VELOCITY-MAP IMAGING PHOTOELECTRON SPECTROSCOPY OF SMALL
MOLECULAR ANIONS
byAllan Maple de Oliveira
B.S., University of Sao Paulo, 2011

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Chemical Physics
2017This thesis entitled:
Velocity-Map Imaging Photoelectron Spectroscopy of Small Molecular Anions

written by Allan Maple de Oliveira
has been approved for the Committee on Chemical Physics
by___________________________________
W. Carl Lineberger___________________________________
Veronica M. Bierbaum

The final copy of this thesis has been examined by the signatories, and wefind that both the content and the form meet acceptable presentation standardsof scholarly work in the above mentioned discipline.

DATE:___________________

ii

Oliveira, Allan Maple (Ph.D. Chemical Physics)
Velocity-Map Imaging Photoelectron Spectroscopy of Small Molecular Anions
Thesis directed by Professor W. Carl Lineberger
Gas phase anion photoelectron spectroscopy presents an opportunity for investigating
molecules that are inaccessible by other experimental techniques, by providing data on the
structure, reactivity and energetics of short-lived radicals and transition state species. Our recent
development of a novel, plasma entrainment source of cold, weakly-bound anions opens a door
to new exotic species to be investigated. In this thesis, I explore the capabilities of photoelectron
spectroscopy and its application to small exotic molecular anions, while further developing andemploying the novel dual-valve ion source.
The thesis begins with a brief history of photoelectron spectroscopy, followed by adescription of the experimental apparatus. The first anion studied using the new anion source isthe weakly bound methide anion (CH3–). This experiment provides the first measurement of theinversion splitting of this simple pyramidal carbanion. The precise measurement of the electron
affinity (EA) of the methyl radical provides accurate measurements of the gas phase acidity ofmethane, which defines the acidity scale of hydrocarbons.
I then explore the spectroscopy of the atmospherically significant HONO molecule, via
photoelectron spectroscopy of the open-shelled HONO– radical anion. HONO– is produced in areaction between OH– and NO, a feat accomplished in the cold, collision-rich environment of thenovel anion source. This experiment allows for the first measurement of the EA of HONO andthe excitation energy to its lowest excited state, the triplet, which is inaccessible by mostspectroscopic techniques.
iii

Next, I investigate of the electronic structure of singly substituted alkoxy radicals. The
new dual-valve source allowed for controlled synthesis of hydroxymethoxide andaminomethoxide. The selective substitution allows us to probe what effect the substituting group
has on the electronic structure of alkoxy radicals, leading to a correlation between the substituent
group’s electronegativity and the EAs and excited state energies of the radicals.
Finally, I investigate the biologically relevant 7-azaindole and its hydrogen bonded
dimer. The photoelectron spectrum of 7-azaindolide provides a measurement of the EA of the 7azaindolyl radical and reveals an unexpected behavior of the spectrum, where most of theobserved signal derives from a process other than direct photodetachment.

iv

DEDICATION

To the lives of my grandparents Geute and Orencio, and of my cousin Ricardo, who sadly parted
this world during my time in Boulder.
May God bless their souls.

v

ACKNOWLEDGEMENTS
As a naïve young man I had little idea of what I was really getting into, but, as I wrote in
my essay for the application process, it was going to be a path full of challenges. It was harderthan what I imagined, but, hey, should it be any different? A Ph.D. is the highest attainable
degree in one’s education! Here I am now, writing my Ph.D. thesis, which pretty much meansthat I succeeded. It wasn’t easy though. It was a long path of difficulties, conflicts with myexperiment, with people that I worked with, but mostly with my inner Self, as I in times had todescend into chaos to then reemerge victorious from the ashes – something that is true foranything meaningful in life. The few paragraphs that follow are what I consider the “trueintroduction” to my thesis, where I acknowledge the difficulties, successes and people that were
essential to its completion.
First, I must thank my Ph.D. thesis advisor W. Carl Lineberger. I had the immense
opportunity of working with one of the great scientists of the century. A person that not only
created a field of research, but also left a legacy of extremely talented scientists, from Hartmut
Hotop, his very first postdoc, to Mark Johnson, Dan Neumark and ultimately Julia Lehman, withwhom I had the pleasure of working. Julia was responsible for a great amount of my learning on
how to succeed in my Ph.D.: from how to work in the lab effectively, to how to write papers andultimately how to be a hard-ass worker. Despite the occasional conflicts we had, I understandthat most of it came from her believing in my potential and wanting me to fully achieve it. It is
possible that I learned more from Julia than what I did from Carl himself. I also had the chanceof working with Yu-Ju Lu, the senior graduate student who trained me initially. Yu-Ju is anextremely talented experimentalist and it was an honor learning some of his magic lab tricks, if
one could say that. In the latter part of my graduate career I had the pleasure of working withvi

Daniel Nelson, another senior graduate student in the group. Dan is a very smart person, one of
the smartest people I know, who became not only a great lab-mate, but also a good friend. Dan
not only has a great technical understanding of laboratory instruments and electronics, but has
also an amazing ability to explain things clearly. I learned a whole lot from my discussions(sometimes heated arguments) with Dan these past six months. Having conversations with him
about science, mathematics, music, politics, philosophy and also videogames, pop-culture andgood beer has been extremely gratifying and fun.
Some other academics must be acknowledged here as well. The professors that compose
my thesis committee are certainly some of them! I thank Mathias Weber, Heather Lewandowski,
Veronica Bierbaum, Barney Ellison for being my thesis committee, and Eric Cornell for being
part of the oral examination committee. Starting in my oral exams, these amazing people mademe understand science as I do today. Our Tuesday morning ion super-group meetings, composedof essentially the research groups of the professors in my thesis committee, was a great place forsharing ideas and organizing my thoughts as I presented my findings there a number of times. I
must also thank other people that believed in me and encouraged me in my endeavors: Margaret
Asirvatham for mentoring me in my teaching aspirations and for believing in my passion andpotential for teaching, Veronica Bierbaum for her kindness and encouragement and theprofessors/instructors with whom I worked with as a teaching assistant, Molly Larsen, Niels
Damrauer and Joseph Falke.
I also have to acknowledge the amazing JILA staff, specifically the JILA shops(instrument, computing, electronics, etc.). Of the staff, a few people deserve special
acknowledgement. The first that comes to mind is Krista Beck, the secretary/assistant of Carl andof other amazing JILA professors. Krista always made JILA events and scheduling things govii

superbly well. From the computing group Jim McKown and Corey Keasling were always there
to fix bugs and (try to) teach me how to write script for my calculations. Also from thecomputing group, J.R. Raith III has to be recognized for his support with computer hardware andWindows problems (curse you DaVis!!!). J.R. and I have spent a good amount of time talking
about video games, old computers, heavy metal and other cool, essential-to-life stuff, so it was
really great having him around for more than just the technical support stuff. From theelectronics shop, James Fung-a-Fat and Terry Brown are gratefully acknowledged for all the help
with lab electronics problems and for being good people to talk to in the hallways. In themachine shop, I have to particularly acknowledge the sometimes grumpy Todd Asnicar and thealways cheerful Hans Green. Not only are these people amazing machinists, but they are also
incredible people to have informal (sometimes formal as well) conversations about the mostvaried topics. From the Supply Office/Building Maintenance, I must acknowledge Brian Lynchfor our chats about good beer and Dave Erickson for the morning chats and his candy basket.
I must also thank my family and friends, who supported me throughout this journey. Herein Boulder I didn’t make a lot of friendships, but the few that I made were certainly a matter ofquality over quantity. Friends like Dan Nelson, whom I mentioned before, Tony Tumminello,
Ricardo Carvalho, Curtis Beimborn and Michael Thompson, were essential to my mental sanity
as we hung out sharing pints of good beer while taking a break from the science work. From all
my Boulder friends, I must thank Andrew Chomas the most, as he has been a true friend for me
and I really hope to keep in touch with him for many years to come. My wife’s family deserves a
big thanks. They really made me part of their family as well and supported us during our time
here. Also, whenever we got the chance to visit, they treated me with the love they would give ason. Finally, my own family is the one that deserves most of my gratefulness. Grandpas andviii

grandmas, uncles, cousins and aunts, and most importantly, Mom, Dad and bro Julian. Thanks
for making me who I am today. I love you very much and miss being closer to you.
Finally, the person I have to thank the most of all is my partner for life, my wife Debora.
She’s the one that has made most of the sacrifice during this journey. She left her job and family
to move to the United States with me with just the mere chance that one day she would beworking towards a Ph.D. herself. Thankfully, her dedication, hard work and discipline has gotten
her the opportunity to study Materials Science at the Colorado School of Mines. I am very
grateful and proud of her achievements, as she not only proved she deserves a Ph.D., but also isdoing it in record time (less than 4 years!) with stellar performance. Her success only makes mestronger and inspires me to be a better person every day. By supporting me each and every day,she’s responsible for a great deal of my achievements, not in graduate school, but in everything
in my life. I could not have done it without her. I love you, Debora.

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CONTENTS

CHAPTER I: INTRODUCTION TO THE THESIS .................................................................................... 1
1.1 Photoelectron Spectroscopy: Fundamentals ....................................................................................... 1
1.2 Photodetachment cross sections and angular distributions ............................................................... 16
1.3 Photoelectron versus other spectroscopic techniques ....................................................................... 22
1.4 Overview of the thesis ...................................................................................................................... 26
1.5 Chapter 1 references ......................................................................................................................... 35
CHAPTER II: EXPERIMENTAL AND THEORETICAL METHODS.................................................... 39
2.1 Experimental Methods ...................................................................................................................... 39
2.1.a Overview of the instrument ........................................................................................................ 39
2.1.b Ion Source .................................................................................................................................. 42
2.1.c Mass Spectrometer ..................................................................................................................... 50
2.1.d Laser System .............................................................................................................................. 55
2.1.e Velocity-map Imaging Spectrometer ......................................................................................... 56
2.2 Theoretical Methods ......................................................................................................................... 60
2.2.a Ab-initio calculations ................................................................................................................. 60
2.2.b Photoelectron spectra simulations .............................................................................................. 62
2.3 Data analysis ..................................................................................................................................... 63
2.3.a Image processing ........................................................................................................................ 63
2.3.b Assignments and uncertainties ................................................................................................... 65
2.4 Chapter 2 references ......................................................................................................................... 68
CHAPTER III: PHOTOELECTRON SPECTROSCOPY OF THE METHIDE ANION (CH3–) .............. 71
3.1 Introduction and Motivation ............................................................................................................. 71
3.2 Experimental Methods ...................................................................................................................... 73
3.3 Experimental Results ........................................................................................................................ 75
3.3.a Introductory remarks .................................................................................................................. 75
3.4.b Photoelectron Angular Distributions.......................................................................................... 79
3.3.c Vibrational structure and electron affinities ............................................................................... 84
3.4 Theoretical Methods and Results ...................................................................................................... 89
3.3.a Anion potential energy surface................................................................................................... 89
3.4.b Photoelectron Spectra and Electron Affinities ........................................................................... 93
3.5 Discussion ......................................................................................................................................... 94
3.5.a Gas-phase Acidities .................................................................................................................... 94x

3.5.b Inversion Splitting, Electron Affinity, and Anion Potential Energy Surface ............................. 97
3.6 Conclusions ....................................................................................................................................... 99
3.7 Chapter 3 references ....................................................................................................................... 102
CHAPTER IV: PHOTOELECTRON SPECTROSCOPY OF THE NITROUS ACID ANION (HONO–).................................................................................................................................................................. 105
4.1 Introduction ..................................................................................................................................... 105
4.2 Methods........................................................................................................................................... 108
4.2.a Experimental ............................................................................................................................ 108
4.2.b Theoretical Methods ................................................................................................................ 109
4.3 Results and Discussion ................................................................................................................... 114
4.3.a Introductory remarks ................................................................................................................ 114
4.3.b Ground State: cis-HONO 𝑋 1A′ ............................................................................................... 118
4.3.c Vibrational Analysis ................................................................................................................. 125
4.3.d Contribution of the trans-HONO– isomer to the photoelectron spectrum ................................ 130
4.3.e Electronic Structure of HONO– ................................................................................................ 137
4.3.f Thermochemistry of HONO ..................................................................................................... 145
4.3.g Triplet State: cis-HONO 𝑎 3A″ ................................................................................................ 147
4.4 Conclusions ..................................................................................................................................... 151
4.5 Chapter 4 references ....................................................................................................................... 153
CHAPTER V: PHOTOELECTRON SPECTROSCOPY OF THE HYDROXYMETHOXIDE ANION(H2C(OH)O–) ............................................................................................................................................ 157
5.1 Introduction ..................................................................................................................................... 157
5.2 Methods........................................................................................................................................... 159
5.2.a Experimental ............................................................................................................................ 159
5.2.b Theoretical Methods ................................................................................................................ 160
5.3 Results ............................................................................................................................................. 168
5.3.a Experimental Photoelectron Spectra and EA(H2C(OH)O•) ..................................................... 168
5.3.b H2C(OH)O• 𝑋 2A Vibrational Assignments ............................................................................. 175
5.3.c H2C(OH)O• 𝐴 2A ...................................................................................................................... 180
5.4 Discussion ....................................................................................................................................... 182
5.4.a H-OCO Torsion ........................................................................................................................ 182
5.4.b Methanediol Thermochemistry ................................................................................................ 187
5.4.c Photodetachment Producing H2C(OH)O• 𝑋 2A and 𝐴 2A Electronic States............................. 188
5.5 Conclusions ..................................................................................................................................... 189
5.6 Geometry optimization and frequencies of hydroxymethoxide and hydroxymethoxy ................... 192

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5.7 Chapter 5 references ....................................................................................................................... 196
CHAPTER VI: PHOTOELECTRON SPECTROSCOPY OF THE AMINOMETHOXIDE ANION,
H2C(NH2)O– .............................................................................................................................................. 199
6.1 Introduction ..................................................................................................................................... 199
6.2 Methods........................................................................................................................................... 201
6.2.a Experimental ............................................................................................................................ 201
6.2.b Theoretical ............................................................................................................................... 202
6.3 Results ............................................................................................................................................. 204
6.3.a Initial remarks .......................................................................................................................... 204
6.3.b Identification of anion with m/z=46......................................................................................... 205
6.3.c Overview and Electron Affinity of Aminomethoxy ................................................................. 207
6.3.d Determination of Aminomethoxy Term Energy, T0(𝐴 ← 𝑋) ................................................... 215
6.3.e Vibrational analysis .................................................................................................................. 219
6.3.f Unassigned transitions .............................................................................................................. 222
6.4 Discussion ....................................................................................................................................... 222
6.4.a Thermochemistry of aminomethanol ....................................................................................... 222
6.4.b Comparison of aminomethoxy with other singly substituted alkoxy radicals ......................... 225
6.5 Conclusions ..................................................................................................................................... 228
6.6 General Optimization Results ......................................................................................................... 230
6.7 Chapter 6 references ....................................................................................................................... 235
CHAPTER VII: PHOTOELECTRON SPECTROSCOPY OF 7-AZAINDOLIDE AND 7-AZAINDOLEDIMER ANIONS...................................................................................................................................... 239
7.1 Introduction ..................................................................................................................................... 239
7.2 Methods........................................................................................................................................... 243
7.2.a Experimental ............................................................................................................................ 243
7.2.b Theoretical ............................................................................................................................... 246
7.3 Results and Discussion ................................................................................................................... 247
7.3.a Overview spectrum of 7-azaindolide ....................................................................................... 247
7.3.b High resolution photoelectron spectra of 7-azaindolide .......................................................... 251
7.3.c Comparison between indolyl and 7-azaindolyl ........................................................................ 268
7.4.d Photoelectron spectrum of (7-azaindole)2– ............................................................................... 270
7.6. Chapter 7 references ...................................................................................................................... 277
BIBLIOGRAPHY ..................................................................................................................................... 281
APPENDICES .......................................................................................................................................... 300

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LIST OF TABLES
Table 3.1: Experimentally determined electron binding energies of each peak and transition
assignments for each peak in the photoelectron spectra of CH3 and CD3…………..................78
Table 3.2: Anisotropy parameter (β) measurements for each peak in the CH3– photoelectron
spectra used. ………......................................................................................................................83
Table 3.3: Observed umbrella mode (ν2) vibrational frequencies and derived spectroscopic
constants of neutral •CH3 and •CD3 (cm-1).....……........................................................................88
Table 3.4: Computational results for the CH3–/CD3– 4D transition state barrier height (EB) and•CH3/•CD3 electronic contribution to the electron affinity (ΔEelec). All values are given inwavenumbers (cm-1). ……….........................................................................................................92298.15ooTable 3.5: Thermal corrections (H298K
− H0K
= ∫0
𝐶𝑝 (𝑇) 𝑑𝑇) for the individual species in
the methane deprotonation thermochemical cycle.........................................................................96

Table 3.6: Summary of major results of Chapter 3, experimental and theoretical……………..101
Table 4.1: Calculated (MP2/aug-cc-pVTZ) equilibrium geometries of cis-HONO–, cis-HONO(S0), and cis-HONO (T1), as well as the difference between geometry parameters of the anion
and neutral structures (Δ = anion structure − neutral structure). Distances are given in Angstroms
and the angles are in degrees. ……….........................................................................................127
Table 4.2: Vibrational transition assignments for the peaks labeled (A–Q) in the photoelectron
spectrum reported in Fig. 4.4. ……….........................................................................................128
Table 4.3: Experimental (previous work and this study) and calculated (this study) vibrationalfrequencies (νi) of neutral cis-HONO (S0). All values are given in cm-1 …................................129
Table 4.4: Comparison of HONO–, HONO (S0), and HONO (T1) harmonic frequencies for thetrans isomer using different levels of theoretical treatment……………………………………140
Table 4.5: Comparison of HONO–, HONO (S0), and HONO (T1) energies and geometries for thetrans isomer using different levels of theoretical treatment……………………………………141
Table 4.6: Comparison of HONO–, HONO (S0), and HONO (T1) energies and geometries for thecis isomer using different levels of theoretical treatment………………………………………143
Table 4.7: Comparison of HONO–, HONO (S0), and HONO (T1) harmonic frequencies for thecis isomer using different levels of theoretical treatment………………………………………144
Table 4.8: Summary of the experimental results of Chapter 4…………………………………146
Table 5.1: Calculated torsional potential energy surface scan (CCSD(T)/aug-cc-pVTZ for̃̃ 1Aʹ and H2C(OH)O• X
̃ 2A, and EOM-CCSD/aug-cc-pVTZ for H2C(OH)O• A
H2C(OH)O– X
2A)………………………………………………………………………………………………165
Table 5.2: Fit parameters of equation 5.1 for each of the potentials…………………………...166
Table 5.3: Calculated minimum energy structure of H2C(OH)O– 𝑋̃ 1A′ (CCSD(T)/aug-cc-pVTZ),H2C(OH)O• 𝑋̃ 2A (ROCCSD(T)/aug-cc-pVTZ), and H2C(OH)O• 𝐴̃ 2A (CIS/aug-cc-pVTZ)...177xiii

Table 5.4: Vibrational transition assignments for the peaks labeled a′–e (Fig. 5.5) and B (Fig.
5.4)……………………………………………………………………………………………...179
Table 5.5: Calculated (ROCCSD(T)/aug-cc-pVTZ) optimized geometries of H2C(OH)O• 𝑋̃ 2A.
……………………………………………………………………………………………..........192
Table 5.6: Calculated (ROCCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies of
H2C(OH)O• 𝑋̃ 2A. ………………………………………………………………………………193
Table 5.7: Calculated (CIS/aug-cc-pVTZ) harmonic vibrational frequencies of H2C(OH)O• 𝐴̃ 2A.
……………………………………………………………………………………………..........194
Table 5.8: Calculated (CCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies of H2C(OH)O–𝑋̃ 1A……………………………………………………………………………………………..195
Table 5.9: Summary of the major results of Chapter 5…………………………………………191
Table 6.1: Optimized structural parameters of H2C(NH2)O– (CCSD(T)/aug-cc-pVTZ) andH2C(NH2)O in its ground (ROCCSD(T)/aug-cc-pVTZ) and excited (CAS(5,4)/aug-cc-pVTZ)
states…………………………………………………………………………………………….230
Table 6.2: Calculated (CCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies (ωi) of
H2C(NH2)O– 𝑋̃ 1A′.……………………………………………………………………………...231
Table 6.3: Harmonic vibrational frequencies (ωi) of H2C(NH2)O•, 𝑋̃ 2A′ (ROCCSD(T)/aug-ccpVTZ). …………………………………………………………………………………………232
Table 6.4: Harmonic vibrational frequencies (ωi) of H2C(NH2)O•, 𝐴̃ 2A″ (CAS(5,4)/aug-ccpVTZ). …………………………………………………………………………………………233
Table 6.5: Calculated rotational constants for aminomethoxy: Anion 𝑋̃1 𝐴′ and neutral ground𝑋̃ 2 𝐴′ (RCCSD(T)/aug-cc-pVTZ, RO for neutral) and neutral excited 𝐴̃2 𝐴″ (CAS(5,4)/aug-ccpVTZ). …………………………………………………………………………………………234
Table 6.6: Calculated (B3LYP/aug-cc-pVTZ) addition reaction enthalpies (Δrxn Ho0K ) between
amide anion (NH2–) and formaldehyde (H2CO) forming the anionic products shown in Fig. 6.1
and electron affinities of the corresponding neutral species. All values include zero-point energy.
……………………………………………………………………………………………..........209
Table 6.7: Vibrational transition assignments for the peaks in the photoelectron spectra (Figs.
6.3, 6.4 and 6.5). ……………………………………………………………………………….221
Table 6.8: Summary of major results of Chapter 6. ……………………………………………224

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LIST OF FIGURES
Figure 1.1: Schematic representation of the photoionization process generating the hydronium
cation, H+.…………………………………………………………………………………………3
Figure 1.2: Schematic representation of a photodetachment process of a generic diatomic
molecule M2…..……………………………………………………………………………….......6
Figure 1.3: Potential energy surfaces of the amide anion (NH2–) and the ground and first excitedstates of the amino radical (NH2). ……………………………………………………………….13
Figure 1.4: Photoelectron spectrum of the amide anion (NH2–) obtained with a photon energy of
3.494 eV (λ = 355 nm). ………………………………………………………………………….14
Figure 1.5: Behavior of photoelectron angular distributions for the cases of detachment fromseveral s-p mixed states.…………………………………………………………………………21
Figure 1.6: Schematic representation of the thermochemical cycle of HA………..…………….25
Figure 1.7: Potential and spectra representative of the photoelectron spectroscopic investigationof the methide anion. ……………………………………………………………………………28
Figure 1.8: Summary of the work reported in chapter 4 depicting photodetachment of HONO–,
accessing the singlet and triplet electronic states of HONO and their behavior as they are formed
via photodetachment of the HONO– anion..……………………………………………………..30
Figure 1.9: Intramolecular interaction trend of singly substituted alkoxy radical as described in
Chapters 5 and 6. ………………………………………………………………………………...32
Figure 1.10: Chemical structures of deprotonated indole (indolide), deprotonated 7-azaindole (7azaindolide) and (7-azaindole)2– anion…………………………………………………………..34
Figure 2.1: Schematic representation of the photoelectron spectrometer………………………..41
Figure 2.2: Specific design and functional details of the dual valve, plasma entrainment ion
source. …………………………………………………………………………………………...45
Figure 2.3: Photograph of the dual valve plasma entrainment ion source described in this section.
The individual components of the source are labeled accordingly………………………………48
Figure 2.4: Ozonide argon clusters (O3–(Ar)n) optimization and cluster size distribution shifts as afunction of valve body temperature. …………………………………………………………….49
Figure 2.5: Detailed schematic representation of the Wiley-McLaren Time-of-Flight mass
spectrometer. …………………………………………………………………………………….51
Figure 2.6: Detailed view of the VMI spectrometer with the velocity-mapping of thephotoelectrons from O2–.…………………………………………………………………………58
Figure 3.1: Photoelectron spectra of CH3–. The experimental spectrum using 1.165 eV (red) or
0.383 eV (black) photon energies are shown in the upper panel………………………………...76
Figure 3.2: Photoelectron spectra of CD3–. Analogous description as Figure 3.1……………….77

xv

Figure 3.3: CH3– photoelectron anisotropy parameter (β) as a function of electron kinetic energy.
……………………………………………………………………………………………............82
Figure 3.4: Schematic potential energy curves (not to scale) of CH3– (black) and CH3 (green) as
a function of the inversion angle (φ). ……………………………………………………………85
Figure 4.1: 1-D electronic potential energy curves (CBS-QB3) for cis-HONO as functions of thecentral 𝑟ON,c bond length. ………………………………………………………………………111
Figure 4.2: The cis-HONO– photoelectron spectrum using 355 nm (3.49 eV) photons………..116
Figure 4.3: Photoelectron spectrum of cis-HONO– using photon energies of 532 nm (2.33 eV,
green), 1064 nm (1.16 eV, purple), and 1613 nm (0.769 eV, orange)………………………….120
Figure 4.4: Scaled experimental photoelectron spectrum (black trace), Franck-Condon factors(green sticks), and convoluted simulation (red)………………………………………………...123
Figure 4.5: Comparison of the calculated (ROMP2/aug-cc-pVTZ) photoelectron spectrum oftrans-HONO– and the experimental data. ……………………………………………………...132
Figure 4.6: Comparison of the calculated photoelectron spectrum of HONO– with both cis(UMP2/aug-cc-pVTZ, green sticks) and trans (ROMP2/aug-cc-pVTZ, blue sticks) isomers, andthe experimental data. ………………………………………………………………………….134
Figure 4.7: Potential energy as a function of the HONO– dihedral angle calculated at the CBSQB3 level of theory. ……………………………………………………………………………136
Figure 4.8: Calculated photoelectron spectrum of trans-HONO– (red trace) with (a) ROMP2/augcc-pVTZ, and (b) CCSD/aug-cc-pVTZ level of theory/basis-set………………………………142
Figure 4.9: Detailed T1 excited state photoelectron spectrum of cis-HONO– using 301 nm (4.12eV) photon energy. The green sticks are the calculated FCFs by the methods described in the
text. …………………………………………………………………………………………….148
Figure 5.1: Calculated (CCSD(T)/aug-cc-pVTZ) 1D potential energy curves of the torsional
coordinate for the electronic states of hydroxymethoxy accessed in the photodetachment process.
……………………………………………………………………………………………..........162
Figure 5.2: Calculated 1D potential energy curves as functions of the torsional coordinate for the
H2C(OH)O– 𝑋̃ 1Aʹ (blue), H2C(OH)O• 𝑋̃ 2A (red), and H2C(OH)O• 𝐴̃ 2A (purple) states………167
Figure 5.3: Upper panel: Experimental anisotropy parameters (β) as a function of electron kinetic
energy. Middle panel: Experimental photoelectron spectrum of H2C(OH)O–, using 3.49 eV (355nm) photon energy. Lower panel: Convolved photoelectron simulations of detachment to theground (green) and excited (blue) electronic states of H2C(OH)O•, along with their sum (reddots). …………………………………………………………………………………................170
Figure 5.4. Upper panel: Experimental photoelectron spectrum of H2C(OH)O– using 2.74 eV(453 nm) photon energy. Lower panel: Calculated (CCSD(T)/aug-cc-pVTZ) Franck-Condon
factors (sticks) and convolved simulation (blue trace)…………………………………………172

xvi

Figure 5.5: Upper panel: Photoelectron spectrum of H2C(OH)O– using 2.33 eV (532 nm) photon
energy. Lower panel: Calculated (CCSD(T)/aug-cc-pVTZ) Franck-Condon factors (sticks) andconvolved simulation (blue trace) with assigned transitions…………………………………...174
Figure 5.6: H2C(OH)O• 𝑋̃ 2A H-OCO calculated (ROCCSD(T)/aug-cc-pVTZ) torsional potential
comparison. …………………………………………………………………………………….185
Figure 6.1: Structural isomers of aminomethoxide discussed in the text………………………208
Figure 6.2: Upper panel: Photoelectron anisotropy parameter (β) of aminomethoxide (black dots)
as a function of electron kinetic energy (eKE). Lower panel: VMI photoelectron spectrum ofaminomethoxide obtained with a photon energy of 3.494 eV………………………………….210
Figure 6.3: Upper panel: Measured anisotropy parameter β associated with the experimental
photoelectron spectrum found in the middle panel. Middle panel: Photoelectron spectrum
obtained using a photon energy of 2.172 eV. Lower panel: Calculated photoelectron spectrum fortransitions from the ground electronic state of the aminomethoxide…………………………...212
Figure 6.4: Photoelectron spectrum obtained using a photon energy of 2.038 eV……………..214
Figure 6.5: Lower panel: Photoelectron spectrum obtained using 2.329 eV photon energy (532nm). Upper panel: Anisotropy parameter β as a function of eKE……………………………...216
Figure 6.6: Experimental photoelectron spectrum obtained with 3.494 eV photon energy (black
trace), calculated FCFs for transitions from the ground state of the anion (𝑋̃1 𝐴′ (v = 0)) to neutral
ground (red sticks) and neutral excited (blue sticks) electronic states of aminomethoxy……...218
Figure 6.7: Upper panel: Photoelectron anisotropy parameter (β) as a function of electron kinetic
energy (eKE) for aminomethoxy (blue dots) and hydroxymethoxy (red dots). Lower panels:
Photoelectron spectrum of hydroxymethoxide (red) and aminomethoxide anions (blue) obtainedwith a photon energy of 3.49 eV (355 nm)……………………………………………………..227
Figure 7.2: Photoelectron spectrum of indolide reproduced from Nelson et al…………….......240
Figure 7.1: Resulting mass spectrum from ion generation procedure described in section 7.2.a.
The displayed range of mass units shows the production of 7-azaindolide and (7-azaindole)2..244
Figure 7.3: Overview photoelectron spectrum of the 7-azaindolide anion obtained with a photon
energy 3.494 eV (black trace) accessing the ground electronic state of 7-azaindolyl.................250
Figure 7.4: Comparison between the experimental low resolution overview spectrum of 7azaindolide (black trace) and calculated spectrum (red sticks)...................................................253
Figure 7.5: Photoelectron spectrum of 7-azaindolide acquired with a photon energy of 2.719 eV
and calculated FCF stick spectrum (red sticks). The eBE axis spans a range of 0.119 eV, andcorresponds to the same magnified region as shown in Figs. 7.3 and 7.4...................................255
Figure 7.6: Compiled photoelectron spectra of 7-azaindolide acquired with various photon
energies plotted as a function of electron Binding Energy (eBE)...............................................261
Figure 7.7: Compiled photoelectron spectra of 7-azaindolide acquired with various photon
energies and plotted as a function of eKE...................................................................................262
xvii

Figure 7.8: Upper panel: Overview photoelectron spectrum of 7-azaindolide (black trace) and theGaussian fit (orange trace) to the apparent underlying baseline (see text for details). Lower panel:
Photoelectron spectrum of 7-azaindolide with a Gaussian continuum (orange trace in the upper
panel) subtracted..........................................................................................................................267
Figure 7.9: Overview photoelectron spectrum of (7-azaindole)2–, accessing the ground and firstexcited states of (7-azaindole)2. This spectrum is obtained with a photon energy of 3.494 eV..272
Figure 7.10: Photoelectron spectrum of (7-azaindole)2– acquired with a photon energy of 1.165
eV.................................................................................................................................................273
Figure 7.11: Detailed photoelectron spectrum of (7-azaindole)2– acquired with a photon energyof 3.494 eV. .................................................................................................................................274

xviii

CHAPTER IINTRODUCTION TO THE THESIS

1.1 Photoelectron Spectroscopy: Fundamentals
Photoelectron spectroscopy is a spectroscopic technique based on the photoelectric effect.
The modelling of this physical phenomenon by Albert Einstein resulted in the award of theNobel Prize in Physics 19211 and lies at the very core of the development of quantum mechanics.
The observed phenomenon, made by the physicist Heinrich Hertz in 1887,2 was the following: A
metallic surface in vacuum exhibited electron emission upon irradiation with light. The curious
thing about this phenomenon was that no electron emission was observed above a specificwavelength, and the number of electrons emitted was not dependent on the wavelength. In otherwords, below certain wavelengths, when emission was observed, the number of electrons emitted
did not change when the wavelength was made shorter (larger photon energy). In addition, after
electron emission was observed, an increase in photon energy made the kinetic energy of theelectron vary linearly with photon energy. The phenomenon was, therefore, modelled as:
𝑒𝐾𝐸 = ℎ𝜈 − 𝜙(1.1)

where eKE is the electron kinetic energy, hν is the photon energy and ϕ is the work function of
the metal. In more intuitive terms, ϕ is the threshold potential, i.e. the minimum energy required
to remove the electron from this metallic surface. If hν  ϕ, no emission was observed and if hν >ϕ, electron emission is observed with a kinetic energy varying linearly with photon energy, thus,
satisfactorily modelling the phenomenon observed by Hertz. The act of measuring the kinetic

1

energy of the emitted electrons in order to determine ϕ was designated “Photoelectron
Spectroscopy.”
A similar phenomenon can be observed in gas phase. In isolated atoms, ϕ is analogously
the energy required to remove an electron from a neutral atom, generating a cation and anelectron. In this case, instead of ϕ, the threshold energy is defined as ionization potential (IP) or
ionization energy (IE). The formation of a cation from a neutral atom/molecule upon interaction
with a photon is defined as “photoionization” and it is illustrated in its simplest example in Fig.
1.1 for the hydrogen atom. Fig. 1.1 displays the photoionization of H, illustrating the physicalrepresentation of the process. If the energy of the photon absorbed by the system is sufficiently
high as to bring the electron from its most stable orbit to an orbit in which the radius tends toinfinity, the once neutral H atom now becomes a positively charged proton, infinitely separated
from the negatively charged electron. The well-known IE of hydrogen atom was later named theRydberg constant (RH) and is one of the best known physical constants, with an experimentally
determined value of 13.6056930090(81) eV.3 If the photon energy is greater than RH, byconservation of energy and momentum and due to the electron’s overwhelmingly smaller mass
when compared to the proton, essentially the entire remaining energy of the photons istransferred to the electron increasing its kinetic energy. We then recover the initial observation ofelectron emission from a metallic surface when irradiated by light in the much simpler system of
an isolated neutral atom.

2

Figure 1.1: Schematic representation of the photoionization process generating the H+ cationfrom neutral hydrogen upon interaction with a photon of energy greater than or equal to ~ 13.6
eV. Here, the energy of neutral H is defined as zero.

3

The analysis of emission of electrons upon interaction with photons can also be applied toanions, which are the focus of this thesis, and can be exemplified in similar terms. Instead of aneutral H atom, we now start with an H atom which possesses an additional electron, forming thehydride anion (H–). In an analogous manner, the interaction of H– with a photon with enoughenergy can bring an electron from H– to a state in which the electron is essentially “free”, i.e.
infinitely separated from the now neutral H atom. The process of forming a neutral atom fromthe corresponding anion is designated “photodetachment”. For the example above the H– atom
will lose an electron, forming H, if h > 0.754 eV.4 For anions, the analogous quantity to the IE
is known to as the electron affinity (EA). The EA represents the minimum amount of energy
necessary to remove an electron from an anion generating a neutral atom. By convention, the EA
is referred to as belonging to the neutral species (from the example above EA(H) = 0.754 eV), as
a positive EA value indicates that energy is gained when the electron is added to the neutral
atom. If the EA is negative, the anion is higher in energy than the corresponding neutral andtherefore, attaching an electron to this species is an endothermic process. For molecules, which
compose the totality of the material described in this thesis, the existence of multiple electronic,
vibrational, and rotational states allows equation 1.1 to be more instructively written as:
𝑒𝐾𝐸 = ℎ𝜈 − 𝑒𝐵𝐸(1.2)

where eBE is the electron binding energy of a specific electronic, vibrational or rotational state,
depending on the system in question. The eBE value that corresponds to the EA is the energy
difference between the generalized ground states of anion and neutral species.
Photoelectron spectroscopy is a technique which relies on measurement of the kinetic
energy of the photodetached electrons. By measuring the kinetic energy distribution of theelectrons that are detached upon interaction with a photon, described here as photodetached4electrons or photoelectrons, a photoelectron spectrum is generated. Once a target molecule isestablished, the photodetachment process for a generalized molecular anion M2– can be broadly
described by:
𝑀2− + ℎ𝜈 → 𝑀2 + 𝑒 − (KE)

(1.3)

While the light source of h will be described in Chapter 2, it is important to state that for
accurate measurements of the photoelectron kinetic energy, laser light is utilized as it provides
high intensity, narrow linewidths, short pulse duration, etc. A well-defined photon energy isnecessary so that the measurement of the kinetic energy and therefore the binding energy can be
precise and accurate. Since the energy levels of molecules are quantized, we see that byassigning discrete values for eBE, for a fixed hν, a discrete spectrum of eKE will be obtained.
Again, by conservation of energy, if hν > EA of the target molecule, photoelectrons will beobserved with the remainder of the energy being deposited in either the kinetic energy of theelectrons or the internal states (degrees of freedom) of the molecule. As will become clear in
Chapter 2, our experimental resolution does not allow for the separation of rotational lines, thus,
the photoelectron spectra provide a vibrationally resolved spectrum of the electronic states of thecorresponding neutral molecule.

5Figure 1.2: Schematic representation of a photodetachment process of a generic diatomic molecule
M2. The blue upward arrow represents the photon energy used to access the neutral ground stateof M2. The orange upward arrow represents a higher photon energy that accesses both electronic
states, the ground and first excited states of M2. The downward red arrow represents the discretemeasured electron kinetic energies that generate the peaks represented in the photoelectron
spectrum PS1, schematically drawn along the y-axis. The kinetic energies associated with thehigher photon energies (orange arrow) were omitted for simplicity.

6

To explain how photoelectron spectra are generated and interpreted, Fig. 1.2 shows aschematic representation of the process. Fig. 1.2 shows three potential energy curves for thearbitrary diatomic molecule M2, the anion ground electronic state (A0), neutral ground state (N0)and one neutral excited state (N1). The curves M2– (A0), M2 (N0) and M2 (N1) show the relative
energy of M2 as a function of the M–M bond length. The blue upward arrow represents a photon
energy that accesses the N0 state. This photon energy generates the photoelectron spectrum PS1.
If a higher photon energy (orange upward arrow) is employed, both N0 and N1 states areaccessed and, as a consequence, both PS1 and PS2 photoelectron spectra are generated. This
figure shows some important quantities that can be obtained from photoelectron spectra. The
peak with the highest observed eKE (or lowest eBE) represents the transition between groundvibrational states of the anion and neutral and is defined as the EA of M2. As was stated above,the existence of discrete energy levels in the molecule results in a photoelectron spectrum withdiscrete peaks, each positioned in the corresponding eBE of the vibrational levels of M2. The
spacing between peaks centers, therefore, provides the measurement of the vibrational frequency(ωe) of the M2 stretching mode in the N0 state. In an analogous manner, when the higher photon
energy is used and the N1 state is accessed, the vibrational frequency of the N1 state can bemeasured. Moreover, the difference between the eBEs of the origin transitions of the N0 and N1
states provides a measurement of the term energy (T0) of M2, which is the energy separation
between these two electronic states.
The photoelectron spectra related to each one of the electronic states of M2 (PS1 andPS2) have different extent the vibrational progressions and relative intensities of the transitions.
This brings us to question what determines the relative intensities of the peaks in a photoelectron
spectrum. Fig. 1.2 shows that the potential energy curves of A0, N0 and N1 have different shapes

7and equilibrium bond distances. The A0 state has a shorter equilibrium M–M bond length and ahigher bond strength. The N1 state has an even longer M–M equilibrium bond length and lower
bond strength than the N0 state. In order to understand this, if we imagine that we instantaneously
remove an electron from M2–, the M2 molecule will find itself away from its equilibriumgeometry. In brief terms, a larger displacement from equilibrium will result in a larger activationof vibrational modes, i.e. longer vibrational progression (such as PS2, Fig. 1.2). In a classicalmechanical picture, if we consider that the atoms M are connected by a spring with spring
constant k the potential energy can be described by:𝑘(𝒓 − 𝒓𝟎 )2
𝜇𝜔02(𝒓 − 𝒓𝟎 )𝑉(𝒓) = −
=−
2
2

(1.4)

where r is the internuclear distance, r0 is the equilibrium bond length, k is the force constant of
the M–M bond, is the reduced mass of M2 and ω0 is the harmonic frequency of the M–M
stretching vibration. One can see that a larger displacement from equilibrium will result in a⃗⃗V). Thus, a larger vibrational activity will belarger force acting on the atoms of M2 (𝐹⃗ = −∇expected if the geometry change between electronic states is larger, as the atoms will vibrate inorder to reach their equilibrium distance in the final state. Although the phenomenology
described by the classical mechanical picture is correct, it lacks quantitative information of what
the relative intensities of the transitions should be.
In order to provide a quantitative model of the vibration of molecules and of theintensities of the peaks in a photoelectron spectrum, a quantum mechanical approach has to betaken. For that, we initially rely on the Born-Oppenheimer approximation which is to consider
that, the electrons, being much lighter than the nuclei, instantly adjust to any nuclear motion.

8

This assumption allows the total Hamiltonian of the system to be separable into its electronic,
nuclear and spin parts:ℋ𝑡𝑜𝑡 ≈ ℋ𝑛𝑢𝑐𝑙𝑒𝑎𝑟 + ℋ𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑖𝑐 + ℋ𝑠𝑝𝑖𝑛(1.5)

which allows the total wavefunction to be written as a product form:𝜓𝑡𝑜𝑡 = 𝜓𝑛𝑢𝑐𝑙𝑒𝑎𝑟 𝜓𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑖𝑐 𝜓𝑠𝑝𝑖𝑛 = 𝜓𝑛 𝜓𝑒 𝜓𝑠(1.6)

In the photodetachment process, again utilizing the Born-Oppenheimer approximation, theremoval of the electron places the initial ground state anion rovibrational wavefunction on thepotential energy surface of the neutral, with the nuclei in the same configuration as the anion
equilibrium structure. For the sake of simplicity, we will proceed with the derivation for thesimple case of the molecule M2 considering only the vibrational component v of the nuclear
wavefunction and that only the ground vibrational level of the anion is populated (see Eq. 1.12
and associated text). We can therefore express the anion wavefunction as a linear combination ofneutral wavefunctions which are eigenfunctions of the neutral state Hamiltonian and therefore
form a complete set of orthonormal functions. By doing this, we obtain the following expression:
𝑎𝑙𝑙 𝑠𝑡𝑎𝑡𝑒𝑠𝜓𝑎𝑛𝑖𝑜𝑛 (v = 0) =∑𝑎v 𝜓𝑛𝑒𝑢𝑡𝑟𝑎𝑙 (v)

(1.7)

v=0

where av are the expansion coefficients that can be obtained by:∞∗(v = 0)𝜓𝑛𝑒𝑢𝑡𝑟𝑎𝑙 (v) = ⟨v𝑖𝑛𝑖𝑡𝑖𝑎𝑙 |v𝑓𝑖𝑛𝑎𝑙 ⟩𝑎v = ∫ 𝑑𝑟 𝜓𝑎𝑛𝑖𝑜𝑛

(1.8)

−∞

We define the FC factor of the vth transition as the square modulus of av:
FCFvth transition ≡ |⟨v𝑖𝑛𝑖𝑡𝑖𝑎𝑙 |v𝑓𝑖𝑛𝑎𝑙 ⟩|
9

2

(1.9)

The FC factor physically represents the projection of the anionic vibrational wavefunction onto aneutral eigenstate. In other terms, it represents the overlap between the initial and final statevibrational wavefunctions. From this, one can see that, if the geometries of anion and neutral
states are similar, or close to similar, the overlap is large, resulting in a0  1. This means that the
expansion shown in eq. 1.8 has the v = 0 expansion term as the largest and essentially only
relevant term. In other words, the anion wavefunction is also an eigenfunction of the neutral
state’s Hamiltonian. In the photoelectron spectrum, therefore, a single transition will be observed
corresponding to the v = 0 in the anion to the v = 0 transition in the neutral. If, however, thegeometries are significantly different between the initial and final states, the overlap of thevibrational wavefunctions v = 0 is small and therefore more terms in the expansion are necessary
to satisfactorily describe the anionic wavefunction. This results in a distribution of amplitudes. In
the photoelectron spectra, this will be observed by a distribution of peaks corresponding to many
quanta of the neutral state vibrations, where the relative intensities of the peaks are directly
proportional to the ratios of the expansion coefficients, i.e. the FC factors.
Understanding the photoelectron spectrum of M2 requires predicting the spacing of thepeaks in PS1 and PS2, i.e. the frequency of the M–M stretching vibration, in addition to the FC
factors. For modelling the M2 vibrational frequency, the quantum harmonic oscillator
approximation is a good model, provided we limit ourselves to dealing with small displacementsof the M–M bond, i.e. sufficiently close to the bottom of the M2 potential energy well. While thefull derivation of this problem is out of the scope of this chapter, it suffices to state that the
problem can be solved analytically by utilizing the potential energy operator analogous to Eq. 1.4(see Ref. 5 for complete derivation). This will result in the following expression for the
eigenvalues (energy levels, Ev) of the problem:101𝐸v = 𝜔𝑒 (v + )2(1.10)

For polyatomic molecules, as those described in Chapters 3 through the end of this thesis, thesingle M–M vibrational coordinate is replaced by the 3N-6 vibrational normal modes, where N is
the number of atoms in the molecule. Within this same approximation, the 3N-6 vibrations areharmonic and independent of each other. When higher vibrational quanta are reached, thepotential energy curve deviates from the parabolic harmonic potential, thus requiring anharmonic
terms to be included in the aforementioned expression. Although the derivation is beyond thescope of this chapter, for the molecules studied here we often utilize the energy levels of ananharmonic oscillator to model their vibrational frequencies. The anharmonic expression for thevibrational energy levels then becomes:
1
1 2
𝐸v, 𝑛𝑡ℎ mode = 𝜔𝑛 (v + ) + 𝑥𝑛𝑛 (v + ) + ⋯2
2(1.11)

where xnn is the first order anharmonicity constant and, considering the precision of ourexperiment, will be the only anharmonic term we will be able to measure. Full a thoroughdescription of vibrational normal modes and their application to spectroscopy, see Refs. 6, 7 andreferences within.
The photodetachment of the amide anion (NH2–), performed in our laboratory during theexperiments described in Chapter 6, presents an instructive example of how the difference inequilibrium geometries between anion and neutral states affect the photoelectron spectra. Fig. 1.3
below shows the potential energy curves of the NH2– as a function of the HNH bending angle(HNH). Both anion and neutral ground electronic states have HNH  102 and essentially
identical curvature of the potential. This means that, if we express the vibrational wavefunctions
11

of the anion utilizing anion vibrational eigenfunctions (as described above), only the very firstfunction of the expansion, the eigenfunction of the ground vibrational state of the anion, will
have a significant expansion coefficient while all the other terms of the expansion will be
negligible. In other words, the projection of the anion wavefunction onto the eigenstates of theneutral molecule will only have significant overlap with one state of the neutral, here, the𝜓𝑛𝑒𝑢𝑡𝑟𝑎𝑙 (v = 0). The photoelectron spectrum associated with the ground state of NH2, shown in
Fig. 1.4 reflects this fact by exhibiting a single transition located at 0.771 eV eBE (EA of NH2)8and no further transitions with significant FC factors. On the other hand, the potential energy
surface of the excited state of NH2 is considerably different than NH2–, with the equilibrium
structure being quasi-linear. In contrast with photodetachment to the ground state, thephotoelectron spectrum associated with the excited state is therefore characterized by a longprogression of peaks, where the spacing between peaks represents the HNH bending vibrationalfrequency on the excited state of NH2.

