Fundamental Insights Into Photo-Induced Charge Transfer in Metal Complexes Through Electroabsorption Spectroscopy

FUNDAMENTAL INSIGHTS INTO PHOTO-INDUCED CHARGE TRANSFER IN METAL COMPLEXES THROUGH ELECTROABSORPTION SPECTROSCOPY

Andrew B. Maurer

A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Department of Chemistry.

Chapel Hill 2020

Approved by:

Gerald J. Meyer

Jillian L. Dempsey

James F. Cahoon

Alexander J. M. Miller

ii ABSTRACT

Andrew B. Maurer: Fundamental Insights into Photo-Induced Charge Transfer in Metal Complexes through Electroabsorption Spectroscopy (Under the direction of Gerald J. Meyer)

As pervasive as light and electron motion is to our world, it comes as no surprise that a long line of research in chemistry has involved developing methods to understand and harness these useful processes.

However, there are limitations to humanity’s knowledge even after the several hundred years of development.

In particular there is hardly a true way to track electron motion during or the identity of the excited state after photon absorption. Chapter 1 establishes a background on the development of photochemistry and provides a thorough delve into the theory and use of electroabsorption spectroscopy, or Stark spectroscopy, which allows for a more descriptive picture of the Franck-Condon state.

2+ Chapters 2 and 3 introduce the home-built Stark apparatus and analyzes a series of Metal(diimine)3 compounds. These chapters outlines the basic principles that can be measured through the use of Stark spectroscopy. Chapter 2 continues by providing insight into how signiﬁcant substituents of the diimines in the 4 and 4’ positions can be to the electron transfer during the metal-to-ligand charge transfer excitation.

Chapter 3 instead of altering the ligand alters the metal center, and provides insight into how the metal center can effect the metal-to-ligand charge transfer. Additionally the results of Chapter 3 indicate a possiblity for a change of polarizaiton during the spin ﬂip process that can be uniquely measured by Stark spectroscopy, enhancing transitions normally hidden due to their low transition probability from the spin change.

Chapter 4 and 5 take a slight deviation by demonstrating a more common application of Stark spectroscopy. In these chapters, Stark spectroscopy is used to assist in conﬁrming the results of the other

iii techniques and theoretical assumptions by providing evidence for the amount of charge transfer, the direction of charge transfer, and the overall efﬁciency of the excited electron for subsequent electron transfers. Chapter

6 outlines the Stark apparatus and the standard operating procedure for the clarity of the reader and for future reference for lab members.

iv To always question and always pursue the truth

v ACKNOWLEDGEMENTS

There seldom is a true opportunity in a lifetime to sit down and thank all the individuals that have made an achievement possible. With the completion of my dissertation, I have the opportunity for such a moment and I ﬁnd the task at hand one of the most daunting I’ve had during my graduate work and my life before. I have been lucky enough to have many friends, family, and coworkers that have shaped me both as a person and as a scientist in ways they may have never known. Each person who is willing to share their perspective of life or science helps alter or reinforce my views on the world and turned me into the person I am today. Even those who I meet in passing have had lasting impacts likely beyond their wildest intentions.

With all this in mind, I would like to take a moment here to reﬂect on the efforts of those around me to thank them for what they have done.

I’d like to begin this acknowledgement with recognizing my parents, Debra and David, and all of my brothers, Daniel, Michael and Matthew, for their guidance and help through my earlier years and their continued efforts today. For my parents, their willingness to put up with any and all of my after school activities and clubs, their support and help in the early years to learn beyond the classroom, their ﬁnancial support in all years of schooling, and so much more I can’t recount it all here. Their help allowed me to focus on my studies and pursue whatever dream I had without a worry in the world, an opportunity for which I can never thank them enough. For my brothers, their friendship in the early years to today will always reassure me I have people I can count on, but beyond that their own personal drives and passions helped to drive me to

ﬁnd my own path in life and excel to the same extents that they did. I doubt they will ever know how much just being themselves helped me grow, and I can only hope that I had a similar effect on them.

vi While I could go on for pages discussing the multitude of college friends that have molded me into who I am today, I wanted to select a few groups of people to whom I owe the most. The ﬁrst bunch I’d like to highlight are my fellow chemistry majors. The whole class was relatively small and allowed for a tightly knit group of friends to develop. These people all pushed me to be the best I could at the subject, with them often times looking to me as a source of knowledge and never wanting to let them down. In particular I’d like to mention Lukas Ronner, Ashley Reeder, Leela Chockalingam, and Dan Nelson. They all helped me stay calm in the face of the mountain of stress that college can bring and not unlike my brothers their strong personalities and successes in life made me want to be the best I could be.

Another group that made my college journey possible is that of the student life on campus. The camaraderie between us brought a vast collection of lifestyle tips and developed many of my current interests outside of chemistry. Through late night on-duty grub hub dinners together, parties, and events I developed a strong sense of family away from home that I’m not sure I’ll ever be able to recreate. This group reminded me that there was so much more to life than just science and studying. Speciﬁcally I’d like to call out Hira

Ahmad and Kyle Mueller for their continued friendship (and teasing of me occasionally) that has always been a breath of fresh air and a reminder that there is a lot more out there. The two of them with the rest of student life taught me how important the balance between work and life can be.

The last group of college friends that I need to make sure I thank I have managed to stay close with and even grow closer since we have left college. I am of course talking about the group known formally as

Team Positivity, consisting of Dan Nelson, Tyler Healy, Ian McIntyre, Shane McGraw and myself. At a simple level we play video games together at least once a week. While some may not understand the bonds that can be built through playing video games online, this group has helped have a consistent dose of teamwork that reminds me how important working with other can be. The group has also helped instill in me the belief that people all can and will try in the right circumstances to be better, and that positive reinforcement, self-reﬂection, and well delivered criticism can make a world of difference. Beyond all that

vii though, keeping close friends with similar interests and having a good laugh every week is something that I doubt I’ll ever fully appreciate.

Over my long academic career I have had many great instructors and advisors who I am glad to have met and can consider my friends. They have motivated my scientiﬁc drive, shaped my learning abilities, and validated my choice to study Chemistry in life. In high school, Paul Vetscher gave me a mind to pursue beyond that which was taught and gave me my love of math, which has proven useful to this day. Also in high school, Jeff Trinh’s teaching style inspired my own teaching style of never giving answers and only asking questions, it also helped my learning abilities in being able to return to fundamentals and work up from there to fully understand a system instead of memorization of details. At Carnegie Mellon University,

David Chickering was my housefellow who instilled me with a sense of responsibility and leadership through his recognition of me as a RA and beyond that as a friend. I still distinctly remember one-on-one meetings with him that involved chatting about life and my dreams, and David, even with his several hundred person large dorm, would remember details about my life from years past.

I would be remisce to not mention and thank potentially the most important faculty member to my development as a chemist, Dr. Stefan Bernhard. Starting with recruiting me into his lab after taking an inorganic chemistry course my freshman year, his recognition for my abilities brought a reviviﬁed drive to learning beyond what is expected. He always was up for talking, usually about science, but that included almost anything. Frequent visits to his ofﬁce to share data or ask for help or guidance in how to approach a problem has given me the tools I’ve used substantially through my own graduate work presented in this dissertation. He may deny his usefulness and assure you that I was easy to work with and point in the right direction, but I know his advising is invaluable to my capabilities as a scientist and teacher. In particular I would like to thank him for allowing me to help him with the construction of home built instruments and allowing me to test my coding abilities for specialized experiments and new analytical techniques.

viii At this time I’d like to move on to my graduate years, and ﬁrst individually thank each person of Jerry

Meyer’s research group (in no order): Ke Hu, Erin Brigham, Ryan O’Donnell, Evan Beauvilliers, Brian

DiMarco, Tim Barr, Tyler Motley, Wes Swords, Catherine Burton, Sara Wehlin, Matt Brady, Cassandra Ward,

Renato Sampaio, Ludovic Troain-Gautier, Bruno Aramburu, Erica James, Rachel Bangle, Michael

Turlington, Daniel Conroy, Zander Deetz, Quentin Loague, and Erin Kober. When choosing groups in the beginning of my ﬁrst year, one of the most attractive qualities of Jerry’s group was not necessarily the research, but the people and the way they treated each other. I don’t doubt that other groups have the same mentalities and friendships, but the collaboration and quick to joke attitudes of members provided levity in an often times what could be a grueling research day. The willingness to discuss topics and learn outside of your expertise always impressed me and I hope that I was able to give back some knowledge to the other members of the group as they had given to me. I’d like to give a special thanks to Eric Piechota, who defending almost a year ago included that I had to “deal with his silly ideas, bad math, and angry rants”. I hope he understands that that goes both ways and I similarly appreciated his suffering through my innumerable stories about games and other life events that I doubt he was substantially interested in. His friendship inside and outside of the lab cannot be understated and he has been missed signiﬁcantly during the last bit of my graduate work.

On the less scientiﬁc side of my graduate years, I’d like to thank my Dungeons and Dragons folk.

Thank you to Jason ‘Many Paws’ Malizia, Dan ‘Uletme’ Garrett, Liz ‘Macaria’ Garrett, Dan ‘Barend’

Druffel, Alex ‘Lemonjello’ Squire, and Evan ‘Lurin’ Feura. Over the last several years, the time we’ve spent exploring imagined worlds and working together has been a blast. Beyond that, the time we’ve played has reignited my creativity to heights it has never before been. Outside of the game you have all been great friends as well, and I hope that we can continue to play for years and remain friends.

Lastly I’d like to thank my advisor, Jerry Meyer, for the long ﬁve and a half years of guidance. As a person, his passion for chemistry, attention to detail, strong writing capabilities, and healthy lifestyle choices are inspiring. Especially after my usual idea board of Eric left after his successful defense, Jerry has allowed

ix me to visit his office continuously to bounce ideas off of him, with me rarely if ever leaving without an answer and more questions. After my first few years of research led to a hard point in my life he was incredibly understanding and supportive of whatever I needed. Beyond that, he helped pull me back out and eventually through his guidance led me to Stark spectroscopy, a field of research that I feel I could spend another five years, or potentially the rest of my life, continuing to investigate. I owe Jerry an unimaginable debt of gratitude for all of the help and guidance he has given me over the years and for making me into the scientist I am today.

To finish my acknowledgements I’d just like to thank everyone one last time. To those who were not specifically mentioned, I’d like you to know that it is unlikely you didn’t have a strong impact on my life, however I simply do not have the space to thank each person individually here. I hope that everyone who has made my journey in life possible to this point realizes the influence they have had on my continuing career and life.

Thank you.

x TABLE OF CONTENTS

LIST OF TABLES ...... xiv

LIST OF FIGURES ...... xv

LIST OF SCHEMES ...... xxii

CHAPTER 1 – Photo-Induced Charge Transfer and Stark Effect Theory ...... 1

1.1 Motivation ...... 1

1.2 Photo-Induced Charge Transfer ...... 2

1.3 Electron Transfer Reactions...... 4

1.4 Electric Fields in Chemistry ...... 6

1.5 Stark Effect Theory ...... 9

1.6 Stark Spectroscopy Theory ...... 16

1.7 Summary ...... 30

REFERENCES ...... 31

2+ CHAPTER 2 – Excited State Dipole Moments of Homoleptic [Ru(bpy’)3] Complexes Measured by Stark Spectroscopy ...... 33

2.1 Introduction...... 33

2.2 Experimental ...... 35

2.2.1 Materials ...... 35

2.2.2 Stark Spectrometer ...... 35

2.2.3 Data Analysis ...... 38

2.3 Results ...... 39

2.3.1 Discussion ...... 45

xi 2.4 Summary ...... 52

2.5 Additional information ...... 52

REFERENCES ...... 58

CHAPTER 3 – Stark Spectroscopic Evidence that a Spin Change Accompanies Light Ab- sorption in Transition Metal Polypyridyl Complexes...... 63

3.1 Introduction...... 63

3.2 Experimental Details ...... 63

3.3 Results ...... 65

REFERENCES ...... 78

CHAPTER 4 – Light Excitation of a Bismuth Iodide Complex initiates I-I Bond Formation Reactions of Relevance to Solar Energy Conversion ...... 81

4.1 Introduction...... 81

4.2 Results ...... 81

4.3 Discussion ...... 84

4.4 Summary ...... 90

REFERENCES ...... 91

CHAPTER 5 – Visible-Light Induced Electron Transfer Chemistry of Osmium (II) Supramolec- ular Assemblies ...... 93

5.1 Introduction...... 93

5.2 Experimental ...... 95

5.3 Results and Discussion ...... 104

5.4 Conclusions...... 119

REFERENCES ...... 121

CHAPTER 6 – Stark Apparatus Description and Operation ...... 127

6.1 Introduction...... 127

6.2 Hardware Description ...... 128

6.2.1 Light Source and optical path ...... 128

xii 6.2.2 Oscilloscope ...... 129

6.2.3 Optical Cell Design and Cryostat ...... 130

6.2.4 Lock-in Ampliﬁer ...... 131

6.2.5 Function Generator and High Voltage Ampliﬁer ...... 132

6.3 Software description and typical operation...... 133

6.3.1 General User Interface ...... 134

6.3.2 Background and Low-Temperature Spectra ...... 135

6.3.3 Stark Spectra ...... 137

6.3.4 Data analysis ...... 139

REFERENCES ...... 145

Appendix A – MATLAB ANALYSIS CODE...... 146

Appendix B – LABVIEW INSTRUMENT CONTROL AND DATA COLLECTION SOFTWARE . . 176

xiii LIST OF TABLES

2.1 Absorption maxima and molar extinction coefﬁcients in butyronitrile at 77K.a ...... 41

2.2 Parameters ∆µ, T r(∆α), and ∆αm derived from equations 2.3-2.5...... 45

2.3 Summary of Values of Oscillator Strength, Dipole Moment Difference, Transition Dipole Moment, Degree of Delocalization, Electron Transfer Distances, Percent Charge Transfer, and Electronic Coupling Elements ...... 49

3 −1 2.4 Summary of HDA values calculated with equations 2.11-2.15. All units are (x10 cm ) . . . . 57

3.1 Tabulation of the different excited states and the Group Theory orbitals they originate from...... 70

3.2 Absorption maxima (ν, cm−1 x103) and molar extinction coefﬁcients (ε,M −1 cm−1 x103) in butyronitrile at 77K...... 73

3.3 The |∆~µ| for 1MLCT transitions...... 74

3.4 |∆~µ|, Charge Transfer Distance, and Percent Charge Transfer for Transitions B and D...... 74

3.5 |∆~µ|, Charge Transfer Distance, and Percent Charge Transfer for Transitions B and D...... 74

– 5.1 Photophysical properties of the indicated osmium [PF6] complexes in acetone...... 105

– 5.2 Relevant reduction potentials and ∆GES values for the indicated osmium [PF6] complexes. . 107 5.3 Changes in dipole moment and angle of the dipole moment change vector with respect to the transition dipole moment for selected transitions of the indicated Os(II) complexes...... 110

xiv LIST OF FIGURES

1.1 The splitting caused by Zeeman (Left) and Stark (Right) effects on the n=2 and n=3 levels of a hydrogen atom. Note: the splitting caused by these effects is substantially smaller than the splitting between principle quantum number energy levels. . . . . 10

1.2 Allowed optical transitions between the n=2 and n=3 levels of a hydrogen atom under the splitting effects due to an applied electric ﬁeld...... 11

1.3 Graphical depiction of a band shape distortion in the presence of an applied electric ﬁeld. . . . . 15

1.4 Demonstration of reassigning coordinates x,y,z in a new basis through the use of direction cosines...... 17

1.5 Angles used with direction cosine to associate the polarization of light and electric ﬁeld with a common basis of the transition dipole moment, µeg...... 25

1.6 Diagrams to deﬁne ζ in the context of a molecular frame (Left) and χ in the context of a laboratory frame (Right)...... 27

2.1 A block diagram of the Stark apparatus that utilized a Xe arc lamp for excitation, a cryostat sample compartment, and a Si photodiode detector. An enhanced view of the sample compartment with relevant terms e,ˆ χ, and F is indicated...... 35

2.2 A pictoral representation of ζ, and how ∆µ and mˆ deﬁne it...... 39

2+ 2.3 (a) The absorption spectra of [Ru(MeObpy)3] in butyronitrile at 77K (black) 2+ and room temperature (red). (b) The absorption spectrum of [Ru(MeObpy)3] in butyronitrile recorded at 77K (black) with an overlaid ﬁt (red). The two dominant MLCT bands are marked with Band A (Blue) and Band B (Magenta) and the individual Gaussians used to ﬁt these data are shown as dashed lines...... 40

2+ 2.4 (a) The 2nd derivative of the ground state absorption of [Ru(MeObpy)3] (red) overlaid on the measured Stark spectrum (black). (b) 1st derivative of the ground 2+ state [Ru(MeObpy)3] (red) absorption spectrum overlaid on the measured Stark spectrum (black)...... 42

2.5 Absorption, ε(¯ν) (a), the Stark spectrum (black) with the fit (red) (b), and the com- 2+ ponents of the fit (1st derivative; green, 2nd derivative; blue) (c) for [Ru(MeObpy)3] 2+ (left) and [Ru(CF3bpy)3] (right). All Stark data is scaled to 1 MV/cm of applied field...... 43

2+ 2.6 The low energy Stark spectrum of [Ru(bpy)3] (black), a 1st derivative component (green), and a 2nd derivative component (blue). The sum of the 1st and 2nd derivative contributions is given in red...... 46

2.7 Change in dipole plotted versus the σpara Hammett parameter demonstrating the correlation between the dipole moment and the inductive effect of the substituent...... 46

2.8 Room Temperature UV-vis of all species investigated in butyronitrile...... 52

xv 2.9 Low Temperature UV-vis of all species investigated at 77K in a butyronitrile glass...... 53

2.10 Absorption, ε(ν) (top), the Stark spectrum (black) with the fit (red), and the 2+ components of the fit (1st derivative; green, 2nd derivative; blue) for [Ru(bpy)3] 2+ (left) and [Ru(dtb)3] (right) . For ease of interpretation all data is scaled to 1 MV/cm of applied field...... 54

2.11 Absorption, ε(ν) (top), the Stark spectrum (black) with the fit (red), and the 2+ components of the fit (1st derivative; green, 2nd derivative; blue) for [Ru(dmb)3] 2+ (left) and [Ru(bpz)3] (right) . For ease of interpretation all data is scaled to 1 MV/cm of applied field...... 55

2+ 3.1 Absorption and Stark spectra (black, with overlaid ﬁts in red) spectra for [Fe(bpy)3] , 2+ 2+ [Ru(bpy)3] , and [Os(bpy)3] . All Stark spectra were scaled to an applied ﬁeld of 1MV/cm...... 65

2+ 3.2 Stark spectra of [Ru(bpy)3] recorded (Left) at different concentrations and (Right) – – using PF6 and Cl anions. All data is scaled to an applied Field of 1 MV/cm...... 66

2+ 3.3 Electroabsorption measurements of [Fe(bpy)3] at the indicated applied field strengths. (Left) Full Stark spectra scaled to an applied Field of 1 MV/cm. (Right) The absolute value of the intensity of the electroabsorption feature measure at the indicated wavelength as a function of the field strength. Overlaid are quadratic fits...... 67

2+ 3.4 Electroabsorption measurements of [Ru(bpy)3] at the indicated applied field strengths. (Left) Full Stark spectra scaled to an applied Field of 1 MV/cm. (Right) The absolute value of the intensity of the electroabsorption feature measure at the indicated wavelength as a function of the field strength. Overlaid are quadratic fits...... 67

2+ 3.5 Electroabsorption measurements of [Os(bpy)3] at the indicated applied field strengths. (Left) Full Stark spectra scaled to an applied Field of 1 MV/cm. (Right) The absolute value of the intensity of the electroabsorption feature measure at the indicated wavelength as a function of the field strength. Overlaid are quadratic fits...... 68

2+ 3.6 Stark spectra of the low energy region of [Os(bpy)3] recorded at different ﬁeld strengths without normalization...... 68

2+ 3.7 The 77K absorption spectrum of [Fe(bpy)3] in butyronitrile (black). Overlaid are individual transitions labelled with reference to Table 3.1 and a summation of the individual transitions (red)...... 71

2+ 3.8 The 77K absorption spectrum of [Ru(bpy)3] in butyronitrile (black). Overlaid are individual transitions labelled with reference to Table 3.1 and a summation of the individual transitions (red)...... 71

2+ 3.9 The 77K absorption spectrum of [Os(bpy)3] in butyronitrile (black). Overlaid are individual transitions labelled with reference to Table 3.1 and a summation of the individual transitions (red)...... 72

xvi 2+ 3.10 A) The Stark spectrum of [Fe(bpy)3 (black) with overlaid analytical (red) and noise-free (blue) second-derivatives of the absorption spectrum. B) The low energy 2+ electro-absorption feature of [Fe(bpy)3] (black) with overlaid ﬁrst- (blue) and second- (pink) derivative contributions and the sum (red)...... 72

4.1 Absorption spectra of BiI3 in CH3CN titrated with tetrabutylammonium iodide (TBAI). The spectra given in bold are assigned to the indicated complexes...... 82

4.2 Transient absorption difference spectra measured at the speciﬁed time delays after pulsed 532 nm excitation (20 mJ/pulse) of BiI3 with six equivalents of TBAI in CH3CN. Inset: An expansion of difference spectra between 600 and 800 nm. – Overlaid in red is the spectrum of I2 CH3CN ...... 83

– 1 4.3 Simpliﬁed molecular orbital diagrams of uncomplexed I2 CH3CN as well as η 2 – and η ligated I2 ...... 84

3– 4.4 Proposed mechanism following iodide to metal charge transfer of a [BiI6] species ...... 85

1 2 – 3– 4.5 Concentration proﬁles of η and η I2 after excitation of [BiI6] Inset: Plot of k2 versus [I–] for the transformation from η2 to η1 diiodide ...... 86

4.6 Top) Low-temperature absorption spectrum (black) with an overlaid ﬁt (red). Bot- tom) Stark spectrum (black) with an overlaid ﬁt (red) and individual derivative contributions ...... 89

4+ 4+ 5.1 Synthetic routes to obtain [Os(CF3bpy)2(tmam)] and [Os(bpy)2(tmam)] ...... 103

4+ 4+ 5.2 UV-Vis absorption spectra of [Os(CF3bpy)2(tmam)] (orange) and [Os(bpy)2(tmam)] (purple) in acetonitrile (solid) and acetone (dash)...... 105

4+ 4+ 5.3 Photoluminescence spectra of [Os(CF3bpy)2(tmam)] (orange) and [Os(bpy)2(tmam)] (purple) in acetone at room temperature (solid) and in butyronitrile at 77K (dash) with the corresponding ﬁt according to a Franck-Condon lineshape analysis...... 106

5.4 Absorption (top) and Stark (bottom) spectra (black, with overlaid ﬁts in red) of 4+ 4+ [Os(bpy)2(tmam)] (left) and [Os((CF3)2bpy)2(tmam)] (right). All spectra were recorded in butyronitrile at 77k and scaled to an applied ﬁeld of 1 MV/cm...... 109

4+ 4+ 5.5 Stark spectra of [Os(bpy)2(tmam)] (left) and [Os((CF3)2bpy)2(tmam)] (right) record with horizontally (blue dots) and vertically (black dots) polarized light (corresponding ﬁt as solid lines). All spectra were recorded in butyronitrile at 77k and scaled to an applied ﬁeld of 1 MV/cm...... 109

5.6 Contour plots Os-CF3 (top) and Os-bpy (bottom) showing the plane that contains the tmam ligand, describing the Coulombic free energy (in eV) experienced without (a) and with (b) an iodide anion present in the tmam pocket...... 111

xvii 5.7 a) Proposed structure of the terionic complexes. b) The chemical shifts of indicated hydrogen atoms of Os-CF3 plotted against the number of TBAI equivalents for 1 Os-CF3 in d6-acetone with up to 8 equivalents. c) H NMR spectra of Os-CF3 with 0 to 8 equivalents of TBAI in d6-acetone showing both the aromatic region and methylene hydrogens of the tmam ligand...... 112

5.8 a) Mole fractions of the indicated species with increasing amount of TBAI. b) 4+ Steady state PL decays of [Os(CF3bpy)2(tmam)] with increasing amount of TBAI. The orange shading represents the increased PL contribution from {Os4+ ...... 115

5.9 Transient absorption spectra measured 1 µs after pulsed 532 nm light (20.5 4+ mJ/pulse) of [Os(CF3bpy)2(tmam)] with 20 eq TBAI. Overlaid in blue is a – spectral modelling based on equal contributions of I2 (reference spectra in purple) and reduced complex...... 117

5.10 Proposed reaction mechanisms for electron transfer and I-I bond formation for A) 4+ Os-CF3 and B) [Ru(dtb)2(tmam)] indicating the excited state electron density by blue color on ligand ...... 119

6.1 A block diagram of the Stark apparatus that utilized a Xe arc lamp for excitation, a cryostat sample compartment, and a Si photodiode detector...... 129

6.2 A top down and side on visualization of an ideal cell...... 130

6.3 Depiction of the sample holder including the non-conductive wafer and the microbinder clips used to afﬁx the cell to the holder...... 131

6.4 Lock-in Ampliﬁer Circuit Diagram...... 132

6.5 Labview GUI ...... 134

6.6 Xenon Arc Lamp Spectral Distribution ...... 137

6.7 Photodiode Responsivity Curve ...... 138

6.8 MATLab GUI ...... 140

6.9 Options Pane in Stark Analysis ...... 141

6.10 Labview GUI ...... 141

6.11 Example Absorption Fit ...... 142

6.12 Example Stark Fit ...... 143

6.13 Example Residual Plot ...... 143

6.14 Example Component Deconvolution ...... 143

A.1 Creation of the class for the low-temperature absorption and background spectra. Interface code for loading a chosen experimental ﬁle and setting a baseline...... 146

xviii A.2 Creation of the ﬁle name for the GUI, and checks to ensure the reference and low-temperature absorption spectrum have the same wavenumber range...... 147

A.3 Creation of the class for the Stark spectra. Details on what properties and methods are included in the class...... 148

A.4 Converts the raw ∆I and Iavg data into ∆ε for processing...... 149

A.5 Corrects the for the baseline for both spectra, with the low-temperature absorption being corrected by a slanted baseline and the Stark spectra being corrected by an average value. Also shown is the calculation of the 0th-, 1st-, and 2nd-order derivatives for the Gaussians in the ﬁt...... 150

A.6 Reading and loading the spectral data from the exported LabView ﬁle...... 151

A.7 GUI commands for the initialization of the ﬁgures, and the toolbar at the top of the GUI. . . . . 152

A.8 Initialization of the Panel in which the user can input data and monitor quantitative ﬁtting results...... 152

A.9 Controls for ﬁle i/o for the absorption and stark spectra...... 153

A.10 Speciﬁc controls for the Parameter Panel, including the addition of Gaussians...... 154

A.11 Speciﬁc controls for the Settings and Monte Carlo Panels...... 155

A.12 Speciﬁc Controls for the Plotting Panel...... 155

A.13 Input of shortcut for hard stop of program and GUI controls for navigation between panels and data table cells...... 156

A.14 Button controls, part 1...... 157

A.15 Button controls, part 2...... 158

A.16 Button controls, part 3...... 159

A.17 Button controls, part 4...... 160

A.18 Input of the raw data into plots within the GUI for visualization...... 161

A.19 Continued data visualization control and establishing the contiuous loop for the program. . . . . 162

A.20 Creation of the class for the Fit of the Stark Spectra and description of the properties and starting parameters of the ﬁt...... 163

A.21 Sets the expected limits of the ﬁt and creation of the data when ﬁtting only to the absorption spectrum...... 164

A.22 Function deﬁned for ﬁtting the Stark and absorption spectra simultaneously. The upper and lower bounds govern the limits of the parameters as set by the program and can be altered to allow or restrict Gaussian band width, amplitude, and position...... 165

xix A.23 Alternative fit performed for confidence only from the absorption only fit to the Stark spectra...... 165

A.24 Plotting the fit at any step of the fitting process to establish the strength of the fit with the given weighting of Stark and absorption data set...... 166

A.25 Absorption data plotting functionalities of the raw data, the ﬁt and the residuals. Maximum number of transitions is established here at ’10’ but may be increased at the risk of overparametizing the ﬁt...... 166

A.26 Stark data plotting functionalities of the raw data and ﬁts. Maximum number of transitions must agree with the maximum number of absorption transitions...... 167

A.27 Monte Carlo ﬁtting method. Randomly picking starting parameters and reperform- ingtheﬁt...... 167

A.28 Output of the Monte Carlo ﬁtting results...... 168

A.29 Calculation of approximated errors from the Monte Carlo ﬁt. It is unlikely that these results will be lower than the experimental error and are used as the functional error of values collected for electron transfer quantities...... 168

A.30 Output of the calculated errors during the Monte Carlo ﬁt...... 169

A.31 Creation of a subﬁgure pop-up that details the Monte Carlo ﬁt, showing a graphical representation of the consistency of the values...... 169

A.32 Exporting the ﬁts for use in subsequent analysis or ﬁgure creation...... 170

A.33 Deﬁnition of the absorption ﬁtting process...... 171

A.34 Definition of the simultaneous fitting process. Additionally the method for fitting the absorption and Stark spectra...... 171

A.35 Output of the ﬁtted data to update the plots after several ﬁtting steps have been performed. . . . 172

A.36 Deﬁnition of the iterative Stark ﬁtting process...... 172

A.37 Plotting of the individual derivatives from the ﬁt and updating their respective fundamental electron transfer quantities...... 173

A.38 Conversion of the calculated Stark parameters into Bχ and Cχ components...... 173

A.39 Creation of the class for the Stark spectral data and the paramaters and methods contained. Additionally the loading of the Stark data from a ’.mat’ ﬁle...... 174

A.40 Extraction of the ﬁlename for display within the GUI, approximating a baseline, normalization of the data and conversion to ∆ε...... 175

A.41 Function for ﬁeld normalization based upon the inputs of ﬁeld strength, pathlength refractive index, and angle...... 175

xx B.1 Initialization of parameters controlled, collected and displayed, part 1...... 176

B.2 Initialization of parameters controlled, collected and displayed, part 2...... 177

B.3 Function for a background correction if the PDA is collecting ambient light. It records the value over a long period of time and averages it out, takes a value four standard deviations from the center to prevent overcorreciton...... 177

B.4 Controls for the lock-in ampliﬁer...... 178

B.5 Monochrometer step control, part 1...... 178

B.6 Monochrometer step control, part 2...... 179

B.7 Monochrometer step control, part 3...... 180

B.8 Baseline collection control...... 181

B.9 Low-temperature absorption collection control...... 182

B.10 Stark spectrum collection control...... 183

B.11 Export of Stark data...... 184

B.12 Export of Low-temperature data...... 185

B.13 Export of reference blank data...... 185

xxi LIST OF SCHEMES

2.1 Ruthenium(II) Tris(4,4’-R-2,2’-bipyridine) complexes investigated...... 34

2.2 Illustration of the distances used where rgeom represents the approximate geometric distance between the metal center and geometric center of the bipyridyl ligand, and rCT is the charge transfer distance calculated from equation 2.6 with the experimentally determined ∆µ values...... 48

3.1 A simplﬁied molecular orbital diagram of the singlet (A and B) and triplet (C and D) electronic transitions utilized to analyze the absorption and Stark spectra. Also shown are molecular orbitals of e symmetry determine by TDDFT...... 69

3.2 The geometric distance, rgeom, and the measured charge transfer distance, rCT , for 2+ the indicated [M(bpy)3] complex...... 75 3.3 The radial distribution functions of the frontier metal d-orbitals. The M-N bond 2+ and M-bpy center distances in [M(bpy)3] are indicated as vertical lines...... 76

xxii CHAPTER 1–Photo-Induced Charge Transfer and Stark Effect Theory

1.1 Motivation

Light driven reactions are older than life itself on this planet as sunlight has been beating down on the

Earth’s surface from the moment it formed. While the spectrum of the Sun was quite different from the spectrum we experience today, it still shone down on the planet and likely inﬂuenced the formation of life itself.1 Within the ﬁrst billion years, plant life began and began to build up the oxygen rich atmosphere we know today.2,3 At the same time further photolysis of the produced oxygen created the protective ozone layer, credited with allowing for animal and human life to exist on this planet.4,5 All of these photochemical processes existed long before humankind’s ability to study or observe it and continues through this day still as a fundamental method of energy accumulation on this planet.

