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A multifaceted investigation of tris(2-phenylpyridine)iridium

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A multifaceted investigation of tris(2-phenylpyridine)iridium

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Content A Multifaceted Investigation of Tris(2-phenylpyridine)iridium by Jordan R. Fine A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMISTRY) May 2013 Copyright 2013 Jordan R. Fine ii DEDICATION To my wife Lydia for her love and devotion To my mother Sherri for pushing me to achieve what she knew I could And my puppies for showing me what unconditional love is iii ACKNOWLEDGMENTS I would not have been as successful in my graduate career had it not been for the help and support of my family, friends, and coworkers. Research is full of setbacks and failures that would make even the supremely confident question their abilities. I am therefore fortunate that I had the encouragement of so many wonderful people to continue to push forward. I am forever indebted to my advisor Curt Wittig. Those in the chemical physics community know that Curt is a talented and insightful scientist, but Curt is also a generous and thoughtful individual. He has shown me that he cares about me and my future. There were times when Curt would push me to excel, whether I wanted to or not, but I know it was because he wanted me to accomplish what was within my potential. I could not have asked for a better mentor. I would also like to thank Professors Andre Vilesov, Hanna Reisler, Anna Krylov, Steve Bradforth, and Vitaly Kresin. I am fortunate to have learned from their teaching and guidance. I hold each of them in high regard. During my time at USC I was fortunate to have worked alongside so many wonderful people. Among these are Dr. Christopher Nemirow, Dr. Zhou Lu, Dr. Oscar Robolledo-Mayoral, Jaimie Stomberg, Stephanie McKean , Lee Ch’ng, Dr. Chirantha Rodrigo, Dr. Russell Sliter, Dr. Luis Gomez, Dr. Sergey Malyk, Anton Zadorozhnyy and Bill Schroeder. I am happy to know each and every one of you. Thank you for making graduate school such a great experience. iv I would also like to thank the staff of the USC Chemistry Department and the USC Machine shop. They were instrumental in my success and I am extremely grateful for all of their hard work. Finally, I want to thank my family. Graduate school and life in general would be much harder if I did not have your love and support. I hope you know how much you all mean to me. v TABLE OF CONTENTS Dedication ii Acknowledgments iii List of Tables vii List of Figures ix Abstract xxii Chapter 1: Introduction 1 1.1 Chapter Contents 3 1.2 References 8 Chapter 2: Experimental Techniques 10 2.1 Photoionization 10 2.1.1 Stepwise Ionization Spectroscopy 13 2.1.2 Fragmentation 17 2.2 Time-of-Flight Mass Spectrometry 19 2.2.1 Overview 19 2.2.2 Resolution 22 2.3 UV-Vis Absorption Spectroscopy 24 2.4 Helium Droplet Matrix Isolation 30 2.4.1 Helium Droplet Production and Characteristics 31 2.4.2 Pulsed Helium Droplet Production 34 2.4.3 The Pick-Up Process 35 2.5 Electron Impact Ionization 36 2.5.1 Interpretation of σ max 38 2.6 Production and Detection of the Ethynyl Radical 40 2.6.1 Experiments and Results 44 2.6.2 Discussion 52 2.6.3 Conclusion 54 2.7 References 56 Chapter 3: Photoionization of Tris(2-phenylpyridine)iridium 64 3.1 Introduction 64 3.2 Experimental Methods and Results 73 3.2.1 Multiphoton Ionization 78 3.2.2 Two-photon Ionization 82 3.2.3 One-photon Ionization 88 3.3 Discussion 88 3.3.1 Low-lying Electronically Excited States 90 3.3.2 Photoionization 96 3.3.3 Ion Yield Spectrum 99 3.3.4 Disposition of Vibrational Energy 100 vi 3.3.5 Comparison with Electronic Structure Theory and Previous Work 102 3.4 Summary 106 3.5 References 108 Chapter 4: Electronic Structure of Tris(2-phenylpyridin)iridium: Electronically Excited and Ionized States 112 4.1 Introduction 112 4.2 Computational Details 115 4.3 Results and Discussion 117 4.3.1 Equilibrium Structures 118 4.3.2 Molecular Orbitals 125 4.3.3 Ultraviolet Absorption Spectrum 132 4.3.4 Phosphorescence from T 1 137 4.3.5 Vibrational Energy Distribution 138 4.4 Summary 143 4.5 References 146 Chapter 5: Investigation of He 4 + Formation via Electron Impact and the Photoionization of Tris(2-phenylpyridine)iridium in Helium Droplets 149 5.1 Introduction 149 5.2 Experimental 150 5.3 Results and Discussion 152 5.3.1 Droplet Sizes 153 5.3.2 Pulse Profile 158 5.3.3 Current Dependence 161 5.3.4 Electron Energy Dependence 162 5.3.5 Pulse Duration Dependence 164 5.3.6 Photoionization of Tris(2-phenylpyridine)iridium in Helium Droplets 170 5.4 References 177 Chapter 6: Future Work 179 6.1 Introduction 179 6.2 Experimental 180 6.3 Discussion 184 6.4 References 186 Bibliography 187 Appendices 200 Appendix A: A Brief Introduction to Density Functional Theory 200 Appendix B: Supplementary Material for Chapter 4 206 Appendices References 241 vii LIST OF TABLES Table 2.1 Ionization potential and C−H bond energy for acetylene and the ethynyl radical. The 193.3 nm absorption cross-section of acetylene is for room temperature. 45 Table 3.1 Bond lengths (Å) for S 0 , T 1 , and D 0 states of Ir(ppy) 3 . 103 Table 4.1 Bond lengths (Å) for S 0 , T 1 , and D 0 states of Ir(ppy) 3 . 119 Table 4.2 Bond lengths (Å) for S 0 and D 0 mer-Ir(ppy) 3 . 121 Table 4.3 Koopmans IE's (eV) for the six highest energy occupied MO's of fac-Ir(ppy) 3 . 125 Table 4.4 BNL percent spin density for fac-Ir(ppy) 3 at the S 0 , T 1 , and D 0 equilibrium geometries. For T 1 and D 0 , only the main contributions are listed. 126 Table 4.5 Vertical and adiabatic IE's (eV) for fac-Ir(ppy) 3 from S 0 and T 1 states at their equilibrium geometries 131 Table 4.6 Orbital character and leading amplitude for the four lowest energy triplet states at the S 0 and T 1 equilibrium geometries: Energies are relative to that of S 0 at its equilibrium geometry. 133 Table 4.7 Orbital character and leading amplitude for the three lowest energy singlet excited states at the S 0 and T 1 equilibrium geometries. Energies are relative to that of S 0 at its equilibrium geometry. 134 Table 5.1 Ir(ppy) 3 vapor pressure vs. temperature 176 Table B.1 Z-matrix for S 0 equilibrium geometry 207 Table B.2 S 0 Standard Nuclear Orientation (Å) 209 Table B.3 Z-matrix for T 1 equilibrium geometry 211 Table B.4 T 1 Standard Nuclear Orientation (Å) 213 Table B.5 Z-matrix for D 0 equilibrium geometry 215 viii Table B.6 D 0 Standard Nuclear Orientation (Å) 217 Table B.7 Shell populations of first six HOMO's at S 0 equilibrium geometry 219 Table B.8 Mulliken charges and spin density the S 0 equilibrium geometry 224 Table B.9 Mulliken charges and spin density the T 1 equilibrium geometry 226 Table B.10 Mulliken charges and spin density the D 0 equilibrium geometry 228 Table B.11 BNL TDDFT excited states – S 0 equilibrium geometry 230 Table B.12 ωB97X TDDFT excited states – S 0 equilibrium geometry 234 Table B.13 Calculated vibrational frequencies for the S 0 geometry. B3LYP – lanl2dz for Ir, 6-31+G* for all other atoms 236 ix LIST OF FIGURES Figure 1.1 Ground electronic state structure for Ir(ppy) 3 ’s most stable isomer (fac-Ir(ppy) 3 ). H atoms are omitted for clarity. Color scheme: green = Ir; blue = N; gray = C. 1 Figure 1.2 The diagram illustrates the effect of triplet harvesting. In organometallic compounds with transition metal centers, such as Ir(ppy) 3 , excited singlet states relax to a low lying singlet state where they show a fast intersystem crossing (ISC) to the lowest triplet state (T 1 ). On the other hand, excited triplets states simply trickle down the triplet manifold to the lowest triplet state. Thus, T 1 harvests both singlet and triplet excitation energy and can efficiently emit. In principle, a triplet emitter can — in the limit of vanishing radiationless decay — exhibit 100% luminescence quantum efficiency . 2 Figure 2.1 Three possible multiphoton excitation schemes are shown above. (a) One-color multiphoton ionization resonance enhanced at the initial transition. (b) A double resonance variant of REMPI; ν 1 is fixed to resonantly enhance the initial two-photon transition while ν 2 is scanned to probe the spectroscopy of the second transition. (c) Two-color multistep photoionization is shown, where ν 1 is fixed and ν 2 is scanned to reveal the various ionization thresholds. 12 Figure 2.2 Schematic representing a stepwise one-color two-photon photoionization pathway. 0 represents the ground state, 1 is a real intermediate absorbing state, and 2 is a state that lies above the ionization energy. The absorption cross- sections for transition 10 ← and 21 ← are σ 1 and σ 2 , respectively. The photon energy (hν) is considered much larger that the thermal energy (k B T). 14 Figure 2.3 Depiction of two fragmentation schemes of multistep ionization. (a) Continued absorption by the parent ion opens up a variety of dissociation channels, which can eventually lead to atomization. (b) Dissociation of the intermediate state will lead to neutral fragments that can be ionized and/or dissociate further. 18 x Figure 2.4 Schematic of a basic TOF system. The interaction region has a height of 2s and is between the repeller and extractor plates, which hold voltages V 1 and V 2 , respectively. A second acceleration region is above the interaction region and has a height of d. The field free region allows the accelerated ions of different mass time to separate. Ions that collide with the micro-channel plate detector (MCP) cause a cascade of electrons creating a small current, which is detected by an oscilloscope monitoring the MCP. 20 Figure 2.5 Diagram showing the origin of the decreased TOF mass resolution as a result of the initial kinetic energy distribution U 0 . (a) Two identical particles with translational energy U 0 but in opposite directions are shown. A is moving away from the detector, B is moving toward the detector. (b) The applied field must counter the initial kinetic energy of A causing it to reverse direction and return to its initial position with energy U 0 towards the detector, whereas B is simply accelerated toward the detector. 23 Figure 2.6 Basic operation of a standard spectrophotometer. A tungsten lamp generates a continuous white light source that is collimated and passes through the absorbing medium. The transmitted light is then scattered using a rotatable grating and slowly passed over a photodetector. Current generated from the transmitted light striking the detector is sent to a recorder that displays the resultant spectrum. 26 Figure 2.7 A natural log plot of the Ir(ppy) 3 vapor pressure divided by P 0 (1 atmosphere) vs. temperature in centigrade. 28 Figure 2.8 Depiction of the (a) UV-Vis vacuum cell, (b) and copper sleeve with end caps. The Ir(ppy) 3 must be added to the cell prior to evacuation. After the cell has been thoroughly pumped, the side port is sealed and the cell is inserted into the sleeve in the order indicated in (c). 29 Figure 2.9 Plot of the gas phase Ir(ppy) 3 absorption spectrum at 270 °C. 30 Figure 2.10 The pressure-temperature phase diagram for 4 He. Dashed lines show typical trajectories for supercricital (upper) and subcritical (lower) expansion isentropes. 32 xi Figure 2.11 Average number of helium atoms per droplet for various backing pressure and nozzle temperatures. The right axis corresponds to the average droplet diameter under the same expansion conditions. Images of the subcritical (lower) and supercritical (upper) expansions are shown. 33 Figure 2.12 The total absolute cross-sections for (a) helium and (b) acetylene along with their corresponding theoretical fit calculated using the BEB method. The electron energy at the point of maximum cross-section is displayed for both experiment and BEB. 37 Figure 2.13 Image showing how the polarizability volume acts as an the effective cross-section for the process of an incoming electron ejecting a bound electron from a target species. 38 Figure 2.14 Schematic representation of the potential energy surfaces involved in the 193.3 nm photodissociation of acetylene. Formation of excited C 2 H (A 2 Π) occurs via two possible routes: (a) tunneling to the continuum through the potential barrier on the A 1 A” curve and/or (b) through internal conversion to the dissociative 2 1 A’ state. Formation of vibrationally excited C 2 H (X 2 Σ + ) occurs by (c) internal conversion to the 2 1 A’ state followed by subsequent diabatic surface hopping to the 1 1 A’ state at the 2 1 A’/1 1 A’ avoided crossing. 42 Figure 2.15 Calculated adiabatic potential energy curves for the lowest 2 Σ + and 2 Π states of C 2 H as functions of the C−H bond length. Full lines represent Σ + symmetry, and dashed lines Π symmetry. 43 Figure 2.16 Experimental apparatus used for acetylene photolysis. The base pressures were, 2x10 -6 (torr) in the expansion chamber, 10 -7 (torr) in the interaction chamber (where the gas was ionized), and 10 -8 (torr) at the MCP detector. The total length of the TOF was 1 m and voltages of 1500, 1350, and -3500 were used for the repeller, extractor and MCP bias, respectively. The nozzle was set approximately 2 cm from a 1 mm diameter skimmer and ~ 15 cm from the interaction region of the TOF. 44 xii Figure 2.17 Calibration line for the actual electron energy as a function of the electron gun control panel electron energy. The ionization potentials for acetylene and helium as well as appearance potentials of doubly ionized argon and the C 2 H ion were used as references for the actual electron energy. 46 Figure 2.18 Pulsed valve expansion profile using argon. The initial part of the profile is consistent with the 250 us open time. The long tail is attributed to a mechanical delay in the nozzle’s closing. 47 Figure 2.19 (a) TOF mass spectrum of acetylene seeded in argon, taken with an electron energy of 60 eV. The inset in (a) is magnified by 4x to better show the acetylene cracking pattern. (b) TOF spectra at several electron impact energies demonstrate the disappearance of the C 2 H peak at sufficiently low electron energy. An electron energy of ~18.4 eV was used in all subsequent experiments to better discern photolyzed C 2 H signal from that of fragmented acetylene. (c) The acetylene depletion signal when photolysing directly in front of the nozzle, as opposed to (d), which is the depletion when photolysing in front of the skimmer ~1.5 cm downstream. The FWHM of (c) is roughly 30 μs while that of (d) is only 15 μs, indicating that photolysing in front of the nozzle disturbs the supersonic expansion. 49 Figure 2.20 (a) Schematic showing the three regions where photolysis of acetylene was attempted. (b) Representation of the suprasil tube attached to the nozzle. 50 Figure 2.21 (a) Acetylene and ethynyl peaks recorded with 193.3 nm beam directly in front of ionization region of TOF. Pure acetylene and a laser power was ~4.9 J cm -2 was used for this measurement. (b) Difference spectrum for laser on minus laser off. The inset in (b) is the region of the difference spectrum corresponding to C 2 H + , between 2.2 and 2.35 μs, and shows that a very small amount of photolyzed C 2 H is present. 52 xiii Figure 3.1 This schematic indicates important features of an OLED (not to scale, typical dimensions are given in parentheses). Electrons are injected from the cathode through a thin protection layer into the electron transport layer, which typically consists of an amorphous organic material. Holes are injected into the hole transport layer from an optically transparent anode (typically an In 2 O 3 / SnO 2 composite) that permits light to exit the device. In the recombination and emission layer, electron-hole pairs form excitons that relax to the dopant excited states (indicated by an asterisk * ) that emit photons. 65 Figure 3.2 (a) Organic molecules (negligible spin-orbit coupling) emit only from the lowest excited singlet S 1 . Because T 1 → S 0 emission is extremely weak, triplet excitation is lost through radiationless decay rather than photon emission, and consequently the maximum quantum yield is 25%. (b) In triplet harvesting, electron-hole recombination leads to exci- tons having a triplet-to-singlet population ratio of 3:1. Excitation cascades down the triplet and singlet manifolds, with internal conversion (IC) and intersystem crossing (ISC) resulting in excitation ultimately residing in the lowest triplet, 3 MLCT (T 1 ), which emits photons. An organometallic compound (in which spin-orbit coupling (SOC) is strong) such as Ir(ppy) 3 experiences relatively fast ISC and efficient T 1 → S 0 phosphorescence. This can result in quantum yield approaching 100%. 67 xiv Figure 3.3 (a) Photoexcitation of ligand-centered 1 LC(π π*) is accompanied by rapid radiationless decay: IC to 1 MLCT followed by ISC to the levels labeled T 1 (energies are not to scale). (b) Absorption spectrum of Ir(ppy) 3 in dimethyl- formamide at 414 K. Note the large σ 1 absorption cross- sections (i.e., units of 10 -16 cm 2 ). The yellow boxed region, 34 150 – 35 775 cm -1 (4.234 – 4.435 eV), corresponds to the portion of the 1 LC ← S 0 system examined in this work. Inset: changing the temperature over the range 295 – 414 K has a minimal effect on the absorption spectrum in the en- ergy range of interest; only slight broadening is observed. In order, from the top trace, the temperatures are: 295, 333, 353, 383, 408, and 414 K. The vertical axis in the inset is not labeled, as the curves are offset from one another for clarity. They are nearly identical over the indicated range. (c) Absorption spectrum of solution phase 2-phenylpyridine, adapted from reference 30. The 1 LC ← S 0 feature is analo- gous to the one in Ir(ppy) 3 . 70 Figure 3.4 Schematic of the experimental arrangement: (a) The main vacuum chamber has a base pressure of 2x10 -9 Torr. (b) Details of the time-of-flight mass spectrometer (TOFMS): Typical mass resolution was m /∆m ~ 200. 74 Figure 3.5 With 415 μJ cm -2 of 35 673 cm -1 (4.423 eV) radiation, only the Ir(ppy) 3 + parent ion is observed (vide infra Figure 3.8). The Ir(ppy) 3 + peak consists of contributions from the major isotopologues (see text for details). (a) The experimental curve (red) is the average of several traces, each of which is comprised of ~ 1000 individual spectra. The blue curve is obtained using the natural isotope abundances and assigning a 2.35 amu FWHM to each mass, as indicated in (b). This fits the experimental trace [red curve in (a)] rather well. 76 Figure 3.6 At a fluence of 1500 mJ cm -2 and photon energy of 35 774 cm -1 (4.435 eV), the mass spectrum is dominated by Ir + , albeit with an IrC + contribution that is ~ 15% as large as that of Ir + . Contributions from Ir(ppy) 2 + and Ir(ppy) 3 + (not shown) are smaller by an order of magnitude. The hydrocar- bon peaks are due to impurity. 79 xv Figure 3.7 (a) Action spectrum obtained by monitoring Ir + while varying the photon energy. Laser fluence was approximately 1400 mJ cm -2 . (b) Expanded view: The vertical dashed lines indicate transitions of (neutral) atomic iridium. 37 Note that the spectra are not offset from zero, i.e., there is an underlying broad continuum. 81 Figure 3.8 Mass spectra recorded at different fluences: The laser fre- quency is 35 357 cm -1 (4.383 eV). At low fluence (bottom trace), photoionization produces the Ir(ppy) 3 + ion exclusive- ly. As the fluence is increased, fragmentation results in the appearance of the Ir(ppy) 2 + ion. At high fluence (top trace), the Ir + peak dominates, indicating severe fragmentation of Ir(ppy) 3 and its photofragments. 83 Figure 3.9 Ir(ppy) 3 + signal versus fluence, Φ, recorded with a photon energy of 35 420 cm -1 (4.391 eV) The straight line has a slope of 2, in accord with 2-photon ionization. 84 Figure 3.10 (a) The black trace is the Ir(ppy) 3 + signal, divided by fluence squared, versus photon energy. The blue dashed trace is the absorption cross-section σ 1 of gas phase Ir(ppy) 3 at ~ 500 K (arb. units). Different ratios of rhodamine 590 and 610 and the corresponding energy regions are designa- ted by horizontal double-sided arrows: (a) 100% 590 (279.5 – 283.1 nm); (b) 590:610 = 9:1 (281.5 – 284.3 nm); (c) 590:610 = 4:1 (283.2 – 286.8 nm); (d) 590:610 = 7:3 (286.2 – 288.1 nm); (e) 590:610 = 3:2 (287.8 – 290.5 nm); ( f ) 100% 610 (290.2 – 292.8 nm). (b) The ion signal (scaled by Φ -2 ) in (a) has been divided by the (blue dashed) absorption spectrum of ~ 500 K gas phase Ir(ppy) 3 also shown in (a). This indicates that the undulation with ~ 270 cm -1 spacing is due to σ 2 . 86 Figure 3.11 Low fluence (< 1 mJ cm -2 ) TOF spectrum acquired by irradiating gaseous Ir(ppy) 3 + with unfocused 193.3 nm light. The peak at 34.2 μs is from Ir(ppy) 3 + . The bifurcation of the Ir(ppy) 3 + peak is consistent with the isotopological profile. The peaks near 6 μs are from hydrocarbon impurity. 89 xvi Figure 3.12 Some important properties and processes of low-lying electronic states are indicated schematically (not to scale). Rapid radiationless decay processes (IC and ISC, with respective lifetimes τ IC and τ ISC ) ensure efficient T 1 produc- tion. Spontaneous emission lifetimes (τ rad ) for the T 1 sub- levels indicated on the far right differ considerably, despite the fact that these levels are close in energy, i.e., 116, 6.4, and 0.2 μs for 19 693, 19 712, and 19 863 cm -1 , respectively, in CH 2 Cl 2 solvent. At room temperature, an observed phosphorescence lifetime of 1.6 μs reflects the complex in- terplay that exists between the T 1 levels. The horizontal lines (above the electronic origins) whose spacing decreases with energy indicate (schematically) vibrational levels. 92 Figure 3.13 Ultraviolet absorption spectra of fac-Ir(ppy) 3 . The calcula- ted spectrum (red) was obtained from the stick spectrum by assigning to each stick a Gaussian FWHM of 0.43 eV. The experimental spectrum (black) was recorded at room temperature in dichloromethane. Peak and shoulder posi- tions (vertical arrows) are in eV. All stick heights have been increased by the same constant factor for viewing convenience, and curve height has been adjusted such that the maximum absorptions are equal. The low-energy, low- intensity wing due to T 1 ← S 0 (2.56 eV) is absent in the cal- culated spectrum because SOC was not included. 105 Figure 4.1 Ground electronic state structures and atom numbering for (a) fac-Ir(ppy) 3 and (b) mer-Ir(ppy) 3 . H atoms are omitted. Color scheme: green = Ir; blue = N; gray = C. Tables 4.1 and 4.2 list geometrical parameters. 118 Figure 4.2 Six highest occupied MO's and three lowest virtual MO's for fac-Ir(ppy) 3 at S 0 geometry using BNL: Orbital labeling fol- lows Hay. Energies of occupied orbitals (Koopmans IE's) are given in Table 4.3. 122 Figure 4.3 Shapes of the electron hole wave functions obtained from Koopmans analyses for cations at the (a) S 0 , (b) T 1 , and (c) D 0 equilibrium geometries. 128 xvii Figure 4.4 Ir(ppy) corresponding to Table 4.4: For the T 1 equilibrium geometry, C1, C2, and C3 correspond to carbons labeled 48, 52, and 50 in Figure 4.1(a) [see also Figure 4.3(b)]. For the D 0 equilibrium geometry C1, C2, and C3 correspond to car- bons labeled 23, 25, and 27 in Figure 4.1(a) [see also Figure 4.3(c)]. 129 Figure 4.5 Orbitals giving rise to T 1 excitation (HOMO and LUMO of S 0 ): left and right columns correspond, respectively, to S 0 and T 1 equilibrium geometries. 131 Figure 4.6 Ultraviolet absorption spectra of fac-Ir(ppy) 3 . The calcu- lated spectrum (red) was obtained from the stick spectrum by assigning to each stick a Gaussian FWHM of 0.43 eV. The experimental spectrum (black) was recorded at room temperature in dichloromethane. Peak and shoulder posi- tions (vertical arrows) are in eV. All stick heights have been increased by the same constant factor for viewing convenience, and curve height has been adjusted such that the maximum absorptions are equal. The low-energy, low- intensity wing due to T 1 ← S 0 (2.56 eV) is absent in the cal- culated spectrum because SOC was not included. Inset: The BNL (red) and ωB97X (blue) spectra differ considerably, the latter being far out of registry with the experimental spectrum. 133 Figure 4.7 The first six BNL excited states at S 0 and T 1 geometries (in eV). Note that the adiabatic ionization energy (AIE) is 5.86 eV. 136 Figure 4.8 (a) Photoexcitation transports populated S 0 vibrational levels to 1 LC, which undergoes radiationless decay on a sub- picosecond timescale, resulting ultimately in T 1 electronic excitation. This maps P(E vib ) to T 1 with additional T 1 vibrational energy given by hν – E T1 , as indicated in (b) and in Figure 4.9. 139 xviii Figure 4.9 The red curve is a plot of equation 4.2 with T = 500 K; see text for details. Following photoexcitation, the total vibrational energy in T 1 is given by hν – E T1 + E vib . The probability density for E vib is P(E vib ), and hν – E T1 = 15 000 cm -1 is chosen as a representative value. When all frequen- cies are changed by ± 10%, the P(E vib ) plots change ac- cordingly (blue and black curves). However, the main qualitative feature is preserved. Namely, a considerable amount of T 1 vibrational energy is distributed with a FWHM that is modest relative to the energy of maximum P(E vib ), e.g., 7800 versus 31 000 cm -1 , respectively, for the red curve. 141 Figure 5.1 (Schematic of the pulsed droplet apparatus. The machine consists of 3 vacuum chambers (1 - 3). Chamber (1) contains the pulsed helium droplet source (B) mounted on a closed cycle cryostat (A) with beam skimmer (C). The source chamber is pumped by a 3000 L/s diffusion pump (P1) backed in series by a roots blower followed by a rotary pump. Chamber (2) houses a ceramic pickup cell (D) wrapped in a tungsten filament. Chamber (2) is pumped by a 1000 L/s turbo-molecular pump (P2). Chamber (3) contains a combination reflectron / linear time-of-flight (TOF) spectrometer (F) as well as an axial quadrupole mass spectrometer (E) followed by a BaF 2 window (G). This UHV chamber is pumped by two 170 L/s turbo molecular pumps (P3 & P4). 151 Figure 5.2 Time dependence of the quadrupole mass spectrometer signal set at M = 8 and M = 16, as indicated, and measured at nozzle temperatures of 18 K (a) and 10.3 K (b). The duration of the nozzle pulse was chosen to be 220 µs in order to give the most intense signal with the shortest open duration. Time zero corresponds to a delay with respect to the nozzle trigger of 2.99 ms and 3.96 ms in panels (a) and (b), respectively. 153 Figure 5.3 Typical TOF mass spectra at 18K (a) and 10.3K (b) with important peaks labeled. The considerable water (M = 18) and protonated water cluster peaks (M = n*18 + 1) indicates pickup of multiple water molecules, due to the relatively high background pressure (10 -6 mbar) in our pick up chamber during the experiments. 155 xix Figure 5.4 Comparison of I 16 /I 8 measured with quadrupole (a) and TOF (b) mass spectrometers at various nozzle temperatures with repetition rates indicated. Both plots exhibit a sharp initial decrease followed by a moderate leveling when moving from low to high temperature albeit with different absolute ratios. The TOF ratios here were measured with 1 mA current, 2 us pulse duration, and 95 eV e-Energy. 157 Figure 5.5 TOF pulse intensity profile vs. delay for small (a) and large (b) droplets as measured with TOF. In (a) and (b), signal for mass 16 was multiplied by 4 and 3 for small and large droplets respectively. (c) and (d) show the delay dependence of I 16 /I 8 throughout the pulse profiles for small and large droplets, respectively. The average value (red line) of each ratio taken over their respective profile (endpoints indicated in red and 95% confidence curves in blue) was 0.058 ± 0.004 and 0.059 ± 0.0035 for small and large droplets respectively. 159 Figure 5.6 Current dependence of the TOF mass spectrometer peak intensities at M = 4, 8, 12, and 16 for small (a) and large droplets (b), as well as I 16 /I 8 for small (c) and large (d) droplets measured at ionization currents ranging from 1 to 5 mA. Intensities for mass 4, 12, and 16 are multiplied by 5 and by 2.5 in (a) and (b), respectively. 161 Figure 5.7 Intensity of the TOF mass 4, 8, 12, and 16 peaks vs. electron energy are shown for small (a) and large (b) droplets as well as I 16 /I 8 for small (c) and large (d) droplets, respectively. In (a) and (b) masses 4, 12, and 16 are multiplies by factors of 5 and 2.5, respectively. 163 Figure 5.8 TOF peak intensity vs. duration of the ionization pulse for small (a) and large (b) droplets followed by I 16 /I 8 for small (c) and large (d) droplets. All ionization pulses were initiated at the maximum intensity of their respective droplet pulse, see Figure 5.5. In (a) and (b) intensities of mass 12 and 16 peaks were multiplied by a factor of 3. 164 Figure 5.9 The effect of the ionizing pulse duration on background H 2 O + TOF intensity at various electron currents. 166 xx Figure 5.10 Plot of I 16 /I 8 for large droplet subtracted by I 16 /I 8 for small droplets. Data is fit the equation [ ] 2 1 exp( ) y a kt b = −− + . Optimized values for a, b, k are 0.1551, -0.0102, and 0.11442, respectively. 168 Figure 5.11 Diagram of the crucible pick-up cell used to imbed Ir(ppy) 3 in helium droplets. The droplet beam was aligned through the crucible openings and the solid Ir(ppy) 3 was placed in the lower half of the crucible. Tungsten wire was wrapped around the crucible and heated. The temperature was measured by a thermocouple just below the exit orifice. 172 Figure 5.12 Full (a) and zoomed in (b) mass spectra of the droplet beam after pickup of Ir(ppy) 3 . The inset in (a) is an expanded view of the droplet signal. The oven temperature in both (a) and (b) is 192 ºC. (c) Ir(ppy) 3 + and (Ir(ppy) 3 ) 2 + progression upon increase of the oven temperature. M = 655 and M = 1310 signals reach a maximum at 192 ºC and 200 ºC, respectively. 174 Figure 5.13 Photoionization mass spectra of Ir(ppy) 3 doped helium droplets recorded at different fluences. The laser wavelength is 266 nm (37 594 cm -1 ) produced by the YAG fourth harmonic. At low fluence (bottom trace) the parent ion (Ir(ppy) 3 + ) is produced exclusively. Note: < 1.0 mJ cm -2 is within the two-photon ionization regime for the gas phase experiments of Chapter 3. Increase in laser fluence causes fragmentation that is consistent with the gas phase experiments of Chapter 3. The peak at M = 0 in (a) and (b) is scattered UV radiation, which served as the t = 0 reference. 175 Figure 6.1 Depiction of the nozzle and discharge assembly. The nozzle operates on a current loop mechanism. Attached to the grounded nozzle faceplate is a Teflon spacer followed by a negatively biased copper electrode. Both spacer and electrode are encased in a Teflon shroud. 182 xxi Figure 6.2 (a) side view of the proposed vacuum chamber. The distance between the nozzle and TOF stack is less than 10 cm. Window 1, 2, and 3 correspond to path 1, 2, and 3 in part (b), respectively. The operating pressures in the source and detection regions are expected to be 10 -5 torr and mid 10 -7 torr, respectively. (b) shows a top view of the proposed vacuum chamber. Three optical paths are illustrated. Path 1 passes directly in front of the nozzle, path 2 crosses the center of the detection region, and path 3 overlaps the molecular beam with anti-parallel propagation. 184 xxii ABSTRACT Arguably the most important green phosphor used in organometallic light emitting devices (OLEDs), tris(2-phenylpyridine)iridium (Ir(ppy) 3 ), is investigated. One- and two-photon photoionization studies are presented and yield a conservative estimate for the upper bound to the ionization energy (6.4 eV). Observed undulations in the two-photon study are due to structure in the ionizing transition that originates from the lowest triplet state (T 1 ), which is populated via fast intersystem crossing (ISC) from the lowest singlet. At low fluence and 500 K – the conditions under which the experiments were carried out – Ir(ppy) 3 + is produced without fragmentation, despite the large amount of vibrational energy distributed over its 177 vibrational degrees of freedom. It is concluded that vibrational energy is transferred efficiently to the cation. Complementary density functional theory (DFT) results using long-range corrected functionals (BNL and ωB97X) affirm this conclusion. Time-dependent DFT is used to compute excited singlet and triplet states to just below the computed ionization energy (5.88 eV). A UV absorption spectrum, in which transitions are vertical from the S 0 equilibrium geometry, agrees with the room temperature experimental spectrum and indicates that transitions are dominated by Frank-Condon factors with ∆ν i = 0. Computed Ir(ppy) 3 equilibrium geometries for the ground state (S 0 ), lowest triplet state (T 1 ), and lowest cationic state (D 0 ) reveal very similar geometries owing to the diffuseness of the molecular orbitals. Calculated Ir(ppy) 3 vibrational frequencies were used to estimate the probability density P(E vib ) at 500 K. In combination with xxiii the vibrational energy imparted through relaxation and ISC following photoexcitation, it is seen that a mean value of nearly 31,000 cm -1 of vibrational energy appears in T 1 , and consequently Ir(ppy) 3 + . Considerable effort was directed toward removing this excess energy prior to ionization. To this end, it proved possible to photoionize Ir(ppy) 3 embedded in helium droplets with 266 nm radiation. The resultant TOF spectra show a strong similarity to the corresponding gas phase spectra. Additionally, low fluence experiments exclusively produced Ir(ppy) 3 + . The combined data suggests a two-photon ionization mechanism for the low fluence experiments. 1 Chapter 1 Introduction The central theme of this dissertation is a comprehensive study of tris(2- phenylpyridine) iridium (Ir(ppy) 3 ). Both experimental and theoretical approaches are explored. Ir(ppy) 3 is best known for its role in organometallic light emitting devices (OLED’s). 1 The utility of Ir(ppy) 3 lies in its ability to efficiently phosphoresce following photoexcitation and / or charge carrier recombination in a solid matrix. The latter means of excitation is attractive from the point of view of display technologies. Figure 1.1. Ground electronic state structure for Ir(ppy) 3 ’s most stable isomer (fac-Ir(ppy) 3 ). H atoms are omitted for clarity. Color scheme: green = Ir; blue = N; gray = C. High photoluminescence quantum efficiency in organometallic complexes, such as Ir(ppy) 3 , originates from the large amount of spin-orbit coupling (SOC) introduced by the heavy metal center. This dramatically increases the rate of intersystem crossing (ISC) in the system, which quickly funnels all singlet excited states into the triplet manifold. 2-5 2 As a result, both singlet and triplet excited states ultimately populate the lowest triplet state (T 1 ), a phenomenon known as triplet harvesting (Figure 1.2). 1,6,7 Moreover, the strong SOC significantly increases the phosphorescence rate, which surpasses radiationless decay as the dominant relaxation mechanism and enables quantum yields near 100% to be achieved. 8,9 Figure 1.2. The diagram illustrates the effect of triplet harvesting. In organometallic compounds with transition metal centers, such as Ir(ppy) 3 , excited singlet states relax to a low lying singlet state where they show a fast intersystem crossing (ISC) to the lowest triplet state (T 1 ). On the other hand, excited triplets states simply trickle down the triplet manifold to the lowest triplet state. Thus, T 1 harvests both singlet and triplet excitation energy and can efficiently emit. In principle, a triplet emitter can — in the limit of vanishing radiationless decay — exhibit 100% luminescence quantum efficiency. Although a great deal of research has been performed on Ir(ppy) 3 , most studies have focused on the relaxation and emission properties due to their role in OLED applications, 3,5,8-17 with only a handful of experimental studies focused on other aspects of this system. 4,18-20 Consequently, measurements of even the most fundamental quantities for Ir(ppy) 3 are either absent or controversial. For example, the only known singlet manifold triplet manifold S 0 S 1 S n T 1 T n fast ISC phosphorescence organometallic emitter 3 experimental value of the Ir(ppy) 3 ionization energy (IE) is 7.2 eV based upon gas-phase electron energy loss spectroscopy (EELS). 20 However, the theoretical work of Hay presents an IE near 6.0 eV. 21 It is shown in Chapters 3 and 4 that an IE of 7.2 eV is inconsistent with recent experimental and theoretical work and that a value of 6.0 is more reasonable. In this manuscript, experimental and theoretical studies of Ir(ppy) 3 shed light on the various ground and excited state properties of Ir(ppy) 3 , including the ionization energy. Results from these complementary approaches are used to describe the behavior of Ir(ppy) 3 over a range of conditions. A detailed description of each chapter is given below. 1.1 Chapter Contents This dissertation is organized as follows: Chapter 2 discusses several experimental techniques used to complete the work presented in chapters 3 – 5. Specifically, photoionization, time-of-flight mass spectrometry (TOFMS), UV-Vis absorption spectroscopy, helium droplet production and characteristics, and electron impact ionization are all presented in detail. Each section is meant as a basic introduction to the technique. Additionally, a final section in chapter 2 discusses preliminary experiments on the production and detection of the ethynyl radical (C 2 H) using 193.3 nm photolysis and electron impaction ionization / TOFMS, respectively. Chapter 3 concentrates on the photoionization of gas phase Ir(ppy) 3 . Experiments using one- and two-photon photoionization schemes coupled with TOF mass 4 spectrometry were carried out to yield a conservative estimate for the upper bound to the ionization energy of Ir(ppy) 3 , i.e. 6.4 eV. This assumes that vibrational energy is transported efficiently to the cation. The one-photon experiment used 193 nm radiation, while the two-photon experiments used tunable UV radiation to excite the ligand- centered ( 1 LC) state, which quickly decays to the lowest 3 MLCT state (T 1 ), followed by a second transition to the ionization continuum. An undulation in the two-photon action spectrum was observed. Comparison of the two-photon action spectrum with the UV absorption spectrum of gas phase Ir(ppy) 3 show the undulation is due to structure in the transition that originates from T 1 . Chapter 4 presents a computational study of Ir(ppy) 3 using density functional theory (DFT). Two long-range-corrected (LRC) functionals (BNL and ωB97X) were used in this study. Equilibrium geometries for the ground (S 0 ), lowest triplet (T 1 ), and lowest cationic state (D 0 ) were calculated for the facial isomer, and S 0 and D 0 were computed for the meridional isomer. Ground state energies of the facial and meridional isomers are compared. It is found that the facial isomer is more stable than the meridional isomer by ~ 220 meV. Because of this fac-Ir(ppy) 3 dominates in most environments. Therefore, focus is on this species. Time dependent density functional theory (TDDFT) is used to calculate excited states of Ir(ppy) 3 . A UV absorption spectrum, in which transitions are vertical from the S 0 equilibrium geometry, was constructed from the TDDFT results and is compared with the room temperature experimental spectrum. The calculated absorption spectrum is in good agreement with the experimental spectrum, which is consistent with Franck-Condon factors dominated by ∆ν i = 0 and the delocalized 5 nature of the orbitals. The calculated T 1 – S 0 energy gap (2.30 eV) is in reasonable agreement with the experimental value of 2.44 eV. Several ionization energies are obtained: adiabatic (5.86 eV); vertical from the S 0 equilibrium geometry (5.88 eV); and vertical ionization of T 1 at its equilibrium geometry (5.87 eV). These agree with a calculation by Hay (5.94 eV), and with the conservative experimental upper bound of Chapter 3 (6.4 eV). Finally, the 177 Ir(ppy) 3 vibrational frequencies were calculated and used to estimate the probability density P(E vib ) at 500 K, i.e. the temperature at which the experiments in Chapter 3 were carried out. In combination with the vibrational energy imparted through 1 LC ← S 0 photoexcitation, it is seen in Chapter 3 that a large amount of vibrational energy appears in Ir(ppy) 3 + without causing fragmentation. Specifically, for hν – E T1 = 15 000 cm -1 , the probability density for total vibrational energy peaks at ~ 31 000 cm –1 with a 7800 cm -1 width. Chapter 5 is comprised of three main topics: the characterization of helium droplets produced by a pulsed nozzle, the origin of the increased He 4 + /He 2 + ratio with increasing droplet size, and the embedding and photoionization of Ir(ppy) 3 in helium droplets. Droplets were generated by expanding cold gaseous helium at high pressure through a solenoid type pulsed nozzle. The average droplet size was determined by computing the mass 16 to mass 8 intensity ratio (I 16 /I 8 ) using quadrupole mass spectrometric measurements and comparing it to the measurements of Gomez et al. 22 This process was repeated for a range of temperatures. Quadrupole measurements are consistent with the results in reference 11 and show a sharp increase in I 16 /I 8 with decreasing T 0 indicating a corresponding rise in droplet size. The quadrupole 6 measurements were compared to TOF measurements under similar conditions and show that the quadrupole I 16 /I 8 is up to ~ 5x larger than that of the TOF. This discrepancy arises from the dramatically different time scales intrinsic to each spectrometer. Additional TOF measurements of the droplet beam were used to characterize the droplet pulse. All characterization experiments were performed with a nozzle temperature of either 10 K or 18 K, which correspond to an average droplet size of 3x10 5 and 5x10 4 , respectively. It is observed that the droplet size is constant throughout the pulse. The effect of electron current and impact energy on the droplets were also tested. The droplet signal shows a linear dependence on electron current, which is consistent with only one electron colliding with a droplet. The changing TOF mass signal vs. electron impact energy reveals that the electron impact ionization cross-section for the droplet is a maximum near that of gaseous helium. The origin of the increased I 16 /I 8 ratio for large droplets is due to the increased probability of forming two exciplex He 2 * molecules within the same droplet, which then combine to form He 4 + . This chapter closes with results from embedding gaseous tris(2-phenylpyridine)iridium (Ir(ppy) 3 ) in helium droplets followed by photoionization. Low fluence photoionization at 266 nm exclusively produced Ir(ppy) 3 + indicating that it follows a two-photon ionization mechanism. This dissertation concludes with a description of future experiments. It is proposed that efficient production of the ethynyl radical (C 2 H) will be achieved via pulsed electrical discharge of an acetylene / argon mixture. The nascent ethynyl radicals can then be detected using electron impact / TOFMS. Initial estimates of the C 2 H concentration at the detection region are on the order of 10 10 molecules cm -3 based upon 7 the work by Van Beek et al. 23 Revised electron impact parameters reveal a 100x increase in the C 2 H ionization efficiency, compared to that calculated in section 2.6. The combined estimates predict approximately 10 7 C 2 H + molecules cm -3 are generated for detection. Additionally, the proposed vacuum chamber introduces three very different optical paths that ensure all opportunities to spectroscopically probe C 2 H are explored. 8 1.2 References 1. Yersin, H. Ed.; Highly Efficient OLEDs with Phosphorescent Materials; Wiley- VCH Verlag: Weinheim, Germany, 2008. 2. Hedley, G. J.; Rusecksas, A.; Samuel, I. D. W. J. Phys. Chem. A Lett. 2008, 113, 2. 3. Hedley, G. J.; Ruseckas, A.; Samuel, I. D. W. Chem. Phys. Lett. 2008, 450, 292. 4. Hedley, G. J.; Rusecksas, A.; Liu, Z.; Lo, S. C.; Bum, P. L.; Samuel, I. D. W. J. Am. Chem. Soc. 2008, 130, 11842. 5. Tsuboi, T. J. Lumin. 2006, 119/120, 288. 6. Yersin, H.; Rausch, A. F.; Czerwieniec, R.; Hofbeck, T.; Fischer, T. Coordin. Chem. Rev. 2011, 255, 2622. 7. Yersin, H. Top. Curr. Chem. 2004, 241, 1. 8. Adachi, C.; Baldo, M. A.; Thompson, M. E.; Forrest, S. R. J. Appl. Phys. 2001, 90, 5048. 9. Adachi, C.; Baldo, M. A.; Forrest, S. R.; Thompson, M. E. Appl. Phys. Lett. 2000, 77, 904. 10. Hofbeck, T.; Yersin, H. Inorg. Chem. 2010, 49, 9290. 11. Tang, K.; Liu, K. L.; Chen, I. Chem. Phys. Lett. 2004, 386, 437. 12. Finkenzeller, W. J.; Yersin, H. Chem. Phys. Lett. 2003, 377, 299. 13. Vacha, M.; Koide, Y.; Kotani, M.; Sato, H. J. Lumin. 2004, 107, 51. 14. Tsuboi, T.; Alaroudi, N. Phys. Rev. B 2005, 72, 125109. 15. Stampor, W.; Meżyk, J.; Kalinowski, J. Chem. Phys. 2004, 300, 189. 9 16. Breu, J.; Stossel, P.; Schrader, S.; Starukhin, A.; Finkenzeller, W. J.; Yersin, H. Chem. Mater. 2005, 17, 1745. 17. Rausch, A. F.; Thompson, M. E.; Yersin, H. J. Phys. Chem. A 2009, 113, 5927. 18. Holzer, W.; Penzkofer, A.; Tsuboi, T. Chem. Phys. Lett. 2005, 308, 93. 