, measures the intensity, then moves on to the next mass. This is done exclusively through custom macros for the software, discussed in the following section, and not through the default scanning and averaging commands. Scanning this way can take some time, particularly when you start averaging scans to improve the signal-to-noise ratio. Unfortunately this is the way data must be collected with our experimental arrangement.

B-2. Data Collection Macros for the Merlin Software

The Merlin software can be automated to some extent through macros written in the PAW macro language (PML). PML is less a programming language and more a list of commands you can use to automate certain functions of the instrument. It is fairly

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restricted in what you can do with it, although it does have certain capabilities you would

expect in a fully-functional language, such as loops, conditional statements, and the

ability to create and write to a file. PML macros are stored in a simple text file saved with

a .pml extension in the methods directory of the data analysis computer’s Extrel directory.

In our system, this is C:\Extrel\methods. Macros are initiated in the Merlin software by

typing the macro name in the ctrl or proc fields and pressing enter. Variables may by

passed in to the macro by either following the macro name with a space and then each

variable’s value (separated by spaces or commas), or defined in parenthesis after the

macro name, with each variable separated by commas. A limit of only five variables may

be passed in to a macro. As an example, calling a macro with five variables is done by

typing one of the following and pressing enter:

macro A B C D E

macro(A, B, C, D, E)

B-1.1. Rxn

if cent; prof; end

pfm = ions(1);plm = ions(2);dfm = ions(3);dlm = ions(4) # stores original ion file table

if %1;else;%1=100;end # Q1 mass to select if %2;else;%2=10;end # Q3 Start mass if %3;else;%3=400;end # Q3 end mass if %4;else;%4=0.1;end # noise threshold if %5;else;%5=5;end # number of averages to take at each point

?%1: ?%2: ?%3: ?%4: ?%5:cr

collect_pause view_add:"pict":cr # added RAS 23 AUg 01

list_clear pict_clear

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ADC_SAMPLES_MIN = 417 scan_time =0.034 s_mass = %2 # s_mass is a local variable (only used in the program) s_step = 0.1 simwid = 0.1

ions k = 1 # k acts as the index for the mass. i.e. at the start mass, k is 1, at start mass + step size, k is 2, etc. # set ion table to select the Q1 mass and scan another mass at Q3 while s_mass < (%3+s_step) ions ions %1,,s_mass, s_mass + 0.0001 fish # collect data prof_to_list(10)

# if the packet arrives at the start or end of the scan, redo it (for some reason this causes it to have very high intensity) maxValue = list_max(10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end

while ((maxPoint < 20) | (maxPoint > 400)) "packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) end

num_avgs = 0 running_sum = 0 scan_area = list_sum(10) * 0.00008 #?scan_area:CR if (scan_area >= %4): "Averaging this mass":CR while (num_avgs < %5) num_avgs += 1 "Averaging ":?s_mass:", scan ":?num_avgs:" out of ":?%5:CR running_sum += scan_area maxPoint = 0 while ((maxPoint < 20) | (maxPoint > 400)) #"packet at boundary, restarting.":CR fish prof_to_list(10)

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maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end scan_area = list_sum(10) * 0.00008 end scan_avg = running_sum / num_avgs else maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end if ((list_sum(10) * 0.00008) >= %4): num_avgs = 2 "Averaging this mass":CR while (num_avgs < %5) num_avgs += 1 "Averaging ":?s_mass:", scan ":?num_avgs:" out of ":?%5:CR running_sum += scan_area maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end scan_area = list_sum(10) * 0.00008 end else scan_avg = (scan_area + (list_sum(10) * 0.00008)) / 2 num_avgs = 2 end end

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list_clear(10) list(k,2) = scan_avg list(k,1) = s_mass list(k,3) = num_avgs # put num of avgs for that point in list 3 pict (s_mass, scan_avg) # adds the new data point to the pict spectrum "Current Mass:":?s_mass:"out of":?%3:CR # Displays current mass s_mass += s_step # increment mass to next step # increase index by 1 k += 1 end s_mass = %2