12

Figure 1.3: Potential energy surfaces of the amide anion (NH2–) and the ground and first excitedstates of the amino radical (NH2). The neutral state surfaces were obtained from Zhou et al.9 andthe anion surface was calculated at the B3LYP/aug-cc-pVTZ level of theory for illustrative
purposes.

13

Figure 1.4: Photoelectron spectrum of the amide anion (NH2–) obtained with a photon energy of
3.494 eV (λ = 355 nm). These spectra exemplify how the geometry change between anion andneutral states is experimentally observed in the photoelectron spectrum by the different extent ofvibrational progressions.

14

So far, the description of modelling of the intensities of the photoelectron spectra
considered that only the anion ground rovibrational level is populated, which is only true for atemperature of 0 K. For higher temperatures, more specifically, vibrational temperatures, theBoltzmann factor (equation 1.12) must be included in the aforementioned formalism.
𝐸 −𝐸
𝒩v
− v 0
= 𝑒 𝑘𝐵 𝑇
𝒩0(1.12)

resulting in:Intensityvth transition = FCFvth transition 𝑒−(𝐸v −𝐸0 )𝑘𝐵 𝑇(1.13)In this work, since that the anions are generated in a supersonic expansion into vacuum (seeChapter 2), it is not necessarily true that the populations on all internal degrees of freedom obey
the Boltzmann distribution and can have significantly different temperatures. Nevertheless, thisformalism is utilized for scaling the FC factor of excited vibrational anionic states. The
transitions that start in an anion vibrationally excited state are commonly designated vibrational
hot bands (vanion= 1, 2, 3 … to vneutral = 0) and sequence bands (vanion= 1, 2, 3 … to vneutral = 1, 2,
3 …).
Before we continue with this description of photoelectron spectroscopy, it is useful todiscuss how the information stated so far relates to the experiments that will be described in thisthesis. In regard to the extent of vibrational progressions, although it is possible that thegeometries of anion and neutral states are similar, in this thesis, the geometries and bondstrengths often change to a significant degree when an electron is added to a neutral molecule.
This results in long vibrational progressions, enabling us to measure the vibrational frequenciesof the neutral molecules. In regards to the temperature of the anions, effort is made to guarantee
15that the anions are internally cold, as will be described in Chapter 2. The presence of vibrational
hot bands can considerably complicate the interpretation of photoelectron spectra due to spectralcongestion, as well as decrease the resolution. For a thorough discussion of this topic, see Ref 10.
1.2 Photodetachment cross sections and angular distributions
The observed intensities in a photoelectron spectrum depend not only on the vibrational
wavefunction overlap (FC factors), but also on the electronic portion of the transition
probabilities when the anion interacts with the electric field generated by the photons. This
electronic part is designated the photodetachment cross section (), and it represents thelikelihood of a transition when a photon interacts with the molecule. Physically is can be thoughtof as the electrical interaction of the light’s oscillating electric field and the orbital’s electron
density in the molecule. This interaction is similar to conventional absorption spectroscopy,
however, the final state of the wavefunction also contains the free electron in a continuum ofstates. Thus, differently from electronic absorption spectroscopy, it is very challenging tocalculate the photodetachment cross section theoretically and hence, it will not be attempted inthis thesis. The description of photodetachment cross sections in this thesis will be, therefore,
qualitative. In order to analyze how  comes to play in the photoelectron intensity, we utilize asimilar formalism as the one employed above. Writing the expression for the transition dipole
moment ( = electronic + nuclear) expectation value, we obtain:𝑃 ≡ ⟨𝜓𝑡𝑜𝑡,𝑓𝑖𝑛𝑎𝑙 |𝝁|𝜓𝑡𝑜𝑡,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ⟩∗∗∗=∫𝑑𝜏 𝜓𝑒,𝑓𝑖𝑛𝑎𝑙
𝝁𝑒 𝜓𝑒,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ∫𝑑𝑞 𝜓v,𝑓𝑖𝑛𝑎𝑙
𝜓v,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ∫𝑑𝑠 𝜓𝑠,𝑓𝑖𝑛𝑎𝑙
𝜓𝑠,𝑖𝑛𝑖𝑡𝑖𝑎𝑙⏟all modes⏟all space⏟spin states≡𝜎

FCF+ vanishing terms (1.14) CHECK
16

spin selection rule

which can be simplified as:
𝑃 = 𝜎 × FCF × δi,i±1/2(1.15)

Here, the overall transition probability is a product of the photodetachment cross section(electronic), the FCF (vibrational) and the spin selection rule, represented as a Kronecker delta
function which determines whether or not the transition is allowed. The spin selection rule will
be described in the later sections. In this section we focus on photodetachment cross sections andhow they vary, and how they play a role in the analysis of photoelectron spectra.
Photodetachment cross sections vary depending on the orbital from which the electron isremoved in the photodetachment event. As an example, removing an electron from a larger outerorbital of the molecule will likely have a larger detachment cross section when compared toremoving an electron from an inner, smaller orbital. In photoelectron spectroscopy, different
electronic states of a neutral molecule are accessed from the anion when the electrons aredetached from different orbitals. Hence, different electronic states of the neutral that are
produced in this process will have distinct cross sections. Generally, for a specific electronic
state, we consider that σ is constant and that the intensity of the transitions observed in thephotoelectron spectra are reasonably accounted for with the FC factor. There are, however, a few
situations where this approximation breaks down. The first and foremost exception is the
behavior of the photodetachment cross section close to detachment threshold (h ≈ EA), as
described in the following paragraphs. There are other less often observed situations where thephotodetachment cross sections vary as a function of the photon energy utilized. For those, adescription will be provided in the individual chapters that compose this thesis, whenever suchdescription is appropriate.

17

The behavior of photoelectron cross sections close to detachment threshold was initiallydescribed by Eugene Wigner in 1948 for atomic systems and is known as the Wigner thresholdlaw:111𝜎 ∝ (𝑒𝐾𝐸)ℓ+2(1.16)

where ℓ is the orbital angular momentum quantum number of the outgoing electron. To clarify
this point, when the photon is absorbed by the electron, the angular momentum the photon (ℓ=1)
is added to that of the electron. The outgoing electron, therefore, possesses |ℓfinal| = |ℓinitial|±1. As
an example, if the initial electron has ℓ=0, i.e. is located in an s-orbital, the outgoing electron
will have ℓ=1, being detached as a p-orbital, or a p-wave. Equation 1.16 shows that if the eKEtends to zero, the cross section also tends to zero, at a rate that is proportional to the exponentℓ + 1/2. The exponent of the expression above being a function of ℓ leads to different electronic
states having different behavior close to threshold. This phenomenon can be utilized to probefrom what type of orbital the photoelectron originated.
Another way of determining the nature of the electronic states from which thephotoelectrons originate is by examining the photoelectron angular distributions. Depending on
the orientation of the molecules with respect to the electric field vector of the photons, theoscillation of the electron density in that molecule’s orbitals can result in detachment in apreferential direction. This preferred direction with respect to the light’s electric field is denoted
the angular distribution of the photoelectrons. Experimentally, the angular distributions of thephotoelectrons can be detected, once an axis of orientation is defined. This is accomplished bydefining a polarization state of the photons. For the example above of an electron at an initialstate with ℓ=0, the outgoing p-wave will be detected as a photoelectron angular distribution

18

perpendicular to the laser polarization vector. If the electron is initially in a p-orbital (ℓ=1), theoutgoing wave can either be an s-wave (ℓ=0) or a d-wave (ℓ=2), the photoelectron angular
distribution is detected as parallel to the laser polarization vector. The photoelectron angular
distribution was modelled by Cooper and Zare in a seminal paper in 1968,12 and is characterized
by the anisotropy parameter β. If we describe the intensity of the photoelectrons (photoelectron
counts) as a function of angle relative to the laser polarization, we can express it by thefunctional form below:

𝐼(𝜃) =𝜎𝛽(1 + (1 + 3 cos2 𝜃)) ; −1 ≤ 𝛽 ≤ 24𝜋2(1.17)

where σ is the photodetachment cross section and β is the anisotropy parameter. By fitting theabove expression to the observed photoelectron angular distribution one can obtain the β value
for those photoelectrons. There are three important values of β that deserve attention. When β = 1, the detachment is parallel to the laser polarization vector, when β = 2, the detachment isperpendicular to the polarization vector and when β = 0 the detachment is isotropic, i.e. equal
photoelectron intensity is observed regardless of its orientation with respect to the polarization
vector. Besides the limiting values of β described above, the angular distribution varies as afunction of the electron’s kinetic energy. The modelling of β as a function of eKE is also
described for atoms in the paper by Cooper and Zare.12 For hydrogenic orbitals, the β(eKE) canbe derived analytically and its functional form is depicted below in Fig. 1.5, where the β(eKE)for a mixed s-p orbital is plotted for several values of a parameter Z, which describes the ratio
between s and p orbital character (see section 3.3.b. for more detail). For molecules, where themolecular orbital formalism has to be utilized, β(eKE) takes more complicated forms. A greatamount of work on modelling angular distributions for molecules was done by Sanov and19

coworkers and is extensively discussed in Refs. 13–16 and in Chapter 3. Since electrons
originating from different orbitals can have distinct angular distributions, the measurement of β
is a powerful tool for identifying electronic states of the neutral molecule and will be extensively
utilized throughout this thesis for that purpose.

20

Figure 1.5: Behavior of photoelectron angular distributions for the cases of detachment fromseveral s-p mixed states, varying as a parameter defined as Z (see chapter 3), which describes theratio between s and p orbital character. Detachment from pure s-orbital (H–) and a pure p-orbital(O–) are exemplified by the red traces. The figure is reproduced from a review by Sanov14 withsome modification.

21

1.3 Photoelectron versus other spectroscopic techniques
Now that the theoretical framework for understanding photoelectron spectroscopy is laidout, we can compare and contrast it to other spectroscopic techniques.
The first aspect of photoelectron spectroscopy that is unique with respect to othertechniques is the fact that the use of a single photon energy (or wavelength) can result in theacquisition of a full spectrum. Techniques such as absorption spectroscopy, being performed in
the ultraviolet or the infrared, require that the wavelength be scanned so that the light frequency
and the molecular vibration are in resonance. Photoelectron spectroscopy, on the other hand,
gives a full spectrum of the molecule with a single frequency of light, since the discrete
vibrational levels in an electronic state result in discrete values of kinetic energy that theelectrons are allowed to have, provided the photon energy is large enough to access these states.
Being able to utilize a single color is practically advantageous, since a single frequency laser,
rather than a broadband light source, can be utilized to obtain the full spectrum. Thus, one canobtain a full vibrational spectrum of the molecule while still taking advantage of the special
properties of laser light, such as high peak power, narrow linewidths and short pulses.
The other major distinction relates to the spin selection rules. While in absorption
spectroscopy we have ΔS = 0 for the spin selection rule, in photoelectron spectroscopy ΔS =±1/2. This is easily understood by noticing that, upon photodetachment, a single electron is lost.
Since electrons have fractional quanta of spin angular momenta, the loss of an electron requires
change of ±1/2 in the spin state of the molecule (see Eq. 1.15). This selection rule is of major
importance and contrasts to other spectroscopic techniques, since either the anion or the neutral
state has to be an open shell radical. This brings us to one of the greatest advantages of22photoelectron spectroscopy when compared to other spectroscopic techniques: The ability to
study radicals.
Radicals are chemical species with an unpaired electron which will rapidly react in order
to fill the orbital vacancy. With very few exceptions such nitric oxide (NO), these species are
extremely reactive and therefore unstable, posing a great difficulty to performing isolated studies
on them. This difficulty comes at a significant cost, since radicals play a major role in chemical
reactivity, from astrochemical, atmospheric and combustion, to biological and polymer
chemistries.17 Knowing the relative energies of radicals and their reactivity is of utmost
importance to the fields of chemical kinetics and dynamics, from gas phase to biologicalprocesses. In photoelectron spectroscopy, the fact that a neutral radical is unstable is almost
irrelevant to the ease of performing the experiment. Provided the anionic form is stable, aspectrum of the neutral will be obtained regardless of its stability.
Another advantage, also related to the stability of the neutral species, is the ability toacquire spectra of transition state species. Briefly, the transition state of a chemical reaction is aparticular configuration of the atoms along that reaction coordinate and is defined as the statecorresponding to the highest potential energy along this reaction coordinate.18–20 If the anion
wavefunction, when projected onto the neutral surface upon photodetachment, accesses a regionof the potential energy surface that contains a transition state, a spectrum of this transition state
can be obtained. Transition states are nearly impossible to probe experimentally due to theirextremely short lifetimes, but depending on the structure of the corresponding anion, obtaining
spectra of transition states can be relatively straightforward. The group of Neumark has done a
considerable amount of investigation of transition state species via anion photoelectron
spectroscopy.21,22 As a prototypical example, take the reaction between F and H2. This reaction
23

plays a major role in the detailed understanding of chemical reaction dynamics and gave Y.T.
Lee the Nobel Prize in chemistry in 1986, together with Dudley Herschbach and John Polanyi.23
The transition state of this reaction can be probed by photoelectron spectroscopy, since theequilibrium structure of the F–H–H– anion has a similar structure as the transition state [F–H–
H]‡.24 This shows how powerful photoelectron spectroscopy can be, allowing uniquemeasurements that are unachievable with other spectroscopic techniques.
Finally, as mentioned in section 1.1, anion photoelectron spectroscopy allows for thedetermination of the electron affinities (EAs) of neutral atoms and molecules. Our research group
has provided a major contribution to the scientific endeavor of determining EAs of atoms andsmall molecules for the past nearly 50 years.25–30 The knowledge of the EAs of molecules is
crucial for understanding chemical reactivity as, similarly to electronegativity, shows how muchan atom or molecule “want” an electron. In fact, the EAs were utilized by Robert Millikan toestablish the electronegativity scale for atoms. Contrary to the electronegativity of atoms, which
is a theoretical value that depends partly on what type of bond the atom is making, the EA can bedirectly measured and is a much more fundamental quantity having applications in nearly all
fields of chemistry (see Ref. 31 and references within). The EA is also an essential part of thethermochemical cycle that results in the measurement of bond strengths, i.e. bond dissociationenergies (D0) and/or gas phase acidities, i.e. gas phase deprotonation enthalpies (Δacid Ho0K).32 A
schematic representation of this thermochemical cycle is depicted below in Fig. 1.6 for thegeneric acid HA, and expressed arithmetically in equation 1.18.

24

Figure 1.6: Schematic representation of the thermochemical cycle of HA involving the quantities
that can be experimentally determined (black boxes), as described in the text.

25o(HA) + EA(A) = D0 (H − A) + IE(H)Δacid H0K

(1.18)

While D0 can be measured to a high degree of accuracy (often < ±0.01 kcal mol-1),33 this is nottrue for gas phase acidities (uncertainties of ~ ±1 kcal mol-1),34 since its measurement depends onthe determination of deprotonation equilibrium constants or acid bracketing with other known
acids.35,36 Hence, a precise determination of the EAs (often < ±0.1 kcal mol-1) can significantly
improve the precision and accuracy of measurements of Δacid Ho0K, provided the values for D0 are
known.
Throughout this thesis, we will explore these characteristics of photoelectron
spectroscopy in order to study exotic neutral species that are of relevance to fundamental
physical chemistry, atmospheric science, combustion chemistry, astrochemistry andbiochemistry. The individual chapters are heavily based on peer reviewed published articles withsome minor modifications.
1.4 Overview of the thesis
In this thesis, we explore the capabilities of photoelectron spectroscopy and its
application to small molecular anions. The anions studied here are generated in a dual-valve
plasma entrainment pulsed anion source (described in detail in Chapter 2). As a majority, theanions are produced in ion-molecule association reactions in the gas phase, a characteristic that is
unique to this source. The thesis then expands upon the experiments described in the Ph.D. thesisof Yu-Ju Lu,37 a previous graduate student in the group, and Ref. 38, in investigating thecapabilities of this source.
A description of the experimental techniques and theoretical methods that were employedthroughout this work are presented in Chapter 2. After that, Chapter 3 investigates the26photoelectron spectroscopy of the methide anion (CH3–), as illustrated in the graphic displayed inFig. 1.7. This chapter will show how a precise determination of the EA of CH3 can drastically
improve the knowledge of the Δacid Ho0K of methane (CH4), which defines the acidity scale ofhydrocarbons in the gas phase.39 The photoelectron spectrum of CH3– also enables the firstexperimental measurement of the umbrella-mode inversion splitting. This project, conducted incollaboration with theorists Professor John F. Stanton, Dr. Joshua H. Baraban and P. Bryan
Changala, contributes to the fundamental knowledge of the simplest carbanion employing stateof-the-art high-level theoretical methods.

27

Figure 1.7: Potential and spectra representative of the photoelectron spectroscopic investigationof the methide anion. This figure is reproduced with permission from Oliveira et al.40

28

In Chapter 4, we investigate the photoelectron spectroscopy of HONO–, the anion of
nitrous acid (HONO), an important atmospheric molecule.41–47 There, we will employ
photoelectron spectroscopy to determine the EA of HONO, which allows for the measurement of
the HO––NO bond dissociation energy through a thermochemical cycle similar to the one
described above. The photoelectron spectrum of HONO– takes advantage of the special spin
selection rules of photoelectron spectroscopy to access the triplet state of HONO via the doublet
anion, providing the first experimental measurement of the triplet state term energy. The
projection of the anionic wavefunction onto the triplet state surface accesses the transition stateof triplet HONO as it dissociates to HO + NO. This shows the advantage of photoelectron
spectroscopy in obtaining spectra of transition states. The summary of this work is depicted
below in Fig. 1.8, showing the structured singlet ground state (S0 in red) and the dissociative
triplet state (T1 in blue).

29

Figure 1.8: Summary of the work reported in Chapter 4 depicting photodetachment of HONO–,
accessing the singlet and triplet electronic states of HONO and their behavior as they are formed
via photodetachment of the HONO– anion. This figure is reproduced with permission from
Oliveira et al.48

30

In Chapters 5 and 6 we investigate the electronic structure of singly substituted alkoxy
radicals (H2C(R)O) via the photoelectron spectra of hydroxymethoxide (H2C(OH)O–) andaminomethoxide (H2C(NH2)O–), respectively. Expanding upon previous studies performed inour group regarding the small alkyl substituted alkoxy radicals,49 we compare the measured EAs
and T0 of these radicals, associating these values to the intramolecular interactions between thesubstituting R group and the oxygen atom, as depicted below in Fig. 1.9. The results takeadvantage of the measurement of the photoelectron angular distributions to identify theelectronic states and provide vibrational frequencies of these radicals. The measured EAs arecoupled to calculations of the gas phase acidities of the associated acids, methanediol(H2C(OH)2) and aminomethanol (H2C(NH2)OH) to provide the O–H bond dissociation energiesof these astrochemically and prebiotically relevant species.50–52

31

Figure 1.9: Intramolecular interaction trend of singly substituted alkoxy radicals as described in
Chapters 5 and 6. This figure shows the increasing strength of the intramolecular interactions insingly substituted alkoxy radicals, from the left: ethoxy, aminomethoxy and hydroxymethoxy.

32

In Chapter 7, we switch gears to investigate a larger polycyclic aromatic molecule:
Deprotonated 7-azaindole (7-azaindolide) and the 7-azaindole dimer (Fig. 1.10). 7-azaindole andits dimer are very relevant to the field of biochemistry and biophysics due to its analogous
structure and pairing properties to Watson-Crick nucleobases, such as Adenine and Thymine. In
our experiment we are able to measure the EA of the corresponding 7-azaindolyl radical.
Drawing a comparison with the photoelectron spectrum of indolide (also shown in Fig. 1.10), weshow how a single isoelectronic substitution can drastically change the behavior of a large rigid
molecule by severely affecting its electronic structure. A dramatic increase in dipole moment,from indole (~ 2.5 Debye) to 7-azaindole (~ 4.6 Debye) results in electron autodetachingtransitions, that are likely accessible through a high density of dipole bound states in 7azaindolyl. This leads to a photoelectron spectrum which behaves in a very unexpected manner,
where most of the intensity of the transitions is not due to direct photodetachment, but due toelectron autodetachment. This interesting feature led us to seek the collaboration of Professor
John Stanton for theoretical calculations and Professor Lai Shen Wang for experiments on
autodetaching dipole bound states.

33

Figure 1.10: Chemical structures of deprotonated indole (indolide), deprotonated 7-azaindole (7azaindolide) and (7-azaindole)2– anion.

34

Although a complete description of 5+ arduous years in the lab is a nearly impossible
feat, this thesis hopes to summarize the major contributions I have made to the field of chemistry
and let those be accessible to scientists for many years to come.
1.5 Chapter 1 references
A. Einstein, “for His Services to Theoretical Physics, and Especially for His Discovery of the
Law of the Photoelectric Effect,” Nobel Prize in Physics, 1921.
1

2

H. Hertz, Ann. Phys. 267, 983 (1887).

3

U.D. Jentschura, S. Kotochigova, E.O. LeBigot, P.J. Mohr, and B.N. Taylor, The Energy
Levels of Hydrogen and Deuterium (Version 2.1), National Institute of Standards andTechnology, Gaithersburg, MD, available online at
http://physics.nist.gov/PhysRefData/HDEL/energies.html., 2017.
4

K.R. Lykke, K.K. Murray, and W.C. Lineberger, Phys. Rev. A 43, 6104 (1991).

5

I.N. Levine, Quantum Chemistry (Pearson Prentice Hall, 2009).

E.B. Wilson, J.C. Decius, and P.C. Cross, Molecular Vibrations : The Theory of Infrared andRaman Vibrational Spectra (Dover Publications, 1980).
6

D.C. Harris and M.D. Bertolucci, Symmetry and Spectroscopy : An Introduction to Vibrational
and Electronic Spectroscopy (Dover Publications, 1989).
7

8

C.T. Wickhamjones, K.M. Ervin, G.B. Ellison, and W.C. Lineberger, J. Chem. Phys. 91, 2762
(1989).
9

S. Zhou, Z. Li, D. Xie, S.Y. Lin, and H. Guo, J. Chem. Phys. 130, 184307 (2009).

10

C. Hock, J.B. Kim, M.L. Weichman, T.I. Yacovitch, and D.M. Neumark, J. Chem. Phys. 137,
244201 (2012).
11

E.P. Wigner, Phys. Rev. 73, 1002 (1948).

12

J. Cooper and R.N. Zare, J. Chem. Phys. 48, 942 (1968).

13

E.R. Grumbling and A. Sanov, J. Chem. Phys. 135, 164302 (2011).

14

A. Sanov, Annu. Rev. Phys. Chem. 65, 341 (2014).

15

R. Mabbs, E.R. Grumbling, K. Pichugin, and A. Sanov, Chem. Soc. Rev. 38, 2169 (2009).

16

A. Sanov, E.R. Grumbling, D.J. Goebbert, and L.M. Culberson, J. Chem. Phys. 138, 54311(2013).
17

A.F. Parsons, An Introduction to Free-Radical Chemistry (Blackwell Science, 2000).

18K.J. Laidler and M.C. King, J. Phys. Chem. 87, 2657 (1983).
35

19

D.G. Truhlar, J. Phys. Chem. 87, 2664 (1983).

20

D.G. Truhlar, B.C. Garrett, and S.J. Klippenstein, J. Phys. Chem. 100, 12771 (1996).

21

D.M. Neumark, Acc. Chem. Res. 26, 33 (1993).

22

M.L. Weichman, J.A. DeVine, M.C. Babin, J. Li, L. Guo, J. Ma, H. Guo, and D.M. Neumark,Nat. Chem. 9, 950 (2017).
D.R. Herschbach, Y.T. Lee, and J.C. Polanyi, “for Their Contributions Concerning the
Dynamics of Chemical Elementary Processes,” Nobel Prize in Chemistry, 1986.
23

24

J.B. Kim, M.L. Weichman, T.F. Sjolander, D.M. Neumark, J. Klos, M.H. Alexander, and D.E.
Manolopoulos, Science 349, 510 (2015).
25

T.A. Patterson, H. Hotop, A. Kasdan, D.W. Norcross, and W.C. Lineberger, Phys. Rev. Lett.
32, 189 (1974).
26

A. Kasdan and W.C. Lineberger, Phys. Rev. A 10, 1658 (1974).

27

W.C. Lineberger and B.W. Woodward, Phys. Rev. Lett. 25, 424 (1970).

28

H. Hotop and W.C. Lineberger, J. Phys. Chem. Ref. Data 4, 539 (1975).

29

H. Hotop and W.C. Lineberger, J. Phys. Chem. Ref. Data 14, 731 (1985).

30

J.H. Lehman and W.C. Lineberger, J. Chem. Phys. 147, 13943 (2017).

31

P. Kebarle and S. Chowdhury, Chem. Rev. 87, 513 (1987).

32

S.J. Blanksby, T.M. Ramond, G.E. Davico, M.R. Nimlos, S. Kato, V.M. Bierbaum, W.C.
Lineberger, G.B. Ellison, and M. Okumura, J. Am. Chem. Soc. 123, 9585 (2001).
33

B. Ruscic, J. Phys. Chem. A 119, 7810 (2015).

34

K.M. Ervin and V.F. DeTuro, J. Phys. Chem. A 106, 9947 (2002).

35

C.H. DePuy and V.M. Bierbaum, Acc. Chem. Res. 14, 146 (1981).

36

C.H. DePuy, J.J. Grabowski, and V.M. Bierbaum, Science 218, 955 (1982).

37

Y.-J. Lu, Photoelectron Spectroscopy of Small Organic Anions Prepared Using a Novel Cold
Ion Source Employing Entrainment of Charged Particles, University of Colorado - Boulder,
2014.
38

Y.-J. Lu, J.H. Lehman, and W.C. Lineberger, J. Chem. Phys. 142, 44201 (2015).

39

C.H. DePuy, S. Gronert, S.E. Barlow, V.M. Bierbaum, and R. Damrauer, J. Am. Chem. Soc.
111, 1968 (1989).
40

A.M. Oliveira, Y.J. Lu, J.H. Lehman, P.B. Changala, J.H. Baraban, J.F. Stanton, and W.C.
Lineberger, J. Am. Chem. Soc. 137, 12939 (2015).
41

A. Indarto, Res. Chem. Intermed. 38, 1029 (2012).

42

D.G. Aubin and J.P.D. Abbatt, J. Phys. Chem. A 111, 6263 (2007).
36

43

V. Bartolomei, M. Sorgel, S. Gligorovski, E.G. Alvarez, A. Gandolfo, R. Strekowski, E.
Quivet, A. Held, C. Zetzsch, and H. Wortham, Environ. Sci. Pollut. Res. 21, 9259 (2014).
44

R. Kurtenbach, K.H. Becker, J.A.G. Gomes, J. Kleffmann, J.C. Lorzer, M. Spittler, P. Wiesen,
R. Ackermann, A. Geyer, and U. Platt, Atmos. Environ. 35, 3385 (2001).
45

B. Alicke, U. Platt, and J. Stutz, J. Geophys. Res. 107, 9 (2002).

46

J. Kleffmann, T. Gavriloaiei, A. Hofzumahaus, F. Holland, R. Koppmann, L. Rupp, E.
Schlosser, M. Siese, and A. Wahner, Geophys. Res. Lett. 32, 5818 (2005).
B.J. Finlayson-Pitts and J.N. Pitts, Chemistry of the Upper and Lower Atmosphere : Theory,
Experiments, and Applications (Academic Press, San Diego, 2000).
47

48

A.M. Oliveira, J.H. Lehman, A.B. McCoy, and W.C. Lineberger, J. Phys. Chem. A 120, 1652
(2016).
49

T.M. Ramond, G.E. Davico, R.L. Schwartz, and W.C. Lineberger, J. Chem. Phys. 112, 1158
(2000).
50

F. Duvernay, A. Rimola, P. Theule, G. Danger, T. Sanchez, and T. Chiavassa, Phys. Chem.
Chem. Phys. 16, 24200 (2014).
51

B.M. Hays and S.L.W. Weaver, J. Phys. Chem. A 117, 7142 (2013).

52

F. Duvernay, G. Danger, P. Theule, T. Chiavassa, and A. Rimola, Astrophys. J. 791, 75(2014).

37this page is intentionally left blank38

CHAPTER II
EXPERIMENTAL AND THEORETICAL METHODS

2.1 Experimental Methods
2.1.a Overview of the instrument
The instrument utilized in the experiments described in this thesis is a Time-of-Flight(TOF) mass spectrometer/Velocity-map Imaging (VMI) anion photoelectron spectrometer. In
this section the instrument will be described in detail. For that, a schematic representation of thephotoelectron instrument is shown in Fig. 2.1. This figure includes imaginary divisions of this
instrument for pedagogical purposes.
Region 1 represents the ion generation region, where the anions of interest will be
produced. Practically, the ion source chamber is kept at a pressure of ~10-6 Torr, rising to~5.010-5 Torr when both valves are operational. The pressure in this chamber is achieved by
way of a 12-inch outer diameter oil diffusion pump. Region 2 comprises the Wiley-McLarentime-of-flight mass spectrometer and the ion focusing electrostatic elements. The region thatencompasses the ion focusing elements and the acceleration stack (see section 2.1.c) contains
two differential pumping apertures, which, by way of two additional oil diffusion pumps, thepressure is brought down from ~10-5 Torr in the source region, to ~10-7 Torr. Region 3 represents
the light source, i.e. the laser systems utilized for the photodetachment experiment. Finally,
region 4 represents the velocity-map imaging photoelectron spectrometer, where thephotoelectrons are detected. This final segment of the instrument, which includes the inline
microchannel plate (MCP) detector, is evacuated by two turbomolecular pumps that reduce the39pressure by another order of magnitude, resulting in operating pressures of ~10-8 Torr. A cold
trap in this region, which can be filled with liquid nitrogen, brings the pressure down to ~10-9
Torr. In the following sections each of these regions, and the apparatus that compose them, will
be individually described in detail.

40

Figure 2.1: Schematic representation of the photoelectron spectrometer. The gray boxed regions
numbered 1 through 4 represent imaginary divisions of the instrument created for explanatory
purposes, as described in sections 2.1.b through 2.1.e in the text.

41

2.1.b Ion Source
The research reported in this thesis makes use of the dual valve plasma entrainment ion
source developed in the group during the past five years. This ion source has been described
previously in an original journal article1 and the Ph.D. dissertation of Yu-Ju Lu,2 so a similar
description will be provided here. In addition, some minor modifications were made and will bereported here.
In Chapter 1, we examined the photoelectron spectroscopic technique and highlighted theadvantages it has over other spectroscopies. One of these advantages is the ability to study
unstable exotic radicals, provided the corresponding anion is stable and can be produced. The
method by which the anions are formed have major implications to the nature of these ions. The
choice of a specific ion source puts constraints on what types of anions can be formed, what thetemperature of these anions can be, and how practical, experimentally, is the production of theseanions. Thus, one of the tasks of the experimentalist is to choose the proper ion source in order toobtain the desired attributes appropriate for the experiment in question. We generate gas phaseions, so that the isolated study of individual molecules via photodetachment can be achieved.
The temperature of these anions is also a principal attribute with which we are concerned, as alower temperature facilitates the interpretation of the spectra, a consequence of the reduced
intensity of vibrational hot bands (see Chapter 1). A lower temperature also enables theformation of anions that are less stable with respect to electron detachment, as it diminishes thedetachment via vibrational excitation and/or energetic collisions with other species present in thesource region. This is crucial for the formation of weakly bound anions, such as methide (CH3–)
and HONO–, as described in Chapters 3 and 4, respectively. Finally, for the experiments we

42desire to accomplish, the capability of rationally synthesizing anions in the gas phase (in loose
terms: “doing chemistry”) is an important feature that the ion source should enable us to perform.
The ion source consists of two orthogonally oriented pulsed General Valves (ParkerHannifin Series 9), as depicted in Fig. 2.2. Of these valves, we designate the one that isperpendicular to the ion trajectory in the WM-TOF the main valve or main expansion. This main
valve produces a supersonic expansion of a buffer gas, which is primarily argon. The supersonic
expansion allows for adiabatic cooling that quickly decreases the rotational temperature of themolecules in the expansion. Supersonic expansions, such as this one have been extensively
utilized in molecular beam and spectroscopic experiments.3–6 Perpendicular to this expansion, weplace another pulsed valve equipped with a pair of electrodes attached to its faceplate. This valve
is designated “side valve” or “side expansion” and it accounts for approximately 10% of the totalpressure rise in the vacuum chamber when both valves are operational. By appropriately timing apulsed negative voltage (see individual chapters for specific voltages) to the front electrode when
the gas flow takes place, we create a glow discharge that generates a plasma. The plasma breaks
apart the neutral species in the gas expansion into electrons, cations and anions, in addition toneutral species and radicals. Discharge sources have been utilized in the past for the generationof metal anions and exotic species with great success.7–10 However, the plasma usually forms
extremely hot species, which results in substantial spectral congestion due to hot bands.
Here is where the specific operating conditions of this source play a major role. The first
condition is that the tension of the springs inside the side valve are set such that the side
expansion operates in a choked effusive flow condition. In this way, the charged species thatcompose the plasma stick together (ambipolar diffusion11) while the hot neutral species quickly
disperse, avoiding unnecessary heating of the main beam. When this plasma “bullet” is picked up
43

by – or entrained in – the main supersonic expansion, the high density of buffer gas provides
collisional cooling to stabilize the formed ionic products. The orthogonal crossing of the plasma
beam and the main expansion also minimizes the interaction between the hot species in the
discharge and the cold buffer gas in the main expansion. In this manner, not only the rotationaltemperature decreases, but the vibrational temperature as well.1
One of the consequences of vibrational cooling is that very large clusters can be formed.
As an example, we can generate OH–(Ar)n clusters with n = 40. At that point, each Ar atom isonly bound by ~0.01 eV, which, when converted to a vibrational temperature corresponds toapproximately 116 K. That is to say that the internal vibrational temperature of OH– has to be <116 K, or the argon atoms in the cluster would boil off and dissipate the energy. Another featurethat is enabled by the efficient vibrational cooling is that, by introducing a small amount(generally < 1%) of a neutral reagent to the main expansion, we can perform chemical reactions
between the ions from the side expansion that are entrained into the main expansion and theneutrals there. The crossed expansions provide a dense, buffer gas rich environment, in which
sufficient collisions take place to stabilize the ionic reaction products. This dual valve ion source
provides a combination of the advantages of a discharge source, where the hard ionization
environment of the plasma enables the formation of unusual species, and the flowing afterglow
source.12–14

44

Figure 2.2: Specific design and functional details of the dual valve, plasma entrainment ion source.
This figure is reproduced from Lu et al.1 with some modifications.

45During the past 3 years some modifications to the original design were made to expand
the capabilities of this ion source. The first one relates to the ability to optimize the formation oflarge clusters. As mentioned above, the main supersonic expansion is responsible for the coolingand cluster formation that takes place in the source. For that, the conditions of the supersonic
expansion are of major importance. By conditions we mean: how dense, collimated and intenseis the expansion. In the general valves, these characteristics of the expansion are greatly affectedby two factors: The cone angle and aspect ratio on the main faceplate and the tension of thesprings inside the valve. A modified faceplate, with a 40° cone angle, 0.5 mm orifice and aspectratio of 7 was custom made for our applications.1,2 The second factor, setting the tension on thesprings, is easily done by rotating the faceplate, so that the compression on the springs which
actuate the main valve solenoid, is changed. While straightforwardly done on a lab bench, this isextremely unpractical when considering that each adjustment requires a breaking of the vacuum
in order to access the valve inside the source chamber. To solve this issue, we designed afaceplate holder that enables the adjustment of the tension of the springs from outside thechamber. This adjustment is realized by rotating the valve body, while the faceplate is kept fixed.
A picture of this attachment is displayed in Fig. 2.3, which shows a photograph of the dual valve
setup as it stands currently.
Cluster size distributions are affected by the temperature of the buffer gas. Therefore, in
addition to the above attachment to the main expansion, we also implemented a cooling/heating
apparatus to control the temperature of the main valve body. This is fulfilled by an aluminum
block that embraces the valve body at a very low clearance. The use of thermally conductive
lubricant improves heat transfer between the block and the valve, whose temperature ismonitored with a thermocouple. In order to heat the aluminum block, we utilize a polyimide46

resistive heater (MINCO). For cooling the block, two procedures can be taken: One is by way of
a Peltier device. Another, more efficient strategy that was implemented was that of fluid cooling.
For that, the aluminum block was designed in such way that a copper tube can pass through theblock in a tight fit. The copper tube extends to the exterior of the chamber where cooling fluid
can be flowed through it, which can range from cooled ethylene glycol (down to ~ 260 K, -13
C), or nitrogen gas at the condensation point (~77 K, -196 C). This enables a variety oftemperatures to be reached, consequently shifting cluster size distributions. An example of this,the formation of ozonide argon clusters (O3–(Ar)n), is depicted below in Fig. 2.4. Controlling thetemperature of the main valve also enables the introduction of neutral reagents of low vapor
pressure in the main expansion. The ability to heat the main valve body will come to be essential
for the introduction of 7-azaindole in the main expansion, as described in Chapter 7.

47

Figure 2.3: Photograph of the dual valve plasma entrainment ion source described in this section.
The individual components of the source are labeled accordingly.

48

Figure 2.4: Ozonide argon clusters (O3–(Ar)n) optimization and cluster size distribution shifts as afunction of valve body temperature.

49

Following their generation, the main expansion carries the formed ions. These ions drift
for approximately 20 cm until they reach a set of parallel plates that constitute the first stage ofthe mass spectrometer. The mass spectrometer is necessary for the separation of the large
collection of ions formed in the expansion, so that the photodetachment experiment on individual
ions can be performed. The mass spectrometer employed throughout this thesis will be describedin the next section.
2.1.c Mass Spectrometer
The dual valve source described in the previous section can generate a large variety ofions. The next stage of the instrument, depicted in Fig. 2.5 represents the Wiley-McLaren timeof-flight (WM-TOF) mass spectrometer15 that initially removes the neutrals and cations and thenseparates the anions by their mass-to-charge ratio.

50

Figure 2.5: Detailed schematic representation of the Wiley-McLaren Time-of-Flight mass
spectrometer. The electrostatic elements that compose the flight stack are labeled according totheir function in the instrument.
51

The physical principle of the time-of-flight spectrometer is quite straightforward: By
giving all the anions the same kinetic energy (Ek), their times of flight (TOF), given a fixed
travel distance (d), will be different by an amount that is directly proportional to the square rootof their mass-to-charge ratio (m/z). Starting with the expression for the kinetic energy, we solve
for the TOF:
1
𝐸𝑘 = 𝑚𝑣 2
2

(2.1)

2𝐸𝑘
𝑑
=
𝑚
𝑇𝑂𝐹

(2.2)

𝑚
𝑇𝑂𝐹 = 𝑑 √
2𝐸𝑘

(2.3)

𝑣=√

We then utilize the electric potential energy (Eelec) to which the ions are subject:
𝐸elec = 𝐸𝑘 = 𝑉 × 𝑧(2.4)

where V is the electric potential in Volts and z is the charge of the ion in Coulombs, to obtain:𝑚 1
𝑇𝑂𝐹 = 𝑑 √
𝑧 2𝑉

(2.5)

In atomic units, the mass-to-charge ratio (m/z) becomes simply the atomic mass of the specificion, given that the anions are singly charged, (z=e). Therefore, we will often refer to the ions m/z
as simply stating the atomic mass of the specific anion in question. As an example, hydroxideanions (OH–) have m/z=17 atomic mass units (amu).

52

In our experiment the anions are extracted by a pulsed negative voltage of ~ -700 V andthen gradually accelerated by a series of plates up to +2300 V (Fig. 2.5). This gives all anions akinetic energy of approximately 3000 eV. The Wiley-McLaren (WM) design makes use of thedual stage acceleration in order to provide a greater mass resolution and also control the point
where the ions are spatially focused (focused in the z-direction Fig. 2.1 and 2.5). For a fullderivation of the WM focusing conditions see the original work by Wiley and McLaren;15
however in summary, the ability to control the spatial focus (z-direction focus) of the ionsenables us to choose either the inline ion detector, where the mass spectra are acquired, or thelaser interaction region for optimal signal in the VMI spectrometer. Immediately after thisacceleration stage, pairs of horizontal and vertical deflectors serve the purpose of steering theions in a desired direction, by voltages of ~50 V above the float potential (+2400 V).
Downstream from this point, we utilize an einzel lens to focus the ions in the x-y plane.
Up to this point, the ions are referenced to their acceleration voltage (+2300 V), i.e. they
have +2300 V as their ground. In order to avoid floating the remainder of the ion optics anddetectors to +2300 V, we utilize a potential switch. This device consists of a long (~1 m)cylindrical metal mesh and takes advantage of the fact that the electric field inside a conducting
cylinder is zero. Thus, while the ions are inside the metal mesh, the voltage on that mesh isquickly switched from +2300 V to 0 V, re-referencing the ions to earth ground. Depending on
the timing of the switch, a set of atomic mass units – those whose TOF puts them inside themetal cylinder when the switch is triggered – are allowed through the instrument. Appendix I
contains a short program written in Mathematica in order to calculate the appropriate times offlights of the anions as a function of their mass-to-charge ratio and their originating position in53

the initial stage of the WM-TOF spectrometer, which is the region between the extraction plate
and the acceleration stack.
Downstream from the potential switch, the mass separated ions can be mass selected by
the use of a mass gate, placed ~ 20 cm before the laser-anion interaction region. The mass gate
selects ions of a desired m/z ratio by pulsing a ~ 250 V voltage on a set of parallel plates. The
electric field generated in the mass gate is perpendicular to the ion trajectory and thus reflects theunwanted ions by appropriately timing the voltage pulse. By that point in the WM-TOF
spectrometer, the ions are mass separated by ~ 250 ns/amu. Therefore, by applying a voltage
pulse of equivalent width, we can mass select ions within a single amu to go through theremainder of the flight tube. Generally, in this experiment, the laser pulse timing is sufficient todetach electrons from anions within a single m/z, but for experiments such those described in
Chapter 4, the use of the mass gate is crucial for reducing photoelectron background as a resultof detachment of ions of masses within 1 amu from the target anion.
Following the mass gate, the ions reach the final region of the instrument: the detection
region. Here, they pass through first stage of the VMI photoelectron spectrometer (described in
section 2.1.e), where they are crossed by the laser beam. Finally, the ions reach an inline
microchannel plate (MCP) detector. Here, the ions are accelerated towards the MCP by the same
voltage that supplies the gain on the detector, which are in the range of +1000 V to +1500 V. Theion intensities versus TOF as detected by the MCPs are captured by a digital oscilloscope,
generating mass spectra.

