Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A new photoelectron/photoion spectrometer for the characterisation of molecules and clusters using XUV… Forysinski, Piotr Wojciech 2011

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2011_fall_forysinski_piotr.pdf [ 12.4MB ]
Metadata
JSON: 24-1.0061935.json
JSON-LD: 24-1.0061935-ld.json
RDF/XML (Pretty): 24-1.0061935-rdf.xml
RDF/JSON: 24-1.0061935-rdf.json
Turtle: 24-1.0061935-turtle.txt
N-Triples: 24-1.0061935-rdf-ntriples.txt
Original Record: 24-1.0061935-source.json
Full Text
24-1.0061935-fulltext.txt
Citation
24-1.0061935.ris

Full Text

A NEW PHOTOELECTRON/PHOTOION SPECTROMETER FOR THE CHARACTERISATION OF MOLECULES AND CLUSTERS USING XUV AND UV RADIATION by Piotr Wojciech Forysinski MChem, Heriot-Watt University, Edinburgh, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in The Faculty of Graduate Studies  (Chemistry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2011 © Piotr Wojciech Forysinski, 2011  Abstract A new photoelectron/photoion spectrometer with a light source tuneable from 17.9 eV to 1.5 eV (bandwidth ≲ 0.7 cm-1) for the characterisation of molecules, clusters and ultrafine aerosol particles is described. The first vibrationally resolved PFI-ZEKE (pulsed field ionisation-zero kinetic energy) photoelectron spectra of acetic acid and difluoromethane are presented, which in the case of acetic acid leads to a revision of earlier values for the adiabatic ionisation energy. For the difluoromethane cation a long-standing mystery regarding its vibrational progression previously observed in low resolution photoelectron spectra is unravelled, and the vibrationally resolved PFI-ZEKE photoelectron spectrum is assigned based on full dimensional anharmonic calculations.  A sodium oven was incorporated into the spectrometer to dope clusters and ultrafine aerosol particles with a single atom of sodium. Doped species are subsequently ionised with a single UV (ultraviolet) photon. The composition of the molecular beam can be assessed independently using XUV (extreme ultraviolet) radiation. The results of comparing these two techniques for the first time on the case study of small acetic acid clusters are presented. Fragmentation processes which occur following sodium capture and subsequent photoionisation are strongly dependent on the particular cluster. For the small acetic acid clusters studied (n ≤ 8) the total number of monomer units which evaporate from the sodium doped cluster is determined to be ≲ 4. This amount of evaporation is insignificant for larger clusters and ultrafine aerosol particles. An almost “fragmentation free” particle sizer for volatile ultrafine aerosol particles is thus proposed based on the sodium doping technique. As a first step towards this goal it is shown that the sodium doping technique can indeed be applied to ultrafine aerosol particles. On the examples of large clusters of acetic acid and dimethyl ether, the technique is demonstrated to preserve the size and chemical composition of the clusters. This is in contrast to other ionisation techniques such as XUV ionisation, for which substantial cluster fragmentation is observed. ii  Preface A large portion of research presented in this thesis has been published in peer reviewed journals. All the measurements were performed on a new photoelectron/photoion spectrometer which I built up over the course of my studies, and was one of the primary operators of throughout this time. The core of the experimental setup is closely based on the design of a previous spectrometer used by Dr. Signorell. I prepared all the technical drawings used for construction and machining, modified the design of some components and designed others. In collaboration with Dr. Zielke I assembled and tested all of the equipment used in the experiment and was involved in the selection of all commercially available components.  A version of Chapter 3 has been published as: PFI-ZEKE Photoelectron Spectrum of CH2F2, Ionisation Potential and Ionic Fragmentation Appearance Potentials, Forysinski, P. W., Zielke, P., Luckhaus, D. and Signorell, R., Phys. Chem. Chem. Phys. 12, 3121 (2010). Dr. Zielke and I recorded all the data and cowrote the manuscript with Dr. Signorell. Dr. Signorell designed the research and Dr. Luckhaus performed the theoretical analysis. Section 3.5 of this chapter is adapted from a further publication which was primarily the work of Dr. Luckhaus: Anharmonic Analysis of the PFI-ZEKE Photoelectron Spectrum of CH2F2 from the Ionization Potential to the Onset of Fragmentation, Luckhaus, D., Forysinski, P. W., Zielke, P. and Signorell, R., Mol. Phys. 108, 2325 (2010).  A version of Chapter 4 has been published as: Adiabatic Ionization Potential of Acetic Acid and Torsional Dynamics of its Cation, Zielke, P., Forysinski, P. W., Luckhaus, D. and Signorell, R., J. Chem. Phys. 130, 211101 (2009). Dr. Zielke and I recorded all the data, Dr. Luckhaus kindly provided theoretical support and Dr. Signorell designed the research project and wrote the manuscript.  iii  A version of Chapter 5 has been published as: Photoionization of Small Sodium-doped Acetic Acid Clusters, Forysinski, P. W., Zielke, P., Luckhaus, D., Corbett, J. and Signorell, R., J. Chem. Phys. 134, 094314 (2011). Dr. Zielke and I recorded all the data and I wrote the first version of the manuscript. Dr. Luckhaus, Dr. Zielke, Jennifer Corbett and I carried out all the calculations. Dr. Signorell designed the research project and wrote the final version of the manuscript.  A selection of results presented in Chapter 6 will be submitted for publication. The data was recorded by Dr. Yoder, Jennifer Corbett, Jessica Litman and myself, I wrote the text and the research was designed by Dr. Signorell.  iv  Table of Contents  Abstract ......................................................................................................................................................... ii Preface ......................................................................................................................................................... iii Table of Contents .......................................................................................................................................... v List of Tables ............................................................................................................................................. viii List of Figures .............................................................................................................................................. ix List of Abbreviations ................................................................................................................................. xiii Acknowledgements ..................................................................................................................................... xv 1.  Introduction ........................................................................................................................................... 1  2.  Experiment ............................................................................................................................................ 7 2.1.  Photoelectron/Photoion Spectrometer........................................................................................... 7  2.1.1.  Overview ............................................................................................................................... 7  2.1.2.  Light source ........................................................................................................................ 11  2.1.2.a  XUV / VUV light source optical layout.......................................................................... 11  2.1.2.b  XUV generation schemes................................................................................................ 15  2.1.2.c  Intensity fluctuations of the XUV light........................................................................... 18  2.1.2.d  UV light source optical layout ........................................................................................ 21  2.1.2.e  Wavelength calibration ................................................................................................... 22  2.1.3.  Sample injection system...................................................................................................... 24  2.1.3.a  Room temperature nozzle ............................................................................................... 27  2.1.3.b  Cryogenic nozzle............................................................................................................. 28  2.1.4.  Sodium pick-up cell ............................................................................................................ 30  2.1.5.  Extractor and TOF mass spectrometer ................................................................................ 34  2.1.5.a  Extractor .......................................................................................................................... 34  2.1.5.b  Ion/electron detectors ...................................................................................................... 42  2.1.5.c  Characterisation of the XUV beam and molecular beam diameters by imaging ............ 44 v  3.  2.1.6.  The vacuum system............................................................................................................. 48  2.1.7.  Temporal synchronisation and data acquisition .................................................................. 50  2.2.  TOF and PIE Spectroscopies ...................................................................................................... 51  2.3.  PFI-ZEKE Photoelectron Spectroscopy...................................................................................... 55  PFI-ZEKE Photoelectron Spectrum of Difluoromethane ................................................................... 62 3.1.  Introduction ................................................................................................................................. 62  3.2.  Experimental ............................................................................................................................... 64  3.3.  Ab initio Calculations .................................................................................................................. 65  3.4.  Results and Discussion ............................................................................................................... 68  3.4.1.  Ionisation energy and fragmentation................................................................................... 68  3.4.1.a  Ionisation energy ............................................................................................................. 68  3.4.1.b  Fragmentation channels .................................................................................................. 73  3.4.2.  PFI-ZEKE photoelectron spectrum ..................................................................................... 76  3.5.  Anharmonic Analysis of the PFI-ZEKE Photoelectron Spectrum of CH2F2 .............................. 81  3.6.  Summary ..................................................................................................................................... 86  4.  PFI-ZEKE Photoelectron Spectrum of Acetic Acid ........................................................................... 88  5.  Photoionisation of Small Sodium Doped Acetic Acid Clusters.......................................................... 96 5.1.  Introduction ................................................................................................................................. 96  5.2.  Experimental ............................................................................................................................... 98  5.3.  Calculations............................................................................................................................... 102  5.3.1.  Ab initio calculations......................................................................................................... 102  5.3.2.  Capture cross-sections for sodium pick-up ....................................................................... 105  5.3.3.  Lifetimes of Na(HAc)n* collision complexes .................................................................... 107  5.4.  Results ....................................................................................................................................... 110  5.4.1.  Monomer and dimer .......................................................................................................... 110  5.4.2.  Trimer ............................................................................................................................... 110  5.4.3.  Tetramer ............................................................................................................................ 114 vi  5.4.4. 5.5.  Monomer and dimer .......................................................................................................... 116  5.5.2.  Trimer ............................................................................................................................... 118  5.5.3.  Tetramer and larger clusters .............................................................................................. 121  Conclusions ............................................................................................................................... 123  Photoionisation of Large Sodium Doped Clusters and Ultrafine Aerosol Particles ......................... 125 6.1.  Introduction ............................................................................................................................... 125  6.2.  Soft Ionisation by Sodium Doping and UV Excitation ............................................................. 128  6.3.  Experimental ............................................................................................................................. 135  6.4.  Results ....................................................................................................................................... 137  6.4.1.  Ammonia........................................................................................................................... 137  6.4.2.  Dimethyl ether................................................................................................................... 137  6.4.3.  Acetic acid ........................................................................................................................ 140  6.5. 7.  Discussion ................................................................................................................................. 115  5.5.1.  5.6. 6.  Larger clusters ................................................................................................................... 115  Discussion and Conclusions...................................................................................................... 142  Conclusions and Outlook .................................................................................................................. 144  Bibliography ............................................................................................................................................. 149  vii  List of Tables Table 2.1 List of 2-photon resonances (2ν1) used for XUV / VUV generation and the wavelength range theoretically attainable using them ............................................................................................................. 17 Table 3.1 Adiabatic ionisation energy (IE) of CH2F2 (C2v conformer of CH2F2+) and appearance energies (AE) of fragment ions after single photon or electron excitation ............................................................... 69 Table 3.2 Equilibrium geometry (C2v) and harmonic wavenumbers of CH2F2 and its cation calculated at the MP2(FC)/aug-cc-pVQZ level of theory ................................................................................................ 72 Table 3.3 Fragmentation energies relative to CH2F2+ including zero point energies (D0) ......................... 74 Table 3.4 List of the experimentally observed band positions and band positions relative to the adiabatic ionisation energy ......................................................................................................................................... 79 Table 3.5 Calculated band positions relative to the adiabatic ionisation energy, and assignment of the principal bands of the calculated vibrational structure of the photoelectron spectrum of CH2F2 ............... 81 Table 3.6 Vibrational energy levels of CH2F2+ relative to the zero-point level of the C2v minimum ........ 84 Table 5.1. Characteristic fragments and masses of HAc and its clusters after XUV ionisation, and masses of Na doped clusters expected in the UV-TOF spectra ............................................................................. 101 Table 5.2. B3LYP/6-311++G(3df, 2p) calculations for neutral and ionic fragmentation ........................ 104 Table 5.3 Properties of different sodium - acetic acid collision complexes. ............................................ 106  viii  List of Figures Figure 2.1 The photoelectron/photoion spectrometer with the XUV / VUV / UV light source .................. 8 Figure 2.2 A photograph of the experimental setup ..................................................................................... 9 Figure 2.3 Section view of the vacuum system.......................................................................................... 10 Figure 2.4 Level diagram of the three XUV generation schemes employed ............................................. 12 Figure 2.5 The optical layout of the XUV light source.............................................................................. 13 Figure 2.6 Efficiency of the XUV light generation by sum frequency four-wave mixing (νXUV = 2ν1+ν2) in a xenon gas jet............................................................................................................................................. 20 Figure 2.7 Configuration of the XUV / VUV laser beam and the three UV laser beams (UVI, UVII and UVIII) relative to the molecular beam ......................................................................................................... 22 Figure 2.8 Calibrated optogalvanic signal recorded by scanning the ν1 dye laser in its fundamental output range using the Fe-Ne lamp ........................................................................................................................ 23 Figure 2.9 Wavelength calibrated, experimental photoacoustic spectrum (a) and literature peak positions (b) of the (2ν1+3ν3) band of acetylene ........................................................................................................ 25 Figure 2.10 The room temperature and the cryogenic nozzle .................................................................... 29 Figure 2.11 The sodium oven assembly. .................................................................................................... 31 Figure 2.12 Mass spectra of sodium doped ammonia clusters at different oven temperatures, recorded at a photoionisation wavelength of 222 nm (5.57 eV)....................................................................................... 34 Figure 2.13 The assembled extractor ......................................................................................................... 35 Figure 2.14 A section through the extractor showing its overlapping shield structure .............................. 36 Figure 2.15 Circuit diagram of the ZEKE extractor in the configuration optimised for pulsed electron extraction (single field configuration)......................................................................................................... 37 ix  Figure 2.16 Trace depicting the rise of a 500 V (82 Vcm-1) electric pulse in the ZEKE extractor in single field configuration optimised for electron extraction.................................................................................. 38 Figure 2.17 The second extractor, designed for use with higher extraction fields for the extraction of heavier particles, and for ion/electron imaging studies ............................................................................... 41 Figure 2.18 Cartoon of the operation of an imaging detector with a 2-axis delay line anode ................... 43 Figure 2.19 Images of difluoromethane ions recorded using a delay-line anode detector at the DC extraction voltages shown, using the ZEKE extractor in single field configuration................................... 45 Figure 2.20 A cut through a representation of the TOF chamber in Simion® used to simulate an image for a particular ionisation volume geometry ............................................................................................... 46 Figure 2.21 Vertical size of the ion image in the plane of the MCP as a function of the XUV beam diameter, as simulated by Simion®, for different extraction voltages........................................................ 47 Figure 2.22 PIE spectrum of the Na(NH3)3 cluster recorded with 1 kV across the double field (WileyMcLaren) configuration of the extractor, applied 1 µs after photoexcitation ............................................. 54 Figure 2.23 Simplified schematic diagram of the energy levels involved in a PFI-ZEKE photoelectron measurement on the example of a diatomic molecule ................................................................................ 56 Figure 2.24 Schematic diagram of high-lying Rydberg states and how they are affected by the electric fields applied in a PFI-ZEKE experiment ................................................................................................... 59 Figure 2.25 PFI-ZEKE spectroscopic scheme employed in this work....................................................... 60 Figure 3.1 PFI-ZEKE photoelectron spectrum of CH2F2 in the region of the adiabatic ionisation energy and photoionisation efficiency spectrum in the same region ...................................................................... 68 Figure 3.2 Energy dependence of the relative yield of the CHF2+ fragment ion in the region of its appearance energy ....................................................................................................................................... 73  x  Figure 3.3 Experimental PFI-ZEKE photoelectron spectrum of CH2F2 between the adiabatic IE and the onset of the lowest ionic fragmentation ...................................................................................................... 77 Figure 3.4 The measured PFI-ZEKE photoelectron spectrum compared with harmonic and anharmonic predictions. .................................................................................................................................................. 83 Figure 4.1 The CH3 torsion mode (ν18) of acetic acid ................................................................................ 89 Figure 4.2 Calculated potentials for the CH3 torsion (ν18) of AA and AAC with corresponding energy levels ........................................................................................................................................................... 89 Figure 4.3 PIE spectrum of AA, calculated photoelectron spectrum of AA at the resolution reported in reference [113], experimental PFI-ZEKE photoelectron spectrum and calculated photoelectron spectrum at a vibrational temperature of 100 K. ........................................................................................................ 91 Figure 4.4 Time of flight mass spectrum recorded at a laser photon energy of 85974 cm-1 ...................... 92 Figure 4.5 The CCO deformation (ν12) mode of the acetic acid monomer ................................................ 93 Figure 5.1 Schematic diagram showing the timing of the laser pulse and of the molecular beam .......... 100 Figure 5.2 Zero point corrected energies (relative to the neutral Na(HAc)3 ground state) and structures for Na(HAc)3 and its neutral and ionic fragments from B3LYP calculations ................................................ 102 Figure 5.3 XUV-TOF spectra recorded under different conditions: Molecular beam contains (a) monomer HAc and dimer (HAc)2; (b) monomer HAc, dimer (HAc)2 and trimer (HAc)3 (amount of tetramer is very small); (c) monomer HAc, dimer (HAc)2, trimer (HAc)3, and tetramer (HAc)4; (d) large clusters .......... 111 Figure 5.4 UV-TOF spectra of Na-doped HAc clusters recorded under different molecular beam conditions as specified in Fig. 5.3: (a) Same conditions as in Fig. 5.3(b) (up to the trimer); (b) Same conditions as in Fig. 5.3(c) (up to the tetramer); (c) Same conditions as in Fig. 5.3(d) (including large clusters). .................................................................................................................................................... 112  xi  Figure 5.5 Ion yield curve (scaled with UV light intensity) as a function of the UV excitation wavelength of (a) NaHAc+ and (b) Na(HAc)2+ ............................................................................................................ 113 Figure 5.6 Unimolecular decay rates as a function of energy for the Na collision complexes of the acetic acid monomer, NaHAc, and the dimer, Na(HAc)2 ................................................................................... 118 Figure 6.1 Schematic representation of the processes which affect observed size distributions of sodium doped species ............................................................................................................................................ 131 Figure 6.2 The sodium capture probability as a function of particle size, exemplified on the case of NH3 particles ..................................................................................................................................................... 132 Figure 6.3 Mass spectra of dimethyl ether clusters as a function of the extraction voltage ..................... 135 Figure 6.4 Mass spectra of large ammonia particles generated, doped with sodium and photoionised with UV light (266 nm) ..................................................................................................................................... 138 Figure 6.5 Comparison of the mass spectrum of dimethyl ether clusters obtained using the sodium doping technique in trace (a) with that using XUV ionisation in trace (b). .......................................................... 139 Figure 6.6 Comparison of the mass spectrum of acetic acid clusters obtained using the sodium doping technique in trace (a) with that using XUV ionisation in trace (b) ........................................................... 141  xii  List of Abbreviations AA  acetic acid  AE  appearance energy, formerly AP: appearance potential  AT  auto-tracker; device which rotates a non-linear crystal as the laser wavelength changes to maintain a non-linear process  a.u.  arbitrary units  BAP  beam access package; name given to harmonic separation unit manufactured by the company Continuum  BBO  β-barium borate, a material used in non-linear crystals  CBS  complete basis set  CPC  condensation particle counter  DMA  differential mobility analyser  DME  dimethyl ether  e  elementary charge  EI  electron ionisation, formerly electron impact ionisation  Eqn  equation  FCU  frequency conversion unit; name given to non-linear crystal housing unit manufactured by the company Sirah  FWHM  full width at half maximum  GWP  global warming potential  IE  ionisation energy, formerly IP: ionisation potential  IR  infrared  IVR  intramolecular vibrational relaxation  J  rotational quantum number  ℓ  angular momentum (azimuthal) quantum number  xiii  m/z  mass to charge ratio: mass in units of u, charge in units of e  MCP  micro channel plate  MPI  multi photon ionisation  MS  mass spectrometry/spectrometer  PE  photoelectron  PEEK  polyether ether ketone  PFI-ZEKE  pulsed field ionisation-zero kinetic energy  PIE  photoionisation efficiency  PMT  photo-multiplier tube  REMPI  resonance enhanced multi photon ionisation  SACM  statistical adiabatic channel model  SHG  second harmonic generation  SMPS  scanning mobility particle sizer  SPI  single photon ionisation  THG  third harmonic generation  TOF  time of flight  u  unified atomic mass unit, formerly amu: atomic mass unit  UV  ultraviolet, 200 < λ < 400 nm  v  vibrational quantum number  VUV  vacuum ultraviolet, 105 nm < λ < 200 nm  XUV  extreme ultraviolet, also EUV, 10 nm < λ < 105 nm  YAG  yttrium aluminium garnet  ZEKE  zero kinetic energy (often implied: ZEKE electron)  xiv  Acknowledgements First and foremost I wish to thank my supervisor, Dr. Ruth Signorell, for her help and guidance over the entire course of my studies. I am very grateful to her for giving me the opportunity to work on a new and exciting research project like this one. I am also extremely appreciative of her patience and dedication to writing endless grant proposals, thanks to which we could acquire all the equipment we needed to make this research project happen.  I consider myself lucky to have worked in the lab with Dr. Philipp Zielke for a number of years, who enthusiastically shared an immense amount of knowledge with me ranging from scientific instrumentation to theoretical chemistry and everything in between. I gratefully acknowledge Dr. Ricardo Viteri for his help with the laser system in the early days of the experiment, and Dr. Bruce Yoder for his helpful insights towards the end. I also thank Dr. Stephan Jauer who laid the foundations of my experiment just before I arrived.  Through the evolution of the experiment I shared the highs and lows of lab work with Dr. Zielke, Dr. Viteri and Dr. Yoder, but also Jennifer Johnson, Jennifer Corbett and Jessica Litman whose friendship I greatly appreciated. I also wish to thank other members of our research group, past and present, whose camaraderie made even the most unsuccessful lab days bearable: Dr. George Firanescu, Ómar Sigurbjörnsson, Kathrin Lang, Thomas Preston, Dr. Egor Chasovskikh, Dr. Kerry Knox and Merrill Isenor.  The experimental setup would have never come to be without the work and support of the Chemistry Department’s mechanical, electronic and glass-blowing workshops. A very special thank you goes to Kenny Bach, Alan Klady, Ken Love, Des Lovrity, Razvan Neagu and Brian Snapkauskas of the mech shop, Brian Greene of the electronics shop as well as Tony Mittertreiner, the technical services manager.  xv  I am greatly indebted to Dr. Luckhaus for generously providing theoretical support for all of our projects, and doing so with such inspiring thoroughness and rigour.  I extend my gratitude to Hansjürg Schmutz at the ETH in Zurich for sharing his detailed knowledge about the ZEKE photoelectron extractor, to Dr. Ingo Dauster for providing drawings of his sodium oven and to Dr. Stephen Ashworth for mailing me one of his last copies of the Fe-Ne transitions atlas. I thank Dr. Takamasa Momose for sharing his experience with cryogenic nozzles with me, and Dr. Keng Chou for his advice and help with our laser system.  Last but not least I would like to thank my parents for their unending support over the years – it has been invaluable to me.  xvi  1.  Introduction  Chemical and physical processes which take place in the Earth’s atmosphere have a profound effect on the quality of all terrestrial life. These processes involve species whose scale ranges from atoms and molecules, through clusters all the way to micron sized aerosol particles. For a more complete understanding of the atmosphere and its dynamics, detailed knowledge about all of its constituents and how they are interrelated is required. Gas phase species such as carbon dioxide or methane are greenhouse gases; chlorofluorocarbons (CFCs) cause the depletion of the ozone layer. Small clusters of molecules, for example the water dimer, may be associated with poorly understood infrared (IR) absorption continua.1,2 Of all the species present in the atmosphere, aerosol particles are the least well characterised. Defined as a suspension of either liquid or solid particles in the gas phase, aerosols represent the single biggest uncertainty in the radiative forcing of climate change.3  Aerosol particles have both a direct and indirect effect on the Earth’s radiative budget. Light absorption and scattering constitute the direct effects, whereas light absorption and scattering from clouds formed as a result of aerosol particles acting as condensation nuclei for water vapour are the cause of the indirect effect. It is the condensation of gas phase species to form droplets or solid particles, and in particular the nucleation step – one of the key processes to understanding aerosol particle formation – which are illunderstood. The size of the critical nucleus – the size of a molecular cluster beyond which further condensation becomes spontaneous – has long been debated in the scientific community.4 Numerous nucleation mechanisms have been proposed, some of which are neutral binary or ternary, ion-induced, or ion-mediated processes.5 Inorganic acids, especially H2SO4, are known to play a significant role in the nucleation process,4 however organic acids are also known to affect the rate of H2O-H2SO4 nucleation rate very significantly.5  1  In order to be able to study nucleation processes, it is necessary to characterise the whole range of species from small clusters up to the smallest of aerosol particles, referred to as ultrafine aerosol particles. The definition of the size range of ultrafine aerosol particles is somewhat vague, beyond being the smallest sub-division of aerosol particles. A cut-off of 100 nm diameter is sometimes applied, however for the purposes of this thesis the range from 0.5 nm to 20 nm diameter will be defined as ultrafine. Molecular  aggregates of smaller size, up to ~ 0.5 nm in diameter, will be referred to as clusters. It is clusters and  ultrafine aerosol particles, not larger species, which are of key importance to the nucleation process and are investigated in this thesis.  To study the nucleation process and thus gain a better understanding of aerosol particle formation, accurate and precise measurements of size distributions as well as chemical compositions of clusters and ultrafine aerosol particles are needed. Due to their small size, these particles are beyond the capabilities of most conventional aerosol particle sizing and characterising instruments. Furthermore, volatile and semivolatile ultrafine aerosol particles are fragmented by the very few measurement techniques which are capable of operating in this size range, and thus intact size distributions cannot be observed.  In this work, a new state-of-the-art instrument to study the fundamental properties of molecules, clusters and ultrafine aerosol particles is presented. It is equipped with a tuneable, tabletop XUV light source  whose energy range extends from 17.9 eV (69.3 nm) to ~1.5 eV (800 nm) and it is capable of detecting  both photoions and photoelectrons. This thesis describes the instrument (Chapter 2) and its first applications to systems ranging from atmospherically relevant molecular ions to in-situ generated ultrafine aerosol particles.  