19. Deaton, J. C.; Switalski, S. C.; Kondakov, D. Y.; Young, R. H; Pawlik, T. D.; Giesen, D. J.; Harkins, S. B.; Miller, A. J. M.; Mickenberg, S. F.; Peters, J. C. J. Am. Chem. Soc. 2010, 132, 9499. 20. Kukhta, A. V.; Kukhta, I. N.; Bagnich, S. A.; Kazakov, S. M.; Andreev, V. A.; Neyra, O. L.; Meza, E. Chem. Phys. Lett. 2007, 434, 11. 21. Hay, P. J. J. Phys. Chem. A 2002, 106, 1634. 22. Gomez, L. F.; Loginov, E.; Sliter, R.; Vilesov. A. F. J. Chem. Phys. 2011, 135, 154201. 23. Van Beek, M. C.; Ter Meulen, J. J. Chem. Phys. Lett. 2010, 337, 237. 10 Chapter 2 Experimental Techniques A variety of experimental techniques were used to complete the work described in this manuscript. Discussing each and every one is unnecessary as most have been exhaustively described elsewhere. For example, detailed reviews of molecular beams – both effusive 1 and supersonic 2 – as well as various methods of laser spectroscopy 3-8 are readily available. This chapter focuses on a few experimental techniques that were an integral part of the work described in chapters 3, 4, and 5. The first three sections address the techniques used in the work described in chapters 3 and 4, and include photoionization, TOF mass spectrometry, and gas-phase UV-Vis absorption spectroscopy. The next two sections address helium droplet matrix isolation and electron impact ionization, which are the basis of the experiments in chapter 5. This chapter ends with a standalone section, which describes experiments that investigated 193.3 nm photolysis of acetylene and the detection of its photoproducts. 2.1 Photoionization Before the invention of the laser, photoionization spectroscopy was limited in its application because it relied on the use of electrical discharge and arc lamps. 9 These conventional light sources were only of marginal utility as the vast majority of chemical systems demand short wavelengths and large spectral intensities to induce atomic or molecular photoionization. 3 Once high intensity lasers were developed, experiments 11 where a single atom or molecule could interact with multiple photons soon followed. Consequently, spectroscopists were now in a position to examine highly excited states, multiphoton transitions, and even photoionization for a wide range of systems. The observation of multiphoton transitions and the resultant excited state can either proceed by detecting fluorescence from the excited state, or by further exciting the system to the ionization continuum. 10-12 While a great deal of information can be gleaned from the fluorescence spectrum, this text will focus on photoionization. There exist a number of variants to the multiphoton photoionization (MPI) technique. The vast majority of such experiments use resonance-enhanced multiphoton ionization (REMPI). Unfortunately, the literature is rife with ambiguous terminology, and even the term REMPI is not confined to one type of experiment. Figure 2.1 provides a sample of the various photoionization schemes. 13 The most common form of REMPI is depicted in Figure 2.1a. While MPI spectroscopy can be complicated with the large laser intensities required to excite the system of interest, it has nonetheless proven to be an effective means of obtaining spectroscopic information. For example, single photon transitions between states of the same parity are forbidden, but when an even number of photons are used to induce a transition the excited state becomes accessible. 14,15 Thus, new spectroscopic information about the system can be inferred from the multiphoton spectrum. 12 Figure 2.1. Three possible multiphoton excitation schemes are shown above. (a) One-color multiphoton ionization resonance enhanced at the initial transition. (b) A double resonance variant of REMPI; ν 1 is fixed to resonantly enhance the initial two-photon transition while ν 2 is scanned to probe the spectroscopy of the second transition. (c) Two-color multistep photoionization is shown, where ν 1 is fixed and ν 2 is scanned to reveal the various ionization thresholds. 13 In contrast to multiphoton photoionization, a series of resonant single photon transitions can be used for ionization (Figure 2.1c). This multistep, or stepwise, photoionization technique is extremely versatile because at low laser intensities each transition may be treated independently. Additionally, precise control over the transitions opens up a multitude of pathways through which the system can be studied. For example, employing multiple laser pulses separated by time delays facilitates probing dynamical processes as they unfold. Also, action spectra generated by multistep photoionization yield spectroscopic information about all transitions involved. Another advantage of the multistep approach is that the single photon transitions have absorption cross-sections that are significantly larger than an analogous multiphoton transition cross-section. 15,16 Thus, the demand for very intense laser pulses is decreased. In systems with sufficiently low ionization, modern lasers are capable of producing frequencies in which a single absorption event is sufficient to produce ions. 0 1 M + + e - M 0 1 E 1 −E 2 = 2hν 2 or ν 1 ν 2 0 1 ν 1 ν 2 0 1 M + + e - M 0 1 E 1 −E 2 = 2hν 2 or ν 1 ν 2 0 1 ν 1 ν 2 ( ) a ( ) b ( ) c 13 For example, the 193 nm photon produced by an ArF laser was able to ionize gas-phase tris(2-phenylpyridine)iridium without ionizing other gaseous molecules present in the vacuum chamber (Section 3.2.3). The work presented in this manuscript exclusively used multistep and single photon photoionization, and therefore will be the focus of this text. Many authoritative reviews and books on the various forms of multiphoton methods are available. 3,10,13-15 2.1.1 Stepwise Ionization Spectroscopy It is worthwhile to consider in detail the rate equations involved in a two-step photoionization process because it provides insight into what information may be extracted from the experiment. In general, the stimulated absorption/emission rates from an initial state to a final state are of the form: 8 () i ii f dN NB dt ρυ → = ± (2.1) where B i→f is a constant, N i is the number of particles in the initial state, ρ(ν) is the photon energy density, and ± corresponds to absorption and emission, respectively. For spontaneous emission, the depopulation rate is: f f i f dN AN dt → = − (2.2) where A i→f is a constant and N f is the number of particles in the excited state. It is useful to rewrite equations 2.1 and 2.2 using more convenient quantities. A i→f can be replaced with 1/τ (units of s -1 ), where τ is the spontaneous emission lifetime of the excited state, 14 and B i→f ρ(ν) may be written as σ i Φ, where σ i is the absorption cross-section for transition i (units of cm 2 ) and Φ is the photon flux (units of photons cm -2 s -1 ). Figure 2.2. Schematic representing a stepwise one-color two-photon photoionization pathway. 0 represents the ground state, 1 is a real intermediate absorbing state, and 2 is a state that lies above the ionization energy. The absorption cross-sections for transition 10 ← and 21 ← are σ 1 and σ 2 , respectively. The photon energy (hν) is considered much larger that the thermal energy (k B T). Now consider the two-photon photoionization scheme in Figure 2.2. If the light source is a monochromatic square pulse of length T, then the transition rates for all three states are: 0 1 0 1 11 dN N NN dt σσ τ = − Φ+ + Φ (2.3) 11 0 1 11 1 2 dN N N NN dt σ σσ τ = Φ− − Φ− Φ (2.4) 2 12 dN N dt σ = Φ (2.5) 0 1 2 Ionization Energy B hv k T >> 1 σ 2 σ 0 1 2 Ionization Energy B hv k T >> 1 σ 2 σ 15 Notice that equation 2.5 assumes that the cationic state has an infinite spontaneous emission lifetime. Adding equations 2.1 and 2.2 and solving for dN 0 /dt yields: 0 1 11 dN dN N dt dt σ   = − +Φ     (2.6) Differentiating equation 2.4 and substituting it into equation 2.6 yields a second order differential equation in N 1 : ( ) 2 2 11 1 2 11 2 2 1 20 d N dN N dt dt σ σ σσ τ  + + Φ+ + Φ =   (2.7) The general solution to which is: 17 { } { } 2 01 2 2 2 1 2 1 2 1 11 exp( ) 1 exp( ) 1 N N TT σσ λλ λλ λ λ  Φ = −−−−−  −  (2.8) with 22 2 bb λ ω =+ − 22 1 b b λω =−− ( ) 1 22 1 22 b σσ τ = + Φ+ 22 12 ω σσ = Φ In the limit of low flux and a long-lived intermediate state (T << τ and ΦT << 1), the exponential terms in equation 2.8 may be expanded in a Taylor series. The expanded terms taken to the second order are 16 ( ) 2 exp( ) 1 2 T TT λ λλ − ≈− + (2.9) Substituting equation 2.9 into 2.8 and simplifying gives a convenient expression for the number of ions created: 22 2 01 2 01 2 2 22 N TN N σσ σσ ϕ Φ = = (2.10) where φ is the laser fluence (units of photons cm -2 ). This result shows that at low fluence, the number of particles ionized from the two-step photoionization scheme is dependent on the square of the laser fluence. A similar result is derived if the above approximations (T << τ and ΦT << 1) are used from the outset, i.e. the stimulated and spontaneous emission terms in equations 2.3 and 2.4 are neglected. Thus, with the above constraints, each transition may be treated independently. Moreover, if the first transition is characterized by an absorption spectrum, then the spectroscopic information of the second transition may be extracted from a photoionization action spectrum (Section 3.2.2). From the above derivation it should be clear that laser intensity has significant influence over the steps by which photoionization occurs. In general, a stepwise photoionization scheme may require n transitions. In the limit of a low fluence, the order (n) of the ionization process is easily determined by measuring the change in the log of the ion-signal with a change in the log of the laser fluence: ( ) ( ) log log ION dN n d ϕ = (2.11) 17 where N ION represents the ion signal. However, as the fluence is increased, the situation becomes more complex. For example, when the laser fluence φ approaches 1/σ for a particular transition the initial and final state populations are equal, and the transition is said to be saturated, i.e. no further absorption is possible for that transition. As a result, the ionization order is decreased, because the saturated transition is independent of laser intensity. 5 While spectroscopy in this regime increases the efficiency of photoionization, 16 spectroscopic information may be lost or difficult to extract. Furthermore, the increase in fluence increases the chances of absorption past ionization, leading to possible fragmentation. Consequently, photoionization spectra are acquired in a regime where the signal depends heavily on laser fluence. 2.1.2 Fragmentation Photoionization can lead to diverse collection of products. As more photons are absorbed, higher potential energy surfaces are accessed. Thus, the extent of fragmentation depends largely on laser fluence and the system’s capacity to absorb. In the soft ionization regime, where the only the minimum number of photons necessary to ionize the system are absorbed, the molecular parent ion is expected to be produced almost exclusively. 10 Alternatively, very high laser fluences can completely reduce a molecule to atomic ions. Photofragmentation can significantly alter the information available from the ion signal, so determining the conditions under which fragmentation occurs is important. Two common mechanisms that contribute to photofragmentation are depicted in Figure 2.3. The first mechanism (Figure 2.3a) is parent ion fragmentation corresponding 18 to dissociation when the parent ion absorbs further. 18,19 In multiphoton ionization experiments of polyatomic molecules, the mass spectra of photoions are rather complicated. The high radiation intensities necessary for two or three photon transitions make it near impossible to prevent absorption past the initial ionization, in which case fragmentation via mechanism one is expected to occur. Figure 2.3. Depiction of two fragmentation schemes of multistep ionization. (a) Continued absorption by the parent ion opens up a variety of dissociation channels, which can eventually lead to atomization. (b) Dissociation of the intermediate state will lead to neutral fragments that can be ionized and/or dissociate further. 14 The second mechanism deals with neutral fragments that can be produced very efficiently after absorption. 20 Although using a stepwise photoionization technique allows for better control of the conditions by which the ionization continuum is reached, fragmentation is still a possibility. Furthermore, if the produced photofragments are neutral, they must be ionized in order to be detected by a mass spectrometer. Consequently, complementary experiments must be used to fully understand the nature of the neutral fragmentation. ABC (ABC)* (ABC)** (ABC) + (ABC) + * (ABC) + ** (AB) + +C (AB) + *+C I.P. ABC (ABC)* (ABC)** (AB)*+C (AB)+C (AB) + +C I.P. (AB)**+C (AB)*+C (AB)**+C A+B+C ABC (ABC)* (ABC)** (ABC) + (ABC) + * (ABC) + ** (AB) + +C (AB) + *+C I.P. ABC (ABC)* (ABC)** (ABC) + (ABC) + * (ABC) + ** (AB) + +C (AB) + *+C I.P. ABC (ABC)* (ABC)** (AB)*+C (AB)+C (AB) + +C I.P. (AB)**+C (AB)*+C (AB)**+C A+B+C ABC (ABC)* (ABC)** (AB)*+C (AB)+C (AB) + +C I.P. (AB)**+C (AB)*+C (AB)**+C A+B+C ( ) a ( ) b 19 2.2 Time-of-Flight Mass Spectrometry Time-of-flight (TOF) mass spectrometry separates ions of different masses by exploiting the importance of mass and velocity in an atom/molecule’s kinetic energy. A thorough description of this technique can be found in the pioneering work of Wiley and McLaren. 21 The following discussion highlights a few important aspects of the technique. 2.2.1 Overview A typical Time-of-Flight (TOF) mass spectrometer consists of an interaction region, a field-free drift region, and a detector (commonly a microchannel plate (MCP) detector). Ions are formed in the interaction region and then accelerated by electric fields produced by a potential gradient. The accelerating electric field can be static or time varying. A system capable of dynamically changing its electric field is more versatile because it can use both pulsed and continuous ionization schemes. Whereas static TOF systems must use a pulsed ionization scheme in order to set time zero. 20 Figure 2.4. Schematic of a basic TOF system. The interaction region has a height of 2s and is between the repeller and extractor plates, which hold voltages V 1 and V 2 , respectively. A second acceleration region is above the interaction region and has a height of d. The field free region allows the accelerated ions of different mass time to separate. Ions that collide with the micro-channel plate detector (MCP) cause a cascade of electrons creating a small current, which is detected by an oscilloscope monitoring the MCP. 22 In an ideal case, a positive ion of charge q is initially at rest between the extractor and repeller plates (Figure 2.4). The plates are separated by a distance 2s. If the plates are charged to voltages V 1 and V 2 (such that V 1 > V 2 ) the ion feels a force equal to q(V 1 – V 2 )/2s. Once the ion reaches the extractor plate it has accumulated a kinetic energy equal to q(V 1 – V 2 )/2. The ion then passes through the second acceleration region where it increases its kinetic energy by qV 2 . Thus, the total kinetic energy of the ion, regardless of mass, is 1 2 2 VV Uq +  =   (2.12) Or in terms of the electric fields MCP Δs D V 2 V 1 d 2s Field Free Flight Tube Extractor Interaction Region Repeller MCP Δs D V 2 V 1 d 2s Field Free Flight Tube Extractor Interaction Region Repeller 21 ( ) 12 U q sE dE = + (2.13) Here, s is the distance the ion travels in the first electric field E 1 , and d is the distance the ion travels in the second electric field E 2 . In the presence of multiple mass species, each ion will have a velocity that depends strictly on its mass m. 2U v m = (2.14) As the accelerated ions traverse the field-free region, they are separated by mass. The flight times of the different ionic species are given by 21 1/2 1/2 1/2 0 0 1/2 0 2 ( , ) 1.02 2 21 k d m TU s k s D Uk     = ++     +     (2.15) where D is the length of the field free flight tube and k 0 is defined as 21 ( ) 12 0 1 sE dE k sE + = (2.16) The coefficient of 1.02 is a conversion factor that arises from using more convenient units, i.e. μs for time, amu for mass, cm for distance, V/cm for electric field, and eV for energy. According to equation 2.15, the total flight time for each species depends on the square root of their mass. Thus, a mass spectrum may be acquired by recording the ion signal as a function of time and using equation 2.15 to convert flight time to mass. TOF mass spectrometry has several advantages over other common methods. One advantage is it enables an entire mass spectrum to be recorded for every ionizing event, with nearly 100% efficiency. 16 For small to medium sized molecules, individual TOF mass spectra 22 are collected within 50 μs. Thus, data collection is more often limited by the repetition rate of the ionizer, e.g. the laser. Furthermore, the accuracy of this technique depends more on the response time of the detector and sample rate of the oscilloscope rather than the precise alignment that is required for other types of mass spectrometers. 2.2.2 Resolution The above discussion presents the principles of TOF mass spectrometry only for ions that start from rest at the center of the ionization region. In actual experiments, ions are initially spread out and possess a range of kinetic energies, which cause ions of the same mass to register at slightly different times. As a result, ion signals have a flight time distribution that limits the mass resolution. The space distribution is due to the finite geometric cross-section of the ionizing source, be it laser or electron gun. Consider a spherical distribution of ions centered between the repeller and extractor plates with a diameter of Δs, as depicted in Figure 2.4. The ions therefore reside at various distances from the extractor grid ranging from s − Δs/2 to s + Δs/2. According to equation 2.13, ions formed further from the extractor grid will gain more kinetic energy than those formed closer to the extractor grid. As a result, ions with the same mass will have different flight times, resulting in a time spread ΔT. However, because the more energetic ions have a longer flight path, there will be a point in space at which the faster ions pass the slower ones – a phenomenon known as space focusing. Ideally ions are spatially focused so that this inflection point occurs at the detector, drastically reducing 23 ΔT. The focusing condition, for which ions of the same mass simultaneously reach the detector, is given by 21 0 0 3 2 k dD s ks  − =   (2.17) Notice that equation 2.17 is independent of mass. Thus, to satisfy this condition for one mass is to satisfy the condition for all masses. Usually D, s, and d are fixed and k 0 is adjusted to achieve optimal conditions, i.e. by varying V1 and V2. In addition to the initial spatial distribution, ions in the interaction region will have an initial velocity distribution. Therefore, the ions possess a range of initial kinetic energies that must be considered. [Note that only ions with velocity components towards or away from the detector will affect the resolution]. After acceleration, each ion will have a combined translational energy U Tot of 0 Tot A U UU = + (2.18) where U 0 is the initial kinetic energy and U A is the acquired energy from acceleration. Figure 2.5. Diagram showing the origin of the decreased TOF mass resolution as a result of the initial kinetic energy distribution U 0 . (a) Two identical particles with translational energy U 0 but in opposite directions are shown. A is moving away from the detector, B is moving toward the detector. (b) The applied field must counter the initial kinetic energy of A causing it to reverse direction and return to its initial position with energy U 0 towards the detector, whereas B is simply accelerated toward the detector. 22 V 2 V 1 Interaction Region A B A B A B U 0 t = 0 t = ΔT V 2 V 1 V 2 V 1 Interaction Region A B A B A B U 0 t = 0 t = ΔT V 2 V 1 ( ) a ( ) b 24 Envision two molecules in the interaction region at the same position s that have identical speeds albeit in opposite directions (Figure 2.5). Once ionized, the ion initially moving toward the detector will be accelerated, while the ion moving away from the detector must first decelerate to a stop and then accelerate toward the detector. Although both ions will acquire the same kinetic energy, they will impact the detector at different times. This time spread can be reduced by decreasing the energy ratio (U 0 /U A ), e.g. using a supersonically expanded beam 3 or increasing the accelerating voltages. In practice both approaches are used. It is also possible to improve the energy resolution by employing energy focusing, i.e. introduce a time delay between ionization and the application of the potential gradient. 21 However, all attempts to reduce the effect U 0 will adversely affect the spatial resolution. Optimum conditions are most often determined empirically, but these equations are a good start. For a more detailed analysis of mass resolution see reference 21. 2.3 UV-Vis Absorption Spectroscopy Absorption spectroscopy is arguably one of the most widely used analytical tools in physics, chemistry, and industry. Infrared and far-infrared spectroscopy are commonly used for gas analysis and identification of chemical structures, 23,24 while visible and ultraviolet spectroscopy are extensively used for quantitative analysis of atoms, ions and chemical species in solution. 3 Consequently, a great variety of spectrometers are commercially available. 25 Absorption spectroscopy operates on the principle that electromagnetic radiation is attenuated due to an interaction with matter. In its most common form, the phenomenon of light attenuation by a homogeneous absorber is given by the Beer- Lambert law: 17 ( ) 0 10 v Cl II ε − = × (2.19) where I 0 is the intensity of light before interaction, I is the intensity after the interaction, ε(ν) is the frequency dependent molar absorption coefficient (units of L mol -1 cm -1 ), C is the absorber concentration (units of mol L -1 ), and l is the thickness of the absorbing material (units of cm). Or, by taking the log of equation 2.19 and defining log(I 0 /I) as the absorbance (A), then: ( ) A v Cl ε = (2.20) In most UV-Vis absorption experiments, the absorber is dissolved to a known concentration in a solvent that is transparent over the desired spectral range. A hollow quartz cell of 1cm thickness is filled with the absorbing solution. Continuous white light is then passed through the cell and dispersed with a rotatable grating, allowing each wavelength to be detected separately with a photomultiplier tube. A diagram of a simple absorption spectrometer is shown in Figure 2.6. 26 Figure 2.6. Basic operation of a standard spectrophotometer. 3 A tungsten lamp generates a continuous white light source that is collimated and passes through the absorbing medium. The transmitted light is then scattered using a rotatable grating and slowly passed over a photodetector. Current generated from the transmitted light striking the detector is sent to a recorder that displays the resultant spectrum. The absorption spectrum of a particular solute can vary from solvent to solvent. This is because molecules are stabilized by their interaction with a solvent, which induces a shift in their absorption or emission spectrum when compared to that of the gas phase. 25,26 In light of the spectral shifts that can occur in solution, it is desirable to obtain the gas phase absorption spectrum. Moreover, certain gas phase multiphoton experiments produce spectra that contain information for multiple transitions, including that which produces the absorption spectrum. Thus, obtaining the gas phase absorption spectrum can help deconvolute the multiphoton spectrum. For example, the multistep photoionization of tris(2-phenylpyridine)iridium (Ir(ppy) 3 ) (Section 3.2.2) involves a one-color two- photon photoionization mechanism. The resultant action spectrum contains spectral features of both the first and second transition. Additionally, the experiment was performed under vacuum, where gaseous Ir(ppy) 3 was prepared by heating the powder to 220°C, thereby imparting a great deal of vibrational energy to the sublimated Ir(ppy) 3 Continuous Light Source Absorption Cell Grating Spectrograph Photodetector Recorder Continuous Light Source Absorption Cell Grating Spectrograph Photodetector Recorder 27 molecules. Therefore, it is important to try and characterize the first transition under similar experimental conditions. Before embarking on this task, several factors must be considered. First, it is advantageous to use a commercial spectrophotometer that can accommodate this type of measurement because it reduces the amount of time required to build a specialized experimental apparatus. However, this usually imposes a limitation on the length of the cell. In this case, a maximum cell length of 7.5 cm could be used. Next, equation 2.20 shows that the magnitude of the absorption is dependent on the extinction coefficient, the concentration, and the cell length. The gas phase extinction coefficient can usually be estimated from a solution phase absorption spectrum. For Ir(ppy) 3 , the extinction coefficient is relatively large, and between 40000 and 48000 L mol -1 cm -1 for the desired spectral range. Concentration depends on vapor pressure, which in turn depends on temperature. Fortunately, the vapor pressure of Ir(ppy) 3 has been characterized by Deaton et al. 27 The natural log plot of the Ir(ppy) 3 vapor pressure relative to 1 atmosphere (P 0 ) vs. temperature in Celsius is shown in Figure 2.7. Using a 7.5 cm cell length, an extinction of 45000, and an absorption of 0.1, which should be sufficient for a modern spectrophotometer, corresponds to a vapor pressure of 10 -3 Torr. This requires heating the cell to a temperature of ~270 °C. The above specifications dictated that a new absorption cell be designed. 28 Figure 2.7. A natural log plot of the Ir(ppy) 3 vapor pressure divided by P 0 (1 atmosphere) vs. temperature in centigrade. 71 A quartz tube with a 2.54 cm outside diameter (OD) was cut to a length of 7.6 cm. Two quartz windows were then soldered to the tube ends, taking care to ensure that the windows were perpendicular to the centerline of the glass tube, and thus perpendicular to the incoming light. A side port was installed to allow the Ir(ppy) 3 powder to be inserted and the cell to be evacuated. An illustration of this vacuum cell is given in Figure 2.8(a). After the powder was added, the cell was then pumped to a base pressure of ~ 10 -6 torr and sealed by fusing together the side port while the cell was under vacuum. Heating the cell in its current state caused Ir(ppy) 3 vapor to condense on the windows. Therefore, the cell needed to be shielded and heated such that the windows were the hottest part of the cell. This was achieved by machining a copper sleeve to fit snugly around the cell (Figure 2.8b). The sleeve was made with a 2.54 cm inner diameter (ID)/3.18 cm OD copper pipe that was cut to a length of just under 13 cm. Two cuts, roughly 90 degrees apart, down 225 250 275 300 325 -15 -14 -13 -12 -11 -10 -9 -8 ln(P/P 0 ) Temperature (°C) 29 the length of the cell created a detachable side panel. A small section at the center of the side panel was removed to accommodate the side port of the vacuum cell. To ensure that the cell windows were not cooled by air currents or radiative cooling, two identical end caps were constructed out of copper. Each end cap is slightly thicker than the copper tube to better retain heat, and contains a hole in the center with a diameter of 0.76 cm. The cell was inserted using the procedure indication in Figure 2.8(c). Figure 2.8. Depiction of the (a) UV-Vis vacuum cell, (b) and copper sleeve with end caps. The Ir(ppy) 3 must be added to the cell prior to evacuation. After the cell has been thoroughly pumped, the side port is sealed and the cell is inserted into the sleeve in the order indicated in (c). To heat the cell, two individual strands of resistive wire were wrapped around the end caps. The wires were attached to separate power supplies, and the temperature was monitored using two thermocouples, one at each end, in order to prevent a temperature gradient from one end of the cell to the other. When acquiring the absorption spectrum, Vacuum Ir(ppy) 3 Powder Quartz Window Vacuum Ir(ppy) 3 Powder Quartz Window 1 2 3 3 1 2 3 3 ( ) a ( ) b ( ) c 30 great care was taken to shield the spectrophotometer from the heating elements. Many commercial spectrophotometers have plastic interiors that will melt if exposed to high temperature. The resultant gas phase absorption spectrum of Ir(ppy) 3 at 270°C is shown in Figure 2.9. 260 270 280 290 300 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Absorbance (a.u.) W avelength (nm) Absorption of Ir(ppy) 3 at 270°C Figure 2.9. Plot of the gas phase Ir(ppy) 3 absorption spectrum at 270 °C. Although the gas-phase absorption spectrum of Ir(ppy) 3 is rather dull, the technique used to acquire it was effective. Thus, it can be applied a variety of systems where sublimation is required in order to obtain gas phase spectra. 2.4 Helium Droplet Matrix Isolation Of all atoms that compose the periodic table, helium seems one of the least likely to be the focus of modern chemistry. At everyday temperatures and pressures, helium behaves as one expects of a chemically inert noble gas. However, helium is the only element that does not solidify at normal pressures, even when cooled to nearly zero Kelvin. 28 Additionally, below a critical temperature of 2.2 K 4 He transforms into a 31 superfluid state ( 3 He experiences a similar transition at 3 mK). 29 Of the many fascinating phenomena observed in this quantum liquid, its vanishingly small viscosity and high heat conductivity are most relevant for its use as a spectroscopic matrix. 30 Introduction of foreign species into superfluid helium poses unique opportunities to study the imbedded species. The high heat conductivity of the helium rapidly cools the impurity to superfluid helium temperature. 4 He, a boson, is quantum mechanically delocalized at very low temperatures, which enables the helium to gently accommodate the imbedded species with minimal interference. What is more, helium is transparent from the far IR to vacuum UV. 31 However, quantum delocalization also permits impurities to move nearly unhindered, leading to unwanted aggregation and adherence to the container walls. 32 With the advent of helium droplet molecular beams it has become possible to confine foreign species in helium while avoiding undesired aggregation. Numerous spectroscopic experiments have shown that 4 He droplets also exhibit superfluid behavior. 33-38 Although 3 He droplets can be formed through expansion, their ultimate temperature of 0.15 K is above the superfluid transition for this isotope. Consequently, 4 He is primarily used for spectroscopic studies. Additional information on helium droplets can be found in a variety of review articles. 31,32,39-43 2.4.1 Helium Droplet Production and Characteristics Helium droplets are produced by expanding pre-cooled helium through a small orifice. 31 In general, there are two major expansion regimes. 32 The most common mode of 32 operation, known as subcritical, adiabatically expands gaseous helium which causes extensive cooling resulting from collisions converting enthalpy into translational energy (Figure 2.10). 2,44,45 As the helium cools, the collisions become less violent, which enables helium to cluster. These clusters, or droplets, cool further via evaporation until they reach an ultimate temperature that is determined solely by the droplet vapor pressure (0.37 K for 4 He and 0.15 K for 3 He). 46 Figure 2.10. The pressure-temperature phase diagram for 4 He. Dashed lines show typical trajectories for supercricital (upper) and subcritical (lower) expansion isentropes. 31 In contrast, supercritical expansions involve helium that is already liquid when it passes through the nozzle. Fragmentation of the liquid followed by evaporation generates the droplets. Although the final droplet temperature is the same in both regimes, the beam properties, i.e. droplet velocity, size, and distribution, depends on the nozzle parameters and type of expansion. 33 Figure 2.11. Average number of helium atoms per droplet for various backing pressure and nozzle temperatures. The right axis corresponds to the average droplet diameter under the same expansion conditions. Images of the subcritical (lower) and supercritical (upper) expansions are shown. 31 Droplet velocities lie in the range of 150 – 450 m/s, depending on the nozzle temperature, with a narrow velocity distribution (Δv/v ≈ 0.01 – 0.03). 32,47 Likewise, the average droplet size is determined by the source conditions. Droplets containing between 10 3 – 10 11 helium atoms are produced by adjusting the nozzle temperature and stagnation pressure, as seen in Figure 2.11. For droplets composed of ~10 4 helium atoms or more, the binding energy between an atom and the droplet approaches the bulk value of ~ 5 cm -1 . In a continuous subcritical expansion, the size distribution is log-normal, with a half-width comparable to the average droplet size. 48 Assuming a spherical droplet, the radius, and consequently the droplet cross-section, may be inferred from the density Fragmentation of Liquid Condensation of Gas Number of 4 He atoms per droplet 10 0 10 1 10 8 10 6 10 3 10 4 10 3 10 2 10 9 10 10 5 10 7 10 2 Mean 4 He Droplet Diamter (Å) 1 10 5 2 20 30 T/K Subcritical Supercritical Fragmentation of Liquid Condensation of Gas Number of 4 He atoms per droplet 10 0 10 1 10 8 10 6 10 3 10 4 10 3 10 2 10 9 10 10 5 10 7 10 2 Mean 4 He Droplet Diamter (Å) 1 10 5 2 20 30 T/K Subcritical Supercritical 34 following the liquid drop model, i.e. a sharp cutoff in helium density at the droplet edge. Using the above approximations, a droplet containing N helium atoms has a radius of 1/3 3 4 bulk N R πρ  =   (2.21) The cross-sectional area, often referred to as the geometrical cross-section, is then 2/3 3 4 bulk N σπ πρ  =   (2.22) The importance of the cross-section is emphasized in later sections. 2.4.2 Pulsed Helium Droplet Production The helium droplet apparatus used in chapter 5 employs a pulsed nozzle. The use of pulsed nozzles as helium droplet sources is a relatively new technique. 40 In general, a pulsed droplet beam is far less characterized than one created by continuous expansions; this is partly because of the additional parameters involved (e.g. pulse width, repetition rate), and partly because of the inherent difficulty in predicting expansions conditions when mechanical components, such as the poppet, behave differently from pulse to pulse. As a result, the underlying physics involved in droplet production by pulsed nozzles are not fully understood; however, there exist a number of advantages to using pulses droplet sources rather than continuous ones. A major advantage to using a pulsed vs. continuous nozzle is the significantly higher beam density that is achieved while maintaining appropriate vacuum conditions. Two immediate benefits arise from the improved density: better signal to noise ratio (due 35 to a higher concentration of species in the interaction region), and more efficient use of material. The latter is particularly important for species that are present in low concentration. A pulsed nozzle is also better suited for use with pulsed lasers. 2.4.3 The Pick-up Process Helium droplets are capable of encapsulating a motley collection of atomic and molecular species upon collision. In most cases, the collision cross-section is equivalent to the geometrical cross-section given by equation 2.22, with an average impact parameter of 2/3R. Any deviation between the collision and geometric cross-sections is attributed to a small percentage of particles being transmitted when impact occurs near the droplet edge. 49 Collisions between the droplets and foreign species take place in a pick-up cell, located downstream from the droplet source, where — because of the relatively large pick-up cross-sections — low partial pressures of the impurity (10 -6 – 10 -7 torr) are sufficient for capture. 31 It has been experimentally observed that the pick-up process is well described by Poisson statistics. 49,50 The probability of capturing k particles is given by ( ) exp( ) ! k nL P nL k σγ σγ = − (2.23) where σ is the capture cross-section, L is the length of the pick-up cell, n is the number density of the dopant in the pick-up cell, and γ accounts for the relative velocities of the colliding species. 49 36 When an atom or molecule is captured by a droplet, the impurity’s internal energy, collision energy, and helium-impurity binding energy are all transferred to the droplet. 49 The transferred energy is quickly dissipated by the helium through evaporation (within 10 -11 seconds), returning the droplet to its quiescent state. 51 By this mechanism, the droplet acts as a nano-cryostat, efficiently cooling molecules to sub-Kelvin temperatures. Consequently, evaporation dictates the size of droplets that should be used for a particular experiment because the evaporative loss must be far less than the number of helium atoms in the pre-collision droplet. While a great many details are known about the pick-up process, the actual dynamics of impurity capture remains an open issue. 42 2.5 Electron Impact Ionization Electron-matter collisions that produce ions constitute one of the most fundamental processes in collision physics. In gas phase collisions, the ionization efficiency is described by the absolute total electron-impact ionization cross-section, σ. 52 At low electron energies, σ is found to rise from zero once the energy of the colliding electron exceeds the ionization energy of the atom/molecule. Immediately above the ionization energy, σ exhibits an electron energy dependence of E 0.127 . 53 Further increase in the impinging electron’s energy corresponds to a sharp increase in σ until a maximum is achieved, σ max . For polyatomic species, σ max typically occurs between 70 – 80 eV and is the reason 70 eV is the standard in analytical mass spectrometry. Beyond this maximum, σ decreases and eventually tapers off. 37 0 250 500 750 1000 1250 1500 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Total absolute cross-section (σ) x 10 17 cm 2 e-Energy (eV) Exp. Ref. 54 BEB Ref. 56 σ max = 3.75x10 -17 cm 2 Ε max (Exp) = 105 eV Ε max (BEB) = 116 eV 0 100 200 300 400 500 600 700 800 0 1 2 3 4 5 Exp Ref 55 BEB Ref. 57 Total absolute cross-section (σ) x 10 16 cm 2 e-Energy (eV) σ max = 5.2x10 -16 cm 2 Ε max (Exp) = 87 eV Ε max (BEB) = 75 eV Figure 2.12. The total absolute cross-sections for (a) helium 54 and (b) acetylene 55 along with their corresponding theoretical fit calculated using the BEB method. 56,57 The electron energy at the point of maximum cross-section is displayed for both experiment and BEB. A direct measurement of absolute cross-sections is challenging, and in most cases relative cross-sections are measured instead. A calibration is then required to convert the measured values into absolute cross-sections. As a consequence, there is considerable variation between reported values of σ, especially when measured with different experimental setups. 52 To remove the uncertainty, considerable effort has gone into measuring cross-sections for a large selection of molecules using a single apparatus. 58-61 While this approach has produced consistent results, every apparatus has its limitations. Thus, it is desirable to find an experimental approach that will yield consistent results. An alternative approach is to determine σ theoretically. Unfortunately, electron impact ionization is a many-body problem, and rigorous quantum mechanical calculation of σ is only feasible for atoms and atomic ions. 62 However, several semi-empirical and semiclassical models have been developed to circumvent this restriction. 63,64 One common approach is the so-called additivity model. 65 This model relies on summing ( ) a ( ) b 38 individual contributions of bonds and functional groups to determine σ max . The additivity method has been shown to reproduce experimental values of σ max for alcohols and halocarbons with good accuracy. 67-68 Another popular method is the point-like Binary- Encounter-Bethe (BEB) model. BEB uses a weighted combination of modified Mott theory for small-impact parameter collisions, and Bethe cross-section theory for large- impact parameter collisions. 56,69,70 When combined with a sufficiently high level of ab initio calculations, BEB yields cross-sections that are in excellent agreement with experiment. 52 Moreover, BEB is not limited to calculation of just σ max . Examples of σ for atoms and molecules are represented in Figure 2.12 by the measured electron impact ionization cross-sections as well as BEB fits for (a) Helium and (b) acetylene. For helium, σ max is approximately 3.75x10 -17 cm 2 and occurs when the electron kinetic energy is 105 eV. The maximum total electron impact ionization cross-section for acetylene is 5.2x10 -16 cm 2 and occurs at an electron energy of 87 eV. 2.5.1 Interpretation of σ max Figure 2.13. Image showing how the polarizability volume acts as an effective cross-section for the process of an incoming electron ejecting a bound electron from a target species. 52 σ e - IN e - OUT e - OUT Polarizability Volume α σ e - IN e - OUT e - OUT Polarizability Volume α 39 The observed shape of an absolute cross-section curve is often explained in terms of a resonance between the de Broglie wavelength of the incoming electron and the size of the atom/molecule’s electron cloud. This correlation between σ and the polarizability volume (α) was first observed by Lampe et al. 71 If we envision the electrons that comprise α as a sphere surrounding the target species, then the effective radius of the electron cloud is given by: 64 ( ) 1/3 3 / 4 r α α π = (2.24) Combining this radius with the root mean square (rms) radius of the electron density, (3/5) 1/2 r a , yields a corresponding rms diameter of the molecule: ( ) ( ) 1/2 1/3 2 3/ 5 3 / 4 rms d α π = (2.25) The only size-related quantity for the incident electron is its de Broglie wavelength. 1/2 2 2 hh p mqE λ   = =     (2.26) where h is Planck’s constant, p is the momentum, m is the mass, q is the charge, and E is the kinetic energy of the incoming electron. This suggests that the peak in the ionization efficiency curve may be due to a resonance condition when the incident electron wavelength matches the effective molecular diameter. 64 This argument is strengthened by using the resonance condition to solve for the electron energy at which σ max occurs. Setting equations 2.25 and 2.26 equal and solving for E shows: 2/3 2 max 54 24 3 h E mq π α    =      (2.27) 40 Equation 2.27 correctly predicts the energy of σ max for most atomic and molecular species. In the molecular case, a rough metric for a local polarizability diameter is the bond length. Consequently, resonance is when the de Broglie wavelength of the incident electron is comparable to various bond lengths of the target molecule. Typical bond lengths in organic molecules lie between 1.3 and 1.5 Å, which correspond to electron energies of 89 and 67 eV, respectively, in good agreement with experiment. 2.6 Production and Detection of the Ethynyl Radical A number of experimental studies of the ethynyl radical (C 2 H) have been carried out in the last thirty years. Many studies have measured the rate coefficients for reactions of C 2 H with a variety of neutral molecules. 72-79 Several spectroscopic studies have aimed to understand the vibrationally cold ground state, 80-82 vibrational levels of the X state, 83-89 and the electronically excited A state, 90-92 while others have used laser induced fluorescence (LIF), UV absorption, and fluorescence detection to examine higher C 2 H excited states and C 2 internal excitations. 93-104 Although C 2 H is a seemingly simple molecule, experimental and theoretical results demonstrate the complexity of this system, and the need for further work. 97 In many experiments, C 2 H is prepared via 193.3 nm photolysis of the C−H bond during supersonic expansion of acetylene (C 2 H 2 ). 93-106 [Note that the energy of a 193.3 nm photon (~6.4 eV) is greater than the D 0 (HCC−H) of 5.7 eV]. 107 Dissociation of acetylene to form vibrationally excited ethynyl radical (C 2 H*) occurs via the mechanisms outlined in Figure 2.14. Briefly, the absorption of a 193.3 nm photon promotes acetylene 41 to its 1 1 A” state. This state is diradical-like with a trans-bent geometry, and a C−C bond order of 2. 105 A barrier of ~560 cm -1 108 inhibits immediate dissociation and arises from an avoided crossing between the 1 1 A” and the 2 1 A”. Instead, the bottle neck created by the barrier slows the direct production of C 2 H* enough to allow internal conversion (IC) to compete with tunneling through the barrier. IC of the 1 1 A” state to the dissociative 2 1 A’ state allows acetylene to form C 2 H*. However, dissociation is not instantaneous, and diabatic surface hopping to the 1 1 A’ state at the 2 1 A’/1 1 A’ avoided crossing readily occurs. 