542.1.d Laser System
In this experiment, the light source utilized for photodetachment is based on a pulsed
Nd:YAG laser (Coherent Infinity). Chapter 1 notes that, in photoelectron spectroscopy, a full
spectrum can be obtained with a single wavelength. However, due to experimental details thatwill be outlined in section 2.1.e, a collection of wavelengths is utilized. The specific wavelengths
utilized in this experiments are described in each of the individual chapters, but a brief overview
of the laser system is provided here.
As any standard Nd:YAG laser, the fundamental lasing line has a wavelength of 1064.4
nm, which gives photons of 1.164 eV of energy. In addition to the fundamental wavelength, we
often utilize the second and third harmonics, namely 532.6 nm (2.329 eV) and 354.9 nm (3.495)
eV, respectively. This Nd:YAG laser provides pulses of ~3 ns, average powers of up to 600
mJ/pulse and linewidths of ~ 250 MHz. The laser can be pulsed at a rate up to 100 Hz, but
normally, the laser is operated at a repetition rate of 80 Hz in order to match the repetition rate of
the pulsed valves in the ion source, which is limited by the pumping speed of the system.
In order to increase the number of available wavelengths to be utilized forphotodetachment, this Nd:YAG laser is also equipped with a commercial UV pumped opticalparametric oscillator (OPO). The OPO is pumped by the third harmonic of the Nd:YAG (354.9nm) and outputs tunable wavelengths ranging from approximately 420 to 650 nm. The principleof operation of OPOs can be found in Ref. 16 or in any laser text book. In addition to the OPO,
we utilize a dye laser (Quanta-Ray PDL-1) to extend the available wavelengths. The dye laser
can be utilized with a vast collection of commercially available laser dyes and also be equippedwith home-built second-harmonic (SHG), sum-frequency (SFG) or difference-frequency (DFG)
generation stages.
55For the photodetachment experiment and the measurement of the photoelectron
anisotropy parameters (see section 1.2), the laser polarization must be set as parallel to the ion
trajectory (horizontal, in the laboratory frame), by depicted as a purple double headed arrow in
Fig. 2.1. For the wavelengths which don’t already have this polarization state at the output of thelaser, the polarization is rotated by way of either a half-waveplate or a polarizing periscope. In
order to decrease the amount of other polarization states in the beam, we utilize a Brewster
window at the laser entry port into the instrument. The Brewster window blocks the verticallypolarized light and thus purifies the polarization state of the photons.
Prior to the chamber entrance window, we focus the laser beam with a 500 mm nominal
focal length converging lens. This increases the photon density in the laser-ion interaction region
and also approximates the originating location of the photoelectrons as a point source, which isextremely important for optimal velocity-mapping (see Ref. 17). The lens is mounted on atranslation stage which allows for micrometric adjustment of the focal point in the x, y and z
directions. The adjustment of the position of the photoelectron originating point is crucial for
optimal resolution to be reached. The photodetachment events take place in the laser-ion
interaction region (yellow spark in Fig. 2.1). Photodetachment is realized by appropriately timing
the laser q-switch trigger, so that the laser pulse and the ion packet of a specific amu areoverlapped temporally. At that time and location, the photoelectrons are extracted by a negative
voltage pulse into the VMI spectrometer, which is described in the following section.
2.1.e Velocity-map Imaging SpectrometerAs was described in Chapter 1, the photoelectron spectra are generated by measuring the
kinetic energy distribution of the photodetached electrons. However, no mention is made as to
how the kinetic energy of the electrons is measured. There are a variety of methods with which56

one can perform this measurement, such as the hemispherical energy analyzer18–20 or a magnetic
bottle.21 In the experiments described in this thesis, we make use of the velocity-map imaging(VMI) method.
The VMI spectrometer is an ingenious device that was developed by Eppink and Parker
in order to improve the imaging of ions in photodissociation experiments.17 The VMI iscomposed of a simple arrangement of a repeller plate, and an acceleration stage (see Fig. 2.6).
Eppink and Parker found that, by use of a position sensitive detector, and by appropriately
setting the voltage ratio between the repeller and acceleration stages (in this experiment
Vrepeller/Vaccel = 0.4), the produced ions could be velocity focused in the directions orthogonal to
the flight path. That is, all particles with the same initial velocity vector are mapped onto thesame point on the detector.17 The resulting image will then contain a two-dimensional projectionof the initial 3D particle distribution, where particles of the same speed are projected onto a
circle of a defined radius, which is directly proportional to their speeds in the detector plane.
In our experiment, we employ the VMI technique to image photoelectrons, as shown in
Fig. 2.1 and 2.6. Subsequent to the interaction with the laser, the 3D photoelectron cloud isvelocity focused onto a position sensitive microchannel plate (MCP)/phosphor screen detector.
The projection on the phosphor screen is then imaged by a CCD camera, which is digitallyacquired by a computer. The VMI images contain rings that correspond to specific electron
velocities. Fig. 2.6 is a cartoon of the VMI process utilizing a specific example ofphotodetachment of molecular oxygen anion (O2–).

57

Figure 2.6: Detailed view of the VMI spectrometer with the velocity-mapping of thephotoelectrons from O2–. The expanding sphere represents the photoelectron 3D cloud which isvelocity-mapped onto the MCP/Phosphor screen detector. The resulting photoelectron spectrum isprocessed by the methods described in section 2.3.a.

58

This detector of course measures the velocity and not the kinetic energy of thephotoelectrons. Although the conversion between velocity and kinetic energy is straightforward(KE = ½ mv2), it results in a major experimental consequence about this type of detection: Theenergy resolution varies with electron kinetic energy. This fact is easily understood since kinetic
energy is quadratic in speed. The initial image can be processed (see section 2.3.a) into an arrayof equally spaced points, that correspond to photoelectron intensity versus electron speed. As weconvert speed to kinetic energy through a Jacobian transformation, the spacing of the points inthe array consequently gets larger as speed increases. This means that a peak at low eKE will benarrower than that same peak at high eKE. In our instrument, specifically, the full width at half
maximum (fwhm) of the observed peaks as a function of eKE follows approximately thefunctional form:
𝑓𝑤ℎ𝑚individual peak (𝑒𝐾𝐸) ≈ 0.003 + 0.03 𝑒𝐾𝐸 [eV]

(2.6)

where we have a constant offset of ~ 3 meV, which is the limiting resolution when small eKEs
are measured, and a linear term that increases with eKE. Thus, in VMI experiments, theresolution is often given as a percent value, corresponding to the ratio fwhm/eKE. In thisexperiment, when considering eKE ≳ 0.3 eV, the ratio between peak full width at half maximum(fwhm) and eKE reaches a constant value of ~3%.
The changing resolution of the VMI might seem like a disadvantage when compared toother types of detection, such as the hemispherical analyzer which possesses constant resolutionof ~ 10 meV. However, this can be utilized to our advantage. By analyzing electrons with low
eKE, equation 2.6 shows that the resolution in our instrument reaches a limiting value of ~3
meV. The detection of slow electrons in VMI instruments in order to obtain better resolution isoften designated Slow Electron Velocity-map Imaging (SEVI). The SEVI technique was59pioneered and extensively explored by Neumark and coworkers in order to obtain high resolution(fwhm ~ 2 cm-1 or 0.2 meV) photoelectron spectra.22,23 In some of the experiments described inthis thesis, a SEVI-like approach is taken in order to obtain resolutions of ~ 3 meV, which islimiting to our experiment.
2.2 Theoretical Methods
2.2.a Ab-initio calculations
Throughout this thesis, we employ quantum chemical calculations in order to predict andinterpret our experimental data. The vast majority of the calculations are performed by theGaussian suite of programs,24 and make use of the plethora of methods and basis sets available
there. The details of each calculation are described in the individual chapters that compose thisthesis. For the majority of the chapters, we utilize single reference methods that vary in accuracy
and computational cost. Gaussian is utilized for calculations using density functional theory
methods, often employing the popular B3LYP (Becke-3 Lee-Yang-Parr) hybrid functional.25 For
the smaller molecules studied, we often employ the high level CCSD(T) (Coupled Cluster
Singles and Doubles with non-iterative Triples) method.26–28 While the basis sets may vary, we
frequently utilize the Dunning-type augmented correlation consistent basis sets (aug-ccpVnZ)29,30 which have proven to give accurate results for the calculations performed here.
Gaussian calculations are not only a very useful resource for predicting relative energies ofmolecules, EAs, T0 and vibrational frequencies of the molecules studied here, but also extremely
practical and straightforward to set up and analyze.
Other types of calculations that were applied, particularly in Chapter 6, are the so called
multireference-type calculations.31 Different from the theoretical methods described above,60

multireference methods are required when the wavefunction of the system cannot be welldescribed by a single Slater determinant. The use of multiple Slater determinants to generate thereference wavefunctions is what defines a multireference calculation. Multireference calculations
encompass methods such as Complete Active Space Self-Consistent Field (CASSCF), Multi
Reference Configuration Interaction (MRCI), among others.31,32 As opposed to the single
reference calculations performed in Gaussian, these calculations are less of “black-boxes”. That
is to say that a more careful analysis of the calculation details must be done. In the CAS
calculations, one of the most important steps is the choice of the active space. This consists ofchoosing the particular orbitals and electrons that are involved in the desired calculation of thetarget molecule, so that the excitations of the electrons in these orbitals are physicallymeaningful. A proper choice can be difficult to do a priori without a great amount of intuitionand previous experience from the user. Nevertheless, there are some strategies that the beginner,such as myself, can follow in order to choose the correct active spaces for these types ofcalculations. Refs. 33 and 34 provide such guidance and Appendix II contains a brief descriptionof the choice of the active space in multireference calculations, as the ones described in Chapter
6. All multireference calculations in this thesis are performed utilizing the Molpro 2012 quantum
chemical software package.32
The calculations described above consist of initial geometry optimizations, providing
numerical values for the energies of the molecules and anions in their equilibrium structure, thus
resulting in the prediction of adiabatic EAs and T0s. In addition, based on a harmonic model, we
also calculate the vibrational normal modes and their corresponding frequencies based on the
optimized equilibrium geometries. These frequencies are paramount for the simulation of the61photoelectron spectra, which aid the interpretation of the experiments and are described in thesubsequent section.
2.2.b Photoelectron spectra simulations
The experimental photoelectron spectra can be theoretically predicted in order to aid theinterpretation of the experimental data. The spectra are simulated utilizing the equilibriumgeometries, harmonic frequencies and normal mode displacement vectors of the anions andcorresponding neutrals obtained from the ab initio calculations described above in order tocalculate the appropriate Franck–Condon (FC) factors (see Chapter 1). In the simulation, the FC
factors are calculated within the harmonic oscillator approximation and by employing the SharpRosenstock-Chen method with Duschinsky rotations.35,36 These calculations can be carried out at
a range of vibrational temperatures (Eqs. 1.12 and 1.13), and thus, can include vibrational hot
bands when appropriate. This procedure generates a discrete spectrum of sticks, where theintensities correspond to the calculated FC factor and the positions correspond to the calculated
vibrational frequency relative to the EA, the transition between the ground vibrational andelectronic level in the anion to ground vibrational level in the neutral electronic states. For thevibrational hot bands, as described in section 1.1, the intensity of the sticks corresponds to thecalculated FC factor times the Boltzmann factor at a specific temperature (see individual
Chapters 3 through 7). For carrying out the above-mentioned simulations, we utilize the
PESCAL37 program, for calculations performed by Gaussian,24 or the ezSpectrum38 program forcalculations performed by Molpro.32
In order to provide a direct comparison between calculation and experiment, the stick
spectrum is convolved with Gaussian functions whose integral is normalized to be equal to the62calculated transition intensity, and whose fwhm is consistent with the varying instrumental
resolution of the VMI spectrometer, as described in section 2.1.e.
2.3 Data analysis
2.3.a Image processing
Once the velocity-map images are acquired, they must be processed into a 1D
photoelectron spectrum. Physically speaking, the acquired images represent a 2D projection of a
3D photoelectron velocity distribution, which must be reconstructed so that all the information
contained in the original 3D distribution is recovered. The photoelectron signal in thereconstructed array is then integrated around the polar angle, resulting in a 1D speed distribution.
In order to do that, the image must be cylindrically symmetric, which is guaranteed provided thepolarization of the photons that generate the photoelectrons is orthogonal to the electron flightpath and then, the original 3D distribution can be recovered by a series of methods.39
The foremost method for recovering the original 3D photoelectron distribution is by wayof an inverse Abel transformation. Abel transformations have been generally utilized in image
processing for this purpose as it projects an axially symmetric emission function onto a plane,
while the inverse Abel transform is used to calculate the emission function given a projection(i.e. a scan or a photograph) of that emission function.40 The methods by which the inverse Abeltransform is carried are plenty, each with their own advantages and disadvantages, and can befound elsewhere.39 The main effects that the algorithm has on the reconstructions is theintroduction of unphysical artifacts such as addition of peaks and/or noise that are not intrinsic tothe data, artificial broadening of the peaks and generation of rising baselines. Ref. 39 contains athorough description of the specifics of each image reconstruction algorithm that is based on the63inverse Abel transform. Through this thesis, we frequently make use of the basis-set expansion
method (BASEX), which was implemented by Dribinski et al.41 BASEX has proven to be a fastand reliable method for image processing with minimal creation of aberrations.
In more recent years other types of reconstruction methods were developed by Dick,42
namely the Maximum Entropy Velocity Image Reconstruction (MEVIR) and Maximum Entropy
Velocity Legendre Reconstruction (MEVELER). These methods reconstruct the images without
the use of an inverse Abel transform. Details of the methods and their implementation can befound in Ref. 42, but briefly, quoting Dick, in contrast to other methods, these methods never
apply an inversion or smoothing to the data. Instead, the program iteratively finds the map whichis the most likely cause for the observed data, while the entropy criterion implemented
minimizes the information content in this map.42 This results in a map that contains noinformation for which there is no evidence in the data, thus minimizing reconstruction
aberrations. We thus frequently utilize this method of image processing. The specific method bywhich the spectra reported in this thesis is reconstructed is described in the individual chapters,
but MEVELER has been the method of choice for the aforementioned features and for its
remarkably accurate image centering algorithm. The issue with centering images is described in
the following paragraph.
Another point worth mentioning is that in order to perform a proper reconstruction, thecenter point of the image must be chosen so that the integration about the cylindrical axis isappropriate. Even a minor error in the choice of the center can significantly alter the position of
the observed peaks in the reconstructed speed distribution since the center represents the point ofzero electron velocity, thus introducing a systematic error to the measurement of the position ofthat peak. In addition, a wrong center can result in reconstruction aberrations. There are several
64

methods by which the center of an image can be chosen, but they often require some amount ofjudgement by the person performing the procedure. The best way to find the correct center is topick an initial center “by eye”, divide the image in four quadrants based on that center point,
symmetrize each of the quadrants into a full image, perform a reconstruction of each of thesefour images, and, finally, compare the reconstructed images. If a target peak in thereconstructions of each of the four quadrants is invariantly in the same position in the 1D
distribution, the center was appropriately chosen. If not, a different center must be chosen andthe procedure repeated. One can see how tedious and impractical is this procedure (see Appendix
III for a painful example of the procedure). The centering algorithm (F2QC) developed by Dick42
and part of the MEVIR/MEVELER package has proven to be remarkably accurate at finding thecorrect center of images, even when compared to the rigorous procedure described above. In
addition to that, the program certainly is not subject to human personal biases, and thus the
F2QC/MEVELER package became our preferred method of analyzing and processing the VMI
images.
2.3.b Assignments and uncertainties
Once the photoelectron spectra are obtained, we must analyze them to extract theimportant information, such as the EAs, vibrational frequencies and T0s. As mentioned in section
1.1, the photoelectron spectra of anions provide a vibrational spectrum of the corresponding
neutral electronic state. The vibrational frequencies of the neutral state are obtained bymeasuring the difference in peak centers between the origin transition of the vibrational
progression, which is the EA of that particular neutral, and a particular peak. However, in orderto know to what type of vibration (i.e. molecular motion) a peak corresponds, we rely on a
combination of physical intuition and comparison with calculation. The physical intuition is65based on what type of geometry change occurs upon photodetachment. This indicates which typeof vibration will be expected to be active (i.e. have a significant FC factor) in the photoelectron
spectrum. The calculated spectrum provides vibrational assignments of individual peaks by acomparison of the positions of the experimental and calculated peaks. The peak that most closely
matches the position of the predicted transition and has a vibrational normal mode that is
expected to be active, is likely the vibration responsible for the intensity of the peak. The
uncertainties in these measurements derive from a combination of the uncertainties associatedwith the statistical error in fitting the peaks to Gaussian functions, the absolute energy scalecalibration and the number of independent measurements of the individual peaks. These
uncertainties are considered to be independent of one another and therefore are added inquadrature and result, on average, in uncertainties of 1 to 2 meV. However, it is important tonote that the error associated with the measurement of the transitions is likely greater than theabove value, due to the presence of unresolved transitions, as described below.
The assignment of peaks that correspond to a single FC active transition are
straightforward. However, when multiple calculated transitions are responsible for the intensityof a single peak, firm assignments become more complicated and therefore are subject to larger
uncertainties. Often, the width of a peak is indicative of whether it is composed of a single ormultiple transitions. By acquiring a calibration spectrum with a previously investigated atomic
anion, we can know what the limiting width at a specific eKE should be, since atoms arecertainly not subject to rotational broadening. The inability of knowing precisely what transition
is responsible for a peak’s intensity consequently increases the uncertainty in our measurements
and are primarily due to two factors. First, since our experimental resolution does not allow for
separation of the rotational structure, the peak center does not necessarily correspond to the band66

origin of a transition. In order to address this, the procedure described by Engelking43,44 forrotational band shifts is employed. The procedure was described correctly in Ref. 43, but there
was an error in the band shift equation reported in that paper which was recognized in Ref. 44.
This Engelking model accounts for the fact that rigid-rotor rotational selection rules appropriate
for a bound-free transition are more complicated than for a bound-bound transition; however, theanalysis is limited to a selection rule of no change in the J, K populations (ΔJ = ΔK = 0). The
offset between the peak center and the band-origin (ΔErot) for an asymmetric top, as a function ofrotational temperature, is given by:
𝐴′
𝐵′
𝐶′
3
𝐵 ′′ − 𝐵 ′∆𝐸rot ≈ −𝑘B 𝑇 [ ′′ + ′′ +
− ]+
2𝐴
2𝐵
2𝐶 ′′ 23

(2.7)

where A, B and C are the rotational constants of the target molecules, which are obtained byeither calculation or a previous measurement. The primed quantities refer to the upper state(neutral) and the double-primed quantities refer to the lower state (anion). Second, many of thepeaks in the experiments are not resolution limited and, therefore, are subject to further
broadening. Specifically, more than one vibrational transition can account for the width of thepeaks, and hence when assigning a transition to a non-resolution limited peak, the actual band
origin of that transition may reasonably be located within a wide range comprising the fwhm ofthat peak. Therefore, for these cases, we utilize the peak fwhm (± fwhm/2) to provide theuncertainties for the assigned transitions. All of these uncertainties have to be accounted for in
the measurements of the vibrational frequencies and quantities such as the EA and T0.
Procedures that are specific to each species studied in this thesis will be described in therespective individual chapters.

67

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Y.-J. Lu, J.H. Lehman, and W.C. Lineberger, J. Chem. Phys. 142, 44201 (2015).

2

Y.-J. Lu, Photoelectron Spectroscopy of Small Organic Anions Prepared Using a Novel Cold
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4

R.E. Smalley, L. Wharton, and D.H. Levy, Acc. Chem. Res. 10, 139 (1977).

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A.T. Droege and P.C. Engelking, Chem. Phys. Lett. 96, 316 (1983).

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O.F. Hagena and W. Obert, J. Chem. Phys. 56, 1793 (1972).

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D.L. Osborn, D.J. Leahy, D.R. Cyr, and D.M. Neumark, J. Chem. Phys. 104, 5026 (1996).

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X. Li, A. Grubisic, S.T. Stokes, J. Cordes, G.F. Gantefor, K.H. Bowen, B. Kiran, M. Willis, P.
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E. Garand, T.I. Yacovitch, and D.M. Neumark, J. Chem. Phys. 130, 64304 (2009).

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F.F. Chen, Introduction to Plasma Physics (Springer US, 1995).

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V.M. Bierbaum, Int. J. Mass Spectrom. 377, 456 (2015).

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E.E. Ferguson, J. Am. Soc. Mass Spectrom. 3, 479 (1992).

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W.C. Wiley and I.H. McLaren, Rev. Sci. Instrum. 26, 1150 (1955).

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C.E. Kuyatt and J.A. Simpson, Rev. Sci. Instrum. 38, 103 (1967).

19

A. Kasdan and W.C. Lineberger, Phys. Rev. A 10, 1658 (1974).

20

R.J. Celotta, R.A. Bennett, J.L. Hall, M.W. Siegel, and J. Levine, Phys. Rev. A 6, 631 (1972).

21

H. Handschuh, G. Ganteför, and W. Eberhardt, Rev. Sci. Instrum. 66, 3838 (1995).

22

M.L. Weichman, J.A. DeVine, D.S. Levine, J.B. Kim, and D.M. Neumark, Proc. Natl. Acad.
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D.M. Neumark, J. Phys. Chem. A 112, 13287 (2008).

24

M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G.
Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P.
Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota,
R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A.
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Montgomery Jr., J.E. Peralta, F. Ogliaro, M.J. Bearpark, J. Heyd, E.N. Brothers, K.N. Kudin,
V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A.P. Rendell, J.C. Burant, S.S.
Iyengar, J. Tomasi, M. Cossi, N. Rega, N.J. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken,
C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C.
Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador,
J.J. Dannenberg, S. Dapprich, A.D. Daniels, Ö. Farkas, J.B. Foresman, J. V Ortiz, J. Cioslowski,
and D.J. Fox, Gaussian 09 Revision B.01, Gaussian Inc. Wallingford, CT (2009).
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69

this page is intentionally left blank70

CHAPTER III
PHOTOELECTRON SPECTROSCOPY OF THE METHIDE ANION (CH3–)

This chapter is partially reproduced from: Oliveira, A.M., Lu, Y.-J., Lehman, J.H., Changala,P.B., Baraban, J.H., Stanton, J.F., Lineberger, W.C., Journal of the American Chemical Society,vol. 137, p. 12939 – 12945 (2015) with permission of the authors.

3.1 Introduction and Motivation
There is great scientific interest in investigating the methide anion (CH3–) and the related
species CH3 (methyl radical) and CH4 (methane). CH4 and CH3 were studied extensively due totheir fundamental importance in combustion and many other chemical processes.1–13 CH3– , hasbeen less studies, but draws significant interest from both applied and a fundamental points ofview.
In the applied science perspective, CH3– is the simplest carbanion, which are anions witha formal negative charge located at a carbon center and ubiquitous in many areas of chemistry.14
Second CH3– is of interest to the astrochemical community as it is present in the atmosphere of
Saturn’s moon Titan, a model system for prebiotic Earth.15–18
On the fundamental science side, CH3– is isoelectronic with NH3 and H3O+, and has asimilar pyramidal structure (C3v point group). This structure results in a double-well electronic
potential energy surface along the umbrella inversion coordinate, which leads to a splitting ofvibrational levels below the barrier to inversion. Because of the numerous experimental and71theoretical studies available for NH3 and H3O+, both have become prototypes in studying
inversion/tunneling splittings, as well as tests for the validity of new theoretical treatments. In
NH3,19–21 the inversion splitting of the ground vibrational state was the transition employed in thefirst MASER,22 and has been experimentally determined as 0.793 cm-1 (24 GHz).19,23 Forhydronium, H3O+, a smaller inversion barrier leads to a much larger splitting of 55.35 cm-1.24–26
Isotopic substitution, i.e. ND3 and D3O+, lowers the inversion splitting to 0.053 and 15.36 cm-1,
respectively.21,26 The inversion splittings of CH3 and its isotopologue, CD3, however, have notbeen experimentally determined.
A photoelectron spectrum of CH3– was initially obtained in 1978 by Ellison et al.27 in ourgroup, resulting in the determination of the EA of CH3 as 0.08 ± 0.03 eV. From thisomeasurement, the gas phase acidity (Δacid H0K) was derived for CH4 as 415.2(7) kcal/mol and is

one of the highest known gas phase acidities,28,29 second only to LiOH.30 DePuy et al. used theCH4 gas-phase acidity as a reference point to determine other alkane acidities.29 This makes aprecise determination of the acidity very important.
The challenge in producing the anion is the principal reason for the lack of experimental
studies on methide.31,32 In Ellison et al.’s27 study, they claimed that CH3– was produced in asurface catalyzed decomposition of ketene (H2C=C=O). Although the ion produced wasundoubtedly CH3–, the formation route was at least mysterious and, according to private
communication with the authors, not easily reproduced. This difficulty can be explained by thesmall EA of CH3, which makes it prone to electron autodetachment, or the large gas phase
acidity of CH4, deeming the deprotonation of methane essentially impossible. The novel ion
source described in Chapter 2 enabled us to produce stable intense beams of anions with weakly
bound electron such as CH3–. The straightforward generation of CH3– through the discharge of72

pure methane and the fact that the VMI detection allows us to obtain much better resolution than
the initially reported spectrum by Ellison, motivated us to revisit the experiment, particularly
hoping that we could determine the inversion splitting in CH3– experimentally.
Besides the experimental work, this project draws attention from theoretical collaborators
as previous computational investigations9,33,34 have failed in reproducing the experimental
spectrum and energetics concomitantly.6,33 The strong anharmonicity of the anion electronic
potential surface complicates the calculation of both the vibrational zero-point energy (ZPE) andthe effective inversion barrier size. The ZPE in combination with the barrier shape has a large
effect on the magnitude of the inversion splitting and therefore, a very high quality surface isrequired for reliable calculations. By comparison with experiment, calculations can possibly
provide very useful information that cannot be measured experimentally, such as the inversion
barrier height and the anion-neutral electronic potential energy surface crossing points.
In this chapter, we report high-resolution photoelectron spectra of CH3 and its
isotopologue CD3–. The experimental results provide a point of reference for building an accurate
potential energy surface for the methide anion. New high-level electronic structure andvibrational calculations of the CH3 and CD3 anions show excellent agreement withexperimental findings.
3.2 Experimental Methods
This experiment employs the negative ion photoelectron velocity-map imaging (VMI)
spectrometer described in Chapter 2. For this study, the ions are generated in our dual valve
pulsed plasma-entrainment anion source using 40 psig argon in the main valve and 20 psig CH473

99.99% purity or CD4 99% atom D in the side valve pulsed discharge assembly operating at -900
V and 40~100 μs.
We use the following wavelengths for photodetachment: 1064 nm (1.165 eV, 3.5
mJ/pulse) and 3239 nm (0.383 eV, 50~100 J/pulse). This mid-IR wavelength comes fromdifference frequency generation (DFG) of 1064 nm with 801 nm (532 nm pumped LDS 798 dyelaser) in a 113 cm3 magnesium oxide doped lithium niobate crystal (MgO:LiNbO3). Thesewavelengths are focused into the interaction region using a 0.5 m nominal focal length CaF2 lens(Thorlabs, Inc.).
The kinetic energy scale is defined primarily by using an internal calibration of theumbrella mode frequency of neutral CH3. In order to verify the accuracy of the photoelectron
kinetic energy measurements, we calibrate our energy scale by comparing the ν2 (v = 0 → v = 4)
umbrella mode frequency (2791(4) cm-1) in neutral CH3 from Yamada et al.5 and Hermann etal.8 using an energy scale calibration from the O2 spacing from (v = 0 → v = 4) transition(4598.84 (3) cm-1)5 and vice-versa. The vibrational level spacings are consistent within 0.0001
eV (1 cm-1) in O2 and 0.0005 eV (4 cm-1) in CH3, which confirms that the energy scale
uncertainty does not significantly affect the electron kinetic energy measurements. The values
and error bars reported herein are weighted averages of all measurements, which include theuncertainty in the energy scale calibration, statistical error in peak center given by a least squares
Gaussian fit to the experimental peaks, and error associated with a displacement from peak
center due to a rotational band-origin shift (see Chapter 2).
While the mid-IR, 3239 nm wavelength can give us the best resolution (see Chapter 2),
the much higher laser flux available with 1064 nm radiation allows for much less noisy data and74

also better adjustment of the conditions necessary for a high resolution experiment. As
mentioned in Chapter 2, the point of interaction between the laser and ion beam is what
ultimately limits the resolution in the experiment, for these reasons both spectra are close toequivalent in overall quality. The mid-IR data, however, provides us the most accurate positionof the CH3 (v = 3) peak, and therefore the best calibration of the spacing CH3 (v = 1 – 3). Thisis taken into account when we weigh the experimental data to obtain the inversion splitting.
3.3 Experimental Results
3.3.a Introductory remarks
The dual valve plasma entrainment anion source35 enables efficient synthesis and coolingof CH3–. The experimental photoelectron spectra of CH3– and CD3–, depicted in the top panels of
Figures 3.1 and 3.2 respectively, show an extended vibrational progression indicative of a large
geometry change upon electron photodetachment. The overall CH3 spectrum is consistent withthe lower resolution one reported by Ellison et al.27 The CD3– photoelectron spectrum reported
here is the only experimental result obtained for this isotopic species. The binding energies
corresponding to the center of each labelled peak are shown in Table 3.1 below. The smallfeatures between peaks C through E are not reproducible and are artifacts from the inverse Abeltransformation when converting the photoelectron images to the 1D spectra.

75

Figure 3.1: Photoelectron spectra of CH3–. The experimental spectrum using 1.165 eV (red) or
0.383 eV (black) photon energies are shown in the upper panel. The peak assignments (upperand lowercase letters) and positions are provided in Table 3.1. The inset shows a raw velocity
mapped photoelectron image using 1.165 eV photon energy, with the direction of the laser
polarization parallel to the y-axis of the graph. Note that the center ring in the image is acontaminant due to detachment from CH2–. The lower panel shows the spectrum calculated bymethods described in section 3.4.
76Figure 3.2: Photoelectron spectra of CD3–. Analogous description as Figure 3.1.

77

Table 3.1: Experimentally determined electron binding energies of each peak and transition
assignments for each peak in the photoelectron spectra of CH3 and CD3. Each eBE value
corresponds to the center of each individual transition, as determined by fitting the peak to a
Gaussian form. The values in parentheses are the uncertainties described in the text.


Peaka

a

C  e– ← CAssign.
eBE / cm-1
𝜈2′ ← 𝜈2′′CD  e– ← CD
Assign.
Peaka eBE / cm-1
𝜈2′ ← 𝜈2′′a

303(10)0 ← 1+a294(8)

0 ← 1+

A

757(9)

0 ← 0+

A

674(8)

0 ← 0+

B

1340(5)1 ← 0−

B

1128(7)1 ← 0−

C

2045(5)2 ← 0+

C

1640(7)2 ← 0+

D

2755(4)3 ← 0−

D

2175(7)3 ← 0−

E

3542(6)

4 ← 0+

E

2748(7)4 ← 0+

F

4308(6)

5 ← 0−

F

3325(5)5 ← 0−

G

5157(5)

6 ← 0+

G

3917(3)

6 ← 0+

H

5977(4)7 ← 0−

H

4545(4)7 ← 0−

I

6860(3)8 ← 0+

I

5170(3)8 ← 0+

Peak labels shown in Figures 3.1 and 3.2.

78

3.4.b Photoelectron Angular Distributions
The eKE dependence of β yields direct information about the hybrid orbital compositionof the methide anion HOMO (see Chapter 2). The photoelectron anisotropy parameter is derived
for each peak in the vibrational progressions shown in Figures 3.1 and 3.2. The intensity (numberof electron counts) as a function of the angle (I(θ)) with respect to the laser polarization at the𝛽radius corresponding to each peak is fit to the form36, 𝐼(𝜃) ∝ (1 + 2 (1 + 3 cos2 𝜃)). The error
in the resulting β values, shown in Figure 3.3, comes from the scatter of the measured β values
across each peak fwhm.
The β values as a function of photodetached electron kinetic energy (eKE) are fit to themodified Wigner-Bethe-Cooper-Zare equation in the work by Sanov et al.37 that describes theangular anisotropy of electron photodetachment from a mixed sp hybrid orbital as a function ofelectron kinetic energy (eKE):𝛽(eKE) =2 𝑍 eKE + 2𝐴 eKE 2 − 4 eKE cos(δ2 − δ0 )1
2
𝐴 + 2𝐴 eKE + 𝑍 eKE

(3.1)

where
𝑍=

1−𝑓 𝐵
𝑓 𝐴

Here, Z and A and B are parameters whose physical significance is described below, and cos(δ2 –δ0) is the relative phase-shift between the outgoing waves of Δl = ±1. The A and B parametersdescribe the scaling of the radial dipole integrals corresponding to the l → l ±1 (A) and l ↔ l – 1(B) photodetachment channels. While there are initially four fitting parameters, Sanov shows that79

for mixing 2s and 2p hydrogenic orbitals, the ratio B/A becomes 8/3, and cos(δ2 – δ0)  1, i.e., nophase-shift between the outgoing electron waves, which reduces the number of fitting
parameters to two. The parameter f is associated with the relative p-character of the initialorbital, where the limiting cases of f = 0 and 1 describe pure s and p orbitals, respectively,
according to the following expression for the HOMO of the anion:|𝜓⟩𝐻𝑂𝑀𝑂 = √1 − 𝑓|𝑠⟩ + √𝑓 |𝑝⟩(3.2)

The ratio of the A and B photodetachment channels (now assumed to be 8/3) is included in thefitting equation through the Z parameter, and weighted by the coefficient (1– f)/ f for the relative
contributions of the s and p orbitals. More detailed information can be found in papers by
Sanov.37–40
The β parameters obtained from the experimental data are shown in Figure 3.3 for theCH3– photoelectron spectra using 1.165 eV and 0.383 eV photon energies. In addition, we
include here photoelectron spectra taken with 2.33 eV and 1.63 eV photon energies (not shownin this thesis). The solid green line in Figure 3.3 is the best fit of Eq. 3.1 to the experimental data,
resulting in f = 0.80 and A = 1.15 eV-1. The grey shaded area depicts the sensitivity of theexperimental fit as f is varied from 0.7 to 0.9, while A is held constant. The dashed horizontal
line at β = 0 corresponding to an isotropic photoelectron angular distribution at all eKE is shownfor clarity. The image inset in Figure 3.3 shows the calculated HOMO of CH3–, which results in f
= 0.89 (dashed blue curve), consistent with the experimental value. The measurements includedin Figure 3.3 are summarized in Table 3.2.
The anisotropy data show experimental evidence of the sp3 hybridization of the
pyramidal CH3– anion. The f factor of 0.80 indicates that the electron is detached from an orbital
80

whose wavefunction has approximately 80% pz-character and 20% s-character. This is very
similar to the expected f factor of 0.75 for an sp3 hybrid orbital. Interestingly, this f factor
decreases to 0.74 if the B/A ratio is allowed to vary away from the assumed 8/3 (2.67). The
resulting B/A ratio is then closer to 2, which is similar to the ratio derived for mixing the larger
3s and 3p hydrogenic orbitals.39

81

Figure 3.3: CH3– photoelectron anisotropy parameter (β) as a function of electron kinetic energy.
The β values (circles) are from the peaks observed in the photoelectron spectra using 0.383 eV(black), 1.165 eV (red), 1.63 eV (blue), and 2.33 eV (green) photon energies. The best fit of Eq.
(1) to the experimental data (f = 0.80, A = 1.15) is shown as the solid green curve and thecalculated value from the CH3– HOMO (f = 0.89) is shown as the blue dashed curve. The grey
shaded area shows the sensitivity of the f factor to the fit to the experimental values. Here, the ffactor was varied by ±0.1 while keeping A constant.

82

Table 3.2: Anisotropy parameter (β) measurements for each peak in the CH3– photoelectron
spectra used. The values are color coded to match Figure 3.3.
•

CH3 + e– ← CH3–
eKE (eV)β𝜈2′ ← 𝜈2′′
2.18
0.5(2)
1 ← 0+
2.10
0.4(2)
2 ← 0−
2.01
0.3(2)
3 ← 0+
1.91
0.2(3)
4 ← 0−
1.82
0.1(2)
5 ← 0+
1.71
0.0(1)
6 ← 0−
1.53
0.4(2)
0 ← 0+
1.46
0.4(4)
1 ← 0−
1.38
0.2(3)
2 ← 0+
1.29
0.0(2)
3 ← 0−
1.19-0.2(3)4 ← 0+
1.09-0.4(4)5 ← 0−
1.07
0.1(2)
0 ← 0+
1.00
0.0(2)
1 ← 0−
0.99-0.5(4)
6 ← 0+
0.91
0.0(1)
2 ← 0+
0.82-0.2(2)3 ← 0−
0.73-0.3(2)4 ← 0+
0.63-0.4(2)5 ← 0−
0.53-0.5(3)
6 ← 0+
0.42-0.6(3)7 ← 0−
0.29-0.3(2)0 ← 0+
0.22-0.5(2)
1 ← 0−
0.13-0.7(2)2 ← 0+
0.04-0.2(1)3 ← 0−

83

3.3.c Vibrational structure and electron affinities
Because of the anion double well potential energy surface along the umbrella inversion
coordinate (see Figure 3.4), the ground vibrational state is split into two levels of opposite parity
with respect to the umbrella inversion. These inversion levels are labelled as 0+, the lower, evenparity inversion level and 0–, the upper, odd parity inversion level. Figure 3.4 shows a schematic
1D representation (not to scale) of the potential energy surfaces of CH3– (black) and CH3 (green)
as a function of umbrella inversion angle (φ), where φ = 0° represents the D3h symmetry planar
structure.
The anion and neutral potential energy curves were calculated by the methods describedin section 3.4 and are the relaxed inversion potential for the anion, where at each value of φ, theC–H bond lengths are optimized. The wavefunctions shown in Figure 3.4 were calculated
numerically using the Numerov method. The symmetries of the wavefunctions of these levels
determine the selection rules in the photoelectron spectrum. The only allowed transitions (i.e.
non-vanishing Franck-Condon factors) are from the anion ν2 (v″ = 0+) to neutral ν2 (v′ = 0, 2,4 …), and anion ν2 (v″ = 0–) to neutral ν2 (v′ = 1, 3, 5 …). Note that the 1+ level refers to thelower inversion ν2 (v″ = 1) level of the anions.

84

Figure 3.4: Schematic potential energy curves (not to scale) of CH3– (black) and CH3 (green) as
a function of the inversion angle (φ). The red and blue arrows indicate the non-zero FranckCondon factors from v″ = 0+ (even wavefunction in red) and v′ = 0– (odd wavefunction in blue)in the anion ground state to even and odd quanta of the neutral state, respectively. The inversion
splitting in the anion state is labelled Δinv. See text for details.

85

The peaks labeled “A” in both spectra correspond to the ν2(v″ = 0+ → v′ = 0) transition,with centers at 0.094(2) eV and 0.083(3) eV, respectively. After a small shift due to theunresolved rotational envelope41 this results in adiabatic EAs of 0.093(3) eV and 0.082(4) eV forCH and CD , respectively. The uncertainties include a contribution due to the estimated 150 ±3
3

50 K anion rotational temperature. This EA(CH3) is consistent with that of Ellison et al. of0.08(3) eV,27 but with an order of magnitude improvement in precision.
The first peak in the each progression, labelled as “a”, corresponds to a vibrational hotband transition. The vibrational frequency of the ν2 (v″ = 0+ → 1+) umbrella mode in the anion is444(13) cm-1 in CH3 and 373(12) cm-1 in CD3 . The spacing between adjacent peaks in thephotoelectron spectra shown in Figure 3.1 and 3.2 gives the vibrational frequencies of CH3 orCD , respectively. The vibrational frequencies in the neutral state have been measured to very
3high precision by Yamada et al.5 (CH3) and by Sears et al.7 (CD3) using diode-laser IRabsorption spectroscopy. Because of the aforementioned vibrational selection rules, however, thepeaks in the photoelectron spectra are irregularly spaced compared to the neutral umbrella mode
frequencies. Specifically, the transitions to the odd vibrational quanta in the neutral are redshifted (to lower electron binding energy) by Δinv, as Figure 3.4 shows. Thus, our measured
relative peak-center positions and the high-resolution IR data will not be consistent unless Δinv istaken into account. The equation below is a sample procedure to obtain the inversion splittingfrom the experimental data:
Δinv (CH3− , 0+ → 0− ) = ν2 ( ̇CH3 , 0 → 3) + eBE[A(v ′′ = 0+ → v ′ = 0)] − eBE[D(v ′′ = 0− → v ′ = 3)]

(3.3)

86

This equation utilizes the high resolution measurement5 of CH3 ν2 (0–3) levels and ourdetermination of the eBE corresponding to the centers of peaks A and D; the primes and double
primes represent ν2 levels in the neutral and anion states, respectively. The equation is also
generalized to the other observed peaks. A weighted least-squares minimization of the difference
between the relative peak spacing and the high-resolution data, where Δinv is the optimization
parameter, is used to determine Δinv. With this procedure, all measured frequencies are utilized in
the determination of Δinv. This procedure results in Δinv of 21(5) cm-1 in CH3 and of 6(4) cm-1 in
CD3. The largest contribution to the reported uncertainties in the inversion splittings is due tothe relative shift in the rotational band origin with increasing vibrational quanta, which is on theorder of 4 cm-1.
The neutral CH3/CD3 vibrational frequencies are shown in Table 3.3. These new data
provide seven additional vibrational levels of the methyl radical, namely ν2 (6-8) in CH3 and ν2(5-8) in CD3. A quadratic fit of the vibrational level spacings as a function of vibrational
quantum number results in vibrational constants ω2(CH3) ~ 627 cm-1, x22(CH3) ~ 18 cm-1,
ω2(CD3) ~ 474 cm-1, and x22(CD3) ~ 11 cm-1, with deviations that fall within the error bars. The
measure vibrational frequencies and spectroscopic constants are shown in Table 3.3.
Experimentally determined properties of the anion and neutral, together with the theoreticalresults are summarized in Table 3.6.

87

Table 3.3: Observed umbrella mode (ν2) vibrational frequencies and derived spectroscopic
constants of neutral •CH3 and •CD3 (cm-1).


C



CD

𝜈2′ ← 𝜈2′′

Previous
work

This
workd

Previous
workc

This
workd

1←0

606.4531a

606(10)457.8136

460(10)2←1681.6369a

688(8)

507.9297

510(10)3←2731.0757a

734(7)

542.2841

542(10)4←3772(4)b769(8)

568.6322

570(10)5←4811(4)b790(9)

584(8)

6←5

830(8)

588(6)

7←6845(6)

635(6)

8←7864(4)

622(6)

Derived Spectroscopic Constantsω2627(1)e474(2)ex2218(1)e11(1)eaRef. 5, bRef. 8, cRef. 7dValues corrected by the inversion splitting. Uncertainties
are described in the main text.
e
The reported uncertainty is the 1 statistical error in aquadratic fit of the inversion corrected peak positions as afunction of vibrational quantum number.

88

3.4 Theoretical Methods and Results
3.3.a Anion potential energy surface
The calculation of the anion potential energy surface uses a reduced dimension
approximation instead of a full dimensional treatment. All HCH bond angles are constrained tobe equal, thereby enforcing threefold symmetry. This leaves the three C–H bond lengths and theumbrella inversion angle φ as the four unconstrained degrees of freedom. The constrained 4D
potential energy surface calculation is justified through the use of test calculations on NH3 where
there is only a few-percent error, which is adequate to the meet the goals of these calculations.
The 4D potential energy surface was calculated using the CFOUR quantum chemistry
package.42 The J = 0 nuclear motion calculations were performed using discrete variable
representation (DVR) bases for the four active vibrational degrees of freedom and numericalevaluation of the kinetic energy operator, as implemented in the program NITROGEN.43 The
initial 4D potential energy surface was calculated at the CCSD(T)/d-aug-pVTZ level of theory
using the CFOUR quantum chemistry package.42 On this surface, the energy of the barrier height
between the planar transition state and the pyramidal equilibrium geometry minima (EB) is
555 cm-1. The EB value is strongly dependent on the use of diffuse basis functions, as might be
expected for this system since the extra electron is more weakly bound at the transition state. The
effect of diffuse basis functions is shown in the first three rows of Table 3.4.
Initial vibrational calculations (see below) on the CCSD(T)/d-aug-pVTZ surface yielded
ground state inversion splittings approximately one-half the measured values, indicating that the
CCSD(T)/d-aug-pVTZ barrier height is probably too high. This reference value was thencorrected for the following effects: 1) triple augmentation, 2) core correlation, 3) higher order89

excitation terms in the correlation treatment (triples and non-iterative quadruples), and finally 4)
extrapolation to the complete basis-set limit (leading to the “Total method/basis-set
corrections”).
Additional contributions to the inversion barrier height include: 1) the diagonal BornOppenheimer correction (DBOC), 2) scalar relativistic effects including one- and two-electron
Darwin and mass-velocity terms, and 3) zero point energy associated with degrees of freedom
not explicitly included in the 4D model, namely the degenerate bending mode. All corrections
described above are shown in Table 3.4, along with corrections to the electronic contribution to
the electron affinity (ΔEelec).
The diagonal Born-Oppenheimer correction (DBOC) arises from the non-separability of
the nuclear and electronic degrees of freedom, and tends to be particularly large for molecules
containing light nuclei. The DBOCs for CH3–/CH3–(TS)/•CH3 and CD3–/CD3–(TS)/•CD3 are:553/542/540 cm-1 and 456/450/450 cm-1, respectively, but largely cancel when we calculate EB
and ΔEelec.
Since the degenerate bending mode (ν4) is not explicitly included in the 4D electronic
potential energy surface calculation, we approximately account for this orthogonal mode byincluding the change in ZPE of ν4 between the anion minima and the transition-state. At the
CCSD(T)/d-aug-pVTZ level of theory, the harmonic frequency of the degenerate bending mode
ν4 (ωbend) at the transition state (1379 cm-1) is reduced by 38 cm-1 relative to its value at theequilibrium geometry (1417 cm-1).
Taking these corrections to be independent, the reported calculated EB and ΔEelec are
obtained by adding all the corrections (which do not include the first line of Table 3.4) to the90initial CCSD(T)/d-aug-pVTZ result (shown in bold). This results in a calculated best estimate forthe barrier height of 386 cm-1, a nearly 25% reduction of the original CCSD(T)/d-aug-pVTZ
value of 555 cm-1. Given that the best estimate barrier height is significantly lower than the
CCSD(T)/d-aug-pVTZ value (386 cm-1), we construct a scaled potential surface, Vs, in terms of
the raw CCSD(T)/d-aug-pVTZ potential energy surface, V0, as follows:

𝑉𝑠 (𝑞⃗) = [𝑉0 (𝑞⃗) − 𝑉0 (𝑟⃗, 𝜑⃗⃗𝑒𝑞 )] × (1 −Δ 𝑇𝑆 𝜃(|𝜑𝑒𝑞 | − |𝜑|)) + 𝑉0 (𝑟⃗, 𝜑𝑒𝑞 )𝑉0 (𝑞⃗𝑇𝑆 ) − 𝑉0 (𝑟⃗𝑇𝑆 , 𝜑𝑒𝑞 )(3.4)

where 𝑞⃗ = (𝑟⃗, φ) = (r1 , r2 , r3 , φ), Δ 𝑇𝑆 is the total transition state energy correction (defined as
positive when the corrections lower the barrier height), and 𝜃(𝑥) is the Heaviside step function.
The form of this scaling is such that 𝑉𝑠 (𝑞⃗𝑇𝑆 ) = 𝑉0 (𝑞⃗𝑇𝑆 ) − Δ 𝑇𝑆 , as desired. The step function
ensures that only points with geometries closer to planarity than the equilibrium geometry(|𝜑| < |𝜑𝑒𝑞 |) are scaled, while the continuity of the surface is maintained. This procedure isvalidated by the agreement between our calculated and measured values for the inversion
splitting, as described below. This scaled surface is used to calculate the anion umbrella
vibrational frequency and inversion splitting. The calculated ground state inversion splittings forCH3– and CD3– are 25.0 and 7.9 cm-1, respectively. This is in excellent agreement with ourmeasured values of 21(5) and 6(4) cm-1. The anion ν2 (v″ = 0+ → 1+) calculated frequencies are412.3 and 335.9 cm-1 for CH3– and CD3–, respectively, which are also in reasonably good
agreement with the experimental values of 444(13) and 373(12) cm-1.