Molecular ions present in the atmosphere, albeit at very low concentrations, are of significance because it is believed that they may partake in an ion-mediated nucleation process.5,6 Furthermore, they play different roles in the atmospheres of other planets and in the interstellar medium. Acetic acid, for 2  example, present in the interstellar medium and in unscreened regions subjected to ionising radiation from stars, is believed to be one of the building blocks of life because together with ammonia it may form glycine.7 In the Earth’s atmosphere, on the other hand, alongside formic acid acetic acid is one of the most abundant organic acids and may affect the H2O-H2SO4 nucleation rate as such.5,8 Detailed knowledge of the molecules’ ionisation energies, the ions’ vibrational dynamics and their ionic fragmentation pathways is thus desired. A spectroscopic technique of choice, when it comes to ionic vibrational dynamics, is pulsed-field ionisation-zero kinetic energy (PFI-ZEKE) photoelectron spectroscopy9-23 (see Section 2.3). The high resolution achievable with this technique, along with its high sensitivity, surpasses that of conventional photoelectron spectroscopy by a large margin.  The capabilities of PFI-ZEKE photoelectron spectroscopy, and the performance of the new photoelectron/photoion spectrometer, are demonstrated on the cases of difluoromethane and acetic acid. Difluoromethane is one of the gases which replaced CFCs in the refrigerant industry because its ozone depletion potential is zero, but it is also a weak greenhouse gas.24 The first vibrationally resolved photoelectron spectrum of difluoromethane is presented in Chapter 3, together with appearance energies for various ionic fragmentation processes measured using photoionisation efficiency (PIE) spectroscopy. The first PFI-ZEKE photoelectron spectrum of acetic acid is reported in Chapter 4, which results in a revision of earlier values for the adiabatic ionisation energy and provides an experimental measure of the energy barrier to CH3 torsion in the molecular cation. These results are obtained despite the low concentration of the acetic acid monomer in the molecular beam – only about 100 ppm. The XUV light source was used for single photon excitation in all these studies.  For any studies aiming at characterising clusters and ultrafine aerosol particles, including studies of the nucleation process, knowledge of the particle number size distribution is a prerequisite. As already mentioned, sizing volatile and semi-volatile clusters and ultrafine aerosol particles represents a major unresolved challenge. The few conventional sizing techniques applicable to ultrafine aerosol particles 3  have major drawbacks. Elastic light scattering, for example, becomes technically extremely demanding in this size range and – so far – prohibitive, while scanning mobility particle sizer (SMPS) instruments cannot operate on volatile or semi-volatile species and typically only go down to the ~ 2.5 nm diameter  size range. A selection of other techniques can be used to glean information on the size of ultrafine aerosol particles (e.g. IR spectroscopy,25 inner shell ionisation spectroscopy,26,27 numerous scattering techniques28-31) however the scope of these techniques is rather limited and extensive modelling has to be performed to extract even crude size information, not to mention the technical challenges involved. In comparison with these techniques aerosol mass spectrometry is rather promising, however fragmentation caused by most ionisation techniques such as electron ionisation (EI) or even XUV single photon ionisation renders it impossible to obtain unfragmented spectra of clusters or ultrafine aerosol particles.  One exception to the above statement is an ionisation technique initially developed by Schulz et al.32,33 and first applied to large volatile clusters of noble gases, water and ammonia by Buck et al..34,35 Buck et al. used the technique primarily to demonstrate the extent of fragmentation induced by commonly employed electron ionisation. The technique in question, hereafter referred to as the sodium doping technique, involves doping the volatile or semi-volatile clusters with a single atom of sodium, typically by passing a molecular beam of the sample through a beam of sodium atoms or an oven containing sodium metal. The addition of such a chromophore to the cluster renders it possible to ionise at a much lower energy than the ionisation energy of the bare cluster itself. This conveniently brings together the ionisation energies of many chemically diverse species into the ultraviolet (UV) range. It also allows for the ionisation of clusters without inducing chemical change, which is a major reason for the evaporation of monomer units using conventional ionisation techniques. Whereas the effectiveness of the sodium doping technique was clearly demonstrated by Buck et al. on a few specific cluster systems, its utilisation in a generic particle sizing instrument for ultrafine aerosol particles was never sought after.  4  The goal of this work is to take the first steps toward the development of an instrument for the quantitative determination of size distributions of ultrafine aerosol particles using the sodium doping technique. To this end steps are undertaken to characterise the technique, demonstrate its applicability to ultrafine aerosol particles, and lay the groundwork for a future instrument which could be used to sample ambient ultrafine aerosol particles.  Whereas the sodium doping technique was established as being soft compared to other ionisation methods, it was also known to cause a small degree of cluster fragmentation which was never fully characterised. These fragmentation processes are studied in the present thesis on the example of small acetic acid clusters consisting of less than 8 molecules. Fragmentation associated with sodium doping can only be characterised by studying small clusters in isolation from other species and by comparing results obtained using the sodium doping technique with results obtained using another, reference ionisation technique. This reference has to provide independent information on the composition of the bare (undoped) clusters in the molecular beam. Finding a suitable reference technique is the challenge, which can be met in this particular case by using XUV single photon ionisation. This is only true because the fragmentation patterns of the smallest acetic acid clusters are known in the literature36 and allow us to determine the composition of the sampled molecular beam. With the ability to compare the two ionisation techniques, processes of sodium capture in the oven as well as fragmentation before and after photoionisation with UV light can be investigated (Chapter 5).  The sodium doping technique’s applicability to larger cluster species and ultrafine aerosol particles is demonstrated in Chapter 6. This is done by recording mass spectra of large acetic acid and dimethyl ether clusters using the sodium doping technique and comparing them with spectra recorded using XUV single photon ionisation. XUV ionisation is believed to be a sufficiently soft ionisation technique for molecular clusters in the literature.37,38 These studies reveal that sodium doping is indeed a viable sizing technique for large species because the original cluster size as well as the chemical composition stay essentially 5  intact. The XUV technique, on the other hand, is shown to be significantly less “soft” than believed.  Spectra of ammonia particles with diameters up to ~ 10 nm demonstrate the ability to detect such heavy species, despite the need for corrections to the detection efficiency. This body of work represents the first steps toward the detailed characterisation of the sodium doping technique for larger and more chemically diverse clusters and ultrafine aerosol particles.  Chapter 7 concludes the work presented in this thesis and provides an outlook for future research.  6  2. Experiment 2.1. Photoelectron/Photoion Spectrometer 2.1.1. Overview The experimental setup is a versatile photoelectron/photoion spectrometer with a tuneable, narrow bandwidth XUV / VUV / UV light source which can be used for excitation and/or ionisation. The principal components of the machine are the XUV light source, a modular sample injection system, an optional pick-up chamber and a TOF mass spectrometer also capable of detecting electrons. The entire experimental setup is shown in Figures 2.1 and 2.2. A section through the vacuum system is shown in Figure 2.3. All the components of the experiment are described in turn within Section 2.1 of this thesis.  All the vacuum chambers and their mounting systems, most of the ion/electron optics, the sample injection system, the pick-up oven, the XUV diffraction grating rotation stage and numerous optical and electrical feedthroughs are all custom designed and custom built components. A close relationship was established and maintained with the Chemistry Department’s Mechanical Workshop and a number of commercial companies which manufactured all the customised elements of the experiment. The CAD program package SolidWorks® was used for all technical design and drawings, and Simion® was used to model the behaviour of ion and electron optics.  7  Figure 2.1 The photoelectron/photoion spectrometer with the XUV / VUV / UV light source. 1: Light source laser system, 2: sample injection chamber, 3: sodium oven chamber, 4: TOF chamber. Plexiglass laser shielding around all the optical tables has been removed for visual clarity. Optics shown on the laser tables do not constitute the entire optical system. Vacuum bellows, assorted tubing and cables are not shown.  8  9 Figure 2.2 A photograph of the experimental setup.  Figure 2.3 Section view of the vacuum system. A: Four-wave mixing chamber, B: monochromator chamber, C: sample injection chamber, D: sodium oven chamber, and E: TOF chamber. Chamber D pertains to research presented in Chapters 5 and 6 of this thesis only, and was not installed for the measurements presented in Chapters 3 or 4. For these measurements chamber C was attached directly to chamber E. A µ-metal shield installed around the extractor and the flight region within the TOF chamber is omitted for clarity. Cables and thermocouple thermometers are not shown.  10  2.1.2. Light source The light source is a broadly tuneable XUV / VUV / UV nanosecond (~ 8 ns) laser system, with a photon energy range from 17.9 eV to ~ 1.5 eV (69.3 nm – 800 nm). In the XUV / VUV range the light is generated in resonance-enhanced two-colour four-wave mixing processes in a pulsed jet of noble gas as non-linear medium. The non-linear processes are pumped by dye lasers, themselves pumped with an Nd:YAG laser. UV light from a frequency doubled dye laser (λ ≥ 220 nm (5.6 eV)) is used directly, and the fundamental dye laser output is used for the visible and IR ranges. In the XUV / VUV range the light is tuneable from 5.6 eV to 17.9 eV (220 nm to 69.3 nm) with a small gap around 11 eV (113 nm). In the XUV / VUV range the light energy is on the nJ/pulse scale and the bandwidth is better than 0.7 cm-1, while in the UV the energy is in the mJ/pulse range and the bandwidth is determined by the dye laser.  An additional, compact, frequency quadrupled Nd:YAG laser was installed to generate 266 nm light at energies up to 10 mJ/pulse. This laser is used as a low maintenance alternative for experiments where laser light at a fixed wavelength of 266 nm is sufficient. It is also being tested for a potential future field instrument where a larger laser system could not be used – see Chapters 6 and 7.  2.1.2.a XUV / VUV light source optical layout Tuneable XUV / VUV light is generated by two different resonance-enhanced two-colour four-wave mixing processes in pulsed supersonic expansions of krypton or xenon gas (the non-linear medium). These are the sum frequency mixing (2ν1 + ν2) and difference frequency mixing (2ν1 – ν2) processes. The frequency of one dye laser beam (ν1) is adjusted such that 2ν1 corresponds to a 2-photon resonance in the noble gas. The frequency of the other dye laser (ν2) can then be tuned so that the (2ν1 + ν2) or (2ν1 – ν2) processes generate tuneable XUV / VUV light. XUV light at a fixed wavelength is also generated by the 3ν1 process. The three processes are depicted in Figure 2.4. XUV / VUV generation schemes for various wavelength ranges will be discussed in Section 2.1.2.b. 11  Figure 2.4 Level diagram of the three XUV generation schemes employed.  The optical layout of the light source is shown in Figure 2.5. The second harmonic (532 nm) or the third harmonic (355 nm) output of a Nd:YAG laser (Continuum Powerlite PR 9010) running at a repetition rate  of 10 Hz with a pulse width of ~ 7 ns is used to pump two dye lasers (both Sirah Cobra-Stretch SL, equipped with capillary amplifiers for enhanced beam profile), one of which is frequency doubled or tripled to generate ν1. The other dye laser can be tuned in its fundamental or doubled output range (ν2). Both dye lasers can be pumped independently with either 532 nm or 355 nm depending on the required output wavelength. The pump power going into each dye laser can be controlled using a Glan-Lazer prism. To generate XUV / VUV light, the two dye laser beams ν1 and ν2 are overlapped using a dichroic mirror and focussed onto the noble gas jet inside the 4-wave mixing vacuum chamber using a fused silica lens mounted on a vacuum flange (see Figure 2.3). To compensate for the varying focal length of the lens at different frequencies (i.e. ν1 and ν2), a telescope is used on the ν2 beam to adjust the beam divergence. The focal point of the lens is located about 1 mm downstream from the 1 mm orifice of the pulsed nozzle  12  13 Figure 2.5 The optical layout of the XUV light source. See the List of Abbreviations on pg. xiv for definitions of the acronyms used.  (General Valve, Series 9), which is operated at a stagnation pressure of ~1.2 bar pure noble gas. The nozzle can be translated laterally as well as vertically to optimise XUV/ VUV signal after the laser beams are aligned.  Both dye lasers are pumped by the same pump laser, therefore any temporal discrepancy in the two dye laser beams is caused primarily by their differing pathlengths. The temporal overlap of the ν1 and ν2 lasers at the lens at the entrance to the four-wave mixing chamber was confirmed using fast photodiodes (DET10A, Thorlabs) to within less than 1 ns. At this location the pulse widths at half maximum of the two dye lasers are about 7 ns.  The desired XUV light generated in the 4-wave mixing process is separated from the fundamentals (ν1, ν2) and other frequencies generated in the non-linear medium (such as 3ν1) by a servo-motor driven  toroidal diffraction grating (275 grooves/mm, optimised for 4 – 25 eV, platinum coating, ~15%  efficiency at 70 nm, Horiba Jobin Yvon) situated in Chamber B (see Figures 2.3 and 2.5). The diffraction grating is placed in a custom built 4-axis adjustable mount on a rotation stage. The stage is mounted on a rigid shaft which is fed outside the vacuum chamber through a custom-built magnetic fluid sealed bearing feedthrough (Trinos Vacuum, now Pfeiffer Vacuum). This is superior to a regular o-ring sealed rotational feedthrough because it does not suffer from any of the drawbacks of using a compressible material for the seal. On the air-side of the feedthrough assembly the shaft is rotated using a servo motor, and its position is monitored using an optical position encoder. A controller which drives the motor uses the position information in a negative feedback loop to maintain a set angle. Stable angular resolution to 0.002° is achieved. Custom written LabView® code is used to communicate with a controller and rotate the grating to any desired position.  After being diffracted by the grating, the desired XUV / VUV light is directed through a series of pinholes into the ion/electron extractor located in the TOF chamber (Chamber D, Figure 2.3). The focal point of 14  the grating lies at a 2 mm diameter pinhole which is located at the entrance of the TOF chamber close to the gate valve. The XUV beam thus diverges again before reaching the extractor where it interacts with the sample. The beam is thus intentionally defocussed to reduce its intensity and prevent the formation of too high a density of Rydberg states or ions which would interact with each other (“space charge effects”).  A photomultiplier tube used as an electron multiplier (Hamamatsu R5150-10; XUV detector in Figure 2.3) is installed beyond the extractor to monitor the XUV / VUV light intensity. The reading is primarily qualitative and since no calibration information is available it cannot be used for quantitative measurements. With energies of about 2 mJ/pulse for both incoming dye laser beams, the energies in the XUV were estimated to be on the order of a few nJ per pulse (~109 photons/pulse) based on estimates provided in reference [23]. The bandwidth of the XUV / VUV light is estimated as better than 0.7 cm-1 based on the spectral linewidth of peaks in the PFI-ZEKE photoelectron spectrum of krypton gas.  2.1.2.b XUV generation schemes It has been said that tuneable XUV / VUV light is generated by either the (2ν1 + ν2) or the (2ν1 - ν2) process. There are however certain limitations regarding what wavelengths can be used for ν1 and ν2. First and foremost, the frequency 2ν1 has to match a two-photon resonance in a suitable non-linear medium. The use of the 2-photon resonance enhancement increases the efficiency of the 4-wave mixing process by a few orders of magnitude.39 The media most commonly used in 4-wave mixing are the noble gases krypton and xenon. Both these gases possess two 2-photon resonances which are particularly efficient for the 4-wave mixing process. The lighter noble gases are not used because equivalent resonances lie too high in energy to be reached easily (vide infra).  15  The limitations to ν2 are primarily technical ones. In the experimental setup described here, 220 nm is the shortest wavelength which can be reached and tuned using a frequency doubled dye laser (with a fundamental output of 440 nm; pumped with 355 nm). The upper wavelength limit is somewhat above 800 nm, generated as the fundamental output of a 532 nm pumped dye laser. Table 2.1 shows the 2-photon resonances used and the wavelength ranges theoretically achievable by tuning ν2. Corresponding 3ν1 wavelengths are also shown. These cannot be tuned, but are higher in energy than the maximum frequency attainable with (2ν1 + ν2) at a particular ν1 wavelength. The 3ν1 process sometimes offers greater intensity because it does not rely on the overlap of two different laser beams, and is thus useful in circumstances were XUV intensity is a more important requirement than specific wavelength.  From Table 2.1 it is obvious that there is actually a gap in the 10.7 – 11.5 eV range which cannot be covered by any of the listed resonances. It would, in principle, be possible to use two equivalent transitions in argon (3p5(2P1/2)4p'[1/2](J=0)←3p6 1S0 and 3p5(2P3/2)4p[1/2](J=0)←3p6 1S0) to extend the attainable XUV range and fill this gap. However, these two resonances would require ν1 to be in the VUV range (184 nm and 187 nm, respectively39) which poses a number of technical difficulties. First, ν1 would now have to be generated in vacuum or in an inert atmosphere, and second, because of the absorption onset of BBO crystals at 189 nm,39 a more exotic non-linear crystal would have to be used. Alternatively the excitation scheme could be changed to follow that described by Rupper and Merkt (attaining the 2-photon resonance with a (νa + νb) photon combination where νa is the output of a F2 excimer laser at 157 nm and νb is the frequency tripled output of a dye laser),39 but this would involve a major addition to the current setup. Given that light in this range was never needed, the use of argon resonances was not attempted.  16  Table 2.1 List of 2-photon resonances (2ν1) used for XUV / VUV generation and the wavelength range theoretically attainable using them. The range is calculated by varying ν2 from 220 nm to 800 nm. Note that the XUV is tuneable in the range shown in columns 2ν1 + ν2 and 2ν1 - ν2, but is at a fixed wavelength at the values shown in the 3ν1 column. The diffraction grating is rotated to select which one of these three processes is used. For any wavelengths longer than 220 nm the frequency doubled output of a dye laser is used directly.  Transition  2-photon  2ν1 + ν2  2ν1 - ν2  3ν1  -1  resonance / cm Krypton  4p5(2P1/2)5p'[1/2](J=0)←4p6 1S0  98855.071 39  69.3 – 89.8 nm  115.8 – 187.3 nm -1  17 Krypton  4p5(2P3/2)5p [1/2](J=0)←4p6 1S0  94092.862 39  144310 – 111355 cm  86356 – 53401 cm  148283 cm-1  17.9 – 13.8 eV  6.6 – 10.7 eV  18.4 eV  71.7 – 93.8 nm  122.6 – 205.6 nm -1  Xenon  5 2  61  5p ( P1/2)6p'[1/2](J=0)←5p S0  89860.038  39  Xenon  61  5p ( P3/2)6p[1/2](J=0)←5p S0  80118.974  39  70.9 nm  139547 – 106593 cm  81593 – 48638 cm  141139 cm-1  17.3 – 13.2 eV  6.0 – 10.1 eV  17.5 eV  73.9 – 97.7 nm  -1  129.3 – 225.2 nm -1  5 2  67.5 nm -1  74.2 nm  135315 – 102360 cm  77360 – 44405 cm  134790 cm-1  16.8 – 12.7 eV  5.5 – 9.6 eV  16.7 eV  79.6 – 108.0 nm  -1  83.2 nm  147.9 – 288.5 nm -1  -1  125574 – 92619 cm  67619 – 34664 cm  120179 cm-1  15.6 – 11.5 eV  4.3 – 8.4 eV  14.9 eV  2.1.2.c Intensity fluctuations of the XUV light Wavelength ranges potentially achievable using the XUV / VUV light source have been shown in Table 2.1. There are, however, a number of other factors which influence the XUV / VUV wavelength range which is actually amenable for spectroscopic studies. There are XUV / VUV wavelengths for which certain ν1 and ν2 combinations result in very low conversion efficiency. Furthermore, for some wavelength ranges the generated light intensity fluctuates very significantly as a function of wavelength because of resonance phenomena with other electronic states of the noble gas. The noble gases are used as non-linear media primarily because of their low density of states. As shown below, even relatively sparse electronic states cause significant light intensity fluctuations. For molecular non-linear media, corresponding intensity fluctuations are even worse and occur over the entire frequency range. A combination of different 2-photon resonances has thus to be utilised to retain the full tuneable range (17.9 eV – 11.5 eV, 10.7 eV – 5.6 eV) (69.3 nm – 108 nm, 116 nm – 220 nm).  Besides being strongly influenced by resonances in the non-linear gas medium, the intensity of the XUV light generated is also affected by the efficiencies of the laser dyes used. The resulting frequencydependent fluctuations in the XUV light intensity influence intensities in ion and electron spectra recorded by tuning the XUV wavelength. This problem is exacerbated by the lack of a reliable, quantitative measurement of the XUV light intensity with which the spectra could otherwise be scaled. While variations in laser dye efficiencies can most often be compensated for by using various laser dyes or dye mixtures with overlapping frequency ranges, fluctuations of the XUV light intensity caused by resonances in the non-linear medium cannot be avoided and their influence has to be clarified. High densities of Rydberg states close to the 2P3/2 and 2P1/2 ionisation energies of xenon and krypton, as well as the autoionisation of states that converge to the higher spin-orbit limit give rise to particularly complex XUV fluctuations in these energy ranges. These resonances were first observed in absorption spectra by Beutler40 and analysed by Fano,41 hence the typical shape of the absorption spectra is often referred to as the Beutler–Fano profile. 18  As an example, the lower traces in Figure 2.6 show the intensity of the XUV light above the first ionisation energy of xenon generated by sum frequency mixing using the two 2-photon resonances in xenon (see Section 2.1.2.b and Table 2.1). The corresponding absorption spectrum of xenon in this region  consists of a series of broad 5p5(2P1/2)nd ← 5p6 transitions and a series of comparatively narrow 5p5(2P1/2)ns ←5p6 transitions.40,42 The intensity of the XUV light in Fig. 2.6 does not simply follow the  absorption spectrum.43 However, some relationships can be found between features in the absorption spectrum and features in the XUV light intensity. Depending on whether the ‘‘2P1/2 resonance’’ (grey traces) or the ‘‘2P3/2 resonance’’ (black traces) is used as the 2-photon resonance, the XUV light intensity is enhanced or depleted close to absorption resonances (e.g. 5p5(2P1/2)7d ← 5p6 or 5p5(2P1/2)9s ← 5p6). The  effect can be limited to a relatively narrow frequency range, but can also extend over a broad range. In addition, the traces for both 2-photon resonances show depletion of the XUV light in a narrow range around the xenon ion absorption lines (102799 cm-1 and 104250 cm-1).42 Fig. 2.6 demonstrates that very large fluctuations in the XUV light intensity can often be avoided by switching between the two 2-photon resonances in xenon in different frequency ranges (in addition to switching between xenon and krypton as the non-linear medium). The remaining light fluctuations still influence the intensities of ion and electron signals in all measured spectra, and definite statements about their intensities cannot be made.  In the particular case shown in Figure 2.6, this allowed the measurement of a complete PFI-ZEKE photoelectron spectrum without encountering difficulties due to low light intensity. This work is presented in Chapter 3 of this thesis. A part of the PFI-ZEKE spectrum is depicted in the upper trace to juxtapose the typical spectral width in such spectra with the width of the light fluctuations.  19  Figure 2.6 Efficiency of the XUV light generation by sum frequency four-wave mixing (νXUV = 2ν1+ν2) in a xenon gas jet. Lower traces: XUV light intensity. The light intensity increases from bottom to top (left scale). All traces are scaled to equal maxima. The black traces were recorded using the “2P3/2 2-photon resonance” in xenon and the grey traces using the “2P1/2 2-photon resonance” (see Table 2.1). Upper trace: PFI-ZEKE photoelectron spectrum of CH2F2 in the same region for comparison – see Chapter 3. The electron signal increases from top to bottom (right scale).  Another effect worthy of note is that the (2ν1 + ν2) and (2ν1 - ν2) processes compete with each other. For a particular wavelength ν2, a sharp increase in one process is usually accompanied by a drop in intensity of the other.  20  2.1.2.d UV light source optical layout In order to perform comparative studies of different ionisation methods, namely the single photon ionisation of clusters using XUV and the single photon ionisation of the same clusters with UV light after doping them with a single sodium atom (see Chapters 5 and 6), a source of UV light was required to complement the XUV / VUV light source. This was initially achieved by tuning the ν2 dye laser output to the UV range (using SHG) and directing it into the extractor over the diffraction grating set at its 0th order. In this configuration the diffraction grating acts as a mirror, but poses an upper limit to the laser power which can be employed. However, in this configuration the convenience of being able to switch from XUV to the UV very quickly is great. This UV beam will be referred to as the UVI beam. When tuneability in the UVI beam was not required and the wavelength was suitable, the ν1 beam was used instead of the ν2 beam. For the collinear configuration of the XUV and UVI beam, see Figure 2.7.  To avoid the power limitations and to protect the XUV diffraction grating, a flip mount and a periscope were added to the setup to direct the ν2 beam directly towards the TOF chamber, bypassing the 4-wave mixing and diffraction grating vacuum chambers. The beam was then aligned through a pair of windows mounted directly on the TOF chamber in an axis perpendicular to the XUV axis (Figure 2.7). This beam will be referred to as the UVII beam. Both the UVI and UVII configurations are tuneable down to about 220 nm (by SHG of the ν2 dye laser).  With the aim of providing a simple alternative to the Nd:YAG pumped dye laser, a compact, frequency quadrupled Nd:YAG laser (Ultra 50, Quantel) was installed and counter propagated along the UVII axis. This will henceforth be referred to as the UVIII beam. This laser provides up to 10 mJ/pulse at 266 nm and was used for all studies which did not require tuneable UV but benefitted from the increased power and ease of operation. The laser was also thus tested with a future field instrument in mind (see Chapters 6 and 7).  21  Figure 2.7 Configuration of the XUV / VUV laser beam and the three UV laser beams (UVI, UVII and UVIII) relative to the molecular beam.  Whereas the UVI beam is divergent when it travels through the extractor, just like the XUV / VUV beam, the UVII and UVIII beams are not, and are used directly out of the outputs of their respective lasers. They do, however, have natural divergence which is more pronounced in the UVIII beam (Quantel laser).  2.1.2.e Wavelength calibration Both dye lasers were calibrated by recording optogalvanic spectra using an iron–neon or a silver–argon lamp (Heraeus). The iron-neon lamp exhibited more exploitable transitions at longer wavelengths (visible, IR) while the silver-argon lamp was used in the UV. Reference data from the MIT tables44 and the Atlas of Optogalvanic Transitions in Neon45 was used. The calibration in the XUV was confirmed to better than ~ 0.5 cm-1 through the observation of weak re-absorption lines of the XUV light due to xenon ions in the 22  vacuum system. An example of one of many optogalvanic peaks used in a calibration procedure is shown in Figure 2.8. A calibration procedure typically involved scanning 5-10 optogalvanic transitions in the wavelength range of interest (at most the output range of one laser dye), fitting each peak with a Gaussian profile, and then fitting a square function to a plot of literature vs. measured peak positions. This function was used to correct the laser wavelength axis of all measured spectra.  Figure 2.8 Calibrated optogalvanic signal recorded by scanning the ν1 dye laser in its fundamental output range (black trace) using the Fe-Ne lamp. A Gaussian peak of the height and width of the experimental peak, but centred on the literature position of the transition44 is also shown (red trace). Please note that the red trace is not merely a fit to the black peak, but shows the (minimal) deviation of the overall calibration at this wavelength. In this particular case the overall calibration is based on 5 optogalvanic transitions over the output range of the laser dye. The laser light was greatly attenuated to prevent saturating the transition. The FWHM of the optogalvanic peak is 0.17 cm-1. 23  On rare occasions where insufficient exploitable optogalvanic transitions were available in a wavelength range of interest, photoacoustic spectra were recorded instead. In these cases the dye laser beam was passed through a glass tube fitted with quartz windows filled with a low pressure (~ 100 mbar) of reference gas. A microphone installed inside the tube was used to record sonic waves generated when the laser became resonant with a rovibrational transition as the laser wavelength was scanned. Acetylene was used as the reference.46,47 An example photoacoustic spectrum is shown in Figure 2.9.  2.1.3. Sample injection system Samples to be analysed are introduced into the vacuum system using a pulsed nozzle (General Valve, Parker-Hannifin) in the sample injection vacuum chamber (see Figure 2.3, Chamber C). A selection of nozzle orifice diameters and shapes were used as appropriate (0.1 mm, 0.25 mm, 0.5 mm, 0.8 mm or 1.0 mm straight, 0.5 mm and 0.8 mm conical orifices). After injection the molecular beam passes through a skimmer (Beam Dynamics, Model 2) of 1.0 mm orifice diameter into the next vacuum chamber. The nozzle can be translated along the injection axis to vary the distance from the orifice to the skimmer, over a range from 0 to 175 mm. Gaseous samples and vapours of liquid samples can thus be introduced into the spectrometer. Samples can be expanded neat or seeded in an inert gas such as helium, argon or krypton. In the case of gaseous samples a mixture with an inert gas can be made in a sample bottle, and in the case of liquid samples the inert gas can be bubbled through the liquid before being injected into the vacuum system.  A number of parameters affect the extent of cooling the sample experiences as it is injected, and thus the rotational, vibrational and translational temperatures of the sample as well as the composition of the molecular beam downstream. Cooling can result in condensation of the sample gas and thus the formation of clusters. These parameters include, but are not limited to: the pressure of the sample gas, the seeding ratio, the nature of the seeding gas, the orifice diameter, the shape of the orifice (straight, conical or 24  Figure 2.9 Wavelength calibrated, experimental photoacoustic spectrum (a) and literature peak positions (b) of the (2ν1+3ν3) band of acetylene (ν1: symmetric C-H stretch, ν3: asymmetric C-H stretch).46,47 The observed intensity distribution is governed by nuclear spin statistics. Experimental peak positions were determined by fitting Gaussian profiles to the peaks in the spectrum, and a plot of experimental peak positions against literature peak positions was made. A second order polynomial was fitted to the data and used to correct the laser wavenumber , in a fashion analogous to the optogalvanic calibration.  trumpet shaped) and the temperature of the nozzle.48-50 Further parameters related to the operation of the nozzle, such as the opening time, the spring tension applied to the poppet (which is the element which actually opens and closes gas flow), the poppet material and the voltage magnitude and scheme applied to the solenoid in the valve also affect the nature of the expansion. Another parameter which determines the 25  composition of the molecular beam which is actually sampled by the laser is the delay time between the nozzle opening and the laser pulse. This is discussed in Section 5.2.  With a particular nozzle (assuming a fixed geometry), there is no control over expansion temperature and only room temperature expansions can be performed. Since temperature and pressure determine the saturation ratio of the gaseous sample and thus its ability to cluster, control over not only pressure but also temperature is desirable. To this end a second nozzle configuration was developed which includes a copper body mounted around the nozzle, cooled and temperature controlled51 by a closed-circuit chiller. The two nozzle configurations are described in more detail below. Information presented in this section is pertinent to both configurations.  Typical backing pressures employed for both nozzle configurations range from 1 to 10 bar (absolute). During operation the pressure in the sample injection vacuum chamber is typically in the 10-5 mbar range,  but can be as high as 1 ⨯ 10-3 mbar depending on the opening time of the nozzle and the backing pressure employed. In both cases the Mach disc of the expansion is located significantly beyond the plane of the skimmer orifice and even the MCP. The sample injection chamber is pumped by a large, 2300 dm3s-1 turbomolecular vacuum pump (see also Section 2.1.6) to extend the range of backing pressures, orifice diameters and nozzle opening times which can be used.  