The current investigations into photochemistry within the academic world today do not reﬂect the beginnings of the ﬁeld. Most of the photoreactions that occur on a daily basis are not immediately observable by the naked eye, but rather seem to just be a part of the aging process. Without proper spectroscopic tools to monitor photoreactions, the earliest interactions that should have been seen were for those of photochromic dyes. Reports have claimed that in times as early as Alexander the Great photoreactions had been observed and understood as a basic concept. His ’Rag Time Band’ of soldiers supposedly carried dyed cloth that when exposed to sunlight would change colors and signal the start of an attack. Likely more instances of observation and utilization of the effects the Sun has had on objects have occured but true investigation into the underlying fundamental principles were not seen for some time.

1 Chemists and scientists of many other ﬁelds have investigated and continue to investigate the

capabilites of photochemistry for a multitude of systems. From doctors and biologists researching skin

cancer6, to physicists probing the very nature of light itself,7 groups from all interests have developed a

strong framework within which modern day photochemistry can exist. The broadness of the topic often times

make it rather daunting task to tackle how it works, but the complexity of these tasks can be broken down to

ﬁnd the photochemical steps. At its core, photo-induced electron transfer involves the chemical effects light

can cause, and so the photochemical steps can be split further into their fundamental units until we have

isolated two fundamental steps that are the same in the aspect of charge transfer but different in their system’s

conditions: absorption of a photon and subsequent electron or energy transfer. As such, this dissertation

serves only to attempt to analyze not even the absorption and electron transfer in general, but to develop a

better understanding for and methods for probing those fundamental steps within organometallic complexes.

1.2 Photo-Induced Charge Transfer

While many will argue that photochemistry originated at different times for different ﬁelds, it is likely

that photochemistry was not discovered as a utilization of photons and not just the heat from the Sun until the

age of Priestly. In the late 18th century, Joseph Priestley studied the inﬂuence light had on the production of

‘dephlogisticated air’ (i.e. O2) in water using a ‘green substance’ (chlorophyll).8 This process is better

known today as photosynthesis. Considering the time from this publication to now when it is still a struggle

to replicate the system into a less complex model system, the difﬁculty of studying these simple steps should

become self-evident. One of the complexities of the system however is it includes both light absorption and

electron transfer, along with several other steps.

Looking to break down the complex process that is photo-induced charge transfer beginning with

light absorption; starting in the early 1800s Theodor Grotthuss developed a simple principle known as the

Principle of Photochemical Activation which states simply that only light which is absorbed by a system can

2 bring about a photochemical change. While a seemingly obvious statement in modern times, this does help to simplify our potential interactions by requiring the absorption and inclusion of the light’s energy within the molecular system. It also rules out the aforementioned thermal reactions driven by simply heat exchange from sunlight.

Following the absorption of a photon, there needs to be a guiding framework for potential use of an excited state. In the early 1900s two German-born physicists, Johannes Stark and Albert Einstein independently developed another law, known as the Photochemical Equivalence Law.9 At its core it establishes that each individual absorbed photon will cause a chemical or physical reaction. While more modern studies show that this law is not necessarily rigidly followed as biphotonic processes have been discovered, the fundamental levels of moderate intensity light sources still follows the Stark-Einstein Law.

Alongside these photochemistry developments, research into photosynthesis was continued by

Ingenhousz and Saussure as they were able to establish the necessity of light in macroscopic photosynthesis.10,11 The difﬁculty however in understanding these studies and their application to the greater picture of electron transfer was that the existence of the electron was not fully established for nearly 100 years when J. J. Thompson and Milikan’s experiments conveyed the presence of the electron as a particle without a doubt.

Even after proof of the electron had come to light, the actual governing principles of their transfers within chemical systems was not fully developed until the 1950s. R. A. Marcus developed the ﬁrst generally accepted outer-sphere electron transfer.12 In collaboration with N. Hush, Marcus was able to further develop the theory to include inner-sphere electron transfer and the complete accepted Marcus-Hush electron transfer theory.13 While this theory is incredibly robust, it only applies a semi-classical approach resulting in some incongruity with experimental results. The theory however does provide a stable groundwork from which others such as J. Jortner were able to extend the theory to a fully quantum mechanical level.14 The details of this electron transfer theory will be included in the next section.

3 With this brief outline of the history and fundamentals of each step, I hope that the statement I made at the outset that nearly 250 years of research on the subject still does not grant us all the answers as we continue to develop a better understanding of these incredible fundamental steps of chemistry. In addition the tools provided by those who have researched for many years past are the only way to proceed forward. This dissertation will discuss the development of a relatively unused technique of Stark spectroscopy to probe the

Franck-Condon states of molecules, or the molecular conﬁguration after absorption of a photon and any required electronic motion without any geometric changes in order to better understand a gap in overall photochemical processes today.

1.3 Electron Transfer Reactions

As was mentioned, the most recent and likely most broadly applicable theory and background to be considered for the importance of the desired fundamental electron transfer quantities is the theory of Marcus and Hush for outer- and inner-sphere electron transfer.12,13 The extended details from Jortner and Kuznetsov to a fully quantum understanding can be read for further details that were deemed unessarily nuanced for the purpose of this dissertation.

In electron transfer reactions, there are three main types of reactions; intermolecular, intramolecular, and interfacial. Intermolecular reactions involve the transfer of an electron between a donor and an acceptor that are dissolved in ﬂuid solution. In this type of reaction they must diffuse and collide to allow for an electron transfer to occur. Intramolecular reactions differ in that the donor and acceptor of the transfer are linked to each other through chemical means. This type of electron transfer is of the most interest to the contents of this dissertation and in particular metal-to-ligand charge transfer chemistry in general. Interfacial follows a lot of similarities to that of the intramolecular electron transfer, however in this case the binding between the donor and acceptor is the binding to a heterogenous surface such as the sensitized dyes that are bound to TiO2 within dye sensitized solar cells.

4 Simply knowing how to classify an electron transfer however is not useful information. The development of Marcus theory allowed for a much more concrete way of understanding the principles involved in electron transfer. The pervasive nature of Marcus theory in modern electron transfer theory stems from the semiclassical expression, eq. 1.1.

2π H2 (∆Go+λ)2 DA − 4λk T kET = √ e b (1.1) ~ 4πλkbT

o Where kET is the electron transfer rate, ∆G is the driving force of the transfer, λ is the reorganization energy, and HDA is the degree of electronic coupling between the donor and acceptor wavefunctions.

While used frequently throughout the literature with estimations for HDA being made by other techniques, it is an element of the equation whose certainty is somewhat lacking. The generalized

Mulliken-Hush expression that follows is eq. 1.2

ν µ max eg HDA = √ (1.2) 2∆µgeom

where νmax is the energy required for the transition in wavenumbers, µeg is the transition dipole moment and

∆µgeom is the change of dipole calculated for a completely localized electron transfer. It should be reiterated that calculation of HDA from this point utilizes assumptions when attempting to calculate the ∆µgeom as the geometric distance is often ill-deﬁned in systems with diffuse orbitals. It is for this reason that establishment of an experimental ∆µ for the electron transfer would allow a more accurate development of this term.

For a 2-state model, the above equation becomes eq. 1.3

ν µ ν µ H = √ max eg = √ max eg (1.3) DA 2 2 1/2 2(µD − µA) 2[(∆µeg) + 4(µeg) ]

5 Where (µD − µA) is the nonadiabatic change in dipole moment and ∆µeg is the change in dipole moment of the electron transfer. It is through Stark spectroscopy that I hope to investigate the dipole moment of electron transfer for use in better understanding not only the excited states of molecules but also to more accurately calculate values through electron transfer kinetic experiments and analysis. Within this dissertation all electron transfers could indeed by classiﬁed as intramolecular, however the principles developed do not necessitate that classiﬁcation.

1.4 Electric Fields in Chemistry

As will soon be more clearly described, the use of an electric field to distort the electronic state of a molecule provides an incredibly precise way to probe only the electronic state of a molecule without any need to account for geometric or diffusional quantities in electron transfer processes. However, it should be noted that this isn’t the first time eletric fields have been utilized or observed in chemistry. While the distinction between physics and chemistry can often be blurred when probing electronic motion, for the sake of discussion it is assumed that any system dealing with discrete electron transfer to, from, or within a molecule can be considered a part of chemistry.

Most of the older literature starting from Priestly, Coulomb, Faraday and Maxwell onward on electromagnetism initially dealt simply with the inﬂuence of a single charged particle, the interaction between two charged particles that eventually ballooned to more complex systems. In recent years electric

fields have been postulated to have strong impacts on the ability for electron transfer processes in solar devices as charge is collected in one location.15 Electric fields have influences in biological processes in many cases such as the impact on the active site of enzymes.16 Interestingly enough in just the last several years, electric fields have begun to be used as a ’smart’ reagent in chemical reactions, catalytic and otherwise, to change the reaction pathway to control ratios of isomeric products and unlocking new pathways for hydrogen abstraction, epoxidation, C-C bond forming reactions and more.17,18

6 The fundamental electric ﬁeld measurments were made originaly by the like of Priestly and Coulomb, through investigating the force felt by a charge at some distance from a source charge, leading to eq. 1.4

Q E = k (1.4) r2 where E is the electric ﬁeld at position r due to a point charge Q and k is a constant that was experimentally determined. This process however only dictates how individual charges interact with each other, not how they operate on a bulk scale and becomes cumbersome in any attempt to extrapolate to multi-charge systems.

The understanding of how these ﬁelds interact with complex molecules or bulk systems wouldn’t be effectively investigated until Faraday and Maxwell continued the development of the electromagnetism.

While potentially observed through the development of magnetism and the theory surrounding it, the link between electric and magnetic fields is generally accepted to first be discoved by Michael Faraday in 1831 when he demonstrated that the introduction of a wire into a magnetic field caused current to flow along the wire. After further developement of Faraday’s work in electromagnetic theory, Maxwell in 1864 published his first of two crowning works which established a unifying mathematical explanation for electromagnetism.

Later on, in 1873, Maxwell published the second of his crowning works, which established most of the fundamental equations still used today in how electric ﬁelds and electric charges interact, as described in eq.

1.5.

Z 1 Z E · da = ρ dV (1.5) S ε0

This equation better known as Gauss’s law describes how electric charges produce an electric ﬁeld, or in a more nuanced form that the total charge contained within a closed surface is proportional to the total electric

ﬂux across the surface. Within the equation, E is the electric ﬁeld, ε0 is the electric constant, and ρ is the total charge expressed as the charge density.

7 The most impactful result for the purpose of this disseration is the ﬁrst effect he detailed; electric charges will attract or repel one another with a force inversely proportional to the square of the distance between them: unlike charges attact and like ones repel. This fundamental logic is what dictates how electric

ﬁelds, or effectively interaction of a charged particle at some given distance, will interact with another charged particle. Using this principle Stark spectroscopy along with many other effects are not just possible to observe but also to explain and predict their interaction.

Given the research of my colleagues I would be remiss to not discuss in some detail the impact electric fields have proven to have within solar devices such as dye sensitized solar cells. In 2010 Ardo et al. reported on observed ’Stark effects’ that were not fully screened.15 This was observed through the injection of electrons into a semiconductor surface that altered the metal-to-ligand charge transfer absorption signal of the sensitizing molecules that were in their ground state. Through many more studies within and outside of the Meyer group, strong evidence for substantial electric fields at the surface has been determined. Evidence has shown that the electric fields generated in these systems can influence the lifetime of the excited states within the device and in turn the overal device performance. This example not only shows a very practical instance of electric fields, but also how quickly on a molecular level charge density can accumulate and at short distances produce an overwhelmingly strong electric field.

The reactivity of enzymes is a substantially complex study for each individual enzyme due to the complexity of the structures created and the environments they exist within. However, as electric fields have become easier to produce and measurements of them on a molecular scale have become possible it has opened a new avenue of research into their reactivity. A recent publication by Fried demonstrated this concept in the measurement of the electric field present within the ketosteroid isomerase enzyme.16 In their studies they observed; electric fields within active sites were generated by all non-covalent interactions, that these interactions could be measured through the use of the vibrational Stark effect, a chemical reaction can be catalyzed by the electric field through the alignment of the field with the transition state of the reaction,

8 and electrostatic catalysis is already pervasive in enzymes due to most biological reactions involving substantial charge rearrangement.

While the prospect of utilizing electric fields as enzymes do provide a exciting avenue forward in sythetic chemistry, the complexity of the theory and the confirmation from experiment due to mechanical constraints often proves difficult as the influences of an external electric field on a reaction influence many components of the reaction. In 2010, Shaik et al. calculated that electric fields could drive Diels Alder reactions, work that was later confirmed in 2016.17,18 This began further testing through calculation and confirmation through experimentation that oriented external electric fields, OEEFs, could be utlized as reagents or more accurately reaction surface manipulators and were no longer just a dream. This process takes advantage of the fact that through applying a strong enough electric field, normally covalent systems can be electronically restructured to a substantially more ionic state, unlocking new reactions and improving the efficiency of those already obtainable. In particular Shaik in a recent publication discusses the possibility of utilizing an electric field to make a hydrogen bond an ionic bond. While these procedures are still being refined and require substantial mechanical improvements to be fully utilized, this basic process of disturbing the electronic structure with an electric field is what is utilized in Stark spectroscopy.

This section intended to make clear the rich history of use and observation of electric ﬁelds and how they work. The discoveries and efforts of those in the past have allowed for nuanced techniques like Stark spectroscopy to be possible.

1.5 Stark Effect Theory

To preface the work and instrumentation contained within this document, a deeper understanding of

Stark spectroscopy is required. Within this and the following section the discovery and evolution of the technique, alongside the relevant theory and results acquired, will be presented.

9 To understand what Stark spectroscopy measures one must ﬁrst analyze what the Stark effect is itself.

Discovered by a German Physicist, Johannes Stark, in 1913, the Stark effect is the perturbation of an absorption and/or emission spectra due to an external applied electric ﬁeld. This effect is the electric analogue of the magnetic ﬁeld induced Zeeman effect discovered 17 years earlier, commonly utilized for nuclear magnetic resonance spectroscopy. Since that time the Stark effect has been used for both absorption and emission spectroscopies, ranging into the vibrational regime.

Figure 1.1: The splitting caused by Zeeman (Left) and Stark (Right) effects on the n=2 and n=3 levels of a hydrogen atom. Note: the splitting caused by these effects is substantially smaller than the splitting between principle quantum number energy levels.

In order to simplify the Stark effect in as friendly terms as possible, a single atom is considered ﬁrst.

With the assumption that the electric ﬁeld will perturb the electronic states in the atom, the basic Hamiltonian for the atom in an electric ﬁeld is described by eq. 1.6,

H = H0 − E~ · P~ (1.6)

10 where H0 is the Hamiltonian in the absence of an external electric field, P~ is the electric moment of the atom, and E~ the applied electric field. A constant, controlled, and known applied electric field is assumed from which it follows that the spectral changes observed due to the Stark effect are governed by the matrix components of P~ . In particular, the only component of the P~ matrix that is relevant is that along E~ . As we can choose any axes for our atom, we align them with the z-axis, so that the z-component alone is of significance. Pz is the dipole radiation of the atom which is polarized with its electric vector parallel to the z-axis. The selection rules and the theory of line intensities are applicable here, however investigation of these would expand this section beyond an intentional scope, and can be found elsewhere.19 In a given atom having two unperturbed electronic states A and B, an electronic transition can occur between these two states provided it follows the appropriate selection rules. Writing (A|P |B) for the matrix component Pz connecting two energy states, selection rules provide that the term will vanish unless:

(a) They follow the Laporte rule, i.e. A and B are of opposite parity

Figure 1.2: Allowed optical transitions between the n=2 and n=3 levels of a hydrogen atom under the splitting effects due to an applied electric ﬁeld.

(b) The angular momentum quantum numbers of A and B are equivalent or off by 1; JA = JB or

JB ± 1

11 (c) Z-component of the angular momentum of the atom are equivalent; MJA = MJB

Considering Russell-Saunders (S–L) coupling where spin angular momentum S and orbital angular momentum L are diagonal when H0 is diagonal we may include the rules:

(d) SA = SB

(e) LB = LA,LA ± 1

With selection rules and basic principles in place we can begin to develop the the Stark effect. At its discovery, Schroedinger¨ had not yet postulated his equation or developed quantum theory towards how we understand it today. However, both for its accuracy as well as established nature we will outline the Stark effect further through Schroedinger’s quantum theory for a hydrogen-like atom.

Again starting from basic principles we have Schrodinger’s equation

δ2ψ δ2ψ δ2ψ 2m + + + e (E − U)ψ = 0 (1.7) δx2 δy2 δz2 ~2

Where me is the mass of an electron and ~ is an abbreviation for h/2π. U is the potential energy of the system and E is the total energy. In the case of a Stark effect, a nucleus of +Ze, where Z is nuclear charge and e is the charge of an electron, and a homogenous ﬁeld of strength D being applied, the potential energy can be described by eq. 1.8

−Ze2 U = + eDz (1.8) r where again the z-axis is the direction of the ﬁeld.

In order to separate the variables a new coordinate system must be used. As has been previously done in Stark spectroscopy, a parabolic coordinate system can be used, through the representation of x, y and z as shown in eq. 1.9. p p ξ − η x = ξη cos ϕ, y = ξη sin ϕ, z = (1.9) 2

12 Using polar coordinate system of ξ, η, ϕ where variable range is deﬁnded as shown in eq. 1.11.

0 ≤ ξ ≤ ∞, 0 ≤ η ≤ ∞, 0 ≤ ϕ ≤ 2π (1.10)

In this coordinate system useful terms for solivng Schroedinger’s¨ equation include eq. 1.11-1.13.

ξ + η r = (1.11) 2

1 δξ2 δη2 δs2 = (ξ + η) + + ξηδϕ2 (1.12) 4 ξ η

4 δ δψ δ δψ 1 1 1 δ2ψ ∆2ψ = ξ + η + + (1.13) ξ + η δξ δξ δη δη 4 ξ η δϕ2

Rewriting Schroedinger’s equation, eq. 1.7, with parabolic coordinates it becomes eq. 1.14.

δ δψ δ δψ 1 1 1 δ2ψ m eD(ξ2 − η2) ξ + η + + + e E(ξ + η) + 2Ze2 − ψ = 0 (1.14) δξ δξ δη δη 4 ξ η δϕ2 2~2 2

To solve this expression we substitute for two functions, one dependent on ξ and one on η, eq. 1.15.

cos ψ = M(ξ)N(η)sin(s − 1)ϕ, (1.15)

Solving we get the two plain differential equations, eq. 1.5 and 1.17;

d2M 1 dM m E Ξ (s − 1)2 1 m eD + + e + − − e ξ M = 0, dξ ξ dξ 2~2 ξ 4 ξ2 4~2

(1.16)

13 d2N 1 dN m + E Ξ0 (s − 1)2 1 m eD + + e + − − e η N = 0 (1.17) dη η dη 2~2 η 4 η2 4~2 where the constants Ξ and Ξ0 must satisfy eq. 1.18

m Ze2 Ξ + Ξ0 = e (1.18) ~2

As described by Epstein? , the approach then follows to pick constants E and Ξ so that one of the integrals becomes ﬁnite at ξ or η = 0 and vanishes at ξ or η = ∞.

This results in reaching the ﬁrst order Stark effect as eq. 1.19,

3 µe α1 = 2 2 (l − m) (1.19) 10 ~ α0

where α0 is a constant determined from the vanishing case, and l and m are the angular and magnetic quantum numbers respectively. The second order Stark effect is found to be described by eq. 1.20,

2 2 mee 2 2 2 α2 = 4 5 17(l + m + n) − 21(l − m) − 9n + 18n + 10 (1.20) 1024~ α0 where n is the principle quantum number.

These derivations provide the foundation for the Stark effect and can be used to determine the expected energy shifts of orbitals of an atom. Ultimately however, the desire is to determine the electric moment of an atom, and not simply to predict and observe the phenomena dictated by the above equations and an applied magnetic ﬁeld. Moreso, the hope would be to apply this analysis to more and more complex systems, i.e. molecules and transition metal complexes. However, within these real molecules there are no longer atomic transitions, but rather broad absorption and emission bands are obtained that can often be represented by symmetric distributions; such as Gaussians and Lorentzians.

14 At a rudimentary level the perturbation of the energy levels of a molecule behaves identical to those of an individual atom. That is to say for a given transition, the required transition energy can be perturbed to a higher or lower energy. With molecules the orientation and directionality of the molecule and transition become important in determining which direction the energy shifts as will be discussed in the following section, however for descriptive purposes assume that the transition is either aligned parallel, anti-parallel, or perpendicular to the applied ﬁeld causing a decrease, increase, or no change in energy respectively for the excitation of interest. In Figure 1.3, this phenomena is broadly depicted through the translation of the gaussian band.

Figure 1.3: Graphical depiction of a band shape distortion in the presence of an applied electric ﬁeld.

The following section illustrates how Stark spectroscopy, lineshape analysis, and the underlying theory can be expanded into the realm of molecules to extract fundamental electronic transition quantities,

FETQs.

15 1.6 Stark Spectroscopy Theory

As with any form of spectroscopy, Stark spectroscopy requires a robust way to model the spectral data. Stark spectroscopy allows determination of numerous, fundamental electronic transitions quantities which include changes of polarizability and dipole moment, ∆α and ∆µ.

Wolfgang Liptay and Jorg¨ Czekalla developed the theory for the effect of an externally applied static electric field on the absorption of polarized light by a sample at thermal equilibrium. In their works they showed that the absorbance change due to the applied electric field scaled quadratically with the field strength. Additionally, they found that the measured Stark spectrum could be expressed as a linear combination of the zeroth-, first-, and second-order derivatives of the absorption spectrum.20–22

Should the reader choose to investigate Liptay and Czekalla’s work they will find a very thorough theoretical analysis. Their key assumptions were absorption of a single photon and one electronic transition event is occurring upon light absorption. The derivation from these initial works is rather cumbersome in nature as often first passes of models tend to be. The derivations herein will be performed using an angular averaging method within the ”direction cosine” method. The direction cosine method refers to the process of defining vectors in different frames by a single set of orthonormal basis vectors. This is a useful tool when comparisons between an individual randomly oriented molecular frame and the laboratory frame are of significance. Within the original derivations of Liptay, the orientation of the molecules in the lab frame is given by their direction cosines with regard to their molecular properties in the molecular frame and the laboratory properties in the laboratory frame.

Within Liptay’s theory for Stark spectroscopy the sample consists of molecules with unrestricted angular mobility. While there are many properties that could be considered, the parameters of importance are those of the electronic excited states and optical transitions to them from a ground state. These parameters are used to deﬁne the individual molecules as well as the overall ensemble, these include the permanent

16 Figure 1.4: Demonstration of reassigning coordinates x,y,z in a new basis through the use of direction cosines.

dipole moment, ~µg, the change in dipole moment after the transition, ∆~µ, the transition dipole moment, ~µeg, the tensors for polarizability, ~α, and for the change in polarizability after the transition ∆~α. As the value of these parameters are innate to each molecule, their orientations within the molecular coordinates are ﬁxed.

For simplicity it is also assumed that the band shapes of transitions in the presence of an applied ﬁeld are negligibly altered from band shapes in the absence of a ﬁeld. In more detail, the band shape function, a

Gaussian, in the presence of ﬁeld, s(ν)F , can be compared to the same function without an applied ﬁeld, s(ν),

s(ν)F = s(ν − ∆ν) (1.21) where ∆ν is the ﬁeld induced shift in frequency, also known as the Stark shift, eq. 1.21. For a small Stark shift relative to the width of the overall band, the change in the shape, ∆s, can be expanded with a power series by the Stark shift as eq. 1.22.

∞ X 1 dns ds 1 d2s ∆s = (−1)n (∆ν)n = − ∆ν + (∆ν)2 (1.22) n! dνn dν 2 dν2 n=1

Terms beyond the squared term are considered negligible and are ignored. The magnitude of ∆s dependent on the ﬁeld strength as will be described later.