91

Table 3.4: Computational results for the CH3–/CD3– 4D transition state barrier height (EB) and•CH3/•CD3 electronic contribution to the electron affinity (ΔEelec). The initial reference

calculation at the CCSD(T)/d-aug-pVTZ level of theory, to which the corrections are applied, isshown in bold. All values are given in wavenumbers (cm-1).

Method/basis-set

EBa

Δ(EB)b

ΔEelecc

CCSD(T)/aug-pVTZ

972 cm-1+417 cm-1-76 cm-1-255 cm-1

CCSD(T)/d-aug-pVTZ (ref. calc.)

555

0

179

0

CCSD(T)/t-aug-pVTZ

503e

-52

184

5

AE-CCSD(T)/d-aug-cc-pCVTZ

537

-18

158

-21

518

-37

253

74

545

-10

375

196

438

-117

433

254

DBOCg

---

1.833

---

1.857

Darwin correctionh

---

3

---

-4

ωbend(TS) - ωbend(min)

---

1.9

---

---

386/410---415/421---

CCSDT(Q)/d-aug-pVTZ
CCSD(T) basis-set extrapolationf

Total method/basis-set corrections

Δ(ΔEelec)dFurther corrections

Final Reported Calculationa

Planar anion transition state 4D barrier heightb

Difference between EB at CCSD(T)/d-aug-pVTZ and EB at this level of calculation.
Difference between anion minimum and neutral minimum (i.e. without zero-point
energy corrections)dDifference between ΔEelec at CCSD(T)/d-aug-pVTZ and ΔEelec at this level ofcalculation.
e
For the anion transition state CCSD(T)/t-aug-pVTZ calculation only, d-aug orbitals wereused on the hydrogens, and the energy was calculated at the CCSD(T)/d-aug-pVTZ
transition state geometry.
fExtrapolation of CCSD(T)/d-aug-pVXZ (X=T,Q,5) values.
gDiagonal Born-Oppenheimer correction calculated at SCF/d-aug-pVTZ plus CCSD
corrections calculated with an aug-pVTZ basis. The values refer to the CH3/CD3 systems
respectively.
hCalculated with MP2/d-aug-pCVTZ .
c

92

3.4.b Photoelectron Spectra and Electron Affinities
In order to calculate photoelectron spectra, we determine Franck-Condon factors (FCFs)
by direct computation of vibrational overlap integrals between the anion and neutral DVR
wavefunctions. The simulated spectra for CH3– and CD3– are shown, respectively, in the lower
panels of Figures 3.1 and 3.2. The Franck-Condon factors (green sticks) were convolved with
Gaussians of varying FWHM that match the experimental resolution (blue trace), where thecalculated FCFs are directly proportional to the area of each peak. The calculated spectrum wasshifted such that the origin transition coincides with the origin of the experimental spectra.
Despite their approximate nature, the simulated spectra match the experimental spectra quite
well, with the main Franck-Condon envelope clearly reproduced.
The calculated values of the electronic contribution to the electron affinity, ΔEelec, at thesame levels of theory as those used to determine the barrier height correction ΔTS are given in
Table 3.4. ΔEelec is the energy difference between the anion and the neutral potential energy
minima; comparison with the experimentally measured adiabatic EA requires a determination of
the anion and neutral ZPEs, since EA = ΔEelec + Δ(ZPE). Here, we estimate a total ΔEelec of 415
cm-1, or 0.051 eV, around half the measured EA values. This yields calculated EAs for CH3 andCD of 0.094 and 0.084 eV, respectively. We conservatively estimate that the ZPE and3electronic contributions to the calculated EA have a total uncertainty of 100 cm-1 (ca. 0.010 eV),to which the electronic part is the main contributor. These results, together with the experimental
findings are reported in Table 3.6.

93

3.5 Discussion
3.5.a Gas-phase Acidities
With the more accurately experimentally determined value for EA(CH3) and the newexperimental measurement of EA(CD3), we can obtain the gas-phase acidity at 0 K of CH4 andCD4. The below equation shows how the gas-phase acidity of CH4 is obtained through thethermochemical cycle (see Chapter 2) using D0(CH3–H) is the bond dissociation energy of theC–H bond in methane (103.340(16) kcal/mol),44 IE(H) and the EA(CH3) of 2.14(6) kcal/mol asreported here.
o(CH4 ) = D0 (CH3 – H) + IE(H) − EA(CH3 )Δacid H0K

(3.5)

o
An analogous procedure is followed to obtain the Δacid H0K
of CD4 using the corresponding

D0(CD3–D) = 105.80(3) kcal/mol,45 IE(D) = 313.67 kcal/mol,46 and EA(CD3) = 1.90(8)okcal/mol. We obtain gas-phase acidities Δacid H0K(CH4) = 414.79(6) kcal/mol ando Δacid H0K
( CD4) = 417.57(8) kcal/mol. Compared to the previously determined value for CH4 of

415.2(7) kcal/mol, this new value is consistent but with an order of magnitude improvement inprecision, a consequence of the better determined electron affinities. In order to obtain the gas298.15

oophase acidities at 298 K, we use the thermal correction H298K
− H0K
= ∫0

𝐶𝑝 (𝑇) 𝑑𝑇 where𝐶𝑝 (𝑇) is the heat-capacity at constant pressure of the individual species.47 Here, the thermal
corrections for CH4, H+ and D+ are obtained from the Active Thermochemical Tables44 and are
non rigid-rotor/anharmonic oscillator (NRRAO) values. For CD4, the thermal correction was
obtained from Pamidimukkala et al.48 For CH3– and CD3–, the heat capacities are calculated fromthe partition functions of the isolated molecules. Here, the rotational contributions to the partition
function are calculated in a rigid-rotor approximation using the calculated rotational constants,
94

while the vibrational contributions are calculated from an explicit sum over the vibrationalenergy levels of the normal modes. We rely on the measured vibrational frequencies (whenavailable) in conjunction with the calculated frequencies. The thermal corrections areosummarized in Table 3.5. This leads to Δacid H298K(CH4) = 416.4(2) kcal/mol, also in agreementowith Ervin’s value of 416.8(7) kcal/mol, and Δacid H298K(CD4) = 419.2(2) kcal/mol.

95298.15oo
Table 3.5: Thermal corrections (H298K
− H0K
= ∫0

𝐶𝑝 (𝑇) 𝑑𝑇) for the individual species in

the methane deprotonation thermochemical cycle.
Species

o
o
H298K
− H0K
(kcal/mol)

CH3–

2.554

H+

1.481

CH4

2.396

CD3–

2.572

D+

1.481

CD4

2.473

96

3.5.b Inversion Splitting, Electron Affinity, and Anion Potential Energy Surface
The inversion splittings of isoelectronic species NH3 and H3O+ and their isotopologues
have been determined previously to very high precision. The corresponding experimental values
are 0.793 cm-1 and 0.053 cm-1 for NH3 and ND3, and 55.35 cm-1 and 15.36 cm-1 for H3O+ andD3O+ respectively.19–21,24,25 One of the most valuable results theoretical calculations can give us
is the barrier to inversion, since it is not an experimentally measurable quantity. In previous
work, Rajamäki et al.49,50 conducted high level 6D potential energy surface calculations of NH3,
H3O+ and their isotopologues, comparing the calculated vibrational frequencies of the umbrellamode and inversion splittings with experimental data. They achieve sub-wavenumber accuracy
for the inversion splittings and report the associated calculated barrier height as are 650 cm-1 for
H3O+ and 1782 cm-1 for NH3. However, the CH3– system presents a larger challenge for accurate
theoretical treatment of the potential energy curve compared to NH3 or H3O+ since neither ofthese simpler species present the possibility of electron autodetachment at planarity.
With this measurement of Δinv and the fundamental anion ν2 frequency, some of the mostimportant parameters are now known in order to accurately map out the potential energy surfaceof the anion. The calculations reported herein reproduce the experimental spectra very well, but
most importantly, reproduce the Δinv and the fundamental ν2 frequency (v″ = 0+ → 1+) of theanion umbrella mode. This gives us confidence in our effective barrier to inversion. Note that insection 3.4 we report a 4D inversion barrier of circa 400 cm-1 which includes the ZPE of thedegenerate bending mode. The effective 1D barrier height (EBeff ), on the other hand, includes thezero-point contributions from the remaining stretching vibrational modes, (which differs
substantially between the pyramidal and planar geometries, indicating a strong crossanharmonicity between the inversion motion and the CH stretches) resulting in an effective 1D97

barrier of 661 cm-1. Our effective 1D barrier is reasonably close to that found by Kraemer et al.33(ca. 833 cm-1), and the tunneling splittings calculated in their work are similar to ours (25.0 and
7.9 for CH3– and CD3–, respectively, from the present calculations versus 19 and 4 cm-1 in
Ref.47). However, it should be emphasized here that our tunneling calculations are based on amultidimensional model, and a focus on 1D barriers and their dynamics can be misleading. For
example, work by Rajamäki et al.,49,50 indicates that the 1D effective barrier for the hydronium
ion inversion is comparable to that calculated here for methide, but the magnitude of thetunneling splitting is significantly greater in the former (55 cm-1 versus 21 cm-1). While this is
surprising at first, the anharmonicities associated with inversion are greater in methide than inhydronium, which is ultimately responsible for the quite different tunneling splittings,
underscoring the sensitivity of this quantity to details of the multidimensional potential surface.
The most recent theoretical work by Dixon et al.,34 at the CCSD(T) level of theory with
aug-cc-pVxZ (x = D, T, Q) basis sets, found that the stability of the anion increases with the sizeof the basis set used. From a complete basis set extrapolation, they predicted a best-estimate
adiabatic EA of 0.07(1) eV, which is in relatively good agreement with the experimentally
determined value. They report that 63% of the EA comes from ΔZPE contributions between theanion and neutral species and that most of their uncertainty comes from the calculation of theanion ZPE. However, the calculated fundamental vibrational frequencies of the ν2 mode werereported as 783.8 cm-1 for CH3– and 496.6 cm-1 for CH3, considerably different from theexperimental values of 444(13) cm-1 (this work) and 606.4531 cm-1 (Ref. 5), respectively. Also,
the calculations show an inversion barrier of 720.5 cm-1 and suggest that the electron is notbound at planarity, i.e. the electronic potential energy surfaces cross before the D3h geometry is
attained. Considering their calculated anion fundamental ν2 (784 cm-1), the ν2 (v″ = 1+)98

vibrational level would be considerably higher than the neutral ZPE (by 420 cm-1), and thereforethe ν2 (v″ = 1+) anion would be unstable with respect to electron autodetachment, a finding that
contradicts our observation of this level persisting for at least several milliseconds.
Unfortunately, there is no reported calculation of the Δinv in the most recent work from Dixon etal. to compare with our experimental and calculated values. With the large basis sets including
diffuse functions and the high level treatment of correlation effects used here, we did notexperience the issue of electron autodetachment at planarity. Accordingly, our quantum
mechanical treatment is entirely adiabatic, an assumption that seems to be borne out by theagreement with experiment. The intersection between the anion and neutral potential energy
surfaces remains an open question. The anion is electronically stable at the anion planartransition state, but unstable at the neutral equilibrium geometry. However, we predict that theuncertainty in the calculated value of ΔEelec is around 100 cm-1, which is enough to move theseam of intersection between anion and neutral surfaces. Indeed, the close energy spacing of theanion and neutral adiabatic surfaces over such a large range of geometries suggests that it isinappropriate to consider anion autodetachment by examining the bare adiabatic surfaces without
explicitly including the effects of vibrational motion.
3.6 Conclusions
In this chapter, we report high-resolution gas-phase photoelectron spectra of CH3– andCD3–, the simplest carbanions. This experiment was possible due to the generation of a stable
intense beam of CH3– anion using the dual valve plasma entrainment source. We determine amuch more accurate value of 0.093(3) eV for the CH3 electron affinity, as well as that of CD3,
0.082(4) eV. With these measured EAs, we determine improved values for 0 K gas-phase
acidities of CH4 and CD4 as 414.79(6) kcal/mol and 417.58(8) kcal/mol, respectively. With the99

available high-resolution vibrational spectroscopy data, we are able to report the firstexperimental determination of the inversion splitting in CH3– and CD3– as 21(5) cm-1 and 6(4)cm-1. We also measure the ν2 (v″ = 0+ → 1+) frequency in CH3– and CD3– as 444(13) and373(12) cm-1, respectively and add a collection of overtone frequencies of the umbrella mode ofmethyl radical. The calculations reported herein are consistent with the experimental findings toa high degree of accuracy. With this in mind, we report a calculated barrier to inversion EB of
386/480 cm-1 for CH3–/CD3–. The dependence of photoelectron angular distributions anisotropy
on photoelectron kinetic energy affirms that the methide anion HOMO arises primarily from sp3
hybridization. These results provide a benchmark for further theoretical studies of the methide
anion. The major results of this work are summarized below in Table 3.6. Questions that remainunanswered and require further theoretical treatment of this system include issues associatedwith a possible anion/neutral electronic potential energy surface crossing in the vicinity of theplanar geometry

100Table 3.6: Summary of major results, experimental and theoretical.
ExperimentCalculation

EA( CH3)

0.093(3) eV

0.094 eV

ΔInv (CH3, ν2 0+ → 0)21(5) cm-1

25.0 cm-1

CH3, ν2 (0+ → 1+)444(13) cm-1

412.3 cm-1

Δacid Ho0K(CH4)414.79(6) kcal/mol-

Δacid Ho298K(CH4)

416.4(2) kcal/mol-

EA(CD3)

0.082(4) eV

0.084 eV

ΔInv (CD3, ν2 0+ → 0)

6(4) cm-1

7.9 cm-1

CD3, ν2 (0+ → 1+)

373(12) cm-1

335.9 cm-1

Δacid Ho0K(CD4)417.58(8) kcal/mol-

Δacid Ho298K(CD4)419.2(2) kcal/mol

-



101

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this page is intentionally left blank104

CHAPTER IV
PHOTOELECTRON SPECTROSCOPY OF THE NITROUS ACID ANION (HONO–)
This chapter is partially reproduced from: Oliveira, A.M, Lehman, J.H., McCoy, A.B.,
Lineberger, W.C., Journal of the Physical Chemistry A, vol. 120, p. 1652 – 1660 (2016) withpermission of the authors.

4.1 Introduction
In the previous chapter, where we reported the photoelectron spectroscopy of CH3–, we
explored the ion source capability of generating exotic species in the glow discharge, taking
advantage of the crossed argon expansion to cool and stabilize the plasma. In this next project wedesire to explore the synthetic capabilities of this source. As mentioned in Chapter 2, a dischargesource of ions is usually faced as a “black magic” source, where it is hard to predict all thegenerated species. While this might provide the opportunity of generating exotic species, a morerational approach to generating ions is of great interest, since it allows us to synthesize gas phaseanions to our needs. While the synthetic capability of this ions source via ion molecule reactions
was demonstrated in Ref. 1, through:OH − (Ar)n + CO → HOCO− + nAr
HONO– is the first time where an anion with unreported photoelectron spectra was studied withthis ion source. The practical reasons choosing HONO– are that we are able to generate verylarge quantities of OH–(Ar)n clusters, and NO is available from gas suppliers and is one of the
few radicals one can obtain directly from a gas cylinder.

105

Scientifically, HONO is a major source of OH radicals in the troposphere.2–5 HONO ispredicted to be formed at night by heterogeneous conversion3 and disproportionation of nitrogendioxide (NO2) through reactions with water or hydrocarbons, as well as by direct emissions inpolluted urban areas.3 The central O–N bond is broken following irradiation by sunlight between
300 and 400 nm, giving rise to OH radicals in the atmosphere.6 Because of its atmosphericimportance, HONO has been the subject of many investigations, both theoretical7–9 andexperimental.10–21 Microwave19,22 and Fourier transform infrared spectroscopic studies14,15 of
HONO in its ground electronic state determined the structure, rotational constants, and six
fundamental frequencies of both cis and trans isomers. In addition, the weakest bond in HONO
was determined to be the central O–N bond, with a ground state bond dissociation energy of
2.079 eV for the lower energy trans isomer.17,23
The electronic states of HONO have also been investigated, with experimental studies
using photon energies spanning UV to deep UV wavelengths to access high-lying electronic
states, giving rise to the production of either OH + NO or H + NO2 in the atmosphere. Using UV
absorption spectroscopy, the 𝐴̃ 1A″ (S1) state of cis-HONO was observed to be 3.26 eV higher inenergy than the 𝑋̃ 1A′ (S0) ground state.24,25 Vertical excitation from the ground electronic state
to the S1 surface, which is repulsive along the HO–NO bond dissociation coordinate, results inbreaking the central O–N bond. This is likely to be the atmospheric pathway for OH radical
formation.26 Yu et al.8 performed complete active space (CAS) calculations on the trans isomerof HONO, investigating the four lowest energy singlet and triplet excited electronic states andtheir stabilities with respect to the HO–NO bond dissociation. The lowest energy excited state,
the 𝑎̃ 3A″ (T1) state, was calculated to be approximately 2.3 eV higher in energy than the S0
ground state and dissociates to OH + NO, but with a small (0.19 eV) barrier along the106dissociation coordinate.8 While this electronic state is energetically accessible with visible lightirradiation, spin selection rules prevent observation of the T1 state by direct absorption methods.9
The T1 state can be accessed, however, via an intersystem crossing transition from the excited 𝐵̃
1A′ (S2) state of HONO.8,27,28 Thus, experimental studies on the T1 state would be useful inunderstanding how this electronic state contributes to atmospheric OH production.
Beyond studying the electronic structure of HONO, there has also been interest in the
proposed mechanisms for HONO formation in the atmosphere.2 In addition to the previously
mentioned pathways, an alternate proposed mechanism for HONO generation is through its
negative ion.18 Negative-ion chemistry of molecules containing H, O and N is relevant in theatmosphere.29 The hydroxide anion (OH–) is known to be formed through hydrogen atom
abstraction from hydrocarbons by O–.29 Van Doren et al.18 have explored the associative
detachment reaction: OH– + NO → HONO + e–. The associative detachment process is believedto arise primarily from autodetachment from HONO– vibrational continuum states, making it aninefficient process compared to dissociation back to reactants.18 However, no experimental data
are available either for the dissociation of HONO– to OH– + NO or the electron affinity (EA) of
HONO. Calculations predict this anion’s dissociation energy to be 0.49 eV18 or 0.86 eV,9 with apredicted EA(HONO) of either 0.15 eV18 or 0.66 eV,9 depending on the level of theory
employed. Experimental data on HONO– are necessary before a conclusion can be drawn
concerning the importance of the anion in the atmosphere or its possible role in the production ofneutral HONO.
In this work, we report photoelectron spectra of cis-HONO–, yielding spectroscopic
information on cis-HONO (S0), EA(cis-HONO), and the dissociation energy of cis-HONO– toform OH– + NO. Electron detachment from cis-HONO– using higher photon energies produces107cis-HONO (T1) in a configuration near a transition state along the central O–N bond dissociation
coordinate. Possible contributions from higher excited states of cis-HONO and contributions
from the trans-isomer are also considered, and are found to provide at most small contributions
to the measured signal. Quantum-chemical calculations provide additional insights into theresulting photoelectron spectrum.
4.2 Methods
4.2.a Experimental
We employ a velocity map imaging (VMI) anion photoelectron spectrometer, describedin detail in Chapter 2. Here we produce HONO– by reacting hydroxide (OH–) with nitric oxide(NO) in the dual-valve pulsed plasma entrainment anion source1 using 40 psig, 0.5% NO inargon in the main supersonic expansion and an effusive flow of 55 psig, 1% O2, 30% H2, balance
Ar in the side valve with pulsed electrical discharge of -2000 V, 40~100 μs. The presence ofNO2 in the 0.5% NO/Ar gas mixture for the main pulsed expansion poses a potential
complication in this experiment. NO2– can be formed in large quantities in the anion source
which is in part due to its high electron affinity (EA = 2.273 eV).30 This results in a large
photoelectron imaging background since NO2– is only one mass unit different from HONO– andcan be several orders of magnitude larger in ion intensity compared to HONO–. We use two
methods to reduce the amount of photoelectron background due to NO2–. First, we remove theNO2 initially present in the 0.5% NO/Ar gas mixture prior to the gas expansion by flowing thealready dilute mixture of 0.5% NO/Ar through a molecular sieve filled copper coil, which isimmersed in a methanol/dry-ice bath (~193 K) followed by an Ascarite (NaOH coated Silica)
trap. This is analogous to the procedure followed by Van Doren et al.18 While this greatly
reduces the amount of NO2 initially present, and therefore reduces the NO2– ion intensity, there is108still a substantial amount of NO2– (approximately 10 times larger ion intensity compared to
HONO–). To further reduce the photoelectron background, we use a pulsed mass gate (seeChapter 2), which deflects the majority of NO2– away from the laser interaction region without
affecting the absolute HONO– ion intensity.
We use different photon energies to obtain well-resolved photoelectron spectra of cisHONO– over the full spectral range of interest. To obtain the full photoelectron spectrum
accessing the lowest state, cis-HONO (S0), we utilize the second harmonic of a Nd:YAG laser(532 nm). For higher resolution ground state spectra, we employ 1064 nm (Nd:YAG
fundamental) and 1613 nm radiation (difference frequency mixing of 1064 nm and dye-laser
generated 640 nm radiation (DCM Exciton Dyes)). The T1 state of cis-HONO is investigatedusing both the third harmonic of the Nd:YAG laser (355 nm) and 301 nm photons fromfrequency doubling the dye-laser generated 602 nm radiation (Rhodamine 640 Exciton Dyes).
The energy scale in the photoelectron spectra accessing cis-HONO (S0) is calibratedusing the O2– photoelectron spectrum.31 To calibrate the photoelectron spectra of detachment toform cis-HONO (T1), we use the photoelectron spectrum of I–.32
4.2.b Theoretical Methods
One-dimensional cuts through the potential energy surfaces (CBS-QB3 composite
method) as functions of the central O–N bond distance (labeled as 𝑟ON,c for the remainder of thismanuscript) with all other coordinates optimized, are plotted in Fig. 4.1. As is seen, in cases ofelectron photodetachment to form the S0 state of cis-HONO, the shift in the equilibrium value of𝑟ON,c between the anion surface (plotted in green) and the S0 surface for cis-HONO (plotted inblack) leads us to expect that there will be evidence of a vibrational progression in at least the109

central O–N stretching mode in the photoelectron spectrum. In contrast, the T1 state of cisHONO at the anion equilibrium geometry is near a transition state along the HO–NO bonddissociation coordinate. In this case, a broad, unresolved photoelectron spectrum is expected.
The difference in the nature of the potential surfaces in the vertical detachment region for the S0(bound) and T1 (dissociative) states of cis-HONO requires different approaches to model thephotoelectron spectra.

110Figure 4.1: 1-D electronic potential energy curves (CBS-QB3) for cis-HONO as functions of thecentral 𝑟ON,c bond length. The red arrow represents a vertical transition from the anion
equilibrium geometry to the ground S0 and excited T1 states of neutral HONO. Note: cis-HONO(T1) is unstable with respect to isomerization to trans-HONO (T1), so what appears to be aminimum on the T1 potential surface near 1.4 Å in this coordinate is actually a saddle point.

111

To aid the interpretation of the photoelectron spectrum following electron detachment toform cis-HONO (S0), ab initio calculations for both cis-HONO– and cis-HONO (S0) were
performed at the MP2/aug-cc-pVTZ (UMP2 for the anion) and CCSD(T)/aug-cc-pVTZ level oftheory/basis-set for geometry optimization and relative energies. This choice of level ofelectronic structure was made based on the consistency between the results of the MP2 andCCSD(T) calculations. The electronic structure of HONO– will be discussed in section 4.3.e, as it
has proven to a rather pathological case for calculations. Using the geometry, harmonicfrequencies, and first-order anharmonicity constants from the MP2/aug-cc-pVTZ calculations,Franck-Condon factors (FCFs) were calculated for transitions from cis-HONO– to cis-HONO(S0) using the PESCAL program.30,33 When available, experimentally determined harmonicfrequencies15,34,35 and first-order anharmonicity constants15 of cis-HONO (S0) were used todetermine the transition energies in the PESCAL simulation. When such information was notavailable, anharmonicity constants derived from the current experimental work or calculated here
(MP2/aug-cc-pVTZ) were used (see Table 4.3 for a summary of the values used in the PESCAL
simulation). It is important that anharmonic corrections for the vibrational energies of cis-HONO(S0) were used in this analysis because of the extended vibrational progression anticipatedfollowing electron photodetachment from cis-HONO–. We do not expect significant populationin excited vibrational levels of the anion because of the unique cooling capability of the ion
source used in this experiment, and indeed, did not see evidence of this (as discussed below).
Thus, the harmonic frequencies for the anion from the UMP2/aug-cc-pVTZ calculations wereused in the FCF calculation. For comparison of the PESCAL calculated FCF stick spectrum withthe experimental data, we convolute the FCFs with Gaussian functions. For each FCF, the112

Gaussian function is characterized by an area equal to the intensity of the calculated FCF and a
FWHM dictated by its position (in eKE).
To model electron photodetachment forming cis-HONO (T1), calculations proceeded in
two steps. First, a two-dimensional scan of the potential energy surface for cis-HONO– as afunction of 𝑟ON,c and the terminal N=O bond length (labeled as 𝑟NO,t for the remainder of thismanuscript) was performed using the CBS-QB3 composite method, as implemented in Gaussian
09.36 For each point in the scan, HONO– was constrained to a planar cis configuration, and theenergy was minimized with respect to the remaining three coordinates (OH bond length and
HON and ONO angles). The potential was calculated for a grid ranging from 1.0 to 2.2 Å in𝑟NO,t and 1.2 to 3.0 Å in 𝑟ON,c in increments of 0.1 Å. Single-point energies for cis-HONO (T1)were calculated at the cis-HONO– geometries from the cis-HONO– two-dimensional potential
energy surface scan. The choice to evaluate the T1 surface at the anion optimized geometries
provided a better representation of the vertical transition region. It should be noted that at large
values of 𝑟ON,c and 𝑟NO,t , which correspond to high energy structures on the anion surface, thelowest energy geometry of HONO– does not correspond to the cis isomer. In these cases, thevalues of the HON and ONO angles, as well as the OH bond length, were constrained to theiroptimized values at the largest values of 𝑟ON,c and 𝑟NO,t for which cis-HONO– did not isomerize.
The anion and T1 potential energy surfaces are used in the calculation of thephotoelectron spectrum based on a two-dimensional model Hamiltonian:𝐻=11
cos 𝜃ONO
cos 𝜃ONO
22(𝑝ON,c+ 𝑝NO,t) + (𝑝ON,c
𝑝NO,t + 𝑝NO,t
𝑝ON,c ) + 𝑉(𝑟ON,c , 𝑟NO,t )
2𝜇NO
2
𝑚N
𝑚N
(Eq. 4.1)

113

where the value of the ONO angle depends on the two NO bond lengths. The calculation was
performed using a discrete variable representation (DVR) for the two NO bond lengths.37 For
𝑟NO,t , 100 DVR points were used in the range of 1.0 to 2.2 Å, while 750 DVR points spanning
1.2 to 6.3 Å were used for 𝑟ON,c . The calculated values of the cis-HONO (T1) potential surface
were extrapolated to values of 𝑟ON,c that extend beyond the range of calculated electronicenergies by assuming an asymptotic form for the potential of𝐶

𝑉asy = 𝑉∞ − 𝑟 6 6

ON,c(Eq. 4.2)

and fitting the 𝑉∞ and 𝐶6 variables to the calculated values of the potential energy at 𝑟ON,c = 2.0
and 2.1 Å.
The calculation of the photoelectron spectrum was performed in two steps. In the first, forevery value of 𝑟ON,c , a one-dimensional calculation of the energies and wavefunctions for the v =0-3 levels in 𝑟NO,t was performed, yielding terminal N=O stretch eigenfunctions. Then the twodimensional Hamiltonian in Eq. 1 was solved in the product basis of sinc-DVR functions37 in thecentral O–N stretch and these terminal N=O stretch eigenfunctions. The treatment of the kinetic
coupling follows earlier work of Gardiner et al. on H4O2+.38,39 The resulting energies andwavefunctions were used to construct a photoelectron spectrum within the Franck-Condon
approximation. This is shown and discussed further in Section 4.3 B.
4.3 Results and Discussion
4.3.a Introductory remarks
An overview photoelectron spectrum of cis-HONO– resulting from electron
photodetachment using 3.49 eV photon energy is shown in Fig. 4.2. Two broad bands of peaks
114

are clearly discernable in the raw image, as well as in the reconstructed photoelectron spectrum:a band at low eBE (high velocity, outer ring of the image), and another at high eBE (lowvelocity, inner rings of the image). The two bands arise from electron photodetachment forming
different electronic states of cis-HONO. Other photodetachment wavelengths will permit
investigation of these bands with much higher photoelectron energy resolution.

115

Figure 4.2: The cis-HONO– photoelectron spectrum using 355 nm (3.49 eV) photons. The inset
is the unprocessed velocity-mapped image of the photodetached electrons, illustrating thedifference in electron angular distribution relative to the laser polarization (red double-headed
arrow) following electron photodetachment forming the ground S0 and excited T1 states of cisHONO.

116

Neutral cis-HONO is a closed-shell singlet in its ground state (S0) configuration.8 The
extra electron in cis-HONO– is added to the π* antibonding orbital (3a″), which is localizedalong the central O–N bond. This electron may be removed in electron photodetachment,
producing the S0 state of cis-HONO. Alternatively, an electron could be removed from the next
highest energy doubly occupied orbital, 10a′.8 Removal of one of these electrons will result ineither a singlet (S1) or triplet (T1) electronically excited state of cis-HONO. The electronic
configurations corresponding to the observed experimental peaks in the photoelectron spectrum
are identified through their relative energies and the photodetached electron angular anisotropy.
In Fig. 4.2, the low eBE band (outer ring of image) extends from ~0.3 eV to ~2 eVelectron binding energy, peaking near 1.1 eV. The photoelectron angular distribution of the low
eBE band has a negative anisotropy parameter, with β = -0.57(2), indicating photodetachmentfrom a π-like molecular orbital. This result is consistent with the primarily π-like character of thecalculated highest (singly) occupied molecular orbital of cis-HONO–. The eBE and anisotropy ofthis band leads us to assign it to electron photodetachment of cis-HONO– forming the ground S0
state of neutral cis-HONO.
The other band in the spectrum in Fig. 4.2 starts near an eBE of 2.6 eV, approximately
2.3 eV higher in energy than the estimated origin of the low eBE band assigned to cis-HONO(S0). The first excited singlet state (S1) is experimentally known to be 3.26 eV higher inenergy24,25 than HONO (S0) for the cis isomer. This would correspond to an eBE of over 3.5 eV,
which is significantly higher in energy than the experimentally observed peaks starting near aneBE of 2.6 eV, and is inconsistent with this band corresponding to S1. While there is no previous
experimental information regarding the T1 state of cis-HONO, calculations performed here
(CBS-QB3 composite method) show an adiabatic excitation energy from S0 to T1 of117

approximately 2.58 eV for the cis-HONO isomer, in agreement with the observed approximate
energy separation between the estimated origins of these two bands. Higher-level
CASSCF/CASPT2 calculations were performed previously, but only for trans-HONO.8 In
addition, the dominant peak in this band has a photoelectron angular distribution with β =+0.75(2). The positive value of β indicates electron photodetachment from an orbital with more
σ-like character than the lower eBE peak, consistent with detachment from the 10a′ second
highest doubly occupied molecular orbital in cis-HONO–. From the combination of the above
attributes, we conclude that the band near an eBE = 2.6 eV is likely from photodetachment toproduce cis-HONO (T1). These electronic state assignments will be validated with higher
resolution spectra, vibrational analyses, and photoelectron spectrum simulations in the following
two sections.
4.3.b Ground State: cis-HONO 𝑋̃ 1A′
In this study, we take advantage of the changing resolution of the VMI detection withelectron kinetic energy in order to obtain a better-resolved photoelectron spectrum by using
lower energy photons to detach the electron from cis-HONO–. The results of this process areillustrated in Fig. 4.3. The 1.16 eV and 0.769 eV spectra, purple and orange traces of Fig. 4.3,
respectively, show well-resolved peaks and an improved signal-to-noise ratio. In contrast, thephotoelectron spectrum using 2.33 eV photon energy mimics the band shown in Fig. 4.2,
showing a broad envelope with no discernable structure. Clearly, the broad photoelectronenvelope observed when using photon energies well above the photodetachment threshold
implies that the anion and neutral states involved have substantial structural differences, and thatboth vibrational congestion and reduced electron energy resolution at these higher electron
kinetic energies conspire to eliminate structure in the photoelectron spectrum. Such spectral118

congestion could be anticipated, since there is a large change in geometry between the anion andneutral (S0) cis-HONO structures based on quantum-chemical calculations performed here at theMP2/aug-cc-pVTZ level of theory/basis. There is a ~0.3 Å (~20%) decrease in 𝑟ON,c from theanion (1.657 Å) to the ground state neutral (1.387 Å) forms of cis-HONO. With the exception of
the OH bond length (which decreases by 0.01 Å, or less than 0.5%), all of the other geometricparameters show ~4-10% increase in the bond lengths/decrease in the angles between the anion
and neutral states. A common photoelectron signature of molecules with large changes in thegeometry between the anion and neutral species is an almost uninterpretable photoelectron
spectrum because of the spectral congestion. In some cases,40,41 an experimental determination of
the EA is very difficult since a large geometry change can result in an extremely weak origin
transition compared to the most intense portions of the photoelectron spectrum.

119Figure 4.3: Photoelectron spectrum of cis-HONO– using photon energies of 532 nm (2.33 eV,
green), 1064 nm (1.16 eV, purple), and 1613 nm (0.769 eV, orange). The change in resolution as
a function of photon energy is characteristic of the VMI detection. The inset graphic shows amagnified view of the peak assigned as the EA.

120

The peak of the photoelectron spectrum reflects the photodetachment transition with thelargest FCF, or the energy difference between the anion and neutral (S0) electronic states of cisHONO at the anion equilibrium geometry. This is referred to as the vertical detachment energy(VDE), and is ~1.1 eV for electron photodetachment to form cis-HONO (S0). However, despite
the nearly 0.8 eV energy difference between the VDE and the origin of the photoelectron
spectrum, the lowest eBE peak at 0.358 eV is clearly visible above the signal-to-noise level whenlower photon energies are used, as seen in the inset in Fig. 4.3. There are no other peaks
observed at lower eBE. This peak is labeled as peak A in Fig. 4.4. In this figure, the concatenatedphotoelectron spectrum of cis-HONO– is plotted using the 1.16 eV spectrum for detachment
energies above ~0.76 eV and the 0.769 eV spectrum is plotted for smaller detachment energies.
The resulting spectrum is shown as the black trace in Fig. 4.4, where the major peaks in theexperimental spectrum are alphabetically labeled. This concatenated spectrum has been corrected
for the change in photodetachment cross section with electron kinetic energy, commonly referred
to as the threshold effect.42 Peak A appears to be a single peak with, again, no observable peaks
to lower eBE, while peaks B-C, D-F, and G-I show the start of a repeating pattern in the peak
progression. We thus assign peak A as the origin transition, i.e. the eBE for peak A is the EA(cisHONO). This assignment is further supported by the photoelectron simulation, discussed below.
It is important to recognize that the centers of these peaks will not necessarily correspond to theband origins of the transitions due to an asymmetry of the rotational band contour, as discussed
in Chapter 2. Applying a small correction for this rotational shift,43,44 the resulting EA(cisHONO) = 0.356(8) eV. The calculated EA for cis-HONO is 0.324 eV, evaluated at the
CCSD(T)/aug-cc-pVTZ level of theory, based on the optimized structures obtained using
MP2/aug-cc-pVTZ (UMP2 for the anion) shown in Table 4.1 below. This value agrees very well121with the experimental EA(cis-HONO). It is also consistent with the calculation performed here ata higher level of theory (CCSD(T)/aug-cc-pVTZ), resulting in EA(cis-HONO) = 0.352 eV. The
convolved and stick representations of the simulated spectrum (red trace and green sticks,
respectively, in Fig. 4) are used as an aid to assign the observed vibrational transitions of thedominant peaks in the experimental spectrum, the results of which are compiled in Table 4.2.

122

Figure 4.4: Scaled experimental photoelectron spectrum (black trace), Franck-Condon factors(green sticks), and convoluted simulation (red). The peak labels (upper case letters) refer to thecis-HONO 𝑋̃ 1A′ (S0) vibrational assignments compiled in Table 4.2. For electron binding
energies below ~0.76 eV, the black trace is identical to the 0.769 eV spectrum in Fig. 4.3, while
for large electron binding energies, the black trace reproduces the 1.16 eV spectrum shown in
Fig. 4.3.

123

The overall convolved photoelectron spectrum simulation shows excellent agreementwith the experimental spectrum, despite the large degree of spectral congestion, particularly foreBE ≥ 0.7 eV. The peaks in the photoelectron spectrum are readily assigned, primarily totransitions to states involving excitation of overtones and combination bands of the central O–N
stretch (ν4) and the ONO bend (ν5) along with states that have one quantum of excitation in theterminal N=O stretch (ν2) and two fewer quanta of excitation in the central O–N stretch. This last
set of states is attributed to the 2:1 Fermi resonance between ν2 and 2ν4. This progression in ν4 is
expected based on the geometry change between the anion and neutral forms of cis-HONO,
discussed above.
The excellent agreement of the simulation with the experimental photoelectron spectrum
provides support for the above peak assignments, particularly the EA, and the two assumptions
that were made regarding the initially prepared cis-HONO–: (1) the anion is vibrationally cold;and (2) cis-HONO– is the dominant isomer present. First, there is no evidence for significant
population in excited vibrational levels of cis-HONO–, which would lead to vibrational hot bands
in the photoelectron spectrum. The addition of hot bands into the photoelectron simulation
greatly reduces its agreement with the experimental data. The absence of vibrational hot-bands
indicates that the anions are vibrationally cold, with vibrational temperatures below 150 K,
typical of this ion source.1 Second, the level of agreement between the experiment andsimulation indicates that the cis isomer of HONO– is the dominant isomer formed in thisexperiment. We however, investigated the effect that including trans-HONO in the photoelectron
simulations, as it is discussed in Section 4.3.d below.

1244.3.c Vibrational Analysis
The calculated spectrum enables the assignment of vibrational transitions attributed to theground state of cis-HONO. The (MP2/aug-cc-pVTZ) equilibrium geometries of HONO–, HONO (S0),and HONO (T1) are reported in Table 4.1. In addition, the changes in geometry parameters

between the anion and neutral structures are listed. As shown in Table 4.1, the most significant
geometry change between the anion and both neutral equilibrium structures is rON,c.
The labeled peaks in the photoelectron spectrum accessing the S0 state of HONO shown in
Fig. 4.4 are assigned to the vibrational transitions listed in Table 4.2 based on the agreement with
the FCFs calculated in PESCAL.30,33 As discussed in the above, the assignments are primarily tovibrational overtones and combination bands involving ν4 (central O-N stretch) and ν5 (ONO
bend). Because of their long vibrational progressions, we can derive harmonic frequencies andfirst-order anharmonicity constants for ν4 and ν5 from the experimental data. To do so, the energyof the vibrational transition relative to the EA (third column in Table 4.2) is plotted as a functionof the vibrational quantum number and fit to a quadratic function. For the O–N stretchingvibration, this fit results in a harmonic frequency of ω4 = 856(12) cm-1 with an anharmonicity
constant of 0(3) cm-1. This corresponds to an experimental fundamental frequency of ν4 =
856(13) cm-1, which is in good agreement with ν4 = 851.94 cm-1 obtained from the previous
high-resolution work.15 This is less anharmonic than our calculated (MP2/aug-cc-pVTZ) x44 =−11 cm-1. The inclusion of an x44 anharmonicity constant of −11 cm-1 in the Franck-Condon
simulation of the photoelectron spectrum significantly decreases the level of agreement between
theory and experiment compared to the reported simulation shown in Fig. 4.4 (which uses x44 =0), giving us confidence in our experimentally derived first-order anharmonicity constant. The
ONO bend was found to be more anharmonic than the O–N stretch, with a harmonic frequency125

of ω5 = 630(5) cm-1 and first order anharmonicity constant of
x55 = −10(2) cm-1. This results in a fundamental frequency of 610(6) cm-1, which is in good
agreement with the previously observed fundamental frequency (609.0 cm-1),34 as well as thecalculated x55 = −7 cm-1 (MP2/aug-cc-pVTZ).
Since we can only definitively assign overtone transitions to these two vibrational modes,
we are unable to obtain vibrational frequencies for all modes of cis-HONO. Nevertheless, thefrequencies derived from the photoelectron spectrum are in good agreement with previous
experimental data, and new experimental anharmonicity constants have also been derived. Table
4.3 shows the spectroscopic constants for neutral cis-HONO experimentally determined in thiswork, as well as a comparison with current literature data and our calculations.

126

Table 4.1: Calculated (MP2/aug-cc-pVTZ) equilibrium geometries of cis-HONO–, cis-HONO(S0), and cis-HONO (T1), as well as the difference between geometry parameters of the anion
and neutral structures (Δ = anion structure − neutral structure). Values in parentheses for the cisHONO (S0) geometry parameters are based on microwave spectroscopic experiments22 forcomparison. Distances are given in Angstroms and the angles are in degrees.
Parametercis-HONO–

cis-HONO (S0)Δ

rHO (Å)0.971

0.980 (0.979)−0.01 0.974

0.00

rON, c (Å)

1.657

1.387 (1.395)

0.27

1.404

-0.25

rNO,t (Å)

1.238

1.192 (1.188)

0.05

1.199

-0.04

∢HON (°)

95.5

104.6 (104.2)

−9.1

101.3

−5.8

∢ONO (°)

108.4

113.3 (113.6)

−4.9

129.7

−21.3

127

cis-HONO (T1)Δ

Table 4.2: Vibrational transition assignments for the peaks labeled (A–Q) in the photoelectron
spectrum reported in Fig. 4.4. Both the absolute peak position (eBE, reported in eV) and theenergy relative to the EA (reported in cm-1) are given. The cis-HONO (S0) (𝜈1′ 𝜈2′ … ) ← cis𝜈′

𝜈′

1

2

HONO– (𝜈1′′ 𝜈2′′ … ) transitions are labeled using the standard shorthand notation (1𝜈1′′ 2𝜈2′′ …) forvibrational transitions. The assignments are based on the results of the photoelectron simulationin PESCAL and refer to the vibrational modes with the largest FCFs for the labeled peaks in thephotoelectron spectrum (Fig. 4.4). The electron binding energy (eV) of each transition is given inparentheses.
Peak

Peak
Position (eV)Energy Relative
to EA (cm-1)

Assignment (Position, eV)

A

0.358

0

000 (0.358)

B

0.438

641

510 (0.434)

C

0.468

887

410 (0.464)

D

0.514

1258

520 (0.507)

E

0.542

1479

410 510 (0.539)

F

0.572

1728

420 (0.569)

G

0.614

2067

410 520 (0.613)

H

0.646

2321

420 510 (0.645)

I

0.675

2554

430 (0.675)

J

0.687

2649

410 530 (0.684)

K

0.718

2899

420 520 (0.718)

L

0.749

3152

430 510 (0.750)

210 410 510 (0.743)

M

0.781

3407

440 (0.781)

210 420 (0.773)

N

0.792

3496

420 530 (0.790)

O

0.824

3756

430 520 (0.824)

P

0.855

4006

440 510 (0.856)

210 420 510 (0.848)

Q

0.889

4280

450 (0.886)

210 430 (0.878)

128

310 (0.521)

210 410 (0.667)

430 530 (0.895)

Table 4.3: Experimental (previous work and this study) and calculated (this study) vibrationalfrequencies (νi) of neutral cis-HONO (S0). All values are given in cm-1. The frequencies andanharmonicity constants (xii) used in the PESCAL simulation30,33 are in bold print.