"Scan complete.":cr # display message that scan is complete string_save(1):if month < 10:"0":end:?month:"_":if day < 10:"0":end:?day:"_":?year:" ":if hour > 12:a = hour - 12:else:a = hour:end:if a < 10:"0":end:?a:"":if minute < 10:"0":end:?minute:if hour < 12:"AM":else:"PM":end:CR "Initiating file:":string_restore:".txt":CR file_write:string_restore:".txt":CR:"# Rxn":CR file_write:string_restore:".txt":CR:"# Acquisition Time: ":string_restore:CR file_write:string_restore:".txt":CR:"# ADC_Samples_Min: ":?adc_samples_min:CR file_write:string_restore:".txt":CR:"# Q1 mass selected: ":?%1:CR file_write:string_restore:".txt":CR:"# Scan range: ":?%2:" - ":?%3:CR file_write:string_restore:".txt":CR:"# Noise Threshold: ":?%4:CR file_write:string_restore:".txt":CR:"# Averages: ":?%5:CR file_write:string_restore:".txt":CR:"# List entries: ":?list_size(1):CR file_write:string_restore:".txt":CR:"# Mass":TAB:"Avg Intensity":CR a = 1 while a <= list_size(1) file_write:string_restore:".txt":CR:?list(a,1):TAB:?list(a,2): CR # Writes the mass and intensity pair to the file a += 1 "Writing file:":string_restore:".txt, please wait...":CR end "File complete. Saved as ":string_restore:".txt":CR

#pict_norm # 23 aug RAS

ions # 23 aug RAS

ions pfm,plm,dfm,dlm # restores original ion file table end

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B-1.2. Q1_scan

if cent; prof; end

pfm = ions(1);plm = ions(2);dfm = ions(3);dlm = ions(4) # stores original ion file table

if %1;else;%1=100;end # Q1 start mass if %2;else;%2=400;end # Q1 end mass if %3;else;%3=10;end # noise threshold if %4;else;%4=20;end # number of averages if %5;else;%5=0.1;end # step size

collect_pause view_add:"pict":cr # added RAS 23 AUg 01

list_clear pict_clear

ADC_SAMPLES_MIN = 625 scan_time =0.05145 # necessary to get 624 samples (about 0.49 ms scan) s_mass = %1 # s_mass is a local variable (only used in the program) s_step = %5

simwid = 0.1

ions k = 1 # k acts as the index for the mass. i.e. at the start mass, k is 1, at start mass + step size, k is 2, etc. # set ion table to select the Q1 mass and scan another mass at Q3 while s_mass < (%2+s_step) ions ions s_mass, s_mass + 0.0001,, fish # collect data prof_to_list(10)

# if the packet arrives at the start or end of the scan, redo it (for some reason this causes it to have very high intensity) maxValue = list_max(10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end

while ((maxPoint < 11) | (maxPoint > 610)) "packet at boundary, restarting.":CR fish prof_to_list(10) 110

maxPoint = list_find(list_max(10),10) end

num_avgs = 0 running_sum = 0 scan_area = list_sum(10) * 0.00008 #?scan_area:CR if (scan_area >= %3): "Averaging this mass":CR while (num_avgs < %4) num_avgs += 1 "Averaging ":?s_mass:", scan ":?num_avgs:" out of ":?%4:CR running_sum += scan_area maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end scan_area = list_sum(10) * 0.00008 end scan_avg = running_sum / num_avgs else maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end if ((list_sum(10) * 0.00008) >= %3): num_avgs = 2 "Averaging this mass":CR while (num_avgs < %4) num_avgs += 1 "Averaging ":?s_mass:", scan ":?num_avgs:" out of ":?%4:CR running_sum += scan_area maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish

111

prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end scan_area = list_sum(10) * 0.00008 end else scan_avg = (scan_area + (list_sum(10) * 0.00008)) / 2 num_avgs = 2 end end

list_clear(10) list(k,2) = scan_avg list(k,1) = s_mass list(k,3) = num_avgs # put num of avgs for that point in list 3 pict (s_mass, scan_avg) # adds the new data point to the pict spectrum "Current Mass:":?s_mass:"out of":?%2:CR # Displays current mass s_mass += s_step # increment mass to next step # increase index by 1 k += 1 end s_mass = %2

"Scan complete.":cr # display message that scan is complete string_save(1):if month < 10:"0":end:?month:"_":if day < 10:"0":end:?day:"_":?year:" ":if hour > 12:a = hour - 12:else:a = hour:end:if a < 10:"0":end:?a:"":if minute < 10:"0":end:?minute:if hour < 12:"AM":else:"PM":end:CR "Initiating file:":string_restore:".txt":CR file_write:string_restore:".txt":CR:"# Q1 Scan":CR file_write:string_restore:".txt":CR:"# Acquisition Time: ":string_restore:CR file_write:string_restore:".txt":CR:"# ADC_Samples_Min: ":?adc_samples_min:CR file_write:string_restore:".txt":CR:"# Scan range: ":?%1:" - ":?%2:CR file_write:string_restore:".txt":CR:"# Noise Threshold: ":?%3:CR file_write:string_restore:".txt":CR:"# Averages: ":?%4:CR