17 In the absence of an applied electric ﬁeld, the absorbance, A, is related to the

A = cl (1.23)

concentration, c, through the Beer-Lambert law, eq. 1.23. This relation is not particularly useful for Stark spectroscopy however, as it does not consider the aforementioned vectors or tensors by which the molecular transitions were deﬁned. To reiterate Beer’s Law in a more beneﬁcial manner, we combine the concentration and path length of our sample into a ensemble of transmission-attenuating molecules, each with an averaged D E interaction between polarized light and the transition dipole moment of the absorption, Φ2 . With this Eµeg in mind, the Beer-lambert law is rewritten as

D E bs A = bs Φ2 = (1.24) Eµeg 3 here b is a constant related to the oscillator strength of the transition, s is the band shape function, and the D E quantity Φ2 is equivalent to the cosine of the angle between the polarization of the incident light and Eµeg the transition dipole moment of the sample. In an isotropically distributed solution, this averages out numerically to be 1/3.

To this point in the discussion, the absorption has not included any perturbation induced by an applied electric ﬁeld. To acomplish this, W (F ), is introduced as the angular distribution function that represents the probability that a molecule will be in a speciﬁc orientation. For an isotropic solution, W=1.

Absorbance in the presence of an external ﬁeld therefore can be given by eq. 1.25,

D 2 E D 2 E D 2 E AF = b (s + ∆s)ΦEµeg W = bs ΦEµeg W + b ∆sΦEµeg W , (1.25)

18 where the shape function, s, does not depend on the orientation while the ﬁeld-induced change in shape, ∆s, does, as was described in eq. 1.22.

Substituting ∆s from eq. 1.22, the absorbance change due to the applied ﬁeld is written as eq. 1.26.

D 2 E D 2 E ds D 2 E ∆A = AF –A = b (s + ∆s)ΦEµeg W = bs ΦEµeg W − b ∆νΦEµeg W dν (1.26) b d2s D E + (∆ν)2Φ2 W 2 dν2 Eµeg

Lastly by taking into account the result bs = 3A/ν from eq. 1.24, both ds/dν and d2s/dν2 can be assessed again to rewrite the ﬁeld-induced absorption change as eq. 1.27.

D 2 E d(A) D 2 E ∆A = AF –A = A 3 ΦEµeg W − 1 + (−3) ∆νΦEµeg W dν (1.27) d2(A) 3 D E + (∆ν)2Φ2 W dν2 2 Eµeg

At this point the aforementioned zeroth, first, and second derivatives of the absorption spectrum can be readily identified within the expression as the first, second, and third terms respectively. This equation provides us with a method to model our Stark spectra, however it does not yet provide a connection between the measured Stark spectrum and the FETQs. In order to reach that point continued modifications must be made.

First investigating the angular distribution function W (F ), which was introduced for purposes of relating the orientation of the molecules to the absorption. At equilibrium, for a given temperature T and an applied electric ﬁeld, F~ , the distribution of molecules by energy can be given by eq. 1.28,

e−E00/kT W = (1.28) e−E00/kT where E00 is the energy of the interaction between the molecule and the electric field. Alternatively, E00 can be defined as a sum of the interactions between the ground-state permanent dipole moment and the field as

19 well as the induced dipole moment in the presence of that same ﬁeld.

1 F 2 X E00 = −~µ · F~ − F~ · ~α· F~ = −µ F Φ − Φ α Φ (1.29) g 2 g F µg 2 F i ij F j ij

Where ΦF µg is the cosine of the angle between the ﬁeld and the z-axis, ΦF i and ΦF j are the direction cosines of the angles between F~ and the axes in a molecular frame, and αij are the components of the polarizability tensor. With the new expression for the interaction energy, combining eq. 1.28 and 1.29 a new expression relating the angular distribution function with the vectors and tensors of interest is achieved.

Continuing to hold the previous assertion that hW i = 1, and operating under the case of a ‘weak’ electric

ﬁeld limit where µF/kT << 1 and αF¯ 2/2kT << 1, we can rewrite the numerator of the angular distribution function as eq. 1.30.

2 2 2 00 µgF µgF F X e−E /kT = 1 + Φ + Φ + Φ α ΦF j (1.30) kT F µg 2k2T 2 F µg 2kT F i ij ij

For the denominator we can include the simpliﬁcations that α¯ is the average polarizability, and that D E Φ = 0 and Φ2 = 1/3, and hΦ Φ i = (1/3)δ . This leads to eq. 1.31, F µg F µg F i F j ij

2 2 2 D 00 E µ F F α¯ e−E /kT = 1 + g + (1.31) 6k2T 2 2kT further simpliﬁcation can be achieved if in eq. 1.31, the second and third terms are replaced by x and considering that x << 1, an approximate relation of 1/(1 + x) = 1 − x can be utilized.

2 2 µgF µgF F 2 P 1 + ΦF µ + 2 2 ΦF µ + ΦF iαijΦF j W = kT g 2k T g 2kT ij 1 + x (1.32) 2 2 2 2 2 2 µgF µgF F X µgF F α¯ = 1 + Φ + Φ + Φ α ΦF j − + kT F µg 2k2T 2 F µg 2kT F i ij 6k2T 2 2kT ij

20 In order to utlize this relation for analysis of experimental data in hopes of reaching FETQs, it is convenient to rewrite it in the context of Legendre polynomials. To do this eq. 1.32 is rearranged as eq. 1.33

W = 1 + Wd1 + Wd2 + Wp (1.33)

Where the individual components are given by eq. 1.34-1.36,

µ F W = g Φ (1.34) d1 kT F µg

µ2F 2 µ2F 2 W = g Φ − g (1.35) d2 2k2T 2 F µg 6k2T 2

F 2 X F 2α¯ W = Φ α Φ − (1.36) p 2kT F i ij F j 2kT ij

To develop a more conceptual picture of W (F ) it is useful to consider the meaning of each term. The

first term “1” is present to describe a purely isotropic angular distribution of molecules. This is both by definition, recall hW i = 1, and what the distribution would be in the absence of an electric field as all subsequent terms would equal zero. The first perturbation term Wd1 describes the orientation of the dipole moments towards the field illustrated by the linear dependence on the field. The second term Wd2 describes the alignment of the dipole moments parallel to the field shown through the quadratic dependence of the field.

The ﬁnal term Wp has two separate components contained within that hold information of the polarization tensors and their alignment with the ﬁeld. It should be noted that Wp is not orientation dependent.

As eq. 1.33 provides a useful representation of W (F ). The only other consideration required is the angular dependence of the Stark shift. In the applied electric ﬁeld, the energy levels are shifted by the Stark effect as was detailed in the previous section. From eq. 1.6 and eq. 1.29 we can see that the Stark shift is determined by the interaction between the effective dipole moment and the applied electric ﬁeld, where the effective dipole moment includes an induced dipole moment due to the polarizability. The Stark shift for the

21 ground and excited states can then be given as equations 1.37 and 1.38 respectively;

1 ∆E00 = E00(F ) − E00(0) = −~µ · F~ − F~ · α~¯· F~ (1.37) g 2

1 ∆E0 = E0(F ) − E0(0) = −~µ · F~ − F~ · α~¯0· F~ (1.38) e 2

0 where ~µg and ~µe are the permanent dipole moments, and α~¯ and α~¯ are the polarizability tensors of the ground and excited states respectively. Relating the ﬁeld induced energy change of the individual electronic levels to the Stark shift of the transition frequency, ∆ν, results in eq. 1.39.

∆E0 − ∆E00 1 1 ∆ν = = − ∆~µ· F~ − F~ · ∆α~¯· F~ (1.39) h h 2h

Similar to the orientation distribution, it is useful to split the Stark shift due to the dipole moment and that due to the polarizability.

∆ν = ∆νd + ∆νp (1.40)

Following the same process as eq. 1.28-1.32

F ∆µ ∆ν = − Φ , (1.41) d h F ∆µ

F 2 X ∆ν = − Φ Φ α Φ (1.42) p 2h F ∆µ F i ij F j ij

Successful reestablishment of the components of the original absorbance change due to the applied

external ﬁeld enables eq. 1.27 to be rewritten in more favorable terms. Substituting Φξ for ΦEµeg provides a

22 shortened notation, eq. 1.43.

2 2 2 2 ∆A = 3A Φξ + ΦξWd1 + ΦξWd2 + ΦξWp − 1 d(A) −3 Φ2∆ν + Φ2∆ν + Φ2∆ν W dν ξ d ξ p ξ d d1 2 d (A) 3 D 2 2E + 2 (∆νd) Φξ dν 2 (1.43) d(A) −3 ( Φ2∆ν W + Φ2∆ν W + Φ2∆ν W + Φ2∆ν W + Φ2∆ν W ) dν ξ d d2 ξ d p ξ p d1 ξ p d2 ξ p p d2(A) 3 D E D E D E + ( (∆ν )2 Φ2W + (∆ν )2 Φ2W + (∆ν )2 Φ2W dν2 2 d ξ d1 d ξ d2 d ξ p

D 2 2E D 2 2 E D 2 2 E D 2 2 E + (∆νd) Φξ + (∆νp) ΦξWd1 + (∆νp) ΦξWd2 + (∆νp) ΦξWp )

Unfortunately, this equation is quite unruly and difficult to utilize. The equation is simplified by removing all terms that have a higher than quadratic dependence on field strength, which for convenience are shown in the last 3 lines of the equation. As a reminder, Wd1 and ∆νd have a linear dependence with the field, Wd2, Wp, and ∆νp have a quadratic dependence. Following this simplification, there are several other steps that

D 2E simplify this equation. An average of orientations is taken, Φξ = 1/3, which when multiplied by the coefficient of the zeroth order term is removed alongside the –1 in the first line. A final averaging assists in

D 2 E D 2 E simpliﬁcation of 3 ΦξWd1 and −3 Φξ∆νd as the resultant expressions contain an odd number of cosine functions (cos3). Angular averaging of an odd number of cosines results in zero. With these adjustments made, a new and substantially more managable equation 1.44 results.

2 2 ∆A = 3A ΦξWd2 + ΦξWp d(A) −3 Φ2∆ν + Φ2∆ν W (1.44) dν ξ p ξ d d1 d2(A) 3 D E + (∆ν )2 Φ2 dν2 2 d ξ

The equation as shown above displays three terms; zeroth-, first-, and second-derivative components. It is also useful to consider the formulation as a separation into five terms; zeroth-, first-, and second-derivative

23 dipole-induced contributions and the zeroth- and ﬁrst-derivative polarizability contributions, allowing for the contribution of the dipole moments and polarizability to be separated.

While the model has been converted and simpliﬁed, it is still not in a usable presentation. The ﬁnal step in the development of the model involves the averaging of the remaining non-zero terms. For this process, the direction cosine method has been chosen although alternative methods can be used. To assist in this process a selection of well established formulas will be used

1 1 1 Φ2 = , Φ4 = , Φ2 Φ2 = (1.45) Ai 3 Ai 5 Ai Aj 15

1 2 1 Φ2 Φ2 = , Φ2 Φ2 = , hΦ Φ Φ Φ i = − (1.46) Ai Bi 15 Ai Bj 15 Ai Aj Bi Bj 30 where A and B represent axes in the lab frame and i and j are molecular axes.

At an initial glance, these expressions allow all of eq. 1.44 to be calculated. The difﬁculty lies in the fact that the transition dipole vector, ~µeg and the ground-state dipole moment vector, ~µg are not always perpendicular, and neither are the ﬁeld and polarization of the light. This is overcome by converting

Φ2 Φ2 to Φ2 Φ Φ where a and b are deﬁned as axes perpendicular to each other and ~µ . It is Eµeg F µg Eµeg F a F b eg useful to know how to average this expression.

D E 1 1 Φ2 Φ Φ = −δ + 3δ δ 3Φ2 − 1 + δ (1.47) Eµeg F a F b 45 ab µega µegb FE 3 ab

Where X δij = ΦaiΦaj (1.48) a

To begin assessing the angular averages of eq. 1.44, combining eq. 1.35 with the ﬁrst term (zeroth-derivative dipole)

24 Figure 1.5: Angles used with direction cosine to associate the polarization of light and electric ﬁeld with a common basis of the transition dipole moment, µeg.

D E 3µ2F 2 D E µ2F 2 3 Φ2 W = g Φ2 Φ2 − g (1.49) Eµeg d2 2k2T 2 Eµeg F µg 6k2T 2

D E D E which rearranged to place µ and µ in the same frame results in Φ2 Φ2 = Φ2 Φ Φ eg g Eµeg F µg Eµeg F a F b where a and b are perpendicular axes to µeg. Applying this to eq 1.44 and the completeness condition,

P 2 a Φaµ = 1, eq. 1.50 is given.

2 2 P P 2 2 D E 1 µ F Φµ a Φµ b µ F 3 Φ2 W = g a g b g 3Φ2 − 1 3δ δ − δ + 5δ − g Eµeg d2 30 k2T 2 FE µega µegb ab ab 6k2T 2 2 2 P P ! 1 µgF Φµga Φµgb X X X = a b 3Φ2 − 1 3 Φ Φ Φ Φ − Φ Φ 30 k2T 2 FE µga µegµg µgb µegµg µga µgb a b ab 2 2 P P 2 2 µgF Φµga Φµgb X µgF + a b Φ Φ − 6k2T 2 µga µgb 6k2T 2 ab ! 2 2 2 2 ! 2 2 X X 1 µgF µgF µgF = Φ2 Φ2 3Φ2 − 1 3Φ2 − 1 + − µga µgb 30 k2T 2 FE µegµg 6k2T 2 6k2T 2 a b 1 µ2F 2 = g 3Φ2 − 1 3Φ2 − 1 30 k2T 2 FE µegµg (1.50)

25 Where now the zeroth-derivative dipole contribution is in terms of an angle determined in the lab frame between the polarization of the light and the applied ﬁeld, ΦFE, and a molecule ﬁxed angle between

the transition dipole moment and permanent ground state dipole moment, Φµegµg .

The next two terms (ﬁrst- and second-derviative dipole) follows a similar process to result in eq. 1.52 and 1.54. D E 3µ ∆µF 2 D E − 3 Φ2 ∆ν W = g Φ2 Φ Φ (1.51) Eµeg d d1 hkT Eµeg F ∆µ F µg

D E µ ∆µF 2 µ ∆µF 2 − 3 Φ2 ∆ν W = g (Φ − 1) 3Φ Φ − Φ + g Φ (1.52) Eµeg d d1 15hkT FE µegµg µeg∆µ µg∆µ 3hkT µeg∆µ and 3 3∆µ2F 2 D E Φ2 ∆ν2 = Φ2 Φ2 (1.53) 2 Eµeg d 2h2 Eµeg F ∆µ

3 ∆µ2F 2 ∆µ2F 2 Φ2 ∆ν2 = 3Φ2 − 1 3Φ2 − 1 + (1.54) 2 Eµeg d 30h2 µeg∆µ FE 6h2

All angular averaging for the dipole-induced absorption changes is completed, but the polarizability-induced changes have not been averaged yet. For the zeroth-derivative polarizability term, following an analagous derivation, eq. 1.55 results.

* + D E 3F 2 X 3F 2α¯ D E 3 Φ2 W = Φ2 Φ α Φ − Φ2 Eµeg p 2kT Eµeg F i ij F j 2kT Eµeg ij 3F 2 X D E X F 2α¯ = Φ2 Φ Φ Φ α Φ − 2kT Eµeg F a F b ai ij bj 2kT ab ij   (1.55) 2 P 2 2 F X αii F α¯ F α¯ = 3Φ2 − 1 Φ α Φ − i + − 10kT FE  µegi ij µegj 3  2kT 2kT ij   2 P F X αii = 3Φ2 − 1 Φ α Φ − i 10kT FE  µegi ij µegj 3  ij

26 and the ﬁrst-derivative term is given by eq. 1.56.

* + D E 3F 2 X −3 Φ2 ∆ν = Φ2 Φ ∆α Φ Eµeg p 2h Eµeg F i ij F j ij   (1.56) 2 P 2 F X ∆αii F ∆¯α = 3Φ2 − 1 Φ ∆α Φ − i + 10h FE  µegi ij µegj 3  2h ij

With all of the angular averaging completed, eq. 1.44 can now be reestablished with the relevant cosine values. As the complete expression is cumbersome, it is ﬁrst written in shortened notation as eq. 1.57

d(A) d2(A) ∆A = F 2 A A + B + C (1.57) χ χ dν χ dν2

Where Aχ,Bχ, and Cχ are the coefﬁcients for the zeroth-, ﬁrst-, and second-order derivative contributions. Continuing from eq. 1.49-1.56 and taking this point in time to assert that the angle between F~ and E~ is χ and the angle between ~µeg and ∆~µ is ζ

Figure 1.6: Diagrams to deﬁne ζ in the context of a molecular frame (Left) and χ in the context of a laboratory frame (Right).

  2 P 1 µg 1 X αii A = 3 cos2 χ − 1 3Φ2 − 1 + 3 cos2 χ − 1 Φ α Φ − i , χ 30 k2T 2 µegµg 10kT  µegi ij µegj 3  ij (1.58) µ ∆µ µ ∆µ B = g (cos χ − 1) 3Φ cos ζ − Φ + g cos ζ χ 15hkT µegµg µg∆µ 3hkT   P (1.59) 1 X ∆αii ∆¯α + 3 cos2 χ − 1 Φ ∆α Φ − i + 10h  µegi ij µegj 3  2h ij

27 ∆µ2 ∆µ2 C = 3 cos2 ζ − 1 3 cos2 χ − 1 + (1.60) χ 30h2 6h2

At this point the goal proposed at the onset has been achieved. Eq. 1.57 represent a relationship between the measureable macroscopic quantities, A(ν), ∆A(ν),F,T, and χ, and the molecular quantities,

µg, ∆µ, α, ∆α, ζ, Φµgµeg , Φµegα, and Φµeg∆α.

Prior to continuing on to the experimental work it is helpful to understand the physical meaning of each derivative contribution and there is one last simpliﬁcation to be made within the context of speciﬁc experimental conditions.

In solution, the zeroth-derivative dipole term best represents the deviation from isotropic (random) distribution of transition dipoles as the ground state dipoles align with the ﬁeld. The absorbance change due to this effect is understood as linear dichroism. It follows then that in the solid state or for molecules with no ground state dipole, the molecules will not deviate from an isotropic ensemble. The zeroth-order derivative will indeed vanish completely if operating at the magic angle, cos2 χ = 1/3 or there is no ground state dipole.

The zeroth-derivative polarizability contribution has a large anisotropy component. In frozen media or with non-polar molecules there is not be a substantial degree of anisotropy. More speciﬁcally in an isotropic ensemble the term vanishes as

X Φµegi∆αijΦµegj =α ¯ (1.61) ij and X ∆αii = 3¯α (1.62) i

The first-derivative dipole contribution is a combination of the orientation of the ground state dipoles with the field and the Stark shift caused by the change in dipole moment. This first-derivative can be

28 considered as a method of detection for the ﬁeld-induced orientation of the molecules that is manifest as an average of red- and blue-spectral shifts in the absorption band, that for an anisotropic sample would be an effective red or blue shift. However, by rigidifying the media this effect as well vanishes or provides little contribution.

The first term in the first-derivative polarizability contribution follows the same vanishing as the zeroth-derivative polarizability contribution. The substantial change here however is the final term contribution of ∆¯α/2h which will be present regardless, allowing for a change in polarizability to be observed.

The second-derivative contribution is not easily simpliﬁed, as there are no polarizability contributions.

This does mean however that the second-derivative contribution is entirely dependent on the change in dipole moment. This expression can be rearranged to emphasize this fact by rearranging Cχ to eq. 1.63,

1 C = ∆µ2 3 cos2 ζ − 1 3 cos2 χ − 1 + 5 (1.63) χ 30h2

As a ﬁnal note for the derivation within this section, eq. 1.57 is rewritten here under the simpliﬁcations of an isotropically frozen sample with no ground state dipole with measurement at the magic angle

∆¯α d(A) ∆µ2 d2(A) ∆A = F 2 + (1.64) 2h dν 6h2 dν2

While the details of this section are substantially more in depth than required for understanding the experimental results, this derivation is of importance for expanding the concepts researched as well as providing an applicable baseline equation prior to the simpliﬁcations often used within the literature (those applied for eq. 1.43). Eq. 1.57-1.60 will be used in future chapters for the modelling of the obtained Stark spectra.

29 1.7 Summary

A rich and detailed history of measurements of electric ﬁelds, electron transfer, and photochemistry has provided the opportunity to probe some of the most intimate qualities of exicited states and electron transfer properties. In this dissertation I intend to address a methodology and ﬁrst results of investigating these properties in organometallic species through the use of Stark spectroscopy.

While Stark spectroscopy can prove to be substantially complicated, multiple methods of derivation including the one chosen here result in a concise model that can be utilized for the analysis of measurements on an ensemble of molecules made by electroabsorption and electroemission experiments. Two primary effects, the field-induced reorientation of the molecules and the Stark shift of their electronic absorption band, are described by these equation. Modern experimental techniques allows for further simplficiation by elimnating the field-induced reorientation through use of films or glasses containing an isotropic ensemble of the molecules. Equations 1.57-1.60 provide the basis for the fitting techniques used in all further chapters and for other researchers in this field and are of paramount importance to understand both final form and underpinnings for the extraction of FETQs from the absorption spectrum of a molecule in the presence of an electric field.

30 REFERENCES

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32 2+ CHAPTER 2–Excited State Dipole Moments of Homoleptic [Ru(bpy’)3] Complexes Measured by Stark Spectroscopy1

2.1 Introduction

2+ The metal-to-ligand charge-transfer (MLCT) excited states of [Ru(bpy)3] and related complexes have been of substantial interest over the past 50+ years. Use of these complexes extends from examination of fundamental principles to applications in photosensitized redox and acid-base chemistry.1–3 An early question concerned whether the excited state was localized on a single bipyridine ligand or was delocalized over all three ligands. Time resolved resonance Raman and Stark spectroscopies provided compelling evidence that the excited state was localized on a single ligand.4–6 Hence, visible light excitation of these complexes is well formulated as promotion of an electron from a metal d-orbital to the π∗ levels of a single bipyridine ligand resulting in a dramatic redistribution of the electronic charge and an 8.3 Debye change in the dipole moment, Eq. 2.17

II 2+ III – 2+* [Ru bpy3] + hν → [Ru (bpy )(bpy)2] (2.1)

The orientation of the excited state dipole has been shown to be of critical importance in excited state

Brønsted acid/base chemistry8, halide release9, and sensitization of wide band gap semiconductors.10–12

Here I report Stark spectroscopic measurements of homoleptic Ru(II) bipyridine with substituents in the 4 and 4’ positions of the bipyridine ligands, Scheme 2.1. The presence of electron withdrawing or donating

1This work was previously published in Journal of Physical Chemistry A, 123 (41), 8745, with contributions from A. B. Maurer, E. J. Piechota, and G. J. Meyer. Reprinted with permission. Copyright 2019 American Chemical Society.

33 Scheme 2.1: Ruthenium(II) Tris(4,4’-R-2,2’-bipyridine) complexes investigated. groups on the bipyridine ligands would be anticipated to inﬂuence the electronic distribution and hence the excited-state dipole moment.13,14 However, there is no direct experimental evidence that supports this expectation and the limited data available no such trend. Shin and coworkers reported Stark spectra of a

n+ family of pentamine Ru pyridine compounds of the general formula, [Ru(NH3)5(py’)] in 50:50 glycerol:water glasses at 77 K.15 Large dipole moment changes were evident through Liptay analysis of

MLCT transitions, however the magnitude of the change was within experimental error the same when an electron donating amine, [Ru(NH3)5(py-4-NH2)](PF6)2, or an electron withdrawing amide,

[Ru(NH3)5(py-4-CONH2)](PF6)2, was present in the para-position of the pyridine ligand, ∆µ= 7.9 + 0.1 D.

Indeed, the changes in dipole moment were surprisingly insensitive to Brønsted acid-base chemistry on the pyridine ligands, the counter-ion, or the ionic strength. Given the importance of dipole moments for applications of MLCT excited states, low temperature absorption and Stark spectra were measured for the six complexes shown in Scheme 2.1. Since vector addition of the ground state dipole in these D3 octahedral complexes results in µg= 0, the changes in dipole moment are reasonably assigned solely to the MLCT excited state. It is recognized that the dipole moment of charged complexes is ill-deﬁned, while the change in

34 Figure 2.1: A block diagram of the Stark apparatus that utilized a Xe arc lamp for excitation, a cryostat sample compartment, and a Si photodiode detector. An enhanced view of the sample compartment with relevant terms e,ˆ χ, and F is indicated.

dipole moments is not,∆µ = µe − µg. However, individual dipoles can be conceived by deﬁning the Ru(II) metal as the origin point of reference. The Stark data reported herein reveal large dipole moment changes upon light absorption ∆µ = 5 -11 D that are shown to be consistent with a two-state model. Further, the magnitude of ∆µ was sensitive to the electron donating (MeO-, tert-butyl-, CH3-) or withdrawing (CF3-) substituents on the bipyridine ligands and is correlated with their Hammett parameters.

2.2 Experimental

2.2.1 Materials

Butyronitrile (CH3(CH2)2CN, Alfa Aesar, 99) was used as received. [Ru(CF3bpy)3](PF6)2,

[Ru(bpy)3](PF6)2, [Ru(dmb)3](PF6)2, [Ru(dtb)3](PF6)2, [Ru(MeObpy)3](PF6)2, and [Ru(bpz)3](PF6)2 were synthesized according to previous procedures.16–20

2.2.2 Stark Spectrometer

The Stark spectrometer apparatus is detailed in Figure 2.2.1. A 150 W Xe arc lamp (USHIO

UXL-151HO) was optically coupled to an f/2 0.2 m monochromator (McPherson Model 272) to yield a 1

35 cm2 probe beam. This beam passed through a Glan-Thompson polarizer then through a sample held at 77 K in a cryostat (Janis) and onto a silicon amplified photodetector (Thorlabs PDA100A). The photocurrent was amplified by a switchable gain on the photodetector. For low temperature absorbance measurements a beam chopper (SR540) was also utilized. The sample consisted of two alkaline earth boro-aluminosilicate glass 0.7 mm thick slides (Corning) cut to ∼2.1 cm x 2.5 cm size and each coated on one side with a transparent conductive layer of indium tin oxide (Delta Technologies). The conductive indium tin oxide sides of the slides were separated by two 63.5 µm thick strips (∼.2 cm x 2.5 cm) of an adhesive Kapton tape further supported by micro-binder clips. The 63.5 µm gap was filled with the desired butyronitrile solution (∼20 µL) by a syringe.

The sample was mounted onto a specialized holder to be placed in the cryostat (Janis). The cryostat used a three chamber system. An external vacuum chamber was held at 1 µTorr pressure to reduce heat exchange with the environment. The external inner chamber was ﬁlled with liquid nitrogen. The innermost chamber was then ﬁlled with ultra-high purity gas under pressure forcing condensation of liquid nitrogen.

Electric connections were made to the sample using insulated manganin wire with alligator clips. Due to the three chamber setup, the samples were extremely stable and optical path pristine. The angle of the sample within the chamber relative to the beam path was set to 45° allowing the angle χ between the probe light polarization vector, eˆ, and the vector of the field, F , to be changed from 90° to 45° with a change from vertical to horizontal polarization. The sample angle relative to light was corrected for the differing indices of refraction for the substrate and solvent in order to obtain the true angle relative to the applied field. An AC high voltage amplifier (Trek Model 20/20C-HS) was used in conjunction with a function generator (SRS

DS345) operating at ω=2900 Hz to supply the electric field. The function generator also provided the sine wave used in lock-in amplification. The lock-in amplifier (SR530) was used to detect the electric field modulated photodiode signal, ∆I, at 2ω. The lock-in output and the amplified photodiode signal were digitized by analog-to-digital conversion through a 500 MHz Oscilloscope (Teledyne LeCroy Wavesurfer

36 3054). Collection of the average amplified photodiode signal, Iavg, allowed the Stark signal to be normalized to the transmittance of the sample and also reduced lamp intensity fluctuations. Data acquisition was performed using in-house written Labview software (National Instruments). The monochromator was stepped to the desired wavelength and allowed to equilibrate for five times the time constant setting before measurements were taken. Stark spectra were acquired using a 1 nm step size with a time constant of 1 s.