Mode Number (i) Description

Experimental νi(Previous Work)

Experimental νi(This Study)a

Calculated νi(This Study)b1

O–H stretch

3426.196c

-

3416

2

N=O stretch

1640.519c

-

1591

3

HON bend

1315.2d

-

1303

4

O–N stretch

851.9431c

856(13)862

5

ONO bend

609.0e610(6)

620

6

Torsion638.5e-664

a

The reported uncertainty is the statistical error in a quadratic fit of the peak positions as afunction of vibrational quantum number. Anharmonicity constants obtained from the fitting
procedure are: x44 = 0(3), x55 = −10(2)bCalculation at the MP2/aug-cc-pVTZ level of theory/basis set; anharmonicity constants: x11= −88, x22 = −10, x33 = −9, x44 = −11, x55 = −7, x66 = −15cFrom Fourier transform spectroscopy;15 anharmonicity constants: x11 = −94.00, x22 = −11.53

d

From Kr matrix isolation study35

e

From Fourier transform spectroscopy34

129

4.3.d Contribution of the trans-HONO– isomer to the photoelectron spectrum
In order to investigate the presence of trans-HONO in the photoelectron spectrum, we
include the calculated spectrum of trans-HONO– in the overall simulation. Because of the
difficulties with calculating the photoelectron spectrum of HONO–, as it will be discussed later,
we focus on the low eBE region (< 0.7 eV, ~3000 cm-1), since the relative peak spacings willcorrespond to well-known vibrational frequencies of the neutral molecule with little contributionof anharmonicities. The results of this analysis, which parallels the calculation of thephotoelectron spectrum for cis-HONO, are shown in Fig. 4.5. As such, previously determinedvibrational frequencies of neutral trans-HONO were used,14 together with the experimentally
known anharmonicities, when available. Where anharmonicities have not been reported, thecalculated MP2/aug-cc-pVTZ values are employed. In order to directly compare the calculated
and experimental spectra, the FCFs were convoluted with Gaussian functions of varying FWHM,
as described in section 4.2 above. In addition, the origin of the trans-HONO vibrational
progression is placed at the measured origin (Peak A) of the spectrum at 0.358 eV, whichassumes that trans-HONO– is the dominant isomer present. While it is expected that the origin of
the trans-HONO spectrum will be at slightly lower electron binding energies than the dominant
cis isomer, the calculated difference between the binding energies is comparable to or slightly
smaller than the width of the Gaussian functions used in the convolution of the calculated FCFs
at an electron binding energy of 0.358 eV. While the transition frequencies for the calculated
photoelectron spectrum can be adjusted to match known values, there is not an analogous
constraint for the intensities. Given the surprisingly large sensitivity of these intensities to thelevel of electronic structure theory used to obtain the optimized structures and normal modes, therelative peak intensities are at best qualitative. As such, the level of agreement between

130

calculation and experiment should be based on peak positions and not necessarily relative
intensities. The relative FCF intensities also vary with the level of theory used, again indicating
the challenges in determining the electronic structure of the anion. Peaks 2 and 3, whichcorrespond to the transitions 510 and 410 of trans-HONO, respectively, are on average ~0.010 eV(or ~80 cm-1) shifted from the experimentally observed peaks B and C. This is beyond theexperimental uncertainty of determining the centers of these peaks (≤ 40 cm-1). The calculated
progression continues to be shifted to lower electron binding energies compared to theexperimentally observed peaks as the electron binding energy increases. In addition, thesimulation predicts peaks (such as peaks 4 and 7) where no peaks are observed experimentally,
while experimentally observed peaks E and G are not anticipated by the calculation. Overall the
calculated spectrum for photodetachment from trans-HONO–, when assuming trans-HONO– isthe dominant isomer, does not reproduce the experiment.

131

Figure 4.5: Comparison of the calculated (ROMP2/aug-cc-pVTZ) photoelectron spectrum oftrans-HONO– and the experimental data. The blue numbers refer to the calculated transitions andthe black letters refer to the experimentally observed peaks, as labeled in Fig. 4.4. The calculated
spectrum was scaled to match the intensity of peak H.

132

Now suppose the peak located at 0.358 eV (Peak A) is the EA of cis-HONO, as
determined in this chapter, and the cis-HONO– isomer is dominant. The calculated Δ(EA)cis-trans~ 0.06 eV (CCSD(T)/aug-cc-pVTZ) was used to shift the simulated trans-HONO– photoelectron
spectrum to lower binding energy relative to EA(cis-HONO), specifically EA(trans-HONO) =0.295 eV. In addition, the trans-HONO– calculated spectrum was scaled such that the origin peakis approximately at the baseline noise level at low eBE (σnoise ~0.6), since no peaks below 0.358
eV were observed experimentally. The origin of the cis-HONO– calculated spectrum was scaled
to be 6.5 times larger than this to match the intensity of peak A, reproducing the stick spectrum
in Fig. 4.4. The overall spectrum containing contributions from the cis and trans isomers wasconvoluted according to the procedure used for Fig. 4.4. The main points of disagreement are theappearance of a shoulder on peak A and the widths of peaks higher than 0.5 eV. As mentioned in
section 4.3.b, the addition of the trans isomer in the calculated photoelectron spectrum decreases
the agreement between the calculated and the experimental spectrum. Fig. 4.6 can be compared
to Fig. 4.4, which contains only the contribution of the cis isomer. This result indicates that cis-HONO– is the dominant isomer. Unfortunately, we are unable to quantify the possible relative
amount of trans-HONO– present because of the reliance on the theoretically predicted
photoelectron spectrum. To quantify the amount of trans-HONO– relative to cis-HONO–, the full
photoelectron spectrum simulations, including the poorly determined high-eBE range, must be
used to integrate the total photoelectron signal and compare this with cis-HONO–. As alreadystated, the poor determination and large variation of the anion geometry and frequencies withlevel of theory indicates the challenge this anionic species presents to electronic structure.
However, there is no experimental evidence that demands the inclusion of trans-HONO–.

133

Figure 4.6: Comparison of the calculated photoelectron spectrum of HONO– with both cis(UMP2/aug-cc-pVTZ, green sticks) and trans (ROMP2/aug-cc-pVTZ, blue sticks) isomers, andthe experimental data. The origin of the trans-HONO progression (0.295 eV) was scaled down to
the noise level.

134One way to qualitatively estimate the relative amount that trans-HONO– could contributeto the spectrum is to investigate the relative energies of both isomers. For this purpose, theisomerization coordinate of HONO– was calculated and plotted in Fig. 4.7 where the potential
energy of HONO– is reported as a function of the dihedral angle. This curve was calculated at the
CBS-QB3 level of theory and constructed by varying the HONO– dihedral angle and allowing
the other coordinates to relax so that the total energy of the system is minimized. As noted inhere, trans-HONO– has a calculated (CBS-QB3) barrier to isomerization of ~0.017 eV, or ~139
cm-1, which is smaller than the harmonic frequency of the torsion vibration, ω6 (161 cm-1, CBSQB3) for trans-HONO–. Based on this, we expect that there can likely be only one and at most
two torsion levels localized in the trans-HONO– minimum on the torsion potential. Including
harmonic zero-point energy in the six vibrational degrees of freedom, the ground state of transHONO– is ~0.016 eV, or ~130 cm-1 higher in energy than cis-HONO–. Using the estimatedrotational temperature of 75±25 K, and using a simple Boltzmann distribution under equilibrium
conditions, a relative population of 2% (50 K) to 13% (100 K) trans-HONO– was obtained.

135

Figure 4.7: Potential energy as a function of the HONO– dihedral angle calculated at the CBSQB3 level of theory. The curve is a relaxed potential energy scan, i.e. it was constructed byvarying the dihedral angle while the other coordinates were allowed to optimize so that the totalenergy of the system was minimized.

136

4.3.e Electronic Structure of HONO–
HONO– presents a surprisingly challenging molecular ion for electronic structure
calculation. While a detailed exploration of the electronic structure of this anion is beyond thescope of the present study, challenges are anticipated based on the analysis of the photoelectron
spectrum obtained for detachment of an electron to access the S0 state of cis-HONO. Analysis of
the results of this part of the study provide a D0(HO––NO) for cis-HONO– of only 0.594(9) eV(See section 4.4.f. Thermochemistry of HONO). This energy is small compared to typicalcovalent bonds and is in line with the expected strength of ion-dipole interactions. Further, thestabilizing interaction between the terminal atoms in cis-HONO– leads to an increase in its
stability relative to the trans isomer. We expect that the delicate balance between weak covalentand longer-range ion-dipole interactions in HONO– are responsible for challenges in describing
this ion with electronic structure calculations.
To better characterize the structure and frequencies of both isomers of HONO– and thelowest energy singlet (S0) and triplet (T1) states of HONO, we performed electronic structure
calculations at several levels of theory: the CBS-QB3 composite method, UMP2/aug-cc-pVTZ,
ROMP2/aug-cc-pVTZ, CCSD/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ. As is illustrated in the
results reported in Tables 4.4 - 4.7, there is considerable variability among these levels of theory,
particularly for the central O–N bond length, rON,c, and the frequency associated with the central
NO stretch. Both isomers show unusually long central O–N distances and the associatedfrequencies are unusually low. These trends are more pronounced for the trans isomer, for which
the binding energy is slightly lower. Comparing the values of rON,c, evaluated at these levels oftheory, we find that it covers a range of 0.2 Å for both isomers! In the cases of the shorter
central NO bond distances, the excess charge is delocalized across ONO, while at longer
137

distances, the excess charge localizes on OH. The situation is further complicated in cis-HONO–
as the description of the normal modes is depends strongly on the level of electronic structure
theory used. These differences lead to large variations in the intensity patterns for the calculated
photoelectron spectrum.
In the case of the cis isomer, the UMP2 calculation provides both geometries and normal
modes for HONO– that are close to the CCSD(T) results. In contrast, the UMP2 calculation fortrans-HONO– provides the longest central NO bond distance and anticipates a vertical
detachment energy that is roughly 2 eV larger than any other level of theory. Clearly the UMP2
calculations are failing to capture the extent of covalency in the trans-HONO– isomer. In thiscase, the ROMP2 calculation appears to provide a better description, and is in generally good
agreement with the results of the CCSD(T) calculations. For this reason, in the discussion that
follows, and the discussion in the text, we focus primarily on the results of the UMP2
calculations for the cis-HONO– and ROMP2 for trans-HONO–. The neutral species are both
described at the MP2 level of theory.
An implication of the large variability in the calculated structure is that the calculated
Franck-Condon progression is unexpectedly sensitive to the level of theory used. As an example,
Fig. 4.8(b) shows the calculated photoelectron spectrum based on the CCSD/aug-cc-pVTZ
calculation. It is not clear if the apparent sensitivity reflects solely challenges in properly
describing the electronic structure of HONO–, or the calculation of the photoelectron spectrum
using harmonic descriptions of the wave functions, or a combination of these two factors.
The high eBE range of the spectrum is also particularly susceptible to the approximations
inherent in employing the Franck-Condon approximation based on harmonic wave functions, as
is implemented in PESCAL, including the lack of anharmonicity in the description of the wave
138

functions and couplings between the vibrational modes. As a consequence, the high variability inthe calculated 𝑟ON,c strongly affects the length of the Franck-Condon progression at this level ofapproximation.

139

Table 4.4: Comparison of HONO–, HONO (S0), and HONO (T1) harmonic frequencies for thetrans isomer using different levels of theoretical treatment (CBS-QB3 composite method,
MP2/aug-cc-pVTZ,

CCSD/aug-cc-pVTZ

andCCSD(T)/aug-cc-pVTZ).

For

the

anion,

ROMP2/aug-cc-pVTZ results are in parenthesis, while the values not in parentheses represent theresults of UMP2 calculations.
CBS-QB3

MP2/aug-cc-pVTZ

CCSD/aug-cc-pVTZ

CCSD(T)/aug-cc-pVTZa

O–H stretch

3776.13782.1 (3788.4)

3823.33762.6

N=O stretch

1568.12357.9 (1608.6)

1519.81687.6

HON bend

900.8

706.6 (815.6)

961.6

873.2

O–N stretch

283.1

249.1 (286.6)

224.4

234.1

ONO bend

533.2

424.5 (454.7)

525.3

478.6

Torsion

161.0

141.0 (127.2)

171.3

208.9

O–H stretch

3775.93754.93817.63759.9N=O stretch

1792.6

1659.91784.01715.2

HON bend

1297.71283.41352.41305.9O–N stretch

834.0

805.3

878.3

816.4

ONO bend

618.7

602.5

675.4

616.7

Torsion

590.5

586.5

565.1

565.1

O–H stretch

3784.23771.43825.7-

N=O stretch

1493.52239.41458.3-

HON bend

1287.31301.71316.8-

O–N stretch

772.0

953.8

824.3

-

ONO bend

484.1

569.3

460.6

-

Torsion

145.0

278.8 i167.2-

trans-HONO–

trans-HONO (S0)trans-HONO (T1)a

The anion geometry converged to a dihedral angle of 184º

140

Table 4.5: Comparison of HONO–, HONO (S0), and HONO (T1) energies and geometries for thetrans isomer using different levels of theoretical treatment. For the anion, ROMP2/aug-cc-pVTZ
results are given in parenthesis, while the values not in parentheses represent the results of
UMP2 calculations. Energies reported are relative to the energy of the trans-HONO– equilibriumgeometry, where T0 is the electronic adiabatic term energy and Tv is the electronic verticaltransition energy (from the anion equilibrium geometry).
CBS-QB3

MP2/aug-cc-pVTZ

CCSD/aug-cc-pVTZ

CCSD(T)/aug-cc-pVTZarHO (Å)0.964

0.968 (0.968)

0.962

0.967

rON,c (Å)

1.811

1.936 (1.845)

1.721

1.808

rNO,t (Å)

1.219

1.193 (1.211)

1.220

1.215

∢HON (°)

92.0

96.0 (93.5)

97.2

97.3

∢ONO (°)

109.6

107.9 (107.9)

107.7

107.9

rHO (Å)

0.968

0.970

0.965

0.969

rON, c (Å)

1.433

1.428

1.405

1.432

rNO,t (Å)

1.166

1.177

1.168

1.174

∢HON (°)

102.3

101.6

102.8

102.0

∢ONO (°)

111.0

110.7

110.7

110.6

T0 (eV)

0.245

0.150 (0.288)

0.211

0.194

Tv (eV)

1.15

3.13 (1.05)

1.01

0.974

EA(trans-HONO) (eV)

0.349

0.214 (0.388)

0.233

0.289

rHO (Å)

0.968

0.970

0.965

-

rON,c (Å)

1.428

1.413

1.412

-

rNO,t (Å)

1.220

1.187

1.221

-

∢HON (°)

102.1

102.6

102.2

-

∢ONO (°)

119.2

127.4

117.9

-

T0 (eV)

2.74

3.03

2.50

-

Tv (eV)

3.00

5.55

2.77

-

trans-HONO–

trans-HONO (S0)trans-HONO (T1)a

The anion geometry converged to a dihedral angle of 184º141

Figure 4.8: Calculated photoelectron spectrum of trans-HONO– (red trace) with (a) ROMP2/augcc-pVTZ, and (b) CCSD/aug-cc-pVTZ level of theory/basis-set. The experimental photoelectron
spectrum using 3.49 eV photons (black, see Fig. 4.2) is shown for comparison. The arrow
indicates the calculated origin of the progression, which was arbitrarily set to a FC intensity of
100.

142

Table 4.6: Comparison of HONO–, HONO (S0), and HONO (T1) energies and geometries for thecis isomer using different levels of theoretical treatment (CBS-QB3 composite method,
MP2/aug-cc-pVTZ, CCSD/aug-cc-pVTZ, and CCSD(T)/aug-cc-pVTZ). For the anion,
ROMP2/aug-cc-pVTZ results are given in parenthesis, while the values not in parentheses
represent the results of UMP2 calculations. Energies reported are relative to the energy of thecis-HONO– equilibrium geometry, where T0 is the electronic adiabatic term energy and Tv is theelectronic vertical transition energy (from the anion equilibrium geometry).
CBS-QB3

MP2/aug-cc-pVTZ

CCSD/aug-cc-pVTZ

CCSD(T)/aug-cc-pVTZ

rHO (Å)0.966

0.971 (0.970)

0.966

0.969

rON, c (Å)

1.696

1.657 (1.772)

1.558

1.663

rNO,t (Å)

1.245

1.238 (1.226)

1.264

1.252

∢HON (°)

93.9

95.5 (92.1)

97.0

94.9

∢ONO (°)

108.0

108.4 (108.0)

107.4

107.6

rHO (Å)

0.980

0.980

0.979

0.978

rON, c (Å)

1.388

1.387

1.391

1.396

rNO,t (Å)

1.180

1.192

1.190

1.187

∢HON (°)

105.9

104.6

105.2

104.6

∢ONO (°)

113.6

113.3

113.1

113.2

T0 (eV)

0.296

0.180 (0.323)

0.230

0.264

Tv (eV)

1.08

0.764 (1.19)

0.899

0.957

EA(cis-HONO) (eV)0.384

0.247 (0.415)

0.315

0.352

rHO (Å)

0.971

0.974

0.967

-

rON, c (Å)

1.415

1.405

1.405

-

rNO,t (Å)

1.229

1.199

1.229

-

∢HON (°)

104.1

101.3

104.1

-

∢ONO (°)

121.7

129.7

120.3

-

T0 (eV)

2.95

3.14

2.73

-

Tv (eV)

3.19

3.97

2.97

-

cis-HONO–

cis-HONO (S0)cis-HONO (T1)143

Table 4.7: Comparison of HONO–, HONO (S0), and HONO (T1) harmonic frequencies for thecis isomer using different levels of theoretical treatment (CBS-QB3 composite method,
MP2/aug-cc-pVTZ, CCSD/aug-cc-pVTZ, and CCSD(T)/aug-cc-pVTZ). For the anion,
ROMP2/aug-cc-pVTZ results are given in parenthesis, while the values not in parentheses
represent the results of UMP2 calculations.
CBS-QB3

MP2/aug-cc-pVTZ

CCSD/aug-cc-pVTZ

CCSD(T)/aug-cc-pVTZ

O–H stretch

3748.13714.3 (3733.8)

3762.83721.7

N=O stretch

1457.91533.4 (1559.7)

1404.61398.9

HON bend

1072.31133.3 (961.2)

1156.51069.9O–N stretch

279.3

336.5 (269.1)

380.6

282.4

ONO bend

581.5

675.1 (529.1)

650.3

590.8

Torsion

305.6

274.8 (198.3)

337.6

289.5

O–H stretch

3584.43591.23672.33609.3

N=O stretch

1720.61610.71732.21658.3

HON bend

1338.11320.21379.81336.7

O–N stretch

892.5

884.2

937.4

875.7

ONO bend

638.2

693.7

678.4

631.4

Torsion

718.2

634.0

670.0

667.1

O–H stretch

3718.23700.13686.8-

N=O stretch

1414.42154.41372.0-

HON bend

1338.2

1369.91395.4-

O–N stretch

771.5

910.6

826.5

-

ONO bend

452.9

558.0

441.7

-

Torsion342.3 i401.2 i64.8 i-cis-HONO–

cis-HONO (S0)cis-HONO (T1)144

4.3.f Thermochemistry of HONO
Using the experimentally measured EA(cis-HONO), we can also obtain the bonddissociation energy (D0) for cis-HONO– → OH– + NO, referred to here as D0(HO––NO), via thethermodynamic cycle,
D0 (HO– –NO) = D0 (HO–NO) + EA(cis-HONO) − EA(OH)(Eq. 4.3)

where D0(HO–NO) = 2.066(4) eV17,23 and the EA(OH) = 1.828 eV.45 This results in D0(HO––NO) = 0.594(9) eV, significantly improving an earlier calculated value of 0.49 eV (Gaussian-2
composite method).18 These results are summarized in Table 4.8. As previously noted, the extra
electron in cis-HONO– is added to a π*-like anti-bonding molecular orbital, mainly localizedalong the central O–N bond. This results in a lengthening and weakening of the central bondupon the addition of an electron, consistent with the experimentally derived decrease in the O–Nbond strength in cis-HONO– compared to neutral cis-HONO.
The very weak central bond of cis-HONO– and the small EA(cis-HONO) imply that it isunlikely that cis-HONO– would be able to be formed via the reaction of OH– + NO andcollisionally stabilized in the troposphere before falling apart or undergoing electron
autodetachment.18 However, if cis-HONO– is formed and stabilized, it would readily undergophotodetachment with any wavelength shorter than about 3000 nm. With a VDE of ~1.1 eV,formation of neutral cis-HONO via photodetachment will preferentially be formed vibrationallyhot, hence requiring less energy for dissociating and producing OH and NO radicals in theatmosphere.

145

Table 4.8: Summary of the Experimentally Determined Quantities: Electron Affinity and Term
Energies of cis-HONO, and the Dissociation Energy of cis-HONO–.
Parameter

Experimental

Electron Affinity

0.356(8) eV

D0(HO––NO)

0.594(9) eV

ΔE(T1 – S0)~ 2.3 eV146

4.3.g Triplet State: cis-HONO 𝑎̃ 3A″
Fig. 4.9 shows the 301 nm (4.12 eV) photoelectron spectrum of cis-HONO–, spanning theT1 excited state of cis-HONO. The excited state spectrum lies ~2.3 eV higher in energy than cisHONO (S0) and consists of three peaks that are an order of magnitude broader (0.09 eV FMWH
at 3.1 eV eBE) than the resolution of the photoelectron spectrometer in this electron kinetic
energy range. This result means that the breadth of these three peaks is intrinsic to the electron
photodetachment and not due to our experimental resolution. The peaks in the spectrum arespaced by roughly 0.195 eV, or 1570 cm-1. This energy is similar to the calculated frequency of
the terminal N=O stretch in cis-HONO (T1) (1414 cm-1, CBS-QB3 composite method). A
terminal N=O stretching vibration contribution to the photoelectron spectrum is also indicatedbased upon the calculated decrease in 𝑟NO,t , from 1.25 Å to 1.23 Å from the anion to neutral (T1)equilibrium structures.

147

Figure 4.9: Detailed T1 excited state photoelectron spectrum of cis-HONO– using 301 nm (4.12eV) photon energy. The green sticks are the calculated FCFs by the methods described in the
text.

148

The potential energy curve for cis-HONO (T1) at the equilibrium geometry of cis-HONO–
exhibits a transition state along the 𝑟ON,c dissociation coordinate, as shown in Fig. 4.1. In order tomodel the experimentally observed photoelectron spectrum, we calculate the FCFs (green-sticks
in Fig. 4.9) by approximating the transitions as bound to bound, as outlined in section 4.2.b.
Essentially, an infinite potential wall is placed at large 𝑟ON,c distances on the T1 potential energy
curve, which allows for quantization of states along this HO–NO bond dissociation coordinate.
While this is an approximation, the placement of an infinite wall only affects the density of states
and not the overall shape of the envelope.
The overall shape of the calculated spectral envelope matches the experimental spectrum
very well. The three main groups of peaks in the calculated spectrum reflect the active terminal
N=O stretching vibration, as expected based on the experimental spacing of the peaks. Withineach of these groups, there are two sets of peaks, which reflect the two regions of the T1 surface
that can be accessed by the ground state wavefunction of the anion. The anion wavefunction has
significant amplitude over a large range of 𝑟ON,c . When this wavefunction is projected onto thetriplet surface, it samples both scattering and bound states in the O–N bond dissociation
coordinate. The relative intensities of these two types of transitions are sensitive to details of thetriplet potential surface. In order to approximately reproduce the experimental peak contour, thetriplet surface was shifted to larger 𝑟ON,c distances by ~0.08 Å relative to the anion surface. This
shift is consistent with the variability of the calculated equilibrium 𝑟ON,c bond length for theanion at several levels of electronic structure theory (see section 4.3.e). Due to the shallow anion
potential energy surface along the central ON bond stretching coordinate, the 𝑟ON,c in the anion
optimized geometry spans a range of 0.2 Å. The potential shift results in an increase in thecontribution of transitions to states that are localized in the well on the T1 state of cis-HONO to149

the overall band contour. In addition, the energy scale of the calculated FCFs was shifted by ~30
meV to larger electron binding energy to more closely match the energetic position of theexperimental spectrum. This shift roughly reflects the difference between the experimentallymeasured and calculated EA(cis-HONO).
The calculation indicates that the majority of the experimental peak breadth is due to thedissociation along 𝑟ON,c , which would lead to the formation of OH and NO radicals. This analysis
does not include other, smaller sources of peak broadening, such as rotational excitation of theseparating OH and NO moieties, as well as activity in other cis-HONO (T1) vibrations. However,out of the possible active vibrations based on the geometry differences between the anion andcis-HONO (T1) equilibrium structures, only the N=O stretch remains bound following
dissociation, and as such (unlike electron photodetachment to form the ground singlet state), only
a progression in this vibration is expected to be reflected in the spectrum. Additional calculations
show that including the torsion coordinate adds some further peak broadening, but does notchange the overall contour. While the triplet potential energy surface is plotted only along one
coordinate in Fig. 1, the local maximum in the blue curve is actually a second order saddle point,with the other imaginary frequency corresponding to the cis-HONO torsion. In other words, atthe equilibrium geometry of cis-HONO–, cis-HONO (T1) is unstable with respect toisomerization to trans-HONO as well as to dissociation to OH + NO, and it is this feature of the
T1 state potential that is responsible for the broadening.
There could also be a contribution to the photoelectron spectrum shown in Fig. 4.9 fromphotodetachment to cis-HONO (S1). Now that there is an experimental measurement of the EAof cis-HONO (0.356(8) eV), and a known S0-S1 term energy (3.26 eV),25 the expected onset ofthe photoelectron spectrum corresponding to cis-HONO (S1) would be near 3.62 eV. The S1 state150

of cis-HONO is known to be dissociative along the central HO-NO bond stretching coordinate8
and so it might also exhibit broadened peaks. Any contribution of the S1 state to thephotoelectron spectrum assigned to detachment to cis-HONO (T1) is not conclusively identified,although there are photodetached electrons with very low kinetic energy seen in both theunprocessed photoelectron image (not shown) and the photoelectron spectrum (Fig. 4.9). Higher
energy photons could be used to explore detachment to cis-HONO (S1), however, this state has
been the focus of many past experimental studies24,25 and current experimental details(particularly the large amount of background photoelectrons when using ultraviolet photon
energies) inhibit this from being pursued further.
The major implication for the cis-HONO (T1) analysis stems from its potential
atmospheric relevance as a source of OH radicals. For the photodissociation of cis-HONO (S0),producing OH radicals in the atmosphere, UV excitation accesses several higher lying singlet
excited states. There is potential for intersystem crossing to play a role in the dissociation
mechanism, as suggested by previous calculations.8,28 The relative energies of the cis-HONO(T1) and cis-HONO (S0) electronic states (~2.3 eV), as well as the dissociation to form OH + NO
from the triplet surface, is instructive to future theoretical investigations.
4.4 Conclusions
We report the experimental photoelectron spectrum of cis-HONO–. In this experiment,
cis-HONO– was formed in an association reaction of OH– and NO in a pulsed plasmaentrainment ion source. We observe the presence of only the cis-HONO– isomer, which is
calculated to be the global minimum on the anion potential energy surface. The reported
photoelectron spectra show photodetachment to both the singlet ground state (𝑋̃ 1A′) and thetriplet state (𝑎̃ 3A″) of neutral cis-HONO. Based on the photoelectron spectrum, we obtain the151

EA(cis-HONO) of 0.356(8) eV, with a VDE of approximately 1.1 eV. The large difference
between the EA and the VDE is indicative of the significant geometry change upon electron
photodetachment, which is consistent with the results of electronic structure calculations. In
addition, detachment to form cis-HONO (S0) exhibits a photoelectron spectrum dominated byexcitation of the central O–N stretching vibration (ν4), further confirming the significant change
in 𝑟ON,c between the anion and neutral species. There are also significant contributions to thephotoelectron spectrum from the ONO bending vibration (ν5), particularly in combination bands
with the central O–N stretching vibration. With the measurement of the EA, we also report the
dissociation energy of the HO––NO bond as 0.594(9) eV. Electronic structure calculations andphotoelectron spectra simulations reported here show excellent agreement with the experimental
data, providing confidence in our vibrational assignments. The previously unobserved cis-HONO(T1) state lies ~2.3 eV higher in energy than cis-HONO (S0). Vertical electron photodetachmentfrom the anion onto the T1 state potential energy surface accesses a transition state which resultsin dissociation to OH + NO, as well as an active bound N=O vibration. Table 4.8 summarizes
these experimentally determined quantities. With this study, we provide new experimental dataon cis-HONO and its lowest lying excited electronic state, as well as information about its
negative ion cis-HONO–. The information contained herein contributes to the knowledge ofneutral cis-HONO as an important atmospheric species and precursor to OH radicals in theatmosphere.

152

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this page is intentionally left blank156

CHAPTER V
PHOTOELECTRON SPECTROSCOPY OF THE HYDROXYMETHOXIDE ANION(H2C(OH)O–)
This chapter is partially reproduced from: Oliveira, A.M, Lehman, J.H., McCoy, A.B.,
Lineberger, W.C., The Journal of Chemical Physics, vol. 145, p. 124317 (2016) with permissionof the authors.

5.1 Introduction
Alkoxy radicals are known to play an important role in tropospheric and combustion
chemistry.1–7 Many experimental and theoretical studies have focused on the effects of adding
various substituents onto the methoxy radical, the simplest alkoxy radical, looking for trends intropospheric reaction kinetics, unimolecular processes, and overall reactivity.1–5,8 Thehydroxymethoxy radical (H2C(OH)O•) is an oxygenated alkoxy radical, proposed to be formed
from the UV photofragmentation of hydroxymethyl hydroperoxide (H2C(OH)OOH), a productfrom the tropospheric oxidation of alkenes.9–13 In addition to the potential atmosphericimportance of the H2C(OH)O• radical, its corresponding anion, hydroxymethoxide (H2C(OH)O–), is the conjugate base of methanediol (H2C(OH)2), considered to be a molecule ofastrochemical and possible prebiotic relevance14–18 as a building block of simple amino acids.19,20
Despite the relevance of the hydroxymethoxy radical to combustion and planetary chemistry,very little is known about its spectroscopy. In fact, H2C(OH)O• has only recently been
experimentally observed. Cao et al.21 detected H2C(OH)O• as a product from the reaction of
atomic hydrogen with formic acid in a krypton matrix isolation experiment. In this experiment,157the radical product was only stable for a few hours at the cryogenic matrix temperatures before
isomerizing to HC•(OH)2. In general, the high reactivity of H2C(OH)O• makes a direct gas phase
experimental observation very challenging.
The comparison of H2C(OH)O• with other alkoxy radicals is an interesting study on theeffects of non-alkyl substituents on the electronic structure of the methoxy radical. Previous
experimental and theoretical work studied the effect of methyl substitutions, forming ethoxy,
isopropoxy, and tert-butoxy radicals.22–26 The substitution of a methyl group for a hydrogen atom
will change the electronic structure of the methoxy radical, breaking its C3v symmetry. For the
ethoxy radical, significant Jahn-Teller distortions were observed in the CH3CH2O– photoelectron
spectrum, where the CH3CH2O• 𝐴̃ state was found to be only 355 cm-1 higher in energy than the
ground 𝑋̃ state.22 The inclusion of vibronic coupling was imperative in order to analyze its
spectrum.24 There was significantly less vibronic coupling observed for the isopropoxy and tertbutoxy radicals.22,26
While the work on interpreting the photoelectron spectra of the ethoxide anion yielded
results that needed to be analyzed with the inclusion of Jahn-Teller distortions and vibronic
coupling,22,24,25,27 recent calculations suggest this will not be the case for hydroxymethoxy.28
Eisfeld and Francisco11 studied low lying electronic states of H2C(OH)O•, focusing on
calculating its electronic absorption spectra (CASSCF/CASPT2, CASSCF/MRCI+Q). Although
they pointed out that nonadiabatic effects might exist between the low-lying electronic states of
H2C(OH)O•, they were not explicitly included in the calculations.11 Dillon and Yarkony,28 on theother hand, explored the ground 𝑋̃ 2A and first excited 𝐴̃ 2A electronic states of H2C(OH)O• (SAMCSCF/MR-SDCI), comparing its electronic structure with other substitutional isomers of themethoxy radical (ethoxy and isopropoxy radicals). This work showed that there are strong158

nonadiabatic couplings between the ground (𝑋̃ 2A) and the first excited (𝐴̃ 2A) electronic states of
H2C(OH)O•.
This chapter presents an anion photoelectron spectroscopic investigation of thehydroxymethoxy radical, as well as the measurement of its electron affinity (EA). Here, theground 𝑋̃ 2A and first excited 𝐴̃ 2A states of H2C(OH)O• are observed through negative ion
photoelectron spectroscopy of H2C(OH)O–. The high reactivity of neutral H2C(OH)O• and its
close relation to methanediol motivates its spectroscopic investigation through its negative ion,
H2C(OH)O–, which is predicted to be more stable by 2.232 eV.11 A comparison with other small
alkoxy radicals is drawn, together with an exploration of the H-OCO torsional motion. Quantum
chemical calculations aid in the interpretation of the photoelectron spectra and provide accurate
thermochemical quantities of the gas phase chemistry of methanediol.
5.2 Methods
5.2.a Experimental
The hydroxymethoxide anion is produced in the dual valve ion source described in
Chapter 2 by the reaction between neutral formaldehyde (H2CO) and the hydroxide anion (OH–).
In order to produce a mixture of pure formaldehyde in argon, a procedure similar to the one
described by Ho et al. is followed.29 Here, a solid sample of polyoxymethylene (formaldehyde
polymer) is heated to 60(5) °C under a 40 psig flow of argon. The principal product from thedecomposition of polyoxymethylene is gaseous monomeric formaldehyde, but water and othersmall oligomers, such as dimeric formaldehyde and trioxane, are also formed. This gaseous
mixture flows through a glass trap equipped with a fritted glass disk and held at -80 °C (dryice/methanol bath) in order to trap these undesired products and prevent repolymerization. The

159

vapor pressure of liquid formaldehyde at this temperature is enough to provide a ~0.8% mixtureof formaldehyde in argon.30
5.2.b Theoretical Methods
In this work, all electronic structure calculations are performed using the Gaussian 09
software package.31 In order to calculate the photoelectron spectra, geometry optimizations andharmonic frequencies are calculated at the CCSD(T)/aug-cc-pVTZ level of theory for
H2C(OH)O–, and ROCCSD(T)/aug-cc-pVTZ for the H2C(OH)O• 𝑋̃ 2A state. For the excited
H2C(OH)O• 𝐴̃ 2A electronic state, geometry optimizations and frequencies are calculated using
CIS/aug-cc-pVTZ, while single point energies were calculated at the EOMCCSD/aug-cc-pVTZ
level of theory. The calculated normal modes and structural parameters are input into the
PESCAL software package, which calculates Franck-Condon factors (FCF) based on the SharpRosenstock-Chen method with Duschinsky rotations.32–34 The resulting FCFs are used togenerate calculated photoelectron spectra.
When the stationary points on the potential surface for the hydroxymethoxy radical are
analyzed, it is found that the minimum energy structure is rotated about the H3-O2-C-O1 torsion
angle (see the inset in Fig. 5.1 for atom labeling), labeled throughout this chapter as φHOCO, by±48° relative to its value at the minimum on the hydroxymethoxide surface, which is at φHOCO =0°. A dihedral angle of 0° is defined as a planar H-OCO moiety in the cis- conformation, as
shown in the inset in Fig. 5.1. Based on this, the minimum for the ground 𝑋̃ 2A state ofhydroxymethoxy has C1 symmetry, while the minimum energy structure of thehydroxymethoxide anion has Cs symmetry. The lowest energy Cs symmetry structure on thehydroxymethoxy surface is 160 cm-1 above the minimum energy structure and corresponds to a160

saddle point on the potential surface. By contrast, the harmonic frequency associated with the HOCO torsion is 240 cm-1. Based on the above, it is not expected that this torsion vibration will
be well-described by a harmonic treatment evaluated at the potential minimum, as is employed in
the PESCAL simulation software. These attributes are also seen for the H2C(OH)O• 𝐴̃ 2A state,although a larger energy difference between C1 and Cs minima is calculated (968 cm-1 energy
difference, 375 cm-1 harmonic frequency of the H-OCO torsion vibration). This is discussed in
more detail in Section 5.5.A. To introduce this large amplitude motion into the Franck-Condon
simulation, the harmonic wavefunctions for the torsion are replaced by the wavefunctions
obtained by solving the one dimensional Schrödinger equation associated with the torsion,
described below. The remaining vibrations are treated at the harmonic level, where the normal
modes and harmonic frequencies are obtained at the Cs saddle point structure forhydroxymethoxy. These frequencies, rather than those obtained at the C1 minimum, are usedbecause the torsion wavefunction for the electronic ground state of H2C(OH)O• has significant
amplitude at this higher symmetry geometry, as is seen in Fig. 5.2.

161

Figure 5.1: Calculated (CCSD(T)/aug-cc-pVTZ) 1D potential energy curves of the torsional
coordinate for the electronic states of hydroxymethoxy accessed in the photodetachment process.
The anion potential energy is as a relaxed scan. The neutral surfaces were constructed by
calculating the energy of the neutral molecule at the optimized anion geometries. The dashedhorizontal lines represent the eigenvalues of these potentials, while their colors, together with the
double headed arrows between the anion and neutral ground states, represent the parity allowedtransitions.
162

In addition, the higher symmetry of the Cs saddle point leads to improved separation of
the torsion from the other vibrations in the construction of the normal modes due to the absenceof coupling between vibrations of Aʹ and Aʺ symmetry in the development of the normal modes
when the Hamiltonian is expressed in symmetry adapted linear combinations of internal
coordinates. This approach is similar to that employed in our earlier study of the photoelectron
spectra of CHX2, X = Cl, Br and I, which contained a similar large amplitude vibrational mode.35
For a further discussion of the separability of the torsional coordinate, see section 5.4.a. To
obtain the torsion wavefunctions, first a one-dimensional relaxed potential energy surface isevaluated for the hydroxymethoxide anion by varying the φHOCO dihedral angle while allowing
all other coordinates to relax to their values at the minimum energy configuration. This scan
(CCSD(T)/aug-cc-pVTZ) was performed from 0° to 180° with variable increments. Table 5.1
shows the calculated points and corresponding energies. In order to better represent the verticaltransition region of the potential, which is sampled in the photodetachment experiment, theneutral surface was constructed by calculating the energies of hydroxymethoxy at the optimized
anion geometries, as shown in Fig. 5.1. These energies were fit to:5

𝑉(𝜑HOCO ) = 𝐴 + ∑ 𝑉𝑛 (1 − cos(𝑛𝜑HOCO ))

(5.1)

𝑛=1

where the value of A provides the energy of hydroxymethoxy at the minimum energy geometryof hydroxymethoxide, e.g. the vertical detachment energy. The optimized fit parameters arelisted in Table 5.2.
The eigenvalues and eigenvectors of this potential were calculated by solving the one
dimensional Schrödinger equation based on

163

𝐻=

1
(𝜑
)𝑝
𝑝
𝐺
+ 𝑉(𝜑HOCO )2 𝜑HOCO 𝜑HOCO ,𝜑HOCO HOCO 𝜑HOCO

(5.2)

1

using a basis of Fourier functions, 𝜓(𝜑HOCO ) = √2𝜋 𝑒 −𝑖𝐽𝜑HOCO with J=(-100,100). The
𝐺𝜑HOCO ,𝜑HOCO term in Eq. (5.2) was evaluated using the expressions given by Frederick andWoywod,36 and fit to an expansion in (1 − cos(𝑛𝜑HOCO )), analogous to Eq. 5.1. Expanding theG-matrix element allows us to account for the effects of geometry changes in the relaxed scan on
the effective mass associated with 𝜑HOCO . Operationally, the value of 𝐺𝜑HOCO ,𝜑HOCO changes byroughly 5% over the range of 𝜑HOCO . The expansion coefficients are also included in Table 5.2.
The FCFs were then obtained by evaluating the overlap of the two lowest energy vibrational
states on the hydroxymethoxide anion potential surface with vibrational states on thehydroxymethoxy neutral surface for the electronic state of interest. Because of the separate
treatment of the H-OCO torsional mode and the remainder of the normal modes of the neutralhydroxymethoxy radical described above, the reported calculated spectrum was obtained byconvolving each FCF of the remaining 3N-7 normal modes (obtained with PESCAL) with thespectrum obtained for the torsional transitions. The resulting FCFs were then convoluted with
Gaussian functions of varying fwhm in order to match the experimental resolution, therefore
providing a direct comparison between the calculated and experimental spectra. This procedure
was repeated for the H2C(OH)O• 𝐴̃ 2A excited state calculations also performed here (CIS/augcc-pVTZ geometry optimization and vibrational frequencies, EOMCCSD/aug-cc-pVTZ single
point energies). The calculations performed here for the optimized geometries and harmonicfrequencies of the anion 𝑋̃ 1A′ and neutral 𝑋̃ 2A, 𝐴̃ 2A states are in good agreement with the ones
reported by Eisfeld and Francisco11 (anion: CCSD(T)/aug-cc-pVQZ, neutral: MRCI+Q/aug-ccpVQZ) and Dillon and Yarkony (SA-MCSCF/MR-SDCI).28
164

Table 5.1: Calculated torsional potential energy surface scan (CCSD(T)/aug-cc-pVTZ) for̃ 2A).
̃ 1Aʹ and H2C(OH)O• X
̃ 2A, and EOM-CCSD/aug-cc-pVTZ for H2C(OH)O• A
H2C(OH)O– X
The offset refers to the relative position of the calculated point to the energy of the anion φHOCO= 0° structure, i.e. summing the offset value to each column will result in the energy of thesepoints relative to the anion minimum energy, which is plotted in Figs. 5.1 and 5.2.
φHOCO /
degrees̃ 1A′)
Eanion (XRelaxed / cm-1

̃ 2A)
Eneutral (XRelaxed / cm-1

̃ 2A)
Eneutral (XVertical / cm-1

̃ 2A)
Eneutral (AVertical / cm-1

0

0

0

0

0

1

0.2

-0.2

-2.9

--

5

6.5

-4.5

-7.2

--

10

26.1

-17.5

-14.5

-47.4

20

102.7

-61.5

-39.2

-122.930

225.4-112.5-48.7-204.340389.4-150.3-56.8-255.850

588.8-159.5

9.8

-210

60

817.5

-131.2

129.5

-67.3

70

1065.9

-62.4

305.9

156.7

80

1321.4

43.3

507.4

435.7

90

1568

176.8

788.2

802.9

120

2104.5587.51314.41652.2150

2241.5

742.9

1280

1955.61802229.1730.11150.4

2004.9Offset017536.9

19768.4

24293

165

Table 5.2: Fit parameters of equation 5.1 for each of the potentials. The A parameter defines theabsolute energy of the V(φHOCO = 0) point. All parameters have units of cm-1. Also included are
the expansion coefficients for the 𝐺𝜑HOCO ,𝜑HOCO term in equation 5.2, which is an expansion in
1 − cos(𝑛𝜑HOCO ), analogous to equation 5.1.
̃ 1A′)
Eanion (XRelaxedFit Parameter̃ 2A)
Eneutral (XRelaxed̃ 2A)
Eneutral (XVertical̃ 2A)
Eneutral (AVertical𝐺𝜑HOCO,𝜑HOCO

0

17695

19821

24536

--

A (relative toanion min.)A (relative topotential min.)V1

0

158.1352.606243.4322.519

1168

488.3

776.361248.2-0.4662V2

227.05-92.52102.63-98.568

0.5921

V3-57.421-117.65-205.24-240.080.08515V4

3.78350.5374-6.1282-42.606

0.01402V5

3.8311-5.71125.5903-1.5042--166

Figure 5.2: Calculated 1D potential energy curves as functions of the torsional coordinate for the
H2C(OH)O– 𝑋̃ 1Aʹ (blue), H2C(OH)O• 𝑋̃ 2A (red), and H2C(OH)O• 𝐴̃ 2A (purple) states. The
vibrational wave functions are plotted in black (even functions) and green (odd functions). All
potentials are the calculated at the optimized anion geometries and cover the same energy range.
These potentials are the same as in Fig. 5.1, but with different angle and energy ranges in order
to better view the wavefunctions.

167

5.3 Results
Following the ion generation procedure described in section 5.2.a, an anion with m/z = 47
was successfully produced. Although H2C(OH)O– is the most stable product with m/z = 47 fromthe association reaction of OH– with H2CO,37 other structural isomers of CH3O2– could exist in
the ion beam. However, the use of photoelectron spectroscopy can unequivocally identify thepresence or absence of these other isomers. The photoelectron spectrum of methyl hydroperoxide(H3COO–) was reported previously by Blanksby et al.,38 and does not match the reported
spectrum here. The other possible isomers at m/z = 47 are H2COOH– and HC(OH)2–. Based onelectronic structure calculations, H2COOH– is unstable with respect to isomerization to
H2C(OH)O– when calculated at B3LYP/aug-cc-pVTZ level of theory/basis. The other possible
structural isomer, HC(OH)2–, is also unlikely, due to the calculated electron affinity of HC(OH)2
being negative (-0.011 eV, B3LYP/aug-cc-pVTZ).
5.3.a Experimental Photoelectron Spectra and EA(H2C(OH)O•)The photoelectron spectrum taken with 3.49 eV photon energy is shown in the middle
panel of Fig. 5.3. The spectrum shows two distinct regions: a structured, regularly spaced
progression ranging from 2.2 to 2.7 eV; and a broader, partially resolved peak which spans from
~2.8 to 3.5 eV. The top panel of Fig. 5.3 shows the anisotropy parameter β as a function of eKE(top horizontal axis). The β parameter has a positive value (β = +0.3(2)) for the broad, high eBE
peak, while peaks A–D show increasingly negative β values, where peak A has β = -0.65(6).
Generally,39 a positive β is associated with a photoelectron originating from an anion molecularorbital with more s-character, while a negative β is associated with photodetachment from ananion molecular orbital with more p-character. A quantitative determination of the fractional s orp character of these anion molecular orbitals is unable to be extracted from this experiment.
168

However, the difference between the photoelectron angular distributions indicates that the tworegions of the spectrum can be associated with detachment to form two different electronic statesof neutral hydroxymethoxy radical. Using a simple symmetry-based analysis, a transition fromthe anion HOMO (aʺ symmetry orbital) is associated with a negative β, while a transition fromthe anion HOMO-1 (aʹ symmetry) is associated with a positive β.40 The ground and first excitedstates of CH2(OH)O•, using the Cs symmetry labels valid at φHOCO = 0°, are described by 𝑋̃ 2Aʺ
and 𝐴̃ 2Aʹ state labels. The molecular orbitals associated with the two lowest energy electronic
states of H2C(OH)O• have also already been calculated,11,28 and are associated with a half-filledaʺ (aʹ) symmetry py (px) orbital at the O1 atom for the ground (excited) electronic state (note: inthis representation, the heavy atoms are taken to lie in the xz plane). Thus, the electron angularanisotropy is consistent with electron detachment from H2C(OH)O– 𝑋̃ 1Aʹ to form H2C(OH)O• 𝑋̃
2Aʺ and 𝐴̃ 2Aʹ states (using Cs symmetry labels). In addition to the evidence provided by the signof the angular anisotropy parameter, the calculated term energy (T0) of the lowest lying excited
H2C(OH)O• 𝐴̃ 2A state puts it approximately 0.38 eV higher in energy than the ground (𝑋̃ 2A)
state.11,28 This value is in good agreement with the energy difference between the origins of thetwo features in Fig. 5.3 Higher lying excited states exist for H2C(OH)O•, but all are calculated tolie more than 3.5 eV above the ground 𝑋̃ 2A state and should not be candidates for thisprogression.11 Thus it is most likely that the higher energy electronic state that is observed is theexcited H2C(OH)O• 𝐴̃ 2A state.