112

file_write:string_restore:".txt":CR:"# Q1 Delta Res: ":?Q1_delta_res:CR file_write:string_restore:".txt":CR:"# List entries: ":?list_size(1):CR file_write:string_restore:".txt":CR:"# Mass":TAB:"Avg Intensity":CR a = 1 while a <= list_size(1) file_write:string_restore:".txt":CR:?list(a,1):TAB:?list(a,2): CR # Writes the mass and intensity pair to the file a += 1 "Writing file:":string_restore:".txt, please wait...":CR end "File complete. Saved as ":string_restore:".txt":CR

#pict_norm # 23 aug RAS

ions # 23 aug RAS

ions pfm,plm,dfm,dlm # restores original ion file table 23 aug RAS end

B-1.3. Q3_scan

if cent; prof; end

pfm = ions(1);plm = ions(2);dfm = ions(3);dlm = ions(4) # stores original ion file table

if %1;else;%1=100;end # Q1 start mass if %2;else;%2=400;end # Q1 end mass if %3;else;%3=10;end # noise threshold if %4;else;%4=20;end # number of averages to take at each point if %5;else;%5=0.1;end # step size

?%1: ?%2: ?%3: ?%4:cr

collect_pause view_add:"pict":cr # added RAS 23 AUg 01

list_clear pict_clear

ADC_SAMPLES_MIN = 625 scan_time =0.05145 # necessary to get 624 samples (about 0.49 ms scan) s_mass = %1 # s_mass is a local variable (only used in the program) s_step = %5

simwid = 0.1

113

ions k = 1 # k acts as the index for the mass. i.e. at the start mass, k is 1, at start mass + step size, k is 2, etc. # set ion table to select the Q1 mass and scan another mass at Q3 while s_mass < (%2+s_step) ions ions ,,s_mass, s_mass + 0.0001 fish # collect data prof_to_list(10)

# if the packet arrives at the start or end of the scan, redo it (for some reason this causes it to have very high intensity) maxValue = list_max(10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end

while ((maxPoint < 11) | (maxPoint > 610)) "packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) end

num_avgs = 0 running_sum = 0 scan_area = list_sum(10) * 0.00008 #?scan_area:CR if (scan_area >= %3): "Averaging this mass":CR while (num_avgs < %4) num_avgs += 1 "Averaging ":?s_mass:", scan ":?num_avgs:" out of ":?%4:CR running_sum += scan_area maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end scan_area = list_sum(10) * 0.00008

114

end scan_avg = running_sum / num_avgs else maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end if ((list_sum(10) * 0.00008) >= %3): num_avgs = 2 "Averaging this mass":CR while (num_avgs < %4) num_avgs += 1 "Averaging ":?s_mass:", scan ":?num_avgs:" out of ":?%4:CR running_sum += scan_area maxPoint = 0 while ((maxPoint < 11) | (maxPoint > 610)) #"packet at boundary, restarting.":CR fish prof_to_list(10) maxPoint = list_find(list_max(10),10) if maxValue = 0 maxPoint = 100 else maxPoint = list_find(list_max(10),10) end end scan_area = list_sum(10) * 0.00008 end else scan_avg = (scan_area + (list_sum(10) * 0.00008)) / 2 num_avgs = 2 end end

list_clear(10) list(k,2) = scan_avg list(k,1) = s_mass list(k,3) = num_avgs # put num of avgs for that point in list 3 pict (s_mass, scan_avg) # adds the new data point to the pict spectrum

115

"Current Mass:":?s_mass:"out of":?%2:CR # Displays current mass s_mass += s_step # increment mass to next step # increase index by 1 k += 1 end s_mass = %2

"Scan complete.":cr # display message that scan is complete string_save(1):if month < 10:"0":end:?month:"_":if day < 10:"0":end:?day:"_":?year:" ":if hour > 12:a = hour - 12:else:a = hour:end:if a < 10:"0":end:?a:"":if minute < 10:"0":end:?minute:if hour < 12:"AM":else:"PM":end:CR "Initiating file:":string_restore:".txt":CR file_write:string_restore:".txt":CR:"# Q3 Scan":CR file_write:string_restore:".txt":CR:"# Acquisition Time: ":string_restore:CR file_write:string_restore:".txt":CR:"# ADC_Samples_Min: ":?adc_samples_min:CR file_write:string_restore:".txt":CR:"# Scan range: ":?%1:" - ":?%2:CR file_write:string_restore:".txt":CR:"# Noise Threshold: ":?%3:CR file_write:string_restore:".txt":CR:"# Averages: ":?%4:CR file_write:string_restore:".txt":CR:"# Q1 Delta Res: ":?Q1_delta_res:CR file_write:string_restore:".txt":CR:"# List entries: ":?list_size(1):CR file_write:string_restore:".txt":CR:"# Mass":TAB:"Avg Intensity":CR a = 1 while a <= list_size(1) file_write:string_restore:".txt":CR:?list(a,1):TAB:?list(a,2): CR # Writes the mass and intensity pair to the file a += 1 "Writing file:":string_restore:".txt, please wait...":CR end "File complete. Saved as ":string_restore:".txt":CR

#pict_norm # 23 aug RAS

ions # 23 aug RAS

ions pfm,plm,dfm,dlm # restores original ion file table 23 aug RAS end

116

Appendix C. Supplementary Rate Constant Plots for Stoichiometric

Titanium and Zirconium Oxides

+ + Rate plots for the reactions of TixO2x and ZrxO2x with methane, ethane, propane, ethylene, and propylene are displayed in Figures C-1 to C-9.