106 Although, IC to the 1 1 A’ state is possible, it is not considered to be an important reaction pathway. 105 Thus, vibrationally excited C 2 H is produced primarily in its ground state. 106 42 Figure 2.14. Schematic representation of the potential energy surfaces involved in the 193.3 nm photodissociation of acetylene. Formation of excited C 2 H (A 2 Π) occurs via two possible routes: (a) tunneling to the continuum through the potential barrier on the A 1 A” curve and/or (b) through internal conversion to the dissociative 2 1 A’ state. Formation of vibrationally excited C 2 H (X 2 Σ + ) occurs by (c) internal conversion to the 2 1 A’ state followed by subsequent diabatic surface hopping to the 1 1 A’ state at the 2 1 A’/1 1 A’ avoided crossing. Figure is adapted from references 97 and 105. The C 2 H ground state is linear with 2 Σ + symmetry, 109 followed by the electronic A state, which is also linear, but of 2 Π symmetry. The A state is only ~3600 cm -1 above the ground state, 91 where it is speculated that there exist strong couplings between the two states. 110 Next is the non-linear B state, which has a CCH angle of ~ 108° and a C−C bond distance that is ~15% longer than the ground state. 102 LIF spectra of the B state (2 2 Σ + ) has been recorded and examined by the Hsu group. 99-104 They observed that non- radiative processes quickly dominate B state decay when the system is excited to vibrational states that are only a few quanta above the initial transition. 103 These results, ~ ~ ~ ~ 193.3 nm 1 1 A’ 2 1 A’ A 1 A” 2 1 A’ a b c C 2 H(X 2 Σ + ) C 2 H(A 2 Π) Energy C−H Bond Length ~ ~ ~ ~ 193.3 nm 1 1 A’ 2 1 A’ A 1 A” 2 1 A’ a b c C 2 H(X 2 Σ + ) C 2 H(A 2 Π) Energy C−H Bond Length 43 and the results of Jackson and coworkers, 93-104 show that excitation of the ethynyl radical at this energy or higher ultimately leads to dissociation into C 2 and H. This conclusion is in agreement with the theoretical work of Duflot et al. 111 The calculated potential energy surface of the B state shows a shallow well along the C−H coordinate that eventually leads to C 2 and H products (Figure 2.15). Figure 2.15. Calculated adiabatic potential energy curves for the lowest 2 Σ + and 2 Π states of C 2 H as functions of the C−H bond length. Full lines represent Σ + symmetry, and dashed lines Π symmetry. 111 Despite the extensive work that has been carried out on C 2 H, a number of important questions remain. For example, what is the D 0 (CC−H)? Hsu and coworkers reported an upper bound of 39,388 cm -1 , 103 while theoretical estimates place D 0 at 37,422 cm -1 . 112 To address this, several high-n Rydberg time-of-flight 113 experiments were planned that would yield D 0 to a few tens of cm -1 . A summary of the work prerequisite to these experiments is given below. Energy (eV) X 2 Σ + 2 2 Σ + 3 2 Σ + A 2 Π 2 2 Π 3 2 Π 1 2 3 4 5 6 0 2.5 5 7.5 10 C 2 (X 1 Σ + g ) C 2 (A 1 Π u ) C 2 (c 3 Σ + u ) C 2 (a 3 Π g ) C 2 (B 1 Σ + g ) C 2 (d 3 Π g ) 7 R C-H (bohr) Energy (eV) X 2 Σ + 2 2 Σ + 3 2 Σ + A 2 Π 2 2 Π 3 2 Π 1 2 3 4 5 6 0 2.5 5 7.5 10 C 2 (X 1 Σ + g ) C 2 (A 1 Π u ) C 2 (c 3 Σ + u ) C 2 (a 3 Π g ) C 2 (B 1 Σ + g ) C 2 (d 3 Π g ) 7 R C-H (bohr) 44 2.6.1 Experiments and Results Several preliminary experiments were performed to try and determine optimal conditions under which to prepare C 2 H using supersonic expansion and 193.3 nm photolysis. This involved the setup and alignment of a 780 μm pulsed nozzle (Parker), installation and calibration of a pulsed electron impact ionization TOF mass spectrometer (Jordan TOF products Inc.), and the modification of a vacuum apparatus to allow 193.3 nm light to pass through the expansion chamber. A diagram of the apparatus is shown in Figure 2.16, and useful quantities for acetylene and C 2 H are displayed in Table 2.1. Figure 2.16. Experimental apparatus used for acetylene photolysis. The base pressures were, 2x10 -6 (torr) in the expansion chamber, 10 -7 torr in the interaction chamber (where the gas was ionized), and 10 -8 (torr) at the MCP detector. The total length of the TOF was 1 m and voltages of 1500, 1350, and -3500 were used for the repeller, extractor and MCP bias, respectively. The nozzle was set approximately 2 cm from a 1 mm diameter skimmer and ~ 15 cm from the interaction region of the TOF. MCP detector skimmer gate valve pulsed nozzle molecular beam TOF stack turbo pump diffusion pump turbo pump expansion chamber CaF 2 window EGUN MCP detector skimmer gate valve pulsed nozzle molecular beam TOF stack turbo pump diffusion pump turbo pump expansion chamber CaF 2 window EGUN 45 Molecule I. P. (eV) D 0 (C−H) (eV) 193.3 nm absorption cross-section (cm 2 ) C 2 H 2 11.46 ± 0.01 a 5.712 ± 0.001 c 1.34 x 10 -19 e C 2 H 11.6 ± 0.5 b ~4.85 d − References (a) 114, b) 115, (c) 107, (d) 112, (e) 116 Table 2.1. Ionization potential and C−H bond energy for acetylene and the ethynyl radical. The 193.3 nm absorption cross-section of acetylene is for room temperature. After installation of the TOF, the emission current was set to the manufacturer recommend settings of 1 mA. Focus energy was set to yield optimum signal for each experiment. Several background spectra were acquired at various electron energies in order to test the performance of the spectrometer. These test spectra were used to determine the operating voltages of the spectrometer. Setting the repeller and extractor plates to 1500 and 1350 volts, respectively, yielded a full width half max (FWHM) of 0.28 amu for argon. The spectra also indicated that the electron energy display on the control panel was not the true electron energy. Therefore, a calibration of the electron energy control was performed. Several gases with known ionization and appearance potentials were leaked into the chamber. The electron energy was then decreased until the mass peak of the respective gas vanished. The energy at which the peak vanished was assumed to be either the ionization or appearance potential and was compared to its accepted literature value. The resultant calibration plot of the actual electron energy vs. the control panel electron energy is shown in Figure 2.17. The data set is fit to a linear regression line, which served as the electron energy calibration for all experiments. 46 20 25 30 35 40 45 50 55 15 20 25 30 35 40 45 y = 0.935x - 4.005 R 2 = 0.996 C 2 H 2 + C 2 H + He + Actual Energy (eV) Panel Energy (eV) Ar 2+ Figure 2.17. Calibration line for the actual electron energy as a function of the electron gun control panel electron energy. The ionization potentials for acetylene and helium as well as appearance potentials of doubly ionized argon and the C 2 H ion were used as references for the actual electron energy. The next experiments were designed to characterize the gas pulse and nozzle operation. Argon was used as the expanding gas. The nozzle was operated at 10 Hz with a backing pressure of 10-15 psig and an open time of 250 μs. The TOF was run at 50 kHz so that multiple TOF spectra from a single gas pulse could be acquired. A density profile of the gas pulse vs. time is shown in Figure 2.18. It is clear from Figure 2.18 that the expansion is not ideal. The pulse has a fast rise in density until it peaks after ~200 μs then begins to decrease. Yet, it does not drop to zero. Instead, the pulse tapers off and maintains a low signal until completely disappearing almost 2 ms later. The taper indicates that the poppet does not fully close, or possibly bounces, once the nozzle is switched OFF. It was determined that there was also a 115 μs delay between when the valve was switched ON and when the valve opened. Both behaviors correspond to some form of mechanical delay that will likely vary from one pulse to the next. However, in 47 most experiments the gas pulse is probed at its empirically determined peak. Doing this avoids such inconsistencies because any deviation in the arrival time of the gas pulse at the probing region will likely be small relative to the ~ 100 μs width of the gas pulse. Moreover, the gas that comprises the tail does not interfere with the gas in the more dense portions of the beam. Thus, the pulse can be treated as if it is of ideal Gaussian shape. Figure 2.18. Pulsed valve expansion profile using argon. The initial part of the profile is consistent with the 250 us open time. The long tail is attributed to a mechanical delay in the nozzle’s closing. With the nozzle and TOF characterized and calibrated, a 15% acetylene/argon mixture was prepared. 99.6% pure acetylene was passed through a Matheson gas purifier (Model 450B) and combined with research grade argon. The tank was left overnight to allow for complete mixing. The mixture was expanded using exactly the same conditions as the pure argon expansion. An image of the TOF spectrum for the gas mixture is shown 48 in Figure 2.19a. To better observe any C 2 H that may be produced, the electron energy was decreased below the appearance potential of C 2 H such that only the C 2 H 2 peak was visible in the TOF spectrum (Figure 2.19b). A 193.3 nm beam from an ArF laser was then introduced. Two CaF 2 windows were added to the expansion chamber using custom window mounts, so that the 193.3 nm beam could pass near the nozzle or skimmer (Figure 2.16). Initially the 193.3 nm beam was directed in front of the nozzle (position 1 of Figure 2.20a). The laser was focused approximately 5 cm after the nozzle with a 100 cm focal length lens at a fluence of 285 mJ cm -2 . The relatively high fluence was used to compensate for the low absorption cross-section of acetylene (Table 2.1). Once the light and expanding gas intersected, a faint blue-green glow appeared. It was determined that the glow was the well-known Swan band from C 2 fluorescence. 117 The fluorescence indicated that photolysis was indeed occurring. This was also reflected by a depletion of the C 2 H 2 peak in the TOF spectrum (Figure 2.19c). Unfortunately, the depletion of the C 2 H 2 peak did not correspond to an increase in either C 2 H or C 2 signal. Whether the nascent radicals reacted, were ejected from the beam, or were in too little in number was unclear at this time. However, the width and magnitude of the C 2 H 2 depletion indicated that the photolysis was interfering with the expansion. As a test, the 193.3 nm beam was aligned just before the skimmer (position 2 of Figure 2.20a). Identical expansion and focusing conditions were used for this experiment. Again, a depletion of C 2 H 2 was observed (Figure 2.20d), with no increase in C 2 H or C 2 signal. In this case, the depletion 49 was nearly 1/3 in magnitude and narrower in time, confirming that the photolysis in front of the nozzle interfered with the expansion. 0 10 20 30 40 50 m/e C 2 + C 2 H + C 2 H + C 2 H 2 + Ar 2+ Intensity (a.u.) Ar + 20 25 30 23.1 eV 22.2 eV 21.3 eV 20.3 eV 18.4 eV 19.4 eV m/e C 2 H + C 2 H 2 + 240 250 260 270 280 290 0 5 10 15 20 25 30 % Depletion C 2 H 2 Laser Delay (µs) 300 310 320 330 0 2 4 6 8 10 % Depletion C 2 H 2 Laser Delay (µs) Figure 2.19. (a) TOF mass spectrum of acetylene seeded in argon, taken with an electron energy of 60 eV. The inset in (a) is magnified by 4x to better show the acetylene cracking pattern. (b) TOF spectra at several electron impact energies demonstrate the disappearance of the C 2 H peak at sufficiently low electron energy. An electron energy of ~18.4 eV was used in all subsequent experiments to better discern photolyzed C 2 H signal from that of fragmented acetylene. (c) The acetylene depletion signal when photolysing directly in front of the nozzle, as opposed to (d), which is the depletion when photolysing in front of the skimmer ~1.5 cm downstream. The FWHM of (c) is roughly 30 μs while that of (d) is only 15 μs, indicating that photolysing in front of the nozzle disturbs the supersonic expansion. ( ) a ( ) b ( ) c ( ) d 50 In light of the previous results, or lack thereof, it was decided that acetylene be photolyzed prior to expansion using a technique this is often employed to initiate photochemical reactions. 118 To achieve this, the nozzle was first modified by creating a cylindrical cavity centered on the nozzle orifice that was approximately 500 micrometers deep, but did not affect the orifice. A Suprasil tube, with a 1 mm inner diameter was set into the cavity and glued to the nozzle (Figure 2.20b). The tube was then illuminated with 193.3 nm light during expansion. Again, depletion of the acetylene peak was observed, with no corresponding increase in C 2 H. When pure acetylene was expanded during illumination, black soot began to build up inside the tube. This indicated that photolysis and subsequent secondary reactions were occurring, but still no photoproducts were detected. Additionally, Suprasil absorbs a small amount of 193.3 nm and caused the tube to become an opaque milky white over time. Using high fluences, like those needed to compensate for the low acetylene cross-section, caused this to occur quickly, which meant that the tube had to be changed often. Figure 2.20. (a) Schematic showing the three regions where photolysis of acetylene was attempted. (b) Representation of the suprasil tube attached to the nozzle. In a final attempt to detect C 2 H, acetylene was photolyzed in front of the TOF stack (position 3 in Figure 2.20a). Ideally, photolysing at the ionization region would skimmer pulsed nozzle molecular beam TOF stack EGUN (1) (2) (3) skimmer pulsed nozzle molecular beam TOF stack EGUN (1) (2) (3) skimmer pulsed nozzle Suprasil tube skimmer pulsed nozzle Suprasil tube ( ) a ( ) b 51 provide the largest concentration of C 2 H that could then be ionized and detected. However, the EGUN physically blocked the laser beam from passing through this region. In light of this, the next best position to photolyze acetylene was in front of the TOF stack. Considering the molecular beam concentration decreases as the inverse of the distance traveled squared, i.e. 1/d 2 , 1 photolysing as close to the ionization region as possible minimized this loss. Additionally, isotropic recoil velocities generated by photolysis cause the photoproducts to expand in a Newton sphere, 119 thereby decreasing the concentration. Thus, photolysing in front of the TOF stack would also minimize the decrease in C 2 H concentration associated with the expanding sphere. The radius of the sphere was also reduced by switching the carrier gas from argon to helium. Expanding a dilute concentration of seeder molecules in a light carrier gas increases the beam velocity of the seeder molecule. 2 The increased beam velocity caused the photolyzed molecules to arrive at the ionization region sooner, and therefore reduced the amount of time in which the Newton sphere could expand. In light of these changes the laser timing and spatial overlap needed to be determined. This was achieved by first attempting to detect photolysis using 8% hydrogen sulfide (H 2 S) in helium. H 2 S was chosen because its absorption cross-section at 193.3 nm is ~15x larger than that of acetylene (6.5x10 -18 cm -1 ). 120 Once optimized, H 2 S signal showed a depletion of nearly 50 percent at modest fluences (80 mJ cm -2 ) and indicated the optimal timing and laser position for photolysis. Immediately after the optimization, the H 2 S mixture was replaced with a similar acetylene mixture and the experiment was run. In this case, no significant depletion was 52 observed, even when expanding pure acetylene and using extremely high laser fluence (~4.9 J cm -2 ). However, a difference spectrum (laser on minus laser off) revealed a very small increase in C 2 H (inset of Figure 2.21b). While this last approach did produce C 2 H, it did not produce an amount that could be effectively studied with the current setup. 2.1 2.4 2.7 C 2 H 2 + Intensity (a.u.) Time (µs) C 2 H + 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Intensity (a.u.) Time (µs) C 2 H + from photolysis x20 Figure 2.21. (a) Acetylene and ethynyl peaks recorded with 193.3 nm beam directly in front of ionization region of TOF. Pure acetylene and a laser power was ~4.9 J cm -2 was used for this measurement. (b) Difference spectrum for laser on minus laser off. The inset in (b) is the region of the difference spectrum corresponding to C 2 H + , between 2.2 and 2.35 μs, and shows that a very small amount of photolyzed C 2 H is present. 2.6.2 Discussion Two important results are derived from the above experiments. First, the absence of appreciable radical signal, even when significant depletion was observed, suggests that the radicals either react, are ejected from the beam, absorb further and dissociate, or are too low in concentration to be measured by the current electron gun. Reaction of the nascent C 2 H is not expected to be a major factor. The C 2 H concentration was kept relatively low to avoid such issues and only when pure acetylene was photolyzed in the ( ) a ( ) b 53 Suprasil tube did any type of soot become visible. Ejection of C 2 H from the molecular beam was most important after the skimmer where collisions from supersonic expansion have ceased. Without the collisions to oppose the recoil generated from photolysis, the Newton sphere could expand freely. However, this effect was minimized by photolysing directly in front of the ionization region and using a lighter carrier gas. Absorption beyond the initial photolysis was a concern, especially considering strong C 2 fluorescence was observed when photolysing immediately after the nozzle. The question as to whether all C 2 H is quickly photolyzed after creation is further complicated by the absence of the C 2 H 193.3 nm absorption cross-section in the literature. However, a range of fluences were used during each attempt at photolysis. And even when the strong glow of C 2 fluorescence was observed, no C 2 was detected. The most likely culprit for the lack of C 2 H signal is low electron impact ionization efficiency. The calculation below shows that the probability of ionizing trace amounts of C 2 H using electron impact ionization is very low. The challenge in detecting trace elements using electron impact ionization is producing enough electron current at the desired electron energy to generate a reasonable amount of target ions. For instance, consider an isolated ethynyl radical in the ionizing region of a TOF. Analogous to the saturation condition in optical spectroscopy, 3 the probability of ionizing the radical approaches 100% when the electron fluence (φ) is comparable to the inverse of the total electron impact ionization cross-section, σ (Section 2.5), i.e. φ ≈ 1/ σ . Thus, if we take the σ of acetylene to be comparable to that of the ethynyl radical, then from Figure 8 σ(ethynyl radical at 20 eV) ≈ 10 -16 cm 2 , which 54 corresponds to an electron fluence of 10 16 cm -2 . For the current setup, the ionizing region has a cross-sectional area (A) of 0.127 cm 2 , and the duration of bombardment (τ) was 5 microseconds. Thus, the required current to achieve ‘saturation’ is: 16 19 6 10 *0.127*1.602 10 C/s 40.6A 5 10 AQ x i x ϕ τ − − = = = (2.28) where Q is the electron charge in Coulombs. Equation 2.28 shows that an electron current of 40.6 amps is needed to produce a flux of 10 16 cm -2 . Unfortunately, the electron gun can only produce a maximum current of 1 mA at 20 eV, which corresponds to a fluence that is ~10 5 times smaller than what is needed. The second important result stems from the absence of a C 2 H 2 depletion signal when photodissociating in front of the ionization region. This suggests that the absorption cross-section of acetylene at 193.3 nm under these conditions is smaller than the room temperature cross-section reported by Seki et al. 116 In fact, all reported cross-sections for C 2 H 2 are reported at room temperature. Thus, if thermal population contributes to the room temperature cross-section then cooling the acetylene would cause the cross-section to decrease. 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In this paper the photoionization of an important OLED species: tris(2-phenylpyridine)iridium, hereafter referred to as Ir(ppy) 3 , is examined. Introductory comments are given below to provide context for what follows. A recent review 1 and book 2 by Yersin (especially the chapter by Yersin and Finkenzeller) provide excellent overviews of the state-of-the-art of OLED research, including a number of fundamental electronic structure considerations. 65 Figure 3.1. This schematic indicates important features of an OLED (not to scale, typical dimensions are given in parentheses). Electrons are injected from the cathode through a thin protection layer into the electron transport layer, which typically consists of an amorphous organic material. Holes are injected into the hole transport layer from an optically transparent anode (typically an In 2 O 3 / SnO 2 composite) that permits light to exit the device. In the recombination and emission layer, electron-hole pairs form excitons that relax to the dopant excited states (indicated by an asterisk * ) that emit photons. Adapted from reference 2. A typical device consists of layers of compounds sandwiched between electrodes that inject electrons and holes into layers. 1-5 Figure 3.1 illustrates the most important features. A number of additional layers that further enhance device performance have been omitted to facilitate focusing on the most important processes. When a voltage is applied across the electrodes, electrons are injected from the cathode through a thin (typically ≤ 1 nm) electron injection and protection layer into the lowest unoccupied molecular orbitals (LUMO's) of molecules in the electron transport layer, which typically consists of an amorphous material such as Alq 3 (q = 8-quinolinolato-O,N). 6,7 The injected electrons migrate slowly by directed site-to-site (polaron) hopping driven by the applied field. electron transport layer (20 nm) hole transport layer (50 nm) recombination and emission layer (40 nm) − cathode (100 nm) anode (100 nm) light output − + − + − + * excited state photon exciton + electron injection and protection layer (1 nm) + − − − + + 66 The anode injects holes by removing electrons from the highest occupied molecular orbitals (HOMO's) of molecules in the hole-transport layer. The electrons and holes move toward each other under the influence of the field and form excitons in an emitter-doped recombination layer. Ideally, the excitons are highly excited states of the emitter molecules, rather than of the organic host, though the latter also can also result (ultimately) in the desired excitation. 8 Electronic excitation cascades down to the molecular excited states (indicated by an asterisk * ) that emit photons. The photons exit via the optically transparent anode, which typically consists of a mixture of In 2 O 3 and SnO 2 , i.e., indium tin oxide (ITO). 4,5 Each charge carrier has spin. In the case of a hole, the spin is that of the residual electron. Because the spins of a combining electron and hole are uncorrelated, both singlet and triplet excitons are formed. Specifically, the spins combine to give one singlet and three triplets. It is generally accepted that each of the four states is formed with equal probability. In other words, three triplets are created for each singlet. 1-3,9 67 Figure 3.2. (a) Organic molecules (negligible spin-orbit coupling) emit only from the lowest excited singlet S 1 . Because T 1 → S 0 emission is extremely weak, triplet excitation is lost through radiationless decay rather than photon emission, and consequently the maximum quantum yield is 25%. (b) In triplet harvesting, electron-hole recombination leads to excitons having a triplet-to-singlet population ratio of 3:1. Excitation cascades down the triplet and singlet manifolds, with internal conversion (IC) and intersystem crossing (ISC) resulting in excitation ultimately residing in the lowest triplet, 3 MLCT (T 1 ), which emits photons. An organometallic compound (in which spin-orbit coupling (SOC) is strong) such as Ir(ppy) 3 ex- periences relatively fast ISC and efficient T 1 → S 0 phosphorescence. This can result in quantum yield approaching 100%. Referring to Figure 3.2(a), following the cascade from the initially formed excitons to lower energies, organic emitters, e.g., polyfluorenes, 10 undergo fluorescence from the excited singlet S 1 . Phosphorescence from the lowest triplet (whose sublevels are shown separated from one another for clarity) is, for all practical purposes, eliminated because of the long triplet spontaneous emission lifetimes that are characteristic of the weak spin-orbit coupling (SOC) regime. Because of these long spontaneous emission lifetimes, T 1 decays non-radiatively. As a result, organic emitters have low electroluminescent quantum yield. 11 In the limit of negligible T 1 → S 0 emission, the maximum quantum yield is 25%. Certain metal-ligand complexes undergo efficient phosphorescence following photoexcitation and / or the passage of electric current through solid hosts that contain fluorescence S 1 T 1 S 0 radiationless decay slow ISC organic emitter phosphorescence 3 MLCT(T 1 ) S 0 fast ISC organometallic emitter (b) (a) 1 MLCT 68 these complexes. 4-7,12 As mentioned earlier, the latter means of excitation is attractive from the point of view of display technologies. Among the most promising of these complexes is Ir(ppy) 3 and similar species. 3 Seminal and extensive contributions by the groups of Thompson, 4,12,14,15 Forrest, 4,12,13,15 and Yersin 16,17 have demonstrated the high potential of this system, and promising paths to device fabrication have been identified. 1,2,4-7,12,15 Related materials can be used to obtain different emission wavelengths such that the primary colors (red, green, and blue) are obtained. For example, this tuning can be achieved by using electron withdrawing and donating groups substituted at the ppy (2-phenylpyridine) ligand. 15,18 Referring to Figure 3.2(b), the triplet states can be made to do useful work by employing a transition metal complex in which the transition-metal atom is responsible for strong SOC. 1-3 In such cases, the intersystem crossing (ISC) rate from 1 MLCT to 3 MLCT (T 1 ) is sufficiently fast to inhibit fluorescence from the lowest excited singlet. 19-22 The acronym MLCT stands for metal-to-ligand charge transfer. This label can be somewhat misleading, as the situation can be more complicated. 23-25 For the sake of brevity, hereafter we shall use the label T 1 instead of 3 MLCT, with the understanding that this T 1 bears no resemblance to the one in Figure 3.2(a), in the sense that it contains enough singlet character to ensure high phosphorescence quantum yields. As a result of efficient energy transfer processes, both singlet and triplet excitons populate the T 1 substates, which decay predominantly via phosphorescence. This is referred to as triplet harvesting. 1-3 Strong SOC significantly increases the phosphorescence rate, enabling it to compete favorably with radiationless decay, and 69 quantum yields therefore can approach 100%. 6,12 A number of organometallic (specifically, organo-transition-metal) complexes have been used as phosphor dopants in OLED's to overcome the efficiency limit imposed by the absence of sufficient spin-orbit interaction. 1-3,26 Internal conversion (IC) and ISC mechanisms are enlisted frequently. Though understood separately, these are unruly in systems that consist of many potential energy surfaces (PES's), unknown coupling parameters, and condensed phase host environments, leaving open important issues: (i) electronic structure of low-lying singlets and triplets including the role of spin-orbit interaction; (ii) vibrational relaxation, e.g., from the regime of quantum chaos to that of good quantum numbers; (iii) interactions with host environments; (iv) electron-hole recombination and transport; and so on. 70 Figure 3.3. (a) Photoexcitation of ligand-centered 1 LC(π π*) is accompanied by rapid radiationless decay: IC to 1 MLCT followed by ISC to the levels labeled T 1 (energies are not to scale). 28 (b) Absorption spec- trum of Ir(ppy) 3 in dimethylformamide at 414 K. Note the large s 1 absorption cross-sections (i.e., units of 10 -16 cm 2 ). 29 The yellow boxed region, 34 150 – 35 775 cm -1 (4.234 – 4.435 eV), corresponds to the portion of the 1 LC ← S 0 system examined in this work. Inset: changing the temperature over the range 295 – 414 K has a minimal effect on the absorption spectrum in the energy range of interest; only slight broadening is observed. In order, from the top trace, the temperatures are: 295, 333, 353, 383, 408, and 414 K. The vertical axis in the inset is not labeled, as the curves are offset from one another for clarity. They are nearly identical over the indicated range. (c) Absorption spectrum of solution phase 2-phenylpyridine, adapted from reference 30. The 1 LC ← S 0 feature is analogous to the one in Ir(ppy) 3 . S 0 Ir(ppy) 3 + + e 1 MLCT (a) T 1 1 LC(ππ * ) σ 1 σ 2 (b) wavenumber / cm −1 20000 25000 30000 35000 2 1 0 34000 35000 36000 1 MLCT 1 LC(ππ * ) T 1 σ 1 / 10 –16 cm 2 260 280 240 220 wavelength / nm 4.0 3.8 3.6 3.4 (c) log (ε / absorbance) 71 Not surprisingly, many singlets and triplets in the energy region of interest need to be taken into consideration. SOC is effective because of near resonances among singlets and triplets, as well as approximate symmetries. Crossings and near crossings of PES's facilitate couplings, and this likely plays an important role. For Ir(ppy) 3 , the papers of Nozaki and Nozaki and coworkers do a good job of combining SOC with time dependent density functional theory (TDDFT) calculations of low-lying singlets and triplets. 25,27 For example, Table 6 in reference 25 lists energy, singlet fraction, and oscillator strength for 140 low-lying excited states. It is seen that spin-orbit interaction plays an important role in coupling the triplet and singlet manifolds. To understand what happens in OLED devices, our understanding of an isolated entity such as Ir(ppy) 3 must evolve to one of the larger system of Ir(ppy) 3 plus its host. In principle we would like to refine the theory of an isolated molecule such as Ir(ppy) 3 as much as possible before addressing the challenge presented by the environment. To this end, one of the most important and fundamental properties of a molecule is its ionization: vertical and adiabatic ionization energies, associated orbital and structural changes, etc. Yet, little is known about the ionization of Ir(ppy) 3 . This is one of the factors that motivated the present study, in which the photoionization of gaseous Ir(ppy) 3 has been examined using a 2-photon photoionization scheme in which the ligand-centered 1 LC(ππ * ) state, hereafter referred to as 1 LC, serves as the intermediate (Figure 3.3). The 1 LC state is, however, an interesting intermediate in that radiationless processes (IC and ISC) rapidly transfer excitation to T 1 , from which photoionization takes place. A 1- 72 photon photoionization experiment (i.e., using 193.3 nm radiation from an ArF excimer laser) was carried out as well. Referring to Figure 3.3, it proved possible to isolate 2-photon photoionization and characterize it over the portion of the 1 LC ← S 0 system indicated by the yellow box. It turned out that photoionization could be achieved with no discernible ion fragmentation. In other words, at sufficiently low fluence, the parent ion, Ir(ppy) 3 + , dominates the mass spectrum. Large molecules such as Ir(ppy) 3 have high densities of electronic states at energies near and above ionization threshold, and it is not always feasible to eliminate the absorption of photons beyond the ionizing transition. In the present case, however, the very large σ 1 values (i.e., > 10 -16 cm 2 , reference 29, see Figure 3.3) and, following absorption of the second photon, rapid radiationless decay in competition with ionization (discussed later) help make this possible. From these 2-photon photoionization experiments, an upper bound to the vertical ionization energy (VIE) was obtained subject to a reasonable assumption about the disposition of Ir(ppy) 3 vibrational energy in the Ir(ppy) 3 + ion, namely, that T 1 vibrational excitation is transferred more-or-less intact to the cation. 31 As mentioned above, 1-photon photoionization at 193.3 nm (51 730 cm -1 , 6.414 eV) was also achieved. Again using the assumption that parent vibrational excitation is carried over to the cation yields an approximate upper bound of 6.4 eV. This value agrees with calculations carried out in our group, which places both the VIE and the adiabatic ionization energy (AIE) at approximately 5.9 eV, as well as a previous calculation that places the VIE at approximately 5.94 eV. 32 73 It is concluded that the ionization energy (both VIE and AIE) of gaseous Ir(ppy) 3 is in the vicinity of 6 eV. This is at odds with a value of 7.2 eV surmised from energy loss spectra, indicating the need to reinterpret the peak at 7.2 eV in the energy loss spectra. 33 It is also shown that the absorption spectrum can be reproduced rather well using vertical excitation from the S 0 equilibrium geometry. This supports the assumption that vibrational excitation is carried more-or-less intact to the cation. In the context of applications that involve organic photovoltaics (OPV's) and OLED's, 1 a molecule's ionization energy (IE) is one of its key properties, as it quantifies a system's electron-donating ability and it is related to the reduction potential. For optimal performance of materials used in OLED devices, the IE's and electron affinities (EA's) (commonly referred to as HOMO and LUMO energies, respectively) of molecules in the active (i.e., light-generating in OLED's and exciton-generating in OPV's) layer needs to be matched to the energy levels of the electrodes. The fact that the IE of Ir(ppy) 3 is low augurs well for its use in OLED devices. Indeed, it is significantly lower than those of either 2-phenylpyridine (8.0 eV) 34 or a bare iridium atom (8.967 eV). 35 3.2 Experimental Methods and Results The absorption spectra of Ir(ppy) 3 shown in Figure 3.3 were recorded using a Varian Cary 300 spectrophotometer. Solutions were prepared by dissolving 6 mg of Ir(ppy) 3 (provided by the Thompson group at USC) in 125 mL of dimethylformamide (DMF). This solvent was chosen because its high boiling point (426 K) 36 enabled spectra to be collected at temperatures up to 414 K. Spectra were also recorded using the solvent 74 dichloromethane (DCM). Though its UV transmission is superior to that of DMF, it cannot be used at the higher temperatures because its boiling point is 313 K. 36 No significant spectral differences were observed with these solvents. Heating was achieved by wrapping the cuvettes in resistive wire and passing current through the wire. Temperature was monitored with a thermocouple. Figure 3.4. Schematic of the experimental arrangement: (a) The main vacuum chamber has a base pressure of 2x10 -9 Torr. (b) Details of the time-of-flight mass spectrometer (TOFMS): Typical mass resolution was m /∆m ~ 200. Laser photoionization was carried out in a chamber that was evacuated using a turbomolecular pump (Leybold Turbovac 1000C), as indicated in Figure 3.4(a). The base pressure was 2x10 -9 Torr. Solid Ir(ppy) 3 was loaded into a stainless steel cylinder and a (b) MCP detector (double chevron) TOFMS photoionization effusive source drift tube 2.00 kV 2.36 kV (a) TOFMS drift tube MCP detector photoionization region turbomolecular pump effusive source d = 0.70cm s = 0.62cm δ s ~ 0.7mm 75 0.5 cm diameter aperture allowed Ir(ppy) 3 vapor to effuse into the chamber. The cylinder was heated using resistive wire. During operation, the cylinder temperature was maintained at approximately 500 K, and the chamber pressure was 5x10 -9 Torr. At 500 K there was no thermal decomposition of the Ir(ppy) 3 sample. Referring to Figure 3.4, mass spectra were recorded using a time-of-flight mass spectrometer (TOFMS). Photoions were produced between two electrodes: a repeller plate and an extractor that consists of a metal ring with a fine nickel mesh in the center. Ions receive an additional 2 kV of kinetic energy after passing through the extractor. They then drift for 51.3 cm before arriving at the double-chevron microchannel plate (MCP) detector. The two meshes indicated with red provide a ground shield, ensuring a field-free drift region. Calibration was carried out using NO photoionization with a variety of voltages applied to the electrodes. The NO + flight times, in combination with the distances indicated in Figure 3.4 (i.e., d = 0.7 cm, s = 0.62 cm, and ∆s ~ 0.7 mm), enabled the length of the drift region to be determined accurately. 76 Figure 3.5. With 415 mJ cm -2 of 35 673 cm -1 (4.423 eV) radiation, only the Ir(ppy) 3 + parent ion is observed (vide infra Figure 3.8). The Ir(ppy) 3 + peak consists of contributions from the major isotopologues (see text for details). (a) The experimental curve (red) is the average of several traces, each of which is comprised of ~ 1000 individual spectra. The blue curve is obtained using the natural isotope abundances and assigning a 2.35 amu FWHM to each mass, as indicated in (b). This fits the experimental trace [red curve in (a)] rather well. Resolution was optimized at the parent ion mass by adjusting the experimental parameters to make the Ir(ppy) 3 + peak as narrow as possible. Voltages of 2.36 and 2.00 kV were applied to the repeller and extractor electrodes, respectively. A voltage of approximately – 1.9 kV was applied to the MCP detector. The magnitude of this voltage was increased over time to counteract degradation of the detector. Signal acquisition was 645 650 655 660 665 3.6 amu experimental simulation (a) (b) mass / amu 645 650 655 660 665 77 carried out using a dual channel Gage Compuscope CS-8012A. The sample rate was 100 MS / s, providing 10 ns bin widths. The repetition rates were those of the lasers, 20 Hz for the 2-photon studies and 10 Hz for the 1-photon study. Typically, ~ 1000 individual spectra were summed. The TOF spectra were processed using custom Labview 8.5.1 programs to yield the mass spectra. Under these conditions, the Ir(ppy) 3 + signal shown in Figure 3.5(a) (solid red line) was recorded using 35 673 cm -1 (4.423 eV) radiation and a fluence of 415 μJ cm -2 . The trace shown is the average of several traces. The peak has a full width at half maximum (FWHM) of approximately 3.6 amu. A significant percentage of this width is due to the isotopic composition of the Ir(ppy) 3 sample. Though the natural abundance of 13 C is only 1.07%, Ir(ppy) 3 + contains 33 carbon atoms. Consequently, (rounded to the nearest tenth of a percent) 70.1% of the Ir(ppy) 3 molecules contain only 12 C atoms, 25.0% contain one 13 C atom, 4.3% contain two 13 C atoms, 0.5% contain three 13 C atoms, and a negligi- ble percentage contain more than three 13 C atoms. Thus, 13 C plays a significant role in the mass spectra. Including the natural abundances of the two iridium isotopes (i.e., 62.7% and 37.3% for 193 and 191 amu, respectively) yields the following isotopologues, where the subscript on C denotes the number of 13 C atoms in Ir(ppy) 3 : 191 Ir / 13 C 0 653 amu 26.2% 193 Ir / 13 C 0 655 amu 44.0% 191 Ir / 13 C 1 654 amu 9.3% 193 Ir / 13 C 1 656 amu 15.7% 191 Ir / 13 C 2 655 amu 1.6% 193 Ir / 13 C 2 657 amu 2.7% 78 The percentages of the relevant masses are: 653 (26.2%); 654 (9.3%); 655 (45.6%); 656 (15.9%); 657 (2.7%); and 658 (0.3%). All but the last of these (which is negligible for the purpose of fitting the curve) are represented by the Gaussian curves indicated in Figure 3.5(b) that were used to fit the peak in Figure 3.5(a). In other words, the peak heights of the contributions in Figure 3.5(b) are proportional to their respective abundances. Each of the constituent peaks was assigned a FWHM of 2.35 amu. This choice is ad hoc. If one wishes, it can be interpreted as a rough measure of the instrumental resolution at 655 amu. Summing the curves in (b) yields the blue curve in (a), which fits the experimental data (red curve). 3.2.1 Multiphoton Ionization Photoionization was carried out using a tunable dye laser and a variety of dye mixtures to cover a reasonable portion of the 1 LC ← S 0 system. The dye laser (Continuum HD 6000) was pumped with the second harmonic of a 10 ns, 20 Hz Nd:YAG laser (Continuum Powerlite 9020). Mixtures of rhodamine 590 and 610 (Exciton) were used. The use of these dye mixtures enabled different tuning ranges to be achieved with the kind of stable, long-term operation that is needed to obtain quantitative 2-photon spectra. The dye laser output was doubled using a KDP crystal in a UV frequency extender (Continuum UVT-3), yielding radiation in the region 279 – 292 nm. 79 Figure 3.6. At a fluence of 1500 mJ cm -2 and photon energy of 35 774 cm -1 (4.435 eV), the mass spectrum is dominated by Ir + , albeit with an IrC + contribution that is ~ 15% as large as that of Ir + . Contributions from Ir(ppy) 2 + and Ir(ppy) 3 + (not shown) are smaller by an order of magnitude. The hydrocarbon peaks are due to impurity. The laser radiation was focused using a 60 cm lens to a diameter of approximately 0.7 mm, resulting in a maximum fluence of approximately 1500 mJ cm -2 . The TOF spectrum obtained using this fluence and a photon energy of 35 774 cm -1 (4.435 eV) is shown in Figure 3.6. The most intense peak (i.e., the doublet centered at 192 amu) is split according to the natural isotopes of iridium. The less intense doublet centered at 204 amu is due to 191 IrC + and 193 IrC + . Signals due to Ir(ppy) 2 + and Ir(ppy) 3 + (not shown) are an order of magnitude smaller than the Ir + peak. The cluster of peaks at lower mass is unaffected by source temperature and it is present in the absence of Ir(ppy) 3 . Therefore, these peaks are attributed to hydrocarbon contamination. Figure 3.7(a) shows the intensity of the Ir + signal as a function of photon energy in the range 34 900 – 35 800 cm -1 (4.327 – 4.438 eV). Fluence of approximately 1400 mJ Ir + IrC + mass / amu hydrocarbons 50 100 150 200 250 0 80 cm -2 was used. The spectrum consists of a number of sharp peaks superimposed on a weak continuum. The only significant effect observed upon increasing the fluence is to increase the amount of underlying continuum. The boxed area in Figure 3.7(a) is expanded in (b). The vertical dashed lines correspond to transitions of neutral atomic iridium. The agreement between the measured spectrum and the dashed lines indicates that the sharp features are due to multiphoton ionization of atomic iridium, 37 itself arising from multiple photon processes. In such high fluence cases, amusing spectra can be recorded, but obtaining detailed information about the low-lying excited states of Ir(ppy) 3 is not feasible. 38 81 Figure 3.7. (a) Action spectrum obtained by monitoring Ir + while varying the photon energy. Laser fluence was approximately 1400 mJ cm -2 . (b) Expanded view: The vertical dashed lines indicate transitions of (neutral) atomic iridium. 37 Note that the spectra are not offset from zero, i.e., there is an underlying broad continuum. At the same time, an important fact follows from atomic iridium spectra such as those shown in Figure 3.7. They indicate that, at least under high fluence conditions, photon energy / cm −1 35350 35450 35550 0.5 1.0 1.5 2.0 (b) 35000 35600 35200 35400 35800 10 8 6 4 2 0 photon energy / cm −1 (a) ion signal (arb. 82 photofragmentation is so severe as to yield significant quantities of iridium atoms that then undergo multiphoton ionization. In fact, neutral photofragmentation dominates. Were neutral iridium atoms produced via photodissociation of an ion precursor, there would have to be an ion partner. There is no evidence whatsoever of Ir(ppy) + , and only a small ppy + signal appears at high fluence. The dominance of neutral fragmentation channels is not surprising, given that previous studies have shown that photolysis is a common, often dominant, pathway for photoexcited organometallic compounds. 39-45 The important conclusion is that the ionization and neutral fragmentation channels are in competition with one another. This bears on interpretation of the ion yield spectra (vide infra Figure 3.10), as discussed later. 3.2.2 Two-photon Ionization An attenuator consisting of a half-wave plate and a Glan-Thompson polarizer was inserted into the beam path. This allowed the laser fluence to be varied over a broad range with good accuracy, with the caveat that this fluence is an average over the near- Gaussian beam shape. First, the polarizer is set for maximum transmission. Then the half- wave plate is inserted between the light source and the polarizer. Fluence is easily adjusted by turning the half-wave plate. Because focusing limits the lowest fluence that can be obtained using this procedure, the focusing lens was removed to examine the low fluence regime. In this case, the radiation passed through a 1 mm diameter aperture. This enabled fluence as low as 50 μJ cm -2 to be achieved with good accuracy. Diffraction over the aperture-sample distance was minimal. 