169

Figure 5.3: Upper panel: Experimental anisotropy parameters (β) as a function of electron kinetic
energy. The black circles are a series of β measured above the fwhm of each resolvable peak inthe spectrum across each peak. The grey shaded regions indicate the average β, where the heightshows the scatter of the β values across this width. Middle panel: Experimental photoelectron
spectrum of H2C(OH)O–, using 3.49 eV (355 nm) photon energy. Peaks A through D are
discussed in the text. Lower panel: Convolved photoelectron simulations of detachment to theground (green) and excited (blue) electronic states of H2C(OH)O•, along with their sum (reddots).
170

The lowest eBE peak in the spectrum, peak A, has a fwhm of 0.036 eV, a value close to
the experimental resolution, suggesting minimal rotational broadening (see Chapter 2).
Surprisingly, all other peaks in the spectrum are considerably broader despite having lower eKE.
This indicates that there are other contributions to the observed width. The 𝐴̃ 2A excited statepeak is located at the high eBE (low eKE) region, where an isolated peak at eKE ~0.5 eV would
be expected to have a width of ~15 meV. The fact that no sharp peaks are observed in the 𝐴̃ 2A
state, particularly at the high binding energy edge of the spectrum, suggests that there is likely alarge degree of spectral congestion in this region of the spectrum (discussed further in Section
5.3.c). The 𝑋̃ 2A ground state progression, on the other hand, also exhibits increasingly broad
peaks regularly spaced by ~0.14 eV (1130 cm-1) as the eKE is decreased (eBE is increased). Thissuggests that peaks B through D consist of multiple vibrational transitions, which are notresolved at this eKE. Therefore, the use of a lower photon energy for photodetachment, yielding
a lower eKE spectrum, should reduce the peak widths and provide a more structured spectrum of
the 𝑋̃ 2A state of hydroxymethoxy radical.
The photoelectron spectrum of hydroxymethoxide obtained with 2.737 eV photons (453nm) is shown in the top panel of Fig. 5.4. The peak labels shown in Fig. 5.4 are the same as theones shown in Fig. 5.3. This spectrum shows more resolved structure compared to the initial low
resolution photoelectron spectrum from Fig. 5.3. Indeed, peaks B-D show additional resolved
structure compared to those peaks in Fig. 5.3. Peak A now has a fwhm = 0.018 eV (fwhm/eKE =3.5%); a factor of two improvement in absolute peak width when compared to the same peak in
Fig. 2. In order to fully resolve the origin transition (peak A) and accurately determine the EA of
H2C(OH)O•, an even lower eKE (therefore higher resolution) photoelectron spectrum using 2.33
eV photon energy is obtained.
171

Figure 5.4. Upper panel: Experimental photoelectron spectrum of H2C(OH)O– using 2.74 eV(453 nm) photon energy. The letters A through D are the same labels shown in Fig. 5.3. Lower
panel: Calculated (CCSD(T)/aug-cc-pVTZ) Franck-Condon factors (sticks) and convolved
simulation (blue trace). The green sticks represent transitions from the vibrational ground state of
the anion while the red sticks are vibrational hot bands, i.e. transitions from an excited
vibrational state of the anion. The calculated stick spectrum was convolved with Gaussianfunctions of varying fwhm in order to match the measured experimental resolution.

172

The high resolution photoelectron spectrum taken with 2.33 eV photons (532 nm) is
shown in the top panel of Fig. 5.5 This spectrum shows peak A with fwhm = 0.008 eV; anotherfactor of two improvement in peak width when compared to the same peak in Fig. 3. Because thetransitions that compose peak A are now clearly resolved, the peaks are relabeled with lowercase
letters for individual assignments. Fig. 4 shows a clear origin of the vibrational progression
centered at 2.2205 eV (peak a), which corresponds to the transition from the ground vibrational
state of the H2C(OH)O– anion to the ground vibrational state of the neutral H2C(OH)O• 𝑋̃ 2A
radical. After a small shift to correct for an unresolved rotational envelope41 (see Chapter 2), andinclusion of the uncertainties associated with the measurement, the EA of the hydroxymethoxy
radical is assigned as 2.220(2) eV. This agrees very well with the calculated EA from this work
(2.19 eV) and with that from a higher level (multireference) calculation (2.232 eV).13 The
uncertainty on the EA and the vibrational frequencies reported below come primarily from theenergy scale calibration.

173

Figure 5.5: Upper panel: Photoelectron spectrum of H2C(OH)O– using 2.33 eV (532 nm) photon
energy. Peaks a–e are described in the text. Lower panel: Calculated (CCSD(T)/aug-cc-pVTZ)
Franck-Condon factors (sticks) and convolved simulation (blue trace) with assigned transitions.
The green sticks correspond to transitions originating from the vibrational ground state of theanion, while the red sticks correspond to transitions with one quantum of excitation in a low
frequency torsional (ν12) mode of the anion.

174

5.3.b H2C(OH)O• 𝑋̃ 2A Vibrational Assignments
The H2C(OH)O• 𝑋̃ 2A vibrational progression, depicted in Fig. 5.4, is characterized by anintense origin transition, followed by a progression of decreasing intensity and increasing
congestion. Based on the changes in geometry between the anion and neutral equilibrium
structures (see Table 5.6), which shows the largest changes occurring in the O1CO2 and H3O2C
angles and rCO2 bond length, one might expect the most active vibrations to consist of OCO andHOC bends, symmetric and asymmetric OCO stretching vibrations, and combination bands
involving these vibrations. The calculated photoelectron spectrum (lower panels of Figs. 5.3 –5.5) indeed shows that the ground 𝑋̃ 2A state progression (features A-D) is composed primarilyof the vibrations ν11 (OCO bend), ν9 (OCO symmetric stretch), ν8 (OCO asymmetric stretch), ν5(out of phase HOC bending/CH2 wagging), and ν4 (HCH bend). See Tables 5.6 – 5.8 for thedescription of the molecular motion associated with all modes. In fact, the center of peaks A-D
are separated (on average) by ~0.14 eV (1130 cm-1), which roughly corresponds to the OCO
asymmetric stretching vibration (ν8). The H-OCO torsion vibration (ν12) is also active, and will
be discussed in detail in section 5.4 below. Eisfeld and Francisco11 report extensive calculations
on the hydroxymethoxy radical and include a simulated photoelectron spectrum of the anion
accessing the ground 𝑋̃ 2A state of the neutral, but not including the HOCO torsional mode. In
spite of the fact that the reported geometries and frequencies of the anion and neutral ground 𝑋̃
2

A state are very similar to the current work, the previous photoelectron spectrum simulation

produces an extended vibrational progression, spanning close to 2 eV. The overall simulated
photoelectron spectrum reported here is in excellent agreement with the experimentally observed
spectrum and so it is used as an aid in order to assign the various vibrational transitions

175

responsible for the dominant peaks in the structured photoelectron spectrum shown in Figs. 5.4
and 5.5.
The spectral congestion apparent in peaks C and D in Figs. 5.3 and 5.4, and confirmed by
the photoelectron spectrum simulation, makes individual transitions within these peaks
impossible to assign. However, peak B appears to be much less congested, and based on theexperimental spectrum, peak B in Fig. 5.4 appears to consist of four peaks. The calculated
spectrum shows that five transitions are primarily responsible for the structure in peak B, namelytransitions from the ground vibrational level of the anion to one quanta each of modes ν9, ν8, ν6,
ν5 and ν4 (labeled in Fig. 5.4). The transitions to the fundamentals in ν9 and ν8, which correspondto the OCO symmetric and asymmetric stretches, respectively, are in a region where the spectralcongestion is minimal and show very good agreement with experiment. Consequently, thesetransitions are unequivocally assigned, and the observed frequencies, calculated from thedifference between the peak positions and the origin (EA) position, are presented in Table 5.4.
The assignments of the ν6, ν5 and ν4 fundamentals are not made due to the larger degree ofspectral congestion.

176

Table 5.3: Calculated minimum energy structure of H2C(OH)O– 𝑋̃ 1A′ (CCSD(T)/aug-cc-pVTZ),H2C(OH)O• 𝑋̃ 2A (ROCCSD(T)/aug-cc-pVTZ), and H2C(OH)O• 𝐴̃ 2A (CIS/aug-cc-pVTZ), as
well as the difference between structural parameters of the anion and neutral structures (Δ =anion structure − neutral structure). Fig. 5.1 shows the atom numbering used in this work. The
values in boldface show the largest geometry changes. These calculated geometries agree wellwith the values in Refs. 11 and 28.

0.01(𝐴̃ 2A)
1.084

0.037

1.099

0.021

1.08

0.041

1.317

1.349

-0.0321.402-0.085𝑟CO2 / Å

1.513

1.405

0.108

1.375

0.138

𝑟OH3 / Å∠H1CH2 / °

0.967

0.964

0.003

0.941

0.026

107

107

0

110.5

-3.5

∠O1CO2 / °

111.7

116.5

-4.8

107.5

4.2

∠O2CH3 / °

96.8

107.7

-10.9

110.5

-13.7

𝜑H3O2CO1 / °

0

47.6

-47.6

70.9

-70.9

𝑟CH1 / Å(𝑋̃ 1A′)
1.121(𝑋̃ 2A)
1.111

𝑟CH2 / Å1.121

𝑟CO1 / ÅParameter

177

Δ

Δ

The higher resolution spectrum presented in Fig. 5.5 has six labeled peaks, all of which
are captured in the photoelectron simulation. From this spectrum, in addition to obtaining an
accurate EA(H2C(OH)O•), transitions to the lowest frequency active modes are resolved, namely
the OCO bending vibration (ν11), the H-OCO torsion vibration (ν12), and a few combination
bands. Peak d can now be assigned as the transition from the ground vibrational level of theanion to the state on the neutral potential with one quantum of excitation in the OCO bend. Peaks
b and aʹ are assigned to transitions involving the H-OCO torsion, namely ν12(vʺ=0→ vʹ=2) andν12(vʺ=1→ vʹ=1), which is further discussed in section 5.4.a. Throughout this chapter, primes(double primes) are used to denote vibrational levels in the neutral (anion) electronic state. The
peak positions (absolute eBE and relative to the EA) for the peaks labeled in Figs. 5.4 and 5.5 aregiven in Table 5.4, together with the aforementioned assignments.

178

Table 5.4: Vibrational transition assignments for the peaks labeled a′–e (Fig. 5.5) and B (Fig. 5.4)
in the photoelectron spectra reported in the main text. Both the absolute peak position (eBE,̃reported in eV) and the energy relative to the EA (reported in cm-1) are given. The H2C(OH)O• (𝑋2

̃ 1A′) (𝜈′′1 𝜈′′2 … ) transitions are labeled using the standard shorthandA) (𝜈′1 𝜈′2 … ) ← H2C(OH)O– (𝑋
𝜈′

𝜈′

1

2

notation (1𝜈1′′ 2𝜈2′′ …) for vibrational transitions. The assignments are based on the results of thecalculated photoelectron spectrum. The question marks indicate the peaks in this region where theassignment is ambiguous (see Figs. 5.4 and 5.5) due to spectral congestion.
Peak Label(Fig. 5.5)
a'
a
b
c
d
e
B
(Fig. 5.4)

Absolute Peak
Center Position
(eV)
2.198
2.220
2.248
2.266
2.287
2.312
2.339
2.358
2.372
2.384

Peak Position
Relative to EA(cm-1)
-181
0
224
364
534
741
963
1110
1225
1320

179

Assignment
1211
000
1220
? 1110 1211
1110
910 1211
910
810
? 610
? 510

and /or1110 1220

5.3.c H2C(OH)O• 𝐴̃ 2A
Photoelectron detachment to form H2C(OH)O• 𝐴̃ 2A results in a relatively unstructured
photoelectron spectrum (Fig. 5.3), peaked at ~3 eV with a fwhm of ~0.5 eV. As mentioned
previously, since there is an approximately constant resolution (fwhm/eKE) of 3%, the narrowest
peaks should be at low kinetic energy (large binding energy), meaning that detachment to the 𝐴̃2

A excited state should be the best resolved in this spectrum. This is not what is observed, which

implies that photodetachment to the 𝐴̃ 2A excited state could result in a large degree of spectralcongestion.
In order to test this hypothesis, a photoelectron spectrum simulation based on excitation
to the 𝐴̃ 2A state of H2C(OH)O• was calculated using the methods described above. Based on themeasured EA(H2C(OH)O•) and the calculated T0 of H2C(OH)O• 𝐴̃ 2A (0.377 eV28 or 0.390 eV11
with respect to H2C(OH)O• 𝑋̃ 2A), the origin of the excited 𝐴̃ 2A state was initially assumed to beapproximately 2.6 eV. The resulting photoelectron spectrum simulation is shown in Fig. 2(bottom panel). The spectrum shows a large degree of spectral congestion, primarily involving
transitions to overtones and combination bands of the H-OCO torsion (ν12), OCO asymmetricstretching (ν9), and out-of-phase HOC bending/CH2 wagging (ν5) vibrations. The simulated
spectrum peaks ~0.3 eV above the origin, and extends for at least another 1 eV. Since theexperimental photon energy used is only 3.49 eV, the simulated spectrum shown in the lower
panel of Fig. 2 is truncated at 3.49 eV. In addition, a threshold scaling factor42,43 is introduced tohelp mimic the low eKE edge of the observed spectrum. Given that the experimentally observed
positive anisotropy indicates this excited 𝐴̃ 2A electronic state is a result of electron detachmentfrom an orbital with relatively more s-like character than when the electron is detached to form
the ground 𝑋̃ 2A state of H2C(OH)O•, the outgoing electron is approximated by a p-wave. Thus,
180the photodetachment cross section scales as eKE𝑙+0.5, or eKE1.5. This means that there is a muchstronger threshold effect for the onset of the excited 𝐴̃ 2A state compared to the ground 𝑋̃ 2A
state. This scaling factor for the detachment cross section is also consistent with why there are noobserved peaks that can be unequivocally assigned to the origin of the excited 𝐴̃ 2A state
spectrum in the low eKE region of the 453 nm spectrum.
The overall photoelectron simulation matches the experimental spectrum very well,
despite the harmonic treatment and assumption of separable vibrational modes, both of which
likely results in undercounting the density of states on the 𝐴̃ 2A potential surface. There is arepeating pattern of peaks in the simulation, spaced by ~1200 cm-1 (0.15 eV, or approximately
one quanta of the neutral ν9 vibration), which is a result of overtones in the OCO asymmetricstretching (ν9) and HOC bending/CH2 wagging (ν5) vibrations. Because the origin of the
H2C(OH)O• 𝐴̃ 2A state is obscured by transitions from the anion to high lying vibrations in the
H2C(OH)O• 𝑋̃ 2A state, there is some uncertainty in the spectrum’s origin, shown in Fig. 2 as
2.615 eV to best match the experimental spectrum while still remaining close to the calculated
origin. The calculated spectrum could just as easily shift by ± 0.15 eV, which is the spacing of
the repeating pattern of peaks in the simulation, and still match the overall experimental
spectrum. However, a shift this large seems unlikely, given the high level multireference
calculations of the H2C(OH)O• 𝐴̃ - 𝑋̃ term energy.11,28

181

5.4 Discussion
5.4.a H-OCO Torsion
i. Separability of the torsional coordinate
The calculated FCFs of the H-OCO torsional mode were treated separately from the othernormal modes. This separate 1D treatment is an approximation that is justified by comparing thestructural parameters and vibrational frequencies of the minimum energy structure (C1symmetry) and the transition state (Cs symmetry, φHOCO = 0°). The corresponding calculated
results are shown below in Tables 5.5 and 5.6, which show that there is a 2±2% change in the
structural parameters and vibrational frequencies between the equilibrium and transition state(φHOCO = 0°) of H2C(OH)O• 𝑋̃ 2A. This implies that the torsional coordinate is indeed acoordinate which is separable from the remaining normal modes and hence it is well treated by
the model discussed in the main text. Similar small changes are calculated between the
H2C(OH)O• 𝐴̃ 2A equilibrium and transition state structures. The H2C(OH)O• 𝐴̃ 2A andH2C(OH)O– 𝑋̃ 1A vibrational frequencies are listed in Tables 5.7 and 5.8, respectively. Tables 5.5
through 5.7 are conveniently listed at the end of this chapter.
ii. HOCO torsion discussion
The relaxed H-OCO torsional potential energy surfaces for the anion and neutral ground𝑋̃ 2A and excited 𝐴̃ 2A states can be found in Fig. 5.1 and 5.2 (also see Tables 5.1 and 5.2). As
mentioned in section 5.2.b, the 𝑋̃ 2A state of the anion has its minimum energy geometry at
φHOCO = 0°. Although there is a higher energy minimum in the trans H-OCO configuration(φHOCO = 180°, ~1200 cm-1 relative to the global minimum), the barrier to conversion from thetrans to cis configurations is too low (on the order of 20 cm-1) to support any bound vibrational
182

levels. For both the ground 𝑋̃ 2A and excited 𝐴̃ 2A states of H2C(OH)O•, the H-OCO torsional
potential exhibits a double well, with the equilibrium structures corresponding to φHOCO = ±48°
and ±70.9° for the 𝑋̃ 2A and 𝐴̃ 2A states, respectively. The multireference treatments of the 𝑋̃ 2A
state surface by both the Yarkony and Francisco groups results in an increase in the φHOCO angle
for the equilibrium H2C(OH)O• 𝑋̃ 2A structure (±59.6° and ±57°, respectively). Depending on thelevel of theory used with single reference methods, this dihedral angle for the equilibrium
structure can range from φHOCO = ±23° (B3LYP/aug-cc-pVTZ) to φHOCO = ±56° (MP2/aug-ccpVTZ). Like the anion, the trans configuration (φHOCO ~ 180°) of the 𝑋̃ 2A state of the neutral ismuch higher in energy than the cis configuration, and is separated from the global minimum by avery small barrier. In the neutral 𝐴̃ 2A excited state, the trans configuration is higher in energy
and unstable with respect to isomerization. In all cases, the relative stabilities of the cis and transisomers arises from the stabilization of the cis isomer due to intramolecular interactions between
the terminal oxygen (O1) and hydrogen (H3) atoms, as illustrated in the inset of Fig. 5.1. This
interaction will be strongest in the anion, where the excess electron is localized on O1 leading toa stronger O–…HO ionic hydrogen bond.
The two equivalent minimum energy structures have C1 symmetry with φHOCO = ±48° or± 70.9°, which are separated by a barrier in both the ground 𝑋̃ 2A and excited 𝐴̃ 2A state neutralelectronic potential energy surfaces. A relaxed potential energy scan has a barrier tointerconversion of 158 cm-1 for the ground 𝑋̃ 2A state surface. For the relaxed scan, the energy of
H2C(OH)O• was calculated at each φHOCO dihedral angle (stepped between 0° and 180°) whileallowing the remaining coordinates to be optimized. In order to provide a comparison between
the neutral vertical and relaxed potentials energy curves (ROCCSD(T)/aug-cc-pVTZ), thesepotentials are shown in Fig. 5.6. As Fig. 5.6 shows, the main difference between these surfaces
183are the location of the minima and the barrier heights, along with an energy offset relative to theanion minimum. The vertical surface is located ca. 2200 cm-1 (0.27 eV) above the relaxed
potential. This is lower than the multireference calculations from Dillon and Yarkony,28 whoreport a barrier to interconversion of 361 cm-1 for the ground 𝑋̃ 2A state, and with Eisfeld andFrancisco, who report a barrier of at most 550 cm-1 for the 𝑋̃ 2A state rotamer interconversion.
The barrier to interconversion for the excited 𝐴̃ 2A state is higher, at 968 cm-1, which agrees very
well with the multireference calculations from Dillon and Yarkony (993 cm-1).28 As mentioned
previously, the vertical detachment region of the potential energy surface is what is accessed in
the photoelectron detachment experiment performed here. In this region, the barrier lowers to
only 50 cm-1 for the ground 𝑋̃ 2A state and 255 cm-1 for the excited 𝐴̃ 2A state. Based on the onedimensional calculations of energies and wavefunctions for the H-OCO torsion performed using
the potential cut shown in Fig. 5.1, we find that in the ground electronic state, the zero-pointlevel lies 11 cm-1 above the barrier to rotamer conversion, and the wavefunction has its largest
HOCO =

0°. In the excited 𝐴̃ 2A electronic state, there is still a barrier with respect

to zero-point motion, and the ground vibrational state lies 99 cm-1 below the barrier to freeinternal rotation. These conclusions agree well with those drawn by Dillon and Yarkony28 based
HOCO, constrained to theequilibrium geometry of the anion)28 and with Eisfeld and Francisco,11 who excluded thiscoordinate from their work for this reason.

184̃ 2A H-OCO calculated (ROCCSD(T)/aug-cc-pVTZ) torsional potential
Figure 5.6: H2C(OH)O• 𝑋

comparison. The green circles and trace represent the relaxed potential energy surface, where allcoordinates were optimized for each value of φHOCO. The red triangles represent the vertical
detachment surface, where the neutral surface was calculated at the optimized anion geometries
for each value of φHOCO. ΔEbarrier represents the 1D barrier height with respect to the potential
minima.

185

The consequences of the anion and the vibrationally averaged structure of neutral
H2C(OH)O• both having Cs symmetry leads to vibrational symmetry selection rules in theelectronic spectra, resulting in vibrational modes ν10 (in plane HCH rock), ν7 (out of plane HCHrock), and ν2 (HCH asymmetric stretch) not being active in the photoelectron spectrum (seeTable 5.6). Moreover, the selection rules of the torsional transitions are determined by the parity
enforced by the symmetry of the potential, as emphasized by the double-headed arrows shown in
Fig. 5.1. Because of the parity selection rules in the torsional coordinate, peak b is assigned as
ν12(vʺ=0→ vʹ=2), or 1220 . Based on the difference in peak positions between peak b and the EA,
the neutral 2ν12 has a frequency of 220(10) cm-1. Peak a′ is assigned as the anion-neutral
sequence band ν12(vʺ=1→ vʹ=1), located 180(60) cm-1 from the origin transition (peak a).
Because the ν12 fundamental frequency for either the anion or neutral cannot be measured
directly, and the neutral H-OCO potential is highly anharmonic, the anion and neutral ν12
fundamental frequencies cannot be directly obtained from the measured 2ν12 overtone or the
position of the ν12(vʺ=1→ vʹ=1) sequence band.
We can, however, use a combination of the calculated anion fundamental frequency
ν12(v″=0→ v″=1) = 269 cm-1 from the anion torsional potential energy surface (which is welldescribed as a harmonic oscillator near its equilibrium structure) in combination with theexperiment to derive the ν12 fundamental frequencies. Using the calculated ν12(v″=0→ v″=1) andthe position of the ν12(vʺ=1→ vʹ=1) sequence band in relation to the EA, the neutral ν12
fundamental frequency ν12(v′ = 0→ v′ = 1) = 90(60) cm-1. By comparison, the calculated neutral
ν12 fundamental frequency (92.3 cm-1) is very close to this value, which is calculated using the
one-dimensional potential shown in Fig. 5.1 (based on the relaxed geometries of the anion).
When a relaxed scan of the neutral 𝑋̃ 2A torsional potential energy surface is used instead, this186

frequency drops to 36.7 cm-1 due to the larger barrier along this cut of the potential. This
comparison further validates the approximations made in the treatment of the torsional mode. In
addition, using this in combination with the measured neutral 2ν12, ν12(v′ = 1→ v′ = 2) = 130(60)cm-1 for H2C(OH)O•. The error bars on these frequencies are defined by the experimental error
bars on the peak positions. This can be compared to the calculated values of 170 cm-1 for theneutral 𝑋̃ 2A potential energy curve calculated at the anion relaxed scan geometries (as shown in
Fig. 5.1) and 155 cm-1 for the neutral 𝑋̃ 2A relaxed surface. Unfortunately, this type of analysis
and comparison of experiment with theory for the H2C(OH)O• 𝐴̃ 2A torsional frequency is notpossible. The torsional frequency for H2C(OH)O• 𝐴̃ 2A could not be measured due to the highly
spectrally congested spectrum (including spectral overlap with detachment to the ground 𝑋̃ 2A
state) and the relatively low-resolution of the spectrum shown in Fig. 5.3.
5.4.b Methanediol Thermochemistry
The measurement of the EAs of molecules can provide information about the gas phasechemistry of their protonated counterpart with the use of a thermochemical cycle. The
thermochemical cycle for methanediol is described by Eq. 3:°(H2 C(OH)2 ) - IE(H)+ EA(H2 C(OH)O)
D0 (H2 C(OH)O–H) = Δacid H0K(5.3)

Here, the EA of H2C(OH)O• is experimentally determined as 2.220(2) eV or 51.19(5) kcal mol-1.
The ionization energy of atomic hydrogen (IE(H)=313.59 kcal mol-1) is known.44 With thisequation, either the O–H bond dissociation energy, D0(H2C(OH)O–H), or the gas phasedeprotonation enthalpy, ΔacidHº0K(H2C(OH)2), of methanediol can be obtained. Since there is noexperimental measurement of either of these quantities, quantum chemical calculations must be
relied upon to obtain one of these values. In this instance, the ΔacidHº0K(H2C(OH)2) was chosen
187since this quantity only depends on calculating formation enthalpies of closed shell species,
namely H2C(OH)O–, H2C(OH)2, and H+. Here, the G4 composite method was used yielding
ΔacidHº0K(H2C(OH)2) = 366 kcal mol-1. Other composite methods were also used and verified thisresult, specifically CBS-APNO (366.4 kcal mol-1) and CBS-QB3 (365.7 kcal mol-1). Since thepredicted uncertainty in these calculations is on the order of 0.8 to 1.5 kcal mol-1, this results in
D0(H2C(OH)O–H) = 104(2) kcal mol-1, using a conservative estimate of the uncertainty. A
previously calculated O–H bond dissociation energy45 of 102.7 kcal mol-1 is in excellent
agreement with our semi-empirical value.
5.4.c Photodetachment Producing H2C(OH)O• 𝑋̃ 2A and 𝐴̃ 2A Electronic States
While it is tempting to compare the photoelectron spectrum of H2C(OH)O– with those ofother alkoxy anions, such as methoxide (CH3O–) and ethoxide (H2C(CH3)O–), this would not bea fair comparison, especially with respect to the Jahn-Teller coupling that was essential for aproper interpretation of the methoxide and ethoxide photoelectron spectra. There, thesubstitution of a methyl group from methoxy to ethoxy was seen as a perturbation of the JahnTeller distortion, and an accordingly strong coupling and small energy difference between theneutral radical ground and first excited electronic states. However, the substitution of a hydroxyl
group drastically changes the electronic structure and any neutral ground/excited electronic state
coupling, as described by Dillon and Yarkony.28 Experimentally, there is at least an order ofmagnitude larger energy difference between the ground and first excited electronic states inhydroxymethoxy compared to ethoxy. While there is still significant coupling between the
ground and first excited electronic states in hydroxymethoxy, exemplified by a low-lying seamof conical intersection, there are substantial differences in the topology of the electronic state
surfaces of hydroxymethoxy compared to the classic Jahn-Teller topology found in the electronic188structure of methoxy radical (or even in the pseudo Jahn-Teller ethoxy radical). See Reference
28 for a thorough discussion on the topic.
The photoelectron simulation of detachment forming H2C(OH)O• 𝐴̃ 2A captures theexperimental data very well (Fig. 5.3). The differences between the experiment and simulation
likely differ mostly due to the separable harmonic treatment employed here. However, it would
be interesting if there is any additional broadening or spectral congestion in the high eBE portionof the photoelectron spectrum that could be due to any nonadiabatic coupling between the twoelectronic states of the neutral. Interestingly, Dillon and Yarkony found that there is a significant
dependence on the φHOCO torsion coordinate for the energy of the seam of conical intersection
between the two states, ranging from ~0.38 eV to ~0.53 eV above the ground electronic state
minimum. This is energetically accessible in the experiments performed here. However, whether
or not photodetachment accesses these regions of strong coupling on the neutral potential energy
surfaces is unknown. While the calculation used here certainly matches the experimental
spectrum qualitatively, a more detailed calculation including the possible effects of nonadiabatic
coupling would be interesting.
5.5 Conclusions
Photodetachment of the hydroxymethoxide anion, H2C(OH)O–, with 355 nm photons
forms the ground (𝑋̃ 2A) and first excited (𝐴̃ 2A) states of H2C(OH)O•. The photoelectron
spectrum provides the electron affinity of H2C(OH)O• (EA = 2.220(2) eV), together with themeasurement of several vibrational frequencies of the hydroxymethoxy radical in its 𝑋̃ 2A
electronic state. These major experimental results are presented in Table X below. The 𝐴̃ 2A
excited state spectrum is characterized by a long vibrational progression which results in a189

mostly unstructured photoelectron spectrum with an 𝑋̃ → 𝐴̃ excitation term energy of ~0.4 eV.
Franck-Condon activity in specific vibrational modes is indicative of a change in the equilibrium
structures between the anion and neutral states. The H-OCO torsion is one of the main active
vibrations in the spectra, along with overtones and combination bands of the OCO stretching and
HOC bending/CH2 wagging vibrations. Motion along the neutral H-OCO torsional double-wellpotentials is not well described by the harmonic oscillator approximation and hence requires
explicit treatment to calculate the associated Franck-Condon factors, unlike the other vibrationalmodes. The resulting calculated photoelectron spectra for detachment to both ground 𝑋̃ 2A and
excited 𝐴̃ 2A states show good agreement with the experimental data, supporting theinterpretation of the spectra. Because of the agreement between calculation and experiment, theinclusion of nonadiabatic vibronic coupling between the electronic states of hydroxymethoxy
does not appear to be necessary to reproduce accurately the experimental photoelectron
spectrum. This observation further separates hydroxymethoxy from other small substituted
alkoxy radicals, such as ethoxy (H2C(CH3)O•), in which the inclusion of vibronic coupling was
crucial to simulating the experimental photoelectron spectrum.

190

Table 5.9: Summary of the major results. The calculated results are based on the CCSD(T)/augcc-pVTZ (EA and vibrational frequencies) and the G4 composite method (gas phase acidity).
ExperimentCalculationb

Electron Affinity / eV
2.220(2)2.19°
ΔacidH 0K(H2C(OH)2)
366(2)/ kcal mol-1
ΔacidH°298K(H2C(OH)2)
367(2)/ kcal mol-1
D0(H2C(OH)O–H)
104(2)a/ kcal mol-1
H2C(OH)O• 𝑋̃ 2A′ Vibrational Frequencies / cm-1
2ν12220(10)261

ν11530(10)526

ν9960(50)982

ν81110(50)
1146
Determined based on experimental and calculated
quantities through the thermochemical cycle shown in
Eq. 5.3bCalculated values are based on harmonic vibrationalfrequencies, except for ν12, as discussed in the texta191

5.6 Geometry optimization and frequencies of hydroxymethoxide and hydroxymethoxy
̃ 2A atTable 5.5: Calculated (ROCCSD(T)/aug-cc-pVTZ) optimized geometries of H2C(OH)O• 𝑋

its equilibrium (φHOCO = ±48°) and transition state (φHOCO = 0°) structures. Bond distances (r) are
given in Angstroms while bond angles () and dihedral angles (φ) are given in degrees. The
atom numbering is based on Fig. 5.1.

1.35
1.41
1.11
1.10
0.96
116.5
104.6
110.2
107.7
123.8
-121.6

Transition
State
1.34
1.41
1.11
1.11
0.96
116.3
107.7
107.7
106.4
122.9
-122.9Δ (TS-Eq)
(%)
0.65
0.32
0.28
0.71
0.04
0.18
2.95
2.28
1.25
0.71
1.12

47.6

0.0

-

Parameter

Equilibrium

rCO1
rCO2
rCH1
rCH2
rOH3
O1CO2
H1CO1
H2CO1
H3O2C
φH1CO1O2
φH2CO1O2
φH3O2CO1(≡ φHOCO)

192

Table 5.6: Calculated (ROCCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies of̃ 2A, for both the equilibrium structure (φHOCO = ±48°) and transition state (φHOCO =H2C(OH)O• 𝑋0°), together with the approximate mode description. All values are reported in cm-1.
𝑋̃ 2A Equilibrium

𝑋̃ 2A Transition

O–H torsion

Structure
239

State
198 i

Δ (TS-Eq)(%)-

OCO bend

547

526

3.8

10

In plane HCH rock

767

747

2.6

9

OCO Sym. Stretch

1002

982

2.0

8

OCO Asym. Stretch

1113

1146

2.9

7

Out of plane HCH rock

1137

1185

4.3

6

In phase HOC bending/CH2 wagging

1310

1258

4.0

5

Out of phase HOC bending/CH2 wagging

1370

1353

1.2

4

HCH bend

1413

1406

0.5

3

HCH Sym. Stretch

2868

2893

0.9

2

HCH Asym. Stretch

2996

2909

2.9

1

OH Stretch

3815

3817

0.0

ωi

Mode description

12
11

193

̃ 2A
Table 5.7: Calculated (CIS/aug-cc-pVTZ) harmonic vibrational frequencies of H2C(OH)O• 𝐴

for both the equilibrium structure (φHOCO = ±70.9°) and transition state (φHOCO = 0°), together
with the approximate mode description. All values are reported in cm-1.
𝐴̃ 2A Equilibrium𝐴̃ 2A Transition

O–H torsion

Structure
375

State
419 i

Δ (TS-Eq)(%)-

OCO bend

523

504

3.6

10

OCO Sym. Stretch

1137

1116

1.8

9

OCO Asym. Stretch

1167

1202

2.9

8

In plane HCH rock

1216

1283

5.2

7

In phase HOC bending/CH2 wagging

1440

1373

4.8

6

Out of plane HCH rock

1514

1422

6.5

5

Out of phase HOC bending/CH2 wagging

1557

1583

1.6

4

HCH bend

1688

1709

1.3

3

HCH Sym. Stretch

3178

3185

0.2

2

HCH Asym. Stretch

3250

3230

0.6

1

OH Stretch

4147

4150

0.1

ωi

Mode description

12
11

194

Table 5.8: Calculated (CCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies of H2C(OH)O–̃ 1A. Note the difference in mode descriptions between the anion and neutral structures. The
𝑋̃ 2A mode
convention used in this paper is to refer to modes based on the neutral H2C(OH)O• 𝑋

numbering/descriptor. All values are reported in cm-1.
ωiMode description

H2C(OH)O– 𝑋̃ 1A

12

O–H torsion

273

11

OCO bend

468

10

OCO Sym. Stretch

771

9

OCO Asym. Stretch

1121

8

In plane HCH rock

1131

7

Out of plane HCH rock

1208

6

In phase HOC bending/CH2 wagging

1310

5

HCH bend1389

4

Out of phase HOC bending/CH2 wagging

1535

3

HCH Asym. Stretch

2269

2

HCH Sym. Stretch

2722

1

OH Stretch

3757

195

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CHAPTER VI
PHOTOELECTRON SPECTROSCOPY OF THE AMINOMETHOXIDE ANION,
H2C(NH2)O–This chapter is partially reproduced from: Oliveira, A.M, Lehman, J.H., Lineberger, W.C., The
Journal of Chemical Physics, to be submitted Dec. 2017.
6.1 Introduction
Alkoxy radicals are an important class of molecules in atmospheric1–5 and combustion
processes,6–12 where they often act as highly reactive intermediates. As an open-shelled species
with the radical center located on the oxygen, complicated further by some radicals possessing
high symmetry, alkoxy radicals often have complex electronic structure making it difficult tofully characterize these molecules spectroscopically. Both their high reactivity and challenging
electronic structure have motivated the investigation of alkoxy radicals using a variety ofexperimental and theoretical methods.13–19 Experimentally, alkoxy radicals have been studied in
the gas phase mainly via spectroscopic techniques.14,20–27 Theoretically, the electronic structureof small alkoxy radicals have been investigated,28–31 particularly with regard to Jahn-Tellerinteractions, spin-orbit splittings, and vibronic couplings.14,30,32–36
Several investigations, including extensive work by Miller and coworkers,32–35 havefocused on building from the simplest alkoxy radical (methoxy) to larger alkyl substituted
radicals, studying how the vibrational and electronic structure are altered upon the addition ofdifferent functional groups.14,32–34,36 For example, the study by Ramond et al.14 investigated theethoxy (H2C(CH3)O•), isopropoxy (HC(CH3)2O•) and tert-butoxy (C(CH3)3O•) radicals via
photoelectron spectroscopy of the corresponding anions and measures their electron affinities
199

(EA) and term energies (T0(𝐴̃ ← 𝑋̃ )). In ethoxy, the term energy was measured as 355(10) cm-1
by Ramond et al.14 via anion photoelectron spectroscopy, agreeing well with the term energy of364(1) cm-1 measured by Jin et al.35 via dispersed fluorescence spectroscopy. Upon further
substitution, forming isopropoxy, the term energy lowers to 68(10) cm-1.35 In addition to theseexamples, the hydroxymethoxy radical (H2C(OH)O•) was investigated via anion photoelectron
spectroscopy to study the effect of non-alkyl substitution.37 The hydroxymethoxy term energy
was found to be T0(𝐴̃ ← 𝑋̃ ) ~ 3300 cm-1, close to an order of magnitude larger than ethoxy.37 In
the present work, we extend this study by investigating the aminomethoxy radical (H2C(NH2)O•)
via anion photoelectron spectroscopy of aminomethoxide (H2C(NH2)O–). A comparison of theT0(𝐴̃ ← 𝑋̃ ) provides a useful insight on how the substituent group affects the electronic structureof substituted alkoxy radicals.
However, the motivation to study the aminomethoxy radical and its corresponding anion
extends beyond a fundamental chemical and electronic structure investigation. The
aminomethoxide anion is the conjugate base of aminomethanol (H2C(NH2)(OH)), an important
prebiotic molecule as a precursor to simple amino acids.38,39 Spectroscopic studies ofaminomethanol are non-existent, due to its inherent instability in the gas phase.40,41 Approaching
the spectroscopy of aminomethoxy via its anion is an attractive strategy as it provides ameasurement of the EA of aminomethoxy. The O–H bond dissociation energy in aminomethanol
can then be obtained in a thermochemical cycle from a measurement of the EA of aminomethoxy
in conjunction with the gas phase acidity of aminomethanol.42
This work investigates the aminomethoxy radical via photoelectron spectroscopy of theaminomethoxide anion (H2C(NH2)O–), with the aid of quantum chemical calculations. The
photoelectron spectrum acquired here using velocity map imaging (VMI) provides the first200

spectroscopic investigation of aminomethoxy, and includes a measurement of the EA, vibrationalfrequencies, and T0(𝐴̃ ← 𝑋̃). The measurement of the EA results in a determination of the O–Hbond dissociation energy of aminomethanol via a thermochemical cycle. Finally, a comparison
between the measured EAs and T0(𝐴̃ ← 𝑋̃ ) of singly substituted alkoxy radicals (H2C(R)O•, R =CH3, NH2 or OH) is performed, establishing a link between identities of functional groups andthe electronic structure of singly substituted alkoxy radicals.
6.2 Methods
6.2.a Experimental
In this experiment, we make use of the instrument described in detail in Chapter 2. The
procedures which are specific to this chapter, in particular regarding the production of the anions
of interest, are described here. The aminomethoxide anion (H2C(NH2)O–, m/z=46) is produced
via the reaction between neutral formaldehyde (H2CO) and the amide anion (NH2–). The ions areproduced using a dual pulsed valve plasma entrainment source, which is described in detail in
Chapter 2 and Ref. 43. Here the main supersonic expansion consists of ~1% H2CO in argon gas(40 psig) as described in Chapter 5, and the secondary expansion, of a mixture of 10% NH3 (35psig, 99.999% purity) in argon, wherein the anions are formed via an electrical discharge (ΔV = 2 kV, Δt ~130 μs). The primary anion formed in such discharge is NH2–, which is able to reactwith neutral H2CO upon crossing of the main and side expansions, forming the desired anionicproducts. The products of this process, specifically anions with m/z = 46, will be described in
section 6.3.b.
For photodetaching electrons from aminomethoxide, we use the second and third
harmonics of a pulsed Nd:YAG laser: hν = 2.329 eV (532.3 nm) and 3.494 eV (354.8 nm),201

respectively. In addition, photons with energies of 2.172 eV (570.8 nm) and 2.038 eV (608.4 nm)
are also employed, and are generated by a 354.8 nm pumped optical parametric oscillator (OPO).
The limits of our instrument resolution are determined from the photoelectron spectrum of areference atomic anion, which is S– for this experiment,44,45 using the above photon energies.
Since our experimental resolution does not allow for separation of the rotational structure, thepeak center does not necessarily correspond to the band origin of a transition. In order to address
this, the procedure described by Engelking46,47 for rotational band shifts is employed (seeChapter 2 in conjunction with Table 6.5).
6.2.b Theoretical
Quantum chemical calculations that did not require the use of high level methods were
performed in the Gaussian 0948 program suite. These concern the neutral and anionic groundelectronic states of aminomethoxy and its structural isomers. The enthalpies for the reaction(Δrxn Ho0K ) between NH2– and H2CO forming various structural isomers of H4CNO– (m/z=46)
together with the EAs of the neutral products (see supplementary material) were calculated using
B3LYP/aug-cc-pVTZ. The energy of excited states of the aminomethoxide anion were calculatedwith the EOM-CCSD method with the aug-cc-pVTZ basis set.
The electronic structure calculations utilized for the generation of simulated
photoelectron spectra were performed by the Molpro program (version 2012.1)49 Specifically,geometry optimization and harmonic vibrational normal mode calculations regarding
aminomethoxide and aminomethoxy were performed using the CCSD(T)/aug-cc-pVTZ(ROCCSD(T) for the neutral radical) level of theory. The excited electronic state ofaminomethoxy (𝐴̃2A″) was calculated using multiconfigurational self-consistent-field (MCSCF)

202

methods with the aug-cc-pVTZ basis set. Specifically, the complete active space method(CASSCF) was used for geometry optimization and calculation of the harmonic vibrational
normal modes. The resulting optimizations are displayed in Tables 6.1 through 6.5, which arelisted at the end of this chapter for convenience. For the MCSCF calculations active spaceconsisting of five active electrons in four active orbitals (CAS(5,4)) was employed. The orbitals
in the active space nominally correspond to the σ(CO), oxygen 2py and 2px, and σ*(CO) orbitals.
This is the same active space (number of electrons, and number and type of orbitals) as the oneused by Dillon and Yarkony for ethoxy50 and hydroxymethoxy51 (also see Appendix II). Thismethod for the excited state was chosen, instead of a couple-cluster based approach as in theneutral ground state, due to the inability of the EOM-CCSD method to handle open-shelledradicals in the Molpro 2012.1 suite and also based on the successful calculations reported inprevious work by Dillon and Yarkony when calculating excited states of substituted alkoxy
radicals.50–52 For simulating the photoelectron spectrum we found that utilizing the higher level,
CCSD(T)/aug-cc-pVTZ calculation for the ground state calculations in combination with the
CASSCF approach for the excited state showed a significantly better agreement with experimentwhen compared with a full CASSCF approach for all the electronic states. Finally, we calculate
the T0(𝐴̃ ← 𝑋̃) using the state averaged multireference configuration interaction with explicitly
correlated energies (SA MRCI-F12), where the geometries and zero-point energies (ZPE) are
obtained from the CAS optimization for the neutral 𝑋̃ and 𝐴̃ states. Molpro was utilized insteadof Gaussian for these cases due to its considerably faster computation times for coupled-cluster
calculations, and due to its significantly larger degree of control over the parameters for
performing calculations with multiconfigurational methods.