The output was averaged 100 times over 100,000 digital samples from the oscilloscope at each wavelength and several scans were typically obtained at different field strengths for an individual sample. Data obtained at different applied fields were normalized by dividing by the square of the applied field. The change in the extinction coefficient due to an external applied field was obtained by correcting the data using Eq. 2.2:

√ 2 2∆I(F ) ∆ = (2.2) 2.303 c l Iavg

√ where the factor of 2 corrects for the collection of the Stark signal at 2ω, the 2 corrects for the rms output of the lock-in, ∆I(F ) is the field-induced change in the transmission intensity through the sample collected by the lock-in amplifier, Iavg is the transmission through the sample in the absence of the field. The data are divided by concentration, c, and the path length, l, to give ∆, the field-induced change in the molar extinction coefficient. To obtain the low-temperature absorption spectra a 200 µm path length cuvette, 80 µL

(Nova Biotech) was filled with neat butyronitrile and frozen to a glass. A beam chopper was used to modulate the probe beam to allow lock-in amplification. The reference sample was removed, and the cuvette was washed with several aliquots of the sample solution. Spectra were taken with concentrations ranging from 0.86 mM to 1.82 mM. Then after refilling the cuvette with the sample butyronitrile solution, it was again frozen to form a glass. The transmission was measured as a function of the wavelength and the log of the ratio to the reference provided the 77K absorption spectra.

37 2.2.3 Data Analysis

The Liptay formalism was used to analyze Stark spectra.21–25

B d C d2 ∆(¯ν) = (fF )2 A (¯ν) + χ ((¯ν)) + χ ((¯ν)) (2.3) χ 15hc dν 30h2c2 dν2

Where F is the magnitude of the applied electric field, f is a correction for the local field felt by the molecule, h is Planck’s constant, c is the speed of light, and (¯ν) is the molecular extinction coefficient spectrum. For an isotropically oriented immobilized sample and the measurement of charge transfer excitation, Aχ is

23,26 27 usually negligibly small. The Bχ term is related to the difference in polarizability , ∆α

5 3 1 B = T r(∆α) + (3 cos2 χ − 1) ∆α − T r(∆α) (2.4) χ 2 2 m 2

Where T r(∆α) is the change in the mean polarizability, ∆αm is a component of ∆α along the transition moment of the molecule, and χ is the angle between the vector of polarization of the light and the

28 vector of the ﬁeld. The Cχ term contains information about the change in dipole moment , ∆µ

2 2 2 Cχ = ∆µ · [5 + (3 cos χ − 1)(3 cos zeta − 1) (2.5)

Where ζ is the angle between ∆µ and mˆ , and mˆ is the transition dipole moment unit vector. These equations relate χ, to the molecular frame by utilizing the ﬁxed relationship between eˆ in the lab frame and the transition dipole moment, mˆ , in the molecular frame, Figure 2.2.

Spectra obtained at any two angles, χ1 and χ2, were used to obtain ∆µ and ζ, or T r(∆α) and αm, from equations 2.3-2.5. This was accomplished through fitting the Stark spectra to a sum of derivatives of the absorption spectra. Two set χ values were utilized, Aχ,Bχ, and ∆µ were redefined as fit parameters from the coefficients of the zeroth, first, and second derivative components, respectively, of a fit for the Stark spectrum.

38 Figure 2.2: A pictoral representation of ζ, and how ∆µ and mˆ deﬁne it.

2.3 Results

2+ Room temperature absorption spectra of [Ru(bpy’)3] complexes shown in Scheme 2.1 were recorded in neat butyronitrile. The intense absorption bands in the visible region were typical of metal-to-ligand-charge transfer (MLCT) transitions, Eq 2.1.5,29–34 Upon cooling to 77K a glass was formed and the absorption spectra were recorded. Figure 2.3a compares the room temperature and 77K spectra, revealing a red-shift and sharpening of the MLCT band as temperature is reduced. The low-temperature

2+ absorption spectrum for [Ru(MeObpy)3] and its modeled spectral components is shown in Figure 2.3b.

The assignment of the underlying transitions that comprise the broad MLCT absorption envelopes has been the subject of many previous studies.35–38 Two dominant and overlapping absorption bands were evident for all the complexes between 20,000 and 24,000 cm−1 (500 to 417 nm). The lower energy transition that ranged from 20,200 to 22,000 cm−1 (495 to 455 nm) was assigned as Band A. An additional MLCT band observed at higher energy, often appearing as a shoulder, was assigned to Band B. The summary of the positions of these bands and the extinction coefﬁcients are provided in Table 2.1. At even higher energies

(>25000 cm−1), ligand centered transitions were observed but were not characterized here.

Application of an oscillating electric ﬁeld permitted the observance of the Stark effect for these complexes. In contrast to the ground state absorption spectra, the Stark spectra for these complexes were highly structured for both MLCT transitions. Two sets of Stark spectra were collected at T= 77K, and at two angles χ = 45°, and χ = 90°, see Figure 2.2.1. The largest change in extinction due to the applied ﬁeld

39 2+ Figure 2.3: (a) The absorption spectra of [Ru(MeObpy)3] in butyronitrile at 77K (black) and room 2+ temperature (red). (b) The absorption spectrum of [Ru(MeObpy)3] in butyronitrile recorded at 77K (black) with an overlaid ﬁt (red). The two dominant MLCT bands are marked with Band A (Blue) and Band B (Magenta) and the individual Gaussians used to ﬁt these data are shown as dashed lines.

40 Table 2.1: Absorption maxima and molar extinction coefﬁcients in butyronitrile at 77K.a Compound Band A (cm−1) ε (M−1 cm−1) Band B (cm−1) ε (M−1 cm−1) 2+ [Ru(MeObpy)3] 20280 10300 21380 7500 2+ [Ru(dmb)3] 21280 15150 22600 14500 2+ [Ru(dtb)3] 21400 19700 22810 15300 2+ [Ru(bpy)3] 21490 21900 22820 17650 2+ [Ru(CF3bpy)3] 21180 18050 22590 16000 2+ [Ru(bpz)3] 22020 19650 23600 13700 aBands A and B are indicated in Figure 2.2

−1 −1 −1 2+ normalized to 1 MV/cm was ∆ε = −238 M cm at 21180 cm (472 nm) for [Ru(CF3bpy)3] , and the

−1 −1 −1 2+ smallest major peak was ∆ε = −37 M cm at 20280 cm (493 nm) for [Ru(MeObpy)3] .

A central aspect of the Liptay treatment is that the changes in dipole moment are described by the second derivative of the absorption spectrum whereas the changes in polarizability are given by the ﬁrst derivative. The contributions of the 1st and 2nd derivatives to the Stark spectrum was better understood by comparison to the analytical derivatives of the absorption spectrum. The 2nd derivative of the ground state and scaled to the most substantial negative peak is shown in Figure 2.4. While the shape of the 2nd derivative was qualitatively similar to the Stark spectra, indicating strong dipole contributions in the transition, there were some noticeable discrepancies. The second derivative of Band A was slightly red shifted in the largest

Stark feature, observed at ∼20000 cm−1 as has been previously reported.15,39 It was inferred that this could be due to a third MLCT at lower energy than Band A with low charge transfer character. In addition, the

Stark spectra had structure at lower energy (<19000 cm−1) for which the visible absorption had low intensity that precluded meaningful 2nd derivative shape analysis. Lastly, the high energy region of the Stark spectra showed some substantial amplitude differences with the second derivative of the absorption spectra, consistent with prior work as the transitions in this region are expected to have different electronic properties.40 To more adequately ﬁt the Stark spectrum, 1st derivative contributions (polarizability) were necessary.

41 2+ Figure 2.4: (a) The 2nd derivative of the ground state absorption of [Ru(MeObpy)3] (red) overlaid on the 2+ measured Stark spectrum (black). (b) 1st derivative of the ground state [Ru(MeObpy)3] (red) absorption spectrum overlaid on the measured Stark spectrum (black).

The Aχ,Bχ, and Cχ terms were extracted from the data by fitting the Stark spectrum, ∆ε(¯ν), to a linear combination of zeroth, first and second derivatives of the absorption spectrum, ε(¯ν), using Eq 2.3. This was done by adjusting the Aχ,Bχ, and Cχ terms to give a best fit as judged by linear least-squares analysis.

Several overlapping transitions in the MLCT region29,41 which made it more difficult to extract the desired electronic structure parameters. Different regions of the spectra require appropriately scaled contributions from each coefficient, as some transitions had stronger changes in dipole moment or polarizability than others. A satisfactory fit was obtained by partitioning the spectrum into bands A and B, then obtaining

Aχ,Bχ, and Cχ for each transition individually. While Bands A and B consisted of multiple Gaussians for purpose of the ﬁt, using more or less bands did not impact the trends reported here, only the quality of the ﬁt.

Analysis with multiple Gaussians per band likely represent less intense transitions that are not easily observed due to large spectroscopic overlap with the major MLCT transitions. The simulated Stark spectrum was calculated from Eq. 2.2 for Ai,Bi,Ci, i = 1 − 2 for a given absorption spectrum ﬁt.

42 Figure 2.5: Absorption, ε(¯ν) (a), the Stark spectrum (black) with the fit (red) (b), and the components of the 2+ 2+ fit (1st derivative; green, 2nd derivative; blue) (c) for [Ru(MeObpy)3] (left) and [Ru(CF3bpy)3] (right). All Stark data is scaled to 1 MV/cm of applied field.

43 A linear least-squares ﬁt of the derivatives of the absorption spectrum to the Stark spectrum with the

2+ 2+ 1st and 2nd derivative contributions is shown in Figure 2.5 for [Ru(MeObpy)3] and [Ru(CF3bpy)3] . The derivatives provided a reasonable ﬁt for the MLCT region, matching the large feature at 20280 cm−1. The ﬁt does not account for the structure at wavenumbers >23000 cm−1 due to the complexity of overlapping ligand centered transitions at higher energies. The focus of this study was concerned with the MLCT region of these complexes and the high energy absorption was not studied further.

After obtaining Aχ,Bχ, and Cχ for each transition, the values of ∆µ, T r(∆α), and ∆αm were calculated as shown in Table 2. The ζ value is not reported here for two reasons; the complexity of assigning the molecular frame in a D3 point group complex, and the proximity to the magic angle, 54.7°, or when

3 cos2 ζ − 1 = 0. The similarity to the magic angle suggests little to no light polarization effect as would have been expected for an isotropically distributed of D3 species. As a result of the mathematical analysis, the uncertainty derived from the collection of data is lower than that generated through ﬁtting. As a result, the tabulated errors were a result of uncertainty arising from the ﬁtting process.

As was previously mentioned, the high (>23000 cm−1) and low (<19000 cm−1) energy regions showed a measureable Stark signal. Low resolution in the absorption spectra at long wavelengths made least-squares analysis unreliable. Minimizing the number of Gaussians, an analysis was attempted for each

2+ region. An example ﬁtting at low energy is shown in Figure 2.6 for [Ru(bpy)3] , where only a positive Stark signal was measured at energies below 19000 cm−1. The ﬁt was made allowing for polarizability contributions. For the >23000 cm−1 region, a change in polarizability component was also required to model the Stark spectra. This high energy, ligand centered transition region has been studied for M=Zn, Fe,

2+ 40 Ru, and Os for a [M(bpy)3] previously by Hug and coworkers. In their study they reported that the ligand-centered transitions in the ultraviolet region (30000-37000 cm−1) demonstrated signiﬁcant 2nd derivative contributions (∆µ) in addition to the expected 1st order contributions (∆α) of the nominally

44 Table 2.2: Parameters ∆µ, T r(∆α), and ∆αm derived from equations 2.3-2.5. −1 ∗ 3 2 3 2 Compound Transition (cm ) ∆µ (fint D) T r(∆α) (A˚ /fint) ∆αm (A˚ /fint) 2+ [Ru(MeObpy)3] 20280 6.3 ± 0.7 0.066 ± 0.034 0.53 ± 0.32 21380 7.1 ± 1.1 - - 2+ [Ru(dmb)3] 21280 7.4 ± 0.5 0.0039 ± 0.002 0.59 ± 0.18 22600 7.9 ± 0.9 - - 2+ [Ru(dtb)3] 21400 7.9 ± 0.6 4 ± 2.8 15 ± 16 22810 6.5 ± 0.8 - - 2+ [Ru(bpy)3] 21490 8.3 ± 0.7 430 ± 110 240 ± 110 22820 5.5 ± 1.0 - - 2+ [Ru(CF3bpy)3] 21180 11 ± 0.3 430 ± 53 100 ± 31 16000 7.3 ± 0.2 - - 2+ [Ru(bpz)3] 22020 8.5 ± 0.8 1100 ± 210 580 ± 180 23680 5.1 ± 1.0 - - * The values on this chart are not corrected for local ﬁeld effects, fint, of the solvent cavity. Predictions 42–44 of fint based a spherical approximation result in local ﬁeld effect corrections of 1.3-1.4 . While inclusion of fint impacts the quantitative values, it does not impact trends observed.

π − π∗ transitions. Their studies revealed mixing of the lower energy MLCT states with ligand-centered states to a degree that was dependent on the energetic separation.

2.3.1 Discussion

In agreement with previous literature7,15,45, large differences in the change in dipole moment, ∆µ, were realized for metal-to-ligand charge transfer absorption of the RuII complexes in butyronitrile glasses,

2 ∆µ= 6.3-11 Debye. The electronic coupling matrix element, HDA, and degree of delocalization, cb , were also investigated to provide further insight into the metal-to-ligand charge transfer process in the studied RuII complexes.

While the absolute values are subject to some uncertainty inherent in the ﬁtting procedure, the trends in ∆µ for the lower energy MLCT transition, Band A, follow with the Hammett parameter of the 4,4’ substitution. For Band B, no direct effect from the electron withdrawing or donating nature of the substituents was apparent. The more electron withdrawing a substituent, the higher the ∆µ for the transition.

45 2+ Figure 2.6: The low energy Stark spectrum of [Ru(bpy)3] (black), a 1st derivative component (green), and a 2nd derivative component (blue). The sum of the 1st and 2nd derivative contributions is given in red.

Figure 2.7: Change in dipole plotted versus the σpara Hammett parameter demonstrating the correlation between the dipole moment and the inductive effect of the substituent.

46 A plot of ∆µ versus the substituent Hammett parameter, σpara, is shown in Figure 2.7. This apparent trend indicates that the inﬂuence of substituents in the 4,4’ position impacted the extent of charge transfer in the

Franck-Condon excited state. Indeed, the more electron withdrawing CF3 groups gave rise to the largest change in dipole whereas the most electron donating MeO group resulted in the smallest change in dipole. To ensure the observed substituent effect, the entire MLCT region was also ﬁt as a single transition to create averaged ∆µ values that also revealed a correlation with the Hammett parameters.

Surprisingly, the higher energy MLCT (Band B) was relatively insensitive to the substituents, the origin of which is poorly understood. Previous work by Shin and coworkers on ruthenium pentaamine complexes with pyridine and pyrazine ligands showed a similar independence of ∆µ on σpara, as observed

2+ 2+ here for Band B. The [Ru(NH3)5py] and [Ru(NH3)5pz] complexes showed a change in dipole of 4.5 and

4.7 D respectively whereas the para-substituted species had changes in dipole of 7.9-8.9 D.15 In this series of complexes the MLCT ∆µ was relatively insensitive to the substituent nature, and only depended on whether the pyridine or pyrazine ligand was substituted. Limited precedence for the inﬂuence of aromatic

4,4’-substituents on such charge transfer transitions exists. McCusker and coworkers reported higher

2+ 2+ extinction coefﬁcients for [Ru(4,4’-(C6H5)2-2,2’-bipyridine)3] than for [Ru(bpy)3] , consistent with charge transfer to the phenyl substiuents in the Franck-Condon excited state.4,16,19,46 A signiﬁcant aspect of the large dipole moment observed in these excited states was due to the charge transfer distance. This can be of major impact when the excited electron is needed to continue in further electron transfer steps. Table 2.3 shows the charge transfer distances, rCT , calculated from the measured ∆µ values assuming the movement of only one electron during the excitation, using Eq. 2.6.

∆µ = e· rCT (2.6)

2+ The calculated charge transfer distances range from from 0.98 to 1.71 Ain˚ [Ru(MeObpy)3] and

2+ [Ru(CF3bpy)3] respectively. These values were distinctly smaller than the expected geometric distances

47 Scheme 2.2: Illustration of the distances used where rgeom represents the approximate geometric distance between the metal center and geometric center of the bipyridyl ligand, and rCT is the charge transfer distance calculated from equation 2.6 with the experimentally determined ∆µ values. made as a ﬁrst approximation, Scheme 2.2. Crystallographic data provide an approximate distance from the

47–51 metal to the bipyridine center of rgeom=2.82 A˚ . The ratio between rCT /rgeom was used to calculate the percent of charge transfer. These values represent the extent of charge transfer from the metal center to the ligand with adiabatic coupling.

To fully characterize these MLCT transitions and the parameters obtained from the Stark spectra, a two-state model was utilized.12,52 This treatment had also been applied previously by Shin and coworkers and has been presented in more detail by Reimers and Hush.15,28 Central to this approach was the oscillator

52 strength, fosc, which were determined using Eq. 2.7

−9 fosc = 4.61x10 εmax∆ν1/2 (2.7)

−1 −1 which applies in the case of a Gaussian transition, with εmax as the molar extinction coefﬁcient (M cm )

−1 and ∆ν1/2 as the full width at half maximum (cm ). From the fosc, the transition dipole moment, µeg, was calculated using Eq. 2.8.52

48 Table 2.3: Summary of Values of Oscillator Strength, Dipole Moment Difference, Transition Dipole Moment, Degree of Delocalization, Electron Transfer Distances, Percent Charge Transfer, and Electronic Coupling Elements 77K 3 −1 a b c 2d e ˚ f g 3 −1 Compound νmax (x10 cm ) fosc ∆µ (D) µeg (D) cb rCT (A) % CT HDA (x10 cm ) 2+ [Ru(MeObpy)3] 20.3 0.07 4.7 3.0 0.19 0.98 34.8 4.4 2+ [Ru(dmb)3] 21.3 0.10 5.6 3.5 0.19 1.15 40.9 5.5 2+ [Ru(dtb)3] 21.4 0.14 5.9 4.0 0.20 1.23 43.7 6.3 49 2+ [Ru(bpy)3] 21.5 0.15 6.2 4.2 0.20 1.29 45.9 6.6 2+ [Ru(CF3bpy)3] 21.2 0.12 8.3 3.8 0.13 1.71 60.8 6.0 2+ [Ru(bpz)3] 22.0 0.14 6.4 3.9 0.18 1.31 47.0 6.4 a b c Oscillator strength calculated using Eq. 2.7. Dipole moment difference calculated from fint∆µ using fint = 1.33. Transition dipole moment calculated using Eq. 2.8. d Degree of delocalization calculated using Eq. 2.9. e Delocalized electron-transfer distanced calculated from ∆µ/e. f g Percent charge transfer calculated from rCT /rgeom. Electronic coupling element calculated from Eq. 2.10 3he2 1/2 µeg = fosc/νmax (2.8) 8πmec

The interaction between two formally localized wavefunctions can be quantiﬁed by determination of

II 2 the degree of delocalization between the Ru center and the bipyridine ligand, cb . Using the previously

2 obtained transition dipole moment, µeg, and the change in dipole moment from experiment, ∆µ, cb was calculated using Eq. 2.9, as15

" 2 1/2# 2 1 ∆µ cb = 1 − 2 2 (2.9) 2 ∆µ + 4µeg

For comparison, the electronic coupling matrix element has also been calculated using generalized

Mulliken-Hush theory.53–55 These values reﬂect the couplings calculated at the geometric distances, Eq. 2.10

νmaxµeg HDA = (2.10) ∆µgeom

where νmax is the band peak position, µeg is the transition dipole moment, and ∆µgeom is the change in

15 dipole moments of localized states, derived from Eq. 2.6 with the geometric distance, rgeom = 2.82 A.˚

−1 Values of HDA ranged from 4400 to 6600 cm , and provided a lower limit to the electronic coupling. An alternative method toward determination of HDA accounting for appropriate charge transfer distances is outlined in the additonal information section, obtaining values on the same order of magnitude. These initial insights on the MLCT transitions of the Ruthenium complexes provided intriguing results with regards to the properties summarized in Table 5.3. Within the change in dipole, the direct effect of the substituents were

2 observed. However, the degree of delocalization, cb , and the electronic coupling, HDA, do not exhibit the

2+ same trend. The degree of delocalization was substantially smaller in the case of [Ru(CF3bpy)3] (0.13), but the values were very similar for the other complexes (0.19-0.20). Similarly, no clear correlation between the inductive effect of the substituent and the electronic coupling was observed. One might anticipate that a

50 smaller change in dipole would correlate with a higher degree of delocalization and/or a larger electronic coupling, however this expectation was not evident in the data.

While the MLCT transitions were found to primarily be dominated by ∆µ contributions, the lower energy transition (Band A) was satisfactorily ﬁt after including contributions from changes in polarization,

∆α. Indeed, the polarizability appears almost exclusively at slightly lower energy than band A, at an energy where the aforementioned third MLCT with low CT character was expected. This transition may correspond to a Laporte forbidden d − d metal-centered transition or a mixed π − π∗/MLCT state resulting in a higher polarizability contribution with little to no CT contribution. A π − π∗ transition would provide small 2nd derivative contributions as the electron motion is minimal in comparison to a classical charge transfer transition. This apparent polarizability contributions to Band A were provided in Table 2.2.

A ﬁnal note worthy of mention is the low-energy region of the Stark spectrum which displayed consistent low amplitude Stark features. It has been previously proposed that these features arise from direct ground state to triplet state charge transfer.38,56,57 Liptay analysis in this region with and without allowing for a polarizability component resulted in ∆µ values that were even higher than that of the singlet MLCT, ∆µ =

15-17 D. The apparent magnitude of the dipole change could be partially attributed to the low resolution of the absorption spectrum and not indicative of the actual dipole of the transition. Additional ongoing studies across multiple metals with different spin-orbit coupling (Fe, Ru, Os) may allow for better interpretation and model development. From the collected data, ﬁtting the Stark spectra to two sets of Gaussian bands, it is reasonable to predict that these transitions likely have a large 3MLCT character as the structure remains dominated by large ∆µ components. It should be noted however, that the positive value of this entire region for every complex indicates the likelihood of strong changes in polarizability accompanying any change in dipole.

51 Figure 2.8: Room Temperature UV-vis of all species investigated in butyronitrile.

2.4 Summary

In conclusion, Stark spectroscopy revealed that electron withdrawing and donating substituents in the

2+ 4,4’ position of a bipyridine ligand in homoleptic [Ru(bpy’)3] complexes had a strong inﬂuence on the light induced change in dipole moment, ∆µ. A correlation between ∆µ and the Hammett paramenters was evident. Further, the ∆µ values provided insight into the degree of metal-ligand coupling,

−1 HDA = 4400 − 6600 cm . Further studies with alternative metals to investigate contributions of spin-orbit coupling and orbital overlap are now underway that promise to provide new insights into the low energy

Stark spectra and the effect of the metal center on charge transfer. Additionally, the investigation of C2 molecular point symmetry is of interest for determining the effects of ancillary ligands on charge transfer.

This is of particular interest for the ﬁeld of dye sensitized solar cells that generally use dyes with anchoring groups that lower the symmetry.

2.5 Additional information

2+ While not necessary for the discussion above, the process illustrated for [Ru(MeObpy)3] and

2+ [[Ru(CF3bpy)3] was carried out for all complexes in Scheme 2.1. The below ﬁgures present this data.

52 Figure 2.9: Low Temperature UV-vis of all species investigated at 77K in a butyronitrile glass.

As was discussed, alternative methods of calculating HDA can be used to better understand the system and what effects the dipole and polarizability effects have on the coupling values or what effect the coupling has on those parameters. The following section illustrates alternative methods of calculation and presents the results of each.

The traditional Mulliken-Hush expression

−2 1/2 2.06x10 νmaxεmax∆ν1/2 H = (2.11) DA d

can be used to calculate HDA with the spectroscopic information of the MLCT transition, where νmax is the energy of the transition, εmax is the Molar extinction coefﬁcient, and ∆ν1/2 is the full-width at half maximum of the MLCT transition. The distance term, d, is often assigned the geometric value of the charge transfer distance, in order to calculate a lower limit for HDA. As illustrated in this chapter and many literature examples, the distance of charge transfer is ultimately oftentimes shorter than the geometric distance.

53 Figure 2.10: Absorption, ε(ν) (top), the Stark spectrum (black) with the fit (red), and the components of the 2+ 2+ fit (1st derivative; green, 2nd derivative; blue) for [Ru(bpy)3] (left) and [Ru(dtb)3] (right) . For ease of interpretation all data is scaled to 1 MV/cm of applied field.

54 Figure 2.11: Absorption, ε(ν) (top), the Stark spectrum (black) with the fit (red), and the components of the 2+ 2+ fit (1st derivative; green, 2nd derivative; blue) for [Ru(dmb)3] (left) and [Ru(bpz)3] (right) . For ease of interpretation all data is scaled to 1 MV/cm of applied field.

55 The generalized Mulliken-Hush model interprets HDA in terms of more fundamental quantities obtained partially from the Stark spectra. In this chapter a generalized expression to calculate the HDA was used,

νmaxµeg HDA = (2.12) ∆µgeom

where µeg is the transition dipole moment and ∆µgeom is the change in dipole of a localized system, calculated assuming the geometric distance, rgeom=2.82 A.˚ Using the geometric dipole moment provides a lower limit as the use of the geometric distance in Eq 2.11 did. The expression above is derived from a

2-state generalized Mulliken-Hush model as

ν µ ν µ H = max eg = max eg (2.13) DA 1/2 (µD − µA) h 2 2i (µeg) + 4 (µeg) where (µD − µA) is the nonadiabatic change in dipole moment, and ∆µeg is the change in dipole moment determined with the experimental Stark spectra. The latter expression of Eq 2.13 was derived through

2 2 2 (µD − µA) = (∆µeg) + 4 (µeg) (2.14) where the nonadiabatic change in dipole moment is related to the effective localized electron-transfer distance

rDA = (µD − µA) /e (2.15) which is generally smaller than the geometric distance, used in eq S1 and S2.

Equations 2.13-2.15 provide a more realistic prediction of HDA, the results of which have been tabulated in Table 2.4. Additionally, eq 2.11 can be related to eq 2.13 through the use of d = rDA instead of d = rgeom.

56 3 −1 Table 2.4: Summary of HDA values calculated with equations 2.11-2.15. All units are (x10 cm ) a b c d Compound HDA HDA HDA HDA 2+ [Ru(MeObpy)3] 4.1 4.4 7.9 7.3 2+ [Ru(dmb)3] 5.1 5.5 8.3 7.7 2+ [Ru(dtb)3] 5.8 6.3 8.6 7.9 2+ [Ru(bpy)3] 6.2 6.6 8.6 7.9 2+ [Ru(CF3bpy)3] 5.5 6.0 7.2 6.7 2+ [Ru(bpz)3] 5.9 6.4 8.5 7.9 a b c d Calculated with eq 2.11 and d = rgeom. Calculated with eq 2.12. Calculated with eq 2.13. Calculated with eq 2.11 and d = rDA.

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62 CHAPTER 3–Stark Spectroscopic Evidence that a Spin Change Accompanies Light Absorption in Transition Metal Polypyridyl Complexes1

3.1 Introduction

The electron spin in the metal-to-ligand charge-transfer (MLCT) excited states utilized for applications in displays, sensing, solar energy conversion, and organic synthesis differ from that of the ground state. Stark and visible absorption spectroscopies directly probe the ‘Franck-Condon’ (FC) excited

2+ state of [M(bpy)3] complexes, where bpy is 2,2’-bipyridine and M is Fe, Ru, and Os. It is shown herein that

Stark spectroscopy is a more sensitive technique than absorption spectroscopy for ∆S 6= 0 electronic transitions and provides experimental values of the excited state dipole moment. In particular, a previously

2+* unresolved low energy transition for solvated [Fe(bpy)3] indicates a paramagnetic FC excited state. Group theoretical and Liptay analysis provides a large dipole moment change, |∆~µ| > 5 Debye, assigned to a

3MLCT excited state comprised of an electron localized on one bpy ligand. The triplet excited state dipole moments were less than or equal to that of the singlets, consistent with a shorter charge transfer distance and a more localized excited state as has been predicted theoretically and reported for organic compounds.1,2

3.2 Experimental Details

Materials. Butyronitrile (CH3(CH2)2CN, Alfa Aesar, 99%) was used as received. Indium Tin Oxide coated glass slides (Corning alkaline earth boro-aluminosilicate glass, Indium Tin Oxide coated one surface,

RS = 70-100 ohms, Delta Technologies) were used as received. [Ru(bpy)3](PF6)2, [Fe(bpy)3](PF6)2, and

3,4 [Os(bpy)3](PF6)2 were synthesized according to previous procedures.