The nozzle is operated at the same repetition rate as the lasers (10 Hz). The opening time of the nozzle can be varied from a minimum of about 350 µs to the ms timescale, where the time averaged pressure in the sample injection chamber (of ~ 32 dm3 volume) reaches the 10-3 mbar regime which is the upper limit for turbomolecular pumps. With the existing nozzle 350 µs is the shortest useable opening time dictated by the mechanics of the poppet action. It was found that the maximum degree of clustering achievable was lower for shorter opening times than it was for longer ones. Longer opening times, typically above  26  600 µs, were hence employed when large clusters had to be generated. Opening times of 1 ms were employed for the spectra presented in Chapter 6.  The mounting system of the nozzle assembly was designed to be versatile and compatible with other sample injection methods. An aerodynamic lens for the injection of aerosol particles was constructed and can easily be installed to inject semi-volatile and non-volatile aerosol samples into the spectrometer. Planned future work with the lens is briefly discussed in Chapter 7.  2.1.3.a Room temperature nozzle The valve used in this simple configuration is a common Series 9 General Valve (Parker Hannifin). This type of valve consists of a magnetic body inside a solenoid which can be used to move a poppet. The poppet is a small body made of a polymer (usually Teflon) which opens or closes the valve as it moves. It is normally pushed against the inside rim of the orifice by a spring, resulting in a ‘normally-closed’ valve. The part of the valve in which the orifice is machined is removable and exchangeable (referred to as the “body” of the valve), and is screwed onto the rest of the valve. In the Series 9 valve a Kalrez® o-ring is used to seal this interface. The tightness of the body on its thread determines the pretension in the spring and thus affects the poppet’s dynamics. A common problem associated with this type of valve is that once the pretension is set and the valve is inserted into a vacuum chamber it cannot be changed easily. To solve this problem, an additional mount was designed to allow the rotation of the valve within the vacuum chamber and thus the adjustment of the pretension from outside the vacuum system. This allowed the online optimisation of valve performance based on ion signals observed on the MCP. The room temperature nozzle and the mount are shown in Figure 2.10(a).  27  2.1.3.b Cryogenic nozzle The cryogenic nozzle assembly consists of a Series 99 General Valve encased in a copper block which can be cooled by circulating a heat transfer liquid through it (of similar design to that in reference [51]). The valve differs from the description above because it relies on a single-use copper gasket to seal the interface between the body and the solenoid instead of an o-ring. This is because Kalrez® is not suitable for use in applications below about -20 °C.52 This unfortunately means that the pretension in the spring is permanently set once when the block is screwed onto the solenoid (copper gaskets of varying thicknesses are used for this purpose). Furthermore, Teflon is also unsuitable at temperatures much below -20 °C (determined by experiment) and thus for lower temperatures Kel-F® poppets are used instead. Kel-F®, however, makes for temperamental poppets which do not seal reliably.  The valve is tightly encased in a copper block and cryogenic vacuum grease (Apiezon, type N) is used to maximise thermal contact. ¼´´ stainless steel tubing is wound around the copper block and connected with liquid nitrogen grade flexible tubing (Swagelok®) through a liquid feedthrough to a closed circuit chiller (Proline 1290 “cooling theromostat”, Lauda). All connections are Swagelok® VCR type, with stainless steel gaskets to equalise thermal expansion coefficients as much as possible. A further copper body is slid onto the cooling coil to increase thermal contact, minimise heat gain and increase thermal mass. The temperature of the assembly is monitored with a couple of thermocouple thermometers. A drawing of this setup is shown in Figure 2.10(b).  It is believed that sample saturation ratios just below 1 are optimal for generating large clusters in the nozzle, without injecting large liquid droplets into the vacuum system. A saturation of 1 can be achieved by adjusting nozzle temperature and gas backing pressure. A large selection of substances of interest in this work have normal boiling points in the range of about - 50° C to 20° C. Being able to cover this temperature range (with a 1 – 10 bar backing pressure range) ensures the coverage of a saturation ratio of about 1 for these substances. For technical reasons a liquid nitrogen based temperature control system 28  Figure 2.10 The room temperature (a) and the cryogenic nozzle (b). The mount which allows the adjustment of the pretension in the valve is shown alongside the nozzle in (a). The mount is clamped on the supporting tube (padlock symbol) to hold the valve body in place, while the solenoid can be rotated by the tube it is mounted on (not visible) through the compression port (marked with an arrow) from outside the vacuum system to adjust the spring tension. The hoses connecting the cooling coil to the feedthrough on the flange and the thermocouple thermometers are not shown in (b).  29  was not employed, and a simple recirculating chiller was used instead. To maximise the range of realisable temperatures, the lowest temperature cryogenic oil that is commercially available (Kryo 85, Lauda) was employed, yielding an operational range of -80° C to +30° C. The setup is however, in principle, suitable for cooling down to liquid nitrogen temperatures. Some of the results obtained using the cryogenic nozzle are presented in Chapter 6.  2.1.4. Sodium pick-up cell In some of the studies presented in this thesis (see Chapters 5 and 6) an oven containing sodium metal was used to dope sample atoms, molecules and clusters in the molecular beam with sodium atoms. The oven is housed in the sodium oven vacuum chamber which can be removed from between the sample injection and TOF chambers if not required (see Figure 2.3). The oven itself (along with the skimmer) is mounted on a cylinder-hat shaped flange mounted inside to minimise the distance the molecular beam has to travel from the first skimmer to the extractor.  The sodium oven is based on a design first developed by Scoles et al.,53 adapted by Schulz et al.,54 and used since then by a number of other researchers.35,55 A drawing of the oven used in this work is shown in Figure 2.11. It consists of two main parts – a 44 mm long horizontal cylinder fitted with apertures on both ends (5 mm diameter), through which the molecular beam passes, and a vertical cylinder which is connected underneath the horizontal one where a reservoir of molten sodium is kept. Heating elements are wrapped around each of the two parts individually. The temperature of both parts is monitored with thermocouple thermometers and controlled individually to stabilise the temperatures at any desired level. For the experiments described in this work single doping with sodium atoms was desired and multiple doping had to be avoided. To achieve appropriate oven conditions, TOF mass spectra of sodium doped ammonia clusters generated from a neat expansion (4 bar absolute backing pressure of pure ammonia)  30  Figure 2.11 The sodium oven assembly. The nozzle and skimmer are shown for clarity. (a) room temperature nozzle, (b) skimmer, (c) sodium cup and lower heating element, (d) sodium pick-up volume and upper heating element. Heating elements (not shown) are wrapped around (c) and (d) to individually heat the components to a desired temperature; thermocouple thermometers (also not shown) monitor the temperatures individually and are used to control the heaters. Note the incline of the cut through (d) which allows liquid sodium to drip back down into (c) without passing through the path of the molecular beam.  31  were recorded at different oven temperatures. Ammonia was chosen because large clusters could readily be generated withthe room temperature nozzle available at the time. A series of TOF spectra obtained is shown in Figure 2.12.  The spectra show that doubly doped clusters begin to appear at 225 °C but still at a very low yield. The signal increase in the singly doped species observed between 200 °C and 225 °C suggests the use of a temperature in this range, because the yield of the doubly doped clusters is still negligible. Temperatures between these two values were thus used for all of the measurements presented in this thesis, depending on particular circumstances. The optimum temperature for the lower part of the oven is comparable but higher than that used by Buck et al. (170 °C, e.g. reference [55]). The equilibrium vapour pressure of  sodium at 225 °C is ~ 1.0 ⨯ 10-3 mbar, corresponding to a density of about 1.5 ⨯ 1017 m-3.56,57  Due to extensive thermal contact of the upper part of the oven with the lower part, the upper part was found to warm up substantially even when it was itself not heated, depending on the temperature setting of the lower part, on the timescale of a few hours. A temperature of 140 °C was therefore set on the upper part to proactively achieve thermal equilibrium conditions more quickly (for a lower part temperature setting of 225 °C). This is substantially above the melting point of sodium (98 °C, reference [58]) and thus any sodium which condenses on the walls can drip back down into the lower part of the oven.  After passing through the sodium oven, the molecular beam travels to the extractor in the TOF chamber. The ionisation volume where the molecular beam intersects the laser beams within the extractor is located 80 mm downstream of the oven. A second skimmer or a simple pinhole (to reduce cross-contamination across vacuum chambers) can be installed along this path. In all the work presented in this thesis, however, no skimmer or pinhole was installed and the molecular beam travelled unhindered through a 20 mm diameter opening. 32  33  ◄ Figure 2.12 (previous page) Mass spectra of sodium doped ammonia clusters at different oven temperatures (set on the lower heating element), recorded at a photoionisation wavelength of 222 nm (5.57 eV). The temperature of the upper element was set to 105 °C in this study. Doubly doped clusters are indicated with dashed lines; triply doped clusters with dash-dot-dash lines. Note that some of the smaller cluster signals are cut off on the scale shown.  2.1.5. Extractor and TOF mass spectrometer The mass spectrometer, equipped for detecting electrons as well as ions, is where photoexcitation takes place, ions and electrons are created, and where they are detected. For some of the studies described in this thesis (Chapters 3 and 4) the TOF chamber (Chamber E, Figure 2.3) is attached directly to the sample injection chamber (Chamber C), and in others (Chapters 5 and 6) it is attached to the sample injection chamber through the intermediate sodium oven chamber (Chamber D).  2.1.5.a Extractor The extractor lies at the heart of photoion/photoelectron spectrometer (Figure 2.3). It is where the XUV or UV light interacts with the sample molecular beam, and where species are field ionised and/or extracted towards the MCPs. The extractor consists of a stack of five equidistant, resistively coupled stainless steel plates which are constructed to optimise the homogeneity of DC and pulsed electric fields generated within. The design is closely based on that used and refined by Merkt et al. (references [18,19,23]). A photograph of the extractor is shown in Figure 2.13. This design will be referred to as the ZEKE extractor throughout the remainder of this thesis.  34  Figure 2.13 The assembled extractor. The molecular beam enters the TOF chamber through the hole visible in the flange under the extractor; the TOF axis is upwards along the page. The green cylinders are resistors and the beige cuboids are capacitors. One of the four square openings for the laser beams is visible at centre between plates 2 & 3 (numbered from the bottom).  The ZEKE extractor plates are cylindrical, of large diameter (70 mm)* and have large, clear (not mesh) apertures in the centre for the sample and ions/electrons to travel through. The large size of the apertures (18 mm diameter) reduces the effect of metal surface imperfections on field homogeneity in the ionisation volume. To the same end the plates are machined thin (1.0 mm) † and polished to a high degree. The plates are equipped with overlapping shields (see Figure 2.14) which protect the inside volume from any stray electric fields, including those that may be created by the resistors and capacitors which connect the *  This diameter refers to the minimum inside diameter of the plates within the shields; these are described below.  †  It should be noted that the incorporation of shields, described below, and the requirement of building the plates and  shields out of a single piece of steel puts a mechanical limit to how thin the plates can be machined. 35  Figure 2.14 A section through the extractor showing its overlapping shield structure. The apertures are 18 mm in diameter, the thickness of the plates is 1 mm and the spacing between successive plates is 14 mm. The shielding structure is 3 mm thick and the distance between overlapping shields on successive plates is (only) 1 mm. The outside diameter of the extractor assembly is 108 mm while the diameter of the thin plates within the shields is 70 mm.  plates. The extractor and flight tube are also encased in a two-layer µ-metal shield to minimise the effect of any external magnetic and electric fields. Two orthogonal laser beams travel into and out of the extractor through apertures cut out in the shields on the plates and the µ-metal shield.  The particular resistors and capacitors employed allow the generation of both very weak and strong electric fields of either polarity, in the range between 0.02 Vcm-1 and 820 Vcm-1. A circuit diagram of the extractor is presented in Figure 2.15. The capacitance of the assembly was carefully tuned to allow pulsing the electric field with very short rise times (~ 35 ns, Figure 2.16) and minimal ringing (amplitude ≤ 5% of voltage applied). These pulsed electric fields were used to field ionise high-lying 36  Figure 2.15 Circuit diagram of the ZEKE extractor in the configuration optimised for pulsed electron extraction (single field configuration). Note that 4 resistors of 4 MΩ each in parallel result in an overall resistance of 1 MΩ. 3 of the 4 resistors between plates 4 and 5 (marked with asterisk) are removed in the Wiley-McLaren configuration optimised for ion extraction (double field configuration, vide infra), resulting in a resistance of 4 MΩ between those plates. The star marks the location where ions are born.  Rydberg states of sample species and extract their ion or electrons (depending on field polarity), as described in Section 2.3. The weak negative electric fields required to extract electrons (in the 0.02 Vcm-1 – 0.66 Vcm-1 range) were generated with a delay generator (Stanford Research Systems DG535) and positive electric fields (up to 820 Vcm-1) were generated using a high voltage switch (GHTS 60, Behlke) powered by a regular high voltage power supply (Acopian).  Because a single uniform electric field is optimal for the pulsed extraction of electrons in a PFI-ZEKE experiment, the base configuration of the extractor generates a single, uniform electric field. This will henceforth be referred to as the ZEKE extractor in single field configuration. Using identical resistance between all the plates assures this condition (as shown in Figure 2.15). However, this configuration  37  Figure 2.16 Trace depicting the rise of a 500 V (82 Vcm-1) electric pulse in the ZEKE extractor in single field configuration optimised for electron extraction (vide infra). Note that ringing is primarily limited to the single over-shoot between 35 and 75 ns.  affords poor mass resolution when used with a positive electric field for ion extraction. As mentioned previously (Section 2.1.2), the diameter of the XUV beam within the extractor is large to reduce space charge effects which could destroy Rydberg states in a PFI-ZEKE experiment. This leads to a broad spatial distribution of ions born in the ionisation region. Ions of the same m/z ratio born at a higher birth potential (further up the extractor) start off behind their counterparts born at a lower potential, but are accelerated more, catch up and eventually overtake them. This leads to broadened peaks in the TOF spectrum recorded on the MCP. With this extractor configuration the mass resolution is only about 50.  To increase the mass resolution, a second configuration involving first order space focussing, as demonstrated by Wiley and McLaren59 was developed. In this configuration the natural “focal plane” 38  (catch-up plane where ions of the same m/z but differing birth locations and thus potentials meet in time*) of the ions is shifted from about 50 mm in front of the extractor to 437 mm, where the MCP is located. This is achieved through applying a different voltage across the last two plates of the extractor stack to generate a second electric field stage. The required electric field ratio between the two stages was initially calculated using simple formulae presented in reference [59], but the optimum setting was found by wiring the last two extractor plates through an electrical feedthrough to a variable resistor located outside the vacuum chamber. The resistance was then adjusted to maximise the sharpness of peaks observed in a TOF spectrum. This resistance was measured and a suitable high voltage resistor was used to replace the variable resistor (see Figure 2.15). With this configuration, henceforth referred to as the ZEKE extractor in double field configuration, the resolution was increased to about 250 (at m/z 50).  It should be noted that the spectrometer is equipped with a short flight tube (437 mm from the ground plate of the extractor to the MCP) to optimise electron detection efficiency, which limits the achievable mass resolution. Planned modifications to the spectrometer to increase the mass resolution are briefly discussed in Chapter 7. The ZEKE extractor in single field configuration was used to extract electrons in all PFI-ZEKE spectroscopic studies presented in this thesis (Chapters 3 and 4). This extractor in double field configuration was used in the complementary photoionisation efficiency (PIE) spectroscopic studies and for all the TOF mass spectra presented in Chapters 3,4 and 5.  Both the single and double field configurations of the ZEKE extractor discussed above have certain limitations. Due to the overlapping shields, the closest distance between consecutive plates is very small (1.0 mm). This puts an upper limit on the voltage which can be applied across the extractor, due to arcing concerns (a rule-of-thumb is not to exceed 1 kVmm-1 across components, even through vacuum). To record mass spectra of heavier particles, for which the detection efficiency of the MCP becomes lower, *  In the limit of first order focusing this “plane” is actually a slab, as the TOF spread is minimised but not reduced to  zero. 39  higher fields are sometimes required to accelerate the ions to greater velocities60,61 (see also Chapter 6). Furthermore, the elongated geometry of the extractor is also not well suited for accurate electron imaging studies. To increase the versatility of the photoion/photoelectron spectrometer, a second extractor was designed with the extraction of heavy ions as well as imaging studies in mind.  A drawing of the second extractor is shown in Figure 2.17. The design is primarily based on the one described by Eppink and Parker (reference [62]) for imaging ions and electrons. It consists of three thin (0.2 mm) stainless steel electrodes: a repeller, extractor and ground electrode. The repeller has a 2 mm diameter hole for the molecular beam to enter the extractor; the extractor and ground plate have 20 mm diameter holes. The unusually small diameter of the entrance hole is warranted by a desirable electrostatic lensing effect,62 and likely necessitates the use of a second skimmer. If the extractor isn’t used for electron imaging, the repeller plate can be exchanged for one with a 20 mm hole instead. In this configuration the extractor will be referred to as the high mass extractor. This extractor assembly is itself not suitable for PFI-ZEKE spectroscopy, but can easily be exchanged with the ZEKE extractor in either configuration when the need arises.  To achieve Wiley-McLaren focussing, the plates can be resistively coupled with 500 MΩ resistors in a fashion analogous to that in the double field configuration of the ZEKE extractor. Alternatively, the repeller and extractor plates can also be connected to separate high voltage power supplies, which allows for precise space/energy focus optimisation while the experiment is running at the cost of the ability to pulse the electric field. This setup was used to record a number of TOF spectra presented in Chapter 6. Intended future applications involving imaging are briefly described in Chapter 7.  40  Figure 2.17 The second extractor, designed for use with higher extraction fields for the extraction of heavier particles, and for ion/electron imaging studies. The configuration shown (small diameter aperture in repeller plate, second skimmer employed directly before extractor) will be used for electron imaging studies; the repeller plate can be exchanged for one with a larger aperture for high m/z ion extraction (high mass extractor).  41  2.1.5.b Ion/electron detectors Ions and electrons are detected using micro channel plates (MCPs) located at the end of the flight region following the extractor. The extractor and the flight region are encased in a two layer µ-metal shield (two concentric cylinders, 1 mm thickness, of 150 and 170 mm diameters) which end just before the detector. For imaging measurements the end of the µ-metal shield can be capped with a stainless steel mesh to isolate the flight tube from the effect of the high voltage on the MCP and render it a true “field-free region”.  For most measurements presented in this thesis, and all measurements not requiring imaging, a simple detector consisting of a chevron stack of two 40 mm diameter MCPs (Photonis or Hamamatsu) and a flat anode located behind them is used (DET40, RoentDek) to detect ions and electrons. In the former case the front of the MCP stack is charged to about – 2450 V and the back is kept at ground potential. In the latter case the front of the MCP stack is kept at ground potential and the back is charged to about +2500 V. In both cases the anode is kept at +200 V relative to the back of the MCP.  For all imaging studies, a stack of two 80 mm diameter MCPs (Burle) with a delay-line anode located behind them is employed instead (HEX80, RoentDek). The delay-line anode imaging detector’s primary advantage over the more conventional combination of a phosphor screen behind an MCP stack and CCD camera(s) to capture the image63 is its inherent ability to simultaneously record hit positions together with corresponding hit times. A spatial resolution of 50 µm together with a time resolution of ~ 200 ps is achievable. The RoentDek HEX80 delay-line anode comprises three independent windings of thin wire located behind the MCP. Each winding is orientated at an angle of 60° to the next. Electrons emerging from the rear surface of the MCP create pulses of current in all three wires. The difference in arrival time of the current at each end of each wire is then used to calculate the position of the hit in that axis. Whereas in principle 2 axes would be sufficient to compute the coordinates of a hit, 3 axes provide  42  ground for error-checking and offer a degree of multi-hit performance. In this case a multi-hit is defined as an instance of 2 or more particles hitting the detector within about a microsecond, which is the usual minimum electronic read-out cycle during which the detector is blind to any other hits. A cartoon depicting the operation of a slightly simpler, 2-axis delay line anode is shown in Figure 2.18.  Figure 2.18 Cartoon of the operation of an imaging detector with a 2-axis delay line anode. The grey sphere can represent an ion or an electron depending on what voltages are applied to the MCP and the anode. The x coordinate of the hit would be proportional to t(x1) - t(x2), and the y coordinate to t(y1) - t(y2).  The delay-line anode imaging detector was used to characterise the dimensions of the XUV beam and the molecular beam in the spectrometer (see next section) and future plans for spectroscopic studies are briefly mentioned in Chapter 7.  43  2.1.5.c Characterisation of the XUV beam and molecular beam diameters by imaging The diameters of the XUV and molecular beams within the extractor were assessed by combining imaging measurements with Simion® simulations. To this end the RoentDek HEX80 imaging detector was used to record images of CH2F2 ions which are formed in the overlapping volume of the two beams. Using predictions from Simion® one can relate the “vertical” size of the image to the diameter of the XUV beam, and the “horizontal” size to the diameter of the molecular beam. Images recorded as a function of extraction voltage are shown in Figure 2.19.  The images were recorded using 2ν1+ν2 XUV light at an energy 400 cm-1 above the ionisation potential (IE = 102636 cm-1, 12.7252 eV, see Chapter 3) for (a) - (c) and 3ν1 XUV light (at 134790 cm-1, see Section 2.1.2.b) for (d). Since the photoionisation process results in the loss of an electron which takes most of the excess energy, the surplus internal energy of the ion above the IE is negligible. Images (a) – (c) are of CH2F2+, whereas image (d) is of a lighter background mass peak. It should be noted that in a TOF mass spectrometer, assuming all other parameters are the same, ion flight paths and therefore images are independent of their mass – only their flight times differ.  Simulations were performed with the Simion® 8.0 program package by importing a simplified model of the TOF chamber from SolidWorks®, charging all the electrodes and other conducting components to the appropriate voltages and flying ions through the system. The experimental geometry as simulated in Simion® is shown in Figure 2.20. Ions were defined as a cylinder of specified diameter (corresponding to the XUV beam diameter) and length (corresponding to the molecular beam diameter) at the intersection of the XUV and molecular beams within the extractor. An initial velocity of 1000 ms-1 downstream was assumed for all ions irrespective of mass (the sample was seeded at 5% in helium gas). The diameter and length of the cylinder were varied in turn to establish a relationship between them and the size of the image. An example of this relationship is shown in Figure 2.21.  44  Figure 2.19 (a)-(c) Images of difluoromethane ions recorded using a delay-line anode detector at the DC extraction voltages shown, using the ZEKE extractor in single field configuration. (d) Image of a background mass peak recorded when the molecular beam was turned off, at 3500V. The approximate sizes  of the intense parts of the images are as follows (vertical ⨯ horizontal): (a) 2 ⨯ 4 mm, (b) 3 ⨯ 6 mm, (c) 3.5  ⨯ 7.5 mm. The vertical size of (d) was treated as ~ 4 mm. In the absence of the molecular beam only the  vertical size of the image is of interest and is representative of the diameter of the XUV beam. Note the colour coded intensity scales adjacent to each image and that the dark blue dots may represent as little as a single hit.  45  Figure 2.20 A cut through a representation of the TOF chamber in Simion® used to simulate an image for a particular ionisation volume geometry. Elevation represents voltage and the red line depicts the paths of ions formed in a cylinder shape within the extractor. The two deflection plates mounted in front of the extractor were used to deflect the ion beam laterally to confirm the orientation of the imaging detector, but are not being used in this experiment or these simulations (and thus remain at ground potential). They were found not to affect the flight path of the ions when not charged.  From the comparison of the experimental images with the simulations it appears that the XUV beam diameter at the centre of the extractor is ~ 1 mm while the diameter of the molecular beam is ~ 2 mm. It  must be stressed that these values are approximate and should not be considered precise – an error of up to ± 1 mm is feasible. The maximum geometric limit for the diameter of the XUV beam at the centre of  the extractor is ~ 4 mm, based on the size of the ν1 and ν2 input beams and the focussing effects of the lens and grating. The images obtained are highly sensitive to laser beam alignment, i.e. XUV – molecular beam overlap, which is subject to slight misalignment on a day-to-day basis. Laser alignment was 46  Figure 2.21 Vertical size of the ion image in the plane of the MCP as a function of the XUV beam diameter, as simulated by Simion®, for different extraction voltages as indicated. A similar graph was obtained by varying the width of the molecular beam and monitoring the horizontal size of the image (not shown).  routinely optimised based on ion or electron signal from the MCP, which is an indirect measure of the overlap, but the method is not guaranteed to be perfectly reproducible. The effective diameter of the XUV is likely to vary somewhat with the intensities of ν1 and ν2 used, but these results should be representative for all the work presented in this thesis.  The diameter of the molecular beam is dependent on the distance between the nozzle and the skimmer as well as the skimmer and the extractor, and a thorough study of this effect was not performed. The data  47  collected is however representative of the configuration used in the studies of difluoromethane and acetic acid as described in Chapters 3 and 4.  2.1.6. The vacuum system The spectrometer components are all housed in custom built vacuum chambers pumped by turbomolecular vacuum pumps, backed by dry (oil-free) foreline pumps. The vacuum chambers are constructed in 316 stainless steel (marine grade), and ISO-K and KF flanges with Viton o-ring seals are used almost exclusively. The flange at the end of the TOF chamber is a copper gasket sealed CF flange, but exclusively for the reason of utility (many commercially available ion/electron detector systems are mounted on CF flanges). The base pressure achievable when using Viton o-ring seals is in the low 10-8 mbar range at room temperature, which is adequate for all the experiments described in this thesis. The ISO-K and KF standard was chosen over the CF standard for ease of assembly and disassembly and because the seals (o-rings) can be reused over a long period of time. Each vacuum chamber is mounted in its own custom built holder which allows a small amount of lateral translation, tilt and vertical adjustment for assembly and alignment purposes (see Figures 2.1 and 2.2).  The four-wave mixing chamber is pumped with a Pfeiffer 521 turbomolecular vacuum pump and has a  background pressure of 2 ⨯ 10-7 mbar, which increases to about 1 ⨯ 10-4 mbar when the noble gas nozzle is in operation. The monochromator chamber, pumped with a Leybold TW300 turbomolecular vacuum pump, has a background pressure of 2 ⨯ 10-8 mbar, which increases to 3 ⨯ 10-7 mbar during operation. The sample injection chamber is backed by a Pfeiffer 2301 turbomolecular pump. Its background pressure  of 6 ⨯ 10-7 mbar increases to about 5 ⨯ 10-5 mbar when the sample injection nozzle is in operation – although in some instances this may be as high as 1 ⨯ 10-3 mbar. The sodium oven chamber is pumped with a Pfeiffer 1201 turbomolecular pump, has a background pressure of 4 ⨯ 10-8 mbar and a pressure of about 6 ⨯ 10-8 mbar when the sodium oven is operation. This increases to 2 ⨯ 10-7 when the molecular  48  beam is on. Finally, the TOF chamber is pumped by a Pfeiffer 521 turbomolecular pump down to a background pressure of 2 ⨯ 10-8 mbar, which increases up to a maximum of about 1 ⨯ 10-6 mbar when the sample injection nozzle is in operation. This is the maximum recommended pressure for MCP operation. The numbers in the names of the turbomolecular pumps are closely related to their maximum volume flow rates for N2, in units of dm3s-1. The four-wave mixing and monochromator chambers’ turbomolecular pumps are jointly backed by a scroll pump (ISP500C, Anest Iwata, 30 m3h-1). The sample injection and sodium oven chambers’ turbomolecular pumps are jointly backed by a dry compressing pump (OnTool DryPump, Pfeiffer, 83 m3h-1). The TOF chamber’s turbomolecular pump is backed by another scroll pump (also ISP500C, Anest Iwata, 30 m3h-1).  Pressures were monitored with hot cathode ionisation gauges (Leybold) and cold cathode ionisation gauges (Pfeiffer Vacuum) in each chamber individually. The two gauge types were used interchangeably except on the TOF chamber, where the use of the strongly magnetic cold cathode gauge was avoided.  To minimise base pressures and prevent sample contamination in the TOF chamber, all materials used within the vacuum system were carefully selected. Where possible grade 316, polished steel was used for all metal components. Kapton® was used as the insulator of choice, but Teflon and PEEK components were used as well. Ceramic material (Caburn) was used both as a thermal and electrical insulator. In a few exceptions components were attached or repaired with TorrSeal (Varian), a vacuum compatible epoxy resin. Cryogenic vacuum grease (Apiezon, type N) was used for thermal contact on the cryogenic nozzle and for thread lubrication in a few exceptional cases.  49  2.1.7. Temporal synchronisation and data acquisition All the time-sensitive components of the experiment are triggered using a number of synchronised delay generators (Stanford Research Systems, DG535). One of the delay generators is internally triggered at 10.0 Hz and triggers a further two, which are needed because of an insufficient number of timing channels available on one unit. Trigger signals for the flashlamps and Q-switches of both the Continuum and Quantel Nd:YAG lasers are provided by the delay generators. Further channels trigger the controllers of the noble gas and sample injection nozzles as well as the high voltage switch used for pulsing voltage on the extractor in PIE spectroscopy. The extractor is powered directly by the delay generator in the case of PFI-ZEKE spectroscopic studies.  Data acquisition is triggered using a fast photodiode placed near a stray reflection of whichever laser beam is in use. An oscilloscope (LeCroy Waverunner 6050A) is used to collect raw data. Both dye lasers and the oscilloscope are controlled using a PC running custom written LabView® software. This allows the collection of spectra from the scope as a function of laser wavelength with a desired level of averaging (number of laser shots) very easily. The same system is used to collect data for photoacoustic, optogalvanic, PIE and PFI-ZEKE spectra. Either one of the lasers can be scanned individually at a desired step size using the program. The resultant data files are a 3D combination of signal as a function of time as a function of laser wavelength. A second custom written LabView® program is used to extract whatever 2D spectrum is desired from a 3D file, again with a desired level of averaging (in the time domain). This technique is advantageous to using a boxcar averaging technique for a pre-set window in the time domain, because no information is lost and the 3D file can be re-used later if it is discovered that more information can be extracted from it than initially thought. This technique is however only possible thanks to the speed of modern day data acquisition hardware, software and processing speed. Recording spectra at a single wavelength is of course a simple matter of using the LabView® program to set the desired number of laser shots to average.  