203

The photoelectron spectra are calculated using the ezSpectrum53 program, by the methods
described in section 2.2.b. These calculations were carried out assuming a vibrationaltemperature of 150 K, based on previous experiments.37,54 This procedure generates a discrete
spectrum of sticks, where the intensities correspond to the calculated FC factor and the positions
correspond to the calculated vibrational frequency relative to the transition between the groundvibrational and electronic level in the anion to ground vibrational level in the neutral electronic
states. In order to provide a direct comparison between calculation and experiment, the stick
spectrum is convolved with Gaussian functions where the integral is equal to the calculatedtransition intensity and the fwhm is consistent with the eKE-dependent instrumental resolution of
the VMI spectrometer.
6.3 Results
6.3.a Initial remarks
Given that the EA of NH2 (0.771 eV)55 is sufficiently less than that of O (1.461 eV),56 thenegative charge on aminomethoxide is largely localized on the oxygen atom, as with the otheralkoxide anions.14,37,57,58 Thus, the EA of the aminomethoxy radical should be similar to the otheralkoxy radicals,14,37,57,58 i.e. near 2 eV. In addition, this formal negative charge on the oxygen
causes a strong intramolecular electrostatic interaction between the oxygen and the amino group.
Upon electron photodetachment, it is expected that the strength of the intramolecular interaction
will be significantly lessened, causing major geometry changes associated with the weakening of
this interaction. For example, the OCN angle and the distance between the oxygen atom and theamino group hydrogen atoms would be larger for the neutral radical compared to the anion. The
calculated equilibrium geometries of aminomethoxide and aminomethoxy are detailed in Table
6.1 and support this physical interpretation. These changes in structural parameters will lead to204

vibrational transitions involving excitation of the HNH wag, OCN bend, and OC or CN
stretches. If there is a sufficiently large degree of structural change, this could result in aphotoelectron spectrum showing an extended vibrational progression. It is also likely thattransitions involving a low-lying excited electronic state would be observed, as is the case withother substituted alkoxide photoelectron spectra. Given that the T0(𝑋̃ ← 𝐴̃) for other alkoxy
radicals range from approximately 70 cm-1 to 3300 cm-1, it might be expected that the T0(𝑋̃ ← 𝐴̃)
for aminomethoxy would lie somewhere within this range. In the following sections, results fromthe experiment are presented, where the anion produced in our ion source with m/z = 46 is
identified as aminomethoxide and its photoelectron electron spectrum is measured with several
photon energies. The EA and T0(𝑋̃ ← 𝐴̃) of aminomethoxy are determined, along with several
vibrational frequencies.
6.3.b Identification of anion with m/z=46
Following the procedure described in section 6.2.a, the mass spectra confirmed the
production of an anion with m/z=46. The identity of m/z=46 was confirmed by the following
series of tests. This mass was only formed when both H2CO was in the main expansion and NH3
was discharged in the side expansion. If only argon is present in the main expansion, thedischarge of NH3 in the side expansion generates a large amount of NH2–, along with several
other N, H containing anions and their clusters with argon. NH2– is a strong base capable ofdeprotonating H2CO59 whereas other anions generated in the NH3 discharge are notthermodynamically capable of doing so. When H2CO is added to the main expansion, thereaction of NH2– with H2CO is confirmed by the appearance of m/z=29 (HCO–).60 In addition to
deprotonating formaldehyde, NH2– can also react with formaldehyde in an association reaction,

205

forming m/z=46. This reaction product can be collisionally cooled and stabilized by the argonpresent in abundance in the main expansion.
In the association reaction between NH2– and H2CO, the formation of a C–N bond is themost likely to occur, resulting in the aminomethoxide anion being formed (inset graphic of Fig.
1). The calculations performed here (CCSD(T)/aug-cc-pVTZ) predict the EA of aminomethoxy
as 1.89 eV, in agreement with the observed EA of 1.944 eV (see section 6.2.b). Other structural
isomers of H4CNO that could arise from photodetachment from other association reaction
products between NH2– and H2CO possess EAs at least 0.6 eV lower than what is predicted foraminomethoxy, as discussed below. However, no photoelectron signal was observed below anelectron binding energy of approximately 1.9 eV, suggesting that it is highly unlikely that theseother isomers are being formed in any significant abundance. Calculations performed here andby Rosenberg,61 suggest that the formation of aminomethoxide from NH2– and H2CO is
exothermic by ~ -40 kcal mol-1. In the gas phase, unless the heat of formation in this reaction isefficiently dissipated, other structural isomers of aminomethoxide could in principle be formed
as well. In our experiment, the energy is removed by collisions with the argon atoms present inabundance in the primary supersonic expansion. The presence of multiple isomers of H4CNO–
could potentially pose difficulty to the interpretation of the photoelectron spectra. In order toinvestigate the likelihood that our photoelectron spectra would show signatures of these otherisomers of aminomethoxide, we calculated (B3LYP/aug-cc-pVTZ) the reaction enthalpies(Δrxn Ho0K ) between NH2– and H2CO forming the anionic products shown in Fig. 6.1, together
with the EAs of the neutral counterparts (Table 6.6). The relative energies between isomers showthat the only expected products would be aminomethoxide (isomer I) and III, but theconsiderably different EAs show that the identification of these isomers in the photoelectron
206

spectra should be straightforward. Based on the experimental spectra, aminomethoxide is thedominant anion with m/z=46 formed in this experiment.
6.3.c Overview and Electron Affinity of Aminomethoxy
The lower panel of Fig. 6.2 displays the photoelectron spectrum of aminomethoxide
acquired with a photon energy of 3.494 eV, which covers the complete range of eBE wherein
photoelectron signal was observed. This figure displays a spectrum which originates atapproximately 1.94 eV (peak labeled A) and has peaks extending to an eBE of approximately 3.0
eV. Even though peak A is located at the highest eKE in this spectrum, it is apparently thenarrowest peak, with a fwhm of 48 meV. This goes counter to the eKE dependence of the VMI
resolution as described above in section 2.a. Also, the fact that this peak is close to resolution
limited, which is 43 meV, indicates that here is likely a large degree of spectral congestion in thisregion of the spectrum. A higher resolution spectrum, obtained with a lower photon energy will
indeed prove this statement in the subsequent analysis. The labels B through D represent thepeaks that are displayed in higher resolution in Fig. 6.3. The upper panel of Fig. 6.2 shows theanisotropy parameter (β) of the spectrum (black circles). The anisotropy parameter is generally
positive for the progression, becoming more positive with higher eBE. The negative values of βcorrespond to the peaks labeled A and C. When this is compared to the overall positive β of therest of the progression, it suggests that two distinct electronic states of aminomethoxy areaccessed using this photon energy. In order to analyze this further, a photoelectron spectrum withhigher resolution is required, and hence we obtain a spectrum using a lower photon energy,58
which is presented in Fig. 6.3.

207

Figure 6.1: Structural isomers of aminomethoxide discussed in the text. The optimized structures
were calculated at the B3LYP/aug-cc-pVTZ level of theory/basis set. See Table 6.6 for relative
energies and calculated electron affinities of the corresponding neutral radicals.

208

o

Table 6.6: Calculated (B3LYP/aug-cc-pVTZ) addition reaction enthalpies (Δrxn H0K ) between
amide anion (NH2–) and formaldehyde (H2CO) forming the anionic products shown in Fig. 6.1
and electron affinities of the corresponding neutral species. All values include zero-point energy.
o b
Neutral EA
𝚫rxn 𝐇0K-1/ eV/ kcal mol
I
-35.4
1.92
II
2.2
-0.11
III
-23.9
1.32
IV
34.1
0.28
a
See Fig.1 for structureb
Relative to the reactants NH2– + H2CO

Producta

209

Figure 6.2: Upper panel: Photoelectron anisotropy parameter (β) of aminomethoxide (black dots)
as a function of electron kinetic energy (eKE). The β values are only displayed where asignificant photoelectron signal was observed. Lower panel: VMI photoelectron spectrum ofaminomethoxide obtained with a photon energy of 3.494 eV. The structure of aminomethoxide is
depicted. The green and black arrows indicate the other photon energies (2.172 and 2.038 eV,
respectively) used to obtain the higher resolution spectra shown in Figs. 6.3 and 6.4.

210

The photoelectron spectrum acquired with a photon energy of 2.172 eV (570.8 nm) ispresented in Fig. 6.3. This results in a higher resolution photoelectron spectrum and reveals a
number of resolved peaks between 1.94 and 2.17 eV eBE, in contrast to the spectrum shown in
Fig. 6.2. The peaks labeled with letters in Fig. 6.2 are indicated in Fig. 6.3 as groups of peaks
under brackets with the same labels. This shows that the proximity between peaks undermined
our ability to resolve the transitions under these brackets when employing the 3.494 eV photon
energy (Fig. 6.2), a problem which is solved by the higher resolution attainable with a lower
photon energy. In this spectrum, the fwhm of peak 1 is 13 meV, significantly narrower than peak
A in Fig. 6.2 (48 meV) an also reasonable close to being resolution limited (9 meV). Fig. 6.3 also
displays the calculated photoelectron spectrum in the lower panel. The red sticks represent
transitions from the ground vibrational and electronic state of aminomethoxide to the groundelectronic state of neutral aminomethoxy (𝑋̃) and the blue sticks represent transitions to theneutral excited electronic state (𝐴̃). From this point onward in this work, the 𝑋̃ and 𝐴̃ states will
always refer to the electronic states of the neutral aminomethoxy. The simulation displayed in
the lower panel of Fig. 6.3 was built by shifting and scaling the stick spectra so that the origin
transitions of the 𝑋̃ and 𝐴̃ states of aminomethoxy matched the position and ratio of the areas ofpeaks 1 and 3, respectively. With the improved resolution, a thorough analysis of the spectrum
can be performed, providing the assignments of the EA, T0(𝑋̃ ← 𝐴̃), and vibrational frequencies.

211

Figure 6.3: Upper panel: Measured anisotropy parameter β associated with the experimental
photoelectron spectrum found in the middle panel. The β values shown correspond to average values
across the top ¼ of each peak in order to minimize the contribution from neighboring peaks to themeasured anisotropy of individual peaks. The error bars correspond to the standard deviation of the mean
β values across the points averaged for each peak. Middle panel: Photoelectron spectrum obtained using aphoton energy of 2.172 eV. Lower panel: Calculated photoelectron spectrum for transitions from theground electronic state of the aminomethoxide (150 K), to vibrational levels of the neutral ground (redsticks) and neutral excited (blue sticks) electronic states of aminomethoxy, convolved to the expected
experimental resolution.

212

For the assignment of the EA of aminomethoxy, we focus on peak 1 of Fig. 6.3 (peak A
in Fig. 6.2), which is the apparent origin of the overall vibrational progression. As mentioned
previously, the CCSD(T)/aug-cc-pVTZ calculations predict the EA of aminomethoxy as 1.89 eV,
in close agreement with the corresponding eBE of the center of peak 1. A comparison between
calculation and experiment suggests that peak 1 arises primarily from the origin of the 𝑋̃ statevibrational progression. In order to establish our best assignment of the EA of aminomethoxy,
we obtain a photoelectron spectrum with a photon energy of 2.038 eV, displayed in Fig. 6.4.
Using this lower photon energy, peak 1 has a fwhm of 9 meV. From the center position of peak 1(1.944(2) eV) and the consideration of the uncertainties and shifts discussed in sections 6.2.a and2.3.b, the EA of aminomethoxy is assigned as 1.944(5) eV. Other important assignments are
based on Fig. 6.4, such as the determination of T0(𝑋̃ ← 𝐴̃). Such assignment is described in thefollowing section.

213

Figure 6.4: Photoelectron spectrum obtained using a photon energy of 2.038 eV. Peak labels are
discussed in the text.

214

6.3.d Determination of Aminomethoxy Term Energy, T0(𝐴̃ ← 𝑋̃)The experimental assignment of the origin of the 𝐴̃ state vibrational progression isdetermined from two factors: experimental peak-specific anisotropy parameters and comparison
with the theoretically predicted photoelectron spectra. In the spectrum obtained with a photon
energy of 3.494 eV (Fig. 6.2), the 𝑋̃ state origin peak (peak A) has a β < 0, while the high eBE
region (above ~2.2 eV) has β values that are greater than 0. As previously mentioned, thischanging anisotropy parameter across the spectrum suggests the presence of transitions to at least
two different electronic states. The high eBE region is likely dominated by transitions to thehigher-lying 𝐴̃ state, which is confirmed by the calculated spectrum over the full range of eBEs
(Fig. 6.6). However, because of the reduced resolution, the origin of the 𝐴̃ state vibrational
progression cannot be determined from the spectrum in Fig. 6.3. From the higher resolution
photoelectron spectrum (Fig. 6.3), an analysis of the β parameter shows that most of the observed
peaks have a near isotropic photoelectron angular distribution (β ≈ 0), apart from peak 3 with β ≈+0.5. A photoelectron spectrum obtained with a slightly higher photon energy of 2.329 eV (Fig.
6.5) further corroborates this observation of the positive anisotropy of peak 3 compared toneighboring peaks. The photoelectron spectrum obtained using 2.329 eV photon energy (532nm) is shown in Figure S1. As mentioned above, this photoelectron spectrum confirms thedistinct positive anisotropy parameter of peak 3. This suggests that peak 3 is dominated by atransition from the anion to the excited 𝐴̃ state of the neutral radical. Although other peaks seemto have positive anisotropies as well, and therefore could be associated with the excitedelectronic state, the large degree of congestion makes a definite assignment very challenging.

215

Figure 6.5: Lower panel: Photoelectron spectrum obtained using 2.329 eV photon energy (532nm) as a function of decreasing eBE. The peak labels are the same as the ones in Fig. 3 of themain text. Upper panel: Anisotropy parameter β as a function of eKE. The β values shown
correspond to average values across the top ¼ of each peak to minimize the contribution to theanisotropy from neighboring peaks. The error bars correspond to scatter of β values across thepoints averaged for each peak.

216

Peak 3 is the lowest eBE peak that does not have an assignment corresponding to atransition from the anion to the ground 𝑋̃ state of the neutral radical. Peak 3 is centered at
2.029(1) eV (Fig. 3), which is 689(16) cm-1 relative to the 𝑋̃ state origin. While this peak spacing
is similar to the HCH torsional frequency of the 𝑋̃ state (see Table 6.3), transitions involving thissymmetry breaking vibrational mode are not allowed. There are no other predicted transitions to
the ground 𝑋̃ state with significant FCFs that could be assigned to peak 3. Given this and theobserved photoelectron angular anisotropy, this peak is assigned to the 𝐴̃ state origin transition.
This assignment is further confirmed by the overall satisfactory agreement between thecalculated and experimental spectra over the full range of eBEs (Fig. 6.6) once the calculated
photoelectron spectrum accessing the excited state is set to originate at peak 3. This agreement isparticularly good with regard to the overall width of the vibrational envelope and the position ofits maximum, located at approximately 2.28 eV eBE. Thus, the T0(𝐴̃ ← 𝑋̃) term energy is
obtained from the highest resolution spectrum (Fig. 6.4) and is determined as 0.085(5) eV. The
calculations performed here (CAS(5,4)//MRCI-F12/aug-cc-pVTZ) to provide the term energy ofaminomethoxy as T0(𝐴̃ ← 𝑋̃) = 0.201 eV. Although the agreement with the experimental
measurement is not completely satisfactory, the experimental evidence of the origin of theground and first excited electronic states is clear.

217

Figure 6.6: Experimental photoelectron spectrum obtained with 3.494 eV photon energy (black
trace), calculated FCFs for transitions from the ground state of the anion (𝑋̃1 𝐴′ (v = 0)) to neutral
ground (red sticks) and neutral excited (blue sticks) electronic states of aminomethoxy. The
green trace represents the convolved calculated spectrum using the experimental resolution.

218

6.3.e Vibrational analysis
In order to conduct a vibrational analysis, we perform simulations of the photoelectron
spectrum by the methods described in section 2.b, with results displayed in the lower panel ofFig. 6.3. For convenience, the transition energies are given relative to the specified electronic
state’s vibrational origin (𝑋̃ or 𝐴̃) and reported in wavenumbers and therefore represent thevibrational frequencies of the final, neutral state. The calculated spectrum provides vibrational
assignments by comparison of the positions of the experimental and calculated peaks (see Tables
6.2 through 6.4). Our calculations predict that the most active vibrations in the photoelectron
spectrum will be the HNH wag, OCN bend, C–N and O–C stretches, based on the geometry
change between the anion and neutral 𝑋̃ and 𝐴̃ states. From a chemical intuition point of view,the loss of a formal charge in the oxygen atom of aminomethoxide upon photodetachment,
forming aminomethoxy, would result in the decrease of the strength of the intramolecularelectrostatic interaction between the oxygen and NH2 moieties. This would result in an increasein the OCN angle, a distancing of the NH2 hydrogens from the oxygen atom, leading to a similar
prediction on the vibrational activity. As the subsequent analysis shows, our experimental
observations indeed confirm our predictions, providing further confidence to the assignments
made here.
Peak 2 is spaced from peak 1 by 496(10) cm-1, a value that agrees well with thecalculated OCN bend harmonic frequency (498 cm-1) of the neutral 𝑋̃ state. This provides ameasurement of the OCN bending frequency 𝜈14 (𝑋̃) = 500(40) cm-1. The transition which ispredicted to dominate peak 4 can be assigned as 𝜈12 (𝑋̃) = 790(30) cm-1, as it agrees well with thecalculated harmonic frequency of the HNH wag (847 cm-1). The assignments of peaks 5 through11 are more complicated due to the presence of transitions whose proximity would make them219

impossible to experimentally separate due to the resolution of the instrument. As an example,
peak 5 is spaced from the 𝑋̃ state origin by 985(13) cm-1, which can correspond to either the first
overtone of the OCN bend in the ground electronic state, 2𝜈14 (𝑋̃), calculated as 996 cm-1, or the
C–O stretch 𝜈11 (𝑋̃), calculated as 1002 cm-1. The ambiguity of the assignments cannot be
eliminated with our experimental resolution which limits our capability of accurately assigningthese transitions. Nevertheless, tentative assignments were made and are reported below in Table
6.7. Other transitions which were not assigned in this section, namely the peaks labeled a and b
are discussed in the following section (6.3.b).

220

Table 6.7: Vibrational transition assignments for the peaks in the photoelectron spectra (Figs.
6.3, 6.4 and 6.5). The absolute peak position (eBE, reported in eV) and the energy relative to theorigin of the neutral ground and excited state progressions (reported in cm-1) are given. The
H2C(NH2)O– (𝑋̃1 𝐴′ ) (𝜈1′′ 𝜈2′′ … ) → H2C(NH2)O• (𝑋̃ 2 𝐴′ or 𝐴̃2 𝐴″ ) (𝜈1′ 𝜈2′ … ) + e– (eKE) transitions
𝜈′

𝜈′

1

2

(second column) are labeled using the standard shorthand notation (1𝜈1′′ 2𝜈2′′ …).
Peak eBE position Spacing from Spacing from Possible assignments of
label
/ eV
Peak 1 / cm-1
Peak 3 / cm-1 transitionsa (2nd column)
1.944(3)0
1𝑋̃1 𝐴′ (v=0) → 𝑋̃ 2 𝐴′ (v=0)
1.971(3)222a?
1.987(9)344b?
2.005(4)494
21410
2.029(1)689
03𝑋̃1 𝐴′ (v=0) → 𝐴̃2 𝐴′′ (v=0)
2.042(3)
803
114
4
1210
2.066(1)986
296
51420 , 1110
2.087(1)1151
461
6910 , 1410
2.101(1)
1265
576
7
810
2.107(3)
1306
616
8
710
2.127(2)
1477
787
9
1310
2.145(1)
1620
930
10
1210
2.161(1)
1748
1059
11
810 1410a
Assignments are tentative with the exception of the vibrational origin transitions(peaks 1 and 3) and are based on the calculated spectrum shown in Fig. 6.3.

221

6.3.f Unassigned transitions
The high resolution photoelectron spectrum in Fig. 6.4 reveals two additional peaks,labeled a and b, which are not accounted for in the calculated spectrum. The spacings from peak
1 to peaks a and b are 220(30) cm-1 and 350(40) cm-1, respectively. The lowest calculated
frequency mode of the 𝑋̃ state of aminomethoxy is the HNH torsion, calculated to be 252 cm-1.
While this vibrational frequency matches the peak spacing fairly well, this is a symmetryforbidden transition. These peaks are also not observed when using a higher photon energy (suchas in the spectra reported in Figs. 6.3 and 6.5), but otherwise using the same experimental
conditions. In anion photoelectron spectroscopy, peak intensities can change as a function ofphoton energy simply as a threshold effect, but such effect decreases peak intensities due todecreasing photodetachment cross section with lower eKE.62 The observation that the integrated
areas of peaks a and b increase in the lower eKE spectrum with respect to other peaks in the
spectrum cannot be explained by threshold effects. These observations suggest that peaks a and b
result from electron autodetachment, which is the most likely explanation of this behavior, as
described in previous investigations.63–70 It is possible that the normally forbidden torsionalmode gains intensity via the autodetachment process. Vibrational activity of Franck-Condon
forbidden modes has previously been attributed to autodetachment in the photoelectron spectrumof small molecular anions, such as H2CCN–.65,71
6.4 Discussion
6.4.a Thermochemistry of aminomethanol
Some basic thermochemical properties of aminomethanol can be obtained from athermochemical cycle42 using the experimentally measured EA of aminomethoxy:222

D0 (H2 C(NH2 )O–H) = Δacid Ho0K (H2 C(NH2 )OH) – IE(H) + EA(H2 C(NH2 )O• )(6.1)

There is no experimental measurement of the O–H bond dissociation energy, D0(H2C(NH2)O–H), or the gas phase acidity, Δacid Ho0K (H2C(NH2)OH), of aminomethanol. Thus, quantum
chemical calculations must be employed to obtain either one of these values. In this work,
Δacid Ho0K(H2C(NH2)OH) was selected since this quantity only depends on calculating theformation enthalpies of the closed shell species H2C(NH2)O–, H2C(NH2)OH, and H+. The G4composite method was applied yielding Δacid Ho0K (H2C(NH2)(OH)) = 374.0 kcal mol-1, where thepredicted uncertainty in these calculations is predicted to be on the order of 1 to 2 kcal mol-1.72
Using the experimentally determined EA(H2C(NH2)O•) = 1.944(5) eV and the well-known
ionization energy of atomic hydrogen,73 D0(H2C(NH2)O–H) is determined to be 106.3 ± 2.0 kcal
mol-1, using a conservative estimate of the uncertainty. Our value derived from a combination ofexperiment and calculation compares nicely to the calculate (G4 composite method) value ofD0(H2C(NH2)O–H) = 107.7 kcal mol-1. Table 6.8 summarized this result, together with othermajor experimental results reported in this chapter.

223

Table 6.8: Summary of major results.
Summary of major results

Experiment Calculation

EA(H2C(NH2)O•) / eV

1.944(5)1.89 eVa

T0(𝐴̃ ← 𝑋̃ ) (H2C(NH2)O•) / eV

0.085(5)0.201 eVb

Δacid Ho0K(H2C(NH2)OH) / kcal mol-1-

374.0cD0(H2C(NH2)O–H) / kcal mol-1

106(2)d107.7ca

CCSD(T)/aug-cc-pVTZ (RO method used for neutral)b

CAS(5,4)//MRCI-F12/aug-cc-pVTZ, see section 6.2.bc

G4 composite method, see section 6.4.adValue based on the thermochemical cycle (Eq. 1) using the

calculated ∆acidHo0K(H2C(NH2)OH)224

6.4.b Comparison of aminomethoxy with other singly substituted alkoxy radicals
It is instructive to compare of the EAs of ethoxy, aminomethoxy, and hydroxymethoxy,
since they have similar atom connectivity, are isoelectronic radicals, but have different functionalgroups attached to the central carbon atom. Comparing the experimentally measured EAs of
H2C(R)O• we see a trend of increasing values: 1.712(4), 1.944(5) and 2.220(2) eV for R= CH3,NH2 and OH, respectively. This trend correlates with the increasing electronegativity of the R
group.
The photoelectron spectra of aminomethoxide and hydroxymethoxide37 (see Chapter 5)
are quite similar to each other, as shown in Fig. 6.7. The analysis of the hydroxymethoxide
photoelectron spectrum presented in Chapter 5 showed significant excitation in OCO stretches
and bends for the transition from the anion to the neutral 𝑋̃ state. The activity of these vibrationalmodes is associated with the weakening of the electrostatic intramolecular interaction between
the hydroxyl group and the oxygen atom. This observation is analogous to the one reported here
for aminomethoxy. While the photoelectron spectra of aminomethoxy and hydroxymethoxy
appear very similar, there is a significant difference between the term energies of these radicals:
T0(𝐴̃ ← 𝑋̃ ) = 0.085(5) eV for aminomethoxy and T0(𝐴̃ ← 𝑋̃ ) ~ 0.4 eV for hydroxymethoxy.37
This five-fold difference between the T0(𝐴̃ ← 𝑋̃) suggests that exchanging the amino group for ahydroxyl group has a significant effect on the electronic structure of these singly substituted
alkoxy radicals. In addition to the their work on ethoxy,50 Dillon and Yarkony performed atheoretical study of hydroxymethoxy51 focusing on its distinct electronic structure. In that study,
they argue that the electronic structure and the topography of the 𝑋̃ and 𝐴̃ states ofhydroxymethoxy are drastically different from the typical Jahn-Teller influenced topography of
ethoxy. This difference is mainly attributed to the strength of the intramolecular interaction225between the hydroxyl group and the oxygen atom. In aminomethoxy, the amino group is alsoable to form a strong electrostatic intramolecular interaction with the O moiety, but the nitrogen
atom is less electron-withdrawing than oxygen and, therefore, polarizes the hydrogen atoms to alesser extent. Aminomethoxy also exhibits an equilibrium geometry in which the hydrogenatoms are not as close to the O moiety when compared to hydroxymethoxy. This is because of
the average geometry of hydroxymethoxy forms a four-membered planar O-C-O-H ring, while inaminomethoxy, the oxygen bisects the HNH angle, causing both hydrogens of the amino group
to be out of the O-C-N plane. Thus, the interatomic distances between the hydrogen and the
opposite oxygen atom are 2.68 Å in aminomethoxy versus 2.29 Å in hydroxymethoxy, which
can make the interaction between these moieties considerably weaker for aminomethoxy thanhydroxymethoxy.

226

Figure 6.7: Upper panel: Photoelectron anisotropy parameter (β) as a function of electron kinetic
energy (eKE) for aminomethoxy (blue dots) and hydroxymethoxy (red dots). The β values weretruncated to exclude points where no significant photoelectron signal was observed. The spectrumof hydroxymethoxide is reproduced from Ref. 37 . Lower panels: Photoelectron spectrum ofhydroxymethoxide (red) and aminomethoxide anions (blue) obtained with a photon energy of 3.49
eV (355 nm) as a function of decreasing electron binding energy (eBE). The inset graphic depicts
the optimized structures of the anions.

227

A comparison between aminomethoxy and other small substituted alkoxy radicals
provides a possible explanation of why the calculated and experimental photoelectron spectrum
presented in Fig. 6.3 have a less than perfect agreement, particularly for peaks above 2.06 eV. Is
has been shown previously that for other small alkoxy radicals, the inclusion of vibronic
coupling, i.e. coupling of electronic and vibrational degrees of freedom, was the primarycontributor to generating accurate calculated photoelectron spectra.37,50–52 Similar toaminomethoxide, the photoelectron spectrum of ethoxide reported by Ramond et al.14 displayed
numerous prominent disagreements between harmonic calculations and the experiment,
particularly regarding peak intensities. This photoelectron spectrum was later investigated by
Dillon and Yarkony,50 who, by including vibronic coupling between the ethoxy 𝑋̃ and 𝐴̃ states in
the calculation, significantly increased the level of agreement between theory and experiment
while also shedding light on why there was disagreement to begin with. Thus, it is likely thatvibronic coupling between the 𝑋̃ and 𝐴̃ states in aminomethoxy is also a dominant contributor to
the disagreement between calculation and experiment for the photoelectron spectrum ofaminomethoxide. However, it is beyond the scope of this work to attempt this level of theory foraminomethoxy.
6.5 Conclusions
In this work, the aminomethoxide (H2C(NH2)O–) anion was successfully produced in thegas phase from the reaction between the amide anion (NH2–) and neutral formaldehyde (H2CO).
The photoelectron spectrum of H2C(NH2)O– obtained with a photon energy of 3.494 eV accesses
the ground (𝑋̃ 2A′) and first excited (𝐴̃ 2A″) electronic states of the neutral aminomethoxy radical(H2C(NH2)O•). The photoelectron spectrum accessing these two electronic states of H2C(NH2)O–is broad, extending for approximately 1 eV. The extent of the progression indicates that there is a228

large degree of geometry change between anion and neutral electronic states upon
photodetachment. Higher resolution photoelectron spectra obtained using photon energies of
2.172 or 2.038 eV resolve vibrational transitions between anion ground state and neutral ground(𝑋̃ 2A′) and excited (𝐴̃ 2A″) electronic states. The high resolution photoelectron spectrum
provides an experimental measurement of the electron affinity of aminomethoxy to be 1.944(5)eV) and the term energy to be 0.085(5) eV. Several vibrational assignments were made by acomparison between experimental and calculated spectrum, which exhibits strong FranckCondon activity mainly in the OCN bending and HNH wagging vibrations of aminomethoxy.
Some significant discrepancies between calculated and experimental peak intensity ratios wereobserved. Because of the small energy separation between the 𝑋̃ 2A′ and 𝐴̃ 2A″ states ofaminomethoxy, and following a comparison with the ethoxy radical, it is suggested that notincluding vibronic coupling between these electronic states likely results in the observed
disagreement between experiment and theory. A comparison between the term energies andphotoelectron spectra of aminomethoxy and other singly substituted alkoxy radicals H2C(R)O•,
ethoxy (R=CH3) and hydroxymethoxy (R=OH) shows that aminomethoxy likely has more
resemblance to ethoxy than with hydroxymethoxy, particularly with regard to their electronic
structure. This difference is in part due to the strength of the electrostatic intramolecularinteraction between the R group and oxygen atom, with CH3 being the weakest and OH
strongest.

229

6.6 General Optimization Results
Table 6.1: Optimized structural parameters of H2C(NH2)O– (CCSD(T)/aug-cc-pVTZ) andH2C(NH2)O in its ground (ROCCSD(T)/aug-cc-pVTZ) and excited (CAS(5,4)/aug-cc-pVTZ)
states, together with the relative change in structural parameters with respect to the anion
structure. The figure shows the atom connectivity and numbering in aminomethoxy.

Descriptionofparameter
rC-O
rC-N
rC-H1
rC-H2
rN-H3
rN-H4
OCN
OCH1
OCH2
NCH1
NCH2
φH1CON
φH2CON
φH3NCO
φH4NCO

Anion(𝑋̃ 1A′)

Neutral(𝑋̃ 2A′)

1.332
1.528
1.124
1.124
1.022
1.022
115.15114.808
114.811102.794102.798
118.764-118.765
52.796-52.902

1.377
1.444
1.102
1.102
1.014
1.014
118.406
106.501
106.474
110.154110.162
123.757-123.757
58.969-59.016% Change% Change(Anion – Neutral 𝑋̃)Neutral(𝐴̃ 2A″)(Anion – Neutral 𝐴̃)

3.38
-5.50
-1.96
-1.96
-0.78
-0.78
2.83
-7.24
-7.26
7.16
7.16
4.20
4.20
11.69
11.56

1.439
1.424
1.081
1.081
0.997
0.997
109.292
108.79108.828112.243112.243120.063-120.082
61.743-61.785

8.03
-6.81
-3.83
-3.83
-2.45
-2.45
-5.09
-5.24
-5.21
9.19
9.19
1.09
1.11
16.95
16.79

230

Table 6.2: Calculated (CCSD(T)/aug-cc-pVTZ) harmonic vibrational frequencies (ωi) of
H2C(NH2)O– 𝑋̃ 1A′ and approximate description of the molecular motions associated with thenormal modes. All values are given in wavenumbers (cm-1).
Vibrationalmode ωi

Calculated
frequencies

Approximate description

Symmetry(Cs pointgroup)(Anion, 𝑋̃ 1A′)

15

276

HNH torsion

A"

14

475

OCN bend

A'

13

818

C–N stretch

A'

12

901

out of phase HNH + HCH twist

A"

11

1041

HNH wag (umbrella)

A'

10

1211

C–O stretch

A'

9

1221

HCH torsion

A"

8

1332

in phase HNH + HCH twist

A"

7

1361

HCH wag

A'

6

1464

HCH bend

A'

5

1631

HNH bend

A'

4

2657

HCH asym. stretch

A"

3

2699

HCH sym. stretch

A"

2

3396

HNH sym. stretch

A'

1

3463

HNH asym. stretch

A"

231

Table 6.3: Harmonic vibrational frequencies (ωi) of H2C(NH2)O•, 𝑋̃ 2A′ (ROCCSD(T)/aug-ccpVTZ) and approximate description of the molecular motions associated with the normal modes.
All values are given in wavenumbers (cm-1).
Vibrationalmode ωi

Calculated
frequencies

Approximate description

Symmetry(Cs pointgroup)(Neutral, 𝑋̃ 2A′)

15

252

HNH torsion

A"

14

498

OCN bend

A'

13

666

HCH torsion

A"

12

847

HNH wag (umbrella)

A'

11

1002

C–O stretch

A'

10

1010

out of phase HNH + HCH twist

A"

9

1132

C–N stretch

A'

8

1344

HCH wag

A'

7

1350

in phase HNH + HCH twist

A"

6

1398

HCH bend

A'

5

1606

HNH bend

A'

4

2958

HCH sym. stretch

A"

3

2987

HCH asym. stretch

A"

2

3502

HNH sym. stretch

A'

1

3587

HNH asym. stretch

A"

232

Table 6.4: Harmonic vibrational frequencies (ωi) of H2C(NH2)O•, 𝐴̃ 2A″ (CAS(5,4)/aug-ccpVTZ) and approximate description of the molecular motions associated with the normal modes.
All values are given in wavenumbers (cm-1).
Calculated
Vibrationalmode ωifrequencies

Approximate description

Symmetry(Cs pointgroup)(Neutral, 𝐴̃ 2A″)

15

416

HNH torsion

A"

14

442

OCN bend

A'

13

871

HNH wag (umbrella)

A'

12

1009

C–O stretch

A'

11

1020

out of phase HNH + HCH twist

A"

10

1195

C–N stretch

A'

9

1455

in phase HNH + HCH twist

A"

8

1497

HCH wag

A'

7

1654

HCH bend

A'

6

1801

HNH bend

A'

5

1930

HCH torsion

A"

4

3195

HCH sym. stretch

A"

3

3247

HCH asym. stretch

A"

2

3740

HNH sym. stretch

A'

1

3826

HNH asym. stretch

A"

233

Table 6.5: Calculated rotational constants for aminomethoxy: Anion 𝑋̃1 𝐴′ and neutral ground 𝑋̃ 2 𝐴′
(RCCSD(T)/aug-cc-pVTZ, RO for neutral) and neutral excited 𝐴̃2 𝐴″ (CAS(5,4)/aug-cc-pVTZ) .
All values are given in cm-1.
Rotational Constants/ cm-1
A
B
C

Anion(𝑋̃1 𝐴′ )
1.384
0.342
0.302

234

Neutral(𝑋̃ 2 𝐴′ )
1.484
0.335
0.302

Neutral(𝐴̃2 𝐴″ )
1.296
0.360
0.312

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238

CHAPTER VII
PHOTOELECTRON SPECTROSCOPY OF 7-AZAINDOLIDE AND 7-AZAINDOLEDIMER ANIONS

7.1 Introduction
Indoles and related species are ubiquitous molecules in biological processes. The
photoelectron spectrum of indolide, or deprotonated indole, was recently investigated by ourgroup.1 A summary of such experiments, showing the overview low resolution spectrum
obtained with a photon energy of 3.494 eV, and a high resolution magnification of the peak
attributed to the EA of the associated indolyl radical, obtained with a photon energy of 2.4500
eV, are displayed in Fig. 7.1. The overview low resolution photoelectron spectrum showed an
extended progression that is well captured by calculation. The use of the SEVI technique (seeChapter 2), where only slow electrons are detected, significantly narrows the lowest eBE peak(gray shaded area) which is dominated by the origin transition (bold stick in the calculate
spectrum). This results in a high precision measurement (±1.7 meV) of the EA of the indolyl
radical, as discussed in Ref. 1. In this chapter, we investigate the analogous 7-azaindolide, which
differs from indolide by a single substitution of a C-H group for an N atom, as depicted in
Scheme 7.1 below. In this chapter we conduct similar experiments the ones reported in Ref.1 forthe analogous species 7-azaindolide.

239

Figure 7.1: Photoelectron spectrum of indolide reproduced from Nelson et al.1 with somemodifications. The calculated transitions and their associated intensities are represented by red
sticks, while the convolution of these sticks with Gaussian functions whose fwhm iscommensurate with the instrument resolution is shown in green. This simulation assumed atemperature of 200 K. The shaded region was also obtained in high resolution, as shown in thelower panel.
240

Scheme 7.1: Chemical structures of indolide, 7-azaindolide and the 7-azaindole dimer anion.
7-azaindole is a heterocyclic aromatic molecule which has attracted attention from thescientific community due to its analogous structure to nucleobases.2–9 The interest in studying 7azaindole arise primarily from its ability to form a stable dimer via hydrogen bonding (seeScheme 7.1).2–6,10–13 Thus, over the past 40 years,8,14–16 7-azaindole has been utilized as a model
system for Watson-Crick nucleobases due to its similar pairing mechanism.3,4,7,14,16–20
Similarly to a DNA base pair, 7-azaindole is involved in excited state double protontransfer within the dimer.3,4,10,14,21–24 Therefore, understanding the double proton transfer
mechanism has been the target of many spectroscopic studies in both condensed3,8,10,16,17,25–29 andgas phases.12,21,30–34 In the studies by the groups of Zewail2–4 and Castleman,35,36 the protontransfer was described by a stepwise mechanism, with a zwitterionic pair as an intermediate.
Other groups claim the double proton transfer is concerted, happening in one single step.21,37,38
Although the dimer has been thoroughly studied, there is still a debate on the proton transfer
mechanism.5,38–42 This ongoing debate motivates a continued investigation of the fundamental
properties of this molecule.

241

Because of the importance of this molecule and, in particular, the coordinates wherein the
proton transfer takes place, a study of isolated 7-azaindole should be illuminating. To achieve
this study, anion photoelectron spectroscopy is an attractive technique, since it can determine theelectron affinity (EA) of the corresponding 7-azaindolyl radical. From this measurement, the gas
phase acidity, Δacid Ho (N–H), or the N–H bond dissociation energy, D0(N–H), of 7-azaindole canbe obtained via a thermochemical cycle.43 While there has been a previous anion photoelectron
study by Nakajima et al.,30 only low resolution anion photoelectron spectra of clusters of 7azaindole anion with 7-azaindole were investigated and, thus, the aforementioned properties
could not be deduced.
This chapter presents the first photoelectron spectroscopic investigation of 7-azaindolide,with interpretation aided by quantum chemical calculations. This study provides a measurementof the EA of 7-azaindolyl together with some unexpected results on the electronic structure ofthis species and its corresponding anion. An analysis of the structure and properties of 7azaindolyl is presented and is based on a comparison with the analogous indolyl, recently
investigated by our group.1 The EA of the 7-azaindole dimer was measured previously, but inlow resolution.30 This presents an opportunity for improving the accuracy of this measurement,
as our instrument allows for i) formation of ions that are internally colder and ii) higher
resolution when employing the measurement of slow electrons, when compared to the previous
study. Thus, we also revisit the photoelectron spectroscopy of the 7-azaindole dimer anion.

242

7.2 Methods
7.2.a Experimental
The photoelectron spectra of 7-azaindolide and (7-azaindole)2– are acquired in the
instrument described in detail in Chapter 2. In this chapter we will solely describe the procedures
which are specific to the generation of 7-azaindolide and (7-azaindole)2–, as well as describing
the wavelengths utilized for the acquisition of the photoelectron spectra reported here.
The production of 7-azaindolide and (7-azaindole)2– is achieved by using a mixture of 15
psi-gauge, ~1% 7-azaindole, balance argon, in the main expansion (see section 2.1.b) and thefrequently used mixture (35 psi-gauge, 1% O2, 30% H2, balance Ar) for the generation of OH–
anions, via a pulsed discharge (-2000 V, ~150 μs). The 7-azaindole sample (98%, SigmaAldrich), utilized without further purification, is introduced in the main expansion by flowing 15
psi-gauge of argon gas over the 7-azaindole sample. Due to the low vapor pressure of 7azaindole at room temperature, the sample is heated to approximately 116 °C in order to attainthe desired 7-azaindole partial pressure in the main expansion. In order to minimize condensationof 7-azaindole in the main valve, we heat the valve body to ~70 °C by way of an aluminum block
equipped with a resistive heater, which is thermally insulated from the chamber and surrounds
the main valve body with low clearance, as described in section 2.1.b. This discharge
successfully generates the hydroxide anion (OH–), and with appropriate timing of the gas pulsesof the main and side valves, the two expansions are overlapped and the anions in the side
expansion are allowed to react with the neutral reagents in the main expansion. The 7azaindolide anion is generated from the deprotonation of 7-azaindole by OH–. The resulting mass
spectrum from this ion generation procedure is displayed below in Fig. 7.2.

243

Figure 7.2: Resulting mass spectrum from ion generation procedure described in section 7.2.a.
The displayed range of mass units shows the production of 7-azaindolide and (7-azaindole)2–.
The other major peak in this spectrum, at m/z = 100, represents the CrO3– anion, which is always
produced in this ion source when discharging an oxidizing mixture through stainless steel
electrodes.

244In order to take advantage of the eKE-dependent resolution of the VMI (see section
2.1.e.), we utilize a collection of wavelengths to obtain photoelectron spectra. Generally, ourlaser source is based on a seeded Nd:YAG laser, which outputs 1064 nm light, utilized for
acquiring the high-resolution spectrum of 7-azaindole dimer. For the overview spectrum
presented in Fig. 7.3, we utilize the third harmonic of the Nd:YAG laser (355.4 nm). For thehigher resolution spectra of 7-azaindolide, we employ a 355.4 nm pumped dye laser (QuantaRay, PDL 1) equipped with either Coumarin 440 or Coumarin 460 dyes. The laser is focused into
the interaction region with the ions with a 0.5 m focal length lens.
For the overview spectra presented in this work, the eKE scale is calibrated utilizing the
known photoelectron spectrum of sulfur anion (S–), which provides the magnification factor(correspondence between pixel on the CCD and electron speed) of the VMI at a particular
operational setting. The spectra obtained with the dye laser are calibrated based on themagnification obtained observing the shift of an individual peak in the spectrum of 7-azaindolide
when employing different photon energies, which in turn are measured with a wavemeter (ATOS
λ-meter, LRL–005).
The uncertainties in the measurements in this experiment result from a combination of
the uncertainties in the energy scale calibration, an unresolved rotational contour44,45 and thestatistical error in the peak centering from the fitting of a Gaussian function to each peak. In
addition, due to unresolved vibrational hot bands and sequence bands, it is possible that a peak’s
maximum position does not correspond to the actual individual transition that would be observedin a cold spectrum where only the vibronic ground state of the anion is populated. The accuracyof the assignment thus depends on calculated spectrum. Depending on the number of predictedtransitions under an observed peak, the uncertainty of the measurement can take different values.
245For example, if the calculation predicts the origin transition as dominant, as happens to be thecase in Fig. 7.2, the uncertainty in finding the eBE of the center of the peak is essentially thestatistical error in fitting the peak to a line shape function. The total uncertainty of themeasurement is almost completely due to the uncertainty in the energy scale calibration (seeChapter 2). In the case that many transitions of similar magnitude are responsible for a peak’s
intensity, the true cold transition can, therefore, be located somewhere within a peak’s fwhm. In
this particular work, for reasons that will become clear in section 7.3, we report ourmeasurements as a peak’s center position ± fwhm/2 from a Gaussian fit to the line shape of eachpeak.
7.2.b Theoretical
The assignments in the photoelectron spectra reported here rely in part on a comparison
with calculations of simulated spectra, which are described in this section. Electronic structure
calculations are performed primarily using the Gaussian 09 suite of programs.46 These
calculations consist of geometry optimization and normal mode calculations of the 7-azaindolide
anion and 7-azaindolyl radical, utilizing the B3LYP/aug-cc-pVTZ method/basis set,47,48 andcalculation of excitation energies with TD-B3LYP, also in the Gaussian 09 suite. With thenormal-mode displacement vectors and vibrational frequency outputs of the ab-initio
calculations as inputs, we utilize the PESCAL program49,50 to generate simulated photoelectron
spectra. By employing the Sharp-Rosenstock-Chen method with Duschinsky rotations, PESCAL
generates a spectrum of Franck-Condon (FC) factors which represent transitions from the anion
electronic and vibrational ground state to vibrational states of the neutral state. PESCAL also
includes the calculation of vibrational hot-bands and sequence bands, transitions that originate
from excited vibrational states of the anionic electronic ground state, by obtaining the pertinent246

FC factor and scaling the transitions by the appropriate Boltzmann factor at a set vibrationaltemperature. Here, we calculate hot-band populations at a temperature of 300 K, a temperature
which is 100 K higher than our previous choice with this anion source,51,52 but reasonable when
we consider that our sample, gas lines and main valve body are on average heated toapproximately 100 °C (or 373 K). While this is a conservative estimate of how cold the
expansion is, as a comparison between experiment and calculation will show, we are not able toquantify the vibrational temperature of the ions, and 300 K is a reasonable upper limit, based onpeak widths and intensities of hot and sequence band transitions. In order to provide a directcomparison between calculated and experimental spectra, the individual FC factors are thenconvolved with Gaussian functions whose fwhm is set to the eKE-dependent instrumental
resolution and whose areas are equal to that of the calculated FC factor.
7.3 Results and Discussion
7.3.a Overview spectrum of 7-azaindolide
The preliminary analysis of the overview spectrum of 7-azaindolide begins with acomparison with the previously studied indolide.1 The photoelectron spectrum of indolide,
presents a convenient predictive model for 7-azaindole, since the only difference between the
structure of 7-azaindolide and indolide is an isoelectronic substitution of an N atom for a C–H
group. In the photoelectron spectrum of indolide (upper panel, Fig. 7.1), most of the observed
vibrational activity is in ring distortion modes, a consequence of the geometry change between
the indolide anion and indolyl neutral radical equilibrium structures. The EA of indolyl was
found to be 2.4315(17) eV, measured in high resolution (see lower panel of Fig 7.1). Based on
the relation between 7-azaindolide and indolide, we expect that 7-azaindolide will behave in avery similar manner. Therefore, it is reasonable to expect that ring distortion vibrations would be247responsible for the vibrational activity in the photoelectron spectrum of 7-azaindolide and that
the EA of 7-azaindolyl would be of a similar magnitude, with a vibrational origin transition
located at ~ 2.5 eV. The analysis of the spectrum in the subsequent paragraphs will confirm theaforementioned expectations. In addition, the calculation of the simulated overview
photoelectron spectrum of 7-azaindolide provides quantitative agreement with the experimental
data accessing the ground electronic state of 7-azaindolyl.
The overview photoelectron spectrum of 7-azaindolide obtained with a photon energy of
3.494 eV is displayed in Fig. 7.3. Upon first analysis, we see that the photoelectron spectrum has
an intense origin transition, located approximately around an eBE of 2.7 eV and a first group of
peaks, spanning from 2.75 to 2.90 eV eBE. The spectrum becomes increasingly more congested
above this eBE showing a second broad progression which spans all the way to 3.494 eV eBE.
Upon comparing the spectra of indolide (Fig. 7.2) to that of 7-azaindolide (Fig. 7.3) one sees
remarkable similarity. The photoelectron spectra span approximately the same range of eBEs andhave a very similar overall shape. The 7-azaindole spectrum is more congested than the spectrumof indole in the high eBE range (above 2.9 eV), but not at the origin. This seems to indicate that
there is a greater extent of geometry change upon photodetachment in 7-azaindole. However, theoverall similarity between spectra suggests that our expectations described above are reasonably
correct.
In order to analyze the photoelectron spectrum in Fig. 7.3, and assign the EA of 7azaindolyl we bring attention to the calculated spectrum, also shown in this figure as the red
sticks and the blue trace. This calculated spectrum was shifted so that its origin transition
matched the position of the lowest eBE peak, the EA of 7-azaindolyl. The calculation has
acceptable agreement with the experiment, which allows us to assign the peaks corresponding to248

the EA of the ground state and some of the observed peaks with reasonable confidence. By a
comparison between experiment and calculation, we observe the lowest eBE transition at ~2.68
eV. The EA of 7-azaindolyl can thus be assigned as the eBE value of the center of the origin
peak, which is obtained by fitting the observed peak with a Gaussian function. From the qualityof the fit of the origin peak using a Gaussian function, we can infer that it is likely dominated bya single vibrational transition, namely the transition from the ground vibrational state of theanion to the ground vibrational state of the neutral. However, the fwhm of this peak of 38 meV islarger than expected (24 meV at 0.804 eV eKE, see Chapter 2), which indicates that moretransitions are responsible for its intensity and width. The calculation corroborates theobservations, as it shows the vibrational origin as the dominant transition under the peak andother hot and sequence band transitions which are a factor of at least five smaller than the origin.
Consequently, we can assign the eBE of the center of this peak as the EA of 7-azaindolyl, whichis 2.69(1) eV, using a conservative uncertainty based on the fwhm of the peak.