63 Stark Spectrometer. Stark spectroscopy was performed using an apparatus detailed in previous work.5 A butyronitrile solution in a thin path length cell comprised of two Indium Tin Oxide coated glass slides was submerged into a liquid nitrogen cooled cryostat and aligned at an angle of 45°relative to the optical path. An oscillating electric potential generated an oscillating electric field across the sample. The electroabsorption spectra were collected with a lock-in amplifier. In addition, a reference spectra of the unperturbed system was collected to normalize the data. This reference spectra was then used to convert the collected data to an extinction coefficient spectrum rather than raw intensity through eq 3.1.

√ 2 2∆I(F~ ) ∆ε = (3.1) 2.303clIavg

The absorption spectra at 77K were also collected using the same optical arrangement. The tabulated data were collected with a beam chopper.

Data analysis. The Liptay formalism, eq 3.2 was used to analyze the stark spectra.6,7

B d C d2 ∆ε(~ν) = (fF~ )2A ε(~ν) + χ (ε(~ν)) + χ (ε(~ν)) (3.2) χ 15hc dν 30h2c2 dν2

Where F is the magnitude of the applied electric field, f is a correction for the local field experienced by the molecule, h is Planck’s constant, c is the speed of light, and ε(~ν) is the molecular extinction coefficient spectrum. For an isotropically oriented immobilized sample, Aχ is negligibly small. The Bχ term is related to the difference in polarizability, ∆~α, and the Cχ term contains information about the change in dipole moment, ∆~µ. A satisfactory fit was obtained by partitioning the spectrum into multiple bands as

8 outlined by Kober et al., then obtaining Aχ, Bχ, and Cχ for each transition individually. Simulated Stark spectra were calculated from Eq. 3.1 for Ai, Bi, Ci, i=1-n where n is the number of transitions assigned to the absorption spectra.

64 2+ Figure 3.1: Absorption and Stark spectra (black, with overlaid ﬁts in red) spectra for [Fe(bpy)3] , 2+ 2+ [Ru(bpy)3] , and [Os(bpy)3] . All Stark spectra were scaled to an applied ﬁeld of 1 MV/cm.

DFT Calculations. Ground-state geometries of all three complexes were optimized with the B3LYP functional using a ﬁxed mixed basis set couple LANL2DZ (for the metal centers) and 6-311G(d,p) (for all other atoms). Solvation effects were considered by using the C-PCM solvent model (CH3CN, ε = 37.64).

Calculations were carried using the Gaussian 09 Package.

3.3 Results

2+ Figure 3.1 shows the visible absorption spectra of the [M(bpy)3] complexes at 77K. The intense absorption bands are due to MLCT transitions with the largest extinction coefﬁcient for Ru, followed by Fe

2+ and Os. The spectrum of [Os(bpy)3] displays long wavelength absorption (550 – 750 nm) that were previously assigned to direct singlet-to-triplet MLCT transitions.8,9 Analogous transitions are absent with the lighter Ru and Fe complexes as is shown in the expanded insets.10–12

Application of a large (> 0.4 MV/cm) electric ﬁeld induced a signiﬁcant distortion to the absorption spectra. The Stark spectra were highly structured throughout the visible region providing resolution that was absent in the absorption spectra, Figure 3.1. Most notably, the low energy region where singlet-to-triplet

65 2+ – Figure 3.2: Stark spectra of [Ru(bpy)3] recorded (Left) at different concentrations and (Right) using PF6 and Cl– anions. All data is scaled to an applied Field of 1 MV/cm.

2+ transitions are expected is much more intense than in the corresponding absorption spectra. For [Os(bpy)3] , several low energy transitions are evident with about the same intensities as those measured at higher

2+ −1 energies. A positive electroabsorption feature for [Fe(bpy)3] at 633 nm (15,800 cm ) was evident, corresponding to an absorption at 585 nm (17,100 cm−1), while the absorption was small, ε < 200 M−1

−1 cm , and no discrete transition was resolved. To ensure reproducibility, chloride and PF6 anions were investigated and measurements were made with variable concentrations and electric ﬁelds, Figures 3.2-3.6.

These experiments also demonstrate the consistent adherence to the quadratic dependence of electric ﬁeld including the lower energy region, as to be discussed in more detail.

Overlaid on the Stark spectra in Figure 3.2 in red are simulations based on group theoretical considerations and Liptay’s treatment.5,7,8,13,14 The transitions shown in Scheme 3.1 and summarized in

Table 3.2 were made based on Kober et al.’s previous report.8 The transitions labeled A and B were predominantly singlet and those labeled C and D were predominately triplet. Note that A and C, as well as B and D, correspond primarily to the same orbital transitions. Also shown in Scheme 3.1 are the molecular

66 2+ Figure 3.3: Electroabsorption measurements of [Fe(bpy)3] at the indicated applied field strengths. (Left) Full Stark spectra scaled to an applied Field of 1 MV/cm. (Right) The absolute value of the intensity of the electroabsorption feature measure at the indicated wavelength as a function of the field strength. Overlaid are quadratic fits.

2+ Figure 3.4: Electroabsorption measurements of [Ru(bpy)3] at the indicated applied field strengths. (Left) Full Stark spectra scaled to an applied Field of 1 MV/cm. (Right) The absolute value of the intensity of the electroabsorption feature measure at the indicated wavelength as a function of the field strength. Overlaid are quadratic fits.

67 2+ Figure 3.5: Electroabsorption measurements of [Os(bpy)3] at the indicated applied field strengths. (Left) Full Stark spectra scaled to an applied Field of 1 MV/cm. (Right) The absolute value of the intensity of the electroabsorption feature measure at the indicated wavelength as a function of the field strength. Overlaid are quadratic fits.

2+ Figure 3.6: Stark spectra of the low energy region of [Os(bpy)3] recorded at different ﬁeld strengths without normalization.

68 Scheme 3.1: A simplﬁied molecular orbital diagram of the singlet (A and B) and triplet (C and D) electronic transitions utilized to analyze the absorption and Stark spectra. Also shown are molecular orbitals of e symmetry determine by TDDFT. orbitals determined by TDDFT for the e symmetry orbitals that comprise the HOMO-LUMO gap. For a full

8 analysis of the electronic structure using group theory in a D3 symmetry please refer to Kober et al.

Using the MO scheme presented, Scheme 3.1; there are four different orbital transitions:

∗ ∗ ∗ ∗ dπA1 → πA2, dπE → πA2, dπE → πE, and dπE → πA2. Following light absorption, the resulting excited state has one electron localized on a ligand orbital and ﬁve electrons in metal localized orbitals. The spin state was determined by the spin of the uncoupled electron in the metal orbitals along with the spin of the electron in the ligand centered orbital as either singlet or triplet. From the four possible orbital transitions, 6 singlet states and 18 triplet states result, Table 3.1.

As the ground state has A1 point group symmetry, transitions to any excited A1 symmetric states are dipole forbidden and likely not observed. The A2 symmetric excited states are predominantly Z polarized,

8,10,11 and as the spectrum of these species are predominantly XY polarized, the A2 MLCT states are expected to be substantially weaker as the transition dipole and electron transfer do not coincide. Lastly, several of the E symmetric states are nearly degenerate in energy and have not been resolved. All of these factors combined reduce the number of states signiﬁcantly. Indeed, with removal of the A1 states, only 18

69 Table 3.1: Tabulation of the different excited states and the Group Theory orbitals they originate from. Transition Resulting States ∗ 1 dπE → πA2 E: 1E 3 E: 2E, 3E, 1A1, 1A2 ∗ 1 dπA1 → πA2 A2: 2A2 3 A2: 2A1, 4E ∗ 1 dπE → πE E: 5E 1 A1: 3A1 1 A2: 3A2 3 E: 6E, 7E, 4A1, 4A2 3 A1: 5A2, 8E 3 A2: 5A1, 9E ∗ 1 dπE → πA2 E: 10E 3 E: 11E, 12E, 6A1, 6A2 states remain. Overlap of positioning and expected weak transitions lead to deﬁning the spectral region

2+ 2+ investigated herein as 10 transitions for [Os(bpy)3] , 8 transitions for [Ru(bpy)3] , and 5 transitions for

2+ [Fe(bpy)3] . The ﬁts of the UV-vis region with the individual transitions is shown in Figures 3.7 - 3.9.

Liptay’s treatment of Stark spectra indicates that a dipole moment change |∆~µ| is associated with the second-derivative of the absorption spectrum and a polarizability change ∆~α with the ﬁrst-derivative.6,15,16

2+ Consistent with previous reports of [Ru(bpy)3] and its derivatives, the Stark spectra were dominated by|∆~µ|.5,17–19 Figure 3.10A shows the most intense electroabsorption features in the Stark spectrum of

2+ [Fe(bpy)3] are also well described by the second-derivative of the absorption spectrum. However, such a

2+ 2+ simple analysis is precluded at long wavelengths for [Fe(bpy)3] and [Ru(bpy)3] due to poor signal-to-noise ratios. Note that a large |∆~µ| requires a significant bleach that is absent in the long wavelength region of the Stark spectra of the Fe and Ru complexes, Figure 3.1 inset. A satisfactory fit was achieved by inclusion of ∆~α, manifest as a first-derivative of the absorption spectrum as is shown in Figure

3.10B.

Large dipole moment changes |∆~µ| were determined for both the singlet and triplet MLCT transitions, Tables 3.3 and 3.4. Since vector addition of the ground state dipole results in ~µ = 0, the

70 2+ Figure 3.7: The 77K absorption spectrum of [Fe(bpy)3] in butyronitrile (black). Overlaid are individual transitions labelled with reference to Table 3.1 and a summation of the individual transitions (red).

2+ Figure 3.8: The 77K absorption spectrum of [Ru(bpy)3] in butyronitrile (black). Overlaid are individual transitions labelled with reference to Table 3.1 and a summation of the individual transitions (red).

71 2+ Figure 3.9: The 77K absorption spectrum of [Os(bpy)3] in butyronitrile (black). Overlaid are individual transitions labelled with reference to Table 3.1 and a summation of the individual transitions (red).

2+ Figure 3.10: A) The Stark spectrum of [Fe(bpy)3 (black) with overlaid analytical (red) and noise-free (blue) 2+ second-derivatives of the absorption spectrum. B) The low energy electro-absorption feature of [Fe(bpy)3] (black) with overlaid ﬁrst- (blue) and second- (pink) derivative contributions and the sum (red).

72 Table 3.2: Absorption maxima (ν, cm−1 x103) and molar extinction coefﬁcients (ε,M −1 cm−1 x103) in butyronitrile at 77K.

Compound νA εA νB εB νC εC νD εD 2+ a a [Fe(bpy)3] 20.0 9.1 18.6 13.2 18.0 7.4 17.1 0.5 2+ a a [Ru(bpy)3] 22.8 17.7 21.5 21.9 19.3 2.6 17.8 0.7 2+ [Os(bpy)3] 22.2 7.6 20.4 9.7 16.7 3.1 14.7 2.9 aThis transition appears as a shoulder measured |∆~µ| is reasonably assigned solely to the MLCT excited state. Hence, visible light absorption promotes an electron from a metal d-orbital to the π∗ levels to a single bipyridine ligand resulting in a dramatic redistribution of the charge and an electronic symmetry that differs from the ground state, Eq.

3.3.19–21 Previous evidence for excited state localization

II 2+ III – 2+* [M bpy3] + hν → [M (bpy )(bpy)2] (3.3) (groundstate) + hν → (F ranck − Condonstate) is found in the solvatochromism of these complexes.22 If instead the FC state had charge equally delocalized over all three bipyridine ligands, a D3 electronic symmetry would result with no change in |∆~µ|, yet with an expected change in polarizability, ∆~α. The field induced spectral changes associated with such a hypothetical molecule, i.e. |∆~α| >> 0 and |∆~µ| = 0, are insensitive to the field orientation with applications as a reporter of interfacial electric fields.23,24

The excited state dipole moment is often related to the charge transfer distance,rCT , required to produce the measured |∆~µ|, Equation 3.4 and Table 3.5.25 The geometric distance from

|∆~µ| = e · rCT (3.4)

73 Table 3.3: The |∆~µ| for 1MLCT transitions. − Compound Transitions (cm 1) |∆~µ| (fintD)∗ 2+ [Fe(bpy)3] 20100 (A) 10.0 ± 0.3 19000 (B) 11.1 ± 0.5 2+ [Ru(bpy)3] 22800 7.1 ± 0.5 21500 8.3 ± 0.8 2+ [Os(bpy)3] 20800 5.1 ± 0.9 22200 6.6 ± 0.7

Table 3.4: |∆~µ|, Charge Transfer Distance, and Percent Charge Transfer for Transitions B and D. − Compound Transitions (cm 1) |∆~µ| (fintD)∗ 2+ [Fe(bpy)3] 18000 (C) 13.5 ± 1.2 17100 (D) 11 ± 3 2+ [Ru(bpy)3] 19300 6.5 ± 0.7 17800 5.3 ± 0.8 2+ [Os(bpy)3] 16700 8.1 ± 0.8 14700 4.5 ± 0.6

the metal to the center of the bipyridine, rgeom, provides a reference for the percentage of metal-to-ligand

2+ 2+ charge transfer, %CT = rCT /rgeom x 100 that was largest for [Fe(bpy)3] and smallest for [Os(bpy)3] in both the singlet and triplet excited states, Scheme 3.2.

As indicated in Scheme 3.3, the separation between metal d-orbital density and the M-N bond distance is largest for iron indicative of weaker ground state coupling and hence more metal character for

Table 3.5: |∆~µ|, Charge Transfer Distance, and Percent Charge Transfer for Transitions B and D. 77K 3 −1 Compound νmax(x10 cm ) |∆~µ| (D)∗ rCT (A˚ )% CT 1MLCT(B) 2+ [Fe(bpy)3] 19.0 8.3 ± 0.4 1.7 ± 0.1 62.5 2+ [Ru(bpy)3] 21.5 6.2 ± 0.6 1.3 ± 0.1 46.1 2+ [Os(bpy)3] 20.8 4.8 ± 0.5 1.0 ± 0.1 35.3 3MLCT (D) 2+ [Fe(bpy)3] 17.1 8.3 ± 2.3 1.7 ± 0.5 62.0 2+ [Ru(bpy)3] 17.8 4.0 ± 0.6 0.83 ± 0.13 29.4 2+ [Os(bpy)3] 14.7 3.4 ± 0.5 0.70 ± 0.10 24.8 a 26 Calculated assuming an internal ﬁeld correciton of (fint) of 1.33

74 Scheme 3.2: The geometric distance, rgeom, and the measured charge transfer distance, rCT , for the indicated 2+ [M(bpy)3] complex.

2+ light induced charge transfer. Indeed, DFT calculations reveal that the FC excited state of [Fe(bpy)3] has the least metal character and hence the most complete charge transfer. The Fe 3d orbitals are indeed considerably more compact than the Ru 4d, or Os 5d, orbitals. The large difference in %CT between the ﬁrst- and second-row supports McCusker’s assertion that the lack of a radial node in the 3d orbitals greatly impact its ground-state electronic structure.27

3 1 2+ 2+ The CT distance was signiﬁcantly shorter than the CT distances for [Ru(bpy)3] and [Os(bpy)3]

2+ and were quite similar for [Fe(bpy)3] whose low amplitude electroabsorption feature resulted in greater experimental uncertainty, Table 3.5. This data is fully consistent with theoretical expectations based on the

Pauli exclusion principle1 and previously reported luminescence studies of acetylide oligomers.2 Group

1 theoretical analysis indicates that the MLCT state is predominantly de → π∗e in character with triplet

3 2+* contributions that increase with spin-orbit coupling. The MLCT of [Ru(bpy)3] is predicted to have the

8 largest contribution from the higher energy de → π∗a2 with a smaller associated |∆~µ|. This may account

2+ 2+ for the larger gap in the singlet and triplet |∆~µ| values for [Ru(bpy)3] relative to [Os(bpy)3] . It should be emphasized that the tabulated values correspond to the FC excited state that subsequently relaxes with accompanying nuclear motion to a thermally equilibrated excited state where spin is a poor quantum number.22

75 Scheme 3.3: The radial distribution functions of the frontier metal d-orbitals. The M-N bond and M-bpy 2+ center distances in [M(bpy)3] are indicated as vertical lines.

A striking aspect of the Stark spectra are the electroabsorption features in the low energy ‘triplet’ region that are far more intense and spectrally resolved than in the absorption or in previously reported magnetic circular dichroism spectra.10–12 Spin-orbit coupling enhances δS 6= 0 transitions to a degree

4 28–30 proportional to the effective nuclear charge raised to the fourth power, Zeff . Their intensity in the Stark spectra also likely emanates from the signiﬁcant dipole moment and polarizability change that accompanies photon absorption. Energy conservation considerations led El-Sayed to conclude that rapid intersystem crossing in organic compounds requires a change in the molecular orbital type.31,32 Theoretical considerations reveals that a multitude of molecular orbitals are available to facilitate a spin change for these metal complexes. Since the initial and ﬁnal molecular orbitals in a singlet-to-triplet transition are necessarily different, it is reasonable to expect an accompanying polarizability change that enhances the electroabsorption intensity.

2+ The observation of high spin character in the FC excited state of [Fe(bpy)3] is relevant to previously reported ultrafast absorption measurements.33–35 While diamagnetic in the ground state, the relatively weak

3 5 ligand ﬁeld splitting of this ﬁrst row metal places both the metal localized T2 and T2 states lower in energy

5 than the MLCT state. Pulsed light excitation has been shown to quantitatively yield the T2 ligand ﬁeld state

76 on a time scale that is normally associated with a single intersystem crossing event and not two that would be

1 3 5 30 required for MLCT → T2 → T2. These kinetic data are better understood with the Stark spectroscopic results that indicate high spin character in the initially formed Franck-Condon excited state.30,36–40

In conclusion, Stark spectroscopy was found to be highly sensitive to spin disallowed ∆S 6= 0

6 2+ transitions in low-spin d [M(bpy)3] complexes. In particular, a new electronic transition at 585 nm,

2+ assigned predominantly as a metal de → π∗e bpy, is reported indicative of a spin change for [Fe(bpy)3] .

Hence spin orbit coupling is sufﬁcient to yield high spin Franck-Condon excited states even with a relatively

III – 2+* light ﬁrst row metal. Large dipole moment changes are consistent with a localized [M (bpy )(bpy)2] excited state. A shorter charge transfer distance was obtained for the triplet states relative to the singlets. The extent of charge transfer in the excited state decreases as the ground state metal-ligand overlap increases, a fact that was not obvious from prior spectroscopic measurements. The presence of multiple molecular orbitals with similar energetics yet different polarizabilities is common in transition metal complexes suggesting that Stark spectroscopy is promising tool for characterization of spin changes that accompany light absorption in inorganic photochemistry.

77 REFERENCES

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[3] Damrauer, N. H.; Boussie, T. R.; Devenney, M.; McCusker, J. K. Effects of Intraligand Electron Delocalization, Steric Tuning, and Excited-State Vibronic Coupling on the Photophysics of Aryl-Substituted Bipyridyl Complexes of Ru(II). Journal of the American Chemical Society 1997, 119, 8253–8268.

[4] Nazeeruddin, M. K.; Zakeeruddin, S. M.; Kalyanasundaram, K. Enhanced intensities of the ligand-to-metal charge-transfer transitions in ruthenium(III) and osmium(III) complexes of substituted bipyridines. The Journal of Physical Chemistry 2005, 97, 9607–9612.

2+ [5] Maurer, A. B.; Piechota, E. J.; Meyer, G. J. Excited-State Dipole Moments of Homoleptic [Ru(bpy)3] Complexes Measured by Stark Spectroscopy. Journal of Physical Chemistry A 2019, 123, 8745–8754.

[6] Jalviste, E.; Ohta, N. Theoretical foundation of electroabsorption spectroscopy: Self-contained derivation of the basic equations with the direction cosine method and the Euler angle method. Journal of Photochemistry and Photobiology C: Photochemistry Reviews 2007, 8, 30–46.

[7] Liptay, W. Die losungsmittelabh¨ angigkeit¨ der wellenzahl von elektronenbanden und die chemisch-physikalischen grundlagen. Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences 1965, 20, 1441–1471.

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[9] Shaw, G. B.; Styers-Barnett, D. J.; Gannon, E. Z.; Granger, J. C.; Papanikolas, J. M. Interligand 2+ electron transfer dynamics in [Os(bpy)3] : Exploring the excited state potential surfaces with femtosecond spectroscopy. Journal of Physical Chemistry A 2004, 108, 4498–5006.

2+ [10] Felix, F.; Ferguson, J.; Giidel, H. U.; Ludilc, A. The Electronic Spectrum of Ru(bpy)3 . Journal of the American Chemical Society 1980, 102, 4096–4102.

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[13] Stanley, R. J.; Jang, H. Electronic Structure Measurements of Oxidized Flavins and Flavin Complexes Using Stark-Effect Spectroscopy. The Journal of Physical Chemistry A 1999, 103, 8976–8984.

[14] Reimers, J. R.; Hush, N. S. Electronic properties of transition-metal complexes determined from electroabsorption (Stark) spectroscopy. 2. Mononuclear complexes of ruthenium(II). The Journal of Physical Chemistry 1991, 95, 9773–9781.

78 [15] Liptay, W. In Dipole Moments and Polarizabilities of Molecules in Excited Electronic States; LIM, E., Ed.; Elsevier, 1974; Vol. 1; pp 129–229.

[16] Mathies, R.; Stryer, L. Retinal has a highly dipolar vertically excited singlet state: implications for vision. Proceedings of the National Academy of Sciences 1976, 73, 2169–2173.

[17] Shin, Y.-g. K.; Brunschwig, B. S.; Creutz, C.; Sutin, N. Electroabsorption Spectroscopy of Charge-Transfer States of Transition-Metal Complexes. 2. Metal-to-Ligand and Ligand-to-Metal Charge-Transfer Excited States of Pentaammineruthenium Complexes. The Journal of Physical Chemistry 1996, 100, 8157–8169.

[18] Oh, D. H.; Sano, M.; Boxer, S. G. Electroabsorption (Stark effect) spectroscopy of mono- and biruthenium charge-transfer complexes: measurements of changes in dipole moments and other electrooptic properties. Journal of the American Chemical Society 1991, 113, 6880–6890.

[19] Damrauer, N. H.; McCusker, J. K. Ultrafast Dynamics in the Metal-to-Ligand Charge Transfer 2+ Excited-State Evolution of [Ru(4,4‘-diphenyl-2,2‘-bipyridine)3] . The Journal of Physical Chemistry A 1999, 103, 8440–8446.

[20] Bradley, P. G.; Kress, N.; Hornberger, B. A.; Dallinger, R. F.; Woodruff, W. H. Vibrational spectroscopy of the electronically excited state. 5. Time-resolved resonance Raman study of tris(bipyridine)ruthenium(II) and related complexes. Deﬁnitive evidence for the ”localized” MLCT state. Journal of the American Chemical Society 1981, 103, 7441–7446.

[21] McCusker, J. K. Femtosecond Absorption Spectroscopy of Transition Metal Charge-Transfer Complexes. Accounts of Chemical Research 2003, 36, 876–887.

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[27] McCusker, J. K. Electronic structure in the transition metal block and its implications for light harvesting. Science 2019, 363, 484–488.

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[29] Clementi, E.; Raimondi, D. L. Atomic screening constants from SCF functions. The Journal of Chemical Physics 1963, 38, 2686–2689.

79 [30] Penfold, T. J.; Gindensperger, E.; Daniel, C.; Marian, C. M. Spin-Vibronic Mechanism for Intersystem Crossing. Chemical Reviews 2018, 118, 6975–7025.

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[32] El-Sayed, M. A. The radiationless processes involving change of multiplicity in the diazenes. The Journal of Chemical Physics 1962, 36, 573–574.

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80 CHAPTER 4–Light Excitation of a Bismuth Iodide Complex initiates I-I Bond Formation Reactions of Relevance to Solar Energy Conversion1

4.1 Introduction

Iodide photo-oxidation is of direct relevance to hydrogen gas production through HI splitting1,2 and to emerging classes of third generation photovoltaic cells3, particularly those based on heavy metals like lead and bismuth.4–6 The chemistry and photochemistry of metal halide complexes is also of general interest4 where a large body of literature indicates that halides form stable metal-halide bonds while oxidized halides do not.7,8 Indeed a literature review revealed only a platinum triiodide complex as a rare example of oxidized iodide ligated to a metal with relevance to oxidative-addition reactions.9 Theoretical studies indicate other examples should exist and their identiﬁcation is of broad interest.10 Here we report a light driven method for the generation of oxidized iodide and I-I bond formation in a metal coordination sphere that yields a metal

– 3– di-iodide adduct [M (I2 )]. More speciﬁcally, ligand-to-metal charge transfer (LMCT) excitation of [BiI6]

– n– 1 4– was found to transiently yield [Bi(I2 )Ix] species. Remarkably, [(η I2)BiI5] was stable for half a millisecond and decayed cleanly to the ground state reactants with no evidence of the disproportionation

– chemistry known for solvated diiodide, I2 CH3CN.

4.2 Results

Shown in Figure 4.1 is the UV-visible absorption spectra of BiI3 CH3CN solution with up to 14.5 equivalents of tetrabutyl ammonium iodide. The spectral data was corrected for the volume change and those

– 3– spectra indicated in bold represent those assigned to BiI3, [BiI4] , and [BiI6] .

1This work was previously published in Journal of the American Chemical Society, 139 (24), 8066, with contributions from A. B. Maurer, K. Hu, and G. J. Meyer. Reprinted with permission. Copyright 2017 American Chemical Society.

81 Figure 4.1: Absorption spectra of BiI3 in CH3CN titrated with tetrabutylammonium iodide (TBAI). The spectra given in bold are assigned to the indicated complexes.

6 −1 – 7 The stepwise formation constants were measured to be K4 > 10 M for [BiI4] and K6 = 6.4x10

−2 3– 11,12 4– M for [BiI6] in good agreement with literature values. It is noted that a seven-coordinate [BiI7] complex has previously been reported that was not observed at the iodide concentrations investigated here.11

The absorption bands are reasonably assigned as LMCT transitions that formally yield a Bi(II) and an iodine

III x– II *x– −1 atom, [I Bi In] + hν → [I Bi In] . The LMCT extinction coefﬁcients range from 5,000 to 14,000 M

−1 3– cm and the [BiI6] species absorbs light strongly through the visible region to beyond 550 nm. Pulsed

3– green light excitation of [BiI6] produced the transient absorption spectra shown in Figure 4.2. An advantage of these kinetic data over those of previous LMCT studies11 was that the absorption transients cleanly returned to baseline on the millisecond time scale with no evidence of net photochemistry. A bleach of the LMCT bands was observed consistent with the formation of new species. A long wavelength

– absorption feature appeared reminiscent of that known for diiodide, I2 . The ﬁgure inset contrasts the low

– energy transient spectra with that of I2 CH3CN. This comparison reveals a poor match, particularly in the

600-700 nm region where the transient species have signiﬁcantly more amplitude.

– Indeed, a careful examination of the data in the 600-800 nm region where I2 absorbs strongly revealed the presence of two transient species. The spectra observed 50 ns after laser excitation had greater

82 Figure 4.2: Transient absorption difference spectra measured at the speciﬁed time delays after pulsed 532 nm excitation (20 mJ/pulse) of BiI3 with six equivalents of TBAI in CH3CN. Inset: An expansion of difference – spectra between 600 and 800 nm. Overlaid in red is the spectrum of I2 CH3CN

– amplitude at 660 nm than I2 CH3CN did, but far less in the 700-800 nm region. At a 500 ns delay time, the amplitude at 660 nm remained unchanged, but the amplitude at 750 nm approximately doubled. By a delay

– time of 100 µs, the amplitude at 660 nm decreased and the spectra now closely resembled that of I2 CH3CN, although a measureable difference in the 675-725 nm region was evident.