83 Figure 3.8. Mass spectra recorded at different fluences: The laser frequency is 35 357 cm -1 (4.383 eV). At low fluence (bottom trace), photoionization produces the Ir(ppy) 3 + ion exclusively. As the fluence is increased, fragmentation results in the appearance of the Ir(ppy) 2 + ion. At high fluence (top trace), the Ir + peak dominates, indicating severe fragmentation of Ir(ppy) 3 and its photofragments. Figure 3.8 shows how changing the fluence affects the mass spectra. The highest fluence (top trace) yields a mass spectrum that is similar to the one presented in Figure 3.6. The Ir + peak dominates. Signals corresponding to Ir(ppy) 2 + and Ir(ppy) 3 + gain intensity as the fluence is decreased. At 88 mJ cm -2 , the Ir + and Ir(ppy) 3 + peaks have approximately equal height, and an IrC n + / IrN n + progression has emerged. When the fluence is below ~ 1.6 mJ cm -2 , the Ir(ppy) 3 + parent ion is isolated, i.e., the mass mass / amu 1.6 mJ cm −2 2.0 mJ cm −2 88 mJ cm −2 300 mJ cm −2 1400 mJ cm −2 Ir + Ir(ppy) 2 + Ir(ppy) 3 + 200 300 400 500 600 700 84 spectrum, for all practical purposes, contains no other peaks. No signal corresponding to Ir(ppy) + has been observed in any of the experiments. Generally, the parent ion is most useful for acquiring information about the molecule and therefore this signal was the main focus of the present study. It should be noted that it was not obvious a priori that it would be possible to isolate the parent ion, particularly in light of the large amount of parent vibrational energy that is present at 500 K. Thus, it was pleasing to find that Ir(ppy) 3 + was the only ion peak in the mass spectrum over a wide range of experimental conditions. Figure 3.9. Ir(ppy) 3 + signal versus fluence, F, recorded with a photon energy of 35 420 cm -1 (4.391 eV) The straight line has a slope of 2, in accord with 2-photon ionization. The fluence dependence of the Ir(ppy) 3 + signal revealed that it is proportional to the second power of the laser fluence, as long as the fluence is less than ~ 1.6 mJ cm -2 (see Figure 3.8). To be on the safe side, we shall take the low-fluence regime to be less log Φ / µJ cm −2 ( ) 2.2 2.4 2.6 2.8 3.0 −1.6 −1.2 −0.8 −0.4 0 0.4 log (ion signal) 85 than 1 mJ cm -2 . Figure 3.9 shows a log-log plot of the Ir(ppy) 3 + signal versus fluence, Φ, obtained with a photon energy of 35 420 cm -1 (4.391 eV). Similar results were obtained using a number of photon energies in the range 34 207 – 35 930 cm -1 (4.241 – 4.455 eV). At slightly higher fluence, but below the regime where significant fragmentation occurs, the Ir(ppy) 3 + signal is no longer proportional to Φ n with n = 2. For example, the range 2- 15 mJ cm -2 is characterized by n = 1.5. This is consistent with some degree of saturation of one or both transitions, as well as a contribution from parent ion fragmentation. The term saturation is most often used to describe the near equality of two state populations that is brought about through the application of an intense, resonant electromagnetic field. In the system under consideration here, the electronically excited states are unstable because of radiationless decay. Therefore, the term saturation is used advisedly, i.e., to describe the regime where the figure-of-merit σΦ assumes values of a few tenths or larger. 46 86 Figure 3.10. (a) The black trace is the Ir(ppy) 3 + signal, divided by fluence squared, versus photon energy. The blue dashed trace is the absorption cross-section s 1 of gas phase Ir(ppy) 3 at ~ 500 K (arb. units). Different ratios of rhodamine 590 and 610 and the corresponding energy regions are designated by horizontal double-sided arrows: (a) 100% 590 (279.5 – 283.1 nm); (b) 590:610 = 9:1 (281.5 – 284.3 nm); (c) 590:610 = 4:1 (283.2 – 286.8 nm); (d) 590:610 = 7:3 (286.2 – 288.1 nm); (e) 590:610 = 3:2 (287.8 – 290.5 nm); ( f ) 100% 610 (290.2 – 292.8 nm). (b) The ion signal (scaled by F -2 ) in (a) has been divided by the (blue dashed) absorption spectrum of ~ 500 K gas phase Ir(ppy) 3 also shown in (a). This indicates that the undulation with ~ 270 cm -1 spacing is due to s 2 . Figure 3.10(a) shows the "fluence-corrected" Ir(ppy) 3 + signal versus photon energy in the range 34 150 – 35 775 cm -1 (4.234 – 4.435 eV). Because the Ir(ppy) 3 + signal varies as the second power of the laser fluence (Φ 2 ) in these experiments, care was 1 3 4 2 (a) (b) (c) (d) (e) ( f ) (a) photon energy / cm −1 1 2 3 34000 34500 35000 35500 (b) 34000 34500 35000 35500 ion signal / Φ 2 (arb. units) 270 cm −1 absorption spectrum σ 2 (arb. units) 87 taken to ensure that the fluence did not deviate more than 5% from 450 μJ cm -2 . To this end, the spectrum in Figure 3.10(a) is composed of six separate spectra recorded using different rhodamine 590 and 610 dye mixtures. The photon energy regions covered by the different dye mixtures are indicated using horizontal double-sided arrows. In addition, the laser fluence was recorded along with the ion signal, enabling the ion signal to be corrected for the modest change of fluence using the Φ 2 dependence. This is the above- mentioned "fluence corrected" signal. The trace in (b) is the black trace in (a) divided by the absorption spectrum shown as the dashed blue line in (a). An ultraviolet absorption spectrum of gaseous Ir(ppy) 3 was obtained by inserting a heated, sealed 10 cm cell containing Ir(ppy) 3 vapor into a commercial spectrophotometer. The cell was heated more at the ends than in the middle to eliminate condensation on the windows. It was wrapped in insulation and inserted into a split copper cylinder having end plates with holes just large enough to permit the radiation to enter and exit. There was no sample degradation at temperatures in excess of 550 K. Reliable ultraviolet spectra were recorded. A portion of one of them is shown in Figure 3.10(a). Division of the black trace in (a) by the absorption spectrum yields a spectrum (in arbitrary units) for the dependence of the ion signal on the ionizing photon energy. This is discussed in Section 3.3. The upper horizontal scale in (b) indicates that the undulation has spacing of roughly 270 cm -1 (33 meV). The undulation seen in Figure 3.10(b) was unanticipated. If anything, a smooth variation of σ 2 versus photon energy was expected. 47,48 Therefore, the photoionization 88 spectrum shown in Figure 3.10 was examined thoroughly to ensure that it is not an artifact. The data were recorded with great care over several months, using six different dye solutions, ensuring that the laser fluence is safely within the 2-photon regime, and taking care to not mistake a variation of laser fluence for a variation of σ 2 . There was no relationship between the undulation and the tuning ranges used with the various dye mixtures. The undulation was repeatable. Possible explanations are discussed in Section 3.3. 3.2.3 One-photon Ionization It also proved straightforward to photoionize Ir(ppy) 3 using a single 193.3 nm (6.414 eV) photon. The output from an ArF excimer laser (Lambda Physik Compex 201) was passed through a 0.7 mm x 12.7 mm aperture. Less than 1 mJ cm -2 (< 10 15 photons cm -2 ) provided adequate signal. No significant changes to the experimental arrangement indicated in Figure 3.4 were required, i.e., only optics and triggering. At low fluence a two peaks near 6 us and a bifurcated peak at 34.2 μs were observed in the TOF spectrum (Figure 3.11). The peaks at 6 μs are attributed to a hydrocarbon impurity based upon our observations from the two-photon experiments. Considering the Wiley-McLauren equations (section 2.2) predict an Ir(ppy) 3 + arrival time 34.4 ± 0.5 μs and the bifurcation of the 34.2 μs peak shows a strong likeness to the isotopological profile of Figure 3.5(b) (see inset of Figure 3.11), it was determined that the peak at 34.2 μs must be Ir(ppy) 3 + . With this conclusion the photon energy provides an additional estimate of an upper 89 bound for the ionization energy, subject to a reasonable assumption about the role played by parent vibrational energy in photoionization, as discussed in the next section. Figure 3.11. Low fluence (< 1 mJ cm -2 ) TOF spectrum acquired by irradiating gaseous Ir(ppy) 3 + with unfocused 193.3 nm light. The peak at 34.2 μs is from Ir(ppy) 3 + . The bifurcation of the Ir(ppy) 3 + peak is consistent with the isotopological profile. The peaks near 6 μs are from hydrocarbon impurity. 3.3 Discussion Referring to Figure 3.10, single-frequency 2-photon ionization was carried out using photon energies throughout the range 34 150 – 35 775 cm -1 (4.234 – 4.435 eV). The 2-photon nature of Ir(ppy) 3 + production in this range was verified at a number of photon energies by recording data of similar quality to those shown in Figure 3.9. With photon energies smaller than 34 150 cm -1 (4.234 eV) it was not possible to obtain such high quality fluence dependence data because the absorption cross-section σ 1 diminishes toward smaller photon energy and our ultraviolet radiation source (doubled dye laser) is less stable. time (μs) 20 30 40 50 60 0 10 34.0 34.5 hydrocarbons 90 It is noteworthy that with the convenient (and significantly smaller) photon energy 28 170 cm -1 (3.492 eV, corresponding to 355 nm) it was not possible to identify a regime where the Ir(ppy) 3 + signal varies as the square of the fluence. Even though the 355 nm radiation is quite user-friendly (being the YAG third harmonic), the photoionization fluence dependence changed erratically from one experiment to the next. For example, nine fluence dependence plots were recorded under what we considered similar conditions. In each case, the Ir(ppy) 3 + signal could be fitted to a Φ n variation. However, the n values spanned a broad range: 1.5 – 3.3. This was surprising because the 355 nm fluence was more stable than the radiation used throughout the range indicated in Figure 3.10. As mentioned above, one of the problems is that the cross-section for absorption of the first photon (σ 1 ) diminishes on the low energy side of the 1 LC ← S 0 peak indicated in Figure 3.3. Consequently, increasing the fluence to overcome smaller σ 1 values raises the possibility of beginning to saturate the σ 2 transition. Of course, the major unknown with 355 nm radiation is the participation of 3-photon processes, as 28 170 cm -1 (3.492 eV) is quite a bit smaller than 34 150 cm -1 (4.234 eV). For example, might 355 nm photoionization be, at least in part, a 3-photon process with some degree of saturation (at times) of the σ 2 and σ 3 transitions? As pointed out by one of the reviewers, competition between 2- and 3-photon processes can be exacerbated by the mode hopping that occurs in YAG lasers that are not injection seeded. 91 In consideration of the above issues, to be on the safe side, all of the spectral scans were limited to the range shown in Figure 3.10. Thus, 34 150 cm -1 (4.234 eV) was used to estimate a very conservative upper bound for the ionization threshold obtained via single-frequency 2-photon ionization, as discussed below. 3.3.1 Low-lying Electronically Excited States Insight into energy transfer and photophysical properties of low-lying electronically excited states of Ir(ppy) 3 is provided by previous experimental studies. The ones most germane to the present study are reviewed here. It is well known that Ir(ppy) 3 exhibits intense (i.e., high quantum yield) phosphorescence from T 1 with an apparent radiative (spontaneous emission) lifetime of approximately 1.6 μs at room temperature. 16,17,20,24,28 This lifetime is phenomenological in the sense that the three T 1 sublevels separately have quite different radiative lifetimes: 116, 6.4, and 0.2 μs, as indicated in Figure 3.12. 17 It is interesting that the term phosphorescence is used with a radiative lifetime as short as 0.2 μs. Specifically, 0.2 μs is comparable to the spontaneous emission lifetimes of a large number of allowed singlet- singlet transitions in small molecules. Keep in mind, however, that so short a lifetime does not, by itself, imply dominant singlet character of the excited state. Specifically, a lifetime of 0.2 μs can arise through the introduction of even modest amounts of 1 LC and / or 1 MLCT character into T 1 via SOC. Because of the short 1 LC → S 0 and 1 MLCT → S 0 spontaneous emission lifetimes (recall the large absorption cross-sections indicated in Figure 3.3), only a modest 92 percentage of 1 LC and / or 1 MLCT character is needed to account for the 0.2 μs lifetime. For example, an estimate of ~ 6 ns was obtained for the 1 MLCT → S 0 radiative lifetime. This was achieved through application of a Strickler-Berg analysis 49,50 to several molecules having similar spectral properties in the region of interest, 30,51-53 and then scaling these lifetimes to the absorption spectrum shown in Figure 3.3. 29 This confirmed that only a few percent of 1 MLCT character mixed into the T 1 state is needed to account for the short lifetime of 0.2 μs. Figure 3.12. Some important properties and processes of low-lying electronic states are indicated schematically (not to scale). Rapid radiationless decay processes (IC and ISC, with respective lifetimes τ IC and τ ISC ) ensure efficient T 1 production. 28 Spontaneous emission lifetimes ( τ rad ) for the T 1 sublevels indicated on the far right differ considerably, despite the fact that these levels are close in energy, i.e., 116, 6.4, and 0.2 μs for 19 693, 19 712, and 19 863 cm -1 , respectively, in CH 2 Cl 2 solvent. 17 At room temperature, an observed phosphorescence lifetime of 1.6 μs reflects the complex interplay that exists between the T 1 levels. The horizontal lines (above the electronic origins) whose spacing decreases with energy indicate (schematically) vibrational levels. Adapted from references 17 and 28. 266 nm τ IC = 300 − 350 fs τ ISC = 70 −100 fs 400 nm Phosphorescence S 0 1 LC 1 MLCT T 1 T 1 sublevels 116 µs 6.4 µs 0.2 µs τ rad 93 The radiative and energy transfer processes that transpire among the three T 1 sublevels are subtle. For example, the different spontaneous emission rates participate in proportion to the respective sublevel populations, which in turn depend on both the temperature and the energy transfer rates among the sublevels. This has been examined assiduously by Yersin and coworkers, 16,17 who have established, through numerous and sophisticated experiments and modeling, the various energy transfer and radiative properties. 16,17 Specifically, in their experiments, emission spectra and decay rates (for T 1 sublevels) were recorded at temperatures as low as 1.5 K and with applied magnetic fields as high as 12 T. Suffice it to say that, leaving aside for the moment a detailed assignment of the electronic character of all low-lying singlets and triplets, the radiative and energy transfer processes of the T 1 sublevels are well understood compared to other Ir(ppy) 3 photophysical and energy transfer processes. It must be kept in mind that non-radiative relaxation processes such as 1 LC → 1 MLCT and 1 MLCT → T 1 , which appear commonly in the literature, are highly simplified (in a sense phenomenological) models. For example, in reality there are several triplets whose energies lie below that of 1 LC, as well as surface crossings. Details of the electronic structure are discussed at length in Chapter 4. With the above caveat in mind, at energies above the T 1 origin region (Figure 3.12), the femtosecond resolution transient absorption measurements of Tang et al. have revealed ultrafast dynamics among the 1 LC, 1 MLCT, and T 1 states. 28 Referring to Figures. 3.3 and 3.12, ultrafast (100 fs) photoexcitation at 400 nm was used to 94 access 1 MLCT. It was found that absorptions at 520 and 580 nm appeared with time constants of 100 fs and 70 fs, respectively. These 520 and 580 nm absorptions remained constant up to the maximum achievable delay (for the given experimental arrangement) of 1.5 ns. The long-lived absorbing state was assigned to phosphorescent T 1 , implicating rapid ISC (i.e., τ ISC values of 100 fs and 70 fs), as indicated in Figure 3.12. This result is consistent with the essentially complete absence of 1 MLCT → S 0 fluorescence that has been noted, 17,20 even at low temperatures. 17 Next, 1 LC was excited at 266 nm, and the transient absorptions at 520 and 580 nm, each originating from T 1 , were fit using a bi-exponential function. 28 With the shorter time constants fixed at the τ ISC values (100 fs and 70 fs, respectively), the other time constants were found to be 300 fs and 350 fs, respectively (Figure 3.12). These longer time constants were assigned to IC from 1 LC to 1 MLCT, i.e., τ IC in Figure 3.12. The bottom line is that this study demonstrated that photoexcited Ir(ppy) 3 relaxes via 1 MLCT to phosphorescent T 1 on a sub-picosecond timescale. Complementary experiments by Hedley et al. used ultrafast methods to probe directly the short-lived 1 MLCT spontaneous emission that follows photoexcitation at 400 nm with 100 fs pulses. 20 These challenging experiments confirmed the results of Tang et al., 28 and also revealed rapid vibrational energy transfer processes, including intramolecular vibrational redistribution. Again, as impressive as these measurements are, one must keep in mind that the electronic structure is more complex that the simplified scheme indicated in Figure 3.12. 95 In the gas phase environments of the experiments reported herein, an Ir(ppy) 3 molecule's energy is conserved (until it emits a photon) following its absorption of a single ultraviolet photon. Therefore, intramolecular processes take place at, for all practical purposes, fixed energies, i.e., the photon energy plus a given molecule's (considerable) internal, that arises from 490 K thermal equilibrium. This differs from the condensed phase environments that have been used in previous studies of laser-initiated dynamics in the Ir(ppy) 3 system. In these latter cases, intramolecular processes take place simultaneously with Ir(ppy) 3 – host interactions. It is safe to assume that processes that take place on time scales of 70-100 fs are completely in the intramolecular regime, and processes that transpire on time scales of 300-350 fs are predominantly intramolecular. In the picosecond regime, however, it is hard to justify the assumption of solely intramolecular mechanisms, as dopant-host vibrational energy transfer processes can be competitive with intramolecular processes. When normal modes are accurate descriptors, dopant-host vibrational energy transfer will likely be slower than intramolecular processes. On the other hand, in the higher-energy regime of vibrational (vibronic) quantum chaos, dopant-host vibrational energy transfer can be rapid. 54 This regime can be accessed through IC and ISC processes. Rapid ISC and the resulting efficient quenching of singlet-singlet fluorescence are consequences of strong (or at least efficient) SOC. Several theoretical studies have addressed this issue. 23-25,27 Of particular note are those of Nozaki 25 and Nozaki and coworkers, 27 who examined effects due to SOC in Ir(ppy) 3 and analogous systems. The Nozaki results on Ir(ppy) 3 25 are in qualitative accord with the experimental results. 28 96 As a result of significant singlet-triplet mixing, it has been suggested that an appropriate picture might be one in which photoexcitation produces the strongly spin- mixed phosphorescent states directly, in which case the term ISC has little meaning. 25 In other words, in a regime where ISC has little or no meaning, the lifetime τ ISC would not be observed. Instead, photoexcitation would access states of mixed 1 MLCT / T 1 character, and each of these states would emit in proportion to its percentage 1 MLCT character. This scenario differs from the case in which a temporally short pulse excites the system, with the pulse's spectral width exceeding significantly the mean energy spacing between adjacent eigenstates. A coherent superposition of eigenstates is created whose short time character is that of the "bright state." In the Tang et al. experiments (400 nm), the bright state given by this coherent superposition is 1 MLCT. This enabled τ ISC to be determined. Indeed, calculations indicate that the emitting states are of predominantly triplet character, 23-25 with only modest percentages of singlet character. This is in agreement with the dilution of the very short singlet-singlet spontaneous emission rates mentioned earlier, in which T 1 acquires a small percentage of singlet character due to SOC. As a testament to the reliability of the calculations, the radiative lifetimes were reproduced, at least qualitatively, when SOC was taken into account. 24 In any event, on the basis of all of the above work, 23-25 it follows that sub-picosecond ISC dynamics are not at all surprising. 97 3.3.2 Photoionization Less is known about the ionization of Ir(ppy) 3 . This is an important fundamental process that enters the world of OLED's through the electron-hole recombination (exciton formation) that initiates the cascade down the energy "ladder" that terminates at T 1 . Yet, only one experimental value for gas phase Ir(ppy) 3 appears in the literature (7.2 eV), 33 and this is based on indirect evidence, as discussed later. Properties such as the adiabatic and vertical ionization energies (AIE and VIE's) are accessible through studies of gas phase Ir(ppy) 3 . Ideally, one would like to prepare samples in which the Ir(ppy) 3 molecules have as little internal excitation as possible. However, to maintain a steady- state of gas phase Ir(ppy) 3 requires elevated temperature, and removing the large amount of vibrational energy imparted to the molecule at such temperatures is challenging. Even if Ir(ppy) 3 were somehow cooled vibrationally, considerable vibrational energy would still be implanted through the IC and ISC processes that follow and / or accompany photoexcitation. Clearly, the role played by Ir(ppy) 3 vibrational excitation must be taken into account. There are two sources of vibrational excitation in the present experiments. First, consider the vibrational energy of a gas phase Ir(ppy) 3 molecule at thermal equilibrium. To obtain sufficient Ir(ppy) 3 density in the region where photoionization takes place (Figure 3.6) required maintaining the oven temperature at approximately 490 K. The effusing Ir(ppy) 3 molecules contain considerable vibrational energy (discussed below) as well as, on average, 3kT / 2 = 510 cm -1 of rotational energy. As mentioned above, a second source of vibrational energy arises through the first photoexcitation step, say at 98 34 150 cm -1 (4.234 eV). The implanted 1 LC excitation undergoes rapid IC to 1 MLCT, which in turn decays rapidly via ISC to T 1 , whose origin lies at approximately 19 700 cm -1 (2.442 eV). 17 Fortunately for OLED applications, T 1 does not undergo ISC to S 0 on any relevant time scale. The amount of vibrational energy imparted via 1 LC ← S 0 photoexcitation is taken as the difference between the photon energy and the T 1 electronic energy, i.e., 34 150 – 19 700 = 14 450 cm -1 (1.791 eV). Of course, vestiges of 1 LC and 1 MLCT electronic excitations remain because a gas phase Ir(ppy) 3 molecule in a collision-free environment has no way other than photon emission to lower its energy. However, these contributions are minor because of the high density of T 1 vibrational states relative to the densities of vibrational states in the 1 LC and 1 MLCT manifolds at the 34 150 cm -1 (4.234 eV) photon energy. It is now assumed that vibrational excitation plays a spectator role in photoionization, i.e., all vibrational excitation in Ir(ppy) 3 , regardless of how it got there, or the specific form it might have, appears as vibrational excitation of the Ir(ppy) 3 + cation. In other words, all Franck-Condon factors between T 1 and the cation are taken as diagonal, i.e., mv i nv k ' = δ mn δ ik , where i and k denote vibrational degrees of freedom such as normal modes, m and n denote numbers of quanta, and the prime denotes the ion. Note that the equilibrium geometry of the cation is quite close to that of T 1 (vide infra Table 3.1), which supports this assumption. Thus, the resulting very conservative upper bound to the ionization energy obtained through single-frequency 2-photon ionization is 99 estimated to be the photon energy plus the T 1 electronic energy, i.e., 34 150 + 19 700 = 53 850 cm -1 = 6.67 eV. Let us now turn to 1-photon photoionization. As discussed in Section 2, it was possible to photoionize 490 K Ir(ppy) 3 vapor using 193.3 nm (6.414 eV) radiation. Again, if it is assumed that all vibrational excitation is transferred intact, this time from S 0 to the cation, a rough upper bound of 6.4 eV is obtained for the VIE. We shall take this to be the experimentally determined upper bound to the VIE, again subject to the assumption that parent vibrational energy is transferred more-or-less intact to the cation. Not surprisingly, it turns out that the AIE and VIE's from S 0 and T 1 geometries do not differ much from one another, as discussed below. 3.3.3 Ion Yield Spectrum The 2-photon Ir(ppy) 3 + yield spectrum shown in Figure 3.10 displays an undulation whose peak-to-peak spacing is ~ 270 cm -1 (33 meV). As mentioned earlier, these data were recorded over several months, using six different dye solutions, ensuring that the laser fluence is safely within the 2-photon regime, and taking care to not mistake a variation of laser fluence for structure in the ion yield spectrum. Possible origins of this undulation are now discussed. Large IC rates, such as the one determined experimentally for 1 LC → 1 MLCT, 28 are consistent with nonadiabatic transitions between potential surfaces taking place via one or more conical intersections. In large systems like Ir(ppy) 3 , the search for such intersections presents a daunting computational challenge, so much so that it is not clear 100 that the benefit merits the effort. Nonetheless, it is well known that this is a common and efficient mechanism for the IC of electronically excited states that can leave a fingerprint in the form of selective vibrational excitation in one or more modes. In general, this could be manifest in the first and/or second photoexcitation steps, accounting for the observed structure, as discussed below. When the 2-photon ion yield spectrum shown in Figure 3.10 was recorded, we could not, at that time, rule out the possibility that the energy dependence of the cross- section for absorption of the first photon, σ 1 (E), is responsible for the structure. There was no report in the literature of an ultraviolet absorption spectrum of either gaseous Ir(ppy) 3 or even gaseous 2-phenylpyridine. Though spectra of these species in solvent display no hint of structure in the region of interest (Figure 3.3), this does not guarantee that the corresponding gas phase spectra are also smooth. This led to the experiments described in Section 2, in which σ 1 (E) was measured for gas phase Ir(ppy) 3 at temperatures > 500 K. No undulation resembling that in Figure 3.10 was discernible in σ 1 (E). This confirmed that σ 1 (E) is not responsible for the undulation in the 2-photon ion yield spectrum. A likely origin of the undulation is competition between the ionization and radiationless decay pathways. In light of the fact that 1 LC ← S 0 photoexcitation leads (via the 1 MLCT intermediate) to T 1 on a sub-picosecond timescale, the absorption of the second photon can take place via one or more predominantly triplet-triplet transitions, with T 1 being the lower state. It is unlikely that the excited state thus produced fluoresces 101 to any significant extent. Rather, it is expected to either ionize or undergo IC and / or ISC. As mentioned above, a signature of IC via conical intersection is selective vibrational excitation, and it is likely that efficient ISC behaves similarly. Even if the photoionization cross-section has no such structure, such a mechanism — radiationless decay in competition with ionization — can account for the spectrum in Figure 3.10. Given such possibilities, including combinations thereof and other scenarios, we are remiss to speculate further on the origin of the undulation indicated in Figure 3.10. 3.3.4 Disposition of Vibrational Energy We have seen that the photoexcitation step: 1 LC ← S 0 , is accompanied by IC to 1 MLCT. At a rigorous level of theory, in the absence of molecular rotation, all molecular eigenstates in this regime are eigenfunctions of vibronic symmetry, which survives breakdown of the Born-Oppenheimer approximation. 55 However, each of these eigenstates contains only a modest amount of 1 LC electronic character, because the latter is diluted through the large density of vibrational states of the lower electronic manifold(s). Thus, as a practical matter, it is safe to assume that the system evolves to one of 1 MLCT vibrational excitation. Likewise, the 1 MLCT → T 1 transition that takes place via ISC also leads to mainly vibrational excitation within the T 1 manifold. Thus, the 1 LC ← S 0 photon energy minus the energy of the T 1 electronic origin is taken as vibrational energy. Adding this to the photoexcited molecule's S 0 vibrational energy gives its total vibrational energy. 102 Turning now to the vibrational energy present in ground electronic state molecules, this is due to thermal population of vibrational levels at 490 K. In light of the fact that there are 177 vibrational degrees of freedom, there is considerable S 0 vibrational energy. An accurate determination of this vibrational energy distribution is challenging. The distribution function for the total amount of vibrational energy consists of (roughly) a delta function (at an energy equal to the photon energy minus the T 1 electronic energy) added to the vibrational energy distribution given by a convolution involving the 177 vibrational degrees of freedom at 490 K. This convolution yields the probability density, P(E vib ), where E vib is the total vibrational energy. In plain language, the delta function accounts for the energy difference between hν and E T1 , with the assumption that the amounts of 1 LC and 1 MLCT character are small relative to that of T 1 vibrations. This distribution function is determined and discussed in Chapter 4. The important point here is that essentially all of this vibrational energy is transported from T 1 to the ion, regardless of the details of its distribution. It is in this sense that vibrational excitation is said to act as a spectator in the ionization step. 3.3.5 Comparison with Electronic Structure Theory and Previous Work In Chapter 4, a detailed theoretical study of the electronic structure of the Ir(ppy) 3 system, including several low-lying states of the cation Ir(ppy) 3 + , is presented. Here, a few of these results are compared to the experimental findings to establish registry between the experimental and computational results. 103 (a) current work, references (b) 24, (c) 32, (d) 56, (e) 57, (f) 14 Table 3.1. Bond lengths (Å) for S 0 , T 1 , and D 0 states of Ir(ppy) 3 . Calculations were carried out for the AIE and for VIE's at the S 0 and T 1 geometries, yielding respective values of 5.86, 5.87, and 5.88 eV. The fact that there is little difference among these is not surprising, given the similar geometries of the S 0 and T 1 states of Ir(ppy) 3 and the Ir(ppy) 3 + ground state, D 0 , (Table 3.1) and the delocalized nature of the orbitals, i.e., the more delocalized the involved orbitals, the less likely it is that there will be a geometry change in going between the equilibrium structures of the electronic states. As mentioned earlier, Franck-Condon factors are expected to be nearly diagonal, where, in the present context, diagonal means mv i nv k ' = δ mn δ ik , where i and k denote vibrational degrees of freedom such as normal modes, m and n denote 2.168 2.169 2.165 2.025 2.023 2.022 2.153 2.154 2.151 2.035 2.035 2.035 2.167 2.167 2.167 2.035 2.035 2.035 2.088 2.088 2.088 2.006 2.006 2.006 2.071 2.071 2.071 2.060 2.060 2.060 2.132 2.132 2.132 2.024 2.024 2.024 2.196 2.175 2.139 2.025 2.036 1.961 2.176 2.169 2.116 2.030 2.048 2.000 2.149 2.184 2.213 2.028 1.975 2.035 1.34 1.34 1.35 1.35 1.405 1.405 1.36 1.36 1.38 1.38 1.42 1.42 1.34 1.33 1.35 1.40 1.40 1.41 1.36 1.36 1.38 1.439 1.42 1.42 1.415 1.415 1.47 1.47 1.44 1.436 1.47 1.467 1.41 1.49 1.47 1.40 1.43 1.485 1.47 1.419 1.34 1.34 1.355, 1.35 1.35 1.40 1.426 1.473 1.395, 1.41 1.41, 1.407 1.47, 1.476 1.361 1.361 1.385 1.385 1.374 1.374 1.345 1.345 1.358 1.358 1.405 1.405 1.396 1.396 1.423 1.423 – – – – – – – – – – 1.331 1.331 1.371 1.371 1.401 1.401 1.409 1.409 1.487 1.487 – – – – S 0 (theory) S 0 (expt) T 1 (theory) D 0 (theory) (a) (b) (c) (d) (b) (a) (a) (e) (f) Ir – N 2 Ir – N 29 Ir – N 42 Ir – C 9 Ir – C 22 Ir – C 49 N 2 – C 3 , N 29 – C 30 N 42 – C 43 N 42 – C 47 C 49 – C 50 C 48 – C 49 C 47 – C 48 C 7 – C 8 ,C 27 – C 28 C 8 – C 9 ,C 22 – C 27 C 9 – C 10 ,C 22 – C 23 N 2 – C 7 , N 29 – C 28 104 numbers of quanta, and the prime denotes the ion. This presupposes that the normal modes of the neutral and the ion can be paired such that a given normal mode applies to both the neutral and the ion. In other words, for a given normal mode, were one to look at the classical motions of the neutral and ion they would be essentially indistinguishable. This is a good assumption in the present system. Thus, our calculations place both the AIE and the VIE's (at the S 0 and T 1 equilibrium geometries) in the vicinity of 5.9 eV. This is in accord with the experimental upper limit of 6.4 eV, and with the calculation of Hay that places the VIE at 5.94 eV. 32 To examine the assumption that vibrational energy is transferred more-or-less intact upon photoexcitation of this system, the 1 LC ← S 0 absorption spectrum was calculated with all S 0 vibrational excitation suppressed. Excitation is vertical from the S 0 equilibrium geometry. In this calculation, 130 excited electronic states were included. Details are given in Chapter 4. Figure 3.13 shows the correspondence between the calculated and experimental spectra. The shape of the experimental spectrum is reproduced, albeit with energy offset that is within the anticipated error bars of the methods employed. 105 Figure 3.13. Ultraviolet absorption spectra of fac-Ir(ppy) 3 . The calculated spectrum (red) was obtained from the stick spectrum by assigning to each stick a Gaussian FWHM of 0.43 eV. The experimental spectrum (black) was recorded at room temperature in dichloromethane. Peak and shoulder positions (vertical arrows) are in eV. All stick heights have been increased by the same constant factor for viewing convenience, and curve height has been adjusted such that the maximum absorptions are equal. The low- energy, low-intensity wing due to T 1 ← S 0 (2.56 eV) is absent in the calculated spectrum because SOC was not included. It was pointed out in Section 2 that we were unable to establish that 355 nm photoionization is a 2-photon process. Adding the 355 nm photon energy to the T 1 electronic energy yields 5.94 eV, which lies below the experimental upper bound of 6.4 eV, is close to our theoretical VIE and AIE values of approximately 5.9 eV, and is equal to the value calculated by Hay. 32 It may well be that our inability to establish the 355 nm photoionization fluence dependence is a reflection of this near coincidence. Thus, we conclude that the AIE is less than 6.4 eV and is most likely ~ 6 eV. The only other experimentally based ionization energy for this species places the VIE at 7.2 eV, 33 which is incorrect. In defense of these authors, however, is the fact that their measurement was 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Energy / eV 3.30 3.04 2.56 2.72 5.08 4.38 experimental BNL 106 not direct, but an inference. Specifically, it was assumed that a peak at 7.2 eV in energy loss spectra (using incident electron energies of 14, 20, 30, and 50 eV) was due to ionization. Apparently this assumption needs to be reconsidered. 3.4 Summary • A regime of single-frequency 2-photon photoionization has been established (i.e., below ~ 1 mJ cm -2 , see Figure 3.9), and it has been shown that the Ir(ppy) 3 + parent ion is, for all practical purposes, the only ion product throughout this regime, despite the fact that the cation is formed with considerable vibrational energy. This is examined computationally in Chapter 4. Photoionization was also achieved using a single 193.3 nm (6.41 eV) photon, again yielding Ir(ppy) 3 + with no discernible fragmentation. • An upper bound for the ionization threshold for gas phase Ir(ppy) 3 has been estimated on the basis of complementary experiments. Central to interpretation of the experimental results is the reasonable assumption that Ir(ppy) 3 vibrational energy is carried over, essentially intact, to its ion. The 2-photon experiments give a very conservative upper bound of 6.67 eV, while the 1-photon experiment gives an upper bound of 6.4 eV. The upper bound of 6.4 eV is consistent with the theoretical values obtained by our group of approximately 5.9 eV (Chapter 4) and by Hay of 5.94 eV. 32 Thus, the AIE is estimated to be ~ 6 eV. The VIE's at the S 0 and T 1 equilibrium geometries are essentially the same as the AIE. A calculation of the Ir(ppy) 3 absorption spectrum, in which vertical excitation from the S 0 equilibrium geometry is 107 assumed, supports the assumption that vibrational excitation is transferred essentially intact upon photoexcitation. • The electrical efficiency of an OLED depends on the embedded molecule's T 1 energy relative to its ionization energy in the solid host. For example the IE's and electron affinities (EA's) (HOMO and LUMO energies, respectively) of molecules in the light- emitting layer needs to be matched to the energy levels of the electrodes. The low value of ~ 6 eV for the ionization energy of isolated Ir(ppy) 3 augurs well for this species and its close relatives. • An undulation with spacing of ~ 270 cm -1 (33 meV) was observed in the Ir(ppy) 3 + 2- photon yield spectrum. It was shown that this is not due to such structure in the energy dependence of the absorption cross-section for the first photoexcitation step, σ 1 (E). Specifically, there is no such structure in the ultraviolet absorption spectrum of 500 K gas phase Ir(ppy) 3 . The most likely origin of this undulation is structure in the energy dependence of σ 2 (E) . Competition between radiationless decay and ionization can play a role. Resolution of the mechanism awaits further experimental work. 108 3.5 References 1. Yersin, H.; Rausch, A. F.; Czerwieniec, R.; Hofbeck, T.; Fischer, T. Coordin. Chem. Rev. 2011, 255, 2622. 2. Yersin, H.; Finkenzeller, W. Editor, Highly Efficient OLEDs with Phosphorescent Materials; Yersin, H. Ed.; Wiley-VCH Verlag: Weinheim, Germany, 2008; pp. 1-97. 3. Yersin, H. Top. Curr. Chem. 2004, 241, 1. 4. Baldo, M. A.; Lamansky, S.; Burrows, P.E.; Thompson, M. E.; Forrest, S. R. Appl. Phys. Lett. 1999, 75, 4. 5. Baldo, M. A.; Thompson, M. E.; Forrest, S. R. Nature 2000, 403, 750. 6. Adachi, C.; Baldo, M. A.; Thompson, M. E.; Forrest, S. R. J. Appl. Phys. 2001, 90, 5048. 7. Adachi, C.; Thompson, M. E.; Forrest, S. R. IEEE 2002, 8, 372. 8. Adachi, C.; Kwong, R. C.; Djurovich, P.;Adamovich, V.; Baldo, M. A.; Thompson, M. E.; Forrest, S. R. Appl. Phys. Lett. 2001, 79, 2082. 9. Baldo, M. A.; O'Brien, D. F.; Thompson, M. E.; Forrest, S. R. Phys. Rev. B 1999, 60, 14422. 10. Leclerc, M. J. Polym. Sci A: Polym. Chem. 2001, 39, 2867. 11. Cleave, V.; Yahioglu, G.; Le Barny, P.; Friend, R.H.; Tessler, N. Adv. Mater. 1999, 11, 285. 12. Adachi, C.; Baldo, M. A.; Forrest, S. R.; Thompson, M. E. Appl. Phys. Lett. 2000, 77, 904. 13. Baldo, M. A.; Forrest, S. R. Phys. Rev. B 2000, 62, 10958. 14. Tamayo, A. B.; Alleyne, B. D.; Djurovich, P.; Lamansky, S.; Tsyba, I.; Ho, N. N.; Bau, R.; Thompson, M. E. J. Am. Chem. Soc. 2003, 125, 7377. 15. Lamansky, S.; Djurovich, P.; Murphy, D.; Abdel-Razzaq, F.; Lee, H.; Adachi, C.; Burrows, P.; Forrest, S. R.; Thompson, M. E. J. Am. Chem. Soc. 2001, 123, 4304. 16. Finkenzeller, W.; Yersin, H. Chem. Phys. Lett. 2003, 377, 299. 109 17. Hofbeck, T.; Yersin, H. Inorg. Chem. 2010, 49, 9290. 18. Liu, X.; Feng, J.; Ren, A.; Yang, L.; Yang, B.; Ma, Y. Opt. Mater. 2006, 29, 231. 19. Hedley, G. J.; Rusecksas, A.; Samuel, I. D. W. J. Phys. Chem. A Lett. 2008, 113, 2. 20. Hedley, G. J.; Ruseckas, A.; Samuel, I. D. W. Chem. Phys. Lett. 2008, 450, 292. 21. Hedley, G. J.; Rusecksas, A.; Liu, Z.; Lo, S. C.; Bum, P. L.; Samuel, I. D. W. J. Am. Chem. Soc. 2008, 130, 11842. 22. Tsuboi, T. J. Lumin. 2006, 119/120, 288. 23. Matsushita, T.; Asada, T.; Koseki, S. J. Phys. Chem. C 2007, 111, 6897. 24. Jansson, E.; Minaev, B.; Schrader, S.; Ågren, H. Chem. 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E.; Zink, J. I. Inorg. Chem. 2008, 47, 2389. 39. Ketkov, S. Y.; Selzle, H. L.; Schlag, E. W.; Domrachev, G. J. Phys. Chem. A 2003, 107, 4041. 40. Ketkov, S. Y.; Selzle, H. L.; Schlag, E. W.; Titova, S. N. Chem. Phys. 2003, 293, 91. 41. Leutwyler, S.; Even, U.; Jortner, J. J. Phys. Chem. 1981, 85, 3026. 42. Leutwyler, S.; Even, U.; Jortner, J. Chem. Phys. Lett. 1980, 74, 11. 43. Engelking, P. C. Chem. Phys. Lett. 1980, 74, 207. 44. Braun, J. E.; Neusser, H. J.; Harter, P.; Stockl, M. J. Phys. Chem. A 2000, 104, 2013. 45. Banares, L.; Baumet, T.; Bergt, M.; Kiefer, B.; Gerber, G. J. Chem. Phys. 1998, 108, 5799. 46. Letokhov, V. S. Laser Photoionization Spectroscopy; Academic Press, Inc.: Orlando, FL, 1987. 47. Antonov, V. S.; Letokhov, V. S. Appl. Phys. 1981, 24, 89. 48. Ashfold, M. N. R.; Howe, J. D. Annu. Rev. Phys. Chem. 1994, 56, 57. 49. Strickler, S. J.; Berg, R. A. J. Chem. Phys. 1962, 37, 814. 50. Birks, J. B.; Dyson, D. J. Proc. R. Soc. Lond. Ser. A 1963, 275, 135. 51. 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Mater. 2005, 17, 1745. 112 Chapter 4 Electronic Structure of Tris(2-phenylpyridine)iridium: Electronically Excited and Ionized States 4.1 Introduction The use of organo-transition-metal complexes as phosphorescent species in light- emitting diodes (OLED's) enables quantum yields approaching 100% to be achieved through a mechanism referred to as triplet harvesting. 1-5 In triplet harvesting, spin-orbit coupling (SOC) enables electronic excitation that originates with electron-hole recombination (i.e., both singlet and triplet excitons) to relax non-radiatively to the lowest triplet, T 1 . In turn, T 1 undergoes T 1 → S 0 phosphorescence with near 100% quantum efficiency. This high quantum efficiency is also a consequence of SOC. 1-7 Namely, SOC results in short enough T 1 → S 0 phosphorescence lifetimes to render T 1 non-radiative decay ineffective. Such OLED's offer great advantage over purely organic counterparts, whose maximum quantum yield is 25%, i.e., the singlet exciton fraction that results from electron-hole recombination with a statistical distribution of spin states. 1-7 In other words, phosphorescence is not a viable means of obtaining photons in organics because SOC is negligible, and consequently triplet excitation is lost rather than harvested. As the light-emitting ingredient in OLED devices, organo-transition-metal complexes play a central role in the rapidly evolving research area of display 113 technologies. With billions of euros at stake, motivation from the high-tech commercial sector has never been higher. At the same time, these complexes are amenable to exacting and symbiotic experimental and theoretical studies. To wit, they are small enough to accommodate rigor, yet large enough to support bulk phenomena in a range of host materials. The OLED systems that are based on organo-transition-metal complexes are both technologically important and scientifically interesting, and their study benefits from, and is well suited to, mix-and-match interdisciplinary approaches. An overview of OLED's as they relate to the experiments and calculations carried out in our groups is presented in the Introduction of Chapter 3. The reader is encouraged to read, at the very least, the Introduction in Chapter 3, as none of this is repeated below. In Chapter 3, several experimental results are presented and discussed, and possible interpretations are considered, in some cases enlisting comparisons with the calculated results presented herein. In the present Chapter, tris(2-phenylpyridine)iridium, hereafter referred to as Ir(ppy) 3 , is examined using time dependent density functional theory; details concerning its use in the present study are given in the next section. The goal is to obtain qualitative — and to the extent possible quantitative — understanding of low-lying singlets and triplets of Ir(ppy) 3 , and of low-lying doublets of the cation Ir(ppy) 3 + . This includes structural properties, spectral properties, molecular orbital (MO) descriptions, and ionization energies. The latter is germane to OLED devices because the ionization energies and electron affinities (commonly referred to as the HOMO and LUMO 114 energies, respectively) of the light-emitting molecules in the active layer need to be matched to the energy levels of the electrodes. There are two low-energy Ir(ppy) 3 isomers: facial and meridional, hereafter referred to as fac-Ir(ppy) 3 and mer-Ir(ppy) 3 , respectively. As discussed later, the energy difference between them is ~ 1800 cm -1 (~ 220 meV), 8,9 with the fac isomer the more stable of the two. This is sufficient to rule out the participation of mer-Ir(ppy) 3 in most environments. Consequently, though some calculations were carried out on the mer- Ir(ppy) 3 system, the main focus of the present study is fac-Ir(ppy) 3 . The work reported herein builds on and complements earlier theoretical studies, 8- 12 and it assists in the interpretation of experimental results, 13-16 including, but not limited to, those presented in Chapter 3. Organization of the Chapter is as follows. Computational strategies and procedures are presented and discussed in Section 4.2. This is followed (in Section 4.3) by the results, and discussions of their relevance to experimental data and practical applications. These results include: equilibrium structures; vertical and adiabatic ionization energies; MO descriptions obtained at the equilibrium structures of the ground state (S 0 ), lowest triplet (T 1 ), and lowest ionized state (D 0 ); the ultraviolet absorption spectrum; comparison to experimental T 1 phosphorescence parameters (T 1 – S 0 energy gap, spontaneous emission lifetimes, and Franck-Condon factors); and an interesting point regarding the probability density for T 1 vibrational energy following photoexcitation of gaseous Ir(ppy) 3 at 500 K, i.e., the temperature at which the experiments presented in Chapter 3 were carried out. The Chapter concludes with a brief summary. 