50  Images obtained on the imaging detector are recorded using Cobold PC software provided by RoentDek. Signals from the delay lines are fed through a multipin feedthrough outside of the vacuum chamber, amplified using an 8 channel amplifier and passed to a time-to-digital-converter card (TDC8HP, RoentDek) installed in the data acquisition PC.  2.2. TOF and PIE Spectroscopies Time of flight (TOF) mass spectrometry is a mass spectrometric technique which is based on the separation in arrival time at a detector of ions depending on their m/z ratio. The ions are created within an extractor all at the same time by an ionisation technique (frequently laser excitation) and are all imparted the same kinetic energy by an electric field applied to the extractor. The acceleration experienced by the ions is dependent on their mass, and thus is their velocity when they leave the extractor. The ions then travel down a field free flight tube, where mass separation occurs as the heavier ions lag behind their lighter counterparts.  TOF-MS is an attractive mass spectrometric technique because it is relatively simple to implement experimentally and has no inherent upper limit to the masses which can be detected. In practice, however, a number of technical challenges present themselves which have to be circumvented to achieve reasonable mass resolution in TOF-MS. These include the necessity to create all the ions at the same time, all in the same place, and with the same initial kinetic energy. The use of a laser beam for the ionisation step, even with a ns laser system, takes care of the time requirement rather nicely. The size of the laser beam, however, may create an initial spatial distribution of the ions which negatively affects the resolution. The initial energy distribution of the atoms, molecules or clusters may be limited by injecting the sample in a molecular beam (and making a dilute mixture of the sample in an inert gas to further equalise their velocities), however this technique becomes less effective as mass increases. To compensate for the initial energy spread in ions of the same m/z ratio, a mass spectrometer equipped with 51  a component called a reflectron can be used (reference [64] and references within). Simply put, a reflectron acts as an elastic rebound volume which allows more energetic ions to penetrate further into it than less energetic ones, and thus gives the less energetic ions which were initially travelling relatively slower a time advantage. The less and more energetic ions catch each other up at a particular point in space after the reflectron, and this is where a detector can be placed.  The initial spatial spread of the ions caused by the finite size of the laser beam also has to be dealt with. Using an iris to reduce the beam size naturally reduces the ion signal intensity observed on the detector, whereas focussing the laser may create too high a density of ions which can then interfere with each other, and/or also lead to undesired multi-photon processes. To alleviate the problem, a multi-stage extractor can be used in place of the single stage extractor which uses only one uniform electric field to extract the ions. This technique was developed by Wiley and McLaren59 and was described in Section 2.1.5.a.  The mass resolution of a mass spectrometer is defined by the following equation:  ܴൌ  ݉ Δ݉  Eqn 2.1  m is the mass of a single ion peak with a FWHM of ∆m, where ∆m is also given in u. In the specific case of TOF-MS, for the analysis of peaks due to a single m/z value, this relationship is often expressed as:  ܴൌ  ‫ݐ‬  2Δ‫ݐ‬ிௐுெ  52  Eqn 2.2  where t is the flight time and ∆tFWHM represents the full width at half maximum, in units of time, of the peak. Both definitions are applicable to a particular mass and only provide an estimate of the performance of the spectrometer at other masses. The former definition was used to report resolution throughout this work.  PIE (Photoionisation Efficiency) spectra are mass spectra recorded as a function of ionisation wavelength. Most commonly a single mass peak is extracted from the TOF spectrum, and its integrated intensity is plotted against the wavelength. In some cases the spectra are recorded with a DC electric field applied to the extractor, whereas in other cases the electric field is pulsed so as to extract the ions just after photoionisation. This serves a dual purpose, the first of which is that if any stray light happens to be hitting the extractor the generation of high energy electrons from the metal surface is avoided. These electrons, when accelerated by the high voltages applied to the extractor, are known to create sizeable ion signal due to electron ionisation. The second reason is that the correction which has to be applied to any excitation energies extracted from a PIE spectrum, to compensate for the lowering of the IE by the electric field, is lower for a pulsed field. This is discussed in more detail for the case of electrons in the following section, although the effect is the same for ions.  Figure 2.22 shows the PIE spectrum of Na(NH3)3 recorded on our instrument. The literature value for the IE of the cluster is ~ 25360 cm-1,65 which compares well with our result, especially after the ~ ‒ 50 cm-1 correction is applied because of the pulsed electric field (see Section 2.3 and Eqn 2.4). However, different strategies for deciding which feature in the PIE spectrum should be considered as the IE are employed in literature. Some researchers use the first significant onset of any ionic signal above baseline65 (marked with a star in Figure 2.22) as indicative of the IE, whilst others use the first break in the signal for this purpose66 (marked with a square). Problems may arise when experimental results are reused without referencing the method employed by the original researchers, as is the case in reference [66]. In all PIE  53  Figure 2.22 PIE spectrum of the Na(NH3)3 cluster recorded with 1 kV across the double field (WileyMcLaren) configuration of the ZEKE extractor, applied 1 µs after photoexcitation. The star and square depict two distinct features of the spectrum inconsistently used to estimate the IE (see text). The feature denoted by the star was used to estimate the IE in this work.  spectra discussed in this thesis the approach used by Nitsch et al. (reference [65]) is employed (star in Figure 2.22). Whether one approach is more scientifically correct than the other can only be decided on a case-by-case basis, by analysing rovibrational state populations and the Franck-Condon factors for transitions into the lowest cationic energy levels.  Because of such uncertainties inherent in PIE spectroscopy, in many cases only photoelectron spectroscopy can unambiguously reveal the true location of the ionisation energy. PFI-ZEKE photoelectron spectroscopy in particular provides very accurate values, and is discussed in the next section.  54  2.3. PFI-ZEKE Photoelectron Spectroscopy PFI-ZEKE (Pulsed Field Ionisation-Zero Kinetic Energy) photoelectron spectroscopy is a high resolution technique used to glean information on energy levels of atomic and molecular ions and small ionic clusters. “ZEKE” spectroscopy entails photo-exciting a system into a continuum of high-lying Rydberg states in a ladder of Rydberg states which converges to the ionic rovibronic state of interest. A schematic diagram showing the energies of Rydberg states is provided in Figure 2.23. These Rydberg states have long lifetimes, commonly in the microsecond regime, because the radius of the Rydberg electron is large and it rarely collides with the ionic core. If the Rydberg state and thus the VUV / XUV energy used lies above the first ionisation energy of a species, excitation will also result in the formation of other prompt ions and electrons. These, however, will form instantaneously upon excitation and a weak electric field can be used to remove them from the extractor. This is referred to as the spoiling or the discrimination field. Rydberg states within a certain range (see below and Figure 2.24) can survive this weak field and remain relatively unaffected by it because the field energy is not enough to ionise them. A few microseconds after photoexcitation, a second, usually stronger, electric field (still on the order of mVcm-1) is applied to the extractor to field ionise these remaining Rydberg states. Figure 2.25 shows a sketch of the timeline for a ZEKE experiment. As soon as the Rydberg states are field ionised, their electrons are extracted by the electric field and directed towards the MCP. It is thus possible to obtain high resolution photoelectron spectra with resolution primarily limited by the laser bandwidth and the magnitude and scheme of the electric fields applied.  The PFI-ZEKE spectroscopic technique was initially developed by Müller-Dethlefs, Sander and Schlag in 1984.9,10 In the original work (3 + 1) photon excitation was used to access the required high energy levels. White and coworkers14 were the first to use single photon excitation in a PFI-ZEKE experiment, however they used a relatively simple argon gas cell to frequency triple UV light to reach the XUV / VUV regime. Merkt and Softley15,16 adapted the light source to a more versatile, and now relatively standard 2-photon  55  Figure 2.23 Simplified schematic diagram of the energy levels involved in a PFI-ZEKE photoelectron measurement on the example of a diatomic molecule. Vibrational levels, drawn in black, are labeled with quantum numbers v. Red lines represent rotational energy levels (quantum numbers J) and blue lines represent Rydberg states which form series (series labelled with quantum number ℓ) that converge upon particular rovibrational states. The rotational lines and Rydberg states are not drawn to scale.  56  resonance enhanced sum frequency 4-wave mixing scheme using a pulsed jet of krypton gas. Merkt and coworkers then went on to perform many involved PFI-ZEKE spectroscopic studies using a similar experimental setup,17-23 and went to great lengths in optimising the ZEKE extractor and electric field pulsing schemes. A similar configuration of PFI-ZEKE spectrometer has also been used by a number of other research groups around the globe.67-71 A number of single-photon excitation PFI-ZEKE spectroscopic studies have also been carried out at synchrotron light sources.11-13  Single-photon excitation PFI-ZEKE spectroscopic studies have also been carried out in the case of sodium doped molecules and molecular clusters, where high energy VUV / XUV light is not required to access the energy range around the IE, which is very low due to the doping alkali atom72-74 (see Chapters 5 and 6).  The lifetimes of the high-lying Rydberg states relied on in the PFI-ZEKE experiment depend on the nature of the species being analysed; Rydberg states of molecular species usually have shorter lifetimes than atomic ones because of their higher density of states. The lifetime of the Rydberg species determines how long a delay between photoexcitation and the application of the field ionisation/extraction electric field can be employed to disperse all prompt species. In general, the longer the delay can be made, the weaker a spoiling field can be used, and the better the quality of the resulting PFI-ZEKE spectrum is. In the case of noble gases delays up to 100 µs can be employed and high quality PFI-ZEKE photoelectron spectra can still be recorded. This is reduced to about 5 - 10 µs in the case of small molecules. The most commonly used delay time in PFI-ZEKE photoelectron spectroscopy is about 1 µs, because the magnitude of the detected electron signal is greater at shorter delays as fewer Rydberg states have decayed.  57  The decay of Rydberg states which are essential to the PFI-ZEKE method is greatly accelerated by the presence of stray electric fields within the extractor (because of the field ionisation of the Rydberg states, described below), and hence the construction of the extractor is of paramount importance. The extractor used in PFI-ZEKE spectroscopic studies presented in this thesis was equipped with shielding elements on all the extractor plates to minimise the effect of any external charges which may build up over the course of the experiment – for a detailed description see Section 2.1.5.a.  The application of an electric field lowers the ionisation energy by an energy ∆E. For a DC electric field, F, the lowering of the IE is typically approximated by the following equation:75-77 ‫ܨ‬ Δ‫ ≅ ܧ‬6ඨ ܿ݉ିଵ ܸܿ݉ିଵ  Eqn 2.3  For a pulsed field, i.e. one applied with a rapid rise time only after photoexcitation, this shift is approximated by the following equation instead:75-77 ‫ܨ‬ Δ‫ ≅ ܧ‬4ඨ ܿ݉ିଵ ܸܿ݉ିଵ  Eqn 2.4  An in-depth explanation can be found reference [75]; for examples of use see references [13,15,16,19,23,68 and 69]. It follows that an electric field applied to a sample of prepared Rydberg states field ionises states which lie within a range of ∆E below the true ionisation energy (see Figure 2.24). In the case of a weak spoiling field only the highest lying Rydberg states are field ionised, but all undesired and already charged prompt species are ejected from the extractor by the field. In the case of the stronger extraction pulse applied after the delay, the remaining, slightly lower-lying Rydberg states are field ionised, extracted, and detected on the MCP. Because the magnitudes of the spoiling and the extraction fields determine which Rydberg states are extracted, a correction has to be applied to peak positions  58  Figure 2.24 Schematic diagram of high-lying Rydberg states and how they are affected by the electric fields applied in a PFI-ZEKE experiment. The grey box depicting Rydberg states field ionised by the extraction pulse can also be limited on the low n side by the shorter lifetimes of the lower-lying Rydberg states, which might already have decayed by the time the extraction pulse is applied. The height of the νXUV arrowhead is meant to roughly imitate the laser bandwidth. Figure adapted from reference [16].  obtained from PFI-ZEKE photoelectron spectra to take this into account. An energy correction obtained using the above equations is added to the measured peak positions to achieve this.  Beside using a DC spoiling field, various other schemes employing pulsed spoiling fields of opposite, or even alike extraction polarities to the polarity of the extraction pulse have been employed by other researchers.76 In our work the use of a weak DC spoiling field resulted in the best signal to noise ratio, whilst the correction for the lowering of the IE was conveniently small because of the small magnitude of the field applied. A correction for the stronger extraction pulse was also applied.  59  Figure 2.25 PFI-ZEKE spectroscopic scheme employed in this work. The electric field pulse is used for the field ionisation of high-lying Rydberg states and the extraction of ZEKE photoelectrons. In the example shown a positive DC field, applied for a few µs, is used as the spoiling field to disperse prompt photoelectrons and photoions.  The primary factor limiting the resolution achievable in PFI-ZEKE spectroscopy, assuming the high-lying Rydberg states of the species under study have a lifetime on the order of at least a microsecond, is the laser bandwidth. The bandwidth of XUV / VUV laser sources which use dye laser systems and 4-wave mixing usually lie in the 0.15 to 1 cm-1 range.39 Our system has a bandwidth ≲ 0.7 cm-1 as described in Section 2.1.2.a. Vibrational structure can be resolved easily with this bandwidth, but the rotational structure of all but the lightest polyatomic molecules cannot.  The spectroscopic technique most closely related to PFI-ZEKE is MATI (Mass Analysed Threshold Ionisation) spectroscopy.  MATI spectroscopy relies on the same principles and provides similar  information as ZEKE spectroscopy, only that in this case ion signal is monitored instead of electron signal. Whereas this reduces the resolution achievable (primarily because stronger electric fields are required to move the heavier ions) it directly provides information on what species is responsible for the signal observed.68 The lack of this information is one of the major drawbacks of PFI-ZEKE spectroscopy, and is most pronounced in studies of clusters where multiple species are almost always present in the  60  molecular beam sampled. In such cases it is hard to unambiguously trace observed signals to individual clusters.  The most common method of proving that an observed PFI-ZEKE signal originates from a particular species (and not another species also present in the molecular beam, such as an oligomer, fragment or impurity) is comparing the PFI-ZEKE spectrum in the region of the adiabatic ionisation potential with a PIE spectrum in the same energy range. If the PIE spectrum exhibits a signal onset at a particular m/z ratio close in energy to the peak observed in the PFI-ZEKE spectrum, it is a strong hint that the PFIZEKE spectrum originates from the species with this m/z. This type of scrutiny is sometimes difficult if the signal onset in the PIE spectrum is very gradual and blends in with baseline noise, for example in the case when the Franck-Condon factor for the excitation into the lowest ionic energy level is very low (in which case the observed PFI-ZEKE peak is also of low intensity). If the observed PFI-ZEKE spectrum matches the theoretically predicted spectrum for a particular species (e.g. see Chapters 3 and 4) it is a further hint that the PFI-ZEKE spectrum genuinely originates from that species. Neither of these hints can be considered definitive, however if both conditions are satisfied there is great likelihood that the PFIZEKE spectrum is due to the species in question.  61  3. PFI-ZEKE Photoelectron Spectrum of Difluoromethane 3.1. Introduction With the intention of thoroughly characterising the performance of the experimental setup with regards to both photoelectron and photoion measurements, studies of the photoionisation of difluoromethane (CH2F2, Freon 32) were undertaken. Measurements on small molecules such as CH2F2 allowed us to assess experimental particulars such as electron detection sensitivity and mass resolution. Interest in difluoromethane arises from the fact that it is one of a series of hydrofluorocarbons which have replaced chlorofluorocarbons in the refrigerant industry. The extreme stability of HF eliminates the possibility of the formation of fluorine radicals, and therefore CH2F2 has an ozone depletion potential of zero. Difluoromethane, however, is also a greenhouse gas with a global warming potential of 550.* Global production of difluoromethane is on the megaton scale.  Photoelectron spectra of difluoromethane have been published numerous times over the last few decades.78-84 Ambiguities in the ordering of ionic electronic states and in particular in the assignment of partially resolved vibrational substructure of the cation prompted multiple reinvestigations, both experimental and theoretical.81,84-91 Furthermore, there have also been numerous studies regarding the fragmentation of the CH2F2 cation and the appearance energies (AEs) of its fragments.84,88-90,92-95 Possibly due to the different techniques employed, experimental values for the ionic AEs scatter over a broad range.  In the present study, single-photon excitation PFI-ZEKE photoelectron spectroscopy in a skimmed free jet expansion is employed to determine the adiabatic ionisation energy of difluoromethane (IE, defined as *  A global warming potential (GWP) of 550 is significant in comparison to that of CO2 (defined as 1), but in  comparison to many other hydrofluorocarbons, CH2F2 is not a potent greenhouse gas (e.g. the GWP of CHF3 is 12000). GWP values are reported on the 100 year horizon; for details see reference [24]. 62  formation of the C2v conformer of CH2F2+) and to investigate the vibrational dynamics of the electronic ground state of the molecular cation. The narrow bandwidth (≲ 0.7 cm-1) and the tuneability of the extreme ultraviolet (XUV) laser light source of the experimental setup allow the resolution of individual vibrational bands, representing a first step towards an assignment of the vibrational structure. Vibrational resolution also enables the determination of an accurate value for the adiabatic ionisation energy of CH2F2. Exploiting the high resolution single photon excitation, we have also determined more accurate upper limits for the appearance energies of the H loss and the F loss ionic fragmentation channels from photoionisation efficiency (PIE) spectra. The extremely low lying H loss channel (in the vicinity of the CH2 stretching fundamental) raises the question of whether the PFI-ZEKE technique can be employed above the onset of fragmentation of the ion. While Hepburn and co-workers67 found a positive answer in the case of HBr, the situation appears to be different for polyatomic cationic fragments.  Based on ab initio calculations, Takeshita86 interpreted the progression of broad bands observed in the conventional photoelectron spectra of CH2F2 in terms of a polyad structure arising from an approximate 1:2:2 resonance of the symmetric CH2 stretch (ν1), CF2 stretch (ν2), and CH2 bend (ν3) fundamentals of the cation. While this also provided a consistent explanation of the total loss of vibrational structure upon deuteration,80 the low resolution spectra do not provide particularly stringent criteria to discriminate between different explanations. Moreover, those ab initio calculations, though qualitatively doubtless correct, were based on relatively modest levels of electronic structure theory (restricted Hartree–Fock with a basis set of double-ζ quality) and only considered totally symmetric vibrations.  In an attempt to clarify the vibrational assignment of the high resolution PFI-ZEKE photoelectron spectrum, we performed ab initio calculations on the MP2/aug-cc-pVQZ level of theory to derive harmonic vibrational transition wavenumbers and Franck-Condon factors for the photoionisation of CH2F2 including all nine vibrational modes. While the improved calculations confirm Takeshita’s interpretation of the broad unresolved vibrational structure in earlier photoelectron spectra,78-84 they still 63  prove insufficient to fully assign the vibrationally resolved PFI-ZEKE photoelectron spectrum. To compare with the experimental results, we also provide theoretical predictions in the complete basis set (CBS) limit of coupled-cluster theory (CCSD(T)) for the adiabatic ionisation energy and for the appearance potentials of the three lowest fragmentation channels, including the HF loss, which appears not to be observable by photoionisation.  3.2. Experimental The CH2F2 measurements were recorded using the experimental apparatus described in Chapter 2, in the configuration where the TOF chamber is attached directly to the sample injection chamber (see Section 2.1.5 and Figure 2.3). The distance between the room temperature nozzle (orifice diameter 1 mm, see Section 2.1.3.a) and the 1 mm diameter skimmer was kept at 30 mm. The sample was expanded from a mixture of 5% difluoromethane (Spectra Gases Inc., 5.0) in He (Praxair, 5.0) at a total pressure of 1 bar.  The PFI-ZEKE photoelectron spectra (see Section 2.3) were recorded with a DC discrimination field of +25 mV cm-1 (discrimination against prompt electrons) and a pulsed extraction field of ‒500 mV cm-1  applied 1 µs after the light pulse. A relatively high extraction pulse was used because the advantage of the gain in signal far outweighed the loss in resolution under the given experimental conditions. Note that this small loss in resolution does not limit the vibrational resolution. The XUV light was tuned in ~0.5 cm-1 increments and 40 laser shots were averaged for each data point. Each PFI-ZEKE trace shown in this Chapter is an average of three measurements with a moving average over five points. The PIE spectra (see Section 2.2) were recorded with a pulsed field of +165 V cm-1 applied 0.5 µs after light excitation.  The PFI-ZEKE photoelectron spectra presented in Section 3.4 are a compilation of measurements with different laser dyes in the tuneable laser ν2. XUV light intensity fluctuations which complicate access to the entire photon energy range used to collect the CH2F2 spectra have been described in Section 2.1.2.c. 64  The use of different noble gases (xenon and krypton), multiple noble gas resonances as well as multiple laser dyes to circumvent these problems have been discussed there.  3.3. Ab initio Calculations Electronic structure calculations were performed with the Gaussian program package96 using Dunning’s correlation consistent polarised valence basis sets with up to hextuple-ζ quality augmented by diffuse functions (aug-cc-pV6Z).97 Electron correlation was accounted for by 2nd order Møller–Plesset perturbation theory (MP2) or by coupled-cluster theory (CCSD(T)) including single, double, and (noniteratively) triple excitations with respect to Hartree–Fock wavefunctions. The equilibrium geometries, relative energies and harmonic vibrational wavenumbers were determined on the MP2/aug-cc-pVQZ level for CH2F2, its cation and relevant fragments thereof in their respective electronic ground states. Unrestricted wavefunctions of doublet species show small contaminations from higher multiplicities,  〈Ŝ2〉 ‒ ¾ ≈ 0.01. Projection onto the doublet space yields electronic energies (PMP2) typically 0.05 - 0.1 eV below the unprojected values (UMP2). For CH2F2 and its cation calculations with restricted open shell reference functions were also performed, which yielded energies (ROMP2) almost exactly halfway between the unprojected and projected values obtained with unrestricted reference functions. These energy shifts proved to be virtually independent of the basis size.  Geometric parameters and harmonic zero point energies were already converged with the quadruple-ζ basis (changes from triple-ζ: bond lengths 0.1 – 0.3 pm, angles 0.1°, zero point energies 10 cm-1). Using the MP2/aug-cc-pVQZ geometries, MP2 energies for up to hextuple-ζ basis sets were computed. The effect on the IE is a small but systematic increase indicating a rather slow convergence, while dissociation energies appear to be converged within about 1% with the quadruple-ζ basis. To assess the effect of higher order correlation on the ionisation potential, single point CCSD(T) calculations were performed for unrestricted Hartree–Fock determinants with aug-cc-pVXZ basis sets (X = 4 and 5). Compared with the 65  UMP2 results there are only marginal changes of the IE by a few meV. This error would be comparable to anharmonic corrections of the vibrational zero point energy.98 Analogous calculations with restricted open shell Hartree–Fock determinants (ROCCSD(T)) agree with unrestricted CCSD(T) results within a few meV. Very similar behaviour was found for the fragment AEs. Electronic energies were extrapolated to the complete basis set (CBS) limit following Halkier et al.99  ௠ ‫ܧ‬஼஻ௌ ൌ  ሺ‫ܧ‬௑௠ െ ‫ܧ‬௑ுி ሻܺ ଷ െ ሺ‫ܧ‬௒௠ െ ‫ܧ‬௒ுி ሻܺ ଷ ுி ൅ ‫ܧ‬஼஻ௌ ܺଷ െ ܻଷ  Eqn 3.1  Here m stands for the treatment of electron correlation (MP2 or CCSD(T)), X and Y for the basis size ுி is the CBS limit of the Hartree–Fock energy. We used (aug-cc-pVXZ, here X = 4 and 5), and ‫ܧ‬஼஻ௌ  ுி ‫ܧ‬஼஻ௌ ൎ ‫଺ܧ‬ுி , which introduces errors of less than 1 meV. Comparing the various approaches we  consider MP2 electronic energies to be accurate within 0.05–0.1 eV, while CCSD(T) energies should be accurate to within 0.01 eV. Fragmentation energies were calculated as the energy difference between separate fragments and CH2F2+ (C2v) including harmonic zero point energy corrections. For the large bases employed we expect basis set superposition errors to be negligible. Harmonic frequencies were calculated at the MP2/aug-cc-pVQZ level.  Franck-Condon factors (FCF) were calculated in the harmonic approximation as the square overlap integrals ‫݊ۦ‬ଵ|݊ଶ ۧ between harmonic oscillator functions in terms of sets of coordinates q1 and q2 defined  by the MP2/aug-cc-pVQZ equilibrium geometries and harmonic force fields of CH2F2 and its cation, respectively. An adaptation of the approach of Malmqvist and Forsberg100 was employed to account for rotating Eckart reference frames.101 The FCF were then calculated by Gauss–Hermite quadrature in an auxiliary coordinate system q0.  ‫ݍ‬௞ ൌ ‫ܦ‬௞బ ‫ݍ‬଴ ൅ ܾ௞ with k ൌ 1, 2  66  Eqn 3.2  q0 was chosen so as to remove (in the limit of ‫ܦ‬௞బ ≈ const) exponential terms that would lead to infinite  Hermite expansions of ‫݊ۦ‬ଵ |݊ଶ ۧ in terms of q0. The structure of ‫ܦ‬௞బ and bk reflects the symmetry of the reference geometries involved, which is C2v in the case of both CH2F2 and its cation. The transformation in Eqn 3.2 is therefore block-diagonal in the irreducible representations of that point group, which is exploited to speed up the computation. Since the various coordinate systems refer to different Eckart frames, ‫ܦ‬௞బ generally depend on q0 and the transformation in Eqn 3.2 becomes non-linear.102 In the  present case the rotation between the Eckart systems vanishes by symmetry for q0 = 0 and remains small  for moderate amplitudes so that ‫ܦ‬௞బ ≈ constant and Eqn 3.2 reduces to the usual Duschinsky rotation. This approximation was checked and calculated FCF were generally found accurate to within better than 1%.  The use of different Eckart reference frames has also to be taken into account in the overlap integral over the Hermite polynomials ߰௡భ ሺ‫ݍ‬ଵ ሻ and ߰௡మ ሺ‫ݍ‬ଶ ሻ.  ‫݊ۦ‬ଵ|݊ଶ ۧ ൌ න ߰௡భ ߰௡మ ݃ଵିଵ/ସ ݃ଶିଵ/ସ ݃଴ାଵ/ଶ ݀‫ݍ‬଴  Eqn 3.3  Here gk are the Jacobian determinants associated with the transformation from space-fixed mass-weighted Cartesian coordinates to the normal coordinates qk in their respective rotating reference frames. In general gk do depend on the geometry (i.e. on q0), but again for moderate amplitudes it is found that gk ≈ constant  produces only negligible errors in the FCF. With the approximations ‫ܦ‬௞బ , ݃௞ ൎ constant the fact that the  ߰௡ೖ ሺ‫ݍ‬௞ ሻ have finite expansions in terms of Hermite polynomials in q0 can be further exploited so that the  Gauss–Hermite quadrature becomes exact for a finite number of points. A seven point quadrature was used for each dimension, which is exact for FCF involving up to a total of 13 quanta in the oscillators of a given symmetry of the neutral and the ion.  67  3.4. Results and Discussion 3.4.1. Ionisation energy and fragmentation 3.4.1.a Ionisation energy Figure 3.1 compares the PFI-ZEKE photoelectron spectrum of CH2F2 (upper trace) with its photoionisation efficiency spectrum (lower trace) in the region of the adiabatic ionisation energy. Note that the term adiabatic IE is used here for the formation of the chemically bound C2v conformer of CH2F2+  and not the possible lower energy conformer CHF+ ⋯ HF (see below) found in calculations (see Table 3.1  and reference [89]).  Figure 3.1 Upper trace: PFI-ZEKE photoelectron spectrum of CH2F2 in the region of the adiabatic ionisation energy (defined as the formation of the C2v conformer of CH2F2+). The electron signal increases from top to bottom (left scale). Lower trace: photoionisation efficiency spectrum in the same region. The ion signal increases from bottom to top (right scale). The dashed grey line marks the experimentally determined adiabatic IE.  68  Table 3.1 Adiabatic ionisation energy (IE) of CH2F2 (C2v conformer of CH2F2+) and appearance energies (AE) of fragment ions after single photon or electron excitation.  Experimental  Adiabatic IE (= IE of C2v conformer)  Theoretical  This work  Lit.  This work  Lit.  12.7252 ± 0.0009 eV (102636 ± 7 cm-1)  12.729 ± 0.001 eV81  12.748 eVa  12.79 eV89  12.70 eV79  12.78 eV91  12.74 ± 0.05 eV84 12.72 eV80 IE CHF+ ⋯ HF AE CHF2+ + H  12.72 eV92,93b  13.065 ± 0.003 eV (105375 ± 25 cm-1)  12.606 eVc  12.61 eV89  13.060 eVa  13.08 eV89  13.3 ± 1 eV93  13.339 eVa  13.34 eV89  14.7 ± 0.1 eV84  14.176 eVa  14.15 eV89  13.08 ± 0.03 eV84 13.11 eV92 13.14 ± 0.02 eV94 13.11 eV95 12.8 ± 1 eV93  AE CHF+ + HF AE CH2F+ + F  14.30 ± 0.06 eV (115300 ± 500 cm-1)  15.28 eV92 14.06 eV95 14.9 ± 1 eV93 AE CHF+ + H + F  17.7 eV92  19.217 eVa,d  18.2 ± 0.4 eV84 a b c  estimate for the CCSD(T) CBS limit.  Quoted as adiabatic IE, but possibly low energy conformer CHF+ ⋯ HF.  ROMP2 CBS limit. d Using the experimental value for the dissociation energy of HF (566.52 kJ mol-1, reference [103]) yields 19.210 eV.  69  The PFI-ZEKE photoelectron spectrum in Figure 3.1 shows a single strong band with a maximum in electron signal at 102633 cm-1 and a full width at half maximum of 15 cm-1. The onset of the molecular ion signal in the photoionisation spectrum in this energy range confirms that the electron signal in the PFI-ZEKE spectrum comes from the field ionisation of Rydberg states of CH2F2. The lack of signal in the ZEKE spectrum as well as in the photoionisation spectrum at frequencies well below 102600 cm-1 (not shown) suggests that the ZEKE band in Figure 3.1 can indeed be assigned to the adiabatic IE of the C2v conformer. Moreover, the relatively favourable Franck-Condon factor (0.006, see Section 3.4.2) in the region of the IE of the C2v conformer and the vanishing Franck-Condon factor to the possible lower  energy conformer CHF+ ⋯ HF (vide infra) found in the calculations provide very strong evidence for this  assignment.  The main uncertainty in the determination of the adiabatic IE from the PFI-ZEKE spectrum in Figure 3.1 comes from the unresolved rotational structure. To account for that, we determined the adiabatic IE from the band maximum with an uncertainty that corresponds to the half width at half maximum (7 cm-1). The lowering of the IE (band maximum) due to field ionisation effects caused by the pulsed extraction field ி  (~0.5 V cm-1) of 4ට௏ ୡ୫షభ cmିଵ ൎ 3 cmିଵ (see Section 2.3) is taken into account by increasing the value of the IE by the same amount. This leads to a value of the adiabatic IE of CH2F2 (C2v conformer) of 102636 ± 7 cm-1 (12.7252 ± 0.0009 eV).  This value agrees with previous experimental results (see Table 3.1) and to our knowledge is the most precise so far. The higher value of 12.729 ± 0.001 eV previously reported by Pradeep and Shirley was recorded using a photoelectron spectrometer with a resolution of 13 meV.81 Taking into account their experimental resolution, this value is consistent with the one reported here. The much lower value of 12.6 eV reported in electron ionisation studies92,93 was quoted as the adiabatic IE, but might also indicate  70  the formation of the low energy conformer CHF+ ⋯ HF (see below). In addition, reference [93] quotes a large experimental error of ± 1 eV for this value.  