249

Figure 7.3: Overview photoelectron spectrum of the 7-azaindolide anion obtained with a photon
energy 3.494 eV (black trace) accessing the ground electronic state of 7-azaindolyl. The calculated
photoelectron spectrum is presented as red sticks (FC factors), while the blue trace is the
convolution of these sticks as described in the text. The gray shaded region represents the regionof the spectrum that will be investigated in higher resolution, which is shown in Figs. 7.4 and 7.5.

250

A preliminary vibrational analysis of the spectrum can also be extracted from thecomparison between experiment and theory. The calculation confirms that the observed peaks
are due to vibrational activity in ring distortion modes, consistent with our expectations from thephotoelectron spectrum of indolide. The reasonable agreement between experiment andcalculation quickly ceases to be true, when we move above 2.9 eV eBE. More prominentdisagreements between theory and experiment appear in the region above 2.9 eV eBE, and theagreement gets progressively worse when we move to higher eBEs. Some degree of
disagreement between calculation and experiment is expected at higher eBE (relative to theorigin transition) due to the increasing contribution of anharmonic effects and number of active
combination bands, leading to a high degree of spectral congestion. As mentioned in section 7.2,
the calculation of the photoelectron spectrum employs the harmonic oscillator approximation.
Therefore, it is not surprising that it fails when trying to reproduce features far from thevibrational origin transition. A further vibrational analysis with proper assignments is notpossible with this experimental resolution, and thus the application of a lower photon energy isnecessary. Such experiments would require the use of a wavelength of ~ 430 nm, which isunfortunately out of the range of tunable wavelengths that we have available. For this reason,and reasons that will become clear later in the chapter, we will not provide a detailed vibrational
analysis beyond the qualitative description done in this paragraph.
7.3.b High resolution photoelectron spectra of 7-azaindolide
To obtain a more accurate measurement of the EA of 7-azaindolyl, we take advantage ofthe eKE-dependent resolution of the VMI by employing a photon energy close to thephotodetachment threshold. This approach is the same as that followed for indolide, as depictedin the lower panel of Fig 7.2, where the origin transition is observed and the EA transition251

measured to an accuracy of ±1.7 meV. We expect to attain a similar precision with thisprocedure for 7-azaindole, based upon the simulation presented in Fig. 7.3, which shows that thepeak is dominated by the origin transition. Specifically, we employ a photon energy of 2.719 eV
and detect electrons whose eBEs correspond to the range depicted as the gray shaded area of Fig.
7.3 (0.119 eV). Based on previous experience with this instrument, we can expect a roughly
constant resolution over this energy range, which is, conservatively,  4 meV. In order to form
our expectations about the appearance of the resulting spectrum, we magnified the gray shaded
area of Fig. 7.3 and displayed it in Fig. 7.4. We thus infer that, with a 4 meV resolution, we
would observe a strong peak corresponding primarily to the EA of 7-azaindolyl, and a couple of
low intensity side bands, corresponding to hot and sequence bands. Thus, a high resolution
spectrum should be able to provide an accurate measurement of the EA of 7-azaindolyl. Notethat the widths of the simulation also preclude additional peaks outside of the shaded region

252

Figure 7.4: Comparison between the experimental low resolution overview spectrum of 7azaindolide (black trace) and calculated spectrum (red sticks). The calculated sticks and shifted
are convolved with Gaussian functions (blue trace) whose fwhm are equivalent to the expected
resolution. The spectrum is displayed over the range of eBE which corresponds to the gray shaded
area in Fig. 7.3.

253For a precise determination of the EA of 7-azaindolyl we obtain a photoelectron spectrum
employing the SEVI technique.53 With a photon energy of 2.719 eV, which is slightly above theexpected detachment threshold (2.69(1) eV, based on Figs. 7.3 and 7.4), we collect the spectrum
presented in Fig. 7.5 (green trace). In Fig. 7.5, the eBE axis spans a range of 0.119 eV (from2.719 eV to 2.600 eV), and corresponds to the same magnified region as shown in Fig. 7.4. The
first striking observation we draw from Fig. 7.5 is that five peaks of roughly the same intensity
are observed in the spectrum, which is very different from our expectation of one major peakwith possible small side bands (Fig. 7.4). This observation suggests that this could be a result of
the much higher resolution we attain at this eKE. However, if we contrast the observed spectrumwith the FCF calculation we see essentially no equivalence. More importantly, when comparing
the spectra in Fig. 7.4 with that in Fig. 7.5, we see that the peaks in the high resolution spectrum
span a considerably broader range of widths than what is expected based on the low resolution
spectrum. As the blue circle and double headed arrow indicate, the measured EA, obtained fromthe lowest eBE peak in Fig. 7.3, can be attributed to peaks “A” or γ, but there are three otherpeaks that are considerably outside the range of expected transitions based on both thecalculation and the low resolution experiment (Fig. 7.3). From this figure, it is evident that the
spectrum resulting from photodetachment with 2.719 eV photons is not equivalent to theoverview spectrum acquired with 3.494 eV photon energy, even though they were acquired
under the same experimental conditions. Thus, it is not possible to precisely assign the EA of 7azaindolyl at this stage.

254

Figure 7.5: Photoelectron spectrum of 7-azaindolide acquired with a photon energy of 2.719 eV
and calculated FCF stick spectrum (red sticks). The eBE axis spans a range of 0.119 eV, andcorresponds to the same magnified region as shown in Figs. 7.3 and 7.4. The peak letter labels are
discussed in the text. The double headed blue arrow represents the low-resolution measurement of
the EA of 7-azaindolyl and the corresponding uncertainty.

255

There are several possibilities that could explain the difference between the spectrapresented in Figs. 7.4 and 7.5. The most obvious explanation for this is that the two spectra aredifferent simply due to different experimental conditions, leading to the production of a different
molecule of the same m/z, such as an isomer of 7-azaindolide. This possibility must be discarded
since, upon this observation, we acquired spectra with these two wavelengths (3.494 eV and
2.719 eV) consecutively, employing the same experimental conditions. We also followed thisprocedure on at least three different days and the same result was recovered. The second option
to explain this phenomenon is that in the 3.494 eV spectrum, due to the larger photon flux
attainable and employed at this wavelength, a sequential photon absorption could lead to theobserved discrepancy. This possibility must also be discarded, since lower light intensities wereused (not shown here) and the same result is again recovered. Finally, an explanation could
derive from a photon energy dependent effect, where the photodetachment cross section ischanging with photon energy. The photodetachment cross sections can vary due to the threshold
effect, especially when close to threshold, as described by the Wigner threshold law (see section
1.2). As the subsequent analysis will show, none of the aforementioned phenomena are able toexplain the photon energy dependence observed for 7-azaindolide. This leaves one plausible
explanation, which is that of electron autodetachment and, as the following analysis will show, islikely the cause for the observations here.
Electron autodetachment is a phenomenon different than direct photodetachment as it
occurs through an initial photon absorption by the anion, raising it to an anion excited state
which is close in energy to a neutral state. The excited anionic state then couples to the neutral
state’s electronic manifold with subsequent release of the electron. The detachment probability inthis case is a function of the photon energy, since the different anion states that are initially256accessed each have a distinct absorption cross section. Therefore, instead of the transition
intensity being well described by the FC factor between anion and neutral vibrational
wavefunctions, now the transition intensity derives from the overlap between the anion groundstate wavefunction and the anion excited state wavefunction. The nature of the electron
autodetaching state can be diverse, depending on the strength of the coupling of the anion state to
the electron continuum. Electron autodetachment can occur if the anion is first raised to anelectronic excited state, where the vibrations of this state are well defined. The initial transition
thus takes places in a similar way to that of absorption spectroscopy, a bound to bound transition,
following the appropriate selection rules. This state, when nearly degenerate with the neutralelectronic state, can couple to this surface and the free electron continuum. This process was
rigorously described for atoms in Refs. 54–56. Another form of electron autodetachment is thatof vibrational autodetachment, where an excited vibrational state of the anion is close to or above
the detachment energy. By way of intramolecular energy redistribution, this above thresholdstate can live for some period of time with subsequent detachment forming the lower energy
neutral molecule. This scenario normally happens when the EA of the neutral is on the order of afew vibrational energy spacings (~ 103 cm-1). For examples such as this one see Ref. 57 andreferences within. Electron autodetachment can also be due to a dipole bound state,58–61 wherein
the electron is first excited to a very large orbit of the anion and, at that point, is essentially onlybound to the neutral molecule via the long range dipole interaction (V(r) ~ 1/r2). That is, theelectron is bound to the permanent dipole of the neutral. This type of electron autodetachment ispossible when the permanent dipole of the neutral molecule is ~ 2 Debye or larger.55,62,63
Regardless of the form, the autodetachment cross section should be very sensitive to photon
energy. Examples of the photon energy dependence of the autodetachment features can be seen257

in the photoelectron spectrum of methylphenoxide51 and indolide,1 recently published by ourgroup, in addition to numerous other references.57–60,62,64,65 An investigation of the photon energy
dependence of the photoelectron spectrum will reveal whether or not electron autodetachment is
a probable explanation and provide insight on the nature of the autodetaching state.
In order to further investigate the photon energy dependence of the spectrum, we obtain
spectra with a collection of photon energies, which are specified in Fig. 7.6. We expect that thepeaks that are due to autodetachment will have their intensities significantly altered. Presumably,a change in peak intensities will occur for all peaks with the exception of those which are due to
direct photodetachment. By using a slightly lower photon energy of 2.699 eV (panel (b)), we
observe four peaks. Upon closer inspection we notice that these four peaks seem to be the same
peaks as the ones in panel (c), with the exception of the peak centered at 2.699 eV eBE (peak A).
If we use a slightly higher photon energy of 2.739 eV, similar peaks are recovered, with anapparent new peak, also centered at 2.699 eV eBE, now in a different position relative to theother peaks. This observation indicates that there is one transition which remains centered at
2.699 eV eBE, while the other four peaks (labeled with Greek letters) are shifting in eBE by anamount that is equal to the photon energy difference between spectra. Panels (e) and (f) continue
to show similar four peaks that are shifting in eBE while also displaying a new broad peak that
also shifts in eBE but whose intensity and shape changes. The peak centered at 2.699 eV,
however, still remains in the same position and with similar intensity. To more clearly illustrate
the invariance with respect to photon energy of certain peaks in the spectrum, we have plotted aselected number of these spectra as a function of eKE in Fig. 7.7. The vertical dashed blue lines
correspond to the center of each of the peaks. One can notice that four peaks labeled with Greek
letters are invariant regardless of the photon energy utilized, i.e. their centers remain in the same258

position and their intensities and widths are roughly identical. We shall describe these peaks as“eKE-invariant peaks” from this point forward in the chapter. In order to comprehend what is
occurring in this experiment we should go back to the conservation law described in equation 1.2
in Chapter 1: eKE = h - eBE, which is true for a photodetachment event. Given that thevibrational eigenvalues of the anion and neutral states are immutable, a change in photon energy
must accompany a change in eKE in order to preserve energy conservation if these peaks are infact due to direct photodetachment. The experimental observations, however, show that this issimply not the case, and thus transitions must indeed be due to electron autodetachment. It
should be noted that another method for identifying autodetaching features is by analyzing theanisotropy parameters of the peaks, but unfortunately, an analysis of the anisotropy of the peaks
in Figs. 7.5 and 7.6 showed all features with β ~ 0, which is expected for detachment close to
threshold. This prevents us from distinguishing between peaks that are due to direct
photodetachment and electron autodetachment. The unexpected result from this experimentrequires further analysis, but for continuing the discussion of the photon energy dependence ofthe photoelectron spectrum, we must first proceed with the assignment of the EA of 7-azaindolyl.
The EA of 7-azaindolyl can be obtained accurately and some tentative vibrational
assignments may be made, in spite of the complication of interpreting the spectrum. By
definition, the EA of an atom or molecule is the energy difference between the generalized
ground state of the anion to the generalized ground state of the neutral. Therefore, the lowesteBE peak that is observed due to direct photodetachment can be assigned as the EA of 7azaindolyl. Such peak is labeled “A” marked with the vertical blue dashed line in Fig. 7.6 and as
the downward pointing green arrow in Fig. 7.7. From the center position of this peak (A) and its
measured fwhm we determine the EA of 7-azaindolyl as 2.699(2) eV. This measured value is in259

close agreement with our calculation (2.642 eV, B3LYP/aug-cc-pVTZ) and certainly within theuncertainty preliminary assignment of the EA in the overview spectrum (2.69(1) eV). In
addition, the four eKE-invariant peaks must be due to an active vibration of neutral 7-azaindolyl.
From comparison between the spacing between the peaks of ~ 0.02 eV (~160 cm-1) and ourharmonic vibrational calculation, there are four normal modes that could be attributed to peaks αthough γ, all of which are out-of-plane ring bending vibrations. These vibrations should normallybe symmetry forbidden. However, the autodetachment selection rules are different than those of
direct photodetachment,59,66 so normally FC forbidden transitions might be observed if they are
due to autodetachment. From the attribution of the eKE-invariant peaks to autodetachment, it ispossible that they represent the symmetry forbidden, out-of-plane ring bending vibrations.

260

Figure 7.6: Compiled photoelectron spectra of 7-azaindolide acquired with various photon
energies plotted as a function of electron Binding Energy (eBE). The dashed blue line indicatesthe origin transition that originates from direct photodetachment (EA of 7-azaindolyl), which iscentered at a constant eBE value (2.699 eV) and corresponds to the EA of 7-azaindolyl. The photon
energies utilized in the acquisition of each spectrum are displayed in the top left corner of eachpanel.
261

Figure 7.7: Compiled photoelectron spectra of 7-azaindolide acquired with various photon
energies and plotted as a function of eKE. The photon energies utilized in the acquisition of each
spectrum are displayed on each panel. The vertical blue lines indicate peaks that are observed atconstant eKE as a function of photon energy (see text) referred to as “eKE-invariant peaks” andlabeled with Greek letters. The green downward pointing arrow represents the only feature in these
spectra that is due to direct photodetachment (EA of 7-azaindolyl).
262

A further analysis of the photon energy experiment described above can offer an
explanation for the autodetaching nature of the photoelectron spectrum of 7-azaindolide. First,
we note panel (a) in Fig. 7.6. The spectrum displayed in this panel was acquired with a photon
energy of 2.649 eV. Now that we have assigned the EA of 7-azaindolyl we can see that the sameeKE-invariant peaks are still present, even when we utilize a photon energy below detachment
threshold. These peaks disappear when we acquire the spectrum with 2.329 eV photons, well
below the EA. We also observe the eKE-invariant peaks when utilizing a photon energy of 2.857
eV, which also shows the appearance of a very broad peak at the low eBE side. This experimentshows that the eKE-invariant peaks are observed over a range of at least 0.208 eV. In theoverview spectrum, if we expand the low kinetic energy region (Fig. 7.7, panel (f)), we see thepresence of similar peaks. Although there is the exclusion of peak  and a small shift in theposition of the remaining peaks (, , and ), this suggests that the autodetaching state is being
accessed even with this photon energy (3.494 eV). This results indicates that the autodetachingstates are accessible over the range of at least 0.845 eV! With this information, we can infer that
there must be a very large number of accessible anion excited states over this range of photon
energies for autodetachment behavior to be observed. In addition, the density of states must belarge enough so that changes in the photon energy do not significantly alter the peak intensities.
Finally, there must be a mechanism by which the remaining energy difference which is notconverted to eKE is dissipated, and the energy conservation relation, eKE = hν – eBE, is obeyed.
To explain the first and second points, a plausible explanation is that these excited states of theanion are dipole bound states. We base this assumption on the fact that the observation of eKEinvariant peaks is not unique to this work, as has been observed previously by Wang andcoworkers in the photoelectron spectrum of the phenoxide anion.65,67 In that work, they found a263

collection of three resonant dipole bound transitions, which were observed at constant eKE whenchanging the photon energy. This observation is similar to those reported here. Dipole boundstates, which are the anion analogs to Rydberg states of neutral molecules, are essentially highly
excited hydrogenic states whose energy spacing is very small, almost approaching a continuum.
Therefore, it allows for the very high density of states that are required for the autodetaching
peak intensities to be insensitive to photon energy. We now offer an explanation for our second
point, the eKE-invariant peaks: 7-azaindolide initially absorbs a photon, taking the electron to
one of the many resonant dipole bound states. The highly excited anion can then relax to a
specific state which has significant overlap with the neutral electronic ground state and theelectron continuum, with the concomitant production of neutral 7-azaindolyl plus the freeelectron which is detected. The remaining energy that is not detected as eKE is thus dissipatedthrough a sink of available states, and the measured eKE is equivalent to the energy difference
between an anion excited state and the final neutral state. In this manner, regardless of the photon
energy utilized, the same peak (or collection of peaks) will be observed at a constant value ofeKE.
The existence of such a high density of dipole bound states, however, requires a numberof conditions to be true. It is known that for a molecule to support a dipole bound state, its
permanent dipole moment has to be ~ 2 Debye or greater.58–60,62,63,65,68 In the same experiment by
Wang and coworkers, eKE-invariant features were observed in the photoelectron spectrum ofphenoxide. Those eKE-invariant peaks were attributed to autodetachment via dipole bound states
The phenoxyl radical has a permanent dipole moment of 4.0 Debye, as predicted by electronic
structure calculations, and thus supports dipole bound states.65,67 Thus, for our conjecture on the
autodetachment via a high density of dipole bound states to be valid, the predicted dipole

264

moment of 7-azaindolyl must be high. Indeed, this is the case, as the calculated permanent dipole
moment of 7-azaindolyl is even larger than that of phenoxyl, with a value of 4.6 Debye. Thisfinding corroborates our hypothesis. However, while in the photoelectron spectrum of phenoxidethe eKE-invariant peaks were observed to significantly change in intensity when different photon
energies were utilized, the eKE-invariant peaks here ( through ) do not change in intensity.
This suggests that, while it is reasonable to attribute the eKE-invariant peaks to autodetachment
via dipole bound states, based on a comparison with a previous study,65,67 some observations stillrequire explanation.
Many questions associated with the intriguing features of the photoelectron spectrum of
7-azaindolide still remain. For instance, one question is related to the wavelength thatphotoelectron signal ceases to be observed, i.e. what the autodetachment threshold is. Anotherpertinent question is to know at which value of photon energy we recover the agreement withcalculation observed in the overview spectrum obtained with 3.494 eV photons, as presented inFig. 7.3. Since the B3LYP calculation done here, which does not account for electron
autodetachment, has acceptable agreement with calculation, we postulate that there must be avalue of photon energy at which the experiment and calculation recover the level of agreement
observed in Fig. 7.3, that was simply a photon energy independent calculation. The use of alarger collection of photon energies should allow for the investigation of how much of the total
photoelectron signal is due to direct photodetachment as opposed to autodetachment. From thespectrum shown in Fig. 7.6, we can conclude that most of the photoelectron signal is due to
autodetachment, with a sole peak, the origin transition, being attributed to direct
photodetachment. In the overview spectrum shown in Fig. 7.3, the spectrum seems to be
primarily composed of direct photodetachment transitions, which can be inferred from the265reasonable agreement between experiment and calculation. However, some of the eKE-invariant
transitions seem to be present and there seems to be a broad continuum of states under theentirety of the spectrum. To illustrate this, we fit this apparent continuum with a Gaussianfunction and artificially subtract this Gaussian envelope from the spectrum, as exhibited in Fig.
7.8. The result of this procedure is encouraging, as the relative intensities of the peaks predictedby the calculation are in much better agreement with the experiment. However, this procedure is
not rigorous, and experiments employing a wider range of photon energies, above and especiallybelow 3.494 eV, which are unavailable in our experimental setup, must be accomplished toanswer these remaining questions.

266

Figure 7.8: Upper panel: Overview photoelectron spectrum of 7-azaindolide (black trace) and theGaussian fit (orange trace) to the apparent underlying baseline (see text for details). Lower panel:
Photoelectron spectrum of 7-azaindolide with a Gaussian continuum (orange trace in the upper
panel) subtracted. Both panels display the calculated FC stick spectrum, together with theconvolution of such sticks with Gaussian functions whose widths correspond to the instrumental
resolution.

267

The results described in the paragraphs above are unexpected, and verifying the validityof our conjectures requires further experiments and calculations. A possible experiment iscurrently being planned in collaboration with Prof. Lai-Sheng Wang. Such experiment will have
two major goals: i) employ a cryogenic ion-trap to cool the 7-azaindolide ions and; ii) employ avariety of photon energies that cover the range between our highest energy dye-laser wavelength(2.857 eV) and the UV wavelength utilized for acquiring the overview spectrum of Fig. 7.3(3.494 eV). The former will investigate whether or not the eKE-invariant features aretemperature dependent, in an experiment similar to the one described in Refs. 65 and 67 forphenoxide. The latter will investigate at which point in photon energy the overview
photoelectron spectrum, with reasonable agreement with calculation (Fig. 7.3), is recovered. In
addition, we have initiated a collaboration with theorist Prof. John Stanton, to accurately
calculate the possible autodetachment states of 7-azaindolide and dipole bound states of 7azaindolyl. Currently, our explanation of the unexpected eKE-invariant peaks in thephotoelectron spectrum of 7-azaindolide is qualitative and derives from comparison with similar
species, such as phenoxide, and the analogous indolide, as described in the following section.
7.3.c Comparison between indolyl and 7-azaindolyl
A comparison between the experimentally determined and calculated properties ofindolyl and 7-azaindolyl can offer some interesting conclusions. Indolyl is a convenientcomparison for a number of reasons. First, its chemical structures are remarkably similar, withthe sole difference being an isoelectronic substitution of an N atom for a C–H group in the 7position. Second, the photoelectron spectrum of indolide also presented signatures of electron
autodetachment. There, some peaks displayed a drastic change in intensity when small changes
in photon energy are made and these results were attributed to electron autodetachment.
268

However, the photon energy dependence is not nearly as dramatic as those observed for 7azaindolide. As Fig. 7.2 shows, the acquisition of the photoelectron spectrum with a photon
energy close to detachment threshold met our expectations, as a photon energy close to thresholdessentially just narrows the observed origin peak, when compared to the overview low resolution
spectrum. The spectrum of 7-azaindolide, on the other hand, presents a very different scenario,
where the spectrum not only shows peaks of changing intensity, but also displays the same fourpeaks over a wide range of photon energies, as described in the previous section.
As mentioned in section 7.3.b, for electron autodetachment to be a viable route, someanion excited state must exist with an excitation energy comparable to the energy of a neutral
state. In aromatic molecules, it is common that many optically accessible anion excitedelectronic states exist in an energy range equivalent to the EA of the neutral state. For example,
in indolide1 and methylphenoxide51 we calculated that there are as many as nine opticallyaccessible anion excited states within the energy range between anion and neutral electronic
ground states. This is also the case for 7-azaindole, where we predict five accessible anion
excited states within the same range of photon energies (TD-B3LYP/aug-cc-pVTZ). In order tointerpret the dramatic difference between the photoelectron spectra of indolyl and 7-azaindolyl,
we shall rely on electronic structure calculations. The calculations performed for both moleculeswith the same level of theory show mostly similar properties with one main exception: thecalculated dipole moment. While indolyl has a rather large dipole moment of 2.6 Debye(B3LYP/aug-cc-pVTZ), which deems it capable of sustaining dipole bound states, the calculated
dipole moment of 7-azaindolyl is 4.6 Debye. The consequence of this is that 7-azaindolyl should
be capable of supporting more dipole bound states, which indeed seems to be the case. While thelarger permanent dipole moment of 7-azaindolyl corroborates the larger contribution of electron269

autodetachment to the overall photoelectron signal, the reason for a qualitatively different
autodetaching behavior remains unexplained. The comparison between the photoelectron spectraof 7-azaindolide and indolide, and the properties of 7-azaindolyl versus indolyl shows that aseemingly small change in molecular structure can result in a qualitatively different electronic
structure and lead to a drastically distinct photoelectron spectrum.
7.4.d Photoelectron spectrum of (7-azaindole)2–
The photoelectron spectra of the (7-azaindole)2– were previously obtained by Nakajima et
al. in a magnetic bottle photoelectron spectrometer30 Here, we revisit the experiment with themuch higher resolution attainable with the VMI. In addition, the employment of the dual-valve
ion source likely produces anions that are considerably colder than the previously employedsingle valve discharge. In Nakajima’s experiment, the photoelectron spectrum of (7-azaindole)2–
was observed to be very broad and unstructured. Although there is a disappointing lack of insighton why the spectrum is so broad, we can infer that it is due to either a large degree of geometry
change between anion and neutral equilibrium structures, a large degree of fluxionality of theneutral dimer (i.e. many low frequency vibrations), or both of these effects in conjunction. It isreasonable to assume that the neutral dimer would have very low frequency vibrational modes
since the two monomers are bound by hydrogen bonds. It is also reasonable that the geometry
change between anion and neutral structures is large, with the addition of an electron to theneutral dimer. The ongoing calculations will reveal if these assumptions are valid.
The overview spectrum of (7-azaindole)2– is shown in Fig. 7.9. This spectrum is similar
to that obtained by Nakajima, but with a considerably larger signal-to-noise ratio. As expectedbased on the Nakajima study, the spectrum is broad and unstructured. We observe
photodetachment to both ground and first excited states of (7-azaindole)2. To better investigate
270the low eBE region of detachment for each of these electronic states of (7-azaindole)2, weacquire spectra employing the SEVI technique. The regions of the spectrum obtained in highresolution are shown as shaded areas in Fig. 7.9.

271

Figure 7.9: Overview photoelectron spectrum of (7-azaindole)2–, accessing the ground and firstexcited states of (7-azaindole)2. This spectrum is obtained with a photon energy of 3.494 eV. The
shaded regions represent the magnified eBE ranges that are acquired in high resolution with 1.165
eV (red) and 3.494 eV (gray) photon energies and are displayed in Figs. 7.10 and 7.11,
respectively.

272

Figure 7.10: Photoelectron spectrum of (7-azaindole)2– acquired with a photon energy of 1.165
eV. The resolution ranges from ~ 3 meV to ~ 18 meV as the eKE ranges from 0.0 to 0.5 eV (seeChapter 2).

273

Figure 7.11: High resolution view of a portion of the photoelectron spectrum of (7-azaindole)2–
acquired with a photon energy of 3.494 eV. The resolution ranges from ~ 3 meV to ~ 18 meV as
the eKE ranges from 0.0 to 0.5 eV (see Chapter 2).

274

The high resolution photoelectron spectra can provide more accurate measurements ofthe EA of (7-azaindole)2 and insight on the vibrational activity upon photodetachment. We will
first focus on the high resolution photoelectron spectrum accessing the ground state of (7azaindole)2 acquired with a photon energy of 1.165 eV (Fig. 7.10). This result shows that, evenclose to threshold, when detecting slow electrons, the spectrum is essentially without structure.
Since there are no well-defined peaks, a precise assignment of the EA of (7-azaindole)2 is notpossible. This results require a modification of the conclusion of previous work by Nakajima etal. In their study, where they report EA (7-azaindole)2 = 0.88(12) eV. This precision seems
optimistic, since the large spectral congestion prevents a precise assignment and we believe it ismore appropriate to determine the EA as an upper bound, as is done here. From the spectrum
showed in Fig. 7.10, considering the noise level of ~ 1.4, we can affirm that true photoelectron
signal is detected at an eBE as low as 0.985 eV, with a 3σ confidence level (~99.7%). We thus
report EA (7-azaindole)2 < 1.0 eV. This value is within the upper limit as measured by Nakajima
et al. The excited state high resolution scan leads to similar conclusions, with the establishmentof the term energy as T0 ~ 2.4(1) eV in agreement with the Nakajima et al. measurement.
However, the excited state vibrational progression does seem more structured when compared to
the ground state progression. From the spectrum in Fig.7.11 we observe a progression of threepeaks, spaced by ~0.04 eV, or ~320 cm-1, which were not observed by Nakajima et al. Thesepeaks can potentially be attributed to a vibration of the excited state of (7-azaindole)2, which will
likely be revealed by the ongoing calculations. Overall, the fact that the spectrum reveals itself to
be highly congested even when investigated in high resolution prevents us from extracting
quantitative information and little more insight than that given by Nakajima et al. study. Thus,
further analysis will not be attempted here.

275

7.5 Conclusions
In this chapter the photoelectron spectrum of 7-azaindolide and 7-azaindole dimer anion
are investigated. The photoelectron spectrum of 7-azaindolide, when acquired in low resolution
with a photon energy far from detachment threshold (3.494 eV), showed reasonable agreementwith calculation, which allowed for a preliminary assignment of the EA of 7-azaindolyl, together
with revealing vibrational activity in ring distortion modes. Upon inspection of the origin
transition in high resolution, the spectrum provided unexpected results. Instead of the expected
narrowing of the origin peak, which would have allowed for an accurate measurement of the EAof 7-azaindolyl, a qualitatively different spectrum was obtained. In the high resolution spectrum
instead of the observation of a strong origin transition, as predicted by calculation, a collection offive essentially equally intense peaks, spanning a much wider energy range, were observed. In
addition, other high resolution spectra obtained with a range of photon energies spanning ~0.2
eV showed that four of these peaks were always observed at the same eKE, regardless of thephoton energy employed, an apparent violation of energy conservation. The unexpected eKEinvariant peaks are attributed to electron autodetachment via a high density of dipole boundstates, which explains the apparent shift in electron binding energies in the photoelectron
spectrum. The high resolution spectra allows for a precise determination of the EA of 7azaindolyl as 2.699(2) eV. A comparison between 7-azaindolyl and the previously investigatedindolyl1 shows how two very similar molecules, where the sole difference is an isoelectronic
substitution of an N atom for a C-H group, can have qualitatively different properties. Of all theproperties, the permanent dipole moment is highlighted, as it is calculated to be 2.6 Debye inindolyl and 4.6 Debye in 7-azaindolyl, a change that could explain the much more prevalent
autodetachment signatures in the photoelectron spectrum of 7-azaindolide when compared to276

indolide. Finally, the photoelectron spectrum of 7-azaindolode dimer anion, previously
investigated by Nakajima,30 is revisited in higher resolution. The photoelectron spectrum of the
dimer showed an unstructured broad spectrum, regardless of the increase in resolution. These
results indicate a large degree of fluxionality of the neutral dimer vibrational structure and very
little information can be obtained from the spectrum. However, we do offer a measurement of
the EA of the neutral dimer, establishing the bound of EA < 1.0 eV.

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299

APPENDICES
Appendix I
Wolfram Mathematica (.nb extension) program to calculate the approximate times-offlight of ions in our instrument, based on the originating position in the initial stage of themass spectrometer.

Defining constants and equations in this experiment
ev:=1.6 10^-19 (*electron charge in Coulomb*)
amu := 1.66 10^-27 (*atomic mass unit in kg*)x1:=0.084 (*m*)(*distance from extraction plate to ground plate*)x2:=0.051(*m*)(*distance from the ground plate to the enf of theacceleration stack*)x3:=2.03(*m*) (*remainder of the flight tube length*)t0[x_,m_,v_,d1_]:=(d1-x)*Sqrt[2 (m*amu)/(ev*v(1-x/d1))](*Initialextraction segment*)
v0[x_,m_,v_]:=Sqrt[2 (ev*v(1-x/0.084))/(m*amu)] (*velocity after
first stage*)t1[d2_,m_,d1_,x_,v_]:=(m*amu*v0[x,m,v]*d2+Sqrt[(d2^2*m^2*amu^2+2*d2^2*2300*ev*m*amu)])/(2300*
ev)(*acceleration stack*)t3[d3_,m_,v_,x_]:=d3*Sqrt[(2*m*amu)/(ev*(2300+v(1x/0.084)))](*free flight path*)f[d2_,m_]:=Sqrt[d2^2*m^2*amu^2+2*d2^2*2300*ev*m*amu] (*fordebugging*)

300

Flight time from extraction to ground plate
Manipulate[t0[x,16,v,x1],{x,0,0.08399},{v,500,1000}]

Velocity after first acceleration stage
Manipulate[v0[x,16,v],{x,0,0.083999},{v,500,1000}]Time from ground plate to end of acceleration stack
Manipulate[t1[x2,16,x1,x,v],{x,0.0001,0.08399},{v,500,1000}]

Approximate total TOF in microseconds for m/z=16
Manipulate[(t0[x,16,v,x1]+t1[x2,16,x1,x,v])*10^6+15,{x,0.000001,0.0839999},{v,100,1500}]

301

Appendix II
The choice of active space in CAS SCF calculations: A case study applied to aminomethoxy
H2C(NH2)OIn this appendix, I will briefly summarize the procedure taken in order to choose theactive space in the CAS calculations performed for aminomethoxy, H2C(NH2)O•.
I ran single point energy calculations (ground and excited, SA-MCSCF) for a collectionof active spaces. The geometry chosen was the neutral ground state optimized structure at the
CCSD(T)/aug-cc-pVTZ level of theory. The aminomethoxy radical has a total of 25 electrons.
These electrons would be distributed in the first 13 orbitals of the molecule. The qualitativedescription of the orbitals is, in increasing energetic ordering (quantities in parenthesis are theorbital occupancy):

1. O 1s (2)2. N 1s (2)3. C 1s (2)4. σ C-H (2)5. σ O-C-N (2)6. σ(pz) C-O (2)7. π C-O (2)8. N sp3 (2)9. σ C-N (2)10. σ C-N (2) + σ N-H (2)11. σ C-O (2)12. O py (1.5)
13. O px (1.5) → HOMO, (has fractional occ. because of State Averaging (SA))----------------------14. σ* C-O (0) → LUMO
15. N 2py (0)16. σ* O-C-N (0)17. etc…

302

The order and the “looks” of the orbitals might change a little with different active
spaces, but are generally qualitatively similar. One thing to keep in mind is that the mostimportant thing to look for are the actual wavefunctions (linear combinations of the molecularorbitals) and not the orbitals.
The predicted ground and first electronic excited states for this molecule are the orbital
configurations which have the unpaired electron in either the O px or the O py orbitals,
respectively. A logical first choice for the active space is, therefore, only to include the HOMO
and the HOMO-1, namely the O px and O py orbitals, since they are the ones to participate in the
excitations. This means that all doubly occupied orbitals are not part of the active space. Keep inmind that in the way this was done, these closed orbitals are still optimized, even though they are
not part of the active space.
The table below shows the active spaces used, with the corresponding ground and excitedstates energies. The notation is the following: cX_oY, meaning X orbitals are closed (but
optimized), and Y orbitals are allowed to have occupancy (this doesn’t mean that they will haveoccupancy!). Number of orbitals in the active space (AS) is therefore AS=(Y-X). So on to thetable:

303

closedoccupiedactivespace

Ground(Hartree)Excited(Hartree)

Delta E
(eV)

10

Elec.
in
active
space
19

3

13

3

14

-169.51949610-169.51048853

0.24510841119-169.53821803-169.52963943

0.2334355

3

16

13

19

-169.59472127-169.58663664

0.2199939

3

17

14

19

-169.61482451-169.60664608

0.2225465

6

14

8

13

-169.53845983-169.52988445

0.2333479

6

16

10

13

-169.59382497-169.58563398

0.2228881

6

19

13

13

-169.66677021-169.65479687

0.3258111

9

13

4

7

-169.51949610-169.51048854

0.2451081

9

14

5

7

-169.54433355-169.53262498

0.3186063

9

19

10

7

-169.61343695-169.60380722

0.2620382

10

13

3

5

-169.51949610-169.51048854

0.2451081

10

14

4

5

-169.54164901-169.53258556

0.2466290

11

13

2

3

-169.51949610-169.51048854

0.2451081

We can see here that, with the exception of o few outliers, the energy difference is pretty
invariant with the choice of the active space. In order to understand what’s going on in each ofthese calculations we have to look not only at the energies, but what is the active space doing to
the actual wavefunctions that result in the eigenvalues for each of the states. In order to do this
we look at the Configuration Interaction (CI) vector coefficients given by Molpro for each of thecalculations.
Starting from the top, with our smallest active space, o11_c13, the wavefunctions are
represented bya2

2aState 1a2

1.00000-0.0000268

State 22a0.0000268

1.00000304

This reads, State 1 is defined by almost exclusively (CI coefficient of 1) the a2
configuration, which means the unpaired electron (a) is located in the first active orbital (O px)
and the second active orbital (O py) is doubly occupied. The story is analogous for State 2,
which now has the unpaired electron in the (O py) orbital, with a doubly occupied (O px).
If we then expand the active space to include all bonding orbitals, leaving only the O, C
and N 1s orbitals closed, we obtain the following CI vector.
State 122222222a2

1.0000000 0.0000000

State 2222222222a-0.0000000 1.0000000

This shows that the inclusion of more of the occupied orbitals did not change the character of thestates, and they are still represented by exactly the same configurations. The orbitals that wereallowed to be excited just remained doubly occupied and the energy is the same. The
wavefunction representing these states therefore, is also the same as in the case that we had 11
closed orbitals, resulting in basically the same eigenvalues.
Now we move on to including virtual orbitals in the active space, i.e. the LUMO andorbitals above. If I just include the LUMO in the active space the CI vectors I get are thefollowing:
State 1222222222a0

0.9951042 -0.0204313

State 222222222a20

0.0204170 0.9949922

State 3222222202a2-0.0955207 0.0019397

State 422222220a22-0.0019761 -0.0953048

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Again, the ground and excited states have the same representation, where the unpaired
electron is in either non-bonding O p-orbitals, hence the energy difference between State 1 andState 2 is very similar to the one where we don’t include the LUMO. The difference here is thatnow we have contributions from excitations from the doubly occupied inner orbitals to the
LUMO, therefore, changing the active space has a bigger effect on the energy when the LUMO
is included. Regardless, the contribution of these other configurations is minor so it seems that
this molecule does not have a strong multireference character. Therefore, for a QUALITATIVE
description of the molecule (does not guarantee that the energetics will be quantitative) even thesmallest active space tested should be sufficient.
After a lot of exploration, we decided to go with the CAS(5,4) active space, namely thec10_o14, which closes (but still optimizes) the first 10 core orbitals and includes 1 unoccupied
orbital in the active space. This active space is the same as the one utilized by Dillon and
Yarkony for hydroxymethoxy, ethoxy and isopropoxy. Again the configuration of the first 2
states is essentially the same as the previous active spaces, hence, the energy is again very
similar. This shows that the aminomethoxy radical does not have a strong multireference
character. Thus, the difficulty in calculating the photoelectron spectrum is likely due to thevibronic coupling between the ground and first excited neutral electronic states, as discussed in
Chapter 6.

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Appendix III
Finding image centers for a proper reconstruction: A case study of the CH3- VMI
photoelectron spectrum.
In the 1064 nm CD3– images, the signal-to-noise is worse than in CH3-; therefore, theability to find the center by just our eyes is not accurate to a pixel. To verify what effect this has
on our spectra and analysis, the center was initially chosen by eye to be {692,592} and then wevaried the x and y center positions for a total of 8 different centers. A full analysis was carriedout for each image center, paying close attention to three things: (1) agreement between energy
scales (O2 and internal CD3 calibration); (2) variation of EAs between determinations (e.g. EA
from v = 4 minus known vibrational frequencies or the EA from the position of v=0 peak); and(3) any observed systematic shift in the determination of the EA. The initial analysis was carriedout with full image reconstructions, and then we replaced one of the quadrants that had poor
resolution and carried out the analysis again with the quadrant replaced image for the best
centers we found. Choosing the correct image center is essentially asking how well we know
where our zero-kinetic energy spot is located in the image. This will greatly affect the absoluteenergy scaling (and obviously the resolution following reconstruction), but not the relative
energy scaling (so the vibrational frequencies and inversion splitting is not affected by this, but
the EA determination is).
Below are three tables showing analysis of three different image centers, specificallyfocused on the EA determination. These are illustrative of the process we went through tovalidate our chosen image center and our new understanding of the error associated withchoosing an image center. The three image centers described below are pixels located:

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Table A3{691,591}

Table A1
{692,592}
Table A2
{692,591}

Table A1: EA determinations for a wrong image center {692,592}; the initial center, picked byeye, and resulted in what appeared to be a very nice reconstruction.
Center: {692,592}

Calibration Species
O2

CD3

EA determination

calibration

calibrationfrom v = 00.08580.0721from v = 1

0.08490.0719from v = 2

0.08430.0720from v = 3

0.08380.0725from v = 4

0.08330.0724

Average EA

0.08410.0722Standard Deviation

0.00070.0003Note that there is no agreement between the different energy scales and there is a clear
systematic shift in the EA determination using the external calibration species. This shows thatthe center is not properly chosen. Since the best CH3, O2, and CD3 data were all taken on thesame day, and we’ve already rigorously tested the CH3 data, we know that the O2 energy scale isgood. In addition, the O2 energy scale calibration is based on peak spacing, but is also consistent
with the reported PES peak positions.
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Table A2. Example with 1 pixel away {692,593}.
Center: Symm. {692,593}

Calibration Species

EA determination

O2
calibration

CD3
calibrationfrom v = 00.08350.0767from v = 1

0.08430.0767from v = 2

0.0836

0.0765from v = 3

0.08360.0771from v = 4

0.08250.0764

Average EA

0.08350.0766

Standard Deviation

0.00080.0003

There are no large systematic shifts in the EA determinations, but the energy scales still
do not agree with each other. Other centers had agreement in energy scales but showedsystematic shifts and poor resolution following reconstruction.

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Table A3: Best center {691,593}, after symmetrization (data used in the paper).
Symm. {691,593}

Calibration Species

EA determination

O2

CD3

CH3

from v = 00.08340.08380.0825from v = 1

0.08360.08320.0820from v = 2

0.08410.08380.0826from v = 3

0.08320.08290.0816from v = 4

0.08380.08340.0822Average EA

0.08360.08340.0822Standard Deviation

0.00030.00040.0004

Total Average

0.0831

Total St dev

0.0007Here, the energy scales agree with each other to about 0.001 eV. We also show the results fromusing CH3 as the calibration species for additional verification. The agreement of the energy
scales and the absence of a systematic shift in the energy scale shows that our zero-kinetic
energy release point, i.e. the image center, is the most accurate we can possibly be, since a 1
pixel change results in a disagreement. Moreover, this center also results in a reconstruction of
acceptable resolution, as seen in Figure 2 in the manuscript and shown below.
Note that the numbers in the tables are averages, without any statistical weighting. The
weighted analysis results in an EA of 0.0833 eV, with an uncertainty of 0.0007 eV. However, we
can potentially still have a wrong center, by an amount smaller than 1 pixel. Since each pixel atthis kinetic energy range corresponds roughly to 0.005 eV, we can have an error bar of ±½ pixel,
or ±0.0025 eV. Adding the uncertainties in quadrature, we get EA(CD3) = 0.083(3) eV.

310