– The classical molecular orbital description of iodine is shown, which correctly predicts the I2 bond

1 ∗ ∗ order of 2 and the presence of three absortion bands. The SOMO-1 to SOMO gap gives rise to a π → σ absorption band in the mid-IR region that has been previously observed.13 The absorption characterized here is assigned to the SOMO-2 to SOMO, π → σ∗, that differs from the older literature based on the symmetry frobidden nature of the transition that is not relevant to the bismuth-diiodide adduct.13 A TD-DFT analysis using multiple functionals and basis sets (B3LYP/aug-cc-pVTZ and PBE0/6-311g** (d,p))14,15 used previously for accurate iodine calculations supports the assignment of 600-800 nm band to the π → σ∗

2 – 2 3– transition. The 660 nm absorp-tion transient is assigned to an η ligated I2 , [(η I2)BiI4] , and the 750 nm

1 1 4– 2 absorption to an η complex, [(η I2)BiI5] . These assignments are made based on the expectation that η ligation will stabilize the iodine π orbitals through interaction with empty bismuth p orbitals while η1 ligation stabilizes the σ∗ through a similar interaction.

83 – 1 2 – Figure 4.3: Simpliﬁed molecular orbital diagrams of uncomplexed I2 CH3CN as well as η and η ligated I2

The use of Stark spectroscopy allows an alternative perspective on the formation of the excited state

16 as it probes only the Franck-Condon state. Figure 4.6 shows the low-temperature absorbance of BiI3 and the Stark Spectrum with their ﬁts. These resulted in ∆µ values for the lowest energy charge transfer at 20200 cm−1 of 3 D, and ∆µ of the second lowest energy transition at 21300 cm−1 of 11 D. These values are

10,11 consistent with the predictions that the lowest energy transitions in BiI3 are LMCTs.

4.3 Discussion

The proposed mechanism for I-I bond formation shown in Scheme 4.4 is consistent with the spectroscopic observations described and additional studies performed as a function of the iodide concentration and the number of absorbed photons (concentration). The reactions are initiated by LMCT light absorption to formally yield Bi(II) and an iodine atom. The iodine atom then reacts with iodide by

2 3– 1 3– intramolecular electron transfer to yield both [(η I2)BiI4] and [(η I2)BiI4] , Figure 4.5. The

2 3– 1 4– [(η I2)BiI4] reacts with an additional iodide to yield [(η I2)BiI5] . Clear experimental evidence for this reaction was illustrated by the kinetics of the η2 species being identical to the generation of the η1 species.

8 −1 −1 The inset of Figure 4.5 shows that the reaction is ﬁrst-order in iodide, kI = 2 x 10 M s . The

1 3– 1 4– [(η I2)BiI4] and the [(η I2)BiI5] were expected to have a similar absorption spectra. While the photochemistry is very different, we note that there is precedence for ligand coordination inducing a change

84 3– Figure 4.4: Proposed mechanism following iodide to metal charge transfer of a [BiI6] species in hapticity, intermolecular ligand induced η5 − η3 ring slippage of Pt(η3/5-Indenyl) complex.17 Thus with mM iodide concentrations the only transient species identiﬁed 100 µs after LMCT excitation was

1 4– [(η I2)BiI5] .

Concerted two electron transfer reactions are often invoked in reductive elimination/oxidation addition reaction chemistry of transi-tion metal complexes.18 However, a composite mechanism with

19 n– discrete, sequential 1 e- transfers can be envisioned. In this regard the [(I2)BiIx] species represent likely 1 e- transfer intermediates in this chemistry. Reduction of the ligated diiodide by a single electron lowers the

I-I bond order to zero and yields two iodide ions. Oxidation by one electron yields molecular I2 that would be expected to dissociate. The η2 linkage isomers would promote addition/elimination in a cis- stereochemistry about the metal and the observation of trans-products would require subsequent ligand rearrangement. Using this example as a model, mechanistic pathways for reductive elimination can be reinvestigated through the use of LMCT light excitation.

85 1 2 – 3– – Figure 4.5: Concentration proﬁles of η and η I2 after excitation of [BiI6] Inset: Plot of k2 versus [I ] for the transformation from η2 to η1 diiodide

1 4– The transiently generated [(η I2)BiI5] returned to ground state products with a ﬁrst-order rate constant of 2.0 x 103 s−1. Increasing the number of absorbed photons by up to a factor of six revealed no evidence for second- or higher-order reactivity and the rate constants were insensitive to the iodide ion

– concentration. This is quite unlike the reactivity of I2 CH3CN that disproportionates cleanly in acetonitrile,

.− − − 9 −1 −1 20 – 2I2 → I3 + I k = 3.3 x 10 M s . At 10 mM concentration, coordination of I2 CH3CN to bismuth enhances its lifetime by over four orders of magnitude. Therefore, while the transient spectrum of

1 4– – [(η I2)BiI5] was very similar to that of I2 CH3CN, the kinetics for relaxation to ground state products were so sufﬁciently different as to be distinguishing.

1 4– An intriguing question is why the [(η I2)BiI5] species lives for half a millisecond? In other words,

II – why doesn’t the Bi rapidly reduce I or I2 ? Answers to these questions remain speculative, in part because bismuth in the formal oxidation state of II has not been directly observed. Attempts to measure

3– photoluminescence emanating from the [BiI6] solutions have thus far been unsuccessful. In fact, LMCT excited states are generally dissociative and do not emit light. A concern was that the BiII generated by light excitation transfers the electron to another species which enables the long lifetimes of the diiodide species.

– However, such a process would lead to a reaction mechanism that was second-order; ﬁrst order in I2 and

86 ﬁrst order in BiII, which is contrary to experiment. Therefore, our speculation is that intersystem crossing to lower lying triplet states facilitated by the heavy bismuth metal accounts for the remarkably long-lived

1 4– [(η I2)BiI5] species that is indeed best formulated as an excited state.

2 3– The formation of the [(η I2)BiI4] and some of the η species occurred within the instrument response time of 10 ns. Such rapid I-I bond formation may occur by unimolecular electron transfer.

Alternatively, LMCT light absorption could promote I-I bond formation in one concerted step. In other

– words, the Franck-Condon state created by light absorption may already possess the I-I bond of I2 ,

III x– II *x– [(I)2 Bi In] + hν → [(I2)Bi In] . Precedence for such reactivity exists in studies of donor-acceptor iodide ion-pairs where high iodide concentrations have induced low energy absorption bands assigned to this concerted pathway.21 In solution processing of lead perovskite solar cells, the solutions are the characteristic yellow color of PbI2, yet turn black when deposited in the solid state as the methyl ammonium perovskites.

In this structure the iodide ions are in close-packed Van der Waals contact of about 4.4 A˚ that can provide the electronic coupling necessary for the con-certed photoexcitation.22 At the iodide concentrations used herein, the Bi is predominantly six-coordinate and the nearest neighbor I-I distance is 4.7 A˚ , with the metal providing enhanced coupling. While the data reported here does not unambiguously demonstrate such a concerted pathway, these observations warrant further study as they are highly relevant to solar energy

− . − .− conversion. In acetonitrile electrolytes, the Eo(I /I ) is 300 mV more positive than is Eo(2I /I2 ), resulting in concerted charge transfer transitions that occur at substantially lower energy and can harvest solar photons at longer wavelengths.

In an attempt to further characterize the LMCT transition and the resulting Franck-Condon state,

Stark spectroscopy was performed. Unfortunately due to the current apparatus set up, measurements with

4– high ionic concentrations prove to be difﬁcult. Several attempts were made to measure the [BiI6] solution used in the transient absorption experiments that resulted in conduction across the capacitor at ﬁeld strength

87 16 less that 1/4 that of usual measurments (<0.1 MV/cm). However, a solution of BiI3 was measured on the

Stark apparatus providing fruitful results.

While admittedly not the same system as that measured in transient absorption, the Stark data did provide insight into the possible Franck-Condon states of BiI3. By perturbing the electronic transitions with an electric ﬁeld, changes in dipole moment could be observed. Figure 4.6 illustrates the low-temperature absorption spectrum and Stark spectrum obtained on a homebuilt apparatus.16 The dipole moment change in the BiI3 case proved to correspond to an electron transfer distance of ∼0.6 A,˚ substantially less than that of the expected bond lengths of ∼3.1 A.˚ These results indicate the possibility that there is a large degree of coupling between the iodide and bismuth orbitals or the overall change in dipole moment is reduced due to the rearrangement of electron density to a point between two iodides, for bond formation. The ﬁrst possibility is unlikely simply due to the fact that the higher energy transition corresponds to a charge transfer distance of

2.3 A,˚ much more appropriate for a direct LMCT with reasonable coupling. As such, it is likely that even without the additional iodides used in the transient absorption experiments, the electron transfer is concerted and from two iodides instead of just one. Future work with the Stark apparatus should allow for accurate investigation of potential concerted steps within photochemical transitions.

The ligated diiodide discovered herein could be utilized for applications in dye sensitized solar cells

– 23,24 (DSSCs). Within these cells, the most commonly used redox mediator is based on mixture of I and I2.

– After excited state injection, the oxidized dye is “regenerated” through iodide oxidation to yield I2 that

– – quantitatively disproportionates to yield I and I3 . This disproportionation chemistry yields iodide products that have unfavorable one-electron reduction potentials that aid in the collection of the injected electrons in the external circuit.24 However, disproportionation comes with a tremendous 1.26 eV free energy loss for the two-electron reaction that decreases the DSSC power output and the open circuit voltage. If

– disproportionation could be prevented and instead I2 diffused to the counter electrode where it was reduced back to iodide, then becomes immediately of interest as that potential difference could signiﬁcantly improve

88 Figure 4.6: Top) Low-temperature absorption spectrum (black) with an overlaid ﬁt (red). Bottom) Stark spectrum (black) with an overlaid ﬁt (red) and individual derivative contributions

89 – device efﬁciency by almost a factor of two. The results described herein indicate that metal-I2 ligation represents a means by which disproportionation can be avoided.

4.4 Summary

The results of spectroscopic studies demonstrate the formation of a transiently stabilized metal diiodide adduct formed by ligand-to-metal charge transfer excitation of a bismuth iodide complex. Through spectral deconvolution a ﬁrst-order rate constant of 2000 s−1 for diiodide decay was obtained corresponding to lifetimes on the millisecond timescale. This relaxation pathway is unusual as diiodide is known to undergo extremely energetically favored disproportionation chemistry in ﬂuid solution. The unexpected stabilization

– of I2 by bismuth is tentatively assigned to spin change to a triplet state assisted by spin-orbit coupling from the heavy bismuth center. Coordination to the bismuth center stabilizes the normally unstable diiodide and its ultimate relaxation did not result in the formation of triiodide. These results provide substantial cause for further investigation into metal halide species for increasing the efﬁciency of the use of iodide as a redox mediator in DSSCs as well as understanding uses of iodide as a hole transport method in solid state photovoltaics.

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92 CHAPTER 5–Visible-Light Induced Electron Transfer Chemistry of Osmium (II) Supramolecular Assemblies

5.1 Introduction

Conversion of relatively cheap chemical feedstock to high energy chemical products that can be stored using sunlight, which will offer alternatives to fossil fuels, is one of the most challenging goals of science and society.1–12 When sunlight drives the formation of stable, covalent bonds, solar energy is stored as chemical energy.13 Water splitting with dihydrogen generation has attracted much attention, yet another promising target is HX splitting through the light-induced formation of halogen atoms that go on to form halogen-halogen bonds in solution according to eq. 5.1. Taking advantage of molecular excited states to oxidize halides could offer an efﬁcient way to store light energy in chemical bonds.2,14–22 Nocera et al. have reported examples of bimetallic complexes that oxidize both bromide and chloride to their respective halogen atom.20–27 Other examples have been reported that focused on the excited-state electron transfer between ruthenium complexes and bromide or chloride.15,16,28,29

. − .− X + X → X2 (5.1)

It has also been demonstrated that the oxidation of iodide by an excited state metal complex can lead

– – 30,31 to the formation of I-I bonds, in the form of I2 and I3 . In particular, the metal-to-ligand charge transfer

(MLCT) excited states of ruthenium polypyridyl complexes have been shown to oxidize iodide in a number of different solvents.32–34 Studies have shown that this oxidation proceeds through a stepwise mechanism, in which the one electron oxidation of iodide yields the iodine atom, I , which further reacts with another iodide

93 – 35,36 ion in solution to form I2 , commonly referred to as the ’single atom pathway’. This reaction mechanism appears to be very general and attempts to tune the reactivity by changing the driving force, showed that electron transfer occurred rapidly via this mechanism, even when the free energy change for the excited-state reaction was near zero.37 Instead of tuning the thermodynamic driving force, another approach to control the excited-state reactivity is to pre-organize reactive species in ground-state supramolecular assemblies. It was shown, for example, that iodide oxidation by ruthenium excited-states was enhanced through a static quenching mechanism in low dielectric solvents.38 Moreover, recently, a ruthenium complex bearing a ligand speciﬁcally designed to bind halides (dea = 4,4’-diethanolamide-2,2’-bipyridine) was shown to undergo n o purely dynamic quenching of the ion-paired complex Ru2+ : I– by a second free anion, rather than static quenching within the ion-pair.39 To promote even stronger ion pairs in solution, ruthenium complexes bearing di-cationic 4,4’-bis(trimethylaminomethyl)-2,2’-bipyridine (tmam) ligands were proposed and ruthenium complexes bearing overall charges of 4+, 6+ and 8+ were synthesized and shown to form ion-pairs with iodide in acetonitrile.40

4+ Recently, [Ru(dtb)2(tmam)] , where dtb is 4,4’-di-tert-butyl-2,2’-bipyridine, was shown to form n o strong Ru4+ : 2I– ion-pairs in acetone solution and the ion pairs were shown to be of importance to the excited-state quenching mechanism.28 When the singly ion-paired species was the dominant species in n o3+∗ solution, dynamic quenching of Ru4+ : I– was observed, whereas, at concentrations where the n o2+∗ doubly-ion-paired species Ru4+ : 2I– was dominant, static excited-state quenching was shown to occur within the ion-pair, independent of external iodide. Hence, both electron transfer and bond formation occurred within one pre-associated terionic complex.

Excited-state dipole orientation was suggested to play an important role in charge screening and

4+ iodide repulsion. In the case of [Ru(dtb)2(tmam)] , the excited-state was localized on the tmam ligand. It was suggested that this additional electron density repelled the ion-paired iodide, which in turn, decreased the rate constant for I-I bond formation, and prevented concerted diiodide bond formation. An approach to

94 reposition the excited-state dipole orientation away from the tmam ligand is to substitute the ancillary ligands with more electron accepting ones, such as 2,2’-bipyrazine. Consequently, the ground and excited-state properties would be drastically shifted and render the reaction between the excited-state and iodide too exothermic, once again preventing the observation of a concerted mechanism.

Osmium complexes are, compared to their corresponding ruthenium complexes, less potent photo-oxidants.41 Overall, the photophysical properties of osmium complexes are similar to those of ruthenium complexes, with some important differences owing to osmium being a third row transition metal.

Importantly, in comparable complexes the osmium metal center is easier to oxidize than the ruthenium.42

However, the ligand-based reductions remain almost unchanged between ruthenium and osmium complexes, which leads to a smaller corresponding HOMO-LUMO gaps in osmium complexes. This smaller energy gap

2+ in osmium polypyridyl complexes is exempliﬁed by the photoluminescence maximum of [Ru(bpy)3] at

2+ 43 ∼610 nm vs. the maximum of [Os(bpy)3] at 740 nm. It follows that osmium excited-states store less free energy, and thus are less potent photo-oxidants. Hence, in order to investigate the importance of excited-state localization in complexes with little driving force for iodide oxidation, two osmium complexes which promoted the formation of terionic assemblies were designed. One complex was designed as a control complex with unsubstituted bpy ancillary ligands, while the second complex was speciﬁcally designed to localize the excited-state on the ancillary ligands, away from the tmam ligand. In addition, the strategy of preorganization of ground-state reactants remediates issues related to the short excited-state lifetime of osmium(II) complexes, which hints at future applications in solar energy conversion schemes.

5.2 Experimental

Materials. Acetone (Burdick and Jackson, 99.98 %) and Acetonitrile (Burdick and Jackson, 99.9%) were used as received. Argon gas (Airgas, 99.998 %) was passed through a Drierite drying tube before use.

Tetrabutylammonium iodide (TBAI, Sigma-Aldrich, ≥ 99.0 %), tetrabutylammonium hexaﬂuorophosphate

95 (TBAPF6, Sigma-Aldrich, for electrochemical analysis, ≥ 98 %), were used as received. Deuterated acetone

44 was purchased from Cambridge Isotope Laboratories, Inc. 4,4’-bis(triﬂuoro)-2,2’-bipyridine (CF3bpy) and

4,4’-bis-(trimethylaminomethyl)-2,2’-bipyridine40 (tmam) were synthesized according to reported protocols.

All other chemicals were obtained from commercial distributors with minimum purity of 98 % and used as received. All solutions were purged with argon for at least 30 minutes before all electrochemical, photoluminescence and titrations experiments.

Nuclear Magnetic Resonance. Characteristic NMR spectra and halide titration experiments were obtained at room temperature on a Bruker Advance III 600 MHz spectrometer equipped with a broadband inverse (BBI) probe. Solvent residual peaks were used as internal standards for 1H(δ =2.05 ppm for

(CD3)2CO) and δ = 3.31 ppm for CD3OD) chemical shift referencing. NMR spectra were processed using

MNOVA.

Electrospray Ionization Mass Spectrometry (ESI-MS). Samples were analyzed with a Q Exactive

HF-X (ThermoFisher, Bremen, Germany) mass spectrometer. Samples were introduced via a heated electrospray source (HESI) at a ﬂow rate of 10 µL/min. One hundred time domain transients were averaged in the mass spectrum. HESI source conditions were set as: nebulizer temperature 100 degrees C, sheath gas

(nitrogen) 15 arb, auxillary gas (nitrogen) 5 arb, sweep gas (nitrogen) 0 arb, capillary temperature 250 degrees C, RF voltage 100 V. The mass range was set to 200-2000 m/z. All measurements were recorded at a resolution setting of 120,000. Solutions were analyzed at 0.1 mg/mL or less based on responsiveness to the

ESI mechanism. Xcalibur (ThermoFisher, Breman, Germany) was used to analyze the data. Molecular formula assignments were determined with Molecular Formula Calculator (v 1.2.3).

UV-Visible Absorption. UV-Vis absorption spectra were recorded on a Varian Cary 60 UV-Vis spectrophotometer with a resolution of 1 nm. The molar absorption coefﬁcient of the two complexes was determined by diluting a stock solution of osmium complex and represent averages of at least three independent measurements.

96 Steady-State Photoluminescence. Room temperature steady state photoluminescence (PL) spectra were recorded on an Edinburgh FLS920 ﬂuorescence spectrophotometer using a 450 W xenon arc lamp as the excitation source and a photomultiplier tube (Hamamatsu 2658P) as the detector. The photoluminescence intensity was integrated for 0.3 s at 1 nm resolution and averaged over three scans. All PL spectra were corrected by calibration of each instrument’s spectral response with a standard tungsten-halogen lamp. The

2+ – PL quantum yield, ΦPL, was measured by comparative actinometry using [Os(bpy)3] ·2PF6 in acetonitrile

(Φ = 0.00462) as a quantum yield standard.45

Temperature control during 77K photoluminescence measurements was maintained by using a Janis

Dual Reservoir VPF system with four-way fused quartz windows. Both 77K spectra were obtained in butyronitrile glasses. The resulting photoluminescence spectra were ﬁt to a single-mode Franck-Condon lineshape analysis, as described previously.46,47 The ﬁt was performed in Wolfram Mathematica 11, using a

Levenberg-Marquardt least squares error minimization method.

Time-Resolved Photoluminescence.Two techniques were used to collect time-resolved data.

Lifetimes determined with both techniques agreed with each other.

Time-resolved PL data were collected on a FLS920 spectrophotometer by time- correlated single-photon-counting (TCSPC). Excitation light pulses at 484 nm were produced by using a diode laser

(Edinburgh Instruments EPL- 485; 93 ps full-width at half-maximum pulse width) operated at 2 MHz (0.122 ns/point). The spectral bandwidth of the emission monochromator was set to 20 nm. A 630 nm, long-pass

ﬁlter was used after the sample to eliminate scatter and second-order grating effects.

Time-resolved PL data were also acquired on a nitrogen dye laser with excitation centered at 445 nm, as described previously.39 Pulsed light excitation was achieved with a Photon Technology International (PTI)

GL-301 dye laser that was pumped by a PTI GL-3300 nitrogen laser. The PL was detected by a Hamamatsu

R928 PMT optically coupled to a ScienceTech Model 9010 monochromator terminated into a LeCroy

Waverunner LT322 oscilloscope. Decays were monitored at the photoluminescence maximum and averaged

97 over 180 scans. Non-radiative and radiative rate constants were calculated from the quantum yields, eq. 5.2,

kr ΦPL = (5.2) (kr + knr) and lifetimes, eq. 5.3. 1 τ = (5.3) (kr + knr)

Electrochemistry. Cyclic voltammetry/square wave voltammetry was performed with a BASi Epsilon potentiostat in a standard three-electrode-cell, i.e. a platinum working electrode, platinum counter electrode and a non-aqueous silver/silver chloride (Pine) reference electrode that was referenced to an external

48 ferrocene (Fe(Cp)2, +650 mV vs NHE) standard. Experiments were performed in 0.1 M TBAClO4 acetone electrolyte.

Halide Titrations. UV-Vis halide titration experiments were performed in acetone using approximately 10 µM of osmium complex. UV-Vis measurements were performed for each of tetrabutylammonium halide salt through additions of approximately 0.3 equivalents. Stock solutions were initially prepared for both complexes and 3 mL of the stock solution was transferred to a quartz cuvette. 3-5 mL titration solutions were then prepared from the same stock solution by adding halide salt to obtain the desired concentrations. The solutions were then titrated into the quartz cuvette in 10 or 20 µL additions. The concentration of complex remained unchanged throughout the titrations by preparing the stock solutions.

Titrating solutions were kept in the dark for the duration of the experiment.

Time-resolved and steady-state PL titration experiments were performed in acetone using approximately 10 µM of osmium complex and TBAI. Solutions were prepared and titration experiment was performed in the same way as for the UV-Vis titrations, but were purged with argon for 30 minutes prior to experiments.

98 The 1H NMR titrations were performed using Bruker Avance III 600 MHz spectrometer equipped

4+ – with a broadband inverse (BBI) probe using 600 µL of a 500 µM [Os(LL)2(tmam)] ·4PF6 solution in deuterated acetone. Titration was performed by 0.25 equivalent additions of TBACl or TBAI (10 µL additions). Each spectrum was averaged over 32 scans and was not corrected for dilution.

Equilibrium Constants. Equilibrium constants were determined by plotting the absorbance change

(∆Abs), which was obtained by subtracting the initial spectrum in the absence of halide from all subsequent spectra, as a function of chloride concentration. The data were ﬁt to a 1:2 stoichiometry expression, eq. 5.4.49

− − 2 ε∆Os:I K1[Os]0[I ] + ε∆Os:2I K1K2[Os]0[I ] ∆Abs = − − 2 (5.4) 1 + K1[I ] + K1K2[I ]

Transient Absorption Spectroscopy. Nanosecond transient absorption measurements were acquired on a setup published previously.50 Brieﬂy, a Q-switched, pulsed Nd:YAG laser (Quantel USA (BigSky)

Brilliant B 5-6 ns full width at half-maximum (fwhm), 1 Hz, ∼10 mm in diameter) were doubled to 532 nm.

The laser irradiance at the sample was varied between 4-80 mJ/pulse. The probe lamp was a 150 W xenon arc lamp and pulsed at 1 Hz with 70 V during the experiment. Signal detection was achieved using a monochromator (SPEX 1702/ 04) optically coupled to an R928 photomultiplier tube (Hamamatsu) at a right angle to the excitation laser. Transient data were acquired with a computer-interfaced digital oscilloscope

(LeCroy 9450, Dual 330 MHz) with an overall instrument response time of ∼10 ns. For excited-state spectra for the 370-800 nm wavelength range, an average of 30 laser pulses were acquired and averaged at each wavelength of interest. Intervals of 10 nm were collected for wavelength between 370 and 600 nm and intervals of 20 nm were collected between 600 and 800 nm. Time-resolved PL data were also acquired using the same laser intensity and wavelength (532 nm) at wavelengths greater than 600 nm.

Single wavelength absorption changes were averaged over 90-180 laser pulses depending on signal to noise level. Samples were prepared in a similar manner as during halide titrations but care was taken to

99 achieve ∼0.2 absorption at 532 nm. Samples were checked routinely (every 180 shots) for photodegradation during higher intensity (30-80 mJ/pulse) laser experiments, with no or minimal changes detected in the

UV-visible spectra.

Determination of Reduced Complex Spectra. The absorption spectrum of the singly reduced Os-CF3

51 complex was determined using a procedure adapted from literature. A 20 µM solution of Os-CF3 with 7 mM tri-anisolamine (MeOTPA)52 was irradiated with 532 nm light (10 mJ/pulse). Transient absorption

+ spectra were consistent with the formation of the reduced Os-CF3 complex and oxidized MeOTPA . The spectra were then normalized at 680 nm, and the known spectrum of MeOTPA+ (obtained through spectroelectrocemistry in 0.1 TBAClO4acetone solution) was subtracted. The same experiment was repeated with a 20 µM solution of Os-CF3 with 25 mM hydroquinone that was irradiated at 16 mJ/pulse, and the resulting difference spectra corresponding to the reduced Os-CF3 overlapped with the previous result.

Stark Spectroscopy. The Stark spectra were obtained through the use of a previously published setup.53 Briefly, a 150 W xenon arc lamp is passed through a monochromator (McPherson 272) and focused into a 1 cm2 area beam on the sample. High concentration samples, ∼3 mM, were placed in a thin path length optical cell and submerged in liquid nitrogen to form a glass. One side of the optical cell is oscillated at 2900 Hz between +1.5 kV and -1.5 kV to generate an oscillating electric field across the sample. The oscillating signal is processed by a lock-in amplifier (SRS 530), an oscilloscope (LeCroy Wavesurfer 3054), and in-house Labview software. An average of 106 data points per wavelength at a 1 nm step width were collected.

Relevant electronic parameters of the dipole moment change, ∆µ, and the angle of the dipole moment change vector with respect to the transition dipole moment, ζ, were determined through the use of

Monte Carlo simulations using a Levenberg-Marquardt least squares minimization method with modulation of each variable. Values were visualized by plotting the extinction coefﬁcient change (∆ε), which was obtained directly from experiment, as a function of wavenumber. The data were ﬁt to a standard 2-state

100 model Liptay Formalism, eq. 5.5.54–56

d(ε) d2(ε) ∆ε = F 2 A ε + B + C (5.5) χ χ dν χ dν2

Theoretical Calculations. Density Functional Theory (DFT) calculations were carried out using the

Gaussian 09 program package, while applying default algorithms and parameters. First, the ground state

(singlet) structures of two osmium complexes with zero, one and two iodide anions located at the positions indicated by 1H NMR, were optimized to their minimum energy. In all calculations, the B3LYP functional was used,57–60 with the LANL2DZ basis set61–63 with an added f-polarization function applied to osmium, cc-PVDZ-PP with an added f-polarization function applied to iodide,64 and 6-311G* applied to all other elements.65 The harmonic vibrational frequencies were calculated for each osmium complex, with all combinations of no iodide or iodide present, with the same level of calculation and by conﬁrming no contribution from negative frequencies, it was conﬁrmed that the resulting structures correlated to true minima of the potential energy surface.

Second-order perturbations analysis of intermolecular interactions of natural atomic charges used for

Coulombic work term calculations were performed with the NBO 3 program, as implemented in the Gaussian program package. The resulting cartesian coordinates of all atoms in the structures and their associated charges were analyzed using a Coulomb’s law expression and visualized using Wolfram Mathematica 11.

Synthesis of [Os((CF3)2bpy)2Cl2]. 4,4’-bis(triﬂuoro)-2,2’-bipyridine (382 mg, 1.31 mmol) and ammonium hexachloroosmate (274 mg, 0.62 mmol) were suspended in a microwave tube containing 8.5 mL of argon sparged ethylene glycol. The reaction mixture was heated under microwave irradiation to reach 200

°C in 3 minutes. The reaction mixture was held at this temperature for 30 minutes. After cooling, 20 mL of a

1M Na2S2O4 aqueous solution was added and the mixture was cooled for 30 minutes in an ice bath. The solution was then ﬁltered and the precipitate was washed with water to remove impurities and with hexane to

101 remove excess of unreacted ligand. The ﬁnal product, [Os((CF3)2bpy)2Cl2] was obtained as a black-purple microcrystalline solid. The complex was used without further puriﬁcation.