115 4.2 Computational Details Two long-range-corrected (LRC) functionals were used: ωB97X and BNL. 17-20 Each treats the long-range Coulomb interaction exactly (i.e., 100% Hartree-Fock exchange), thus ensuring proper asymptotic behavior and mitigating the notorious self- interaction errors. 21 Specifically, these functionals reduce the unphysical charge delocalization that is often observed when using standard functionals such as B3LYP. They also eliminate contamination of time dependent density functional theory (TDDFT) results by an artificially low-lying Rydberg manifold that converges to the Koopmans ionization energy (IE), which is underestimated when using non-LRC functionals. A brief introduction to density functional theory (DFT) is provided in Appendix A. Our choice is based on the following considerations. The ωB97X functional has been carefully parameterized and benchmarked. 17,18 It consistently gives more accurate structures and standard thermochemical quantities than, for example, B3LYP. Thus, structures calculated using ωB97X are taken as our best estimates. The BNL functional has been developed for excited states. Its range-separation parameter ω is system- dependent, and it is chosen such that the Koopmans IE is equal to the vertical ionization energy (VIE), a condition that should be satisfied for the exact exchange-correlation functional. BNL performs well for excited and ionized states, including ionization from lower orbitals. 19,20 Thus, we expect its IE's and excited state energies to be of higher quality than the ωB97X ones. 116 Structures of fac-Ir(ppy) 3 and mer-Ir(ppy) 3 in the S 0 , T 1 , and D 0 states were optimized using the ωB97X functional. 18,19 For the iridium atom, the lanl2dz basis was employed, whereas 6-311G++(d,p) was used for all other atoms. 22,23 The range- separation parameter ω in the BNL functional was optimized such that the VIE that was computed using the energy differences method (ΔSCF) matched the HOMO energy (Koopmans IE) at the S 0 equilibrium geometry. This yielded ω = 0.17 a o -1 . 17 The default ω value for BNL is 0.50 a o -1 , and the ω value in ωB97X is fixed at 0.3 a o -1 19,24,25 (as mentioned above, BNL ω values are system specific). The IE's were calculated using Koopmans theorem, which has been shown to yield accurate results for the BNL functional, owing to its LRC character and a system- specific choice of ω. Moreover, the BNL orbitals provide a reasonable representation of the ionized state, which is not the case for B3LYP. The shape of the hole in the ionized state can be verified by calculating the spin density: ρ(α) – ρ(β), for each MO. This ac- counts for non-Koopmans character, i.e., orbital relaxation. This analysis was carried out for D 0 at selected geometries. Excited states were calculated at the S 0 and T 1 geometries using TDDFT with ωB97X and BNL functionals and lanl2dz and 6-311+G(d,p) bases. At the S 0 geometry, 50 singlet and 50 triplet states were calculated using ωB97X, spanning the energy range 2.86 – 6.31 eV. With BNL at the S 0 geometry, 130 singlets and 130 triplets were calculated, spanning the energy range 2.56 – 5.66 eV. With BNL at the T 1 geometry, only the 10 lowest singlet and 10 lowest triplet states were calculated. 117 The TDDFT excited state energies and oscillator strengths were used to calculate absorption spectra. Gaussian shaped spectral densities, g i (E), were assigned to each of the transitions in a given theoretical "stick spectrum." Specifically, the absorption spectrum was simulated as a sum of Gaussian spectral densities, g i (E), each having the same width parameter σ: 2 2 1/ 2 2 ( ) ( ) (2 ) exp 2 i i i E E g E f σ σ − −   = π −     (4.1) The factor f i is the oscillator strength of the electric dipole transition from the S 0 ground state to the i th electronic state. Each Gaussian spectral density is centered at its excited state energy, E i . The width parameter σ is related to the full width at half maximum (FWHM) of the Gaussian distribution according to: FWHM = 2(2ln2) 1/2 σ = 2.35 σ. All calculations were carried out using the QChem electronic structure package. 26 4.3 Results and Discussion In this section, the strategies and procedures described in Section 4.2 are applied to calculations of properties of Ir(ppy) 3 and Ir(ppy) 3 + . A number of technical details and data sets that are omitted from the text for the sake of brevity are included in Appendix B (AB). Reference to AB is made whenever appropriate. Energies and frequencies are given in wavenumbers (cm -1 ), with eV counterparts in parentheses. On occasion, kcal mol -1 is used, i.e., when comparing to literature values given in these units. 118 4.3.1 Equilibrium Structures The ground electronic state structures of fac-Ir(ppy) 3 and mer-Ir(ppy) 3 are indicated in Figure 4.1. As discussed below, their energies differ by ~ 1800 cm -1 (~ 220 meV) with fac-Ir(ppy) 3 the more stable of the two. Table 4.1 lists selected bond lengths for fac-Ir(ppy) 3 at its S 0 and T 1 equilibrium geometries, and for Ir(ppy) 3 + at the equilibrium geometry of the lowest energy cation state, D 0 . Table 4.2 lists selected bond lengths for the S 0 and D 0 equilibrium geometries of mer-Ir(ppy) 3 . The z-matrices and relevant energies are provided in AB. Figure 4.1. Ground electronic state structures and atom numbering for (a) fac-Ir(ppy) 3 and (b) mer- Ir(ppy) 3 . H atoms are omitted. Color scheme: green = Ir; blue = N; gray = C. Tables 4.1 and 4.2 list geometrical parameters. (a) (b) 119 (a) current work, references (b) 10, (c) 9, (d) 27, (e) 28, (f) 29 Table 4.1. Bond lengths (Å) for S 0 , T 1 , and D 0 states of Ir(ppy) 3 . Referring to Table 4.1, the equilibrium bond lengths of ground state fac-Ir(ppy) 3 are compared with results of x-ray diffraction measurements of fac-Ir(ppy) 3 27,28 and of its tolylpyridine analog fac-Ir(tpy) 3 , 29 as well as with previous theoretical estimates. 9,10 The T 1 equilibrium structure is compared to the calculations of Jansson et al. 10 Referring to Table 4.2, the calculated mer-Ir(ppy) 3 structure is compared with the crystallographic structure of its tolylpyridine analog: mer-Ir(tpy) 3 . 16 Variations in the experimentally determined bond lengths arise, at least in part, because of different experimental conditions. For example, the high pressure 2.168 2.169 2.165 2.025 2.023 2.022 2.153 2.154 2.151 2.035 2.035 2.035 2.167 2.167 2.167 2.035 2.035 2.035 2.088 2.088 2.088 2.006 2.006 2.006 2.071 2.071 2.071 2.060 2.060 2.060 2.132 2.132 2.132 2.024 2.024 2.024 2.196 2.175 2.139 2.025 2.036 1.961 2.176 2.169 2.116 2.030 2.048 2.000 2.149 2.184 2.213 2.028 1.975 2.035 1.34 1.34 1.35 1.35 1.405 1.405 1.36 1.36 1.38 1.38 1.42 1.42 1.34 1.33 1.35 1.40 1.40 1.41 1.36 1.36 1.38 1.439 1.42 1.42 1.415 1.415 1.47 1.47 1.44 1.436 1.47 1.467 1.41 1.49 1.47 1.40 1.43 1.485 1.47 1.419 1.34 1.34 1.355, 1.35 1.35 1.40 1.426 1.473 1.395, 1.41 1.41, 1.407 1.47, 1.476 1.361 1.361 1.385 1.385 1.374 1.374 1.345 1.345 1.358 1.358 1.405 1.405 1.396 1.396 1.423 1.423 – – – – – – – – – – 1.331 1.331 1.371 1.371 1.401 1.401 1.409 1.409 1.487 1.487 – – – – S 0 (theory) S 0 (expt) T 1 (theory) D 0 (theory) (a) (b) (c) (d) (b) (a) (a) (e) (f) Ir – N 2 Ir – N 29 Ir – N 42 Ir – C 9 Ir – C 22 Ir – C 49 N 2 – C 3 , N 29 – C 30 N 42 – C 43 N 42 – C 47 C 49 – C 50 C 48 – C 49 C 47 – C 48 C 7 – C 8 ,C 27 – C 28 C 8 – C 9 ,C 22 – C 27 C 9 – C 10 ,C 22 – C 23 N 2 – C 7 , N 29 – C 28 120 crystallographic structure reported by Breu et al. 28 showed that the fac-Ir(ppy) 3 crystal has a racemic unit cell (three Δ and three Λ complexes in the P3 point group). Thus, though isolated ground state fac-Ir(ppy) 3 molecules are of C 3 symmetry, they can develop different equilibrium bond lengths when exposed to local environments. Table 4.1 includes entries from one of the three data sets reported in reference 28. Specifically, the set chosen for comparison with our calculated values is the one that displays the largest differences with our values. Differences in bond lengths among the data sets reported in reference 28 are within 0.03 Å of one another. Differences between all reported experimental values are slightly larger, i.e., approximately 0.04 and 0.05 Å for Ir–N and Ir–C bond lengths, respectively, but less than 0.02 Å for all other bond lengths. All crystallographic structures are of similar quality, with a reported bond length uncertainty of < 1%. 121 S 0 (theory) S 0 (expt) D 0 (theory) (a) (b) (a) Ir-N 2 2.193 2.151 2.275 Ir-N 22 2.079 2.044 2.083 Ir-N 42 2.068 2.065 2.077 Ir-C 9 2.101 2.086 2.094 Ir-C 29 2.078 2.076 2.070 Ir-C 49 2.006 2.020 1.973 N 2 -C 3 , N 22 -C 23 1.34 1.34 N 42 -C 43 1.34 1.34 N 2 -C 7 , N 22 -C 27 1.35, 1.36 1.35, 1.354 N 42 -C 47 1.355 1.353 C 9 -C 10 , C 29 -C 30 1.404, 1.40 1.40, 1.394 C 49 -C 50 1.404 1.404 C 8 -C 9 , C 28 -C 29 1.414, 1.41 1.40, 1.406 C 48 -C 49 1.413 1.42 C 7 -C 8 , C 27 -C 28 1.48, 1.47 1.47, 1.47 C 47 -C 48 1.464 1.47 (a) current work, (b) reference 16. Table 4.2. Bond lengths (Å) for S 0 and D 0 mer-Ir(ppy) 3 . The fac-Ir(ppy) 3 ground state structure was optimized with no symmetry constraints. It deviates slightly from C 3 symmetry due to numerical thresholds used in optimization, and the inability of Cartesian integration grids to support groups like C 3 . Our calculated structure is similar to the one reported by Jansson et al., 10 and it is in reasonable agreement with other theoretical values, 9 despite the fact that they were obtained at a lower level of theory. The computed Ir–C and Ir–N bond lengths are closest to the experimental values reported in reference 29. The deviations are 0.001 and 0.04 Å for Ir–C and Ir–N, respectively. The N–C and C–C bond lengths are within 0.01 Å of the values reported in reference 27, while deviations from the values reported in reference 28 are about 0.03 Å. 122 Figure 4.2. Six highest occupied MO's and three lowest virtual MO's for fac-Ir(ppy) 3 at S 0 geometry using BNL: Orbital labeling follows Hay. 10 Energies of occupied orbitals (Koopmans IE's) are given in Table 4.3. 1 π 2b π 2b π six highest energy occupied MO's d 2 d 1a d 1b * 2a π * 2b π three lowest energy virtual MO's * 1 π 123 Referring to Figure 4.2, π 2a * and π 2b * are components of a doubly degenerate e orbital. Consequently, T 1 and D 0 each exhibit Jahn-Teller distortion that breaks C 3 symmetry. In T 1 , relative to the S 0 values, two ligands move away from the iridium atom and one is drawn closer to the iridium atom. Specifically, the closer ligand corresponds to Ir–C 49 and Ir–N 42 our calculations (see Figure 4.1 for numbering of atoms). The D 0 structure follows a similar pattern. The Ir–C 22 and Ir–N 2 bonds contract, whereas the other metal-ligand bonds lengthen relative to their S 0 values. An interesting difference between T 1 and D 0 is that the contracted bonds in D 0 are not part of the same ligand. These structural changes are consistent with the MO shapes, as discussed later. Calculations were also carried out for the mer-Ir(ppy) 3 isomer whose structure is indicated in Figure 4.1(b). The results are summarized in Table 4.2. When using ωB97X and BNL, the mer isomer is calculated to be less stable than the fac isomer by 280 and 220 meV (2270 and 1760 cm -1 , 6.5 and 5.0 kcal mol -1 ), respectively. These values are total electronic energy differences, ΔSCF. This is consistent with previous theoretical 8,9 and experimental 16 results. Despite the apparent similarity between the fac and mer isomers seen in Figure 4.1, bonding is different. In the mer isomer, the three nitrogen atoms lie in a plane that contains the iridium atom (with two nitrogen atoms lying on a straight N–Ir–N line), whereas in the fac isomer the nitrogen atoms form an equilateral triangle with the iridium atom out of the plane on the C 3 axis. This difference, in which the mer isomer is obtained 124 from the fac isomer by rotating a single ligand 180º about its C Ir N ∠ −− bisection line, places two phenyl groups, and consequently two pyridyl groups, trans to one another. As shown in Table 4.2, and referring to the mer isomer indicated in Figure 4.1(b), its trans Ir–C bonds (i.e., Ir–C 9 and Ir–C 29 ) are longer than the Ir–C bonds in fac- Ir(ppy) 3 , while the remaining mer Ir–C 49 bond length is nearly equal to the fac Ir–C bond length. Also note that the remaining Ir–C 49 bond has an environment that is similar to that of the fac Ir–C bonds, in the sense that it is perpendicular to two Ir–N bonds (i.e., Ir– C 24 and Ir–C 42 ). Thus, it is not surprising that their lengths are similar. On the other hand, the trans Ir–C bonds do not share the same environment as the Ir–C bonds in the fac isomer, in the sense that they are perpendicular to all three Ir–N bonds. The extended Ir–C bond lengths are consistent with the weaker structural trans- effect, often called the trans influence, 30,31 of a pyridyl group relative to a phenyl group. A similar analysis of the mer Ir–N bonds shows that the trans N–Ir–N bonds are noticeably shorter than in the fac isomer. This is again consistent with the weaker structural trans-effect of the pyridyl group. Our predicted mer structure is in reasonable agreement with the x-ray data for mer-Ir(tpy) 3 , i.e., bond lengths are within 0.04 Å of the experimental values. 16 In making comparisons to the experimental work presented in Chapter 3, it is possible to rule out significant participation of the mer-Ir(ppy) 3 isomer. Specifically, the energy gap between the fac and mer isomers, say 220 meV (i.e., the BNL value), is large enough that at 500 K the mer-Ir(ppy) 3 population is only exp(−E mer / kT ) = exp(−5.12) ≈ 125 0.6% of that of fac-Ir(ppy) 3 . Thus, hereafter only the fac-Ir(ppy) 3 isomer will be considered. 4.3.2 Molecular Orbitals The molecular orbitals (MO's) of fac-Ir(ppy) 3 that are most relevant to the present study are shown in Figure 4.2, and the orbital energies (Koopmans IE's) for the six highest energy occupied MO's are listed in Table 4.3. As mentioned earlier, the use of an LRC functional reduces artificial delocalization caused by self-interaction error. Consequently, the LRC functionals used here yield MO's that represent the character of the excited and ionized states better, for example, than does B3LYP. In addition, the Koopmans IE's with BNL are more reliable. 32 Table 4.3. Koopmans IE's (eV) for the six highest energy occupied MO's of fac-Ir(ppy) 3 . Referring to Figure 4.2, the three highest occupied molecular orbitals at the S 0 equilibrium geometry are of mixed 5d – π character. They are labeled: d 1a , d 1b , and d 2 , and they will also be referred to as HOMO-1, HOMO-2, and HOMO, respectively. The d 2 HOMO is dominated by the iridium 5dz 2 orbital, but with a π contribution that arises almost entirely from the phenyl groups. The d 1a and d 1b orbitals, which are components d 2 d 1a ,d 1b π 2a ,π 2b π 1 − 5.87 − 6.06 − 7.15 − 7.27 − 7.42 − 7.49 − 8.45 − 8.59 MO BNL ωB97X 126 of a doubly degenerate e orbital, consist of combinations of d-orbitals, with a somewhat larger contribution from the phenyl groups than in the case of d 2 . The three lowest energy MO's in Figure 4.2 are primarily of π character, with most of the electron density residing on the phenyl groups. They have less than 4% iridium character. The lowest energy virtual orbitals are primarily of π * character in the pryidyl group. These lowest virtual orbitals are of e and a symmetries, with π 2a * and π 2b * being components of a doubly degenerate e orbital. From the Jahn-Teller theorem, single occupancy of e orbitals will lead to symmetry lowering in excited and ionized states. This is consistent with orbital localization in which the HOMO becomes asymmetrically distributed among the ligands. It is also consistent with the results reported by Jansson et al. 10 a For S 0 there are 3 identical sets of carbon atoms (C 1 , C 2 , C 3 ), so the listed percentages (~4) need to be multiplied 3 to account for the 9 main participating carbon atoms. Table 4.4. BNL percent spin density for fac-Ir(ppy) 3 at the S 0 , T 1 , and D 0 equilibrium geometries. For T 1 and D 0 , only the main contributions are listed. This above picture is consistent qualitatively with previous findings. 9-11 However, relative to previous calculations, our orbitals are more localized, owing to the use of LRC functionals. This was confirmed by a shell population analysis of S 0 (details are given in S 0 T 1 D 0 67 58 61 Mulliken spin density of hole Ir C 1 C 2 C 3 ~4 a 12 10 ~4 a 11 13 ~4 a 6 10 127 AB). Iridium comprised 58% of the HOMO character, but only 48% of the HOMO-1 and HOMO-2 character. The shape of the hole in the cation has been verified by spin density calculations that account for non-Koopmans character, i.e., orbital relaxation. The spin density analysis is in qualitative agreement with a Koopmans description of the electron hole (Figure 4.3). A summary of Mulliken spin densities of the cation at S 0 , T 1 , and D 0 geometries is given in Table 4.4, and the HOMO's from which an electron is removed are shown in Figure 4.3. It is seen that structural relaxation causes the amount of iridium character in the electron hole to increase from 58% to 65%. The complete list of Mulliken spin densities for all three geometries is provided in AB. 128 Figure 4.3. Shapes of the electron hole wave functions obtained from Koopmans analyses for cations at the (a) S 0 , (b) T 1 , and (c) D 0 equilibrium geometries. Referring to Figure 4.3(a) and Table 4.4, the HOMO at the S 0 geometry, and therefore the character of the cation hole of S 0 , is the d 2 orbital indicated in Figure 4.2. [Note that the orbital shown in Figure 4.3(a) is identical to the d 2 orbital in Figure 4.2.] Therefore, the hole is symmetric with the iridium atom hosting most of the hole spin density. The remaining ≈ 35% is distributed over the three phenyl groups. In each phenyl group (see Figure 4.4), carbons C1, C2, and C3 account for most of the spin density. (a) (c) (b) 129 At the D 0 and T 1 equilibrium geometries, the HOMO differs considerably from that of the S 0 equilibrium geometry. First, the HOMO at the D 0 equilibrium geometry has a large percentage of its density on the phenyl group drawn closest to iridium. It resembles the d 1a orbital in Figure 4.2. Much of the hole spin density in the cation resides on the carbons C1, C2, and C3 indicated in Figure 4.4. Now consider T 1 at its equilibrium geometry. The ligand closest to the iridium atom contains nearly all of the ligand portions of the HOMO and LUMO that describe T 1 , as indicated in Figure 4.5. Note that the HOMO in Figure 4.5(d) is identical to the electron hole wave function (at the T 1 equilibrium geometry) in Figure 4.3(b). In contrast to the D 0 hole in Figure 4.3(c), the T 1 hole in Figure 4.3(b) has more amplitude over the pyridyl group of the closest ligand. The pyridyl atoms hosting most of the spin density are those labeled N42, C44, and C46 in Figure 4.1(a). Figure 4.4. Ir(ppy) corresponding to Table 4.4: For the T 1 equilibrium geometry, C1, C2, and C3 correspond to carbons labeled 48, 52, and 50 in Figure 4.1(a) [see also Figure 4.3(b)]. For the D 0 equilibrium geometry C1, C2, and C3 correspond to carbons labeled 23, 25, and 27 in Figure 4.1(a) [see also Figure 4.3(c)]. 130 Furthermore, because the character of the HOMO changes from d 2 at the S 0 geometry to d 1a at the D 0 and T 1 geometries, the electronic character of the cation ground state changes upon these displacements. In other words, the d 2 and d 1a /d 1b orbitals (and consequently the respective diabatic states of the cation) change their relative order. This is not surprising in view of the small energy gap between them (0.19 eV) at the S 0 geometry. The Koopmans IE's for the six highest-energy occupied MO's are listed in Table 4.3. Due to small deviations from C 3 symmetry, the energies of degenerate e orbitals are slightly different (< 0.01 eV), so we report the average of the two values. As seen in Table 4.3, the density of electronic states in the cation is rather high, i.e., there are 6 cation states in the range: 5.87 – 7.27 eV. The difference between the BNL and ωB97X values is due to different values of ω. Based on the previous benchmarks and reported VIE values, the BNL results are expected to be more reliable. Adiabatic and vertical IE's calculated as a total energy difference are presented in Table 4.5 for S 0 and T 1 geometries. The small difference between the BNL VIE and AIE values (≤ 0.02 eV) for S 0 and T 1 suggests that structural relaxation caused by the removal of a single electron is small, possibly because of the delocalized character of the orbitals. The use of ωB97X results in a larger difference between VIE and AIE than BNL for both S 0 and T 1 (0.09 eV for S 0 and 0.46 eV for T 1 ). 131 Figure 4.5. Orbitals giving rise to T 1 excitation (HOMO and LUMO of S 0 ): left and right columns correspond, respectively, to S 0 and T 1 equilibrium geometries. Table 4.5. Vertical and adiabatic IE's (eV) for fac-Ir(ppy) 3 from S 0 and T 1 states at their equilibrium geometries. The only previously reported theoretical estimate of the VIE from S 0 is 5.94 eV, 9 while the only previously reported experimental value is an indirect inference of 7.2 eV. 15 Our experimental study (Chapter 3) provides a conservative VIE upper bound of 6.4 eV. S 0 T 1 5.87 3.40 BNL ωB97X VIE AIE VIE AIE 5.86 3.38 6.42 3.98 6.33 3.52 S 0 equilibrium geometry HOMO LUMO LUMO HOMO T 1 equilibrium geometry 132 Both BNL and ωB97X values (5.87 and 6.42 eV, respectively) agree with this experimentally derived upper bound. However, the BNL value is the more accurate estimate for the reasons given in Section 4.2. 4.3.3 Ultraviolet Absorption Spectrum Figure 4.6 shows experimental and calculated ultraviolet absorption spectra. All excited state energies and oscillator strengths were evaluated at the ground state equilibrium geometry. As discussed in Section 4.2, BNL gives the most reliable excited states. Therefore, it is the BNL spectrum that is compared to the experimental spectrum. Though ωB97X yielded good values for ground state equilibrium structures (Figure 4.1, Tables 4.1 and 4.2), it is inferior insofar as excited states are concerned, e.g., see the comparison in the inset in Figure 4.6. The ωB97X spectrum was computed using the first 50 singlets, whereas for the BNL spectrum, 130 singlets were necessary to achieve convergence. Selected BNL excitation energies are given in Tables 4.6 and 4.7. A complete list of the calculated excited states and oscillator strengths that were used to construct the theoretical spectra is given in AB. 133 Figure 4.6. Ultraviolet absorption spectra of fac-Ir(ppy) 3 . The calculated spectrum (red) was obtained from the stick spectrum by assigning to each stick a Gaussian FWHM of 0.43 eV. The experimental spectrum (black) was recorded at room temperature in dichloromethane. Peak and shoulder positions (vertical arrows) are in eV. All stick heights have been increased by the same constant factor for viewing convenience, and curve height has been adjusted such that the maximum absorptions are equal. The low- energy, low-intensity wing due to T 1 ← S 0 (2.56 eV) is absent in the calculated spectrum because SOC was not included. Inset: The BNL (red) and ωB97X (blue) spectra differ considerably, the latter being far out of registry with the experimental spectrum. Table 4.6. Orbital character and leading amplitude for the four lowest energy triplet states at the S 0 and T 1 equilibrium geometries: Energies are relative to that of S 0 at its equilibrium geometry. T 1 T 2 T 3 T 4 2.56 2.61 2.62 2.83 d 2 → π 1 * d 2 → π 2a * d 2 → π 2b * d 2 → π 2a * d 2 → π 2b * d 1b → π 2a * 0.89 0.59 − 0.54 0.59 0.53 0.67 2.30 2.74 2.78 2.82 d 2 → π 1 * d 1a → π 1 * d 2 → π 2b * d 1b → π 1 * d 2 → π 2a * d 2 → π 2b * 0.87 0.71 0.47 0.46 − 0.46 0.51 state energy leading character amplitude energy leading character amplitude S 0 geometry T 1 geometry 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Energy / eV 3.30 3.04 2.56 2.72 5.08 4.38 experimental Energy / eV 3 4 5 6 BNL ωB97X BNL 134 Referring to equation 4.1, a width parameter of σ = 0.185 eV (corresponding to Gaussian FWHM of 0.43 eV) was obtained from a least-squares fit of the BNL spectrum to the experimental spectrum. No attempt was made to calculate absolute intensities. Thus, the vertical axis in Figure 4.6 is not labeled. The BNL curve was scaled such that its maximum is the same height as the maximum of the experimental spectrum. These calculations do not include contributions from triplets due to SOC. The low-energy part of the experimental spectrum has been assigned to singlet-triplet transitions, 14 where it is understood that the "triplets" contain modest amounts of singlet character. The shoulder at 2.56 eV in the experimental spectrum is the same as our T 1 value (Table 4.6). Note that T 2 and T 3 , though close in energy to T 1 at the S 0 equilibrium geometry, are much higher in energy than T 1 at the T 1 equilibrium geometry (Figure 4.7). Table 4.7. Orbital character and leading amplitude for the three lowest energy singlet excited states at the S 0 and T 1 equilibrium geometries. Energies are relative to that of S 0 at its equilibrium geometry. The two intense bands at energies higher than 4 eV have been assigned to ligand- centered transitions ( 1 LC ← S 0 ). The broad absorbance below 4 eV is due primarily to spin-allowed transitions that terminate on metal-to-ligand charge transfer states ( 1 MLCT). S 1 S 2 S 3 2.69 2.80 2.81 d 2 → π 1 * d 2 → π 2a * d 1b → π 2a * 0.94 0.90 0.90 2.62 2.91 2.96 d 2 → π 1 * d 2 → π 2a * d 2 → π 2b * 0.95 0.82 0.84 state energy character amplitude energy character amplitude S 0 geometry T 1 geometry 135 The shoulder at 2.56 eV in the experimental spectrum is attributed to 3 MLCT by analogy with organic compounds. These assignments are qualitative because configuration interaction and spin-orbit coupling result in mixed state character. 12 The label MLCT is correct in the sense that metal-to-ligand electron transfer dominates. However, orbital analyses show that, in addition, a significant amount of charge is transferred from the phenyl to the pyridyl groups. Intra-ligand charge transfer also participates in ligand-centered transitions that involve asymmetric orbitals, e.g., π 2a * ← d 1a . The BNL and experimental spectra are in agreement in terms of locations of maxima and overall shape. The ωB97X spectrum (Figure 4.6, inset) is blue-shifted by almost 1 eV, and relative intensities of the three major bands match the experimental spectrum significantly less well. It is clearly of inferior quality and will not be considered further insofar as excited states are concerned. In assigning line shapes, the same FWHM (0.43 eV) was used for each transition. The high density of electronic states gives rise to broad bands. Because of the delocalized nature of the orbitals involved in the transitions, it is expected that the Franck-Condon factors are near diagonal, i.e., ∆ν i = 0. Thus, transitions were taken as vertical from the S 0 equilibrium geometry, i.e., the nuclear degrees of freedom are treated classically. It would be unreasonable to expect a better match between experiment and theory. 136 Figure 4.7. The first six BNL excited states at S 0 and T 1 geometries (in eV). Note that the adiabatic ionization energy (AIE) is 5.86 eV. At the T 1 equilibrium geometry, the 10 lowest singlets and 10 lowest triplets were calculated. Figure 4.7 and Tables 4.6 and 4.7 compare energies of excited states at the S 0 and T 1 equilibrium geometries. There are significant changes in the excited states between the S 0 and T 1 equilibrium geometries. For example, singlet and triplet potential surfaces cross (Figure 4.7). S 0 D 0 2.3 2.4 2.5 2.6 2.7 2.8 2.9 T 1 T 2 , T 3 S 1 S 2 S 3 S 0 5.88 2.91 2.82 2.78 2.74 2.62 2.30 0.17 Energy 0.00 5.87 2.81 2.80 2.69 2.62 2.56 Triplet geometry Singlet geometry ~ ~ ~ ~ S 1 S 2 T 2 T 3 T 1 T 4 D 0 5.86 AIE 137 4.3.4 Phosphorescence from T 1 Phosphorescence originates from T 1 vibrational levels, and in condensed phases it is assumed that vibrational relaxation takes place rapidly on the phosphorescence timescale. In other words, it is assumed, and rightly so, that the T 1 vibrational level populations are in thermal equilibrium during phosphorescence. Though the lowest frequency Ir(ppy) 3 vibrational modes most likely couple well to the host, the picture of intramolecular vibrations remains nonetheless useful. According to our calculations, at its equilibrium geometry the electronic energy of T 1 is 0.44 eV less than that of the next highest triplet, T 2 , whose energy is 0.04 eV below that of T 3 and 0.08 eV below that of T 4 . From the right hand column in Figure 4.7, one might consider subtracting 0.17 eV from 2.30 eV to obtain a T 1 → S 0 emission origin of 2.13 eV. However, Yersin and coworkers have demonstrated, through detailed experimental studies carried out at temperatures as low as 1.5 K and with external magnetic fields as high as 12 Tesla, that the energy of the T 1 → S 0 origin is 2.44 eV, and that this value depends little on the detailed nature of the host material. 14 Of course, the calculations do not include zero-point energy whereas the experiments do. More importantly, it is not the case that a calculation of the vertical electronic energy difference at the T 1 equilibrium geometry corresponds to the phosphorescence origin. The Ir(ppy) 3 molecule has 177 vibrational degrees of freedom, so an even-handed apportionment of 0.17 eV over these degrees of freedom results in each oscillator acquiring, on average, only 7.7 cm -1 . Also, if one calculates the average 138 magnitude of the differences between the S 0 and T 1 equilibrium bond lengths listed in Table 4.1, this yields just 0.018 Å. Moreover, of the 21 bond lengths listed in Table 4.1, three of the differences are a bit larger than the rest: Ir–C 49 , C 48 –C 49 , and C 47 –C 48 . For the remaining 18, the average magnitude of the difference between the S 0 and T 1 equili- brium bond lengths is only 0.0088 Å. Thus, most of the bond lengths differ little in going between S 0 and T 1 equilibrium geometries. The picture this presents is one in which Franck-Condon factors for transitions that originate from the T 1 zero-point level are dominated by (0, 0) contributions. Thus, the origin observed by Yersin and coworkers corresponds to our calculation of the energy of T 1 at its equilibrium geometry (2.30 eV) minus the energy of S 0 at its equilibrium geometry (0.00 eV). This agrees with the experimental value of 2.44 eV. Again, the calculations do not include vibrational zero-point energy nor do they include spin-orbit interaction, which results in additional shifts. 9 Note that the zero-field splitting of the three T 1 sublevels examined by Yersin and coworkers are minuscule on the energy scale of Figure 4.8, e.g., 19 693, 19 712, and 19 863 cm -1 in dichloromethane. 14 It is concluded that the theoretical and experimental values of the phosphorescence origin are in quite reasonable agreement. 4.3.5 Vibrational Energy Distribution As mentioned earlier, at 500 K a significant amount of energy is present in the 177 vibrational degrees of freedom of ground electronic state gas phase Ir(ppy) 3 . This 139 energy is of course above and beyond the zero-point energy. The probability density for this "thermal" vibrational energy, E vib , shall be referred to as P(E vib ). The molecule's rotational energy, whose average value at 500 K is 520 cm -1 , shall be left aside. It is modest relative to E vib , and for the most part it is unavailable in gas phase intramolecular processes because of angular momentum conservation. Figure 4.8. (a) Photoexcitation transports populated S 0 vibrational levels to 1 LC, which undergoes radiationless decay on a subpicosecond timescale, resulting ultimately in T 1 electronic excitation. This maps P(E vib ) to T 1 with additional T 1 vibrational energy given by hν – E T1 , as indicated in (b) and in Figure 4.9. In addition, radiationless decay transforms 1 LC electronic excitation to T 1 electronic excitation, with mere vestiges of 1 LC and 1 MLCT electronic character S 0 Energy / 10 4 5 4 3 2 1 1 LC (a) 1 LC ← S 0 T 1 hν − E T 1 (b) P(E vib ) 140 distributed throughout the T 1 vibronic levels. Thus, the amount of vibrational energy imparted to T 1 via 1 LC ← S 0 photoexcitation is approximately equal to hν – E T1 (see Figure 4.8), where E T1 is the T 1 electronic energy. This energy is taken to be approximately 19 700 cm -1 , as the sublevel energies are 19 693, 19 712, and 19 863 cm -1 in dichloromethane. 14 Adding hν – E T1 to the vibrational energy due to 500 K thermal equilibrium, E vib , gives the total amount of T 1 vibrational energy. Once again, it is assumed that this is transformed essentially intact to vibrational excitation of the Ir(ppy) 3 + cation. However, whereas hν – E T1 is simply a number, the vibrational energy due to 500 K thermal equilibrium is distributed according to P(E vib ), and it is important to have at least a qualitative picture of how P(E vib ) varies with E vib . For example, this variation gives the spread of vibrational energies carried over to the cation. The main idea is illustrated schematically in Figure 4.8. Figure 4.8(a) indicates how 1 LC ← S 0 photoexcitation transfers vibrational energy from S 0 to 1 LC, which in turn undergoes rapid radiationless decay (horizontal red arrow). In other words, a given S 0 molecule has a probability density P(E vib ) for being found in a small energy range centered at E vib . Therefore photoexcitation maps P(E vib ) to essentially the same probability density in 1 LC, which in turn transfers it to T 1 , as indicated in Figure 4.8. Pursuant to the above, a calculation of the 177 normal mode frequencies of Ir(ppy) 3 was carried out using B3LYP with lanl2dz and 6-31+G* at the optimized geometry. The level of electronic structure theory that used in this calculation is 141 adequate, as the goal is a qualitative understanding of the shape of P(E vib ) versus E vib . It is worth noting that P(E vib ) is not a strong function of vibrational frequency values, as discussed below and illustrated in Figure 4.9. Figure 4.9. The red curve is a plot of equation 4.2 with T = 500 K; see text for details. Following photoexcitation, the total vibrational energy in T 1 is given by hν – E T1 + E vib . The probability density for E vib is P(E vib ), and hν – E T1 = 15 000 cm -1 is chosen as a representative value. When all frequencies are changed by ± 10%, the P(E vib ) plots change accordingly (blue and black curves). However, the main qualitative feature is preserved. Namely, a considerable amount of T 1 vibrational energy is distributed with a FWHM that is modest relative to the energy of maximum P(E vib ), e.g., 7800 versus 31 000 cm -1 , respectively, for the red curve. Carrying out calculations at the S 0 equilibrium geometry given in Table 4.1 resulted in five small-curvature saddle points, which are likely to be artifacts of numerical integration on a grid. When calculating density of states, the imaginary frequencies 7500 cm −1 P(E vib ) 7800 cm −1 8100 cm −1 T 1 vibrational energy / 10 3 cm −1 0 20 30 hν − E T 1 E vib / 10 3 cm −1 calculated frequencies ×1.1 calculated frequencies calculated frequencies × 0.9 10 5 15 25 30 20 35 40 45 15 10 5 25 142 associated with these saddle points were replaced ad hoc with real frequencies of the same magnitudes: 45.7, 45.5, 31.6, 15.6, and 12.7 cm -1 . As long as these frequencies are significantly smaller than kT, the calculated P(E vib ) probability density is insensitive to their values. For example, increasing or decreasing these five frequencies by a factor of two causes the shapes of curves such as those in Figure 4.9 to change by no more than the thickness of the traces. Likewise, horizontal displacements are small, e.g., decreasing these five frequencies by a factor of two shifts the peak by + 25 cm -1 , which is minuscule on the scale of Figure 4.9. All of the frequencies are given in AB. With the vibrational frequencies in hand, the vibrational density of states ρ(E vib ) was calculated by using the MultiWell Program Suite, specifically, the Densum program, which employs the Beyer-Swinehart algorithm for harmonic oscillators. 33-36 This ρ(E vib ) was then multiplied by e − E vib / kT (with T = 500 K) to obtain P(E vib ): P(E vib ) = Z −1 ρ(E vib )e − E vib / kT (4.2) where Z is the partition function. Plots of P(E vib ) are given in Figure 4.9. Figure 4.9 illustrates the fact that altering the frequencies by a modest amount has a modest affect on the total T 1 vibrational energy. Specifically, combining P(E vib ) and hν – E T1 gives the probability density for vibrational energy within T 1 following 1 LC ← S 0 photoexcitation (Figure 4.8). Referring to Figure 4.9, for an assumed value of hν – E T1 = 15 000 cm -1 , the total T 1 vibrational energy peaks at ~ 31 000 cm -1 with a FWHM of ~ 7800 cm -1 . From the plots in Figure 4.9, it follows that the main (qualitative) result would not change were a higher level of theory enlisted. 143 On the one hand, the use of a 500 K sample results in vibrational energy that we would rather were not present. On the other hand, the amount of vibrational energy imparted via photoexcitation is considerable and inevitable in experiments with gaseous Ir(ppy) 3 . 4.4 Summary Electronic structure theory has been used to examine a number of excited singlet and triplet states of Ir(ppy) 3 and a few low-lying states of Ir(ppy) 3 + . Specifically, time- dependent density functional theory (TDDFT) calculations were carried out using long- range-corrected (LRC) ωB97X and BNL functionals. There is good agreement with several previous experimental and theoretical results, 8-14,16 as well as with the experimental results presented in Chapter 3. The main conclusions are listed below. • Yersin and coworkers have carried out detailed experimental studies of T 1 → S 0 phosphorescence. 14 They report a 2.44 eV electronic origin and phosphorescence lifetimes of 0.2, 6.4, and 116 μs for the T 1 sublevels in dichloromethane. 14 The present calculations yield 2.30 eV, in agreement with the 2.44 eV experimental value. It was pointed out in Chapter 3 that just a few percent of 1 LC / 1 MLCT character is sufficient to reconcile the short phosphorescence lifetime of 0.2 μs because of the large oscillator strengths of the singlet-singlet transitions: 1 LC ← S 0 and 1 MLCT ← S 0 . This degree of singlet-triplet mixing is in qualitative agreement with calculations of Nozaki that include SOC. 12 144 • The 1 LC ← S 0 transition is accompanied by rapid radiationless decay of 1 LC, resulting ultimately in population of the phosphorescent state, T 1 . The number of electronically excited states having energy less than or equal to the photon energy is larger than the trio of states ( 1 LC, 1 MLCT, and T 1 ) used in phenomenological models aimed at reconciling experimental results. In addition, potential surfaces cross, e.g., as seen in going between the S 0 and T 1 equilibrium geometries (Figure 4.7). • A calculation of the ultraviolet absorption spectrum was carried out using 130 excited singlets obtained with the BNL functional. Oscillator strengths were calculated for vertical excitation from the S 0 equilibrium geometry. The resulting stick spectrum was assigned a Gaussian shape with FWHM of 3470 cm -1 (0.43 eV) for each transition. This calculated spectrum is in agreement with the experimental room temperature absorption spectrum. This agreement is consistent with Franck-Condon factors dominated by ∆v i = 0 , as expected for the delocalized nature of the orbitals involved. • The calculated adiabatic and vertical (S 0 and T 1 equilibrium geometries) ionization energies are 5.86, 5.87, and 5.88 eV, respectively. These values agree with the calculated result of 5.94 eV reported by Hay, 9 as well as with the conservative experimental upper bound of 6.4 eV reported in Chapter 3. It is concluded that the ionization energy is in the vicinity of 6 eV. This low ionization energy is advantageous for OLED applications. • The probability density for finding a gas phase Ir(ppy) 3 molecule with "thermal" vibrational energy E vib at temperature T is: P(E vib ) = Z −1 ρ(E vib )exp(−E vib / kT ) , where 145 Z is the partition function. This can be combined with the vibrational energy imparted through photoexcitation, hν – E T1 , to obtain the probability density as a function of total vibrational energy. In rough terms, for 500 K this probability density peaks at ~ 31 000 cm -1 (3.84 eV) with a FWHM spread of ~ 7800 cm -1 (0.97 eV) (Figure 4.9). It is interesting that, despite this large amount of vibrational energy, 2-photon ionization is dominated by the parent cation Ir(ppy) 3 + , with no discernible fragmentation over a significant frequency range (Chapter 3). • Qualitative understanding of the photophysics of this system is assisted greatly by the MO's obtained at the S 0 , T 1 , and D 0 equilibrium geometries. 146 4.5 References 1. Yersin, H.; Finkenzeller, W. Ed; Highly Efficient OLEDs with Phosphorescent Materials; Yersin, H. Ed.; Wiley-VCH Verlag: Weinheim, Germany, 2008. 2. Yersin, H.; Finkenzeller, W. Editor, Highly Efficient OLEDs with Phosphorescent Materials; Yersin, H. Ed.; Wiley-VCH Verlag: Weinheim, Germany, 2008; pp. 1-97. 3. Yersin, H. Top. Curr. Chem. 2004, 241, 1. 4. Rausch, A. F.; Homeier, H. H. H.; Yersin, H. Top. Organomet. Chem. 2010, 29, 193. 5. 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Kin. 2009, 41, 748. 149 Chapter 5 Investigation of He 4 + Formation via Electron Impact and the Photoionization of Tris(2-phenylpyridine)iridium in Helium Droplets 5.1 Introduction In recent years, studies involving superfluid helium nanodroplets have evolved into a rich field of research. 1-4 Helium droplets provide an ultracold matrix in which to perform a variety of spectroscopic studies on embedded species. 5 In this matrix isolation technique, a well-known number of molecules are embedded inside helium droplets via gas phase collisions. These experiments were predated by studies of SF 6 molecules attached to heavier gas clusters where the utility of the nanocluster technique was demonstrated. 6 In the spectroscopy that follows, helium plays a predominantly spectator role due its optical transparency over a large frequency range and vanishingly low viscosity. Experiments involving helium nanoclusters typically use free jet expansion to force cold (9 - 20 K) helium at 20-80 bar out of a 5 um (continuous) or ~ 1 mm (pulsed) nozzle to produce the clusters. In this so called subcritical regime, the initial state of the helium is well within the gaseous region of the phase diagram. 7 The expanding helium cools because of an adiabatic change in state along isentropes in the phase diagram to temperatures and pressures well below the critical point. 5 As a result, condensation of the helium occurs to form “hot” clusters. The droplets then undergo rapid evaporative 150 cooling to dissipate residual energy until they reach an equilibrium temperature of about 0.4K. 8 The average size of He droplets is an important parameter, which dictates the size and number of species that can be embedded and the required pickup pressure for this process. The size distribution of droplets between 10 3 – 10 7 atoms has been determined in continuous He droplet beams via scattering of the neutral droplet beam 9 or deflection of charged droplets. 10 More recently, attenuation of He droplet beams, caused by collisions with He gas, have extended droplet size measurements up to 10 11 He atoms. 11 In this work, a pulsed He droplet beam is used. 12 The work of Gomez et al. 11 has shown that quadrupole mass spectra obtained via electron impact ionization of a He droplet beam are sensitive to the average droplet size. In particular, they observed a nearly 10 fold increase in the intensity ratio of the signal due to splitter ions He 4 + to He 2 + (i.e. mass 16 to mass 8, I 16 /I 8 ) upon increase of the average droplet size from ~ 10 4 to ~ 10 9 atoms. 