The experimental result also agrees well with our theoretical predictions (Table 3.1). With the data given in Table 3.2, an unrestricted MP2 calculation yields an adiabatic IE of 12.746 eV for a hextuple-ζ basis  set. As a result of slight spin contamination 〈Ŝ2〉 - ¾ ≈ 0.014 this value overestimates the ionisation energy. Spin projection of the unrestricted wavefunction reduces the value to 12.676 eV, while a MP2 calculation with an open shell restricted wavefunction yields 12.710 eV. Extrapolation to the CBS limit following the approach of Halkier et al.99 yields values of 12.690 eV and 12.723 eV, respectively. Unrestricted CCSD(T) calculations yield 12.719 eV and 12.732 eV for quadruple and quintuple-ζ bases, respectively, which extrapolates to a CBS limit of 12.750 eV. The corresponding ROCCSD(T) value is 12.747 eV. Taking the last two values as boundaries we arrived at 12.748 ± 0.002 eV as our best theoretical estimate for the adiabatic ionisation energy of CH2F2 (Table 3.1). This result lies within 2 kJmol-1 (0.02 eV) of the experimental value and is thus significantly closer than previous predictions obtained by G3 extrapolation methods.89,91 Anharmonic corrections to the vibrational zero point energy tend to reduce the IE since the cation is much less rigid than the neutral of difluoromethane. We estimate a reduction by about 0.01 eV.98  In line with earlier theoretical studies,89 the current calculations predict a lower lying ionic species  CHF+ ⋯ HF mentioned above. Its structure is proposed to be a CHF+ radical cation intermolecularly  bound to an HF molecule. Due to the major geometrical change with respect to the neutral ground state structure the calculated Franck-Condon factor for this transition is zero within our numerical accuracy (≤ 10-12). Therefore, this species cannot be observed in spectra obtained in this work. However the appearance potentials of the molecular ion reported by Torres et al.93 and by Lifshitz and Long92 of 12.6 eV using electron ionisation seem to be consistent with the energy calculated for this conformer  (see Table 3.1). The different mechanism of electron ionisation might allow the formation of CHF+ ⋯ HF. 71  A similar discrepancy between fragmentation after photoionisation and electron ionisation in the case of the H loss channel from CH3Cl+ was described by Baer et al. (reference [104]). As far as we are aware a complete explanation was never presented.  Table 3.2 Equilibrium geometry (C2v) and harmonic wavenumbers of CH2F2 and its cation calculated at the MP2(FC)/aug-cc-pVQZ level of theory using unrestricted wave function for the ion. Changes relative to MP2(FC)/aug-cc-pVTZ are given in parentheses in terms of the least significant digits. Within a given irreducible representation modes are numbered in order of decreasing wavenumber. reference [86] are given in columns 4 and 5 for comparison.  r(C-H) / pm r(C-F) / pm HCH / ° FCF / ° ω1 (a1) / cm-1 ω2 (a1) / cm-1 ω3 (a1) / cm-1 ω4 (a1) / cm-1 ω5 (a2) / cm-1 ω6 (b1) / cm-1 ω7 (b1) / cm-1 ω8 (b2) / cm-1 ω9 (b2)/ cm-1  CH2F2 a  CH2F2+ a  CH2F2 b  CH2F2+ b  108.36 (-9) 135.65 (-28) 113.67(+8) 108.36(-4) 3125 (-1) 1562 (-4) 1132 (+3) 533 (+3) 1293 (+5) 3212 (+2) 1204 (+5) 1476 (+1) 1110 (+0)  117.24 (-18) 126.88 (-35) 85.06 (-28) 116.81 (+4) 2528 (+10) 1292 (+5) 1062 (+7) 605 (+5) 1001 (+1) 2122 (+8) 627 (+5) 1498 (+2) 1084 (+3)  108.7 133.5 112.45 104.47 3258 1659 1224 580  118.5 124.6 77.66 117.00 2650 1412 1288 659  a  This work. Vibrational mode assignments for CH2F2+: (1) CH2-stretch, (2) CF2-stretch, (3) CH2-bend, (4) CF2-bend, (5) CH2-twist, (6) CH2-stretch, (7) CH2-rock, (8) CF2-stretch, (9) CH2-wag b  HF/MIDI-3 (double-ζ quality) results from reference [86].  72  Results from  3.4.1.b Fragmentation channels The appearance energies of ionic fragments discussed in this section should be treated as upper limits. Fragment ions can possibly be formed at lower energies than the ones reported, but with yields below our detection limit.  3.4.1.b.i  H loss  The inset in Fig. 3.2 shows that the TOF resolution allows the molecular ion (m/z = 52) and the fragment ion (m/z = 51, CHF2+) to be clearly distinguished. The onset of the fragmentation process lowest in energy, the loss of a hydrogen atom, is shown in Fig. 3.2. The relative yield of the fragment ion, i.e. the intensity of the m/z = 51 signal divided by the sum of the intensities of the m/z = 51 and m/z = 52 signals, is plotted against the excitation wavenumber.  Figure 3.2 Energy dependence of the relative yield of the CHF2+ fragment ion in the region of its appearance energy. Inset: Time-of-flight spectrum of the molecular ion (CH2F2+) and the H loss fragment (CHF2+) recorded after ionisation with a much higher XUV photon energy of 115235 cm-1.  73  The curve shows a rather sharp onset at 105375 cm-1, marked as the appearance energy with a dashed line. The uncertainty is estimated to be ± 25 cm-1 (grey area). Compared with experimental literature values (see Table 3.1) the appearance energy determined in this work is significantly lower (several kJmol-1) ‒ clearly a chemically significant difference. The estimated uncertainty is an order of magnitude smaller than for the most precise value reported so far. The experimental upper limit of 2739 ± 25 cm-1 for the lowest dissociation energy of CH2F2+ (see Table 3.1) compares well with our theoretical prediction of 2510 cm-1 (Table 3.3). Anharmonic corrections are expected to increase this value to about 2600 cm-1.98  Table 3.3 Fragmentation energies relative to CH2F2+ including zero point energies (D0). Electronic energies are CBS limits99 of CCSD(T)-aug-cc-pVXZ calculations for X = 4 and 5. The changes relative to X = 5 are given in parentheses in terms of the least significant digits. Vibrational zero point energies are included in the harmonic approximation. Equilibrium geometries and harmonic wavenumbers were calculated at the MP2/aug-cc-pVQZ level of theory.  D0 / cm−1 -929 (-147)a 2510 (+11) 4751 (+60) 11499 (+86)  CH2F2+ → CHF+ · · · HF CH2F2+ → CHF2+ + H CH2F2+ → CHF+ + HF CH2F2+ → CH2F+ + F a  3.4.1.b.ii  RO-MP2 CBS limit.  F loss  The loss of a fluorine radical, the second lowest fragmentation channel observed in this study, appears at significantly higher energies. The AE is determined to be 115300 ± 500 cm-1 or 14.30 ± 0.06 eV (relative ion yield not shown). The uncertainty of the spectral position of the onset of the F loss is higher than that for the H loss because the increase in the yield of the CH2F+ fragment ion with increasing photon energy  74  is much more gradual. Apart from reference [95], the AE determined in this work is again significantly lower than previously reported experimental values (see Table 3.1). The observed threshold for fluorine ions still exceeds the theoretical predictions by about 0.1 eV or 10 kJ mol-1, which is consistent with the fact that the observed thresholds constitute upper boundaries. 150 kJmol-1 above the lowest fragmentation channel, the F loss competes with a much faster H loss. Apparently it takes several kJ mol-1 excess energy for the F atom production to reach our detection limit.  3.4.1.b.iii  HF loss and H + F loss  Previous electron ionisation studies by Torres et al.93 report the onset of the fragmentation of CH2F2 into a CHF+ radical cation and a HF molecule at 13.3 eV. This agrees perfectly with our CCSD(T) prediction of 13.339 eV (Table 3.1). He and Wang89 obtained a similar result if one compares the energy difference between the neutral ground state and the ground state energy of CHF+ + HF (13.34 eV, see Table 3.1). Note, however, that their adiabatic IE is 0.065 eV higher than the present experimental value, while the current theoretical prediction lies only 0.022 eV above it.  The formation of CHF+ was not observed in the expected energy range in the present study. The  mechanism proposed by He and Wang involves CHF+ ⋯ HF as an intermediate, which is separated from  the C2v form of CH2F2+ by a barrier of 1.12 eV.89 This species has a calculated energy relative to the CH2F2 ground state of 12.6 eV, but it is inaccessible by single photon photoionisation because of a vanishing Franck-Condon factor (see above). This restriction may not hold for electron ionisation where  the CHF+ ⋯ HF seems more likely to form (see Section 3.4.1.a), which would explain why the  fragmentation CHF+ ⋯ HF → CHF+ + HF might have been observed by electron ionisation, but not by  single-photon ionisation. Two further values for the AP of CHF+ were reported in the literature.  Lifshitz and Long92 determined a value of 17.7 eV for the AP of CHF+ by electron ionisation and Seccombe et al. reported the onset of the CHF+ signal using photoionisation at a similarly high energy 75  (18.2 ± 0.6 eV), which they interpreted as HF loss. Considering the high energies and the fact that the second study used photoionisation it is believed that two sequential bond fissures leading to CHF+ + F + H are more likely to be the mechanism of the observed fragmentation (Table 3.1). This assignment is also supported by the present calculations.  3.4.2. PFI-ZEKE photoelectron spectrum Figure 3.3 shows the PFI-ZEKE photoelectron spectrum of CH2F2 from its adiabatic ionisation energy (formation of C2v CH2F2+) to the onset of the first dissociation channel (H loss). Shown are the regions in which vibrational transitions of the CH2F2+ cation were observed. The spectrum is assembled from multiple segments measured with different xenon resonances and laser dyes (see Sections 2.1.2.b and 2.1.2.c), and each segment is an average of three measurements with a running average over five points applied.  No ZEKE electron signal was observed above the onset of the first fragmentation channel (indicated by the dashed line). Exciting a molecule to a Rydberg state above the lowest fragmentation channel of its corresponding ion leaves the core with sufficient energy to fragment. Whether ZEKE electrons can still be recorded depends on the timescale of the fragmentation and the stability of the Rydberg states. Earlier work by Hepburn and co-workers67 with HBr demonstrated that in some cases it is possible to record PFIZEKE photoelectron spectra above the fragmentation onset. Hepburn and co-workers postulated that the fragmentation of the ionic core does not necessarily affect the Rydberg electron, which is still available for pulsed field ionisation a few microseconds later. However, they explained the width of the band which they recorded above the fragmentation onset as being broadened by the short lifetime of the fragmenting state. In the case of CH2F2, we could not observe vibrational bands above the H loss onset. We can only speculate about the reasons. The fragmentation process might be sufficiently fast to broaden the bands  76  Figure 3.3 Upper trace: Experimental PFI-ZEKE photoelectron spectrum of CH2F2 between the adiabatic IE and the onset of the lowest ionic fragmentation (marked by the dashed line). The electron signal increases from top to bottom. Bottom trace: Calculated photoelectron spectrum of CH2F2. The peak heights correspond to the harmonic Franck-Condon factors.  such that the electron signal at a certain frequency is below our detection limit. This would be possible significantly above the dissociation limit, e.g. for the 3ν3 overtone (see Table 3.5). Closer to the dissociation limit our harmonic calculations predict only very weak transitions. Here the fluctuations in the XUV light intensity discussed in Section 2.1.2.c become increasingly hard to avoid, which makes the observation of very weak or broad signals particularly difficult. Another explanation for the absence of ZEKE signal above the dissociation limit might be an insufficient number of Rydberg electrons that  77  survive the fragmentation. In contrast to fragmenting Rydberg states of HBr, which result in a Rydberg atom,67 the dissociation of the CH2F2+ ionic core produces a polyatomic Rydberg molecule which is generally more prone to electron loss than a Rydberg atom.  The PFI-ZEKE photoelectron spectrum in Figure 3.3 is in overall agreement with the previously reported low resolution photoelectron spectra,78-84 but only the high resolution afforded by the PFI-ZEKE technique unveils the details of the vibrational fine structure. The spectrum is not simply a regular vibrational progression as the low resolution photoelectron spectra might suggest, but rather a complex structure of groups of near degenerate vibrational transitions (“polyads”).  A list of the observed  vibrational transitions is provided in Table 3.4. In addition to the strong transitions at 102636 cm-1 (ground state, 0–0 transition), around 103700 cm-1 (1st polyad), and around 105000 cm-1 (2nd polyad) several weak bands appear in the region between 104300 cm-1 and 104600 cm-1.  The 0–0 transition and the polyads in our high resolution spectrum coincide with the first three of a progression of broad bands observed in previous photoelectron spectra. Several attempts had been made to assign that progression.78-81 The increasing broadening towards higher excitations excluded a single progression of overtones, so a polyad structure arising from near degenerate vibrational modes was proposed early on. The complete loss even of coarse vibrational structure in conventional photoelectron spectra of CD2F280 indicated the direct involvement of CH modes in the progression observed for CH2F2. The frequency shift upon deuteration would lift the incidental near-degeneracy required to produce the regular coarse structure. Potts et al.78 assigned the polyad structure in the CH2F2 photoelectron spectrum to a CH2 bending mode (ν3). Pullen et al.79 stated that the polyads may be related to the CF2 asymmetric stretch mode (ν8), the CH2 rocking mode (ν7), the CH2 twist mode (ν5), and the symmetric CF2 stretch (ν2). Brundle et al.80 agreed with the assignment made by Potts et al., but proposed a possible vibrational mode degeneracy in light of the CD2F2 data. Pradeep and Shirley81 proposed a near-degeneracy of ν2, ν3, and the overtone of the CF2 bending mode (2ν4). Note that we number modes of a given irreducible representation 78  in the order of decreasing wavenumbers. When a different numbering scheme was used in the literature we adjusted it to conform to Table 3.2.  Table 3.4 List of the experimentally observed band positions (values reported are 3 cm−1 higher than their respective peak centres to compensate for the lowering of the IE due to the pulsed electric field) and band positions relative to the adiabatic ionisation energy. Intensity assessment should be treated as a guideline only due to fluctuations in the light intensity as discussed in Section 2.1.2.c.  Abs. ν~ / cm−1  ν~ rel. to IE / cm  Intensity  102636 103605 103773 103882 104305* 104370* 104401* 104453* 104521* 104569* 104736 104849 104893 104917 105036 105127  Adiabatic IE 969 1137 1246 1669 1734 1765 1817 1885 1933 2100 2213 2257 2281 2400 2491  Strong Strong Strong Strong Medium Weak Weak Weak Weak Weak Strong Weak (shoulder) Strong Medium (shoulder) Strong Medium  *  −1  Peaks between the first and second polyad  In 1990, Takeshita86 finally provided a consistent explanation for the low resolution photoelectron spectra. With harmonic vibrational transition wavenumbers and Franck-Condon factors derived from RHF calculations with a double-ζ basis set he reproduced both the coarse structure observed for CH2F2 and its loss upon deuteration. According to these results, the polyad structure in the photoelectron spectra of difluoromethane arises from the near 1 : 2 : 2 resonance of the symmetric CH2 stretch (ν1), 79  CF2 stretch (ν2), and CH2 bend (ν3) modes of CH2F2+. Takeshita’s model, however, predicts two bands in the range of the 1st polyad around 1300–1400 cm-1, which is clearly at odds with the high resolution ZEKE spectrum (three strong transitions in the range 970 – 1250 cm-1, see Figure 3.3). The relatively large errors in the harmonic wavenumbers (see Table 3.2) can only explain part of the discrepancy. The additional bands observed in the ZEKE spectrum might indicate contributions from CF2 bend (ν4) overtones to the polyad structure as suggested by Pradeep and Shirley, or even contributions from nontotally symmetric modes (proposed by Pullen et al.), which Takeshita did not consider in his calculations. With only the ground state of the neutral populated in the jet expansion the Franck-Condon approximation only allows transitions to totally symmetric levels of the ion, but these may well include combinations and overtones of non-totally symmetric modes.  At least on a harmonic level, our high level ab initio calculations (MP2/aug-cc-pVQZ) do not lend support to either explanation. The calculated harmonic photoelectron spectrum is shown as a stick spectrum in the bottom trace of Figure 3.3. Calculated harmonic vibrational wavenumbers of the cation from the current work are listed in Table 3.5 together with assignments and Franck-Condon factors for the most prominent transitions. The calculated harmonic spectrum reproduces the overall polyad structure and confirms the dominant role of the ν2, ν3 near-degeneracy. As proposed by Takeshita, levels with the same value for 2 ν1 + ν2 + ν3 (here ν is the number of quanta) indeed give rise to polyads of near resonant transitions in the range where strong ZEKE signals are observed, but a harmonic model is clearly inadequate to assign the newly resolved vibrational fine structure. Even with all non-totally symmetric modes included, fewer transitions are calculated with significant Franck-Condon factors than there are peaks in the experimental spectrum. Barring a breakdown of the Franck-Condon principle, such as the pseudo-breakdown observed, e.g., in PFI-ZEKE photoelectron spectra of the dimers or argon and krypton,105,106 this leaves strong anharmonic resonances as the only possible explanation. Pronounced anharmonic effects are indeed to be expected in view of the proximity of the first ionic fragmentation channel. Anharmonicities will shift the band positions, while new bands may arise from strong resonant 80  interactions. Anharmonic calculations are clearly necessary for a detailed analysis of the vibrational fine structure observed in the PFI-ZEKE spectrum of difluoromethane, which in turn provides access to the underlying dynamics of its molecular cation. A full-dimensional anharmonic vibrational analysis of the difluoromethane cation has been performed and is summarised below in Section 3.5.  Table 3.5 Calculated band positions relative to the adiabatic ionisation energy, calculated Franck-Condon factors, and assignment of the principal bands of the calculated vibrational structure of the photoelectron spectrum of CH2F2. See Table 3.6 for a revision of these assignments based on the anharmonic analysis.  mode  ν~ rel. to IE / cm  F-C Factor  assignment  υ3 υ2 2υ3 υ3 + 2υ7 υ2 + υ3 υ1 2υ2 2υ3 + υ4 υ2 + υ3 + υ4 3υ3  0 1062 1292 2124 2316 2355 2528 2585 2730 2960 3187  0.0063 0.0176 0.0090 0.0212 0.0014 0.0254 0.0051 0.0071 0.0010 0.0010 0.0140  adiabatic ionisation energy CH2 sym. bend CF2 sym. stretch  −1  CH2 sym. stretch  3.5. Anharmonic Analysis of the PFI-ZEKE Photoelectron Spectrum of CH2F2 A full-dimensional anharmonic vibrational analysis of the PFI-ZEKE photoelectron spectrum of difluoromethane was subsequently undertaken by Luckhaus et al. in our group (reference [98]). Only an abridged overview of the results obtained will be provided here in the interest of integrity. The theoretical analysis involved the construction of nine-dimensional ab initio potential functions complete up to fivebody terms directly from ab initio calculations using Møller-Plesset and coupled cluster theory together with up quadruple-ζ basis sets (MP2(CCSD(T)) (5B//4B)). Anharmonic vibrational calculations were then  81  performed with a grid-based technique (see reference [98] for details). As expected based on the very low first ionic fragmentation channel, pervasive anharmonic resonances in the vibrational dynamics of CH2F2+ involving strong interactions between both symmetric and non-symmetric modes do in fact dominate the PFI-ZEKE photoelectron spectrum.  The calculated anharmonic spectrum is shown in Figure 3.4, compared to the previously presented harmonic and experimental spectra. Agreement between the anharmonic and experimental spectra is remarkably good. Unlike the harmonic calculations, the anharmonic analysis shows three peaks in the region of the 1st polyad, all three in close agreement with the experimental spectrum. At higher energies, closer to the dissociation limit, the spectra become more complicated and the agreement somewhat deteriorates, however the 5 principal peaks of the 2nd polyad are still reproduced well. Transitions observed in the PFI-ZEKE photoelectron spectrum and their suggested assignments based on the anharmonic analysis are listed in Table 3.6.  The assignments are given in terms of the leading contributions of harmonic product basis functions to the corresponding eigenfunctions (right-most column, Table 3.6). Strongly resonant interactions between both symmetric and non-totally symmetric modes (primarily overtones of the CH2-rocking mode (ν7) and overtones of the CH2-twist mode (ν5)) have significant contributions to the intensity observed in the spectrum. The strong 1 : 2 Fermi resonance between the CH2-bend (ν3) and the CH2-rock (ν7) plays a leading role in the 1st polyad and has significant contributions in the 2nd polyad as well. The 2nd polyad is characterised by extremely anharmonic transitions which have the character of many different vibrational modes, overtones and combination bands (vide infra).  The assignments confirm the leading role of the symmetric CF2 stretch (ν2) and CH2 bend (ν3) modes in the observed progression as proposed by Takeshita,86 however the role of the CH2 stretch (ν1) cannot be confirmed. The CH2 stretch fundamental excitation does not appear to survive the onset of ionic 82  Figure 3.4 The measured PFI-ZEKE photoelectron spectrum compared with harmonic and anharmonic predictions. 83  fragmentation (H loss), which dominates the vibrational dynamics at energies over 2000 cm-1 above the IE. Pervasive state mixing is observed – with increasing energy eigenfunctions become more ‘dilute’ so that assignments in terms of overtones and combination tones start to lose their meaning. This effect is very pronounced in the case of the symmetric CH2-stretch fundamental (ν1), which has a largest single contribution of the corresponding basis function to any eigenfunction of only 21%. The eigenvalue in this case is 1936 cm-1, about 500 cm-1 below the harmonic value. This phenomenon is the spectroscopic reflection of the onset of dissociation, which can be roughly described as a combination of CH2-rocking (ν7) with the CH2-stretch (ν1, ν6) motions.  Within experimental uncertainties, the anharmonic analysis of the spectrum not only doesn’t indicate the breakdown, but instead confirms the validity of the Franck-Condon approximation because the calculated Franck-Condon factors match the intensities observed in the experimental spectrum fairly well. It should be noted that the confidence level regarding relative peak intensities in the experimental PFI-ZEKE spectrum is rather low due to the light intensity fluctuations described in Section 2.1.2.c. The close agreement between experiment and theory also serves to prove that the PFI-ZEKE photoelectron spectrum does indeed originate from CH2F2+ and is not a product of autoionisation signals or other spurious effects.  The anharmonic calculations predict an intensity gap of about 500 cm-1 above the onset of the H loss channel in the PFI-ZEKE spectrum. This is consistent with the fact that no signal was observed in this  ► Table 3.6 Vibrational energy levels of CH2F2+ relative to the zero-point level of the C2v minimum. Experimental values are band positions observed in the PFI-ZEKE photoelectron spectrum relative to the 0-0 transition (adiabatic IE) at 102636 cm-1. Calculated transition wavenumbers and Franck-Condon factors (FCF) are derived from the 5-body expansion of the UMP2/aug-cc-pVTZ potential with up to 4-body CCSD(T)/aug-cc-pVQZ corrections. 84  PFI-ZEKE -1  (cm ) a1  ZPE  b2  a  10 ⨯ FCF  Assignment b  5683  2.2  ν0 (92)  597  0.2  ν4 (92)  -1  3  (cm )  969  s  959  3.7  ν3 (49); 2ν7 (32)  1137  s  1131  3.0  2ν7 (45); ν3 (40)  1246  s  1251  3.6  ν2 (82); 2ν2 (6)  1564  w  1559  0.2  ν3+ν4 (52); ν4 + 2ν7 (30)  1669  m  1734  w  1732  0.3  ν4+2ν7 (48); ν3 + ν4 (37)  1765  w  1817  w  1809  1.6  ν3+2ν7 (26); 4ν7 (10); 2ν3 + 2ν7 (9)  1885  w  1933  w  1936  1.9  ν6+ν7 (23); ν1 (21); 2ν5 (9)  2100  s  2078  5.0  2ν3 (52); 2ν5 (10); 4ν7 (8)  2213  w(sh)  2213  3.8  ν2 + ν3 (41); ν2 + 2ν7 (24); ν3 + 2ν7 (6)  2253  5.3  ν3 + 2ν7 (28); 4ν7 (14); ν2 + ν3 (12)  2257  s  2388  4.8  ν2+2ν7 (39); ν2+ ν3 (24); 2ν3 (5)  2281  m(sh)  2494  2.7  2ν2 (59); 3ν2 (9); ν2 + 2ν7 (9)  2400  s  2491  m  a2 b1  rel. intensity  UMP2//CCSD(T)  a  2854  c  1255  c  1408  c  940  ν5 (91)  523  ν7 (88)  1661  3ν7 (26); ν3 + ν7 (22); ν6 (14)  1761  ν6 (31); 3ν7 (21); ν2 + ν7 (15)  1811  ν2 + ν7 (52); ν6 (21)  1045  ν9 (89)  1406  ν8 (63); ν5 + ν7 (23)  1491  ν5 + ν7 (60); ν8 (25)  Relative intensity: s = strong, m = medium, w = weak, sh = shoulder  b  a1: ν1 = CH2 stretch, ν2 = CF2 stretch, ν3 = CH2 bend, ν4 = CF2 bend. a2: ν5 = CH2 twist. b1: ν6 = CH2 stretch, ν7 = CH2 rock. b2: ν8 = CF2 stretch, ν9 = CH2 wag Leading contributions in percent of product basis functions are given in parantheses. c  Assignments of ν5, ν6, and ν9 in Ar matrix IR spectra (reference [107])  85  energy range in the experimental study. However, this leaves open the possibility of the existence of longlived high-lying molecular Rydberg states of difluoromethane within a few hundred wavenumbers of the dissociation threshold, which are not observed in the PFI-ZEKE spectrum because of a zero FranckCondon factor for the transition to the cationic state. All transitions more than 500 cm-1 above the onset of the H-loss channel likely involve cationic states with sufficiently short lifetimes that the PFI-ZEKE electron signal would be broadened into being below our detection limit (in this energy range worsened due to XUV intensity fluctuations, see Section 2.1.2.c).  3.6. Summary The PFI-ZEKE photoelectron spectrum of difluoromethane for the first time unveils the vibrational fine structure of the broad bands previously observed in conventional photoelectron spectra. The PFI-ZEKE spectrum was recorded from the adiabatic ionisation energy (formation of the C2v conformer of CH2F2+) to the onset of the first ionic fragmentation channel, the H loss. No ZEKE signal was observed above the H loss channel. Values of 102636 ± 7 cm-1 for the adiabatic ionisation energy, 105375 ± 25 cm-1 for the fragmentation of the ion by H loss, and 115300 ± 500 cm-1 for the fragmentation by F loss are reported. Fragmentation yielding an HF fragment could not be observed, despite previous evidence by electron ionisation studies. The formation of CHF+ presumably proceeds via a CHF+ ⋯ HF intermediate, which is inaccessible to single-photon ionisation, but apparently much more readily formed by electron ionisation.  Harmonic calculations of the photoelectron spectrum of difluoromethane were performed in an attempt to analyse the fine structure of the PFI-ZEKE photoelectron spectrum. These calculations confirm Takeshita’s model86 where the polyad structure arises from the near-degeneracy of the symmetric CF2 stretch (ν2) and CH2 bend (ν3) modes, and of their overtones with the symmetric CH2 stretching (ν1) vibration. While a significant participation of other modes can be ruled out on a harmonic level, a detailed analysis of the vibrational structure is not possible without taking anharmonic contributions into account.  86  Their effect on the PFI-ZEKE spectrum is strong for difluoromethane, whose potential supports only a modest number of bound states below its first dissociation limit in the vicinity of the CH2 stretching fundamental. Full-dimensional anharmonic calculations of the photoelectron spectrum were subsequently carried out and are briefly presented in Section 3.5.98  The anharmonic calculations do indeed confirm that pervasive anharmonic resonances dominate the vibrational dynamics of CH2F2+ and that the real picture is very different from that suggested by the harmonic model. The symmetric CF2 stretch (ν2) and CH2 bend (ν3) modes are confirmed to play a dominant role in the spectrum, however their systematic resonance with the symmetric CH2-stretch (ν1) cannot be confirmed. The CH2-stretch fundamental excitation does not survive the onset of dissociation into H + CHF2+, which completely dominates the vibrational dynamics above 2000 cm-1. Peaks observed above 2000 cm-1 are shown to be of highly mixed character, with contributions from many vibrational modes, overtones and combination bands to each peak. The close agreement between the theoretical and experimental spectra negates the violation of the Franck-Condon approximation, and proves the peaks observed in the PFI-ZEKE photoelectron spectrum to indeed be due to CH2F2+.  87  4. PFI-ZEKE Photoelectron Spectrum of Acetic Acid Acetic acid (CH3COOH) (AA) is one of the most abundant organic acids in the Earth’s atmosphere, along with formic acid (HCOOH).8 Organic acids are believed to affect the H2SO4-H2O nucleation rate, which is the primary means of aerosol particle formation from the gas phase.8,108 The nucleation rate affects the concentration of aerosol particles in the atmosphere, which have a very significant and very poorly understood effect on the radiative balance of the Earth (see also Chapter 6). In this and the following chapters, a detailed study of the acetic acid monomer and its clusters of increasing size, up to the nanometer size range, is presented. The present chapter is devoted to the AA monomer and its cation (CH3COOH+) (AAC).  Interest in acetic acid and the acetic acid cation exists also in astrobiology, due to indications that AA is one of the building blocks of life.7 Glycine, for example, is known to be formed from ammonia and AA. Since AA is found in the interstellar medium and in meteorites, it could have been brought to Earth by asteroids, comets, or meteorites. In unscreened regions of space it is exposed to ultraviolet radiation, which in the extreme ultraviolet (XUV) region leads to ionisation and fragmentation. While the spectroscopic properties of carboxylic acids have been investigated extensively,109-112 studies on the spectroscopy and photochemistry of their cations are comparatively limited113-117 in spite of their essential role in understanding astrochemistry and thus the origin of life.  The value of the first adiabatic ionisation energy (IE) of AA has been debated for more than 40 years. Reported values scatter between 10.35 and 10.70 eV, i.e. over a range of more than 2500 cm−1 (see references [113, 115, 117] and references therein). Other important issues with implications for the reaction kinetics of AAC concern the dynamics of its low frequency modes, especially the CH3 torsion (Figure 4.1) with its unknown potential barrier (H) and tunnelling efficiency (Figure 4.2). In this work we employ pulsed field ionisation zero kinetic energy (PFI-ZEKE) photoelectron spectroscopy  88  (see Section 2.3, references [9,118-120] and references therein) in combination with supersonic cooling to address these open questions.  Figure 4.1 The CH3 torsion mode (ν18) of acetic acid.  Figure 4.2 Calculated potentials for the CH3 torsion (ν18) of AA and AAC with corresponding energy levels (labels ν and ν+, respectively, and C3v tunnelling symmetry labels in order of increasing energy).  89  The determination of the IE of AA and the torsional dynamics of AAC have turned out to be an experimental challenge. Photoelectron spectroscopy is the method of choice, but the resolution of spectrometers is often limited, while the extraordinary stability of the AA dimer further complicates the situation. The monomer is the dominant species only at high temperatures and low pressures, which can be realised in low pressure cells or effusive beams. Under such conditions, however, hot bands and thermally broadened rotational contours make the accurate determination of the IE and the torsional dynamics impossible. Figure 4.3(b) shows a simulation of the photoelectron spectrum of AA with the highest resolution yet reported.113 The observed bands are structureless and broad due to hot bands and broad rotational structure. No torsional structure is observed and the position of the IE remains unclear.  To tackle this problem, we employ a custom-built PFI-ZEKE photoelectron spectrometer (Chapter 2) with a supersonic expansion of 1.7% AA seeded in helium at a total pressure of 1 bar. This approach allows us to measure the photoelectron spectra of cold AA monomers selectively, very sensitively, and with high resolution (about 0.7 cm−1). The selectivity in PFI-ZEKE spectroscopy is achieved by laser excitation of very high lying Rydberg states that converge to a rovibrational level of AAC, which are field ionised (0.19 Vcm-1) after a time delay (2 µs). The time delay, together with a weak DC discrimination field (0.09 Vcm-1), ensures that prompt ions and electrons (from AA itself and its oligomers present in the molecular beam) leave the ionisation region before the Rydberg states are field ionised and their electrons are detected. The excitation is effected in a single step by the ns XUV laser (bandwidth ≲ 0.7 cm−1).  Supersonic cooling of the sample is a prerequisite to reduce the contributions from hot bands and to narrow the rotational structure. Cooling, however, leads to the predominant formation of dimers and larger oligomers with only traces of monomer left in the sample, as illustrated in the time of flight mass spectrum shown in Figure 4.4. Note that the mass resolution is limited as the setup is optimised for sensitive electron detection (defocused laser beam and short flight tube). The arrow indicates the very small AAC monomer peak, while all the other peaks are fragments of oligomers.36,114 With only about 90  Figure 4.3 Black traces depict electron signal and the red trace depicts ion signal. (a) Photoionisation efficiency spectrum of AA in the region of the adiabatic IE. (b) Calculated photoelectron spectrum of AA monomer at a temperature of 298 K and a resolution as reported in reference [113]. (c) Experimental PFIZEKE photoelectron spectrum. (d) Calculated photoelectron spectrum at a vibrational temperature of 100 K.  91  100 ppm AA monomer in the supersonic beam, demands on the selectivity and sensitivity of the electron detection are very high.  The PFI-ZEKE photoelectron spectrum in the region of the first adiabatic IE is shown in Figure 4.3(c) together with a calculated spectrum for a vibrational temperature of 100 K in trace (d). Photoionisation spectra of AA (shown in Figure 4.3(a)) and of its oligomers (not shown) confirm that the ZEKE spectrum arises solely from AA because only AA shows a threshold in this region. The main band at 85912 cm−1 is the transition between the vibrational ground states of the neutral (v = 0) and the ion (v+ = 0) (see Figure 4.2).  Figure 4.4 Time of flight mass spectrum recorded at a laser photon energy of 85974 cm-1. The AAC monomer is labelled with an arrow. The spectrum is dominated by fragments of the dimer (Di), the trimer (Tr), the tetramer (Te) and the pentamer (Pe). Note that the appearance of (AA)(n-1)H+ in the XUV photoionised mass spectrum is characteristic of the presence of (AA)n in the molecular beam, for small n. Mass to charge ratio is given in u/e.  92  Our simulation of the rotational structure shows that the width of this band is determined by the rotational structure with a rotational temperature of 10 K. The A,E torsional tunnelling splitting or the rotational structure cannot be resolved with our laser. The calculated tunnelling splitting is 0.35 cm−1 in AA and 0.06 cm−1 in AAC. The simulation of the rotational structure reveals a high average density of more than 100 transitions per cm−1. The bands on the high frequency side at 85937 and 85976 cm−1 are torsional transitions between states as labelled in Figure 4.2. The second band system at 86269 cm−1 is the excitation of one quantum of the CCO deformation motion ν12 of AAC (Figure 4.5). This transition is also accompanied by CH3-torsional transitions on the high frequency side. The signal of this band system is about a factor of 3 less than for the first band system because the light intensity in this region drops by a  factor of ~3 due to the four-wave mixing efficiency (see Section 2.1.2.c). This band is scaled accordingly in Figure 4.3(c).  Figure 4.5 The CCO deformation (ν12) mode of the acetic acid monomer.  