Synthesis of [Os(bpy)2Cl2]. 2,2’-bipyridine (747 mg, 4.8 mmol) and ammonium hexachloroosmate

(1.0 g, 2.3 mmol) were suspended in 40 mL or argon sparged ethylene glycol. The reaction mixture was heated at reflux for one hour under argon. After reaction, the mixture was cooled to room temperature and 40 mL of a saturated Na2S2O4 aqueous solution was added. The mixture was cooled in an ice bath for 30 minutes prior to being filtered. The precipitate was washed with water and diethylether. The final product,

[Os(bpy)2Cl2] was obtained as a black-purple microcrystalline solid. The complex was used without further puriﬁcation.

4+ – – Synthesis of [Os(bpy)2(tmam)] 4PF6 . [Os(bpy)2Cl2] (100mg, 0.174 mmol) and tmam 2PF6 (103 mg, 0.174 mmol) were combined with 15 mL of an EtOH/H2O 1:1 mixture in an ACE tube. The mixture was purged with argon for 30 minutes after which the tube was sealed and the reaction was heated at 120 °C for

48 hours. After reaction, the mixture was brought to room temperature and evaporated under reduced pressure. The residue was dissolved in methanol and filtered on a 0.2 µm syringe filter. The filtrate was concentrated under reduced pressure and purified by size exclusion LH20 column chromatography using

MeOH as eluent. The desired fraction was collected and evaporated under reduced pressure. The residue was

ﬁnally dissolved in water and precipitated by the addition of a saturated NH4PF6 aqueous solution. The precipitate was ﬁltered, washed with water and diethylether to yield a brown solid (185mg, 79%). 1H NMR

(600 MHz, Acetone-d6): δ 8.94 (s, 2H), 8.81 (t, J = 7.6 Hz, 4H), 8.25 (d, J = 6.0 Hz, 2H), 8.09 - 8.03 (m, 4H),

7.97 (d, J = 5.6 Hz, 2H), 7.91 (d, J = 5.6 Hz, 2H), 7.71 (dd, J = 6.0, 1.8 Hz, 2H), 7.55 - 7.51 (m, 2H), 7.46 -

7.42 (m, 2H), 4.89 (s, 4H), 3.40 (s, 18H). 13C NMR (600 MHz, Acetone-d6): δ 161.32, 159.62, 159.56,

152.74, 152.59, 151.67, 138.82, 137.68, 132.95, 129.56, 129.34, 129.31, 125.54, 67.71, 53.91. HRMS

2+ (ESI-MS) m/z: [M-(2PF6)] Calcd for C38H44N8P2F12Os 547.12937; Found 547.12610.

102 4+ 4+ Figure 5.1: Synthetic routes to obtain [Os(CF3bpy)2(tmam)] and [Os(bpy)2(tmam)] .

4+ – Synthesis of [Os((CF3)2bpy)2(tmam)] 4PF6 . [Os((CF3)2bpy)2Cl2] (100mg, 0.118 mmol) and tmam

– 2PF6 (70 mg, 0.118 mmol) were combined with 15 mL of an EtOH/H2O 1:1 mixture in an ACE tube. The mixture was purged with argon for 30 minutes after which the tube was sealed and the reaction was heated at

120 °C for 3 days. After reaction, the mixture was brought to room temperature and evaporated under reduced pressure. The residue was dissolved in methanol and filtered on a 0.2 µm syringe filter. The filtrate was concentrated under reduced pressure and purified by size exclusion LH20 column chromatography using

MeOH as eluent. The desired fraction was collected and evaporated under reduced pressure. The residue was

(600 MHz, Acetone-d6) δ 9.44 (d, J = 7.4 Hz, 4H), 8.99 (s, 2H), 8.44 (d, J = 6.1 Hz, 2H), 8.36 (d, J = 6.0 Hz,

2H), 8.31 (d, J = 5.9 Hz, 2H), 7.75 (m, J = 5.0 Hz, 6H), 4.90 (s, 4H), 3.40 (s, 18H). 13C NMR (600 MHz,

Acetone-d6) δ 161.16, 160.81, 160,26, 154.44, 153.51, 139. 45, 133.18, 129.68, 122.75, 67.56, 54.00.

+ HRMS (ESI-MS) m/z: [M-(PF6)] Calcd for C42H40N8P2F24Os 683.10414; Found 683.09993.

103 5.3 Results and Discussion

4+ The synthesis of [Os(LL)2(tmam)] complexes, where tmam is

4,4’-bis-(trimethylaminomethyl)-2,2’-bipyridine and LL is 2,2’-bipyridine (bpy) or

2– 4,4’-(CF3)2-2,2’-bipyridine (CF3), is shown in Figure 5.1. [OsCl6] was reacted with 2,2’-bipyridine or

4,4’-(CF3)2-2,2’-bipyridine in ethylene glycol at 200 °C to yield the corresponding [Os(LL)2(Cl)2] complexes. These were then reacted with tmam in EtOH/water mixtures to yield the ﬁnal complexes. The

ﬁnal products were puriﬁed by size exclusion (LH20) column chromatography and precipitated as the

– hexaﬂuorophosphate (PF6 ) salts after ion metathesis.

The photophysical and photochemical properties of the complexes were characterized in argon purged acetonitrile and acetone. The absorption spectra of both complexes are shown in Figure 5.2. The intense bands (ε = 80,000-100,000 M−1 cm−1) at ∼290 nm were identiﬁed as ligand centered (LC) π − π∗ transitions, based on assignments reported on related osmium polypyridyl complexes.66,67 Similarly, the absorption bands beyond ∼400 nm were assigned as metal-to-ligand charge transfer (MLCT) bands.42,66,67

The MLCT transitions at 400-550 nm, with a higher molar absorption coefﬁcient (ε = 15,000 M−1cm−1), were assigned as spin allowed 1MLCT transitions. The tailing absorption bands beyond 550 nm were assigned as singlet-to-triplet excitations.67 These formally spin forbidden transitions are expected to be more intense in osmium complexes than in ruthenium complexes due to increased spin orbit coupling.42,67

Visible light excitation of either complex resulted in room temperature photoluminescence (PL) centered at 815 nm and 775 nm for Os-bpy and Os-CF3 respectively. The electron-withdrawing triﬂuoromethyl substituents on the ancillary ligands of Os-CF3 led to a 40 nm (∼79 meV) hypsochromic shift in the PL compared to the unsubstituted 2,2’-bipyridine complex. The corresponding excited-state lifetimes were well described by a ﬁrst order kinetic model. These were relatively short, 68 and 54 ns for Os-bpy and

Os-CF3 respectively in argon purged acetone. Consequently, the non-radiative decay rate constants for the

104 4+ 4+ Figure 5.2: UV-Vis absorption spectra of [Os(CF3bpy)2(tmam)] (orange) and [Os(bpy)2(tmam)] (purple) in acetonitrile (solid) and acetone (dash).

– Table 5.1: Photophysical properties of the indicated osmium [PF6] complexes in acetone. [a] [b] [a] [c] [d] [e] [e] Complex MLCTmax (ε) PLmax τ Φ kr knr 4+ 4 7 [Os(bpy)2(tmam)] 439 (13,300), 493 (12,200) 815 68 0.0014 6.80 x10 1.85 x10 4+ 4 7 [Os(CF3bpy)2(tmam)] 438 (14,100), 491 (13,700) 775 54 0.0037 2.06 x10 1.47 x10 [a] [b] −1 −1 [c] [d] 2+ PL maximum in nm. M cm . ns. Measured by comparative actinometry using [Os(bpy)3] Φ = 0.00462 as reference. 43 [e] s−1

7 −1 osmium complexes were relatively large (knr∼ 10 s ) compared to related ruthenium complexes (knr∼

6 −1 68,69 10 s ). The excited-state lifetimes, quantum yields, kr, knr and other relevant photophysical data are gathered in Table 5.1.

Reversible oxidations associated with the metal centers were measured by cyclic voltammetry and square wave voltammetry. The oxidations were centered at +1.28 and +1.10 V vs NHE for Os-CF3 and

Os-bpy respectively. Notably, the potential measured for Os-bpy was ∼500 meV less positive than the metal

4+ 47 centered oxidation in the corresponding, [Ru(bpy)2(tmam)] complex, which agrees with previously

42 n/n−1 published correlations. The Os-CF3 complex displayed a reversible E1/2(Os ) ligand-centered reduction at -0.62 V vs NHE in 0.1 M tetrabutylammonium perchlorate (TBAClO4) acetone electrolyte.

105 4+ 4+ Figure 5.3: Photoluminescence spectra of [Os(CF3bpy)2(tmam)] (orange) and [Os(bpy)2(tmam)] (purple) in acetone at room temperature (solid) and in butyronitrile at 77K (dash) with the corresponding ﬁt according to a Franck-Condon lineshape analysis.

Scanning more negatively resulted in a broad, irreversible reduction wave which was assigned to the tmam ligand.47,70 In the case of Os-bpy, a similarly broad, irreversible reduction wave was recorded at ∼ -0.7 V vs

NHE, which was used to estimate a ﬁrst reduction potential for Os-bpy.

Blakley and DeArmond showed by spectroelectrochemical correlation that the excited state localizes electron density onto the ligand which is ﬁrst electrochemically reduced.71 The electrochemical responses of the osmium complexes were suggestive of different excited-state localization. The ﬁrst reduction supported the assignment of the Os-CF3 excited-state localized on the 4,4’-(CF3)2-2,2’-bipyridine ligand and the

III – 4+* formulation of the excited state as [Os (CF3 bpy)(CF3 bpy )(tmam)] . However, in the case of Os-bpy, the excited-state assignment was not as straightforward due to the irreversible electrochemistry. However, the

III 2+ 72 2,2’-bipyridine centered reduction in the related [Os (bpy)3] occurs 300 mV (-0.99 V vs NHE) more negative than the one observed in the present case. Hence, this supported the formulation of the excited state

III – 4+* as [Os (bpy)2(tmam )] .

106 – Table 5.2: Relevant reduction potentials and ∆GES values for the indicated osmium [PF6] complexes. 5+/4+ [a] 4+/3+ [a] 3+/2+ [a] [b] 4+∗/3+ [a] Complex E(Os ) E(Os ) E(Os ) ∆GES (eV) E(Os ) 4+ [Os(bpy)2(tmam)] +1.10 ∼ -0.7 - 1.73 ∼1.0 107 4+ [Os(CF3bpy)2(tmam)] +1.28 -0.62 ∼ -0.8 1.80 1.18 [a] V vs NHE. [b] Determined from blue edge tangent straight line ﬁt of room temperature PL spectra. These assignments were further strengthened by the results obtained by Stark spectroscopy, Figures

5.4 and 5.5. Figure 5.4 represents the absorption spectra measured at 77K in butyronitrile. Both osmium complexes displayed typical MLCT absorption features with transition in the 550-750 nm region that corresponded to direct singlet-to-triplet MLCT transitions.73,74 A large electric ﬁeld (> 0.4 MV cm–1) was then applied to generate the corresponding Stark spectra, Figure 5.4. When probed with different polarized light, Figure 5.5, the Stark effect allowed to determine the charge transfer angle relative to the transition

75 dipole moment, closely aligned with the ground state dipole moment. For Os-CF3, the lowest energy

1MLCT transition has different intensities whether a horizontally or vertically polarized probe beam was used. This was in contrast with Os-bpy where the same lowest energy 1MLCT transition was uniform, regardless of polarization of the probe light. The angle of the dipole moment change vector with respect to the transition dipole moment, ζ, and dipole moments, ∆µ, for each of the three major bands in the Stark spectrum are gathered in Table 5.3.

The dipole moment change derived from Stark spectroscopy also provided valuable information for the characterization of the transitions and the excited-state electronic structure. The largest dipole moment change, i.e. 12.9 D, was observed for the excitation to the (CF3)2bpy ligands. Dipole moment changes associated with 2,2’-bipyridine ligands were of smaller magnitude, i.e. ∼10.5 D. These values are in agreement with the trends that would be expected based on substituents effects, as reported on prototypical ruthenium(II) substituted 2,2’bipyridine complexes.53

Overall, the results obtained through Stark spectroscopy and electrochemistry were complementary in formulating an excited state localized on the 4,4’-(CF3)2-2,2’-bipyridine ligand for Os-CF3 and on

4,4’-bis-(trimethylaminomethyl)-2,2-bipyridine for Os-bpy.

The excited-state reduction potential was determined for each complex from the corrected PL spectra

4+*/3+ 4+/3+ and measured reduction potentials: E1/2(Os ) = E1/2(Os )- ∆GES, where ∆GES is the free energy stored in the excited state that was extracted from the PL spectra.76 The osmium complexes were not very

108 4+ Figure 5.4: Absorption (top) and Stark (bottom) spectra (black, with overlaid ﬁts in red) of [Os(bpy)2(tmam)] 4+ (left) and [Os((CF3)2bpy)2(tmam)] (right). All spectra were recorded in butyronitrile at 77k and scaled to an applied ﬁeld of 1 MV/cm.

4+ 4+ Figure 5.5: Stark spectra of [Os(bpy)2(tmam)] (left) and [Os((CF3)2bpy)2(tmam)] (right) record with horizontally (blue dots) and vertically (black dots) polarized light (corresponding ﬁt as solid lines). All spectra were recorded in butyronitrile at 77k and scaled to an applied ﬁeld of 1 MV/cm.

109 Table 5.3: Changes in dipole moment and angle of the dipole moment change vector with respect to the transition dipole moment for selected transitions of the indicated Os(II) complexes. Complex Transition (cm−1) ζ(°) ∆µ (D) 4+ [Os(bpy)2(tmam)] 19800 49 ± 12 7.8 ± 0.6 21600 34 ± 9 10 ± 0.5 22900 33 ± 6 11 ± 0.6 4+ [Os(CF3bpy)2(tmam)] 20100 30 ± 8 12.9 ± 0.5 21800 82 ± 7 9.2 ± 0.5 22600 85 ± 7 8.2 ± 0.4

4+*/3+ potent photooxidants with excited-state reduction potentials of E1/2(Os ) = ∼1.0 and 1.18 V vs NHE for

Os-bpy and Os-CF3, respectively. The relevant electrochemical and thermodynamic properties for the complexes are gathered in Table 5.2.

Density Functional Theory (DFT) calculations were performed to gain insight into the charge distribution of the osmium (II) complexes and their ability to form ion-pairs with selected halides. The structures of both complexes, with and without halides, were ﬁrst optimized by DFT calculations and then natural bond order (NBO) analysis was performed on the optimized structures.77? ,78 A Coulomb’s law style calculation, eq. 5.6 was used to visualize contour plots that showed the free energy interaction between the iodide and each atom in the osmium complex (Figure 5.6).

Z(I−)Z(Os4+)e2 Gw = (5.6) 4πε0εra

In this equation e is the elementary charge, ε0 is the vacuum permittivity, εr is the relative permittivity and a is the distance between the charged species. Z(I−) is the charge of the iodide and

Z(Os4+) the charge of the osmium complex, where the individual charges assigned to each atom were used, rather than an approximate spherical model with delocalized charge. Figure 5.6a highlights the very large free energy (∼ 450 meV) of interaction between free iodide and the tmam binding “pocket” of the osmium

110 Figure 5.6: Contour plots Os-CF3 (top) and Os-bpy (bottom) showing the plane that contains the tmam ligand, describing the Coulombic free energy (in eV) experienced without (a) and with (b) an iodide anion present in the tmam pocket. complex. The structures optimized with one iodide present in the tmam binding “pocket” (Figure 5.6b) highlight the large free energy (∼ 300 meV) of interaction with a second halide close to the osmium center.

These DFT and NBO calculations were correlated with experimental results obtained through 1H

NMR spectroscopy. The atomic resolution provided by 1H NMR conﬁrmed the tmam ligand as the ﬁrst binding site as evidenced by drastic shifts in the 3,3’ H atom resonance (∼0.9 ∆ppm) with small or no changes to the 3,3’-H resonances of the ancillary ligands, for Os-CF3 and Os-bpy, respectively, Figure 5.7.

The roofed-doublet pattern for the methylene H atoms that became apparent after 1 equivalent of iodide was added, has been previously reported and is fully consistent with the ion pairing imposing a more rigid configuration.47 The shifts in the 3,3’ tmam resonances also saturate beyond 1-2 equivalents, while other resonances still shifted with increasing halide concentration. This further supported the hypothesis of the tmam pocket as the primary binding site. A second binding site, closer to the metal center, was suggested by simultaneous shifts of the 5,5’ H atom resonances on the tmam ligand and the 6 and 5 H atoms resonances on the ancillary ligands for both complexes. There was no spectroscopic experimental evidence that pointed towards the second iodide influencing the position of the first iodide within the tmam binding pocket. While higher order species could not be ruled out, the dominant species at high iodide concentration was consequently determined as a 1:2 ion pair; [Os4+:2I–]2+.

111 Figure 5.7: a) Proposed structure of the terionic complexes. b) The chemical shifts of indicated hydrogen atoms of Os-CF3 plotted against the number of TBAI equivalents for Os-CF3 in d6-acetone with up to 8 1 equivalents. c) H NMR spectra of Os-CF3 with 0 to 8 equivalents of TBAI in d6-acetone showing both the aromatic region and methylene hydrogens of the tmam ligand.

112 The addition of halides also induced substantial shifts in the UV-Vis absorption spectra of the osmium complexes. In the case of Os-CF3, the addition on iodide induced a decrease and shifts in absorption of the main MLCT bands. The absorption changes in the UV-Vis spectra were used to estimate equilibrium

6 −1 4 −1 49,79 constants, Keq1 = 1.6 x10 M and Keq2 = 9.4 x10 M for the iodide ion pairs. From DFT and NBO analysis, iodide stabilization in the tmam pocket was approximately 450 meV, or 43 kJ mol−1, while the measured equilibrium constants provided approximately 35 and 28 kJ mol−1. This discrepancy highlighted a tendency of the theoretical calculations to overestimate equilibrium constants for ion-pairing while using the

Coulomb’s law approach.

Two pathways for iodide oxidation and I-I bond formation have been reported. In the ﬁrst, stepwise mechanism, electron transfer to form the iodine atom (I ) occurs ﬁrst. This is then followed by diffusion in

– solution and reaction with excess iodide to form I2 . In the second concerted mechanism, both electron transfer and bond formation occur simultaneously, eq. 5.7.

S∗ + I− → S− + I.

. − .− (5.7) I + I → I2

∗ − − .− S + 2I → S + I2

/– From a thermodynamic viewpoint, the I potential is reported at 1.23 V vs NHE in CH3CN, but remains elusive in acetone. A formal reduction potential associated with the concerted mechanism was estimated as 300 meV less positive than the stepwise mechanism. Hence, at ﬁrst approximation, the Os-bpy was not predicted to be a strong enough photooxidant to initiate excited-state one-electron transfer with iodide according to the stepwise mechanism, as this reaction would be uphill by approximately 230 meV. A concerted mechanism would be slightly exothermic. Experimentally, Os-bpy did not react with iodide as evidenced by steady-state and time-resolved photoluminescence experiments with increasing amounts of iodide where an increase and blue shift in the steady-state PLI, with a concomitant increase in the

113 excited-state lifetime were observed. This was attributed to iodide induced torsional restriction resulting from interactions with the ligands. As vibrational relaxation pathways were restricted, this decreased the non-radiative decay rate constant. The driving force for light-induced oxidation of iodide by Os-CF3 was estimated to be 50 meV uphill for the stepwise mechanism and 250 meV downhill for to the concerted mechanism. However, it has been previously shown that electron transfer can occur with rate constants close to the diffusion limit with no or even unfavorable driving force (∆G = 0 or + 0.04 eV).11

The excited-state quenching behavior recorded for Os-CF3 with TBAI was suggestive of ruthenium tmam-complexes previously reported, Figure 5.3.28 The steady-state photoluminescence intensity (PLI) decreased when iodide was added, and saturated at concentration of iodide greater than 8 equivalents, Figure

5.3b. Time resolved PL decays measured after pulsed light excitation were ﬁt to single exponential decays throughout the titration. The lifetimes decreased with added iodide, and saturated at a lifetime of 21 ns with more than 8 equivalents of iodide. The time-resolved PL also revealed a decrease in initial intensity, characteristic of a static quenching mechanism. An equilibrium constant for the ground state adduct, Keq =

1.8 x 104 M−1, was extracted from the initial decrease in accordance with a static Stern-Volmer model. This

4 value is slightly lower compared to the one determined by UV-Vis titration experiments (Keq = 9.4 x 10

M−1). However, values extracted from photoluminescence measurements report on the excited state behavior, as opposed to UV-Vis technique which probes the ground state of a complex.

The Stern-Volmer analysis of the excited-state quenching data, Figure 5.3 revealed an unusual shape that saturated at higher iodide concentrations, consistent with the formation of a novel luminescent species during the course of the experiment. The Stern-Volmer data was modelled by considering the presence of three photoluminescent species, which were as follows: (i) the initial complex with an excited-state lifetime

τ0 = 54 ns, (ii) a singly ion-paired species that was dynamically quenched by iodide, and (iii) the terionic species with an excited-state lifetime of ∼20 ns. From a previously described model, a dynamic quenching

114 Figure 5.8: a) Mole fractions of the indicated species with increasing amount of TBAI. b) Steady state 4+ PL decays of [Os(CF3bpy)2(tmam)] with increasing amount of TBAI. The orange shading represents the increased PL contribution from {Os4+ :2I–}duringthecourseoftheexperiment.c)Stern − 4+ V olmerplotof[Os(CF3bpy)2(tmam)] withT BAIinacetone.d)correspondingStern − V olmerbyremovingthecontributionof{Os4+ : 2I–}.

115 11 −1 −1 rate constant (kq = 1.8 x 10 M s ) was extracted, which was close to the calculated diffusion limit for

11 −1 −1 28,80–82 charged species in acetone, kdiff = (1.8-3.6) x 10 M s .

Additionally, when the PL resulting from the increasing concentration of terionic species present in solution was subtracted from the overall PL, Figure 5.3d, the apparent red-shift was also removed. The resulting Stern-Volmer analysis then took on a shape typical for complexes undergoing a combination of dynamic and static quenching, with no contribution from additional luminescent species. The data were ﬁt

4 −1 according to a a quadratic Stern-Volmer expression, from which a static (KS = 9.4 x10 M ) and dynamic

−1 11 −1 −1 quenching rate constant (KD = 15200 M which gives kq = 2.81 x10 M s ) could be extracted.

Interestingly, KS was identical to the second equilibrium constant determined experimentally by UV-Vis

11 −1 −1 titrations whereas kq was close to the previously determined value (kq = 1.8 x 10 M s ) and also fell within the diffusion limit for charged species in acetone, eq. 5.8.

(P LI ) 0 = 1 + (K + K )[Q] + K K [Q]2 (5.8) (P LI) D S D S

Pulsed 532 nm light excitation of both osmium complexes in argon purged acetone resulted in absorption difference spectra, which in agreement with literature precedence, showed a bleach of the ground state MLCT absorption and excited-state transitions in the near-UV region and beyond 700 nm.83 For

Os-CF3, which was investigated for its reactivity with TBAI, the two ground-state excited-state isosbestic points were identiﬁed at 399 and 705 nm. The absorption spectrum of the reduced Os-CF3 complex was obtained by transient absorption spectroscopy measurements preformed in the presence of known electron donors, such as MeO-TPA or hydroquinone.39,51 In the presence of 20 equivalents of TBAI, pulsed 532 nm laser excitation of Os-CF3 resulted in the appearance of new transient absorption features that were well

– described by equal concentrations of reduced Os-CF3 and I2 , Figure 5.9. The two peaks at 470 and 540 nm were assigned to the reduced osmium complex. The main absorption features at wavelengths below 400 nm

116 Figure 5.9: Transient absorption spectra measured 1 µs after pulsed 532 nm light (20.5 mJ/pulse) of 4+ [Os(CF3bpy)2(tmam)] with 20 eq TBAI. Overlaid in blue is a spectral modelling based on equal contribu- – tions of I2 (reference spectra in purple) and reduced complex.

– and beyond 600 nm were attributed to I2 , with some contributions from the reduced complex. The band at

∼750 nm, which could not be fully accounted for by spectral simulation was speculated to be due to a

– 84 I2 adduct. In all experiments, the UV-Vis spectra remained unaltered before and after transient absorption experiments, precluding any permanent photochemistry.

3+ – Both photoproducts, i.e. the reduced osmium complex (OsCF3 ) and I2 , absorbed light at 399 nm.

At low iodide concentrations, kinetic analysis of photoproducts was precluded by low photoproduct yields.

At high concentrations (20-40 equivalents), transient absorption studies revealed no iodide dependent rate constants. At 40 equivalents of iodide, the change in absorbance at 399 nm could be satisfactorily described by a single exponential kinetic function, although this absorption reported on two species. The corresponding lifetime of 26± 6 ns was determined, while the excited-state decay at 40 equivalents of iodide was determined to be 18 ± 2 ns. This indicated that, within experimental error, the reduced osmium complex was a primary photoproduct.

117 An overall scheme was proposed for the Os-CF3 complex, where following light excitation, the excited state localized on one of the ancillary CF3 ligands, away from the tmam ligand. At concentrations of iodide where the terionic complex is the predominant species in solution, the external iodide concentration no longer impacted the excited-state quenching, which indicated that an intra-ionic electron transfer mechanism was operative. Within the terionic species, electron transfer was proposed to occur from the iodide located closer to the metal center following light excitation with an observed rate constant of approximately 5.6 x 107 s−1, based on the PL decay. This iodide was expected to be more easily oxidized, as it was stabilized to a lesser extent (∼240 meV) and was believed to have enhanced coupling with the metal center, relative to the iodide in the tmam pocket.

4+ The results obtained herein were compared to the reported [Ru(dtb)2(tmam)] , where dtb is

4,4’-di-tert-butyl-2,2’-bipyridine. In this case, light excitation resulted in electron transfer from the ion-paired iodide to the ruthenium (II) center in 70 ns, Figure 5.10B. The I-I bond formation was slower (80 ns) due to suggested Coulombic repulsion between the remaining iodide anion in the tmam pocket and the reduced tmam ligand. It was proposed that the iodide anion in the tmam pocket was expected to move away from the reduced ligand while the iodine atom diffused towards iodide to form a bond. In the case of Os-CF3, electron transfer occurred more very rapidly following light excitation (∼18 ns). The electron localization on the 4,4’-(CF3)2-2,2’-bipyridine ligand, in agreement with electrochemistry and as postulated by Blakley and

DeArmond, did not induce any Coulombic repulsion between the tmam ligand and the iodide species, Figure

5.10A. Hence, the iodide anion in the tmam binding pocket could move closer to the iodide atom and form the corresponding I-I bond in ∼26 ns. At this stage, the succession of events that led to the formation of the bond in diiodide remained speculative.

118 Figure 5.10: Proposed reaction mechanisms for electron transfer and I-I bond formation for A) Os-CF3 and 4+ B) [Ru(dtb)2(tmam)] indicating the excited state electron density by blue color on ligand

5.4 Conclusions

In conclusion, two novel osmium complexes were synthesized, which promoted terionic structures with iodide through the use of a dicationic tmam ligand. Spectroscopic data indicated that similar terionic

– structures were formed with both osmium complexes and I . Upon visible light excitation, the Os-CF3 terionic complex was shown to oxidize iodide in acetone, contrary to Os-bpy. The Os-CF3 excited-state underwent rapid electron transfer and subsequent I-I bond formation as evidenced by transient absorption spectroscopy. At concentrations below 8 equivalents, a combination of static and dynamic quenching mechanisms was determined. An intra-ionic mechanism independent of external iodide concentration was determined at concentrations exceeding 8 equivalents. The excited-state lifetime saturated at ∼20 ns and rapid diiodide bond formation was determined. The excited-state dipole was determined to be oriented away from the tmam binding pocket in Os-CF3, which possibly contributed to the more rapid electron transfer and

I-I bond formation compared to related ruthenium (II) complexes. The kinetic and thermodynamic data did not conclusively reveal whether a concerted or stepwise intra-ionic mechanism was operative. Further kinetic

119 studies such as ultrafast transient spectroscopy to determine the nature of the mechanism should be undertaken. These perspectives should help determine the inﬂuence that the excited state localization may have on the quenching and bond formation mechanism and how this may be accounted for in the future designs of complexes capable of driving covalent bond formation.