11 Here we study the utility of this approach using a pulsed He droplet beam in conjunction with time-of-flight (TOF) and quadrupole mass spectrometry. 5.2 Experimental The pulsed He droplet apparatus has been described previously (Figure 5.1). 12 Briefly, helium is expanded through a General Valve series 99 solenoid type nozzle with an orifice diameter of 1 mm. The orifice was specially modified by machining a conical 90º opening as described in reference 12. A Parker Iota One controller operates the nozzle. The valve is attached to the second stage of a Sumitomo RDK 408 close cycle 151 cryo-cooler, and its temperature is measured by solid state temperature sensors and controlled via resistive heating. The lowest expansion temperature achievable by this setup is ~ 9 K at a repetition rate of 1 Hz. Figure 5.1. Schematic of the pulsed droplet apparatus. The machine consists of 3 vacuum chambers (1 - 3). Chamber (1) contains the pulsed helium droplet source (B) mounted on a closed cycle cryostat (A) with beam skimmer (C). The source chamber is pumped by a 3000 L/s diffusion pump (P1) backed in series by a roots blower followed by a rotary pump. Chamber (2) houses a ceramic pickup cell (D) wrapped in a tungsten filament. Chamber (2) is pumped by a 1000 L/s turbo-molecular pump (P2). Chamber (3) contains a combination reflectron / linear time-of-flight (TOF) spectrometer (F) as well as an axial quadrupole mass spectrometer (E) followed by a BaF 2 window (G). This UHV chamber is pumped by two 170 L/s turbo molecular pumps (P3 & P4). In the majority of experiments described below, He was expanded at two nozzle temperatures, T 0 = 10.3 and 18 Kelvin, both at a stagnation pressure of P 0 = 20 bar and repetition rate of 10 Hz. Mass spectra were recorded using a Jordan TOF Products time- D 152 of-flight mass spectrometer placed perpendicular to the droplet beam, and an axial quadrupole mass spectrometer (Extranuclear Laboratories), both equipped with electron impact ionization source. The TOF and quadrupole ionizers are placed ~ 104 and ~ 113 cm downstream from the nozzle, respectively. The default ionization settings for the TOF were 3 mA current, 2 microsecond (μs) ionizer pulse duration, and 95 eV electron energy. Any adjustment to these parameters is either noted or it is the parameter being varied. The quadrupole ionizer was set at 2 mA current, and 99 eV electron energy. 5.3 Results and Discussion A variety of measurements on helium droplets produced by a puled nozzle were performed using electron impact ionization. Initially, quadrupole time-of-flight (TOF) measurements were used to determine the average droplet size for the two expansion regimes based upon work by Gomez et al. 11 (section 5.3.1). Quadrupole measurements are consistent with the results in reference 11 and show a sharp increase in I 16 /I 8 with decreasing T 0 indicating a corresponding rise in droplet size. The quadrupole results are compared to those of a TOF mass spectrometer using similar electron impact ionization parameters and show that the quadrupole I 16 /I 8 is ~ 5x larger than that of the TOF. This discrepancy arises from the dramatically different time scales used by each type of spectrometer. Additional TOF measurements of the droplet beam were used to characterize the droplets produced by the puled nozzle (section 5.3.2 – 5.3.4). The origin of the increased I 16 /I 8 ratio for large droplets is due to the increased probability of forming two exciplex He 2 * molecules within the same droplet. The He 2 * formation 153 mechanism is addressed in section 5.3.5. Finally, this chapter closes with the experiments on doping and photoionization of gaseous tris(2-phenylpyridine)iridium (Ir(ppy) 3 ) in helium droplets. Low fluence photoionization at 266 nm exclusively produced Ir(ppy) 3 + indicating than it follows the two-photon mechanism described in Chapter 3. This suggests that the photoionization experiments discussed in section 3.2.2 are possible using helium droplets. 5.3.1 Droplet Sizes 0 500 1000 1500 Intensity time (µs) Mass 8 Mass 16 Ratio = 0.08 T 0 = 18 K 0 500 1000 1500 2000 Ratio = 0.224 T 0 = 10.3 K Intensity time (µs) Mass 8 Mass 16 Figure 5.2. Time dependence of the quadrupole mass spectrometer signal set at M = 8 and M = 16, as indicated, and measured at nozzle temperatures of 18 K (a) and 10.3 K (b). The duration of the nozzle pulse was chosen to be 220 µs in order to give the most intense signal with the shortest open duration. Time zero corresponds to a delay with respect to the nozzle trigger of 2.99 ms and 3.96 ms in panels (a) and (b), respectively. Figure 5.2(a) and (b) shows the time dependence of the quadrupole mass spectrometer signal at nozzle temperatures of 10.3 K and 18 K respectively. In each case two measurements were performed using a quadrupole mass filter set at M = 8 and M = 16 (as indicated) and recorded by a digital oscilloscope. Time zero in (a) and (b) () a () b 154 corresponds to a delay with respect to the leading edge of the nozzle trigger pulse of 2.99 ms, and 3.96 ms, respectively. The delays are consistent with the mechanical delay of the pulsed valve (i.e. roughly 350 µs), 13 and the time of flight of the droplets from the nozzle to the ionizer separated by ~ 1.13 m. The velocity of the droplets in (a) and (b) were obtained via TOF measurements and were found to be ~ 297 m/s and ~ 411 m/s respectively. Each of the time profiles in Figure 5.2 consists of two peaks. The peak at earlier arrival times corresponds to He 2 + and He 4 + ions that are ejected from the droplets upon electron beam ionization. These ions are accelerated by ~ 20 V and detected after a flight time (after ionization) of about ~ 300 μs. The peaks at later arrival times correspond to ionized droplets with masses larger than ~ 10 4 . The mass of these droplets exceeds the 300 amu range of the present mass filter. Due to their large mass, the clusters are not deflected by the mass filter and therefore proceed with normal flight along the axis, which is the origin of the delay with respect to the small fast ions. The relative intensity of the second peak is larger at lower nozzle temperature. This is ascribed to larger sizes of the droplets obtained at lower T 0 . The intensity ratio of mass 16 to mass 8 (I 16 /I 8 ) of the fast peaks can be used to determine the average size of the droplets. Similar ratios have been determined for continuous droplet beams where the average droplet size is well known. 11 Here we obtained I 16 /I 8 = 0.08, and 0.224 at nozzle temperatures 18 K and 10.3 K respectively. A comparison of our ratios with those of Gomez et al. 11 indicates the average number of atoms per droplet (<N He >) is approximately 5x10 4 and 3x10 5 for 18 K and 10.3 K, 155 respectively. Hereafter we shall refer to droplets obtained at 18 K and 10.3 K as small and large droplets, respectively. Previous measurements indicate that <N He > of droplets produced by a pulsed nozzle are comparable to those produced by a continuous nozzle, but at nozzle temperatures that are several degrees higher that of the continuous nozzle; 11 The proximate cause of which is the larger orifice diameter that is used with the pulsed nozzle. 12 Due to a larger orifice diameter the gas spends more time in the expansion, which apparently facilitates formation of larger droplets. 10 20 30 40 50 60 70 0 (H 2 O) 2 H + H 3 O + H 2 O + He + 3 Intensity m/e 18.05 K He + 2 0 10 20 30 40 50 60 70 0 H 3 O + (H 2 O) 3 H + H 2 O + He + 2 Intensity m/e 10.3 K Figure 5.3. Typical TOF mass spectra at 18K (a) and 10.3K (b) with important peaks labeled. The considerable water (M = 18) and protonated water cluster peaks (M = n*18 + 1) indicates pickup of multiple water molecules, due to the relatively high background pressure (10 -6 mbar) in our pick up chamber during the experiments. Figure 5.3 shows two typical TOF spectra at 18K and 10.3K. The strong He 2 + peak followed by a succession of small He n + peaks is the telltale sign of helium droplet production. 14 Water greatly contributes to the spectra, which is particularly noticeable in small droplets, and is caused by the relatively high base pressure in our interaction () a () b 156 chamber (10 -6 mbar). There are also various peaks that correspond to water clusters; most notably mass 19 (H 3 O + ). The strong H 3 O + signal, but weak (H 2 O) n •H + signal in small droplets suggests that large water clusters are not formed in the small droplets. However, large droplets possess a greater capture cross-section. Thus, effective capture of up to 9 water molecules is observed (M = 145, not shown in Figure 5.3). In large droplets the H 3 O + signal is weaker with respect to the strong He 2 + signal, which is likely due to an abundance of larger clusters, and presumably their inefficient fragmentation upon ionization. The ionization branching ratio also shifts towards He n + ions in larger droplets. Regardless of the differences, it is clear that there is good droplet production at both temperatures. Figure 5.4 shows a comparison of I 16 /I 8 measured with quadrupole and TOF mass spectrometers at various temperatures – nozzle repetition rates are indicated. For quadrupole measurements the maxima of the corresponding peaks were used to obtain the ratios. With TOF, mass peak areas were used to calculate the intensity ratio. In both measurements an increase of I 16 /I 8 with decreasing nozzle temperature is observed. However, at low nozzle temperatures I 16 /I 8 is about a factor of 5 smaller in the TOF measurements, whereas at higher temperatures the values are comparable. This incongruity is surprising, considering both techniques use electron impact ionization. Therefore, the discrepancy between the two methods indicates some difference in the extraction of ions. Below a general description of the two mass spectrometric techniques is provided to point out crucial differences. 157 8 10 12 14 16 18 20 22 0.0 0.1 0.2 0.3 0.4 0.5 1 Hz 4 Hz 10 Hz I16/I8 Temperature (K) 8 10 12 14 16 18 20 22 0.00 0.02 0.04 0.06 0.08 0.10 1 Hz 4 Hz 10 Hz I16/I8 Temperature (K) Figure 5.4. Comparison of I 16 /I 8 measured with quadrupole (a) and TOF (b) mass spectrometers at various nozzle temperatures with repetition rates indicated. Both plots exhibit a sharp initial decrease followed by a moderate leveling when moving from low to high temperature albeit with different absolute ratios. The TOF ratios here were measured with 1 mA current, 2 us pulse duration, and 95 eV e-Energy. The extraction technique employed by the TOF system uses a voltage pulse to create an equipotential between repeller and extractor plates. Without a potential gradient the ionizing electrons are free collide with droplets passing between these plates, thereby creating positive ions. As described earlier the default ionization pulse lasts for 2 µs. When the pulse is switched off, and the potential gradient restored, ionized atoms and clusters are accelerated to ~ 1800 eV down a 1 meter tube toward a micro channel plate (MCP) where their collision with the MCP is detected. The entire process from ionization to detection occurs in less than 30 μs for masses up to ~ 200 amu when using standard voltages. In comparison, the quadrupole mass spectrometer employs a continuous extraction method, where the ionizing electrons constantly bombard droplets as they pass through the ionizing region. With a droplet flight velocity of ~ 350 m/s, and a 1 cm path through the ionizing region, droplets spend about 30 μs in the ionizing region. After () a () b 158 exiting the ionizing region positive ions are mildly accelerated (~ 20 V) toward a detector followed by mass selection in the quadrupole. The time lapse from ionization to detection in the quadrupole occurs within ~ 300 μs. The above comparison shows that the time droplets spend in the ionizer region before extraction seems to be the most obvious difference between the two methods. If the creation of positive ions were instantaneous, there should be no difference in the observed relative intensities. Thus, any disparity in measured intensities may indicate that the mechanism leading to ionization (in particular the formation of He 4 + ions) is not instantaneous and may include some intermediate steps. 5.3.2 Pulse Profile In order to elucidate the origin of the differences in the quadrupole and TOF intensities, several additional measurements were performed. Figure 5.5 shows the time profile of the He 2 + and He 4 + signals vs. delay between the nozzle trigger and ionizing pulse trigger of the TOF mass spectrometer, measured at high (a) and low (b) nozzle temperatures. As mention above, the ionizing pulse width was 2 µs. The pulse profile in Figure 5.5(a) exhibits a spike at the beginning of the profile followed by broad shoulder of lower intensity. These features are reproduced in both mass signals. The spike is attributed to the mechanical inconsistency of the nozzle. The He 2 + peak has a full width at half maximum (FWHM) of ~ 180 μs, which is close to the 220 μs pulse driving the nozzle. Figure 5.5(b) He 2 + signal shows a broad pulse profile 159 with no sharp peak in the beginning and has a FWHM of ~ 200 μs again consistent with the 220 μs driving pulse. 2.8 2.9 3.0 3.1 3.2 0 Mass 8 Mass 16 Intensity Delay (ms) T 0 = 18K 3.7 3.8 3.9 4.0 4.1 4.2 0 Mass 8 Mass 16 Intensity Delay (ms) T 0 = 10.3K 2.8 3.0 3.2 0.00 0.02 0.04 0.06 0.08 0.10 I16/I8 Delay (ms) 3.6 3.8 4.0 4.2 0.00 0.02 0.04 0.06 0.08 0.10 I16/I8 Delay (ms) Figure 5.5. TOF pulse intensity profile vs. delay for small (a) and large (b) droplets as measured with TOF. In (a) and (b), signal for mass 16 was multiplied by 4 and 3 for small and large droplets respectively. (c) and (d) show the delay dependence of I 16 /I 8 throughout the pulse profiles for small and large droplets, respectively. The average value (red line) of each ratio taken over their respective profile (endpoints indicated in red and 95% confidence curves in blue) was 0.058 ± 0.004 and 0.059 ± 0.0035 for small and large droplets respectively. At T 0 = 18 K the gas pulse arrived at the ionization region at a median value of 2.99 ms after the nozzle was triggered, but at 3.96 ms when T 0 = 10.3 K, which () a () b ( ) c () d 160 corresponds to droplet beam velocities of ~ 411 and ~ 297 m/s, respectively. In a continuous expansion, droplet speeds obtained between T 0 = 18 K and 10 K were found to be 400 and 240 m/s, respectively. 15 The agreement is considered satisfactory, considering the use of a different nozzle sources and that the actual pulsed nozzle temperature is expected to be higher than measured by our sensor, which was mounted a short distance from the nozzle, due to heat release associated with motion of the piston. Figure 5.5(c) and (d) shows that I 16 /I 8 remains approximately constant during the most intense part of the pulse, with values of 0.058 ± 0.004 and 0.059 ± 0.0035 for small and large droplets, respectively. The slight disagreement between ratio values for Figure 5.5(c) and (d) and those of Figure 5.4(b) is primarily due to the different currents used (section 5.3.3). On the wings of each pulse the ratio increases, however, mass 8 decreases to zero, while mass 16 reverts to the O + background signal. Thus, the increased ratio at the pulse edges (when the signal drops to less than 10% from its maximum) does not reflect the droplet size. It appears that the average cluster size is relatively constant throughout the pulses, and the ratio at the center of the pulse, gives the most reliable value of I 16 /I 8 . 161 5.3.3 Current Dependence 0 1 2 3 4 5 0 Mass 4 Mass 8 Mass 12 Mass 16 Intensity Current (mA) T 0 = 18 K 0 1 2 3 4 5 0 Mass 4 Mass 8 Mass 12 Mass 16 Intensity Current (mA) T 0 = 10.3 K 1 2 3 4 5 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 I16/I8 Current (mA) 1 2 3 4 5 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 I16/I8 Current (mA) Figure 5.6. Current dependence of the TOF mass spectrometer peak intensities at M = 4, 8, 12, and 16 for small (a) and large droplets (b), as well as I 16 /I 8 for small (c) and large (d) droplets measured at ionization currents ranging from 1 to 5 mA. Intensities for mass 4, 12, and 16 are multiplied by 5 and by 2.5 in (a) and (b), respectively. The current dependence of the mass signals and I 16 /I 8 are shown in Figure 5.6(a) – (d). To facilitate data comparison, signals for masses 4, 12, and 16 were multiplied by factors of 5 and 2.5 for small and large droplets, respectively. It is seen that the intensity of all peaks scale approximately linearly with ionizing current. Consequently, I 16 /I 8 is approximately constant with current for small and large droplets. However, a very small () a () b ( ) c () d 162 initial decrease in I 16 /I 8 is observed with increasing current. An effect that is more pronounced in large droplets. The difference in I 16 /I 8 at 1 and 3 mA for both large and small droplets mostly accounts for the different observed ratio values between Figures 5.5(c), (d) and those of Figure 5.4(b). Any small difference that remains is likely due to uncertainty in the measurement. Buchenau et al. 16 previously examined the effect of electron current on droplet ionization using a quadrupole mass spectrometer. Their work focused on lower electron current (between 0 and 1 mA), but they observed, via log-log plots, a roughly linear dependence on He + signal vs. electron current. The agreement between this work and that of reference 16 indicates there is no change in mechanism of the ionization at the higher electron currents. 5.3.4 Electron Energy Dependence Figure 5.7(a) and (b) plots mass signals vs. electron energy. It is seen that all mass signals increase as the electron energy is increased from 40 to 90 eV. The fast initial rise from 40 – 65 eV followed by the slower increase from 65 – 90 eV is consistent with a changing electron impact ionization cross-section (section 2.5). The very low He 4 + signal at E = 40 eV is consistent with its appearance potential of 37.5 eV as found previously. 16 Interestingly, I 16 /I 8 show similar increase with electron energy in both large and small droplets - reflecting a faster rise of the M = 16 signal than that of M = 8. Therefore, we concluded that the electron energy of higher than about 40 eV is essential for the 163 preferential formation of He 4 + , and that at least one formation mechanism of He 4 + is likely similar in large and small droplets. 40 50 60 70 80 90 0 Mass 4 Mass 8 Mass 12 Mass 16 Intensity e-Energy (eV) T 0 = 18 K 40 50 60 70 80 90 0 Mass 4 Mass 8 Mass 12 Mass 16 Intensity e-Energy (eV) T 0 = 10.3 K 40 50 60 70 80 90 0.00 0.02 0.04 0.06 I16/I8 e-Energy (eV) 40 50 60 70 80 90 0.00 0.02 0.04 0.06 I16/I8 e-Energy Figure 5.7. Intensity of the TOF mass 4, 8, 12, and 16 peaks vs. electron energy are shown for small (a) and large (b) droplets as well as I 16 /I 8 for small (c) and large (d) droplets, respectively. In (a) and (b) masses 4, 12, and 16 are multiplies by factors of 5 and 2.5, respectively. () a () b ( ) c () d 164 5.3.5 Pulse Duration Dependence 0.5 1 2 4 8 16 32 64 128 0 Mass 8 Mass 12 Mass 16 Intensity Duration (µs) T 0 = 18 K 0.5 1 2 4 8 16 32 64 128 0 Mass 8 Mass 12 Mass 16 Intensity Duration (µs) T 0 = 10.3 K 1 2 4 8 16 32 64 128 0.00 0.02 0.04 0.06 I16/I8 Duration (µs) 1 2 4 8 16 32 64 128 0.00 0.05 0.10 0.15 0.20 I16/I8 Duration (µs) Figure 5.8. TOF peak intensity vs. duration of the ionization pulse for small (a) and large (b) droplets followed by I 16 /I 8 for small (c) and large (d) droplets. All ionization pulses were initiated at the maximum intensity of their respective droplet pulse, see Figure 5.5. In (a) and (b) intensities of mass 12 and 16 peaks were multiplied by a factor of 3. The dependence of the intensity of the TOF mass peaks vs. ionization duration (Δt) is shown in Figure 5.8(a) and (b) for small and large droplets, respectively. In both cases the ionization pulses were initiated (t = 0) at the maximum of the M = 8 signal, i.e. 2.99 and 3.96 ms after the nozzle trigger pulse, for small and large droplets, respectively () b ( ) c () d () a 165 (see Figure 5.5). At T 0 = 18K the signal levels initially increase with the duration of the ionization pulse, reach a maximum at approximately Δt = 4 μs and then decrease. In small droplets, the signals at mass 8, 12 and 16 show a very similar dependence, resulting in a nearly constant I 16 /I 8 ratio. The decrease at longer times is due to the decrease in droplet number density at the end of the droplet pulse (see Figure 5.5). Because ionization is triggered during the most intense portion of the droplet beam, any signal, especially that originating from the creation of ions at longer times, is in competition with the decreasing droplet density. For short Δt, this effect is small, but at Δt > ~ 30 μs the droplet density begins to decrease rapidly, which significantly affects signal intensity. In large droplets, mass 8 and 12 behave similar to those in the small droplet measurements, but mass 16 reaches maximum at Δt ~ 16 μs, where the He 4 + signal becomes larger than He 3 + (see Figure 5.8b). This delayed rise in mass 16 signal results in a considerable increase of I 16 /I 8 from ~ 0.04 at Δt = 1 μs to nearly 0.2 at Δt =16 μs. This shows that He 4 + signal behaves differently in large droplets than mass He 2 + or He 3 + , which suggests a different or an additional mechanism of He 4 + formation in large droplets. At this point we note that there is an optimal duration of the ionization pulse, beyond which no significant signal increase is observed. Figure 5.9 shows the intensity of background H 2 O + signal vs. Δt at 1, 3, and 5 mA electron current. Clearly, the greatest increase in signal is acquired within the first ~ 4 μs of irradiation. The signal then saturates upon longer irradiation. Therefore, the majority of signal at any duration must be due to ions created in the 4 μs preceding extraction. This behavior is likely related to 166 the finite lifetime of ions inside the ionization region. For example, the root mean squared velocity of gaseous water at room temperature is ~ 640 m/s. Thus, a water molecule at the center of the ionization volume, which must travel ~ 6 mm to escape extraction, vacates the region in less than 9 μs. 0 5 10 15 1 mA 3 mA 5 mA Intensity Duration (µs) Figure 5.9. The effect of the ionizing pulse duration on background H 2 O + TOF intensity at various electron currents. I 16 /I 8 vs. duration levels at t ≈ 30 μs for large droplets, where it reaches a value similar to that obtained with the quadrupole mass spectrometer (Figure 5.8d). It is important to note that the time of ~ 30 μs is very similar to the time droplets spend passing through the ionization region of the quadrupole mass spectrometer. As noted above, the signal behavior in small droplets appears to be the same for mass 8, 12, and 16. Therefore we propose that these clusters are formed in small droplets via a nearly instantaneous ejection of He n + ions from the droplets (mechanism 1). The decrease in peak intensity with increasing n suggests that mass 8 is the favored cluster in 167 this formation mechanism. The deviation in mass 16 from this trend in large droplets suggests that an additional mechanism is involved. Buchaneau et al. have proposed that in addition to direct formation, mass 16 arises from the reaction of two He 2 * exciplex molecules that combine on the surface of a droplet to form He 4 + , which is then ejected (mechanism 2). 16 Accordingly, two excited helium atoms (He*) are first created by a single energetic electron passing through the droplet. Both He* quickly form bubbles and migrate to the surface of the droplet where they become trapped. 17 From bulk helium studies 18 it is known that He* decays with a time constant of ~ 15 μs to produce metastable (He 2 *(v=16) a 3 Σ u + ) excimers. Here we assume that same formation time is applicable to He* on the surface of the droplet. The two He 2 * on the surface finally combine and produce He 4 + , which is then ejected. An estimate of the time “roaming” on the surface before reaction occurs is given by: 22 o 2 2/3 min oo 10 ** 4 (2.2A) N 0.2 * (0.4 ) 5A*30*10 A/ S roa g He He A s dv K s π τ µ = =  (5.1) where A S is the surface area of the droplet, N is the number of atoms in the droplet taken to be 3x10 5 atoms, v He2* (0.4K) is the velocity of He 2 * at 0.4 Kelvin, and d He2* = 5 Å is a diameter of He 2 *, which replaces the cross-section for 2D kinetics. It is seen that any additional delay due to “roaming” is short, and that the delay in He 4 + formation via mechanism 2 must be due to the ~ 15 μs formation time of the He 2 *. This is in qualitative agreement with the He 4 + maximum at 16 μs. Mechanism 2 is of minor importance in small droplets because of the low probability of creating of two He* with the same 168 electron. The low probability is justified because the electron’s mean free path is comparable to the small droplet diameter. 11 0.5 1 2 4 8 16 32 64 128 0.00 0.05 0.10 0.15 Ratio Difference Simultaneous Growth I 16 /I 8 Duration (µs) Figure 5.10. Plot of I 16 /I 8 for large droplet subtracted by I 16 /I 8 for small droplets. Data is fit the equation [ ] 2 1 exp( ) y a kt b = −− + . Optimized values for a, b, k are 0.1551, -0.0102, and 0.11442, respectively. To better test the validity of mechanism 2 we subtracted I 16 /I 8 of large droplets by I 16 /I 8 of small droplets. This approach is justified as follows: first, small droplets exhibit no trace of the delayed He 4 + rise observed in large droplets and therefore He 4 + is expected to be formed via mechanism 1; and second, mechanism 1 is expected to participate regardless of droplets size. Additionally, I 16 /I 8 better accounts for the decreasing droplet density of the pulse. Thus, the resultant data points, seen in Figure 5.10, eliminate any contribution of mechanism 1 from the I 16 /I 8 ratio of large droplets. Scharf et al. showed that in bulk helium He 2 * is formed via exponential growth to an equilibrium value using: 18 [ ] 0 1 exp( / ) GG t τ = −− (5.2) 169 where G is the number of He 2 * at time t, G 0 is the number of He 2 * at equilibrium, and τ is the formation time constant of He 2 *. In helium droplets where only one or two He 2 * species are expected, G becomes the probability of formation, and equation 5.2 becomes: [ ] 1 exp( / ') Pt τ =−− (5.3) Here τ is replaced with τ’ in anticipation of a new time constant due to the slightly different environment. In the case of two He 2 * forming simultaneously the total probability is the product of the individual probabilities. Thus: [ ] 2 1 exp( / ') TOT Pt τ =−− (5.4) Figure 5.10 shows the subtracted ratios fit by the following curve: [ ] 2 1 exp( ) y a kt b = −− + (5.5) Here b accounts for a deviation from zero baseline and a accounts for the arbitrary amplitude. Thus, the most import parameter k should better represent the true time constant and will be unaffected by an arbitrary baseline or saturation amplitude. Fitted values of a, b, k are 0.1551, -0.0102, and 0.11442, respectively. This yields a value for τ’ = 1/k = 8.74 μs. The fit is in very good agreement with the experimental data and provides compelling evidence that mechanism proposed by Buchenau et al. is reasonable. It is unclear why the reaction time in droplets is roughly one half that of bulk helium. Future work on recombination lifetime would entail setting a delay between electron irradiation and extraction. Varying the delay between irradiation and extraction would help pin down the creation lifetime of He 4 + and its dependence on droplet size. An alternate approach would be to use a continuous droplet beam. Removing the competition 170 with decreasing droplet signal would enable the signal to reach saturation / equilibrium. Varying parameters under these conditions, such as duration and droplet size, would facilitate a better understanding of this process. 5.3.6 Photoionization of Tris(2-phenylpyridine)iridium in Helium Droplets Great interest in the tris(2-phenylpyridine)iridium (Ir(ppy) 3 ) molecule stems from its application in OLED displays. One- and two-photon photoionization experiments of gaseous Ir(ppy) 3 are presented in Chapter 3. A major concern in these experiments is the large amount of internal energy imparted to the Ir(ppy) 3 molecules during sublimation. In general, it is desirable to cool molecules to their lowest quantum state prior to probing for spectroscopic information. Unfortunately, attempts to cool the gaseous Ir(ppy) 3 molecules using supersonic expansion and small helium droplets (<N He > ~ 10 4 ) using the apparatus described in Chapter 3 were unsuccessful. 19 However, by increasing the droplet size to <N He > ≈ 5x10 4 using the pulsed droplet apparatus, it proved possible to imbed and photoionize gaseous Ir(ppy) 3 molecules in droplets. Ir(ppy) 3 molecules were inserted into droplets by heating solid Ir(ppy) 3 in a ceramic oven aligned with the droplet beam axis. This pick-up cell (section 2.4.3) has two orifices for the droplet beam to pass through and is wrapped in resistive tungsten wire (Figure 5.11). The oven is heated by passing current through the tungsten filament with a K-type thermocouple attached below the exit orifice of the oven to monitor the oven temperature. 171 Figure 5.11. Diagram of the crucible pick-up cell used to imbed Ir(ppy) 3 in helium droplets. The droplet beam was aligned through the crucible openings and the solid Ir(ppy) 3 was placed in the lower half of the crucible. Tungsten wire was wrapped around the crucible and heated. The temperature was measured by a thermocouple just below the exit orifice. As the temperature increased, mass peaks at M = 655 and M = 1310 amu appeared in the TOF mass spectra (Figure 5.12). Referring to figure 5.12(c), the Ir(ppy) 3 + and (Ir(ppy) 3 ) 2 + signals were a maximum at an oven temperature of 192 ºC and 202 ºC, respectively. As seen from Table 5.1, the Ir(ppy) 3 vapor pressure at 192 ºC and 202 ºC is ~ 7x10 -6 Torr and 2x10 -5 Torr, respectively. 20 These pressures are sufficient to produce an effusive beam, which will contribute to the Ir(ppy) 3 TOF signal. Fortunately, measurement of the effusive signal shows a contribution of less than 1/30 th of the overall Ir(ppy) 3 signal. Typically, as the dopant vapor pressure increases, peaks due to dopant clusters, such as dimers, trimers, etc. become more prominent. This is also seen in Figure 5.12(c). As the cell temperature rises from 192 ºC to 200 ºC the M = 1310 peak due to Ir(ppy) 3 dimers increases. However, at 211 ºC and beyond all mass signals, including those of the pure droplets, decrease rapidly. The loss of all signal hints that the entire beam is being blocked. We attribute the blockage to a pressure increase inside the pick-up cell as more droplet-impurity collisions occur. Specifically, the energy imparted to the droplet upon capture of the impurity causes rapid evaporation of He atoms from the droplet. tungsten wire thermocouple orifice 172 Consequently, this evaporation, and further droplet collisions with the evaporated helium, causes a pressure increase inside the oven, which blocks the remainder of the droplet beam. The local pressure build-up would likely be reduced if the oven orifices were widened. However, the focus of this study was the Ir(ppy) 3 monomer. Thus, the oven temperature was set to 192 ºC to maximize the insertion of only one Ir(ppy) 3 molecule in the droplets. With the doping process characterized, 266 nm light from the YAG fourth harmonic was used to photoionize the embedded Ir(ppy) 3 via multiphoton absorption. The TOF spectra obtained with focused and unfocused 266 nm radiation are shown in Figure 5.13. Referring to Figure 5.13, the spectrum obtained at high fluence shows a pronounced fragmentation peak that is consistent with the gas phase experiments of Chapter 3. However, at low fluence the parent ion is produced, but at a much lower intensity. The baseline oscillations in 5.13(b) are due to transient electrical noise. Both spectra show the absence of any He n + progression, which is consistent with the higher ionization energy of helium (~24.6 eV). 173 0 500 1000 2•Ir(ppy) + 3 Intensity (a.u.) m/e Ir(ppy) + 3 0 20 40 60 80 100 He + 2 600 800 1000 1200 Ir(ppy) 3 •H 2 O + 2•Ir(ppy) + 3 Intensity (a.u.) m/e Ir(ppy) + 3 600 800 1000 1200 221 211 200 192 179 172 151 101 (Ir(ppy) 3 ) + 2 m/e Oven Temperature °C Intensity (a.u.) Ir(ppy) + 3 Figure 5.12. Full (a) and zoomed in (b) mass spectra of the droplet beam after pickup of Ir(ppy) 3 . The inset in (a) is an expanded view of the droplet signal. The oven temperature in both (a) and (b) is 192 ºC. (c) Ir(ppy) 3 + and (Ir(ppy) 3 ) 2 + progression upon increase of the oven temperature. M = 655 and M = 1310 signals reach a maximum at 192 ºC and 200 ºC, respectively. () b () a ( ) c 174 Figure 5.13. Photoionization mass spectra of Ir(ppy) 3 doped helium droplets recorded at different fluences. The laser wavelength is 266 nm (37594 cm -1 ) produced by the YAG fourth harmonic. At low fluence (bottom trace) the parent ion (Ir(ppy) 3 + ) is produced exclusively. Note: < 1.0 mJ cm -2 is within the two- photon ionization regime for the gas phase experiments of Chapter 3. Increase in laser fluence causes fragmentation that is consistent with the gas phase experiments of Chapter 3. The peak at M = 0 in (a) and (b) is scattered UV radiation, which served as the t = 0 reference. It was shown in Chapter 3 that photoionization of gaseous Ir(ppy) 3 at photon energies between 4.424 - 4.435 eV and fluences < 1.6 mJ cm -2 is a two-photon process. Although a fluence study of Ir(ppy) 3 photoionization in helium droplets was not performed, the TOF spectra in Figure 5.13 are consistent with those of Chapter 3. This Ir + Ir(ppy) 2 + Ir(ppy) 3 + 5.0 mJ cm -2 < 1.0 mJ cm -2 mass/amu 200 300 400 500 600 700 0 100 ~ 500 mJ cm -2 175 suggests that at low fluence the photoionization of Ir(ppy) 3 in helium droplets using 266 nm is also a two-photon process. Table 5.1. Ir(ppy) 3 vapor pressure vs. temperature 20 Temperature (C) Vapor Pressure (torr) 150 9.47589×10 -8 160 3.00606×10 -7 170 9.05189×10 -7 180 2.59624×10 -6 190 7.11514×10 -6 200 1.86857×10 -5 There are several advantages to employing helium droplets for the photoionization of Ir(ppy) 3 . The high heat conductivity and low temperature of the droplets quickly extract and dissipate all energy imparted to Ir(ppy) 3 during sublimation. Moreover, the transfer of internal energy from Ir(ppy) 3 to the droplet occurs quickly, such that, for two-photon photoionization, the first and second transition may occur from the lowest vibrational level of the singlet ground state (S 0 ) and the lowest triplet state (T 1 ), respectively. Another benefit to using helium droplets for this particular experiment is that photoionization in helium droplets requires an additional 1230 cm -1 needed to eject the electron from the droplet. 21 Loginov et al. observed that the value of 1230 cm -1 was invariant for droplets with radii large than 38 Å, 21 which is the case in these experiments. This means that only cases where the energy of the photon(s) is greater than the ionization energy by 1230 cm -1 will cations be observed. In cases where the electron is 176 not ejected from the droplet, subsequent electron–cation recombination will occur and no signal will be detected. Thus, successful photoionization of Ir(ppy) 3 using 193.3 nm would correspond to a revised ionization energy (IE) upper bound of 6.26 eV (6.41 – 0.15). However, the actual situation is more complex as the droplet environment is considerably different than that of a vacuum. Helium abhors electron density, which results in broadened and shifted electronic spectra. 22,23 The magnitude of such spectral shifts are typically on the order of a few hundred wavenumbers. 23 The electron-helium interaction has also been shown to reduce the ionization potential. 21 The situation is further complicated by the finite size of the droplets. In this case, a reasonable approach is to apply a polarizable continuum model. 24 In this model, the IE of the embedded molecule varies as: 21 ( ) 21 0 1 IE( ) = IE 8 e R R ε πε − ∞ − − (5.6) where IE ∞ is the vertical ionization threshold in bulk helium, e the electron charge, ε 0 is the permittivity of free space, and ε is the dielectric constant of the cluster. Although the polarizable continuum model provides a way to compensate for the changing IE as a function of droplet size, the IE in bulk helium is still unknown! Thus, the main benefit of using droplets for Ir(ppy) 3 photoionization lies in its ability to remove internal energy. The expected spectral shifts are indicative of the uncertainty in the IE upper bound. Overall, photoionization of Ir(ppy) 3 inside helium droplets would greatly compliment the gas-phase experiments of Chapter 3. 177 5.4 References 1. Choi, M. Y.; Douberly, G. E.; Falconer, T. M.; Lewis, W. K.; Lindsay, C. M.; Merritt, J. M.; Stiles, P. L.; Miller, R. E. Int. Rev. Phys. Chem. 2006, 25, 15. 2. Tiggesbaumker, J.; Stienkemeier, F. Phys. Chem. Chem. Phys. 2007, 9, 4748. 3. Krasnokutski, S. A.; Huisken, F. J. Phys. Chem. A 2010, 114, 7292. 4. Stienkemeier, F.; Lehmann, K. K. J. Phys. B 2006, 39, R127 . 5. Toennies, J. P.; Vilesov, A. F. Angew. Chem. Int. Ed. 2004, 43, 2622. 6. Gough, T. E.; Mengel, M.; Rowntree, P. A.;Scoles, G. J. Chem. Phys. 1985, 83, 4958. 7. Buchenau, H.; Knuth, E. L.; Northby, J.; Toennies, J. P.; Winkler, C. J. Chem. Phys. 1990, 92, 6875. 8. Harms, J.; Hartmann, M.; Toennies, J. P.; Vilesov, A. F.; Sartakov, B. J. Molec. Spec. 1997, 185, 204. 9. Lewerenz, M.; Schilling, B.; Toennies, J. P. Chem. Phys. Lett. 1993, 206, 381. 10. Knuth, E. L.; Henne, U. J. Chem. Phys. 1999, 110, 2664. 11. Gomez, L. F.; Loginov, E.; Sliter, R.; Vilesov, A. F. J. Chem. Phys. 2011, 135, 154201. 12. Slipchenko, M. N.; Kuma, S.; Momose, T.; Vilesov, A. F. Rev. Sci. Inst. 2002, 73, 3600. 13. Sliter, R. Infrared and Raman Spectroscopy of Molecules and Molecular Aggregates in Helium Droplets, Ph. D. Dissertation, University of Southern California, Los Angeles, CA, 2011. 14. Peterka, D. S.; Kim, J. H.; Wang, C. C.; Poisson, L.; Neumark, D. M. J. Phys. Chem. A 2007, 111, 7449. 15. Schilling, B. Ph. D Dissertation, University of Gottingen, Gottingen, Germany, 1993. 16. Buchenau, H.; Toennies, J. P.; Northby, J. A. J. Chem. Phys. 1991, 95, 8134. 178 17. Scharf, D.; Jortner, J.; Landman, U. J. Chem. Phys. 1988, 88, 4273. 18. Keto, J. W.; Soley, F. J.; Stockton, M.; Fitzsimmons,W. A. Phys. Rev. A 1974, 10, 872, 887. 19. Nemirow, C. Multiphoton Investigation of tris(2-phenylpyridine)iridium. Ph. D. Dissertation, University of Southern California, Los Angeles, CA, 2011. 20. Deaton, J. C.; Switalski, S. C.; Kondakov, D. Y.; Young, R. H; Pawlik, T. D.; Giesen, D. J.; Harkins, S. B.; Miller, A. J. M.; Mickenberg, S. F.; Peters, J. C. J. Am. Chem. Soc. 2010, 132, 9499. 21. Loginov, E.; Rossi, D.; Drabbels, M. Phys. Rev. Lett. 2005, 95, 163401. 22. Schmied, R.; Carcabal, P.; Dokter, A. M.; Lonij, V. P. A.; Lehmann, K. K.; Scoles, G. J. Chem. Phys. 2004, 121, 2701. 23. Brauer, N. B.; Smolarek, S.; Zhang, X.; Buma, W. J.; Drabbels, M. J. Phys. Chem. Lett. 2011, 2, 1563. 24. Jortner, J. Z. Phys. D 1992, 24, 247. 179 Chapter 6 Future Work 6.1 Introduction An open question in this dissertation is whether the ethynyl radical (C 2 H, section 2.6) can be produced in sufficient quantity, such that detection with electron impact ionization / time-of-flight (TOF) mass spectrometry is possible. It was shown in section 2.6 that 193.3 nm photolysis of acetylene (C 2 H 2 ) was able to produce C 2 and C 2 H molecules. However, detection of these species using electron impact ionization / TOF mass spectrometry was inadequate, because either the concentration and / or the electron impact ionization efficiency was too low to effectively monitor the nascent species. In light of the previous results, it is proposed that C 2 H is more aptly produced by electrical discharge of a supersonically expanding acetylene / carrier gas mixture. Both continuous and pulsed discharge sources have been developed, 1,2 but a pulsed source is particularly promising due to the large molecular density produced while maintaining reasonable vacuum. Therefore, production of C 2 H will be achieved via pulsed electrical discharge. This approach has been used previously to generate OH radicals from a gaseous water / argon mixture. 3 Reported measurements of the OH centerline flux using pulsed discharge have been as high as 2.2x10 17 molecules sr -1 s -1 , which corresponds to a concentration of ~ 3x10 12 molecules cm -3 approximately 1 cm after the nozzle. 3 Additionally, the radical species are created prior to expansion, which allows the radicals to cool in the expansion that follows. 180 6.2 Experimental The proposed nozzle and discharge setup is similar to that used by McCarthy et al. 4 A rendering of the nozzle and discharge geometry is depicted in Figure 6.1. A commercially available pulsed valve (R. M. Jordan) with a 500 um nozzle will be used. The valve operates based on a current loop mechanism, which avoids the inconsistency of poppets and the need to constantly replace them. The valve has a repetition rate 10 Hz and a pulse duration of ~ 50 μs. Attached to the nozzle faceplate is a 5 mm Teflon spacer followed by a copper electrode. Both the spacer and electrode are encased in a Teflon housing. The electrode will initially be set between – 2.0 and – 2.5 kV, with the nozzle faceplate wired to ground. This insures that the electron current flows against the gas stream. Operation with a positively biased electrode is known to cause an unstable discharge with less efficient radical generation. 2 Discharge initiates by the rise in local pressure when the valve opens. The discharge automatically terminates once the local pressure returns to vacuum. C 2 H is generated by collisions between the flowing discharge electrons and the expanding acetylene molecules. 181 Figure 6.1. Depiction of the nozzle and discharge assembly. The nozzle operates on a current loop mechanism. Attached to the grounded nozzle faceplate is a Teflon spacer followed by a negatively biased copper electrode. Both spacer and electrode are encased in a Teflon shroud. The acetylene mixture will contain 10% or less acetylene in Argon and expanded using a backing pressure between 1 – 2 psia. Compared to the 3 % mixture and 1 psia backing pressure of reference 3, the proposed conditions should increase the number density by a factor of 5. In fact, under similar expansion conditions a total beam density of 3x10 13 has been measured approximately 8 cm past the nozzle, 5 which would correspond to an acetylene concentration of 10 12 molecules / cm -3 at the detection region. The mixture concentration may need to be fine-tuned to prevent reactions among the radicals during expansion. The above conditions allow for source and detection chamber pressures of about ~ 10 -5 and mid 10 -7 torr, respectively. To ensure a stable discharge, several precautions need to be taken. First, a gating circuit will be used to prevent current from flowing 50 us prior to and 50 us after the gas current loop copper electrode -2.4 kV 5 mm Teflon spacer insulating Teflon housing 182 pulse begins and ends, respectively. This will reduce that probability of gas leaks triggering a discharge. In addition, ballast resistors must be implemented to ensure the current does not rise above a reasonable value. In the absence of such a limitation, arcing may occur due to the negative resistance characteristic of the gas, which will pit the surface of the electrodes. The asymmetry created by a pit in the electrode surface will prevent a stable uniform discharge from occurring and the electrode will need to be replaced. As noted above, after discharge the molecules are left to cool via expansion and travel to the detector. Detection will again use electron impact ionization coupled with TOF mass spectrometry, albeit with a few changes to the setup described in section 2.6. A new vacuum chamber will be constructed, in which the distance between the nozzle and TOF detection region is minimized (Figure 6.2a). A distance of 10 cm or less is easily achieved. The small separation between source and detector will minimize the loss of signal due to molecular beam propagation. The nozzle will be ~ 2 cm away from a 1 mm skimmer, which were optimal conditions for the experiments described in section 2.6. Additionally, the detection chamber will contain three very different optical paths in anticipation of future experiments on C 2 H (Figure 6.2b). Path 1 will cross the source chamber directly in front of the nozzle and skimmer, path 2 will pass diagonally through the center of the TOF stack assembly, and path 3 will pass through the rear of the detection chamber in order to overlap the molecule beam. These paths will insure that all opportunities to optically probe C 2 H are explored. 