The IE of AA, the torsional barrier height H of AAC, and the corresponding tunnelling splittings are derived from an analysis of the torsional structure observed in the PFI-ZEKE photoelectron spectrum. We assume separability between rotational |r〉, CH3 torsional |τ〉, vibrational |v〉, and electronic degrees of freedom with nonseparable interactions minimised by imposing orthogonality between infinitesimal vibrations, rotations, and torsions. Vibrations are treated as harmonic, except for the torsion, whose eigenfunctions are calculated explicitly in a discrete variable representation.121  93  Spectra were simulated within the Franck-Condon (FC) approximation for transition probabilities  ܲሺ‫ ݎ‬ା ߬ ା ߭ ା ← ‫߭߬ݎ‬ሻ ∝ ൭෍ ݂ℓ ሺ‫ݎ‬, ‫ ݎ‬ା ሻ൱ ∙ |‫ ߬|߬ۦ‬ା ۧ|ଶ ∙ |‫ ߭|߭ۦ‬ା ۧ|ଶ ℓ  Eqn 4.1  where (+) indicates ionic functions. The rotational contributions fℓ, which depend on the photoelectron’s  orbital angular momentum ℓ, are not known explicitly and therefore replaced with a phenomenological  Gaussian band shape. The vibrational FC factors account for geometry change and Duschinsky rotation.101 The spectrum is given by the convolution of rotational, torsional, and vibrational factors. All equilibrium geometries, harmonic force fields, and torsional potentials were calculated within density functional theory (B3LYP/6-31+G*).96 At this level of theory the bare potential barriers (without zero point effects) along the minimum energy torsional path amount to 111 and 270 cm−1 for the neutral and the ion, respectively. In our calculations we employ these potential functions directly on the equidistant grid that defines the discrete variable representation for the solution of the torsional eigenvalue problem.121 The torsional potential of the neutral was scaled linearly by a factor of 1.53 to match the experimental barrier height of 170 cm−1.122 The analogous scaling factor for the torsional potential of the ion, as well as the adiabatic IE and the torsional temperature were varied to match the PFI-ZEKE photoelectron spectrum, resulting in an IE of 85912 ± 5 cm−1, a torsional barrier of H = 316 ± 10 cm−1, and a torsional temperature of 100 K.  The distance of 357 ± 5 cm−1 between the two strongest transitions at 85912 and 86269 cm−1 is a direct measure of the CCO deformation mode of the AAC (ν12). The doubling of the torsional barrier height upon ionisation hints at a significant shortening of the C–C bond. B3LYP calculations predict a shortening of the C–C bond by about 1 pm largely independent of the basis set employed (1.6 pm for the PBE0 functional113), but the effect is more pronounced at the MP2/aug-cc-pVTZ level, which yields a bond length reduction by 2.1 pm. It may be instructive to note that even CCSD(T)/aug-cc-pVTZ  94  (geometry optimised at the MP2 level) underestimates the torsional barrier by about 20% (145 and 264 cm−1 for the neutral and the ion, respectively). The increase in the torsional barrier upon ionisation drastically reduces the tunnelling efficiency by almost one order of magnitude. The accompanying increase in the spacing of torsional energy levels produces corresponding changes in the partition function of AAC which will be most relevant at low temperatures.  In summary, we have shown that the combination of PFI-ZEKE photoelectron spectroscopy with supersonic cooling of an AA/helium mixture allows the determination of an accurate adiabatic IE of AA, thus ending a 40 year long debate. Supersonic cooling is essential to avoid the congestion caused by hot bands and broad rotational contours, while only a very sensitive and selective spectroscopic method can cope with the exceedingly small AA monomer concentrations in the supersonic expansion. Our experiments have enabled the analysis of the low frequency torsional dynamics of the cation, which will be important for statistical theories of the chemical reaction kinetics of AAC, especially at the low temperatures prevalent in space.  Finally we would like to emphasise two more general aspects of this investigation. Our results illustrate the importance of detailed modelling for a reliable quantitative analysis of experimental photoelectron spectra, a point that has not always been appreciated as exemplified in occasionally exaggerated claims of accuracy. Second, this study demonstrates that with due attention to detail and optimisation, PFI-ZEKE photoelectron spectroscopy can achieve sufficiently high sensitivity to study molecules present only in trace amounts. With this work on the acetic acid monomer, a foundation has been laid for further work on clusters (Chapter 5) and eventually larger aerosol particles (Chapter 6) of acetic acid.  95  5. Photoionisation of Small Sodium Doped Acetic Acid Clusters 5.1. Introduction As a stepping stone to investigating larger systems, in this Chapter we investigate the photoionisation of the smallest of acetic acid clusters doped with single atoms of sodium. The technique of sodium doping followed by single photon ionisation with UV light has been used to obtain “fragmentation free” size distributions of large atomic and molecular clusters, whereas most conventional ionisation techniques (e.g. electron ionisation) cause the evaporation of very significant numbers of monomer units.34,35 In this work we apply the technique to small acetic acid clusters to precisely assess the influence of the sodium doping process and of the subsequent photoionisation of sodium doped species with regards to evaporation from the doped cluster. A more general discussion of the sodium doping technique is provided in Chapter 6 where we extend our focus to larger clusters.  Numerous studies have been devoted to the interaction of sodium atoms with gas phase clusters consisting of polar molecules, with the primary objective of better understanding the concept of solvation (references [32,33,35,54,55,65,66,74,123-135] and references therein). These studies consequently focussed on the determination of size specific properties such as ionisation energies, structures, vibrational frequencies, and dissociation energies. Most of the reported data pertain to sodium doped ammonia and sodium doped water clusters (references [32,33,35,54,55,65,74,123-135] and references therein), with only a few exceptions.34,66  It appears that the issues of sodium doping, collision complex lifetimes, photoionisation efficiency, and neutral and ionic fragmentation were addressed in less detail,33,54,65,114,128 although understanding these processes is essential for correlating ionisation energies with the ionic appearance energies actually measured in photoionisation experiments. The general assumption is that only a small number of  96  monomers evaporate from the cluster as a result of sodium doping. Fragmentation following (soft) ionisation is also assumed to be of only minor importance. The excess energy after ionisation is sometimes used to estimate the number of evaporated monomers without regard to any further details of the processes involved. For the smallest clusters, the loss of any molecules is obviously significant, and in particular it is to be expected that the underlying processes are size dependent, i.e., they depend on the specific energetics.  In the present work, we have tried to address these issues for the case of small acetic acid clusters. A peculiarity of acetic acid is its ability to form a very strongly bound dimer, which has no permanent dipole moment, while the binding of additional monomers is much weaker. This hierarchy of forces makes the acetic acid system particularly interesting to study sodium uptake, collision complex lifetimes, and fragmentation. The acetic acid clusters were formed by supersonic expansion similar to many other studies on gas phase sodium-doped clusters. Sodium doping happened in a standard sodium oven.53,54 Photoionisation with ultraviolet (UV) light and subsequent time-of-flight ion detection were employed to study the properties of the sodium-doped clusters at energies in the region of their ionisation energies. From UV-photoionisation alone, however, it is impossible to determine the original composition of acetic acid clusters in the molecular beam. An essential feature of the present study is the combination of UV photoionisation spectroscopy with independent extreme ultraviolet (XUV) photoionisation to assess the original composition of the beam. The latter allows direct ionisation of bare acetic acid clusters with known fragmentation patterns.36,114 The experiments were complemented by density functional calculations of cluster geometries and energies136 and by theoretical estimates of the pick-up and fragmentation kinetics of the collision complexes using the statistical adiabatic channel model (SACM).137,138  97  5.2. Experimental The measurements were recorded using the experimental apparatus described in Chapter 2, in the configuration where the sodium oven chamber is installed between the sample injection chamber and the TOF chamber (see Section 2.1.5 and Figure 2.3).  The acetic acid (HAc) clusters were generated in a pulsed seeded supersonic expansion from a sample reservoir containing 17 mbar HAc (glacial, Fisher Scientific) in helium (Praxair, 5.0) at a total pressure of 1 bar (sample identical to that used in the measurement of the PFI-ZEKE photoelectron spectrum of HAc, see Chapter 4). The supersonic jet created by the General Valve was skimmed by a 1.0 mm diameter skimmer and passed through the oven. A total nozzle opening time of about 600 µs was employed. The oven is located about 80 mm upstream of the ionisation region within the extractor in the TOF chamber. The sodium oven was heated to 225 °C on the bottom and 140 °C on the top (see Section 2.1.4).  PIE spectra were recorded using +1 kV DC applied across the ZEKE extractor in double field (WileyMcLaren) configuration (see Section 2.1.5.a). All XUV measurements reported in this Chapter use a photon energy of 134790 cm-1 (16.7 eV, 74.2 nm) generated by the 3ν1 process in xenon gas (see Section 2.1.2.b). For the UV measurements the doubled output of a dye laser was used; this was directed over the grating set to its 0th order to ensure that the molecular beam was probed at the same position by both the UV and XUV laser beams (the ν2 laser beam was aligned for sum frequency generation, 2ν1+ ν2, also). Low UV light intensities (~ 10-3 mJ mm-2 ns-1) were used to minimise electron ionisation, which is frequently an issue with DC extraction fields because free electrons, produced by the primary ionisation or by stray UV photons hitting metal surfaces, are quickly accelerated to energies far above molecular ionisation energies.  98  The UV light was used for photoionisation of the Na doped clusters at photon energies close to their ionisation energies. The corresponding TOF spectra will be called “UV-TOF spectra” throughout the remainder of this chapter. The XUV light was solely used as an independent check to monitor and adjust the composition of the molecular beam (vide infra). The energy of the XUV photon is high enough to ionise HAc and (HAc)n clusters (see Chapter 4). Direct photoionisation of (HAc)n clusters leads to known fragmentation patterns,36,114 which allow us to draw conclusions about the molecular beam composition. The most characteristic fragmentation path of a cluster with n monomer units leads to the formation of a protonated cluster ion with (n − 1) monomer units along with smaller fragments Fj.  ሺ‫ܿܣܪ‬ሻ௡ ൅ ݄ߥ௑௎௏ → ሺ‫ܿܣܪ‬ሻሺ௡ିଵሻ ‫ ܪ‬ା ൅ ෍ ‫ܨ‬௝ ௝  Eqn 5.1  (HAc)(n−1)H+ is thus characteristic for a molecular beam containing (HAc)n (see also Figure 4.4). A list of characteristic XUV fragments along with their masses is given in Table 5.1. These TOF spectra are referred to as “XUV-TOF spectra” hereafter.  In a molecular beam, it is not possible to form larger clusters without forming smaller clusters at the same time. The reverse, however, is possible, i.e., keeping the abundance of larger clusters negligible or at least very low, while producing small clusters. To clarify from which Na doped parent cluster [Na(HAc)n] a given Na doped fragment arises in the UV-TOF spectra, we have recorded spectra under different conditions, systematically increasing the maximum cluster size as monitored by the XUV-TOF spectra. Correlations between different maximum cluster sizes in the XUV-TOF spectra with changes in the UV-TOF spectra can thus be established (Section 5.4). The composition of the molecular beam sampled by the laser was altered primarily by changing the time delay between the sample gas pulse and the trigger of the laser pulse. As this delay is increased, the part of the sample gas expansion actually probed by the ionising laser moves from the beginning to the end of the expansion (see Figure 5.1). Moving from  99  the beginning toward the center of the sample gas pulse gradually increases the amount of cooling in the molecular beam, which in turn increases the maximum cluster size that is formed. While optimising the nozzle timing to enhance the formation of larger clusters can reduce the relative amount of the smallest clusters, this decrease is not very significant. Time intervals between the appearance of successive cluster sizes in the sampled molecular beam were found to be longer on the rising edge of the expansion and hence this edge was used for all the work presented in this chapter.  Figure 5.1 Schematic diagram showing the timing of the laser pulse and of the molecular beam. The time axis is not drawn to scale and the profile of the molecular beam is drawn for illustrative purposes only. To change the composition of the sampled molecular beam t1 is kept constant and t2 is varied; this configuration is chosen to avoid changing the laser timing while it is running. Case (a) depicts when the beginning of the expansion is sampled (small clusters dominate) and case (b) depicts when the central part of the expansion is sampled (large clusters dominate).  100  Table 5.1 Upper part: characteristic fragments and masses of HAc and its clusters after XUV ionisation. Lower part: masses of Na doped clusters expected in the UV-TOF spectra.  Masses of fragments after XUV ionisation a (HAc)n + hνXUV → (HAc)n+ → Fi+ + Σ Fj Original ion (HAc)n+  Fragment ions Fi+  Mass of Fi+ / u  HAc+  CH3CO+  43  +  45  COOH HAc+ (HAc)2  +  HAcH  60  +  61  (HAc)COOH (HAc)3  +  HAcH  +  61  (HAc)CH3CO (HAc)4  +  (HAc)n  +  105  +  (HAc)2H  +  (HAc)3H  +  (HAc)(n-1)H  +  103 121 181  +  1 + 60(n-1) (only for small n; see also Chapter 6)  Masses of Na doped clusters Na(HAc)n+ expected after UV ionisation Ion  Mass / u  NaHAc+  143  Na(HAc)3+  203  Na(HAc)4  +  263  Na(HAc)5  +  323  Na(HAc)2  a  83 +  References [36,114]  101  5.3. Calculations 5.3.1. Ab initio calculations Ab initio calculations at the B3LYP/6-311++G(3df,2p) level of theory136 were performed for the neutral and ionic sodium doped acetic acid trimer and for a series of possible fragments thereof. Dissociation energies with (D0) and without (De) zero-point correction are given in Table 5.2. Figure 5.2 illustrates these results for the trimer fragmentation process together with the structures of the various clusters.  Figure 5.2 Zero point corrected energies (relative to the neutral Na(HAc)3 ground state) and structures for Na(HAc)3 and its neutral and ionic fragments from B3LYP calculations. (AIE): adiabatic ionisation energy, (VIE): vertical ionisation energy.  We have chosen this particular level of density functional theory (DFT) since it provides a reasonable description of strongly hydrogen-bonded structures and their energetics. It also yields ionisation energies typically within a few 100 meV of experimental values, which justifies its use for the calculations of 102  acetic acid clusters and their complexes with sodium ions. The use of B3LYP to describe the corresponding neutral complexes resulting from the initial sodium pick-up is more problematic. The longrange interaction is dominated by dispersion (vide infra), which semilocal density functionals such as B3LYP usually fail to describe. Therefore, dispersion contributions to the binding energy of Na collision complexes might not be properly described. We have tested the B3LYP results against several density functionals that incorporate empirical atom-atom dispersion corrections (B97D, wB97XD, X3LYP, M062X; see reference [136] and references therein). All methods lead to virtually the same equilibrium structures, both for neutral and for ionic complexes. The dispersion-corrected functionals consistently show stronger sodium binding than B3LYP, but the differences vary widely between 10% and more than a factor of 2, depending not only on the cluster size but also on the particular dispersion-corrected functional. In the case of Na doped HAc clusters the empirical atom–atom dispersion corrections apparently fail to provide quantitatively reliable predictions, so that we can only consider them as an indication of the uncertainties of the Na binding energies. Since all DFT calculations largely agree in terms of calculated equilibrium structures and the energetic ordering of fragmentation channels, we conclude that the B3LYP functional provides at least a qualitatively correct picture of the energetics. Calculated ionisation energies are expected to be slightly overestimated by the B3LYP/6-311++G(3df,2p) calculations, which yield a value of 5.421 eV for Na, 0.282 eV above the experimental IE of 5.139 eV (reference [139]). Assuming this error to be approximately constant we have subtracted 2273 cm−1 from all calculated ionisation energies.  103  Table 5.2. B3LYP/6-311++G(3df, 2p) calculations for neutral and ionic fragmentation. All energies are counterpoise corrected for the basis set superposition error. 2273 cm-1 have been subtracted from calculated ion energies to match the experimental ionisation energy of Na atoms (5.139 eV or 41449 cm-1).  Na(HAc)n i NaHAc  Na(HAc)3  Na(HAc)4  De / cm-1  D0 / cm-1  → Na(HAc)n-i(+) + (HAc)i  1611  a  ∆Evertical / hc cm-1 b  ∆Eadiabatic / hc cm-1 c  34971 d  32536 e  42932  42932  45658 d  30802 e  0 1  Na(HAc)2  a  → Na(HAc)n-i + (HAc)i  1483  0 1  5199  5569  40540  38105  2  1493  2254  43703  43703  47596 d  32483 e  0 1  7646  7210  52868  38012  2  7528  7982  42953  40518  3  6811  7475  48924  48924  47794 d  31754 e  0 1  5316  4860  52456  37343  2  7645  7273  52931  38075  3  10516  10852  45823  43388  4  8524  9350  50799  50799  a  Fragment energies relative to the respective neutral parent cluster Na(HAc)n.  b  ∆Eadiabatic + ion reorganisation energy (vertical ionisation energy – adiabatic ionisation energy)  of Na(HAc)n-i(+). c  D0 of Na(HAc)n + adiabatic ionisation energy of Na(HAc)n-i.  d  Vertical ionisation energy.  e  Adiabatic ionisation energy.  104  5.3.2. Capture cross-sections for sodium pick-up The capture probability is determined by the interaction potentials between sodium atoms and (HAc)n clusters, by the collision energy, by the densities of the species involved, and by the length of the pick-up  cell. We have estimated the thermally averaged cross-section 〈σ〉 for the capture of a sodium atom by the  various acetic acid clusters using a Langevin model,140 assuming long-range interaction potentials  dominated by isotropic dispersion and induction terms: ܸୢ୧ୱ୮ ൌ െ  ‫ܥ‬ୢ୧ୱ୮ 3 ‫ܧ‬ூ ሺNaሻ‫ܧ‬ூ ሾሺHAcሻ௡ ሿ ߙሺNaሻߙሾሺHAcሻ௡ ሿ ൌെ ଺ ܴ 2 ‫ܧ‬ூ ሺNaሻ ൅ ‫ܧ‬ூ ሾሺHAcሻ௡ ሿ ܴ଺  ܸ୧୬ୢ ൌ െ  ‫ܥ‬୧୬ୢ 1 ߤሾሺHAcሻ௡ ሿଶ ߙሺܰܽሻ ൌ െ ܴ଺ 4ߨߝ଴ ܴ଺  Eqn 5.2  Eqn 5.3  where R is the inter-particle distance. Ionisation energies (EI), polarisability volumes (α), and dipole moments (µ) of the various species are given in Table 5.3. Within the Langevin model, the capture crosssection σ(E) as a function of collision energy E is given by ଶ ߪሺ‫ܧ‬ሻ ൌ ߨܾ୫ୟ୶ ൌ ߨቆ  27ሺ‫ܥ‬ୢ୧ୱ୮ ൅ ‫ܥ‬୧୬ୢ ሻ ቇ 4‫ܧ‬  ଵ/ଷ  Eqn 5.4  where bmax is an effective capture radius. Averaging over the relative velocities of sodium atoms and acetic acid clusters yields average capture cross-sections 〈σ〉. A thermal velocity distribution at a temperature of 498 K is used for the sodium atoms, and a constant and uniform velocity of 1000 ms−1 is  assumed for (HAc)n in the molecular beam. The capture cross-section 〈σ〉 together with the Na concentration in the oven (~ 1.7 × 1019 m−3)  56,57  and the length of the pick-up region (44 mm) yield the  capture probability p. 105  Table 5.3 Properties of different sodium - acetic acid collision complexes: collision energy <E>, maximum angular momentum <ℓmax>, capture cross-section <σ>, capture probability p, and decay times τj (see Section 5.3.3 for details).  Collision complex ‫ۦ‬Eۧ / hc cm-1 ‫ۦ‬ℓmaxۧ  ‫ۦ‬σۧ / Å a  p  τ1  d  τ2  d  2  Na-HAc  Na-(HAc)2  Na-(HAc)3  Na-(HAc)4  1070  1243  1313  1350  220  250  176 b  102 (100)  c  120  b  τ4  136 (135)  c  146 b  54%  60%  64%  67%  2 ps  ∞  140 ns  50 ps  100 ps  7.5 µs  500 ns  70 µs  ∞  τ3 d  a  265 b  d  10 s  The thermally averaged capture cross-section is derived from Equation 5.4 as described in  Section 5.3.2. The Na-oven temperature was T = 498K. b  Parameters used for the calculation of capture cross-sections:  Polarisabilities: α(Na) = 24.1 Å3 (reference [141]), α(HAc) = 4.74 Å3, α((HAc)2) = 9.78 Å3, α((HAc)3) = 14.82 Å3, α((HAc)4) ≈ 2α((HAc)2). Dipole moments: µ(HAc) = 1.67 D (reference [142]), µ((HAc)3) = 1.9 D, µ((HAc)2) = µ((HAc)4) = 0. Ionisation energies: EI(Na) = 5.139 eV (reference [139]), EI (HAc) = 10.7 eV (Chapter 4), EI ((HAc)3) = 9.5 eV, EI ((HAc)4) ≈ EI ((HAc)3). Except where noted, values were calculated in this work at the B3LYP/6-311++G(3df,2p) level. c  d  Values in parentheses are the capture cross-sections for µ((HAc)n) = 0. Decay channel Na(HAc)n → Na(HAc)n – j + (HAc)j : τj = 1 / k(‫ۦ‬Eۧ,‫ۦ‬ℓmaxۧ); Eqns 5.10 & 5.11.  106  Values of 〈σ〉 and p for collisions between sodium and different acetic acid oligomers are listed in Table 5.3. The values are very similar, even though the dimer and the tetramer do not have a permanent dipole moment. The dispersion interaction is evidently much more important for the capture process than  the induction interaction, as illustrated by the values of 〈σ〉 for HAc and (HAc)3 given in parentheses, which were calculated neglecting Vind. Despite the very approximate character of the above calculations, it is clear that even small species without a permanent dipole moment quite readily pick up a sodium atom.  5.3.3. Lifetimes of Na(HAc)n* collision complexes The capture probabilities derived from the Langevin model indicate a uniformly high pick-up efficiency, but whether the collision complexes formed in the sodium oven chamber enter the ionisation region in the TOF chamber intact or not depends on their lifetimes. With a molecular beam velocity on the order of 1000 ms−1 it takes the Na(HAc)n complexes about 80 µs to travel the distance to the ionisation region. The unimolecular decay rates of the collision complexes can be estimated by statistical rate theories. We have chosen the statistical adiabatic channel model (SACM) of Quack and Troe,137 since it encompasses practically all other statistical theories as limiting cases.138 Assuming barrierless dissociation and fast intramolecular energy redistribution (this assumption may not always be correct – see Chapter 6), we determined the decay rates of all possible fragmentation channels of the neutral collision complexes to estimate their lifetimes, and to elucidate the product distribution and energy disposal of the fragmentation.  Within SACM the unimolecular decay rate as a function of energy E and angular momentum quantum number J is given by ݇ሺ‫ܧ‬, ‫ܬ‬ሻ ൌ  ܹሺ‫ܧ‬, ‫ܬ‬ሻ ݄ߩሺ‫ܧ‬, ‫ܬ‬ሻ  Eqn 5.5  where h is Planck’s constant, ρ is the density of reactant states, and W is the number of open decay channels, which are defined in terms of the reactant (Er) and product (Ep) levels they connect. 107  The associated channel potentials Vrp(q) describe the adiabatic change of the corresponding energy levels along the reaction coordinate q from the reactant state, Vrp(q), to the product state, Vrp(∞) = Ep. At energy E a channel is open if max൫ܸ௥௣ ൯ ൑ ‫ܧ‬ ௤  Eqn 5.6  In correlating reactant and product levels any exact or approximate symmetries (conservation laws) are accounted for either in detail, i.e., level by level, or on average by appropriate symmetry numbers. For simplicity the channel potentials are formulated for a dissociating Morse oscillator with a single interpolating function between reactant and product energy levels: ܸ௥௣ ሺ‫ݍ‬ሻ ൌ ‫ܦ‬௘ ሺ1 െ ݁ ିఉ௤ ሻଶ ൅ ൫‫ܧ‬௣ െ ‫ܦ‬௘ ൯ሺ1 െ ݂ሻ ൅ ൫‫ܧ‬௥ െ ‫ܧ‬௓௤ ൯݂ ൅ ܸୡୣ୬୲ ሺ‫ݍ‬ሻ  Eqn 5.7  All energies are referred to a common energy zero, in this case the reactant zero-point level. EZq is the vibrational zero-point energy in the reaction coordinate q. For the interpolation of the channel potential, we use the simple exponential damping originally suggested in reference [137]: ݂ሺ‫ݍ‬ሻ ൌ ݁ ሼିఉ௤ሽ  Eqn 5.8  The centrifugal potential Vcent(q) is approximated for two separating point masses:  ‫ݎ‬௘ ଶ ܸୡୣ୬୲ ሺ‫ݍ‬ሻ ൌ ‫ܤ‬௘ ቈ൬ ൰ െ ݂቉ ൈ ሾ ݂ሺ‫ ܬ‬െ ℓሻ ൅ ℓ ሿሾ ݂ሺ‫ ܬ‬െ ℓሻ ൅ ℓ ൅ 1 ሿ ‫ݎ‬௘ ൅ ‫ݍ‬  Eqn 5.9  where ℓ is the orbital angular momentum of the separating fragments and q is taken as the change of the distance between their centres of mass, from its equilibrium value re with corresponding rotational constant Be. The Morse parameter β was determined from the dissociation energy De and the harmonic wavenumber  of the  oscillator  assigned  to the reaction coordinate, all calculated at the  B3LYP/6-311++G(3df,2p) level of DFT. We set the universal damping parameter in f(q) equal to β, 108  which is consistent with the loose transition state assumption implicit in the Langevin model for the capture process.  Densities of state were determined by direct count assuming harmonic oscillators and rigid asymmetric tops. We have tested the effect of anharmonicities in the case of NaHAc, by explicitly treating the dissociating Morse oscillator and the tunnelling CH3 rotor (with the appropriate symmetry number three). At the relevant energies, the anharmonic count yields k(E,J) values 10%–20% above those obtained in the harmonic approximation (mostly because of CH3 torsion), which is negligible for the purposes of the present study. For the determination of W(E,J) the energy levels of conserved and disappearing oscillators were treated separately. The former correlate with the internal vibrations of the fragments, while the latter correlate with fragment rotation and orbital motion. Detailed angular momentum conservation was observed. Collision complex lifetimes were determined for the average collision energy 〈E〉 and J = 〈ℓmax〉 (see Table 5.3). ߬ൌ  1 ݇ሺ〈‫〉ܧ‬, 〈ℓ௠௔௫ 〉ሻ  Eqn 5.10  We assume that the initial angular momentum of the (HAc)n in the beam is negligible, compared with the  maximum orbital angular momentum for successful capture, 〈ℓmax〉, given by the Langevin model: ԰ଶ 〈ℓ௠௔௫ 〉ଶ ൎ 2ߤ〈‫〉ܧ‬  〈ߪ〉 ߨ  Eqn 5.11  where µ is the reduced mass of the fragments.  The topics of sodium capture cross-sections and Na(HAc)n* collision complex lifetimes are touched upon again in Section 6.2.  109  5.4. Results 5.4.1. Monomer and dimer As explained in Section 5.2, photoionisation with XUV light was used to probe the cluster composition in the molecular beam. XUV-TOF mass spectra recorded at different times in the supersonic expansion are presented in Figure 5.3. Trace (a) depicts the spectrum for conditions under which only the monomer (HAc) and the dimer (HAc)2 are present in the part of the molecular beam that is sampled. This is demonstrated by the fact that only fragments characteristic of the monomer and dimer are observed (Table 5.1). Under these conditions, no signals of sodium doped species of the monomer or the dimer, or any fragments thereof, were observed in the UV-TOF spectra (not shown) recorded at photoionisation wavelengths ranging from 223 to 302 nm. Na(HAc) and Na(HAc)2 are either not formed in the pick-up chamber, they dissociate in the neutral state while travelling from the pick-up oven to the ionisation region, or they are not ionised efficiently enough by the UV laser to be recorded. This is further discussed in Section 5.5.1.  5.4.2. Trimer When the expansion is optimised for clusters up to the trimer with only very minor amounts of tetramer present, a strong signal at m/z = 83 corresponding to Na(HAc)+ (Table 5.1) is observed in the UV-TOF spectrum at ionisation wavelengths between 223 and 300 nm (Figure 5.4(a)). While a weak signal at m/z = 143 in the spectrum shown in Figure 5.4(a) indicates the presence of small amounts of Na(HAc)2+, the absence of any signal at m/z = 203 means that no Na(HAc)3+ is formed from Na(HAc)3. Figure 5.3(b) depicts the corresponding XUV-TOF spectrum recorded under the same conditions. The characteristic dimer and trimer fragment ions (Table 5.1) show up strongly, which proves the predominance of clusters up to the trimer under these conditions in the molecular beam. The very weak fragment peak at m/z = 181, which is characteristic of the tetramer, shows that the abundance of (HAc)4 in the beam is only minor.  110  Figure 5.3 XUV-TOF spectra recorded under different conditions: Molecular beam contains (a) monomer HAc and dimer (HAc)2; (b) monomer HAc, dimer (HAc)2 and trimer (HAc)3 (amount of tetramer is very small); (c) monomer HAc, dimer (HAc)2, trimer (HAc)3, and tetramer (HAc)4; (d) large clusters. The species are identified by their characteristic fragments given in Table 5.1. Note that the signals in traces (a) - (d) are scaled by different factors for masses above 70 u. Also note that the m/z scale in trace (d) differs from traces (a) to (c).  111  Figure 5.4 UV-TOF spectra of Na-doped HAc clusters recorded under different molecular beam conditions as specified in Figure 5.3: (a) Same conditions as in Figure 5.3(b) (up to the trimer); (b) Same conditions as in Figure 5.3(c) (up to the tetramer); (c) Same conditions as in Figure 5.3(d) (including large clusters). The masses of the various Na-doped HAc clusters are given in Table 5.1.  As mentioned in Section 5.4.1, the UV-TOF spectra of the monomer and dimer do not exhibit any sodium-doped fragments, so that neither of the species can be at the origin of the m/z = 83 fragment in Figure 5.4(a). Furthermore, the XUV-TOF spectrum in Figure 5.3(b) clearly shows that the tetramer content is minor and that no larger clusters are present under these conditions. Therefore, the m/z = 83 fragment must definitely originate from Na(HAc)3. From the ion yield as a function of the UV photon energy shown in Figure 5.5(a), we estimate an approximate value for the appearance energy of the m/z = 83 fragment of 4.13 ± 0.05 eV (33333 ± 450 cm−1). By appearance energy we mean the onset of a particular ion signal as a function of the UV excitation wavelength. The mass calibration of the m/z = 83 peak was confirmed by adding a small quantity of krypton gas to the sample bottle containing HAc and  112  Figure 5.5 Ion yield curve (scaled with UV light intensity) as a function of the UV excitation wavelength of (a) NaHAc+ and (b) Na(HAc)2+.  helium. UV and XUV TOF spectra were then recorded in quick succession of each other. The characteristic isotopic pattern of krypton superimposed on the UV-TOF spectrum signal clearly identified the observed peak as being m/z = 83.  The origin of Na(HAc)2+ (m/z = 143) is less obvious than that of Na(HAc). As shown later in Section 5.4.3, the m/z = 143 fragment is characteristic of the Na-doped tetramer Na(HAc)4. It thus seems likely that the small m/z = 143 contribution in the UV-TOF spectrum arises from the small amount of Na(HAc)4 and hence is unrelated to Na(HAc)3. We have tried to confirm this hypothesis by systematically increasing the amount of tetramer in the molecular beam, while still avoiding the formation of larger clusters. The m/z = 143 signal intensity observed in the UV-TOF spectrum was indeed found to scale linearly with the tetramer concentration, as determined from the m/z = 181 signal in the XUV TOF 113  spectra. The uncertainty of this method is rather large, but we can still conclude that the dominant contribution to the Na(HAc)2+ signal comes from Na(HAc)4 and not from Na(HAc)3.  How the Na(HAc)+ fragment is formed from Na(HAc)3 and why Na(HAc)2+ is not (or only in extremely small amounts) is further discussed in Section 5.5.2, where we also explain the absence of Na(HAc)3+.  5.4.3. Tetramer Figure 5.3(c) depicts the XUV-TOF spectrum under conditions when clusters up to the tetramer are present in the molecular beam. The m/z = 181 fragment signal (Table 5.1) proves the increased abundance of Na(HAc)4 compared with Fig. 5.3(b), where almost no tetramer was formed. Figure 5.4(b) shows the UV-TOF spectrum recorded under these conditions. With the significantly increased amounts of (HAc)4 in the beam, the Na(HAc)2+ fragment at m/z = 143 now appears as a strong signal at photoionisation wavelengths between 223 and 300 nm. It is clear that this fragment must have been formed from Na(HAc)4. For the appearance energy of Na(HAc)2+ in the tetramer UV-TOF, determined in the same way as described above for the Na(HAc)+ fragment, we find a value of 4.13 ± 0.05 eV (33333 ± 450 cm−1) (see Fig. 5.5(b)). Within experimental uncertainties this is the same value as found for Na(HAc)+ in the trimer UV-TOF. No ion signals are observed at higher m/z values in the tetramer UV-TOF of Figure 5.4(b), specifically proving the absence of any parent ions Na(HAc)3+ (m/z = 203) or Na(HAc)4+ (m/z = 263) under tetramer conditions.  When optimising the conditions for the tetramer, it is impossible to avoid the presence of trimer in the molecular beam. Therefore, the Na(HAc)+ fragment (m/z = 83) observed in Fig. 5.4(b) can in principle arise from Na(HAc)4 as well as from Na(HAc)3, which was clearly identified as the source of Na(HAc)+ in the trimer UV-TOF (Figure 5.4(a) and see Section 5.4.2). From the UV-TOF spectrum in Figure 5.4(b) it is thus not possible to decide whether the Na(HAc)+ arises solely from Na(HAc)3 or whether Na(HAc)4  114  also contributes to the m/z = 83 signal. Again, we have tried to identify the clusters with which this fragment correlates by systematically changing the cluster composition of the molecular beam. Although the results confirm the Na doped trimer as the major source of the m/z = 83 fragment, we cannot exclude a contribution from the Na doped tetramer because of the large uncertainty of this method.  5.4.4. Larger clusters Finally, we changed the expansion conditions to include oligomers larger than the tetramer. The corresponding XUV-TOF spectrum is shown in Figure 5.3(d). Albeit in very low abundance, clusters up to (HAc)8 are present in the beam, as can be seen from the occurrence of their characteristic fragments (see Eqn 5.1). The UV-TOF spectrum in Figure 5.4(c) shows that the presence of larger clusters leads to an additional signal at m/z = 263 due to Na(HAc)4+. For larger clusters it becomes increasingly difficult to draw a line between successive oligomers being present in the molecular beam. As a consequence, it is more difficult to trace the Na(HAc)4+ fragment back to a particular acetic acid oligomer. From our experiments, the m/z = 263 signal seems to correlate with the presence of the pentamer. Apart from this fragment, no other Na doped clusters were observed under these conditions, presumably a consequence of limited sensitivity combined with the low abundance of larger clusters. Note also that the m/z = 203 [Na(HAc)3+] fragment is still not observed, even in the presence of larger clusters (see Section 5.5.3 for a brief discussion).  