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126 CHAPTER 6–Stark Apparatus Description and Operation

6.1 Introduction

The Stark apparatus is designed to measure fundamental electron transfer quantities, or FETQs; extinction coefficients, transition dipole moments, change in dipole moment, change in polarizability, and the operative angle between the molecular axis (ground state dipole moment vector) and the charge transfer vector. The hardware includes a high voltage amplifier in conjunction with a function generator to provide the high oscillating field strength required to make electro-absorption measurements. High concentration samples are frozen into a glass after being submerged in liquid nitrogen contained within a 3-chamber cryostat. While the results of an experiment post-analysis provide FETQs, the apparatus itself monitors

fluctuations in transmission intensity with a photodiode amplifier in conjunction with a lock-in amplifier allowing for resolution of sub-millisecond modulation and amplified photodiode amplitudes of < 200 µV. As described below, the experiments that can be performed by the apparatus are either low-temperature absorption spectroscopy or electro-absorption spectroscopy, also known as Stark spectroscopy.

For low-temperature absorption spectroscopy, the sample is not perturbed by an oscillating electric

ﬁeld. Instead, a beam chopper is introduced to modulate the probe beam at a frequency which the lock-in ampliﬁer is then referenced to. The rest of the details of the instrumentation are identical, and as such the instrumental set up for both experiments is combined into one description section.

The apparatus built is loosely based on Professor Robert J. Stanley’s Stark apparatus at Temple

University1, however the hardware and software have been substantially modiﬁed. The Stark apparatus used in the work contained within this dissertation was developed at UNC Chapel Hill in 2018-2019. The design

127 was my own with LabVIEW based software that I wrote for instrument operation and with modiﬁed

MATLAB based software received from Robert J. Stanley’s group for data analysis. I also led the mechanical engineering aspects of the instrument with Eric J. Piechota who also assisted with the overall instrument design and troubleshooting. Matthew Verber and Collin McKinney in the UNC electronic shop also assisted with troubleshooting and noise analysis.

This chapter is intended to be a physical description and brief summary of the experiments that can be performed by the Stark apparatus. For a more exhaustive review of the underlying theory refer to Chapter 1, sections 5 and 6. For more in depth display of the software code and hardware refer to Appendices A and B.

6.2 Hardware Description

6.2.1 Light Source and optical path

Thin path length optical cells are illuminated by a probe beam generated from a Xenon arc lamp after passing through a monochromator, Figure 6.1. The light source is a 150 W Xe arc lamp (USHIO

UXL-151HO), the output irradiance is given in Figure 6.6. This light source is optically coupled to an f/2 0.2 m monochromator (McPherson Model 272). The monochromator was computer controlled and modulated step wise through the use of a McPherson Model 798A-4 Scan Controller. The monochromatic light is then passed through a Glan-Thompson polarizer. In a low-temperature absorption experiment the beam then passes through the beam chopper (SRS Model SR540 Chopper Controller). In both Stark and absorption experiments the beam is focused to a point on the cell within the sample chamber and then refocused onto the collecting ampliﬁed photodiode (Thorlabs PDA100A). The responsivity of the photodiode is presented in

Figure 6.7. Illumination intensity is kept constant through the use of a power supply (OBB Lamp Power

Supply) whose current is controlled to keep the arc lamp at a consistent 150 W.

128 Figure 6.1: A block diagram of the Stark apparatus that utilized a Xe arc lamp for excitation, a cryostat sample compartment, and a Si photodiode detector.

6.2.2 Oscilloscope

Data collection and communication with the computer is managed by a Teledyne LeCroy Wavesurfer

3054 500 MHz oscilloscope. It collects the raw signal from the photodiode, amplified signal from the lock-in amplifier, and monitoring signal from the high voltage amplifier. The maximum sampling rate of the oscilloscope is 4 GS/s and a maximum time resolution of 500 ps. As the sampling rate is simultaneous for all inputs on the oscilloscope, there is no resolution loss for utilizing multiple inputs.

The act of measuring a voltage requires current flow. Because the amplitude of the desired signal is relatively small, too high of a sampling rate can result in drawing enough current to distort the intensity of the signal. It was empirically found that reducing the the sampling rate to 100 kS/s, corresponding to 10 ns resolution, provided no measurable influence on the amplitude of the signal. The oscilloscope also provides the ability to change the terminal resistance at each input, and as such to further prevent any signal influence of the measurement process, the terminals were set to 1 MΩ for signal read out and 50 Ω for the monitoring signal from the high voltage amplifier.

129 Figure 6.2: A top down and side on visualization of an ideal cell.

6.2.3 Optical Cell Design and Cryostat

The optical cell design used in Stark spectroscopy experiments has varied over the years as is evident in the prior literature.1–4 These cells generally consist of two conductive transparent slides with the sample in some rigid media, i.e. frozen glass or polymer, across which the potential difference (i.e. field) can be modulated. Any of the previously designed cells would work within this Stark apparatus. However, the specific requirements of the cell design is dependent on the capabilities of other parts of the general apparatus, in particular the high voltage amplifier and size of the sample chamber. For this reason a specific cell design as shown in Figure 6.2 and described below was developed and consistently used.

The sample was made of two alkaline earth boro-aluminosilicate glass slides of 0.7 mm thickness

(Corning) cut to 2.2 cm x 2.5 cm size. Each slide was coated on one side with a transparent conductive layer of indium tin oxide (Delta Technologies). The conductive indium tin oxide sides of the slides were separated by two 63.5 µm thick strips ( .2 cm x 2.5 cm) of an adhesive Kapton tape further supported by micro-binder clips. The internal chamber is then ﬁlled with a high concentration solution of the desired sample in a solvent well suited to forming a frozen glass.

130 Figure 6.3: Depiction of the sample holder including the non-conductive wafer and the microbinder clips used to afﬁx the cell to the holder.

The sample is mounted with a micro-binder clip onto a specialized holder composed of a metal rod with a non-conductive insulating plastic wafer to which the sample is clipped, Figure 6.3. This holder is run through the cap of the cryostat to allow for minimal heat exchange from the inner chamber. The cryostat

(Janis) uses a three chamber system. An external vacuum chamber was held at 1 µTorr pressure to reduce heat exchange with the environment. The external inner chamber was ﬁlled with liquid nitrogen. The innermost chamber was then ﬁlled with ultra-high purity gas under pressure forcing condensation of liquid nitrogen. Electric connections were made to the sample using insulated manganin wire with alligator clips.

Due to the three chamber setup, the samples were extremely stable and the optical path was pristine. The cell was positioned at a 45°angle relative to the beam path, Figure 6.1.

6.2.4 Lock-in Ampliﬁer

As has been mentioned, due to the small change in transmission with even very strong (0.1-1 MV/cm)

field strengths, multiple methods of signal amplification are required. The photodiode used in collection has a built in amplifier that assists in this, however due to the transmission intensity without a field, amplification from the photodiode is limited. Additionally, noise is extremely prevalent in the amplitude region of

131 Figure 6.4: Circuit diagram of the SRS 530 lock-in ampliﬁer from Stanford Research Systems.

investigation. The use of a lock-in ampliﬁer ampliﬁes the µV signal to a V signal for further processing and

eliminates noise.

Figure 6.4 is a circuit diagram for the lock-in ampliﬁer used (SRS SR530 Lock-In Ampliﬁer). The

ampliﬁcation occurs through the multiplication of the raw signal by a sinusoid generated internally as a

reference frequency. In this process, a time average produces only a non-zero result for the matching

frequency component present in the raw data. Additionally, the lock-in ampliﬁer is connected to the

computer for ease of control of settings during the experiment.

6.2.5 Function Generator and High Voltage Ampliﬁer

The function generator used is a SRS Model DS345 30 MHz Synthesized Function Generator. It

provides both the reference signal for the lock-in ampliﬁer through the output of a transistor-transistor logic,

or a square wave, signal from the ‘Sync’ output at the selected frequency of the experiment. The other output,

‘Function’, provides a sinusoidal signal to drive the high-voltage ampliﬁer.

132 The high-voltage amplifier (Trek Model 20/20C-HS) simply amplifies the signal provided from the function generator to create the oscillating electric field across the plates. It is of substantial note to ensure the RC time constant of the amplifier can operate properly at the frequency chosen on the function generator and that this frequency is also feasible for the RC time constant of the cell. Additionally, the limitations of

field generation may be dependent on the voltage thresholds of the high-voltage amplifier. In this case, the amplifier multiplies the incoming signal by 2kV/V and has the ability to go ± 20 kV. The maximum slew rate of the amplifier is > 450 V/µs.

6.3 Software description and typical operation

The software for the Stark experiment is divided into two different programs: 1) the LabVIEW software which manages the control of the experiment and exporting of raw data; and 2) the MATLAB software which analyzes the combination of multiple electro-absorption experiments and the low-temperature absorption experiments to extract the FETQs of interest.

The software that controls the Stark apparatus is written in LabVIEW and is designed to make analysis as hands-off, robust, and fast as possible. This is accomplished by allowing for control of most hardware through the use of the computer, locking all controls other than an emergency stop during the course of the experiment to prevent unintentional changes, and utilization of the large amount of data collected per data point (1 GS per individual wavelength). The software that analyzes the data to extract the relevant FETQs is designed for ease of use and presentation of all possible relevant data or residuals. This is accomplished through an intuitive user interface and the complete control of absorption bands through manual control of every parameter and ﬁtting parameter.

133 Figure 6.5: The Graphical User Interface of the software used to collect data.

6.3.1 General User Interface

The overall user interface of the instrumental control and data collection software can be seen in

Figure 6.5. The experiments performed are chosen by a simple button press to record a background absorption spectrum, a low-temperature absorption spectrum, or a Stark spectrum. The individual details of the experiment will be discussed below. During the process of the experiment only two user interactions can be made: pressing the ‘Stop’ button to end the experiment and introduction of points at which the sensitivity of the experiment must be adjusted. All data collected is not automatically saved. In order to save the data, it must be exported using the ‘Export’ buttons in the same panel as the experiment initiation buttons.

Background spectrum will be automatically saved as Solvent Reference Date with the Solvent inputted by the user and date automatically applied. The low-temperature spectrum and Stark spectrum export names are inputted by the user.

Common parameters that are independent of the experiment are the start and end wavelengths for the scan, the wavelength step of the experiment and the respective inputs from the oscilloscope. In order to assist the modelling process it is advisable to keep the wavelength range and step size the same between

134 experiments. The inputs received from the oscilloscope will automatically be set to standard values that are appropriate provided no hardware changes have been made. Below, an overview, user-deﬁned parameters, and workup are discussed for each experiment.

6.3.2 Background and Low-Temperature Spectra

Overview: The background, i.e. solvent, and low-temperature absorption spectra are analogous to standard UV-visible absorption spectroscopy, however the samples are frozen in a glass. Due to the complications that can arise in cracking of the glass in a larger sample cell, these experiments are performed on an identical beam path and utilize the same photodiode as the Stark spectrum counterpart. Background and low-temperature absorption spectra are necessary beyond a room temperature solution absorption spectrum to model the Stark spectra as band narrowing and shifting frequently occurs upon rigidifying a sample. The absorption spectrum is needed during the analysis process where the individual electronic transitions are ﬁt to the absorption spectrum and their respective 0th, 1st, and 2nd derivatives are taken for modelling purposes.

The background and low-temperature spectra experiments are simpler and safer than the Stark experiment as they require no high electric ﬁelds and only two values are recorded at each wavelength. A short pathlength (200 µm) optical cell is utilized for these absorption experiments. This cell is placed in the cryostat and set at a 45° angle relative to the probe light path. Some hardware changes may be necessary before beginning the experiment. The function generator and high-voltage ampliﬁer are not needed for this experiment. The signal that is to be locked-in is received from the beam chopper controller. Connecting a

BNC cable between the fouter output of the controller and the reference input port of the lock-in amplifier is required. The beam chopper itself must be turned on and is typically set to 610 Hz. The last consistent change that will need to be confirmed is that the lock-in amplifier is set to ‘f’ mode, not ‘2f’ mode. This can be done on the hardware or via the control panel in the software. During the experiment the oscillating amplitude of the transmission intensity, or on-off modulation from the beam-chopper, is locked-in to and a high resolution

135 spectrum can be obtained from even the short path length optical cell. At each wavelength 100 sets of 106 data points output by the lock-in amplifier are averaged then recorded as a single data point. The wavelength is stepped and five times the time constant is allowed to create a buffer for the lock-in amplifier to readjust to the new wavelength. This process continues until a necessary sensitivity switch or the experiment ends.

User-deﬁned parameters: The user will need to manage several parameters for any given experiment.

The sensitivity setting on the lock-in amplifier should be set pre-experiment via the hardware or the control panel in the software. A generally advisable setting for these type of experiments tends to be maximum sensitivity range, 500 mV, as the oscillating signal made is the on/off made with to the beam chopper and in turn a rather substantial signal. The sensitivity of the photodiode amplifier is the final parameter for the user to set both prior to and during the experiment. The sensitivity setting depends primarily on the initial wavelength of the experiment.

Operation:As discussed earlier, the intention is to give the user a relatively input free experiment process to allow them to work on other projects or data analysis during the long experiment times. However, the nature of the experiment does require some monitoring and minor experimental changes during the course of the scan. Figure 6.6 below shows the Xe lamp spectrum and Figure 6.7 shows the responsivity of the photodiode ampliﬁer (PDA). These factors when combined lead to the need for adjustment of the photodiode sensitivity during the experiment. To determine when the user should change the sensitivity, the wavelength at which the transmission saturates the PDA should be found that is dependent on the absorption proﬁle. It is advised to scan the wavelengths prior to the experiment using the monochromator controller panel in software to determine at what wavelengths the sensitivity needs to be changed. The user can then input these in the ‘Sens switch’ boxes and activate them with the switch. If need be, these sensitivity switches can be changed or added during the course of the experiment as well. As the change in sensitivity results in an amplitude shift, it is important to reconcile these differences.

136 Figure 6.6: A spectral distribution diagram of the USHIO UXL - 151HO Xenon Arc lamp reproduced from a USHIO brochure.

There are two settings available in the software for the sensitivity adjustment, dynamic or constant. √ Constant applies a 10 factor for the transmission intensity measurement, the ratio between two 10 db units,

each time the sensitivity is changed. Alternatively, the dynamic does not apply any rigid factor, but instead

recollects the data of the previous wavelength and calculates the appropriate ratio for the sensitivity change.

Once all these options are completed and chosen, simply pressing the ‘Baseline’ for a background spectrum

or ‘Scan’ for the low-temperature spectrum is all that is needed. When the program reaches a sensitivity

switch wavelength, it will pause the programming and display a pop-up. Simply change the sensitivity on the

PDA and wait for the lock-in to equilibrate then press okay to resume the experiment. Upon completion, the

saved data may be exported into a ‘.mat’ ﬁle to be read by the analysis software. Alternatively export to a

‘.csv’ ﬁle format is available.

6.3.3 Stark Spectra

Overview: The signiﬁcance of the Stark spectrum has been detailed substantially throughout this

entire dissertation. Application of an electric ﬁeld across a rigid sample allows for the extraction of FETQs.

For purpose of the experiment, an oscillating high voltage is applied to one of the TCO coated glass slides.

137 Figure 6.7: A response curve of the PDA100A switchable gain Si Photodiode ampliﬁer reproduced from Thorlabs.

The voltage applied is monitored and displayed in real-time in order to ensure that the experiment values appropriate to the experiment are being utilized. The experiment functions on the same parameters as the background and low-temperature absorption experiments in that at each wavelength 100 sets of 106 data points are averaged from the oscilloscope to represent a single data point, and after stepping one wavelength the system waits for ﬁve times the time constant before collecting data again.

User-deﬁned parameters: The user will need to manage many of the same parameters that were managed in the solvent (background) and low-temperature absorption experiments. The sensitivity on the lock-in ampliﬁer should be preset on the hardware or the control panel in the software. An advised setting of

500 or 200 µV is recommended to ensure detection without saturation of the lock-in ampliﬁer.

Operation: For the same reasons mentioned above, the responsitivity of the photodiode and spectral distribution of the Xe arc lamp, sensitivities must be managed prior to experimentation. The same process as above follows, by migrating the wavelength and ensuring that neither the average raw intensity, Iavg, output from the photodiode nor the ∆I from the lock-in ampliﬁer saturate. Inputting wavelengths to switch the sensitivity of the photodiode may be done prior to or during the experiment. The Iavg value and Stark √ measurement follows the same 10 factor.

In addition to the general averaging of large data sets for a single point, the post ampliﬁed signal must be corrected to transform the data from a change in transmission intensity (∆I) to a change in absorbance.

138 To accomplish this the software while collecting ∆I spectra also acquires a baseline of Iavg. Through this the signal can be transformed to a change in absorbance, ∆A using eq. 6.1,

√ 2 2∆I(F~ ) ∆A = (6.1) 2.303lIavg

√ where the factor of 2 corrects for the collection of the Stark signal at 2ω, the 2 corrects for the rms output of the lock-in, ∆I(F~ ) is the field-induced change in the transmission intensity through the sample collected by the lock-in amplifier, Iavg is the transmission through the sample in the absence of the field. The data are divided by the path length, l, to give ∆A, the field-induced change in the absorbance. This process is automatically carried out by the experimental software after data collection, but it should be known that this is why both Iavg and ∆I are collected during the experiment.

6.3.4 Data analysis

The data analysis software is relatively intuitive to use, however this section will brieﬂy detail the operation of the software. For a more speciﬁc understanding of the underlying processes refer to Appendix A.

General User Interface: Upon opening the software a user interface, UI, is presented as shown in

Figure 6.8. The ’save’ and ’load’ buttons can be used to save the current project or load a previously worked up project back into the software. Clicking on the ’Files’ tab will present the opportunity to add or remove

Stark spectrum ﬁles with the ’+’ and ’-’ buttons in the bottom right. Additionally the low-temperature absorption and solvent background spectrum can be uploaded through the ’Load Absorption’ and ’Load

Reference’ buttons respectively. Once the ﬁles are loaded, the appropriate experimental parameters can be input. These include: the polarization of light (Pol), the angle of incidence (Inc), the applied ﬁeld (FVrms), sample concentration (Conc(mM)) and the path length (Path(µm)).

Initial Fitting Process: Clicking on the options tab will present a new window in the top left, Figure

6.9. This window allows you to set the baseline region in both your absorption and Stark spectrum. These

139 Figure 6.8: The graphical user interface of the software used to analyze the data. values will automatically be set to the last 10% of the data points in the ﬁle inputted. Additionally the region of the spectrum that needs to be ﬁt must be chosen. The last item is to change the sovlent refractive index to the appropriate value for the solvent used.

Once those values are all set, proceed to the ’Fitting’ button to reveal another window in the same position, Figure 6.10. In this window you can add speciﬁc transitions of one or more gaussians that the data will be ﬁt to. This can be done by simply clicking the ’+’ button on the bottom right then moving to the absorption spectrum display and click with the mouse for each gaussian in a transition (there can be just a single gaussian). After selecting gaussian positions simply press enter to produce the gaussians. The parameters of the transition will appear in the top part of the top left panel to give the amplitude (M −1 cm−1), position (cm−1), full-width at half-maximum (cm−1) and the corresponding transition (if multiple gaussians appear in one transition). The bottom part of this pane will be populated with default values for

T r(∆~α), ~m · ∆~α · ~m, ∆~µ, and ζ. Recalling from Chapter 1 that the Aχ terms should be negligible, they are in a toggle panel in the top right labeled ’Aχ’.

140 Figure 6.9: The options panel for selecting ﬁtting parameters and establishing the baseline of the absorption and Stark spectra.

Figure 6.10: The Graphical User Interface of the software used to collect data.

141 Figure 6.11: A sample ﬁt of the absorption graph.

Selecting the ’Absorption’ option allows for first fitting the absorption spectrum to the desired transitions without any influence from the recorded Stark spectrum. Pressing the fit button will cause a nonlinear least squares method to fit the low tempearture absorption. The process will be complete when the text above the pane says in red text ’COMPLETE’. In the absorption spectrum display, the transitions should present a good fit to the absorption spectrum. The experimental spectrum is black, the total fit is red and individual components are colored in series, Figure 6.11.

Provided a good fit is obtained, select ’Simultaneous’ instead of ’Absorption’ and press fit again. In this case the weighting option in the ’options’ tab is used to weight the absorption and Stark spectral data in the fitting. A value of ’1’ represents an equal balance, lower is higher influence from the absorption and higher is higher from the Stark data. If the fit proceeds as intended, the top right panel will show a good fit of each Stark spectrum, Figure 6.12, and the bottom right panel will show the residuals of the fits (black from absorption and colored from each Stark spectrum), Figure 6.13.

The lower left panel shows the Stark data, black points, with the overall ﬁts, red, with the individual transition 0th-, 1st-, and 2nd-order derivative contributions; cyan, green and blue respectively, Figure 6.14.

Final Fitting: Once a satisfactory ﬁt is obtained, more robust values ar obtained through a spectral modelling ’MonteCarlo’ process. Selecting the ’MonteCarlo’ button will provide a new window with only one option, and the number of iterations. This process repeats the ﬁtting given the weighting selected in the options tab the number of iterations, with each iteration altering the starting point of various variables. After

142 Figure 6.12: A sample ﬁt of the Stark graph.

Figure 6.13: A sample residual plot of well ﬁt absorption and Stark spectra.

Figure 6.14: A sample plot of Stark data with ﬁt and individual component contributions.

143 the process is complete, the data is output with an estimated error from the ﬁtting process that is displayed.

Clicking the ’Plot Results’ button will pop up a new window with four graphs showing the variance of values based on their initial input from the Monte Carlo simulations. These results will help confirm or refute the reproducibility of the values obtained. After the fitting is completed the spectra and their fits can be exported using the ’Export Results’ button which exports a ’.csv’ file that can be input into other graphical analysis software for further analysis or publication.

144 REFERENCES

[1] Stanley, R. J.; Jang, H. Electronic Structure Measurements of Oxidized Flavins and Flavin Complexes Using Stark-Effect Spectroscopy. The Journal of Physical Chemistry A 1999, 103, 8976–8984.

[2] Bublitz, G. U.; Boxer, S. G. STARK SPECTROSCOPY: Applications in Chemistry, Biology, and Materials Science. Annual Review of Physical Chemistry 1997, 48, 213–242.

[3] Karki, L.; Hupp, J. T. Electroabsorption Studies of Metal-to-Ligand Charge Transfer in 2+ Ru(phenanthroline)3 : Evidence for Intrinsic Charge Localization in the Initially Formed Excited State. Inorganic Chemistry 1997, 36, 3318–3321.

[4] Boxer, S. G. Stark Realities. The Journal of Physical Chemistry B 2009, 113, 2972–2983.

145 APPENDIX A–MATLAB ANALYSIS CODE

Figure A.1: Creation of the class for the low-temperature absorption and background spectra. Interface code for loading a chosen experimental ﬁle and setting a baseline.

146 Figure A.2: Creation of the ﬁle name for the GUI, and checks to ensure the reference and low-temperature absorption spectrum have the same wavenumber range.

147 Figure A.3: Creation of the class for the Stark spectra. Details on what properties and methods are included in the class.

148 Figure A.4: Converts the raw ∆I and Iavg data into ∆ε for processing.

149 Figure A.5: Corrects the for the baseline for both spectra, with the low-temperature absorption being corrected by a slanted baseline and the Stark spectra being corrected by an average value. Also shown is the calculation of the 0th-, 1st-, and 2nd-order derivatives for the Gaussians in the ﬁt.

150 Figure A.6: Reading and loading the spectral data from the exported LabView ﬁle.

151 Figure A.7: GUI commands for the initialization of the ﬁgures, and the toolbar at the top of the GUI.

Figure A.8: Initialization of the Panel in which the user can input data and monitor quantitative ﬁtting results.

152 Figure A.9: Controls for ﬁle i/o for the absorption and stark spectra.

153 Figure A.10: Speciﬁc controls for the Parameter Panel, including the addition of Gaussians.

154 Figure A.11: Speciﬁc controls for the Settings and Monte Carlo Panels.

Figure A.12: Speciﬁc Controls for the Plotting Panel.

155 Figure A.13: Input of shortcut for hard stop of program and GUI controls for navigation between panels and data table cells.

156 Figure A.14: Button controls, part 1.

157 Figure A.15: Button controls, part 2.

158 Figure A.16: Button controls, part 3.

159 Figure A.17: Button controls, part 4.

160 Figure A.18: Input of the raw data into plots within the GUI for visualization.

161 Figure A.19: Continued data visualization control and establishing the contiuous loop for the program.

162 Figure A.20: Creation of the class for the Fit of the Stark Spectra and description of the properties and starting parameters of the ﬁt.

163 Figure A.21: Sets the expected limits of the ﬁt and creation of the data when ﬁtting only to the absorption spectrum.

164 Figure A.22: Function deﬁned for ﬁtting the Stark and absorption spectra simultaneously. The upper and lower bounds govern the limits of the parameters as set by the program and can be altered to allow or restrict Gaussian band width, amplitude, and position.

Figure A.23: Alternative fit performed for confidence only from the absorption only fit to the Stark spectra.

165 Figure A.24: Plotting the fit at any step of the fitting process to establish the strength of the fit with the given weighting of Stark and absorption data set.

Figure A.25: Absorption data plotting functionalities of the raw data, the ﬁt and the residuals. Maximum number of transitions is established here at ’10’ but may be increased at the risk of overparametizing the ﬁt.

166 Figure A.26: Stark data plotting functionalities of the raw data and ﬁts. Maximum number of transitions must agree with the maximum number of absorption transitions.

Figure A.27: Monte Carlo ﬁtting method. Randomly picking starting parameters and reperforming the ﬁt.

167 Figure A.28: Output of the Monte Carlo ﬁtting results.

Figure A.29: Calculation of approximated errors from the Monte Carlo ﬁt. It is unlikely that these results will be lower than the experimental error and are used as the functional error of values collected for electron transfer quantities.

168 Figure A.30: Output of the calculated errors during the Monte Carlo ﬁt.

Figure A.31: Creation of a subﬁgure pop-up that details the Monte Carlo ﬁt, showing a graphical representation of the consistency of the values.

169 Figure A.32: Exporting the ﬁts for use in subsequent analysis or ﬁgure creation.

170 Figure A.33: Deﬁnition of the absorption ﬁtting process.

Figure A.34: Definition of the simultaneous fitting process. Additionally the method for fitting the absorption and Stark spectra.

171 Figure A.35: Output of the ﬁtted data to update the plots after several ﬁtting steps have been performed.

Figure A.36: Deﬁnition of the iterative Stark ﬁtting process.

172 Figure A.37: Plotting of the individual derivatives from the ﬁt and updating their respective fundamental electron transfer quantities.

Figure A.38: Conversion of the calculated Stark parameters into Bχ and Cχ components.

173 Figure A.39: Creation of the class for the Stark spectral data and the paramaters and methods contained. Additionally the loading of the Stark data from a ’.mat’ ﬁle.

174 Figure A.40: Extraction of the ﬁlename for display within the GUI, approximating a baseline, normalization of the data and conversion to ∆ε.

Figure A.41: Function for ﬁeld normalization based upon the inputs of ﬁeld strength, pathlength refractive index, and angle.

175 APPENDIX B–LABVIEW INSTRUMENT CONTROL AND DATA COLLECTION SOFTWARE

Figure B.1: Initialization of parameters controlled, collected and displayed, part 1.

176 Figure B.2: Initialization of parameters controlled, collected and displayed, part 2.

Figure B.3: Function for a background correction if the PDA is collecting ambient light. It records the value over a long period of time and averages it out, takes a value four standard deviations from the center to prevent overcorreciton.

177 Figure B.4: Controls for the lock-in ampliﬁer.

Figure B.5: Monochrometer step control, part 1.

178 Figure B.6: Monochrometer step control, part 2.

179 180

Figure B.7: Monochrometer step control, part 3. 181

Figure B.8: Baseline collection control. 182

Figure B.9: Low-temperature absorption collection control. 183

Figure B.10: Stark spectrum collection control. 184

Figure B.11: Export of Stark data. Figure B.12: Export of Low-temperature data.

Figure B.13: Export of reference blank data.

185