183 Figure 6.2. (a) side view of the proposed vacuum chamber. The distance between the nozzle and TOF stack is less than 10 cm. Window 1, 2, and 3 correspond to path 1, 2, and 3 in part (b), respectively. The operating pressures in the source and detection regions are expected to be 10 -5 torr and mid 10 -7 torr, respectively. (b) shows a top view of the proposed vacuum chamber. Three optical paths are illustrated. Path 1 passes directly in front of the nozzle, path 2 crosses the center of the detection region, and path 3 overlaps the molecular beam with anti-parallel propagation. MCP detector skimmer gate valve pulsed nozzle TOF stack turbo pump diffusion pump turbo pump source chamber window 1 window 3 window 2 EGUN TOF EGUN path 1 path 3 path 2 ( ) a ( ) b 184 Ionization is achieved through electron impact (section 2.5). The electron gun will operate at 80 eV and the highest electron current possible (between 5 – 10 mA). The duration of bombardment will also be increased from 2 to 12.5 μs. An increased electron energy corresponds to a ~ 5 fold increase in the electron impact cross-section (section 2.5), the 5 – 10 mA current results in a 5 – 10 fold increase in collision probability with respect to the previous experiments (section 2.6), and the increased ionization time contributes a factor of 6. In total, these changes will increase the probability of C 2 H ionization to > 10 -3 . 6.3 Discussion As mentioned above, the radical number density just after leaving the nozzle will be at least 10 12 molecules cm -3 . Seeing as the decrease in concentration scales as the inverse of the distance traveled squared, 6 approximately 10 cm downstream, a concentration of ~ 10 10 molecules cm -3 is expected. Using the electron impact settings discussed earlier the probability of ionization will be greater than 10 -3 . Thus, the worst case scenario yields a C 2 H + concentration at of 10 7 molecules cm -3 , which is easily detected using TOF. Several radical and ion products are expected from the discharge source. Considering radical / ion generation in electrical discharge follows an electron impact mechanism, it is reasonable to assume that similar “cracking pattern” to that observed in the electron impact / TOF measurements will be present. However, the TOF mass spectrometer only observes ions. Therefore, the discharge voltage will be tuned, most 185 likely reduced, to maximize radical formation. The radicals can then be ionized and detected with the TOF mass spectrometer. One difficulty arises with using 80 eV as the electron impact ionization energy. At this energy fragmentation of acetylene creates C 2 + , C 2 H + , and C 2 H 2 + ions, and a very small amount of CH + . This cracking pattern will mask subtle changes in the ion signal. Consequently, a difference between spectra with the discharge on and discharge off will reveal the C 2 H signal produced. Once C 2 H signal is detected all parameters will be tuned to optimize this signal. In summation, pulsed electrical discharge of an acetylene/carrier gas mixture shows great promise as a reliable and robust source for C 2 H production. A new vacuum chamber and improved electron impact / TOF parameters yield encouraging estimates for C 2 H detection. With the ability to monitor the C 2 H species, optical probing of this species with one or more of three optical schemes will provide new spectroscopic information on this fundamental molecule. 186 6.4 References 1. Crabtree, K. N.; Kauffman, C. 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In contrast, density functional theory (DFT) uses electron density, not wave functions, to describe the system. The appeal of using electron density over wave functions lies in its simplicity. In general, wave functions are very complicated and depend on 4N variables, where N is the number of electrons in the system, while the electron density depends only on three spatial variables. 3 Consequently, DFT calculations have a computation cost that is comparable self-consistent field (SCF) single particle calculations 4 with an accuracy comparable to MP2. 5 This makes electronic calculations on large and/or complicated systems tractable, and is the reason the use of DFT has increased dramatically over the last 40 years. 6 201 The entire field of density functional theory rests on two fundamental theorems proved by Kohn and Hohenberg 7 and a set of equations derived by Kohn and Sham. 8 The first theorem states: The ground-state energy from Schrodinger’s equation is a unique functional of the electron density. To fully appreciate the above theorem requires understanding the nature of a “functional”. First, consider an arbitrary function of n variables f(x). The function f(x) takes n independent variables as its argument and returns a unique value f(x). Similarly, a functional of the form F[f(x)] returns a number when f(x) is used as the argument. For example: ( ) ( ) 1 1 F f x f x dx − =   ∫ (A.2) is a functional of f(x). Theorem 1 may now be restated as: The ground state energy from Schrödinger’s equation E can be uniquely expressed as E[ρ(r)], where ρ(r) is the electron density of the system. Once the energy is determined, all other system properties follow. Although theorem 1 proves the existence of this energy functional, it does not provide further information about the functional. However, the second theorem by Hohenberg and Kohn defines an important property of the functional: The electron density that minimizes the energy of the overall functional is the true electron density corresponding to the full solution of the Schrödinger equation. Hence, if the “true” energy functional form were known, varying the electron density until the energy is minimized would reveal the exact solution to the Schrödinger equation. 202 Both Hohenberg-Kohn theorems may be written as: ( ) ( ) ( ) ( ) ( ) 0 min ncl ncl N E T r J r E r r V dr ρ ρ ρ ρρ → = + + +             ∫      (A.3) where E 0 is the ground state energy, and the four terms on the right are functionals for the electron kinetic energy, Coulomb interaction between electrons, Coulomb interaction between nuclei, and interaction between electrons and nuclei, respectively. Note that equation A.3 is written in atomic units, as are all equations in this appendix, and employs the Born-Oppenheimer approximation. Of these terms, only J[ρ(r)] and the electron-nuclei interaction term are known. The explicit forms of the other two contributions are unknown. To address the unknown forms of the kinetic and nuclear functionals, Kohn and Sham concentrated on computing everything that is known exactly and finding approximate forms for everything else. They achieved this by using the kinetic energy of a non-interacting system and combining all other unknown terms into one functional: 8 ( ) [ ] ( ) ( ) ( ) S SD ncl XC E r T J r r V dr E r ρ ρρ ρ = Φ+ + +             ∫      (A.4) where E[ρ(r)] is the energy of the real interacting system, T S [Φ SD ] is the Hartree- Fock electron kinetic energy, and E XC [ρ(r)] is the exchange-correlation energy that accounts for everything unknown. In practice, E XC [ρ(r)] is separated into E X [ρ(r)] + E C [ρ(r)]. However, we shall keep the form E XC [ρ(r)] for the sake of simplicity. Note that T S [Φ SD ] uses Slater determinants, which are exact wave functions for a non- 203 interacting system. 3 Applying the variational principle to equation A.4 yields the following self-consistent equations: 9 ( ) ( ) 2 2 2 1 12 1 1 2 M A XC SDi i SDi A A r Z dr V r rr ρ ε   − ∇+ + − Φ = Φ     ∑ ∫   (A.5) where V XC is the exchange-correlation potential defined as δE XC / δρ. Analogous to the Hartree-Fock equations, A.5 represents a pseudo-eigenvalue problem than must be solved iteratively. 3 It is important to observe that no approximations, aside from Born-Oppenheimer, have been made, i.e. the Kohn-Sham approach is in principle exact. The approximation enters when a derived form of V XC , and consequently E XC , is used. Hence, the perpetual challenge to improving DFT methods is finding better approximations to the exchange-correlation functional. Virtually all approximate exchange-correlation functionals are based upon the local density approximation (LDA), which treats electron density as a uniform electron gas. In this system, electrons move over a positive charge distribution created by the nuclei such that the total ensemble is electrically neutral. This approximation allows E XC to be written as: 8 ( ) ( ) ( ) ( ) LDA XC XC E r r r dr ρ ρ ερ =     ∫    (A.6) Here, ε XC is the exchange-correlation energy per particle of a uniform electron gas with density ρ(r). Another interpretation to equation A.6 is the term ρ(r)ε XC is the weighted probability of finding electron density at the point in space r. In the unrestricted case, the electron density is split into ρ(r) α and ρ(r) β that extends LDA 204 to the local spin-density approximation (LSDA). 3 For the most part, DFT coupled with LDA/LSDA performs as well as to slightly better than the Hartree-Fock approach. The next logical step to improve LDA/LSDA was to consider not only the electron density, but also the gradient of the electron density. In other words, LDA/LSDA accounts for only the first term of a Taylor expansion of the density. Thus, incorporating higher order terms should produce more accurate approximations. Unfortunately, simply incorporating gradients in the electron density does not lead to improved accuracy. Blindly introducing higher order terms removes the error cancelation that contributes to the accuracy of LDA/LSDA, and distorts the physical picture that makes LDA/LSDA meaningful. For example, the sum rule no longer applies, i.e. spatial integration of an exchange-correlation hole (the repulsive cavity created by an electron’s density) does not yield the charge of an electron. 3 However, by forcing these “holes” to obey the appropriate sum constraints we arrive at the workhorses of DFT collectively known as generalized gradient approximations (GGA) functionals. GGA functionals are of a general form: 3 ( ) ( ) ( ) ( ) ( ) ( ) , f ,, , GGA XC E rr rr r r dr αβ αβ α β ρ ρ ρ ρ ρ ρ    = ∇∇    ∫      (A.7) where f[ρ(r) α, ρ(r) β , ∇ ∂ρ(r) α, ∇ ρ(r) β ] is some functional. These functionals are complex mathematical constructs that have been chosen to satisfy the appropriate boundary conditions. In addition, it is often the results and not the underlying physics that govern the choice of these constructs. 3 In this sense, it is difficult to 205 draw a physical picture from the form of the GGA exchange-correlation functional. However, this permits different functionals to be mixed and matched in order to achieve better results. The collection of exchange and correlation functionals is further expanded by combining GGA, LDA, and HF treatments to achieve what are collectively known as hybrid functionals. Currently, the most popular hybrid functional is B3LYP that was suggested by Stephens et al. 10 B3LYP uses various GGA and LSD functionals weighted by semi-empirical coefficients determined by Becke. 11 The success of B3LYP is fueled by its good performance, even with difficult open-shell transition- metal chemistry. 3 However, approximate functionals, including B3LYP, are prone to self-interaction errors, i.e. where an electron contributes to a bulk potential that then acts on this electron creating an artificial self-interaction. 3 Long-range corrected functionals (LRC), like those used in chapter 4, implement 100% Hartree- Fock exchange for the long-range Coulomb interaction, which mitigates this self- interaction. The impressive results achieved by LRC functionals mean that they will likely replace B3LYP as the front runners of modern density functional theory. 206 Appendix B Supplementary Material for Chapter 4 The data used to construct tables and figures in Chapter 4 are given here beginning with the z-matrices and Cartesian coordinates for the S 0 , T 1 , and D 0 equilibrium geometries. Next are the Mulliken charges and spin densities for each cation at its respective geometry. The Mulliken analysis is followed by the ground state "shell populations" of the first six HOMO's (i.e., HOMO, HOMO-1, etc.) to show the atomic contributions to each molecular orbital. How the populations were computed is also given. Next, the results of the BNL and ωB97X TDDFT calculations at the S 0 equilibrium geometry are listed. The table contains only singlets. Without SOC, only excited singlets have oscillator strength with S 0 and therefore were used to construct the absorption spectrum. Finally, the Ir(ppy) 3 S 0 vibrational frequencies are listed. Z-matricies for Equilibrium Geometries The columns for the z-matrices below are labeled as follows: (a) atom number; (b) atom; (c) bond length (Å); (d) atom to which the current atom is connected; (e) bond angle; (f) center atom of dihedral angle; (g) dihedral angle. 207 Table B.1. Z-matrix for S 0 equilibrium geometry a b c d e f g 1 Ir 2 C1 2.022446 3 C2 1.404535 1 127.565023 4 H3 1.086057 2 119.014367 1 -1.067994 5 C3 1.387399 2 121.818939 1 179.561533 6 H5 1.087104 3 119.631649 2 179.855448 7 C5 1.395346 3 120.748027 2 -0.320281 8 H7 1.085402 5 120.698815 3 -179.833071 9 C7 1.383408 5 119.052468 3 0.519936 10 H9 1.086494 7 118.926866 5 179.978896 11 C9 1.40044 7 120.235889 5 -0.185909 12 C11 1.471922 9 122.188246 7 178.02043 13 N12 1.351975 11 114.828365 9 179.151581 14 C13 1.338578 12 119.930566 11 178.007835 15 H14 1.085953 13 115.838605 12 -179.003959 16 C14 1.38071 13 122.866282 12 0.651586 17 H16 1.08346 14 120.14115 13 -179.324622 18 C16 1.392298 14 118.020707 13 -0.249991 19 H18 1.085439 16 120.488133 14 -179.336428 20 C18 1.381226 16 119.329149 14 0.062421 21 H20 1.082865 18 120.266689 16 -179.142522 22 C1 2.023439 2 96.036581 3 -5.444014 23 C22 1.403829 1 127.705969 2 91.780995 24 H23 1.086156 22 119.033759 1 -0.783377 25 C23 1.387452 22 121.840061 1 179.507891 26 H25 1.086935 23 119.705857 22 179.712337 27 C25 1.395262 23 120.690302 22 -0.123281 28 H27 1.085416 25 120.589475 23 -179.727328 29 C27 1.383189 25 119.090049 23 0.218533 30 H29 1.086567 27 118.919163 25 179.829061 31 C29 1.400286 27 120.262687 25 -0.10011 32 C31 1.471926 29 122.155867 27 179.115507 33 N32 1.351564 31 114.734591 29 179.099383 34 C33 1.338089 32 120.057407 31 179.213868 35 H34 1.085925 33 115.557917 32 -179.1191 36 C34 1.380783 33 122.89688 32 0.659773 37 H36 1.083358 34 120.186413 33 -179.950613 38 C36 1.392892 34 117.911438 33 -0.356574 208 39 H38 1.085431 36 120.558013 34 -179.717481 40 C38 1.381691 36 119.368437 34 -0.043381 41 H40 1.082915 38 120.284676 36 -179.556678 42 C1 2.025406 2 95.836638 3 91.384582 43 C42 1.404896 1 127.962451 2 -6.063495 44 H43 1.086302 42 119.058801 1 -0.730982 45 C43 1.387625 42 121.842466 1 179.720178 46 H45 1.087138 43 119.65475 42 179.869153 47 C45 1.395255 43 120.764884 42 -0.106873 48 H47 1.085067 45 120.748387 43 -179.838192 49 C47 1.383039 45 119.012315 43 0.177612 50 H49 1.086349 47 118.797538 45 179.708626 51 C49 1.399849 47 120.273082 45 -0.074407 52 C51 1.471557 49 121.972814 47 178.717392 53 N52 1.351521 51 114.952042 49 -179.195048 54 C53 1.338537 52 119.878729 51 178.511114 55 H54 1.08596 53 115.815578 52 -178.840661 56 C54 1.381082 53 122.951127 52 1.019915 57 H56 1.083308 54 120.166103 53 179.946922 58 C56 1.392764 54 117.958418 53 -0.210127 59 H58 1.085376 56 120.417102 54 179.825177 60 C58 1.380813 56 119.287692 54 -0.413776 61 H60 1.082728 58 120.26533 56 -179.616612 209 Table B.2. S 0 Standard Nuclear Orientation (Å) I Atom X Y Z ---------------------------------------------------- 1 Ir 0.009744 -0.002078 -0.021299 2 N -0.608071 -1.778575 1.056498 3 C 0.019125 -2.317207 2.109200 4 C -0.434933 -3.450358 2.755102 5 C -1.596253 -4.052997 2.277660 6 C -2.239470 -3.508159 1.184011 7 C -1.727121 -2.359543 0.569866 8 C -2.308099 -1.697308 -0.608857 9 C -1.625113 -0.552554 -1.082660 10 C -2.162288 0.064801 -2.224610 11 C -3.300666 -0.420671 -2.852233 12 C -3.958657 -1.549735 -2.363354 13 C -3.457659 -2.184897 -1.241585 14 H -3.969969 -3.066483 -0.866752 15 H -4.850301 -1.927592 -2.852809 16 H -3.684592 0.083864 -3.735361 17 H -1.668277 0.942502 -2.631610 18 H -3.139927 -3.967316 0.795872 19 H -1.990155 -4.943611 2.756920 20 H 0.108208 -3.847540 3.604102 21 H 0.921935 -1.808004 2.433169 22 C 1.332213 -1.124314 -1.063396 23 C 1.086657 -1.898528 -2.208400 24 C 2.089511 -2.633918 -2.823631 25 C 3.389280 -2.629399 -2.316344 26 C 3.669114 -1.876284 -1.190413 27 C 2.658226 -1.131808 -0.570201 28 C 2.913637 -0.301296 0.617897 29 N 1.827147 0.338185 1.105063 30 C 1.941607 1.134726 2.174130 31 C 3.137347 1.336397 2.834506 32 C 4.267600 0.681232 2.351357 33 C 4.155188 -0.135829 1.242823 34 H 5.025680 -0.646650 0.850378 35 H 5.230500 0.812626 2.834802 36 H 3.180073 1.992021 3.695899 37 H 1.026257 1.623361 2.494446 38 H 4.682869 -1.872554 -0.799371 39 H 4.171579 -3.208797 -2.796381 40 H 1.861737 -3.217830 -3.711658 210 41 H 0.084369 -1.918190 -2.626453 42 N -1.230786 1.390032 1.086333 43 C -2.033819 1.076433 2.110337 44 C -2.847243 2.000825 2.734999 45 C -2.826515 3.312066 2.267333 46 C -2.002309 3.639788 1.208529 47 C -1.203552 2.656418 0.613723 48 C -0.316411 2.865866 -0.541988 49 C 0.343853 1.716043 -1.034570 50 C 1.157088 1.899198 -2.164978 51 C 1.308368 3.141572 -2.763725 52 C 0.655398 4.263929 -2.252906 53 C -0.157674 4.120865 -1.142832 54 H -0.665404 4.996074 -0.746992 55 H 0.776450 5.236008 -2.720353 56 H 1.945065 3.242408 -3.639079 57 H 1.673257 1.041909 -2.587052 58 H -1.984488 4.651788 0.823643 59 H -3.457899 4.068940 2.721947 60 H -3.488434 1.696114 3.553480 61 H -2.015386 0.037309 2.425260 211 Table B.3. Z-matrix for T 1 equilibrium geometry a b c d e f g 1 Ir 2 C1 1.960661 3 C2 1.408154 1 128.96714 4 H3 1.085789 2 118.243755 1 0.124374 5 C3 1.379839 2 122.370014 1 -179.297635 6 H5 1.084579 3 120.935203 2 179.753881 7 C5 1.429032 3 119.430973 2 -0.088252 8 H7 1.087169 5 118.897993 3 179.848727 9 C7 1.363612 5 122.001244 3 0.006373 10 H9 1.084499 7 119.706094 5 179.960207 11 C9 1.433843 7 120.006217 5 -0.125189 12 C11 1.400328 9 124.021502 7 -179.366043 13 N12 1.400585 11 115.278922 9 179.786797 14 C13 1.330822 12 119.276906 11 179.052245 15 H14 1.087486 13 115.702095 12 -179.087045 16 C14 1.38451 13 123.767747 12 1.150541 17 H16 1.082828 14 120.014681 13 179.700867 18 C16 1.421257 14 118.231809 13 -0.843532 19 H18 1.084981 16 120.42283 14 -179.491423 20 C18 1.362857 16 119.24321 14 0.093647 21 H20 1.084004 18 120.107639 16 -179.37437 22 C1 2.025169 2 95.401004 3 91.310713 23 C22 1.403115 1 127.342268 2 -3.710646 24 H23 1.086312 22 119.071393 1 -1.589484 25 C23 1.387298 22 121.783782 1 178.859141 26 H25 1.086636 23 119.628007 22 -179.711743 27 C25 1.394247 23 120.663747 22 -0.119468 28 H27 1.084953 25 120.722903 23 -179.835254 29 C27 1.382948 25 119.027274 23 0.365129 30 H29 1.086151 27 118.78023 25 -179.763564 31 C29 1.399425 27 120.444523 25 -0.157718 32 C31 1.471801 29 121.948281 27 179.102605 33 N32 1.349496 31 115.066231 29 178.559079 34 C33 1.338077 32 120.036219 31 178.839851 35 H34 1.08598 33 116.020165 32 -179.358325 36 C34 1.380466 33 122.794331 32 0.617333 37 H36 1.083233 34 120.271759 33 -179.819315 38 C36 1.392573 34 117.999069 33 -0.438103 39 H38 1.085314 36 120.427105 34 -179.682301 212 40 C38 1.38067 36 119.347159 34 0.129568 41 H40 1.082587 38 120.232196 36 -179.263148 42 C1 2.036201 2 95.584561 3 -5.732148 43 C42 1.403042 1 128.605627 2 88.896672 44 H43 1.086882 42 119.272166 1 -0.713106 45 C43 1.388907 42 121.790322 1 179.683617 46 H45 1.086821 43 119.745462 42 179.607431 47 C45 1.394412 43 120.706731 42 -0.133669 48 H47 1.08513 45 120.691654 43 179.914261 49 C47 1.382896 45 119.05978 43 -0.031183 50 H49 1.085933 47 118.814828 45 179.729695 51 C49 1.399237 47 120.283478 45 0.027783 52 C51 1.473492 49 121.576817 47 179.539649 53 N52 1.350621 51 115.493367 49 179.750349 54 C53 1.339431 52 120.333182 51 179.614085 55 H54 1.086279 53 115.626035 52 -179.125507 56 C54 1.381092 53 122.500547 52 0.53632 57 H56 1.083272 54 120.252439 53 179.994659 58 C56 1.392739 54 118.051494 53 -0.217558 59 H58 1.085458 56 120.521957 54 -179.758594 60 C58 1.380581 56 119.449001 54 -0.07276 61 H60 1.082446 58 120.135859 56 -179.805464 213 Table B.4. T 1 Standard Nuclear Orientation (Å) I Atom X Y Z ---------------------------------------------------- 1 Ir -0.019227 0.023884 -0.051622 2 N 0.893739 -1.623116 1.077766 3 C 1.755509 -1.503129 2.094331 4 C 2.319714 -2.591681 2.728694 5 C 1.975841 -3.862878 2.275851 6 C 1.091588 -3.989943 1.223140 7 C 0.551501 -2.846790 0.623198 8 C -0.382256 -2.850687 -0.514466 9 C -0.770644 -1.588997 -1.018731 10 C -1.642146 -1.592270 -2.118369 11 C -2.105927 -2.773139 -2.679663 12 C -1.717713 -4.007623 -2.160756 13 C -0.855237 -4.040072 -1.080186 14 H -0.558498 -5.003857 -0.676715 15 H -2.081935 -4.931684 -2.597304 16 H -2.783755 -2.734747 -3.528104 17 H -1.956184 -0.644248 -2.545815 18 H 0.823514 -4.970885 0.851814 19 H 2.400130 -4.746061 2.742621 20 H 3.015528 -2.447114 3.546212 21 H 1.993133 -0.488575 2.400222 22 C 1.694555 0.166410 -1.141921 23 C 2.065081 -0.552469 -2.288415 24 C 3.283618 -0.343227 -2.921227 25 C 4.188918 0.596728 -2.430004 26 C 3.857921 1.321192 -1.299520 27 C 2.630638 1.111193 -0.661132 28 C 2.244680 1.874037 0.538987 29 N 1.035796 1.568588 1.058100 30 C 0.584950 2.208745 2.144844 31 C 1.318279 3.186781 2.787566 32 C 2.570418 3.511853 2.271626 33 C 3.032642 2.856187 1.148035 34 H 4.002806 3.102245 0.735814 35 H 3.179005 4.277276 2.742760 36 H 0.918107 3.681311 3.664367 37 H -0.402238 1.913147 2.488474 38 H 4.563995 2.055308 -0.922979 39 H 5.140288 0.760990 -2.925405 40 H 3.534064 -0.914363 -3.811317 214 41 H 1.379275 -1.289267 -2.698426 42 N -1.775668 0.120657 1.165225 43 C -2.049171 -0.558752 2.276390 44 C -3.232958 -0.433366 2.983353 45 C -4.221508 0.458744 2.486484 46 C -3.973856 1.156620 1.342362 47 C -2.733284 1.002356 0.648294 48 C -2.366623 1.657422 -0.533808 49 C -1.020118 1.347815 -1.095470 50 C -0.640935 2.015056 -2.276108 51 C -1.466710 2.920048 -2.910965 52 C -2.755138 3.201201 -2.360476 53 C -3.200348 2.600818 -1.219966 54 H -4.185364 2.841419 -0.835267 55 H -3.399668 3.913803 -2.869118 56 H -1.152448 3.417911 -3.821835 57 H 0.334609 1.795933 -2.699470 58 H -4.722003 1.833190 0.945385 59 H -5.165515 0.578311 3.007771 60 H -3.389879 -1.013306 3.884221 61 H -1.271255 -1.237783 2.617547 215 Table B.5. Z-matrix for D 0 equilibrium geometry a b c d e f g 1 Ir 2 C1 1.974711 3 C2 1.40894 1 126.643255 4 H3 1.084614 2 119.419379 1 0.218888 5 C3 1.386076 2 121.094457 1 -178.57675 6 H5 1.08502 3 119.963632 2 178.970535 7 C5 1.393602 3 120.165421 2 -0.927248 8 H7 1.084925 5 120.11332 3 -179.885853 9 C7 1.390587 5 120.247837 3 0.045584 10 H9 1.084663 7 118.842088 5 -179.50194 11 C9 1.389786 7 120.07878 5 0.456065 12 C11 1.476088 9 122.595944 7 179.79467 13 N12 1.349129 11 114.647528 9 178.94898 14 C13 1.337913 12 120.041109 11 177.878772 15 H14 1.08571 13 116.149977 12 -178.436872 16 C14 1.382076 13 122.340242 12 0.937388 17 H16 1.082999 14 120.050129 13 -179.473234 18 C16 1.390471 14 118.303661 13 -0.145721 19 H18 1.084686 16 120.540223 14 -179.542025 20 C18 1.383778 16 119.365489 14 -0.323638 21 H20 1.08269 18 120.083887 16 -179.496106 22 C1 2.027768 2 96.494738 3 -1.801654 23 C22 1.395284 1 126.868788 2 90.129443 24 H23 1.085736 22 119.653594 1 0.348033 25 C23 1.389926 22 120.929722 1 -179.341689 26 H25 1.085904 23 119.710962 22 179.685182 27 C25 1.393044 23 120.611962 22 -0.060733 28 H27 1.084666 25 120.352201 23 179.660108 29 C27 1.384611 25 119.568993 23 -0.453817 30 H29 1.085827 27 118.983416 25 -179.985795 31 C29 1.398846 27 120.006861 25 0.295549 32 C31 1.471277 29 122.698297 27 -179.371387 33 N32 1.3543 31 114.904961 29 179.74008 34 C33 1.342619 32 120.700238 31 -179.903085 35 H34 1.085402 33 115.968366 32 -179.434184 36 C34 1.376406 33 122.337289 32 0.682323 37 H36 1.082799 34 120.198209 33 179.925475 38 C36 1.394787 34 117.973166 33 -0.410128 39 H38 1.084961 36 120.172208 34 179.888403 216 40 C38 1.381617 36 119.751984 34 -0.026752 41 H40 1.082653 38 120.281552 36 -179.775089 42 C1 2.035182 2 99.631309 3 97.266787 43 C42 1.397774 1 125.451998 2 -3.072514 44 H43 1.085207 42 120.115306 1 -1.454419 45 C43 1.389832 42 120.955679 1 179.277084 46 H45 1.085715 43 119.467118 42 179.674354 47 C45 1.39127 43 120.619436 42 -0.309973 48 H47 1.084262 45 120.533648 43 -179.927733 49 C47 1.384233 45 119.307237 43 0.115892 50 H49 1.085181 47 119.000234 45 -179.968059 51 C49 1.397569 47 120.403449 45 0.005916 52 C51 1.472585 49 122.530193 47 179.853375 53 N52 1.350962 51 114.977915 49 178.956408 54 C53 1.340872 52 119.832164 51 178.81841 55 H54 1.084632 53 116.553053 52 -179.026785 56 C54 1.379442 53 122.714935 52 0.992874 57 H56 1.082908 54 119.982881 53 179.907089 58 C56 1.391889 54 118.173559 53 -0.359192 59 H58 1.084846 56 120.597908 54 -179.945839 60 C58 1.38163 56 119.248686 54 -0.214533 61 H60 1.08247 58 120.263845 56 -179.473843 217 Table B.6. D 0 Standard Nuclear Orientation (Å) I Atom X Y Z ---------------------------------------------------- 1 Ir 0.011572 -0.059961 -0.067414 2 N -1.322670 -1.231929 1.143560 3 C -1.000718 -1.806498 2.313535 4 C -1.901031 -2.552422 3.039845 5 C -3.186087 -2.712962 2.521875 6 C -3.516157 -2.129622 1.313722 7 C -2.562646 -1.378859 0.619154 8 C -2.777291 -0.694105 -0.665250 9 C -1.678231 0.021747 -1.185329 10 C -1.852670 0.703174 -2.390338 11 C -3.068040 0.664313 -3.063584 12 C -4.142127 -0.057158 -2.547456 13 C -3.997706 -0.733202 -1.347767 14 H -4.841132 -1.292373 -0.954090 15 H -5.087007 -0.089110 -3.079133 16 H -3.180385 1.197832 -4.002693 17 H -1.027153 1.268239 -2.812294 18 H -4.509980 -2.251732 0.901968 19 H -3.924750 -3.292442 3.065675 20 H -1.604495 -2.999502 3.980397 21 H 0.016251 -1.646729 2.657550 22 C 0.770606 -1.667540 -0.927088 23 C 0.212269 -2.390438 -1.999837 24 C 0.861346 -3.491664 -2.535755 25 C 2.077777 -3.915065 -2.003636 26 C 2.648462 -3.235554 -0.932973 27 C 2.011629 -2.123845 -0.394409 28 C 2.569270 -1.359035 0.738259 29 N 1.807825 -0.322950 1.146766 30 C 2.230995 0.469210 2.138442 31 C 3.431010 0.259620 2.791262 32 C 4.219610 -0.814012 2.392724 33 C 3.786671 -1.627709 1.360589 34 H 4.395282 -2.462022 1.035423 35 H 5.171608 -1.007669 2.875156 36 H 3.741479 0.929337 3.583710 37 H 1.580946 1.298996 2.398553 38 H 3.591800 -3.589666 -0.531462 39 H 2.584192 -4.778252 -2.422580 40 H 0.422758 -4.024944 -3.372727 218 41 H -0.731704 -2.067900 -2.425597 42 N -0.678644 1.784838 0.941196 43 C -1.594851 1.862228 1.917165 44 C -1.990340 3.060171 2.475180 45 C -1.413846 4.231773 1.993144 46 C -0.478051 4.156253 0.979496 47 C -0.119108 2.913689 0.453635 48 C 0.852706 2.706743 -0.633223 49 C 1.062096 1.379779 -1.050019 50 C 1.980068 1.153395 -2.079508 51 C 2.658517 2.208858 -2.677285 52 C 2.442851 3.517893 -2.258302 53 C 1.540584 3.762640 -1.237462 54 H 1.376597 4.785506 -0.914241 55 H 2.973763 4.340144 -2.724840 56 H 3.362415 2.005850 -3.478592 57 H 2.164311 0.143880 -2.432509 58 H -0.025611 5.057664 0.586435 59 H -1.696630 5.195579 2.403024 60 H -2.733407 3.071115 3.262848 61 H -2.021149 0.924731 2.257451 219 Shell populations The electron density of a molecule having N electrons is: () r ρ  = /2 2 2 | ( )| N a a r ψ ∑  . Expanding () a r ψ  in an atomic basis, i.e., () a r ψ  = c aµ φ µ (implied summation), yields () r ρ  = 2 c aµ * c aν φ µ * φ ν a N /2 ∑ = 2 C aµν φ µ * φ ν a N /2 ∑ . The a th MO contains 2 electrons, so integration and minor manipulation yields 3* 1 () Tr() a a aa C d r C S CS CS µν ν µ µν νµ µµ φφ = = = = ∫  , where S νµ is an overlap matrix element. Thus, Tr(CS) = 1. The distribution of electrons in the a th MO over the atomic orbitals is given by the diagonal elements. Table B.7. Shell populations of first six HOMO's at S 0 equilibrium geometry HOMO-5 HOMO-4 HOMO-3 HOMO-2 HOMO-1 HOMO 1 Ir s 0.00167 0 0 0 0.00001 0.00441 2 Ir p 0.00113 0.00058 0.00065 0.00644 0.00657 0.00087 3 Ir d 0.06378 0.04395 0.04375 0.96495 0.95605 1.15212 4 N1 s 0.00037 0.00008 0.00007 0.00118 0.00069 0.00152 5 N1 p 0.01643 0.04729 0.001 0.01165 0.01322 0.01347 6 N1 d 0.00051 0.00087 0.00015 0.00226 0.00221 0.00245 7 C1 s 0.00001 0.00002 0.00003 0.0001 0.00091 0.00124 8 C1 p 0.02855 0.03185 0.00173 0.02701 0.00365 0.00508 9 C1 d 0.00203 0.00491 0.00003 0.00059 0.00114 0.00083 10 C2 s 0 0.00001 0 0.0001 0.00024 0.00006 11 C2 p 0.0519 0.10676 0.0001 0.00402 0.01016 0.01062 12 C2 d 0.00061 0.00043 0.0001 0.0016 0.00012 0.00032 13 C3 s 0.00001 0 0 0.00001 0.00001 0.00006 14 C3 p 0.00185 0.00007 0.00152 0.02634 0.00071 0.00644 15 C3 d 0.00295 0.00549 0.00002 0.00042 0.00055 0.00052 16 C4 s 0.00005 0.00001 0 0.00003 0.00001 0.00011 17 C4 p 0.05623 0.09226 0.00089 0.00997 0.00693 0.00592 18 C4 d 0.00018 0.00058 0.00005 0.00147 0.00018 0.00062 19 C5 s 0.0001 0.00001 0 0.00004 0.00026 0.00036 220 20 C5 p 0.01386 0.03559 0.00079 0.01828 0.00362 0.00988 21 C5 d 0.00415 0.00931 0.00007 0.00154 0.00177 0.00227 22 C6 s 0.00007 0.00002 0.00006 0.00002 0.00132 0.00106 23 C6 p 0.10047 0.21913 0.00066 0.06042 0.04699 0.05043 24 C6 d 0.00198 0.00337 0.00012 0.00092 0.00093 0.00105 25 C7 s 0.00028 0.00007 0.00001 0.00001 0.00164 0.00039 26 C7 p 0.01024 0.02447 0.00178 0.02877 0.03786 0.03299 27 C7 d 0.00446 0.00814 0.00045 0.01064 0.01279 0.01143 28 C8 s 0.00012 0.00003 0.00015 0.00002 0.0008 0.00076 29 C8 p 0.10269 0.14665 0.00512 0.08618 0.03901 0.03369 30 C8 d 0.00243 0.00591 0.00003 0.00053 0.00083 0.0008 31 C9 s 0.00008 0.00002 0.00003 0.00001 0.00019 0.00012 32 C9 p 0.13294 0.28442 0.00038 0.00054 0.00715 0.00664 33 C9 d 0.00117 0.00128 0.00018 0.00528 0.00284 0.00256 34 C10 s 0.00001 0 0 0 0.00004 0.00001 35 C10 p 0.00055 0.00874 0.00314 0.10862 0.04863 0.05056 36 C10 d 0.0056 0.01091 0.00008 0.00023 0.00007 0.00007 37 C11 s 0.00001 0.00001 0.00001 0 0.00003 0.00014 38 C11 p 0.10932 0.18833 0.00376 0.02123 0.00209 0.0013 39 C11 d 0.00151 0.00409 0.00007 0.0049 0.00278 0.00291 40 H1 s 0.00002 0.00001 0.00005 0.00004 0.00065 0.00042 41 H1 p 0.00199 0.00347 0.00008 0.00057 0.00007 0.00007 42 H2 s 0.00011 0.00002 0.00002 0 0.00002 0 43 H2 p 0.00001 0.00017 0.00006 0.00251 0.00113 0.0012 44 H3 s 0.00028 0.00009 0.00006 0.00003 0.0019 0.00085 45 H3 p 0.00248 0.00539 0.00001 0.00001 0.00019 0.00018 46 H4 s 0.00012 0.00003 0.00005 0.00008 0.00077 0.00017 47 H4 p 0.00212 0.00239 0.0002 0.00165 0.00104 0.00063 48 H5 s 0.00008 0 0 0.00003 0.00014 0.00038 49 H5 p 0.00104 0.00168 0.00003 0.00028 0.00016 0.00014 50 H6 s 0 0.00002 0.00001 0.00004 0.00014 0.00004 51 H6 p 0.00003 0 0.00003 0.00064 0.00002 0.00018 52 H7 s 0.00001 0.00002 0.00004 0.00008 0.00029 0.00004 53 H7 p 0.00116 0.00245 0 0.00011 0.0003 0.0003 54 H8 s 0.00017 0.00003 0.00013 0.00019 0.00034 0.00057 55 H8 p 0.0007 0.00072 0.00009 0.00065 0.00002 0.00006 56 C12 s 0.00031 0.00002 0.00006 0.00129 0.0004 0.00035 57 C12 p 0.00963 0.01263 0.01457 0.05663 0.00855 0.03544 58 C12 d 0.00444 0.00192 0.00677 0.01682 0.00677 0.01153 59 C13 s 0.00015 0.00017 0.00001 0.00067 0.00027 0.00069 60 C13 p 0.10342 0.02081 0.13206 0.08633 0.03645 0.03752 221 61 C13 d 0.00235 0.00181 0.00425 0.00124 0.00009 0.00086 62 C14 s 0.0001 0.00004 0 0.00021 0.00003 0.00011 63 C14 p 0.12984 0.07058 0.21865 0.00646 0.0008 0.00697 64 C14 d 0.0012 0.00011 0.00135 0.00585 0.00206 0.00285 65 C15 s 0.00001 0 0 0.00004 0.00001 0.00001 66 C15 p 0.00036 0.00951 0.00285 0.11751 0.03318 0.05844 67 C15 d 0.00553 0.00225 0.00889 0.00007 0.00024 0.00006 68 C16 s 0.00001 0.00001 0 0.00002 0.00002 0.00013 69 C16 p 0.10937 0.02978 0.16408 0.01161 0.01173 0.00169 70 C16 d 0.00143 0.00151 0.00274 0.00584 0.0015 0.0033 71 C17 s 0.00006 0.00005 0.00003 0.00101 0.00045 0.00097 72 C17 p 0.09729 0.06193 0.16181 0.08554 0.0165 0.05634 73 C17 d 0.00199 0.00057 0.00296 0.00133 0.00052 0.0011 74 C18 s 0.00009 0 0.00001 0.00015 0.00014 0.00036 75 C18 p 0.01379 0.00678 0.0294 0.00347 0.01903 0.00933 76 C18 d 0.00402 0.00258 0.00694 0.00264 0.00047 0.00252 77 N2 s 0.00027 0.0001 0.00002 0.00006 0.00166 0.00165 78 N2 p 0.01573 0.00969 0.03879 0.01303 0.01082 0.01465 79 N2 d 0.00051 0.00032 0.00069 0.00152 0.00311 0.00234 80 C19 s 0.00002 0.00003 0.00001 0.0006 0.00051 0.00117 81 C19 p 0.0277 0.01619 0.01809 0.00862 0.0226 0.00452 82 C19 d 0.00196 0.00123 0.00376 0.0009 0.00074 0.00092 83 C20 s 0 0.00001 0 0.00008 0.00027 0.00005 84 C20 p 0.05039 0.0307 0.07721 0.01151 0.0012 0.01195 85 C20 d 0.00059 0.00039 0.00017 0.00035 0.0014 0.00028 86 C21 s 0.00001 0 0 0.00002 0.00001 0.00007 87 C21 p 0.00175 0.00128 0.00043 0.00392 0.02378 0.00599 88 C21 d 0.00287 0.00178 0.0038 0.00078 0.00012 0.0006 89 C22 s 0.00005 0.00001 0 0.00001 0.00004 0.00012 90 C22 p 0.05477 0.03407 0.0608 0.01298 0.00286 0.00695 91 C22 d 0.00018 0.00007 0.00056 0.00031 0.00138 0.00059 92 H9 s 0.00007 0 0 0.00018 0.00001 0.00039 93 H9 p 0.00102 0.00066 0.00108 0.00033 0.00009 0.00017 94 H10 s 0 0.00002 0 0.00005 0.00014 0.00004 95 H10 p 0.00003 0.00002 0.00001 0.00009 0.00059 0.00017 96 H11 s 0.00001 0.00006 0 0.00011 0.00024 0.00003 97 H11 p 0.00113 0.0007 0.00177 0.00031 0.00005 0.00034 98 H12 s 0.00016 0.00008 0.00009 0.00013 0.00044 0.00054 99 H12 p 0.00068 0.00042 0.0004 0.00021 0.00046 0.00006 100 H13 s 0.00002 0.00004 0.00002 0.0004 0.00033 0.00038 101 H13 p 0.002 0.00052 0.00306 0.00034 0.00029 0.00008 222 102 H14 s 0.00012 0.00004 0.00001 0.00002 0 0 103 H14 p 0.00001 0.00019 0.00005 0.00271 0.00076 0.00139 104 H15 s 0.00027 0.00012 0.00003 0.0014 0.00069 0.00074 105 H15 p 0.00242 0.00134 0.00415 0.00018 0.00002 0.00019 106 H16 s 0.00014 0.00006 0.00003 0.00044 0.00036 0.00014 107 H16 p 0.00215 0.00021 0.00239 0.00185 0.00079 0.00069 108 N3 s 0.00028 0.00004 0.0001 0.00154 0.00033 0.00154 109 N3 p 0.01445 0.01638 0.03359 0.01177 0.01287 0.01418 110 N3 d 0.00049 0.00036 0.00068 0.00307 0.00149 0.0023 111 C23 s 0.00002 0.00002 0.00003 0.00091 0.00014 0.00115 112 C23 p 0.02727 0.00369 0.03124 0.01058 0.02043 0.00418 113 C23 d 0.00183 0.00138 0.00374 0.001 0.00069 0.00091 114 C24 s 0 0 0.00001 0.00034 0.00001 0.00006 115 C24 p 0.0475 0.0254 0.08505 0.00413 0.009 0.01206 116 C24 d 0.0006 0.00002 0.00055 0.00065 0.0011 0.00025 117 C25 s 0.00001 0 0 0.00001 0.00001 0.00007 118 C25 p 0.00195 0.00113 0.00049 0.01079 0.01711 0.00536 119 C25 d 0.00273 0.00114 0.00457 0.00016 0.00074 0.00061 120 C26 s 0.00006 0 0.00002 0.00003 0.00003 0.0001 121 C26 p 0.05261 0.01628 0.08047 0.00089 0.01512 0.00715 122 C26 d 0.00016 0.0003 0.00035 0.00072 0.00097 0.00056 123 C27 s 0.00011 0 0 0.00024 0.00004 0.00037 124 C27 p 0.01267 0.01265 0.02477 0.01159 0.01103 0.00886 125 C27 d 0.00379 0.00243 0.00728 0.00058 0.00263 0.00246 126 C28 s 0.00006 0.00005 0.00003 0.00109 0.00026 0.00106 127 C28 p 0.09154 0.05464 0.17318 0.00927 0.093 0.05691 128 C28 d 0.00189 0.00138 0.00226 0.00051 0.00136 0.0011 129 C29 s 0.00031 0.00001 0.00004 0.00119 0.00052 0.00037 130 C29 p 0.00939 0.00303 0.02334 0.01311 0.05206 0.03586 131 C29 d 0.00418 0.00303 0.00587 0.00768 0.01538 0.01214 132 C30 s 0.00014 0.00008 0.00011 0.00066 0.00022 0.00072 133 C30 p 0.0977 0.06432 0.09536 0.01151 0.10948 0.03929 134 C30 d 0.00221 0.00134 0.0048 0.00024 0.00109 0.00085 135 C31 s 0.00008 0 0.00004 0.00012 0.00011 0.00012 136 C31 p 0.12214 0.07957 0.21639 0.00423 0.00331 0.00666 137 C31 d 0.00115 0.00084 0.0007 0.00076 0.00706 0.00297 138 C32 s 0 0.00001 0 0.00003 0.00002 0.00001 139 C32 p 0.00035 0.00003 0.0117 0.00158 0.14834 0.0596 140 C32 d 0.0052 0.00361 0.00786 0.00016 0.00015 0.00006 141 C33 s 0.00001 0 0.00001 0.00003 0 0.00014 142 C33 p 0.10291 0.07491 0.12658 0.00171 0.02121 0.00193 223 143 C33 d 0.00134 0.00076 0.00351 0.00038 0.00692 0.00336 144 H17 s 0.00002 0.00005 0.00001 0.00063 0.00007 0.0004 145 H17 p 0.00188 0.00142 0.0023 0.00004 0.00059 0.00009 146 H18 s 0.00012 0 0.00005 0.00001 0.00002 0 147 H18 p 0.00001 0 0.00023 0.00003 0.00342 0.00142 148 H19 s 0.0003 0 0.00011 0.00162 0.0004 0.00083 149 H19 p 0.00228 0.00151 0.0041 0.0001 0.00009 0.00018 150 H20 s 0.00011 0.00005 0.00005 0.00071 0.00012 0.00017 151 H20 p 0.00204 0.00136 0.00137 0.00045 0.00216 0.00073 152 H21 s 0.00007 0 0.00001 0.00006 0.00012 0.00039 153 H21 p 0.00098 0.00027 0.0015 0.00002 0.0004 0.00017 154 H22 s 0 0 0.00003 0.00019 0 0.00004 155 H22 p 0.00003 0.00003 0.00001 0.00028 0.00041 0.00015 156 H23 s 0.00001 0.00002 0.00005 0.00035 0.00001 0.00004 157 H23 p 0.00106 0.00058 0.00195 0.00014 0.00023 0.00034 158 H24 s 0.00018 0.00015 0.00003 0.00051 0.00004 0.00054 159 H24 p 0.00069 0.00012 0.00073 0.00015 0.00051 0.00005 224 Mulliken Charges for the S 0 , T 1 , and D 0 States. Table B.8. Mulliken charges and spin density the S 0 equilibrium geometry atom charge spin density 1 Ir 0.078 0.672 2 N 0.873 0.003 3 C -0.132 0.020 4 C -0.402 0.014 5 C -0.645 0.001 6 C -0.351 0.003 7 C -0.273 -0.008 8 C 0.378 0.033 9 C 0.333 -0.020 10 C -0.149 0.035 11 C -0.415 -0.005 12 C -0.564 0.039 13 C -0.279 -0.019 14 H 0.178 0.000 15 H 0.257 -0.002 16 H 0.260 0.000 17 H 0.266 -0.002 18 H 0.222 0.000 19 H 0.287 0.000 20 H 0.274 0.000 21 H 0.212 0.007 22 C 0.081 -0.020 23 C -0.133 0.039 24 C -0.273 -0.006 25 C -0.543 0.045 26 C -0.448 -0.022 27 C 0.339 0.038 28 C -0.097 -0.007 29 N 0.827 0.004 30 C -0.107 0.020 31 C -0.394 0.014 32 C -0.592 0.001 33 C -0.281 0.004 34 H 0.230 0.000 35 H 0.288 0.000 36 H 0.275 -0.001 37 H 0.198 0.007 225 38 H 0.164 0.000 39 H 0.260 -0.002 40 H 0.260 0.000 41 H 0.255 -0.002 42 N 0.810 0.005 43 C -0.089 0.017 44 C -0.443 0.018 45 C -0.720 -0.001 46 C -0.631 -0.002 47 C 0.224 -0.014 48 C 0.467 0.045 49 C 0.147 -0.011 50 C -0.241 0.037 51 C -0.314 -0.008 52 C -0.532 0.047 53 C -0.319 -0.019 54 H 0.171 0.000 55 H 0.258 -0.002 56 H 0.261 0.001 57 H 0.253 -0.002 58 H 0.219 0.000 59 H 0.287 0.000 60 H 0.273 -0.001 61 H 0.204 0.006 226 Table B.9. Mulliken charges and spin density the T 1 equilibrium geometry atom charge spin density 1 Ir 0.205 0.582 2 N 0.909 0.001 3 C -0.157 0.013 4 C -0.368 0.013 5 C -0.786 -0.002 6 C -0.548 -0.003 7 C 0.305 -0.013 8 C 0.688 0.031 9 C 0.019 0.002 10 C -0.292 0.040 11 C -0.182 -0.010 12 C -0.807 0.033 13 C -0.340 -0.011 14 H 0.172 0.000 15 H 0.251 -0.001 16 H 0.258 0.001 17 H 0.266 -0.002 18 H 0.213 0.000 19 H 0.285 0.000 20 H 0.270 0.000 21 H 0.215 0.004 22 C 0.361 -0.024 23 C -0.139 0.011 24 C -0.380 0.002 25 C -0.517 0.001 26 C -0.462 -0.006 27 C 0.276 0.000 28 C -0.249 0.004 29 N 0.856 0.003 30 C -0.143 0.016 31 C -0.373 0.003 32 C -0.613 0.008 33 C -0.267 -0.001 34 H 0.224 0.001 35 H 0.288 0.000 36 H 0.272 0.000 37 H 0.227 0.006 38 H 0.164 0.000 39 H 0.252 0.000 227 40 H 0.256 0.000 41 H 0.247 0.000 42 N 0.776 0.032 43 C -0.108 0.001 44 C -0.435 0.050 45 C -0.659 -0.011 46 C -0.567 0.027 47 C 0.078 -0.034 48 C 0.441 0.125 49 C -0.123 0.004 50 C -0.098 0.059 51 C -0.221 -0.017 52 C -0.610 0.113 53 C -0.302 -0.042 54 H 0.181 0.001 55 H 0.267 -0.005 56 H 0.272 0.000 57 H 0.258 -0.003 58 H 0.220 -0.001 59 H 0.289 0.000 60 H 0.276 -0.002 61 H 0.205 0.005 228 Table B.10. Mulliken charges and spin density the D 0 equilibrium geometry atom charge spin density 1 Ir 0.166 0.606 2 N 0.769 0.014 3 C -0.105 0.016 4 C -0.430 0.003 5 C -0.532 0.006 6 C -0.312 0.000 7 C -0.284 -0.016 8 C 0.280 0.025 9 C 0.218 -0.027 10 C -0.073 0.019 11 C -0.512 -0.004 12 C -0.482 0.031 13 C -0.310 -0.016 14 H 0.178 0.000 15 H 0.256 -0.001 16 H 0.258 0.000 17 H 0.233 -0.002 18 H 0.222 0.001 19 H 0.290 0.000 20 H 0.271 0.000 21 H 0.205 0.006 22 C -0.252 0.015 23 C -0.308 0.097 24 C -0.136 -0.031 25 C -0.722 0.126 26 C -0.285 -0.026 27 C 0.747 0.095 28 C 0.299 -0.024 29 N 0.784 0.001 30 C -0.117 0.012 31 C -0.385 0.020 32 C -0.649 -0.004 33 C -0.635 0.009 34 H 0.218 -0.001 35 H 0.286 0.000 36 H 0.274 -0.001 37 H 0.190 0.003 38 H 0.177 0.001 39 H 0.264 -0.005 229 40 H 0.269 0.001 41 H 0.262 -0.004 42 N 0.938 0.000 43 C -0.150 0.008 44 C -0.355 0.007 45 C -0.663 0.004 46 C -0.301 -0.001 47 C -0.325 0.010 48 C 0.543 -0.006 49 C 0.596 0.016 50 C -0.370 0.019 51 C -0.350 0.001 52 C -0.554 -0.001 53 C -0.492 -0.005 54 H 0.169 0.000 55 H 0.253 0.000 56 H 0.259 0.002 57 H 0.224 -0.001 58 H 0.220 0.001 59 H 0.285 0.000 60 H 0.270 0.000 61 H 0.212 0.004 230 Excited Electronic States for the S 0 Equilibrium Geometry Table B.11. BNL TDDFT excited states – S 0 equilibrium geometry S n E(S n ) f (oscillator strength) 1 2.69 0.004 2 2.80 0.006 3 2.81 0.006 4 3.03 0.007 5 3.04 0.059 6 3.05 0.061 7 3.15 0.007 8 3.20 0.022 9 3.20 0.026 10 3.27 0.009 11 3.27 0.008 12 3.34 0.043 13 3.41 0.045 14 3.41 0.048 15 3.62 0.007 16 3.67 0.008 17 3.67 0.008 18 3.72 0.017 19 4.06 0.001 20 4.26 0.001 21 4.26 0.001 22 4.33 0.074 23 4.33 0.073 24 4.36 0.103 25 4.38 0.126 26 4.48 0.003 27 4.48 0.004 28 4.49 0.007 29 4.50 0.003 30 4.50 0.115 31 4.55 0.010 32 4.57 0.038 33 4.58 0.039 34 4.63 0.068 35 4.63 0.041 36 4.63 0.031 231 37 4.66 0.030 38 4.66 0.032 39 4.70 0.014 40 4.71 0.011 41 4.71 0.013 42 4.73 0.034 43 4.74 0.035 44 4.74 0.040 45 4.75 0.001 46 4.76 0.019 47 4.78 0.000 48 4.79 0.001 49 4.79 0.001 50 4.82 0.035 51 4.83 0.041 52 4.85 0.013 53 4.86 0.019 54 4.90 0.014 55 4.95 0.001 56 4.96 0.004 57 4.96 0.004 58 4.97 0.002 59 4.98 0.003 60 4.99 0.014 61 5.01 0.029 62 5.01 0.035 63 5.02 0.034 64 5.03 0.008 65 5.03 0.002 66 5.05 0.031 67 5.05 0.002 68 5.06 0.003 69 5.08 0.001 70 5.08 0.003 71 5.08 0.002 72 5.10 0.110 73 5.11 0.003 74 5.13 0.004 75 5.14 0.003 76 5.15 0.003 77 5.16 0.029 232 78 5.16 0.004 79 5.17 0.014 80 5.17 0.014 81 5.18 0.024 82 5.18 0.029 83 5.25 0.080 84 5.25 0.025 85 5.25 0.075 86 5.27 0.024 87 5.27 0.004 88 5.27 0.005 89 5.28 0.001 90 5.31 0.030 91 5.31 0.035 92 5.32 0.001 93 5.32 0.000 94 5.35 0.003 95 5.36 0.058 96 5.37 0.025 97 5.38 0.021 98 5.39 0.049 99 5.39 0.051 100 5.40 0.003 101 5.42 0.002 102 5.44 0.014 103 5.44 0.021 104 5.45 0.010 105 5.46 0.011 106 5.46 0.004 107 5.47 0.009 108 5.47 0.015 109 5.47 0.007 110 5.48 0.002 111 5.49 0.012 112 5.49 0.008 113 5.50 0.009 114 5.51 0.049 115 5.52 0.001 116 5.53 0.000 117 5.57 0.030 118 5.57 0.003 233 119 5.57 0.002 120 5.59 0.012 121 5.59 0.012 122 5.60 0.037 123 5.62 0.001 124 5.62 0.000 125 5.63 0.002 126 5.64 0.002 127 5.64 0.002 128 5.65 0.000 129 5.66 0.002 130 5.66 0.002 234 Table B.12. ωB97X TDDFT excited states – S 0 equilibrium geometry S n E(S n ) f (oscillator strength) 1 3.80 0.054 2 3.80 0.057 3 3.82 0.091 4 4.21 0.094 5 4.21 0.098 6 4.30 0.007 7 4.34 0.011 8 4.34 0.013 9 4.39 0.016 10 4.50 0.030 11 4.58 0.028 12 4.58 0.029 13 4.86 0.073 14 4.86 0.073 15 4.94 0.353 16 4.98 0.112 17 4.98 0.120 18 5.04 0.071 19 5.21 0.008 20 5.21 0.006 21 5.23 0.074 22 5.35 0.050 23 5.35 0.048 24 5.40 0.071 25 5.51 0.006 26 5.52 0.006 27 5.60 0.001 28 5.62 0.057 29 5.62 0.062 30 5.63 0.047 31 5.64 0.009 32 5.65 0.018 33 5.69 0.018 34 5.90 0.080 35 5.90 0.067 36 5.92 0.104 37 5.93 0.116 38 5.94 0.102 235 39 5.98 0.119 40 6.00 0.074 41 6.01 0.072 42 6.01 0.030 43 6.08 0.124 44 6.09 0.007 45 6.09 0.005 46 6.19 0.012 47 6.20 0.012 48 6.22 0.019 49 6.31 0.032 50 6.31 0.040 236 Vibrational Frequencies for the S 0 Equilibrium Geometry Table B.13. Calculated vibrational frequencies for the S 0 geometry. B3LYP – lanl2dz for Ir, 6-31+G* for all other atoms Mode frequency 1 i45.71 2 i45.5 3 i31.62 4 i15.55 5 i12.66 6 13.51 7 51.8 8 53.11 9 55.48 10 95.55 11 96.75 12 104.85 13 147.79 14 162.23 15 166.15 16 178.82 17 195.22 18 197.62 19 227.27 20 229.84 21 257.11 22 266.85 23 269.46 24 273.31 25 279.17 26 301.97 27 303.68 28 376.2 29 378.14 30 386.55 31 421.19 32 421.55 33 425.02 34 440.56 35 441.68 36 448.04 237 37 485.28 38 488.06 39 489.97 40 512.34 41 512.93 42 513.94 43 568.33 44 568.87 45 571.18 46 645.03 47 645.7 48 647.46 49 652.32 50 655.23 51 656.32 52 679.75 53 680.52 54 686.75 55 742.09 56 744.14 57 746.41 58 750.22 59 751.1 60 751.19 61 759.41 62 761.96 63 765.22 64 779.31 65 780.25 66 782.48 67 815.83 68 817.48 69 820.12 70 884.77 71 887.02 72 890.98 73 891.13 74 892.58 75 895.6 76 952.43 77 956.09 238 78 959.22 79 966.58 80 975.33 81 977.65 82 997.69 83 999.01 84 1002.07 85 1004.18 86 1007.79 87 1010.39 88 1040.69 89 1041.86 90 1044.05 91 1046.39 92 1047.09 93 1048.33 94 1062.66 95 1063.96 96 1072.63 97 1092.63 98 1095.28 99 1096.01 100 1098.84 101 1102.87 102 1107.81 103 1142.51 104 1144.18 105 1148.8 106 1165.5 107 1166.18 108 1168.43 109 1192.79 110 1194.31 111 1196.58 112 1203.21 113 1203.51 114 1208.13 115 1289.13 116 1294.43 117 1297.6 118 1319.67 239 119 1321.21 120 1324.51 121 1335.97 122 1338.41 123 1343.4 124 1363.85 125 1364.52 126 1365.71 127 1378.56 128 1378.71 129 1378.96 130 1475.47 131 1476.54 132 1477.56 133 1492.54 134 1494.33 135 1494.51 136 1506.21 137 1507.1 138 1510.26 139 1531.31 140 1534.57 141 1535.97 142 1618.55 143 1619.46 144 1620.15 145 1643.24 146 1644.34 147 1645.29 148 1660.05 149 1661.48 150 1663.72 151 1677.87 152 1679.06 153 1679.9 154 3179.66 155 3180.92 156 3181.78 157 3187.14 158 3188.89 159 3189.55 240 160 3203.51 161 3203.88 162 3205.65 163 3206.89 164 3207.59 165 3209.33 166 3211.78 167 3212.12 168 3213.43 169 3214.37 170 3215.06 171 3217.6 172 3238.08 173 3238.5 174 3240.07 175 3243.1 176 3244.84 177 3248.86 241 Appendices References 1. Atkins, P. W.; Friedman, R. S. Molecular Quantum Mechanics, 4 th ed; Oxford University Press: New York, NY, 2005. 2. Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory; Dover Publications: Mineola, NY, 1996. 3. Koch, W.; Holthausen, M. C. A Chemist’s guide to Density Functional Theory, 2 nd ed; Wiley-VHC Verlag: Weinheim, Germany, 2002. 4. Car, R. Quant. Struct.-Act. Relat. 2002, 21, 97. 5. Sun, Y. Y.; Lee, K.; Wang, L.; Kim, Y.; Chen, W.; Chen, Z.; Zhang, S. B. Phys. Rev. B 2010, 82, 073401. 6. Argaman, N.; Makov, G. Amer. J. Phys. 2000, 68, 69. 7. Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864. 8. Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133. 9. Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, NY, 1989. 10. Stephens, P. J.; Devlin, J. F.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. 11. Becke, A. D. J. Chem. Phys. 1993, 98, 5648.