5.5. Discussion Four distinct processes determine which Na doped species can be observed in the UV-TOF spectra. The first of these is the sodium pick-up itself, the probability of which is estimated here from the calculations of the capture cross-section described in Section 5.3.2. The second is the lifetime of the Na–(HAc)n collision complex and its fragmentation kinetics, which depends on the collision energy and on the  115  angular momentum. In this work the redistribution of energy within the Na–(HAc)n collision complex is assumed to be very fast, and the SACM calculations described in Section 5.3.3 assume that equilibrium energy distribution is present from the moment of Na pick-up. Those calculations provide, at least, an order of magnitude estimate for the lifetimes of the different clusters studied here, together with the product distribution and energy disposal of the fragmentation process. The third and the fourth factors are the photoionisation efficiency and the fragmentation pattern of the ionic Na–doped clusters. The absence of a particular ionic fragment cluster in the UV-TOF spectrum thus does not necessarily prove the absence of the corresponding neutral species in the molecular beam, but might simply indicate a particularly small photoionisation cross-section. This series of processes is further discussed in Section 6.2, in the context of using the sodium doping followed by UV photoionisation technique as a means of particle sizing for larger particles.  5.5.1. Monomer and dimer The calculated cross-sections for Na pick-up by HAc and (HAc)2 are comparable to those of the trimer and tetramer (Table 5.3), but no Na-containing fragments are observed in the UV-TOF spectra under conditions when (HAc)3 and higher oligomers are practically absent in the part of the beam sampled (Section 5.4.1). Given that the trimer clearly does pick up Na atoms (Section 5.4.2), the monomer and the dimer probably do so just as efficiently. In particular it is worth noting that the missing permanent dipole moment of (HAc)2 does not significantly affect the collision cross-section, which is dominated by dispersion interactions.  If it is not the low Na uptake, it must be the lifetimes of the NaHAc and Na(HAc)2 collision complexes that explain why no ion peaks are observed in the UV-TOF spectra of HAc and (HAc)2. The results from SACM calculations in Table 5.3 clearly demonstrate that NaHAc* and Na(HAc)2* dissociate by breaking the Na-cluster bond shortly after Na pick-up. (The asterisk emphasizes that the collision complexes are  116  formed in an excited state.) Figure 5.6 shows the corresponding unimolecular decay rates as a function of  energy for J = 0, 100, 〈ℓmax〉. The curves illustrate the increase of the threshold energy with J due to the  centrifugal potential, but even at threshold the Na–HAc collision complex barely survives a few hundred nanoseconds. For the dimer complex threshold lifetimes of almost 1 ms seem to suggest that Na(HAc)2 could reach the ionisation region intact, but very small excess energies of 50 - 100 cm−1 suffice to reduce the lifetimes of both complexes by about 5 orders of magnitude. At the average collision energy of 1070 cm−1 the Na-doped monomer loses its sodium atom within 2 ps after its formation – far too quickly for any He atom collisions to stabilise it. The situation for the dimer is similar. The loss of Na happens within 100 ps for this cluster. In principle, the collision complex could stabilise by evaporating a HAc monomer, which is the main stabilisation mechanism for larger clusters (vide infra), but the unusually high dissociation energy of (HAc)2 (4797 cm−1 or about 57 kJmol-1) makes this channel inaccessible at the collision energy of 1243 cm−1. It would require at least an additional 2027 cm−1 to evaporate a monomer from the collision complex (Table 5.2). As a consequence, both the Na doped monomer and the Na doped dimer already fragment in the oven and never reach the ionisation region (the flight time from the oven to the ionisation region amounts to about 80 µs). The effects are sufficiently large (many orders of magnitude) that our conclusions are not affected by the uncertainties of the calculated dissociation energies (see Section 5.3.1), which translate into uncertainties in calculated lifetimes of about an order of magnitude.  117  Figure 5.6 Unimolecular decay rates as a function of energy for the Na collision complexes of the acetic acid monomer, NaHAc, and the dimer, Na(HAc)2. D0 = V00(∞) - V00(0) - EZq is the Na + (HAc)n dissociation limit including zero-point corrections, see Eqn 5.7.  5.5.2. Trimer The UV-TOF spectrum of the Na doped trimer shows a strong signal only due to Na(HAc)+ (m/z = 83), while the weak signal at m/z = 143 most likely originates from residual Na(HAc)4 in the beam and not from Na(HAc)3 (see Section 5.4.2). The following scheme illustrates the most likely formation channel of the m/z = 83 fragment ion and explains why m/z = 143 is unlikely to be formed from Na(HAc)3.  118  ܵ‫ ݌݁ݐ‬1 ∶ Na ൅ ሺHAcሻଷ → NaሺHAcሻ∗ଷ ܵ‫ ݌݁ݐ‬2 ∶ NaሺHAcሻ∗ଷ → ൜ ܵ‫ ݌݁ݐ‬3 ∶  NaሺHAcሻ ൅ ሺHAcሻଶ NaሺHAcሻଶ ൅ HAc  NaሺHAcሻ ൅ ݄ν୙୚ → NaሺHAcሻା NaሺHAcሻଶ ൅ ݄ν୙୚ → NaሺHAcሻା ଶ  ሺhigh PI cross െ sectionሻ ሺlow PI cross െ sectionሻ  ܵ‫ ܧܯܧܪܥ‬1. In the case of the acetic acid trimer, sodium pickup (Step 1) is obviously successful in line with the calculated pick up probability of 64% (Table 5.3). The resulting Na(HAc)3* collision complex has an internal energy of 8788 cm−1 (binding energy + collision energy; Figure 5.2 and Tables 5.2 – 5.3). According to Figure 5.2, three neutral dissociation channels Na(HAc)3* → Na(HAc)3−i + (HAc)i are open for the excited complex, corresponding to the evaporation of a monomer (i = 1) or a dimer (i = 2), or the dissociation back into a sodium atom and a trimer (i = 3). All three channels are close in energy, which is mainly a consequence of the formation of strongly bound acid dimer units (Figure 5.2). Note that multiple evaporation, e.g., of two monomers, is energetically not possible. SACM calculations (Table 5.3) predict the stabilisation by evaporation (τ1 = 140 ns, τ2 = 7.5 µs) to be much faster than the loss of the sodium atom (τ3 = 70 µs). Therefore, NaHAc and Na(HAc)2 are formed quickly (Step 2) and constitute the two major species that reach the ionisation region. UV ionisation of NaHAc forms Na(HAc)+, which is observed as a strong peak at m/z = 83. The photoionisation cross-section of this process is expected to be high because the relatively small difference between the vertical (34971 cm−1) and the adiabatic ionisation energy (32536 cm−1) of 2435 cm−1 (ion reorganisation energy, see Table 5.2) indicates only minor geometry changes upon ionisation and hence favourable Franck-Condon factors. Furthermore, the  119  calculated ionisation energies nicely bracket the observed appearance energy of the m/z = 83 fragment (33333 ± 450 cm−1, Section 5.4.2), which confirms the mechanism of Scheme 1. According to the SACM calculations the NaHAc fragment is formed with an average vibrational excitation of Evib = 270 cm−1 yielding a lower bound to the appearance energy of ΔEadiabatic − Evib = 32266 cm−1 (see Table 5.2).  Figure 5.2 also illustrates why Na(HAc)2+ (m/z = 143) is not likely to be observed when formed from Na(HAc)3, even though it is expected to be the major decay fragment arriving at the ionisation region. The corresponding adiabatic and vertical ionisation energies are almost 2 eV apart - a large reorganisation energy resulting from major geometry changes - which in turn implies extremely unfavourable FranckCondon factors and hence a small photoionisation cross-section, even high above the adiabatic ionisation energy. Evaporation leaves the remaining Na(HAc)2 with only modest vibrational excitation of 1150 cm−1, so that low Franck-Condon factors are the most plausible reason why Na(HAc)2+ is not observed in the UV-TOF spectrum following sodium pickup by (HAc)3.  We stress again that the uncertainties of the calculated energetics discussed in Section 5.3.1 do not affect the above conclusion, since the arguments are based on order of magnitude considerations and the calculated energetic ordering of different fragmentation channels is quite reliable. Let us assume for a moment that a significant fraction of Na(HAc)3* could reach the ionisation region, even though this is not in agreement with the SACM results discussed above. In this case, the fragmentation would have happened after UV photoionisation of Na(HAc)3*. The energetics as well as the observed appearance energies for Na(HAc)+ and Na(HAc)2+ would be consistent with this (Figure 5.2). At photoionisation energies above 33333 cm−1 (in between the adiabatic and vertical ionisation energies of Na(HAc)3), the photoionisation efficiency might be high enough to form Na(HAc)3+, which would then immediately decay into NaHAc+ + (HAc)2 and Na(HAc)2+ + HAc. The fact, however, that Na(HAc)2+ (m/z = 143) is not observed (or only in very small amounts) clearly speaks against this scenario, as do of course the SACM results. Whenever NaHAc+ is observed in the UV-TOF spectrum, Na(HAc)2+ should also be 120  observed, if the fragments were to originate from ionic dissociation of Na(HAc)3+ (Figure 5.2). Furthermore, in this case the Na(HAc)2+ yield should be even higher than that of NaHAc+ because the latter lies significantly higher in energy (about 2500 cm−1). Again, the experimental spectrum of Figure 5.4(a) clearly contradicts such a scenario. While the UV-TOF of the trimer cannot be convincingly explained in this way, an analogous scenario provides the most likely explanation in the tetramer case.  5.5.3. Tetramer and larger clusters For the tetramer and larger clusters, it is much more difficult to determine the major formation channels of the ions observed in the UV-TOF spectra. The interpretation of the experimental data is less clear in this case, since the spectra of larger clusters always contain contributions from smaller clusters. Furthermore, fragmentation patterns of larger systems are likely to be more complex due to the increased number of possible fragments. Here the combination of experimental results with the theoretical prediction of energetics and fragmentation kinetics proves instrumental in drawing a consistent picture of the processes underlying the observed UV-TOF spectrum.  The Na uptake probability of Na(HAc)4 in the Na oven is similar to that of the smaller clusters (Table 5.3), and its fragmentation kinetics bear strong analogies to those of Na(HAc)3. The SACM calculations confirm the increasing dominance of monomer evaporation stabilising the original collision complex Na(HAc)4* (Step 1 in Scheme 2).  The loss of HAc monomer is many orders of magnitude faster than any of the other possible dissociation channels. According to the B3LYP calculations, the available energy ( D0 + 〈E〉 = 10700 cm−1 ) is just not  enough to evaporate a trimer (Table 5.2), so that the production of NaHAc is expected to be insignificant. While the evaporation of a dimer is possible, evaporation of a single monomer is much faster than any of the other decay channels, since it is strongly favoured energetically. According to the SACM calculations,  121  ܵ‫ ݌݁ݐ‬1 ∶  NaሺHAcሻ∗ସ  NaሺHAcሻଷ ൅ HAc → ቐ NaሺHAcሻଶ ൅ ሺHAcሻଶ ሺvery slowሻ NaሺHAcሻ ൅ ሺHAcሻଷ ሺnegligibleሻ  ܵ‫ ݌݁ݐ‬2 a ∶ NaሺHAcሻଷ ൅ hν୙୚ → NaሺHAcሻା ଷ b ∶ NaሺHAcሻଶ ൅ hν୙୚ → NaሺHAcሻା ଶ c ∶ NaHAc ൅ hν୙୚ → NaHAc ା ܵ‫ ݌݁ݐ‬3 ∶ NaሺHAcሻା ଷ → ൜  ሺlow PI cross െ sectionሻ  NaHAc ା ൅ ሺHAcሻଶ NaሺHAcሻା ଶ ൅ HAc  SCHEME 2. on average 86% of the excess energy stays with the remaining Na(HAc)3 in the form of vibrational excitation Evib = 5022 cm−1, so that the evaporation of a second monomer would be energetically possible, but the corresponding lifetime is on the order of 10 ms. Of all the possible sodium containing fragments of the tetramer that could reach the ionisation region (Step 2), Na(HAc)3 is by far the dominant one, and it will carry significant internal excitation. The energy disposal predicted by SACM (86% of total available energy as vibrational excitation) accords with previous observations for Na(H2O)n clusters.128 The ionisation of Na(HAc)3 (Step 2a) and subsequent fragmentation in the ionic state (Step 3) is the only path that forms both the m/z = 83 and the m/z = 143 fragments observed in Figure 5.4(c). In other words, this path must contribute to the UV spectrum if Step 1 is the dissociation in the neutral state as suggested in Scheme 2. This path is consistent with the energetics in Figure 5.2 and with the fact that no m/z = 203 [Na(HAc)3+] is visible in the UV spectrum. The observed appearance energy of Na(HAc)2+ (33333 ± 450 cm−1) also fits perfectly into the scheme, which predicts a value of 32990 cm−1 (ΔEadiabatic − Evib, see Table 5.2). The appearance energy for the monomer fragment ion NaHAc+ formed via Scheme 2 would lie 2500 cm−1 higher, a further independent hint that the m/z = 83 signal in the 122  UV-TOF arises from Na(HAc)3 rather than from Na(HAc)4. The fact that the observed values for the m/z = 83 and m/z = 143 appearance energies are the same (within experimental uncertainties) must be considered a mere coincidence. We note again that direct photoionisation of the Na-doped dimer (Step 2b) is unlikely to contribute to the m/z = 143 signal in the UV-TOF spectrum not only by kinetic arguments, but also because of the large ion reorganisation energy (Figure 5.2). Finally, photoionisation of the Na doped monomer (Step 2c), if formed, could in principle contribute to the m/z = 83, but obviously not to the m/z = 143 signal.  5.6. Conclusions The determination of ionisation energies of sodium doped molecular clusters from UV photoionisation spectroscopy is a standard approach to investigate size-dependent properties of these clusters. In the present study, we have combined this method with XUV photoionisation and with modeling of cluster energetics and fragmentation kinetics to obtain information on the cluster composition in the molecular beam prior to ionisation. The example of small sodium doped acetic acid clusters demonstrates how crucial such independent information is for the proper interpretation of the ultraviolet photoionisation spectra (Figure 5.4). Only the combination with XUV spectra (Figure 5.3) and the prior knowledge of characteristic fragmentation patterns made an unambiguous assignment of the UV-TOF spectra possible.  No ion signals are observed in the UV-TOF spectra if only Na(HAc) and Na(HAc)2 are present in the molecular beam because of fast dissociation of the collision complexes into their original components. For the sodium doped dimer, this is a consequence of the strong (HAc)2 bond, which makes evaporation of an acetic acid monomer impossible. It is worth noting that the sodium capture itself is not the limiting step, since it is dominated by the dispersion interaction, which is quite similar for all the clusters studied here. The major UV ion signals of Na(HAc)3 and Na(HAc)4 are NaHAc+ (m/z = 83) and Na(HAc)2+ (m/z = 143), respectively. NaHAc+ originates from dissociation of Na(HAc)3 in the neutral state and 123  subsequent photoionization of NaHAc. In this case, the appearance energy of m/z = 83 roughly corresponds to the ionisation energy of NaHAc. Na(HAc)2+, by contrast, is formed from Na(HAc)4 in a sequential fragmentation in the neutral and in the ionic state. The measured appearance energy of m/z = 143 provides absolutely no measure for the ionisation energy of Na(HAc)2. The fact that both appearance energies have the same value is purely coincidental.  Without the additional information from XUV experiments and from modeling, the interpretation of the UV spectra and of the observed appearance energies would probably have been rather different from the scenario unravelled in the present study. Statements about fragmentation and the assignment of ionisation energies based on standard UV photoionisation experiments alone can be uncertain and make further conclusions tenuous, in particular for small clusters. Na doping followed by UV photoionisation is not a good technique for ‘sizing’ the smallest of clusters, but it allows one to obtain information on the influence of the sodium doping and photoionisation induced fragmentation processes. These studies help us to pin-point key processes which have to be considered in a particle sizer for larger clusters/ultrafine aerosol particles. Sodium doping in the context of sizing these larger clusters is discussed in Chapter 6.  124  6. Photoionisation of Large Sodium Doped Clusters and Ultrafine Aerosol Particles  6.1. Introduction In this chapter the study of the sodium doping of molecular clusters followed by UV photoionisation, as introduced in Chapter 5 for small acetic acid clusters, is extended to particles of much greater size and a “fragmentation free” ultrafine aerosol particle sizing instrument is proposed based on the technique.  Aerosol particles have traditionally been sized by light scattering techniques. With decreasing size, however, the wavelengths required to scatter off the particles become shorter (in the XUV range for ultrafine aerosol particles) and increasingly difficult to work with. Furthermore, refractive index data is required to obtain size information and becomes increasingly sparse in the XUV range. An important advantage of the technique is its ability to be used for volatile particles, but a disadvantage is the lack of chemical information to be obtained.  SMPS (scanning mobility particle sizer) devices are an important class of aerosol particle sizing instruments which go down well into the ultrafine aerosol particle range. SMPS instruments are composed of two main components, a DMA (differential mobility analyser) and a CPC143,144 (condensation particle counter). The DMA imparts the particles a well characterised distribution of charge, and then separates them based on their mobility in an electric field. The particles then travel into the CPC where they pass through a supersaturated vapour (usually butanol or water) which condenses onto the aerosol particles, enlarging them to µm diameters so that they can be counted by means of laser light that they scatter. Modern SMPS instruments are capable of sizing particles down to ~ 2.5 nm diameter. Recent developments, albeit still in the research phase, have brought this limit down to  125  1 nm.145,146 The method is extremely sensitive, however SMPS provides only a size distribution and absolutely no chemical information. Most importantly in the present context, however, the instrument does not work with volatile or semi-volatile systems.  Other techniques which may be used to size aerosol particles include IR spectroscopy,25 inner shell ionisation,26,27 helium atom scattering,28 electron scattering,31 neutron and x-ray scattering29,30 and mass spectrometry. Except mass spectrometry, however, all these techniques suffer from severe limitations and are not broadly applicable. For example, in the case of IR spectroscopy approximate size information of clusters in the nm range can indeed be extracted from experimental data, but very extensive modelling is needed in order to do so. The other techniques suffer from similar problems and provide only a rough estimate of size.  TOF mass spectrometers have been used in mass spectrometric studies of clusters,34,35,37,38,114,147 ambient atmospheric cluster ions148 and non-volatile ultrafine aerosol particles149 because they conveniently do not have a theoretical upper mass limit. Quadrupole mass spectrometers have also been used.150 The upper mass limit does indeed become a technical limitation for masses over about 1⨯106 u, which become too heavy to be detected with most ion detectors. This does, however, allow the study of an important range of ultrafine aerosol particles.  The ionisation step imperative to mass spectrometric analysis poses a significant challenge because most conventional ionisation techniques, such as electron ionisation (EI), may cause very significant fragmentation of weakly bound aerosol particles thus rendering it impossible to measure unfragmented size distributions.34,35 Many soft ionisation techniques have been developed over the years, but most are not “soft” enough for volatile or semi-volatile aerosol particles. Others are inherently selective toward some species over others, which is not acceptable for a generic particle sizing instrument. Techniques used include chemical ionisation,151,152 low energy electron ionisation (PERCI),153 resonance enhanced 126  multi photon ionisation (REMPI),35 multi photon ionisation (MPI)149 and single photon ionisation (SPI) above the ionisation threshold.37,38,114,147 It has to be noted that the requirements regarding the “softness” of the ionisation technique are very stringent for volatile clusters or volatile ultrafine aerosol particles. Whereas the average intramolecular bond strength is on the order of a few 100 kJmol-1, strong intermolecular hydrogen bonds are only on the order of ~10 kJmol-1 and intermolecular bonds are even weaker in van der Waals clusters. In this work, the term “soft ionisation” is used in the context of retaining the size and chemical composition of such weakly bound clusters and aerosol particles.  A special ionisation technique which involves doping the sample species with an atom of sodium and single photon ionising the doped species with a UV photon32,33,54,65,124 was used by Buck and coworkers34,35,55 to ionise large noble gas clusters as well as water and ammonia clusters. This technique, referred to hereafter as the “sodium doping technique”, is believed to be the softest of the aforementioned techniques. It has so far been characterised for a number of well-defined systems by Buck et al. and established as indeed being soft in comparison with electron ionisation. A generalisation of the approach for the construction of an ultrafine aerosol particle sizer, however, has never yet been sought and is proposed here. The goal of the present study is to apply the sodium doping followed by UV photoionisation technique to ultrafine aerosol particles and develop a quantitative instrument which will be capable of sizing these particles in a “fragmentation free” fashion. The instrument, encompassing a TOF mass spectrometer, could also provide a limited level of chemical information based on the particles’ total mass, at least in the lower mass range.  In this Chapter the first steps undertaken towards such an instrument are presented. Processes involved in the sodium doping technique are presented in Section 6.2 and ways in which they have to be taken into account in the context of a generic ultrafine aerosol particle sizing instrument are discussed. The first measurements which show that large clusters beyond the systems studied by Buck et al. are nondestructively ionised by the sodium doping technique are shown in Section 6.4. These clusters are shown 127  to have undergone little or no chemical change by comparison with spectra of the same sample recorded with XUV single photon ionisation.  6.2. Soft Ionisation by Sodium Doping and UV Excitation Interest in doping small molecular aggregates with alkali atoms, especially sodium, was sparked in 1986 by the work of Schulz and coworkers on sodium-water clusters.32 In the early days focus was primarily on how the water – sodium reaction behaves as one studies it from the microscopic to the macroscopic scale, and on the concept of electron solvation32,33,35,54,55,65,66,74,123-135 (see also Section 5.1). In later work by Buck and coworkers, the potential for “fragmentation free” detection of volatile clusters using the technique was realised and large noble gas, water and ammonia clusters were studied.34,35 In this research the sodium doping technique was used to demonstrate that electron ionisation does lead to strong fragmentation of weakly bound clusters, in contrast to what was previously believed. On the specific and only case of large ammonia clusters, the technique was found comparable to (1+1) REMPI.35  The technique relies on attaching a sodium atom to small aerosol particles so that the doped clusters can then be ionised by relatively low energy UV photons, otherwise incapable of surmounting the ionisation energy of the parent species. This is believed to be advantageous over direct ionisation of the parent cluster for a number of reasons. A reason introduced in the literature by Buck et al. with respect to noble gas clusters is that the potential energy surface of the cluster’s cationic state, formed after direct ionisation of the parent cluster, is frequently much more strongly bound than in the neutral state.35 This leads to a large difference between the adiabatic and vertical ionisation energies, and to low Franck-Condon factors into the lowest energy levels of the cation. Ionised species are therefore typically formed in vibrationally excited states, and this energy can lead to evaporation of monomer units from the particle. The ground and cationic potential energy surfaces of the sodium doped species are, however, relatively similar due to  128  the nature of the cluster-sodium bonding,35 which reduces this problem. This argument is not applicable to all chemical systems and does not, in our opinion, provide a complete explanation.  A further advantage of the dopant chromophore is the fact that the ionisation energies of even chemically diverse species are brought together into a fairly narrow and easily accessible UV range. Whereas the ionisation energies of bare, atmospherically relevant atoms, molecules and their clusters span a range of at least 7 eV, sodium doped species have IEs spanning about 2.5 eV only (the IEs of sodium doped clusters typically decrease as a function of size, with a dependence on the chemical nature of the species, often attributed to inner and outer solvation shells66). This allows the use of a single UV wavelength for many different substances whilst minimising the excess energy potentially introduced by the photon’s excess energy. Furthermore, the photon energy range required to cover near-threshold ionisation for all atmospherically relevant species now occupies a narrower energy spread in a more easily accessible energy range (UV), whereas the corresponding range for the direct ionisation of the bare cluster is much greater and in an energy range significantly technically harder to generate (XUV). The issue of excess energy by excitation with a photon higher in energy than the ionisation energy is, however, likely taken care of by the fact that after photoionisation the emerging photoelectron carries away most of the energy anyway. 37,38  Another downside of direct single photon ionisation with regard to weakly bound molecular aggregates which does not seem to have been discussed thoroughly in literature is the release of energy due to ionic chemistry triggered by the VUV / XUV photon. This property is very sensitive to the chemical system, but in molecules with accessible fragmentation channels, energies on the order of up to a few eV (a few hundred kJmol-1) may be released if the ionised monomer unit undergoes fragmentation. This energy can then directly go towards the evaporation of many monomer units, in weakly bound cases on the order of a few 10s of molecules.  129  In Chapter 5, it is shown that when using the sodium doping technique on small clusters, the sodium  capture process may result in the evaporation of ~ 2 monomer units to stabilise the neutral doped cluster.  A further ~ 2 units may be evaporated upon photoionisation to stabilise the cationic cluster. These  numbers are likely to vary with the specific chemical system, but will not change sufficiently to exceed a total of “a few” monomers evaporated from the parent cluster. Whereas for the smallest clusters this means the technique cannot be used for “sizing”, this amount of monomer loss is completely inconsequential to a larger particle, especially in comparison with other available ionisation techniques (see Section 6.4).  The ultimate goal of this work is to develop the sodium doping technique into a quantitative method for measuring the size distributions of ultrafine aerosol particles. To achieve this goal all the processes involved in the sodium doping technique and their effects on what is observed on the MCP ion detector have to be considered and eventually corrected for if necessary. An overview of the results from this work is presented here and further characterisation is underway in our research group. The different processes which have to be considered are shown schematically in Figure 6.1.  In the current experimental setup, clusters and ultrafine aerosol particles are created in a cryogenic molecular beam nozzle (see Section 2.1.3.b) by varying the temperature and pressure (Process I). This affords a lot of flexibility in the generation of particles over a broad size range. The molecular beam thus formed is skimmed and passed to the sodium oven.  The sodium capture probability (Process II) is the next step, and was discussed briefly in Chapter 5 in the context of small clusters. Figure 6.2 shows the dependence of the capture probability as a function of size as presented in reference [154]. The figure pertains to ammonia clusters but very similar behaviour is predicted for other species such as water, carbon dioxide or ethanol. For small particles with diameters  130  Figure 6.1 Schematic representation of the processes which affect observed size distributions of sodium doped species. I. particle generation during supersonic expansion (in systems where the particles are generated in situ), II. sodium capture probability, III. any scattering out of the molecular beam as a result of the collision with sodium, IV. fragmentation of neutral sodium doped species, V. ionisation efficiency determined by ionisation cross-section, VI. ionic fragmentation and VII. MCP sensitivity variation with particle mass. Label locations are not necessarily accurate; for details see text.  below 1 nm, long range dispersion forces yield greater sodium capture cross-sections and therefore have to be considered – however a relatively high capture probability is predicted regardless. In the case of larger particles, above 1 nm diameter, the hard sphere diameter determines the capture cross-section. This leads to two conclusions – for these particles the sodium capture probability is independent of chemical composition, and can easily be corrected for with a geometric factor.  The collision with a thermalized sodium atom may for the lightest particles be significant enough for them to be scattered out of the molecular beam before they reach the ionisation volume (Process III), but is insignificant for large particles and can largely be ignored in the context of the ultrafine aerosol particle sizing instrument. 131  Figure 6.2 The sodium capture probability as a function of particle size, exemplified on the case of NH3 particles. An oven temperature of 225 °C was used. For particles below 1 nm in diameter the long range interactions incorporated into the Langevin model dominate the capture probability, but for larger particles the geometric diameter determines the probability. Figure adapted from reference [154].  As soon as a sodium atom is captured, the lifetime of the doped species determines whether or not it may reach the ionisation region, travelling the distance between the sodium oven and ionisation region at the velocity of the molecular beam – a time of ~80 µs. (Process IV). An important aspect in connection with this lifetime is the question of how fast the collision energy can be redistributed into the particle. The determining step is most likely intramolecular vibrational relaxation (IVR) within the immediate collision partner molecules. Because this is a local process, we do not expect the lifetime with respect to sodium dissociation to strongly depend on the size of the species being doped. Thus, only very minor size dependent corrections are expected for the sodium “sticking” probability. From the small cluster work  132  presented in Chapter 5 it is known that in cases where the sodium atom does not dissociate from the cluster (i.e. it “sticks”), the cluster loses on the order of only a few monomer units to stabilise itself instead. This amount of fragmentation is insignificant for larger clusters and ultrafine aerosol particles.  If the lifetime of the sodium doped species is sufficiently long to be carried to the ionisation volume, it interacts with the ionising laser (Process V). The number of sodium doped clusters ionised by the laser depends on the ionisation cross-section of the species, which is probably similar for different aerosol particles because the ionisation process is likely primarily localised on the sodium atom. Therefore, this process also does not require a correction for species of different size. Following the ionisation process, there may be some excess energy which can cause a second round of fragmentation (Process VI), this time in the ionic state. From the work done with small clusters in Chapter 5 it is known that only a few molecules are likely to evaporate from the doped cluster at this stage, which, again, is insignificant for larger species.  Finally, the MCP ion detector response varies as a function of particle mass (Process VII). This effect can be ignored for low masses if a sufficiently high extraction voltage is used, as was done in Chapter 5 and in all referenced sodium doping work. However, the detector sensitivity at higher masses is reduced and the count of heavy ions is artificially decreased. This can be accounted for using a correction based on the approach published by Gilmore and Seah.60 The spectra presented in this chapter are not corrected for MCP sensitivity, however it is shown that such a correction is imperative to the correct interpretation of spectral intensities.  Figure 6.3 shows the mass spectra of dimethyl ether (DME) clusters recorded at different extraction voltages with intensities normalised for the strongest signal. The signal intensities observed for the heavier particles, even below m/z = 500, are shown to increase relative to the intensities of their lighter counterparts as the extraction voltage is increased throughout the voltage range used (up to 4 kV). This 133  indicates that either a higher extraction voltage than 4 kV is needed to ignore MCP sensitivity in this mass range, or that a size dependent correction should be applied to mass spectra recorded at these extraction voltages. In cases where heavy ion signals fall below the detection limit a correction is clearly insufficient. These findings are consistent with reference [60], where it is shown that 100% detection  efficiency for particles of about m/z = 1100 is only reached at ~ 10 keV ion energy. They indicate,  however, that caution has to be exercised in interpreting peak intensities of heavier species in published results which do not correct for MCP sensitivity.  To allow for the quantitative analysis of size distributions obtained using the sodium doping technique, the processes outlined above have to be considered for particles of different sizes. It appears that corrections for the sodium capture and for the MCP detection efficiency would be largely sufficient towards this goal. Both of these corrections can be implemented and will be applied to future work in our research group.  A number of points about the particle sizing instrument have to be proven in laboratory based studies before it can be considered for ultrafine aerosol particle sampling. These could be listed chiefly as 1. applicable over a useful size range, i.e. 0 - 20 nm, 2. suitable for volatile, semi-volatile and non-volatile species, 3. with minimal chemical selectivity, 4. useful, within limitations, for chemical composition analysis and 5. relatively simple so as to be used in a future portable field instrument. In Section 6.4 we show the first data obtained with the intention of starting to address these key points.  