+ Figure C-1. Rate plots for the reactions of TixO2x with methane.

117

+ Figure C-2. Rate plots for the reactions of TixO2x with propane.

+ Figure C-3. Rate plots for the reactions of TixO2x with ethylene.

118

+ Figure C-4. Rate plots for the reactions of TixO2x with propylene.

+ Figure C-5. Rate plots for the reactions of ZrxO2x with methane.

119

+ Figure C-6. Rate plots for the reactions of ZrxO2x with ethane.

+ Figure C-7. Rate plots for the reactions of ZrxO2x with propane.

120

+ Figure C-8. Rate plots for the reactions of ZrxO2x with ethylene.

+ Figure C-9. Rate plots for the reactions of ZrxO2x with propylene.

121

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Vita Christopher L. Harmon EDUCATION Ph.D. in Chemistry Aug. 2016 The Pennsylvania State University, University Park, PA B.S. in Chemistry, Minor in Physics Apr. 2009 Brigham Young University, Provo, UT

RESEARCH EXPERIENCE Graduate Research Assistant Nov. 2009 – Present Group of Prof. A. W. Castleman, Jr., Department of Chemistry, the Pennsylvania State University Undergraduate Research Assistant Jan. 2007 – Apr. 2009 Group of Prof. David V. Dearden, Department of Chemistry and Biochemistry, Brigham Young University Student Contractor June 2007 – Aug. 2007, Apr. 2008 – June 2008 Group of Dr. Kevin Dreher, National Health and Environmental Effects Research Laboratory, US Environmental Protection Agency, Research Triangle Park, NC

PUBLICATIONS  Harmon, C. L.; Krstic, M.; Bonačić-Koutecký, V.; Castleman, A. W., Jr. Differing Selectivity and Reactivity of Stoichiometric Titanium and Zirconium Oxide Cations with Small Hydrocarbons: Observation of a TiO Etching Reaction. In preparation.  Cheng, S.-B.; Harmon, C. L.; Castleman, A. W., Jr. On the Electronic Structure of the Diatomic VO anion: A Combined Photoelectron Imaging Spectroscopic and Theoretical Investigation. J. Chem. Phys. To be submitted.  Gunaratne, K. D. D.; Berkdemir, C.; Harmon, C. L.; Castleman, A. W., Jr. Probing the Valence Orbitals of Transition Metal-Silicon Diatomic Anions: ZrSi, NbSi, MoSi, PdSi, and WSi. Phys. Chem. Chem. Phys. 2013, 15, 6068–6079.  Tyo, E. C.; Nöβler, M.; Rabe, S.; Harmon, C. L.; Mitrić, R.; Bonačić-Koutecký, V.; Castleman, A. W., Jr. Exploring Similarities in Reactivity of Isovalent Species: A Combined Theoretical and Experimental Investigation. Phys. Chem. Chem. Phys. 2012, 14, 1846–1849.  Gunaratne, K. D. D.; Berkdemir, C.; Harmon, C. L.; Castleman, A.W., Jr. Investigating the Relative Stabilities and Electronic Properties of Small Zinc Oxide Clusters. J. Phys. Chem. A 2012, 116, 12429–12437.  Iordanov, I.; Gunaratne, K. D. D.; Harmon, C. L.; Sofo, J.; Castleman, A. W., Jr. Broad Photoelectron Spectrum and Lowered Electron Affinity Due to Hydrogen in ZnOH: A Joint Experimental and Theoretical Study. J. Chem. Phys. 2012, 136, 214314.  Tyo, E. C.; Nößler, M.; Harmon, C. L.; Mitrić, R.; Bonačić-Koutecký, V.; Castleman, A. W., Jr. Investigating Reactive Superoxide Units Bound to Zirconium Oxide Cations. J. Phys. Chem. C 2011, 115, 21559–21566.  Reber, A. C.; Khanna, S. N.; Tyo, E. C.; Harmon, C. L.; Castleman, A. W., Jr. Cooperative Effects in the Oxidation of CO by Palladium Oxide Cations. J. Chem. Phys. 2011, 135, 234303.