Abstract (if available)

Abstract Arguably the most important green phosphor used in organometallic light emitting devices (OLEDs), tris(2-phenylpyridine)iridium (Ir(ppy)3), is investigated. One- and two-photon photoionization studies are presented and yield a conservative estimate for the upper bound to the ionization energy (6.4 eV). Observed undulations in the two-photon study are due to structure in the ionizing transition that originates from the lowest triplet state (T1), which is populated via fast intersystem crossing (ISC) from the lowest singlet. At low fluence and 500 K – the conditions under which the experiments were carried out – Ir(ppy)3+ is produced without fragmentation, despite the large amount of vibrational energy distributed over its 177 vibrational degrees of freedom. It is concluded that vibrational energy is transferred efficiently to the cation. Complementary density functional theory (DFT) results using long-range corrected functionals (BNL and ωB97X) affirm this conclusion. Time-dependent DFT is used to compute excited singlet and triplet states to just below the computed ionization energy (5.88 eV). A UV absorption spectrum, in which transitions are vertical from the S0 equilibrium geometry, agrees with the room temperature experimental spectrum and indicates that transitions are dominated by Frank-Condon factors with ∆νi = 0. Computed Ir(ppy)3 equilibrium geometries for the ground state (S0), lowest triplet state (T1), and lowest cationic state (D0) reveal very similar geometries owing to the diffuseness of the molecular orbitals. Calculated Ir(ppy)3 vibrational frequencies were used to estimate the probability density P(Evib) at 500 K. In combination with the vibrational energy imparted through relaxation and ISC following photoexcitation, it is seen that a mean value of nearly 31,000 cm-1 of vibrational energy appears in T1, and consequently Ir(ppy)3+. Considerable effort was directed toward removing this excess energy prior to ionization. To this end, it proved possible to photoionize Ir(ppy)3 embedded in helium droplets with 266 nm radiation. The resultant TOF spectra show a strong similarity to the corresponding gas phase spectra. Additionally, low fluence experiments exclusively produced Ir(ppy)3+. The combined data suggests a two-photon ionization mechanism for the low fluence experiments.

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Asset Metadata

Creator Fine, Jordan R. (author)

Core Title A multifaceted investigation of tris(2-phenylpyridine)iridium

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry (Chemical Physics)

Publication Date 10/19/2012

Defense Date 10/19/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag helium droplets,Ir(ppy)3,OAI-PMH Harvest,OLED,photoionization,TDDFT

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wittig, Curt F. (committee chair), Bradforth, Stephen E. (committee member), Kresin, Vitaly V. (committee member)

Creator Email jordan_fine@dcgsystems.com,jordanf@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-127286

Unique identifier UC11292008

Identifier usctheses-c3-127286 (legacy record id)

Legacy Identifier etd-FineJordan-1388.pdf

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Document Type Dissertation

Rights Fine, Jordan R.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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