134  Figure 6.3 Mass spectra of dimethyl ether clusters as a function of the extraction voltage used. The high mass extractor was used for this study, however for technical reasons a maximum extraction voltage of only 4 kV was realisable at the time. The traces are intensity normalised to the most intense cluster, in this case n = 5.  6.3. Experimental The mass spectra presented in this chapter were recorded using the experimental apparatus described in Chapter 2, in the configuration where the sodium oven chamber is installed between the sample injection chamber and the TOF chamber (see Section 2.1.5 and Figure 2.3).  Molecular clusters and ultrafine aerosol particles were generated in situ by supersonic expansion using the cryogenic nozzle (Section 2.1.3.b). Temperature control was not always required and the recirculating chiller was sometimes only used to stabilise the nozzle temperature at 20 °C. An orifice diameter of 0.25 mm was employed in these studies. The ammonia (Praxair, 4.5) and dimethyl ether (Specialty Gases 135  of America, 99.7%) samples were injected neat at 2 and 4 bar absolute pressure, respectively. The acetic acid (glacial, Fisher Scientific) sample was prepared as 17 mbar acetic acid in 2 bar absolute pressure of helium (Praxair, 5.0). The sodium oven was operated at a temperature of 210 °C on the bottom and 130 °C on the top (see Section 2.1.4).  The mass spectra shown were recorded using the high mass extractor (Section 2.1.5.a) with two separate high voltage power supplies charging the repeller and extractor plates, which allowed for the optimisation of Wiley-McLaren focussing with ease. The mass resolution thus obtained was ~ 300 at m/z = 3000. Due  to this setup and the power supplies available at the time, however, we were limited to a total extraction voltage of 5 kV. A slightly lower extraction voltage of 4 kV was shown to be too low, even for clusters in the 500 u range, to be detected with maximum efficiency, hence spectra recorded at 5kV most probably suffer from the same problem. Cluster ion signal intensities in the spectra presented are not corrected for this effect and should therefore not be treated quantitatively. A correction will be applied as part of future work underway in our research group.  The mass spectra using XUV ionisation are recorded using the 3ν1 process of the lower krypton resonance (70.9 nm, 17.5 eV). The UV spectra shown were recorded using the UVIII beam of the Quantel laser at  266 nm, with ~ 10 mJ/pulse laser energy. The central part of the molecular expansion at a total opening time of 1 ms was sampled by the laser in each case to maximise the cluster size distribution observed (see Section 5.2).  136  6.4. Results 6.4.1. Ammonia With the objective of demonstrating for the first time the applicability of the sodium doping technique to larger systems in the ultrafine aerosol particle range, studies of ammonia particles were undertaken. Figure 6.4 shows four mass spectra of sodium doped ammonia particles generated in situ in a neat expansion of ammonia gas under different nozzle conditions adapted to obtain different particle size distributions.  Whereas any quantitative analysis of the spectra without applying the MCP sensitivity correction is meaningless, qualitatively it is clear that particles in the ultrafine aerosol particle range can indeed be studied using the sodium doping technique. Furthermore, it is shown that different size distributions of such particles can be generated in situ in the experiment only by varying expansion conditions (temperature and pressure).  6.4.2. Dimethyl ether Chemical changes and structural rearrangements in clusters following ionisation lead to release of energy which can be used to evaporate molecules from the clusters, thereby altering their initial size. With the intention of investigating the amount of chemical change induced in large clusters by ionisation using the sodium doping technique, results were compared to another “soft” ionisation technique – the single photon XUV ionisation of bare clusters. Besides the sodium doping technique, ionisation with XUV would likely be considered the softest ionisation technique available for molecular clusters.37,38  The mass spectra of DME clusters recorded using XUV ionisation and UV ionisation after sodium doping are shown in Figure 6.5. Both spectra were recorded under identical experimental conditions in rapid  137  Figure 6.4 Mass spectra of large ammonia particles generated, doped with sodium and photoionised with UV light (266 nm). The spectra were recorded using the ZEKE extractor in single field configuration at a total voltage of 4.5 kV. The following expansion conditions of neat ammonia pressure, nozzle temperature and resulting saturation ratio were utilised: (a) 3 bar, 21°C, 0.34 (b) 3 bar, -2°C, 0.76 (c) 3.5 bar, -2°C, 0.89 (d) 6 bar, 21°C, 0.69. Note the y-axis scale change between (a) and all other spectra, and the x-axis change between (a), (b) and (c), and (d). The particle diameter was calculated from mass using the density of solid ammonia at 77 K 155 assuming spherical particles.  138  Figure 6.5 Comparison of the mass spectrum of dimethyl ether clusters obtained using the sodium doping technique in trace (a) with that using XUV ionisation in trace (b). High intensity sub-monomer fragment signals are cut off on the scale shown in trace (b). The labels indicate clusters Na(DME)n in trace (a) and (DME)nH in trace (b). The small peaks observed between ether peaks in trace (a) in some instances also in trace (b) are due to ether clusters with a single water molecule incorporated.  139  succession of each other. The XUV and UVIII laser beams were temporally synchronised to sample the same portion of the molecular beam.  The XUV spectrum shows a distribution dominated by protonated DME clusters and DME monomer fragments, in agreement with previous literature studies using MPI.156 However, this distribution is clearly shifted to much smaller clusters compared to the distribution observed using the sodium doping technique. In the case of DME, the XUV spectrum shows a size distribution smaller than the UV spectrum size distribution by ~ 10 monomer units. This is a very significant change, even if the determination of the number itself is somewhat approximate. Furthermore, trace (a) shows a distribution of chemically unchanged species, doped with a single atom of sodium only. As discussed previously, the loss of only a few monomer units from the original clusters is expected in this technique, but it appears that besides this loss and the addition of a sodium atom the cluster remains chemically unchanged. The XUV ionisation method is shown, at the very least in this particular case, to not be very “soft” after all. Reasons for this change are briefly discussed in Section 6.5.  6.4.3. Acetic acid Analogous studies as for the large ether clusters described above were also performed for large acetic acid clusters. Acetic acid was chosen to build on previous work on small acetic acid clusters presented in Chapter 5. The spectra recorded are shown in Figure 6.6.  In the case of large acetic acid clusters the difference in the size distributions obtained using the two ionisation techniques is even more striking. A visual estimate of a loss of about ~ 20 monomer units is made for the XUV spectrum compared to the UV spectrum. Once again, protonated clusters and cluster fragments are observed in the XUV spectrum while the UV spectrum only shows sodium doped species. It should be noted that – even in the UV spectrum – the ion signals observed originate from larger clusters which have evaporated a few monomer units, as demonstrated for m/z = 83, 143 and 263 in Chapter 5. 140  Figure 6.6 Comparison of the mass spectrum of acetic acid clusters obtained using the sodium doping technique in trace (a) with that using XUV ionisation in trace (b). Intense signals due to AA cluster fragments at m/z 83, 143 and 263 (see Chapter 5) are cut off on the scale shown in trace (a). The labels indicate clusters Na(AA)n in trace (a) and (AA)nH in trace (b).  141  6.5. Discussion and Conclusions The combination of the sodium doping technique with direct XUV ionisation of bare clusters is unique to our experiment, and allows for a novel comparison of the two techniques. The sodium doping technique had only in one specific case of ammonia clusters been compared to (1+1) REMPI by Buck et al.,35 where it was found to be comparable within experimental uncertainties. Beside the sodium doping technique, XUV ionisation is believed to be the softest ionisation technique available for molecular clusters.37,38 Its comparison with the sodium doping technique is therefore of significance.  Potential problems with XUV ionisation technique which may lead to monomer evaporation from the parent cluster potentially involve 1. excess energy above the vertical IE, 2. excess energy in the form of vibrational excitation above the adiabatic IE at the vertical IE, 3. chemical changes and structural rearrangements after ionisation. Of these the first is not believed to be a problem because the photoelectron should take most of the excess energy.37,38 The second is likely less severe than the third because it only involves vibrational energy, whereas the third may involve much larger energies which come about as a result of bond breaking. Chemical changes and structural rearrangements upon ionisation are therefore expected to drive the evaporation of molecules from parent clusters after XUV photoionisation. This argument is also true for most other ionisation techniques. Disregarding this, XUV ionisation has been used in a number of studies of clusters of water, ammonia, methanol, formic acid, acetic acid and acid-water mixed systems.37,38,114,147 In work by Bernstein et al., a VUV (10.5 eV, 118 nm) photoionised mass spectrum of acetic acid was shown to be similar to conventional EI (70 eV) spectra,36 albeit with slightly different fragmentation branching ratios.114  The energy released upon chemical changes in the large ionic clusters of dimethyl ether is sufficient to evaporate about ~ 10 monomer units as demonstrated in Figure 6.5. An equivalent number in the case of  large acetic acid clusters is ~ 20 monomer units (Figure 6.6). These numbers are relative to the sodium 142  doping technique, which itself results in the evaporation of a maximum of a few monomer units. The amount of evaporation observed in XUV spectra is clearly very significant and shows that, at least for the two cases shown here, XUV ionisation cannot be considered a “soft” ionisation technique. Energetic analyses of the possible chemical changes upon direct ionisation are currently under investigation in our research group to provide a theoretical basis for the above observations.  The sodium doping technique is not affected by such chemical changes because the energy involved in the UV ionisation step is clearly insufficient to ionise the bare cluster itself. The UV spectra of dimethyl ether and acetic acid presented demonstrate that this is indeed the case. The absence of any molecular fragments shows that no ionic chemistry is taking place in the clusters upon ionisation beyond the sodium doping and its associated loss of a few monomer units during the sodium capture and photoionisation processes. The sodium doped and UV ionised spectra can therefore be considered as “fragmentation free” ionised as is presently possible.  To conclude, the sodium doping technique has been demonstrated to work with systems of the size of ultrafine aerosol particles on the example of ammonia particles. By comparison with ionisation using XUV radiation, the technique is shown not to induce chemical changes in the cluster. Such evaporation is  extensively observed in XUV ionisation, which leads to the evaporation of several ~ 10 monomer units from the original cluster. The sodium doping technique results in the evaporation of only a few monomer units itself (Chapter 5). These findings show it to be a truly soft ionisation technique. The result that the  sodium doping technique is softer than XUV ionisation is beneficial to the technical simplicity of the future ultrafine aerosol particle sizing instrument, because the complexity of the incorporation of a sodium oven and the use of a UV laser is far less than that of using an XUV light source. These results are therefore promising for the construction of a generic, quantitative ultrafine aerosol particle sizing instrument based on the sodium doping technique. Further characterisation work towards this goal is, however, necessary and is currently underway in our research group. 143  7. Conclusions and Outlook A new, state-of-the-art photoelectron/photoion spectrometer has been built, tested, and used for a series of investigations. The experimental setup evolved from a PFI-ZEKE photoelectron spectrometer, employed in studies of atmospherically relevant species – difluoromethane and acetic acid – to an ultrafine aerosol particle TOF mass spectrometer equipped for fragmentation free size distribution measurements of volatile particles. The experimental setup is described in Chapter 2.  The PFI-ZEKE photoelectron study of CH2F2 was used to fully characterise the instrument with regards to both electron and ion measurements (Chapter 3). The investigation elegantly demonstrated the capabilities of PFI-ZEKE spectroscopy compared to conventional photoelectron spectroscopic methods. The vibrational resolution of the PFI-ZEKE photoelectron spectrum unravelled a long-standing mystery regarding the origin of a broad progression of peaks observed in earlier low resolution spectra. Following comparison with harmonic, and ultimately anharmonic calculations of the vibrational dynamics the measured spectrum was almost completely assigned. The assignment revealed strong resonances between symmetric and non-totally symmetric vibrational modes and the onset of transitions at higher energies which can no longer be attributed to individual normal modes, due to the onset of cationic fragmentation. Measurements of appearance energies of cationic fragments also raised the question about the difference between electron ionisation and photoionisation at the same energy.  Studies of a system of increasing size, from the molecular, through the small molecular cluster to the aerosol particle scale, were undertaken on the case study of acetic acid. As a first stepping stone, a PFIZEKE photoelectron spectroscopic investigation of the acetic acid monomer was undertaken (Chapter 4). This study demonstrated the sensitivity achievable in PFI-ZEKE spectroscopy, as the acetic acid  monomer was only present in the molecular beam at a concentration of ~ 100 ppm. Furthermore, the importance of careful theoretical analysis of photoelectron spectra was demonstrated – a previous band-  144  centre assignment of the adiabatic ionisation energy was inaccurate because the band centre, at the low resolution of the photoelectron spectrum, was shifted due to the presence of torsional hot bands on the high energy side and broad rotational structure. These were resolved in the PFI-ZEKE photoelectron spectrum measured in this work.  In the second stepping stone, the technique of doping clusters or aerosol particles with an atom of sodium followed by UV photoionisation as a soft ionisation method, intended for future use with aerosol particles in a “fragmentation free” particle sizer, was assessed with the smallest of acetic acid clusters (Chapter 5). Our experimental setup is unique in allowing direct comparison between XUV ionisation of the undoped species and UV ionisation of the sodium doped species. In cases where XUV ionisation data is available in the literature, the composition of the molecular beam can be assessed using XUV ionisation and the same sample can then be probed with UV light. Our study reveals that for small clusters (AA)n with n ≤ 8, the sodium doping and the UV photoionisation processes depend strongly on the particular cluster, and are not fragmentation free. It is shown how sodium capture probability, the lifetimes of the sodium collision complexes and processes induced by UV photoionisation determine which clusters are actually observed. This means that great caution has to be exercised in interpreting ion signals of the form Na(X)n in UV photoionisation spectra of sodium doped substances X, because the species may not originate from (X)n, but from (X)n+m instead, where m represents the number of monomer units lost as a result of sodium capture and UV photoionisation. In the case of small acetic acid clusters, the number of monomer units evaporated is estimated at m ≲ 4 but varies on a case-by-case basis.  Chapter 6 explores the sodium doping technique as a “fragmentation free” sizing method for semi-volatile and volatile ultrafine aerosol particles. The study of small clusters in Chapter 5 revealed that only a few monomer units are evaporated in the sodium doping and UV photoionisation processes. For ultrafine aerosol particles the loss of a few monomer units becomes negligible in comparison to their overall size.  145  The sodium doping technique is thus likely to be much softer than other ionisation methods, of which XUV single photon ionisation is considered to be among the softest.  One of the major issues with most ionisation techniques, including XUV single photon ionisation, are chemical changes and structural rearrangements which happen after the ionisation of a monomer unit within a cluster. Energy released in these processes leads to the evaporation of many monomer units from the aerosol particle. UV photoionisation spectra after sodium doping are thus compared with XUV spectra to test this statement. In Chapter 6 we show this to be up to ~ 10 units in the case of large dimethyl ether clusters and ~ 20 units in the case of acetic acid clusters. XUV single photon ionisation is therefore proven, in some cases, to be far from a “soft” ionisation technique. The same, however, holds true for other ionisation techniques such as electron ionisation. Sodium doping followed by UV photoionisation does not suffer from this effect and can be used as a relatively fragmentation-free reference. Except for the addition of a sodium atom, the sodium doping technique leaves the chemical composition largely intact. Experiments with other substances are currently underway in our laboratory to investigate these findings systematically.  Work presented in Chapter 6 shows the potential of the sodium doping followed by UV photoionisation technique in the construction of a particle sizer for volatile as well as semi-volatile and non-volatile aerosol particles in the 0 – 10 nm size range. The technique has to be characterised in more detail and for a greater range of chemical systems, and in particular it has to be developed into a quantitative method before it can be applied in an instrument to sample ambient aerosols. The construction of a field instrument is envisioned, but carries with it a number of technical challenges which have to addressed first with the laboratory based instrument.  The instrument would, for example, greatly benefit from increased mass resolution, for the easier observation of irregular peaks (e.g. clusters containing molecular fragments in XUV spectra, clusters 146  doped with H2O in UV spectra) and for easier access to chemical composition information in the case of detecting mixed systems, as naturally occurring aerosol particles invariably are. To this end a reflectron TOF mass spectrometer system (RETOF, Jordan TOF products) equipped with sensitive Z-gap MCP detectors will be installed. This mass spectrometer will operate in reflectron mode for increased mass resolution in the smallest particles, and in linear detection mode for heavier particles for which only total mass information is accessible. For a future field instrument, a similar but more portable system manufactured by Tofwerk157,158 will be employed. To sample aerosol particles, initially from a smog chamber and ultimately from the atmosphere, an aerodynamic lens or a critical orifice inlet system will be installed.  One of the most desirable research avenues to be explored with the particle sizer in the future is the study of the ill-understood nucleation process which involves clusters from the subnanometer to the nanometer size range. This could be achieved by studying samples of water mixed with acids, both inorganic and organic. The incorporation of even small amounts of acids to water clusters has been shown to have a significant impact on the clusters’ stabilities, growth rates, and thus performance as condensation nuclei.37,150,159 The acetic acid with H2O mixed system is currently under investigation in our laboratory.  A challenge recently undertaken by spectroscopists is measuring PFI-ZEKE photoelectron spectra of large molecular aggregates. Loginov and Drabbels160 recently reported ZEKE photoelectron spectra of sodium doped helium nanodroplets Na(He)n where n ≈ 5000. They found that the high-lying Rydberg states (n ≳ 100) had a lifetime of over 1 µs, which is quite long for such a large system and seems  promising for PFI-ZEKE studies of other similar systems. Our instrument would be ideally suited for studies of analogous clusters of species other than helium.  Finally, it would be instructive to analyse the energy distribution of electrons and ions created in the UV and XUV photoionisation processes described above. This can be accomplished by imaging studies which 147  will be undertaken using the RoentDek imaging detector described and used preliminarily in Section 2.1.5.c, as well as a regular phosphorescent screen equipped with a CCD camera. A technical hurdle currently being dealt with is the requirement to focus the XUV beam within the extractor, which necessitates using a different XUV diffraction grating and altering the geometry of the 4-wave mixing vacuum system.  To conclude, the present thesis describes a new photoelectron and photoion spectrometer for the characterisation of a broad range of systems, from molecules to nanometer sized aerosol particles. The experimental setup has been built and its successful operation has been demonstrated on a selection of examples.  148  Bibliography 1.  Ptashnik, I. V., Smith, K. M., Shine, K. P. and Newnham, D. A., Q. J. R. Meteorolog. Soc. 130, 2391 (2004).  2.  Cormier, J. G., Hodges, J. T. and Drummond, J. R., J. Chem. Phys. 122, 114309 (2005).  3.  IPCC, 2007: Climate Change 2007: The Physical Science Basis. Contribution of the Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. (Cambridge University Press: Cambridge, UK and New York, USA, 2007)  4.  Zhang, R., Science 328, 1366 (2010).  5.  Kulmala, M. et al., Science 318, 89 (2007).  6.  Mirme, A. et al., Boreal Environ. Res. 12, 247 (2007).  7.  Brack, A., The Molecular Origins of Life: Assembling Pieces of the Puzzle. (Cambridge University Press: Cambridge, UK, 1998).  8.  Nadykto, A. B. and Yu, F., Chem. Phys. Lett. 435, 14 (2007).  9.  Müller-Dethlefs, K., Sander, M. and Schlag, E. W., Chem. Phys. Lett. 112, 291 (1984).  10.  Müller-Dethlefs, K., Sander, M. and Schlag, E. W., Z. Naturforsch., A: Phys. Sci 39, 1089 (1984).  11.  Shiell, R. et al., Chem. Phys. Lett. 315, 390 (1999).  12.  Jarvis, G. K., Song, Y., Ng, C. Y. and Grant, E. R., J. Chem. Phys. 111, 9568 (1999).  13.  Onuma, T. et al., J. Mol. Spectrosc. 198, 209 (1999).  14.  Tonkyn, R. G., Winniczek, J. W. and White, M. G., Chem. Phys. Lett. 164, 137 (1989).  15.  Fielding, H., Softley, T. P. and Merkt, F., Chem. Phys. 155, 257 (1991).  16.  Merkt, F. and Softley, T. P., J. Chem. Phys. 96, 4149 (1992).  17.  Palm, H. and Merkt, F., Chem. Phys. Lett. 270, 1 (1997).  18.  Signorell, R., Palm, H. and Merkt, F., J. Chem. Phys. 106, 6523 (1997).  149  19.  Merkt, F. et al., J. Phys. B: At. Mol. Opt. Phys. 31, 1705 (1998).  20.  Signorell, R. and Merkt, F., Faraday Discuss. 205 (2000).  21.  Merkt, F., Signorell, R., Palm, H., Osterwalder, A. and Sommavilla, M., Mol. Phys. 95, 1045 (1998).  22.  Signorell, R., Hollenstein, U. and Merkt, F., J. Chem. Phys. 114, 9840 (2001).  23.  Signorell, R., PhD Thesis: Struktur und Dynamik von Molekülkationen (1999).  24.  Haughton, J. T. et al. Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change: Weather, 388. (Cambridge University Press: Cambridge, UK, 2001).  25.  Firanescu, G., Luckhaus, D. and Signorell, R., J. Chem. Phys. 125, 144501 (2006).  26.  Flesch, R., Kosugi, N., Bradeanu, I. L., Neville, J. J. and Rühl, E., J. Chem. Phys. 121, 8343 (2004).  27.  Flesch, R. et al., Phys. Rev. Lett. 86, 3767 (2001).  28.  Buck, U. and Meyer, H., J. Chem. Phys. 84, 4854 (1986).  29.  Deschamps, A. and De Geuser, F., J. Appl. Crystallogr. 44, 343 (2011).  30.  Heller, W. T., Acta Cryst. D 66, 1213 (2010).  31.  Voisin, C. et al., Phys. Rev. Lett. 85, 2200 (2000).  32.  Schulz, C. P., Haugstätter, R., Tittes, H. U. and Hertel, I. V., Phys. Rev. Lett. 57, 1703 (1986).  33.  Schulz, C. P., Haugstätter, R., Tittes, H. U. and Hertel, I. V., Z. Phys. D: At. Mol. Clusters 10, 279 (1988).  34.  Schütte, S. and Buck, U., Int. J. Mass Spectrom. 220, 183 (2002).  35.  Bobbert, C., Schütte, S., Steinbach, C. and Buck, U., Eur. Phys. J. D 19, 183 (2002).  36.  Mori, Y. and Kitagawa, T., Int. J. Mass Spectrom. Ion Processes 84, 319 (1988).  37.  Heinbuch, S., Dong, F., Rocca, J. J. and Bernstein, E. R., J. Chem. Phys. 126, 244301 (2007).  150  38.  Dong, F., Heinbuch, S., Rocca, J. J. and Bernstein, E. R., J. Chem. Phys. 124, 224319 (2006).  39.  Rupper, P. and Merkt, F., Rev. Sci. Instrum. 75, 613 (2004).  40.  Beutler, H., Z. Phys. A: Hadrons Nucl. 93, 177 (1935).  41.  Fano, U., Nuovo Cimento 12, 154 (1935).  42.  Saloman, E. B., J. Phys. Chem. Ref. Data 33, 765 (2004).  43.  Lago, A., Hiber, G. and Wallenstein, R., Phys. Rev. A 36, 3827 (1987).  44.  Phelps, F. M. MIT Wavelength Tables, Vol. 2, Wavelengths by Element. (The MIT Press, Cambridge, Massachusetts; London, England: 1982).  45.  Ashworth, S. H. and Brown, J. M. An Atlas of Optogalvanic Transitions in Neon. (Science and Engineering Research Council: Oxford, UK, 1991).  46.  Campargue, A., Biennier, L. and Herman, M., Mol. Phys. 93, 457 (1998).  47.  Scherer, G. J., Lehmann, K. K. and Klemperer, W., J. Chem. Phys. 78, 2817 (1983).  48.  Hagena, O. F. and Obert, W., J. Chem. Phys. 56, 1793 (1972).  49.  Hagena, O. F., Rev. Sci. Instrum. 63, 2374 (1992).  50.  Miller, D. R., Free Jet Sources, in Atomic and Molecular Beam Methods Volume 1, 14. (Oxford University Press: New York, USA, 1988).  51.  Slipchenko, M. N., Kuma, S., Momose, T. and Vilesov, A. F., Rev. Sci. Instrum. 73, 3600 (2002).  52.  McNally, W., Selecting the Correct Elastomer for your Mechanical Seal Application, at http://www.mcnallyinstitute.com, retrieved on July 20th 2011.  53.  Stienkemeier, F., Higgins, J., Ernst, W. E. and Scoles, G., Phys. Rev. Lett. 74, 3592 (1995).  54.  Bobbert, C. and Schulz, C. P., Eur. Phys. J. D 16, 95 (2001).  55.  Steinbach, C. and Buck, U., J. Chem. Phys. 122, 134301 (2005).  56.  Makansi, M. M., Muendel, C. H. and Selke, W. A., J. Phys. Chem. 59, 40 (1955).  57.  Bowles, K. J. and Rosenblum, L., J. Chem. Eng. Data 10, 321 (1965). 151  58.  Marsh, K. N. Recommended Reference Materials for the Realization of Physicochemical Properties. (Blackwell Scientific: Oxford, UK, 1987).  59.  Wiley, W. C. and McLaren, I. H., Rev. Sci. Instrum. 26, 1150 (1955).  60.  Gilmore, I. S. and Seah, M. P., Int. J. Mass Spectrom. 202, 217 (2000).  61.  Fraser, G. W., Int. J. Mass Spectrom. 215, 13 (2002).  62.  Eppink, A. T. J. B. and Parker, D. H., Rev. Sci. Instrum. 68, 3477 (1997).  63.  Jagutzki, O. et al., IEEE Trans. Nucl. Sci. 49, 2477 (2002).  64.  Mamyrin, B. A., Int. J. Mass Spectrom. Ion Processes 131, 1 (1994).  65.  Nitsch, C., Schulz, C. P., Gerber, A., Zimmermann-Edling, W. and Hertel, I. V., Z. Phys. D: At. Mol. Clusters 22, 651(1992).  66.  Dauster, I., Suhm, M. A., Buck, U. and Zeuch, T., Phys. Chem. Chem. Phys. 10, 83 (2008).  67.  Mank, A., Nguyen, T., Martin, J. D. D. and Hepburn, J. W., Physical Review A: At., Mol., Opt. Phys. 51, R1 (1995).  68.  Hepburn, J. W., Chem. Soc. Rev. 25, 281 (1996).  69.  Mo, Y., Yang, J. and Chen, G., J. Chem. Phys. 120, 1263 (2004).  70.  Woo, H. K., Zhan, J., Lau, K. -C., Ng, C. Y. and Cheung, Y. -S., J. Chem. Phys. 116, 8803 (2002).  71.  Matsui, H., Zhu, Y. -F. and Grant, E. R., Laser Chem. 16, 151 (1996).  72.  Rodham, D. and Blake, G. A., Chem. Phys. Lett. 264, 522 (1997).  73.  Wang, K., Rodham, D. A., McKoy, V. and Blake, G. A., J. Chem. Phys. 108, 4817 (1998).  74.  Peng, X. and Kong, W., J. Chem. Phys. 117, 9306 (2002).  75.  Schlag, E. W., ZEKE Spectroscopy. (Cambridge University Press: Cambridge, UK and New York, USA, 1998).  76.  Merkt, F., Annu. Rev. Phys. Chem. 48, 675 (1997).  77.  Chupka, W. A., J. Chem. Phys. 98, 4520 (1993).  152  78.  Potts, A. W., Lempka, H. J., Streets, D. G. and Price, W. C., Phil. Trans. Roy. Soc. Lond. A. 268, 59 (1970).  79.  Pullen, B. P. et al., J. Chem. Phys. 53, 768 (1970).  80.  Brundle, C. R., Robin, M. B. and Basch, H., J. Chem. Phys. 53, 2196 (1970).  81.  Pradeep, T. and Shirley, D. A., J. Electron. Spectrosc. Relat. Phenom. 66, 125 (1993).  82.  Banna, M. S. and Shirley, D. A., Chem. Phys. Lett. 33, 441 (1975).  83.  Bieri, G., Åsbrink, L. and von Niessen, W., J. Electron. Spectrosc. Relat. Phenom. 23, 281 (1981).  84.  Seccombe, D. P., Tuckett, R. P. and Fisher, B. O., J. Chem. Phys. 114, 4074 (2001).  85.  Shastri, A., Raja Sekhar, B. N., Jeet Singh, P. and Deo, M. N., Spectrosc. Lett. 42, 219 (2009).  86.  Takeshita, K., Chem. Phys. Lett. 165, 232 (1990).  87.  Su, G. L. et al., J. Chem. Phys. 122, 54301 (2005).  88.  Xi, H. -W. and Huang, M. -B., Chem. Phys. Lett. 430, 227 (2006).  89.  He, Y. -L. and Wang, L., Struct. Chem. 20, 461 (2009).  90.  Seccombe, D. P., Chim, R. Y. L., Tuckett, R. P., Jochims, H. W. and Baumgaሷrtel, H., J. Chem. Phys. 114, 4058 (2001).  91.  Ma, N. L., Lau, K. -C., Chien, S. -H. and Li, W. -K., Chem. Phys. Lett. 311, 275 (1999).  92.  Lifshitz, C. and Long, F. A., J. Phys. Chem. 69, 3731 (1965).  93.  Torres, I., Martínez, R., Sánchez Rayo, M. N. and Castaño, F., J. Phys. B: At. Mol. Opt. Phys. 33, 3615 (2000).  94.  Martin, R. H., Lampe, F. W. and Taft, R. W., J. Am. Chem. Soc. 88, 1353 (1966).  95.  Lossing, F. P., Bull. Soc. Chim. Belg. 81, 125 (1972).  96.  Frisch, M. J. et al., Gaussian 03 (2004).  97.  Wilson, A., van Mourik, T. and Dunning Jr., T. H., J. Mol. Struct. THEOCHEM 388, 339 (1996).  153  98.  Luckhaus, D., Forysinski, P. W., Zielke, P. and Signorell, R., Mol. Phys. 108, 2325 (2010).  99.  Halkier, A. et al., Chem. Phys. Lett. 286, 243 (1998).  100. Malmqvist, P. -Å. and Forsberg, N., Chem. Phys. 228, 227 (1998). 101. Luckhaus, D., Phys. Chem. Chem. Phys. 10, 6215 (2008). 102. Lucas, N. J. D., J. Phys. B: Atom. Molec. Phys. 6, 155 (1973). 103. Chase Jr., M.W., J. Phys. Chem. Ref. Data Monogr. 9, 1 (1998). 104. Baer, T., Werner, A. S., Tsai, B. P. and Lin, S. F., J. Chem. Phys. 61, 5468 (1974). 105. Signorell, R. and Merkt, F., J. Chem. Phys. 109, 9762 (1998). 106. Signorell, R., Hollenstein, U. and Merkt, F., J. Chem. Phys. 114, 9840 (2001). 107. Andrews, L. and Prochaska, F. T., J. Chem. Phys. 70, 4714 (1979). 108. Zhang, R. et al., Science 304, 1487 (2004). 109. Maçôas, E. M. S., Khriachtchev, L., Pettersson, M., Fausto, R. and Räsänen, M., J. Am. Chem. Soc. 125, 16188 (2003). 110. Zielke, P. and Suhm, M. A., Phys. Chem. Chem. Phys. 9, 4528 (2007). 111. Yoon, Y. H., Hause, M. L., Case, A. S. and Crim, F. F., J. Chem. Phys. 128, 084305 (2008). 112. Birer, O. and Havenith, M., Annu. Rev. Phys. Chem. 60, 263 (2009). 113. Limão-Vieira, P. et al., Chem. Phys. 324, 339 (2006). 114. Hu, Y. J., Fu, H. B. and Bernstein, E. R., J. Chem. Phys. 125, 184308 (2006). 115. Leach, S., Schwell, M., Jochims, H. W. and Baumgärtel, H., Chem. Phys. 321, 171 (2006). 116. Baptista, L. et al., J. Phys. Chem. A. 112, 13382 (2008). 117. Knowles, D. J. and Nicholson, A. J. C., J. Chem. Phys. 60, 1180 (1974). 118. Reiser, G., Habenicht, W. and Muሷller-Dethlefs, K., J. Chem. Phys. 98, 8462 (1993). 119. Hollenstein, U. et al., Mol. Phys. 105, 1711 (2007). 154  120. Schulenburg, A. M. and Merkt, F., J. Chem. Phys. 130, 034308 (2009). 121. Luckhaus, D., J. Chem. Phys. 113, 1329 (2000). 122. Ilyushin, V., Kleiner, I. and Lovas, F. J., J. Phys. Chem. Ref. Data 37, 97 (2008). 123. Hertel, I. V., Hüglin, C., Nitsch, C. and Schulz, C. P., Phys. Rev. Lett. 67, 1767 (1991). 124. Schulz, C. P., Gerber, A., Nitsch, C. and Hertel, I. V., Z. Phys. D: At. Mol. Clusters 20, 65 (1991). 125. Selegue, T. J. and Lisy, J. M., J. Phys. Chem. 96, 4143 (1992). 126. Hashimoto, K. and Morokuma, K., J. Am. Chem. Soc. 117, 4151 (1995). 127. Takasu, R., Misaizu, F., Hashimoto, K. and Fuke, K., J. Phys. Chem. A 101, 3078 (1997). 128. Bewig, L., Buck, U., Rakowsky, S., Reymann, M. and Steinbach, C., J. Phys. Chem. A 102, 1124 (1998). 129. Buck, U. and Steinbach, C., J. Phys. Chem. A 102, 7333 (1998). 130. Schulz, C. P. et al., J. Chem. Phys. 119, 11620 (2003). 131. Salter, T. E., Mikhailov, V. and Ellis, A. M., J. Phys. Chem. A 111, 8344 (2007). 132. Gao, B. and Liu, Z. -F., J. Chem. Phys. 126, 084501 (2007). 133. Cwiklik, L., Buck, U., Kulig, W., Kubisiak, P. and Jungwirth, P., J. Chem. Phys. 128, 154306 (2008). 134. Hashimoto, K. and Daigoku, K., Phys. Chem. Chem. Phys. 11, 9391 (2009). 135. Liu, H. T., Müller, J. P., Zhavoronkov, N., Schulz, C. P. and Hertel, I. V., J. Phys. Chem. A 114, 1508 (2010). 136. Frisch, M. J. et al., Gaussian 09 (2009). 137. Quack, M. and Troe, J., Ber. Bunsenges. Phys. Chem. 78, 240 (1974). 138. Quack, M. and Troe, J. Statistical Adiabatic Channel Models in Encyclopaedia of Computational Chemistry, Volume 4, 2708. (Wiley: New York, USA, 1988).  155  139. Lias, S. G., Ionization energy evaluation in NIST Chemistry Webbook, NIST Standard Reference Database Number 69 edited by P. J. Linstrom and W. G. Mallard (National Institute of Standards and Technology, Gaithersburg, MD) at http://webbook.nist.gov, retrieved on July 18th 2011. 140. Pilling, M. J. and Smith, I. W. M., Modern Gas Kinetics. (Blackwell Scientific: Oxford, UK, 1987). 141. Holmgren, W. F., Revelle, M. C., Lonij, V. P. A. and Cronin, A. D., Phys. Rev. A. 81, 053607 (2010). 142. Dorosh, O. and Kisiel, Z., Acta Phys. Pol. A 112, S-95 (2007). 143. Nolan, P. J. and Pollak, L. W., Proc. Roy. Irish. Acad. 51A, 9 (1946). 144. Aitken, J., Trans. Roy. Soc. Edinburgh 35, 1 (1888). 145. Jiang, J., Chen, M., Kuang, C., Attoui, M. and McMurry, P., Aerosol Sci. Technol. 45, 510 (2011). 146. Jiang, J. et al., Aerosol Sci. Technol. 45, 2 (2011). 147. Belau, L., Wilson, K. R., Leone, S. R. and Ahmed, M., J. Phys. Chem. A 111, 10075 (2007). 148. Junninen, H. et al., Atmos. Meas. Tech. 3, 1039 (2010). 149. Alvarez, M., Vezmar, I. and Whetten, R., J. Aerosol Sci. 29, 115 (1998). 150. Goken, E. G. and Castleman, A. W., J. Geophys. Res. 115, D16203 (2010). 151. Hearn, J. D. and Smith, G. D., Anal. Chem. 76, 2820 (2004). 152. Harris, W. A., Reilly, P. T. A. and Whitten, W. B., Anal. Chem. 79, 2354 (2007). 153. Lafranchi, B. W. and Petrucci, G. A., Int. J. Mass Spectrom. 258, 120 (2006). 154. Corbett, J. L., MSc Thesis (2011). 155. Olovsson, I. and Templeton, D. H., Acta Cryst. 12, 832 (1959). 156. Wei, S., Tzeng, W. B. and Castleman Jr., A. W., J. Chem. Phys. 95, 5080 (1991). 157. Steiner, W. E. et al., Rapid Commun. Mass Spectrom. 15, 2221 (2001). 158. Decarlo, P. F. et al., Anal. Chem. 78, 8281 (2006). 156  159. Goken, E. G., Joshi, K. L., Russo, M. F., van Duin, A. C. T. and Castleman, A. W., J. Phys. Chem. A 115, 4657 (2011). 160. Loginov, E. and Drabbels, M., Phys. Rev. Lett. 106, 083401 (2011).  157  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0061935/manifest

Comment

Related Items