Dynamics of a Microsolvated Ion-Molecule Reaction
Rico Otto
Fakult¨at f¨ur Mathematik und Physik Albert-Ludwigs-Universit¨at Freiburg
The figure on the title page depicts the transition from chemical reactions in − the liquid phase to the gas phase as microsolvated OH (H2O)n water clusters react with CH3I. The image of the droplet has been taken from Wikimedia Commons, Fir0002/Flagstaffotos.
Dynamics of a Microsolvated Ion-Molecule Reaction
Inaugural-Dissertation zur Erlangung des Doktorgrades
der Fakult¨at f¨ur Mathematik und Physik der Albert-Ludwigs-Universit¨at Freiburg im Breisgau
vorgelegt von Dipl.-Phys. Rico Otto aus Dresden
im August 2011 Dekan: Prof.KayK¨onigsmann LeiterderArbeit: Prof. RolandWester Referent: Prof.RolandWester Korreferent: Prof.HanspeterHelm Pr¨ufer: Prof.GerhardStock Prof. Frank Stienkemeier Tag der m¨undlichen Pr¨ufung 21.10.2011 I
List of publications covered in this thesis:
• Microsolvation in ion-molecule reactive scattering R. Otto, J. Brox, S. Trippel, M. Stei, T. Best, R. Wester, (submitted)
• Near threshold photodetachment spectroscopy of the cold trapped water cluster − anion H3O2 R. Otto, A. von Zastrow, S. Jezouin, T. Best, R. Wester, (to be submitted).
• Pr¨azises Timing - Neue Experimente in einer 22-Pol-Ionenfalle erlauben den Nachweis von Ionen mit hoher Massenaufl¨osung R. Otto, T. Best, R. Wester, Heiko Seel, Physikjournal Oktober 2010, Sonderheft: Best of Messtechnik.
• How can a 22-pole ion trap exhibit 10 local minima in the effective potential? R. Otto, P. Hlavenka, S. Trippel, J. Mikosch, K. Singer, M. Weidem¨uller, R. Wester, J. Phys. B 42, 154007 (2009).
• Absolute photodetachment cross section measurements of the O− and OH− anion P. Hlavenka, R. Otto, S. Trippel, J. Mikosch, M. Weidem¨uller and R. Wester, J. Chem. Phys. 130, 061105 (2009).
• Nonstandard behavior of a negative ion reaction at very low temperatures R. Otto, J. Mikosch, S. Trippel, M. Weidem¨uller , R. Wester, Phys. Rev. Lett. 101, 063201 (2008).
• Photodetachment of cold OH− in a multipole ion trap S. Trippel, J. Mikosch, R. Berhane, R. Otto , M. Weidem¨uller, R. Wester, Phys. Rev. Lett. 97, 193003 (2006). II
In addition the author has contributed to the following publications:
• Absolute photodetachment cross-section measurements for hydrocarbon chain anions T. Best, R. Otto, S. Trippel, P. Hlavenka, A. von Zastrow, S. Eisenbach, S. Jezouin, and R. Wester, E. Vigren, M. Hamberg, and W.D. Geppert (submitted to The Astrophysical Journal)
• Reactions of ions with laser aligned molecules S. Trippel, M. Stei, R. Otto, P. Hlavenka, M. Weidem¨uller, R. Wester, (to be submitted to Phys. Rev. A).
• Nanosecond Photofragment Imaging of Adiabatic Molecular Alignment S. Trippel, M. Stei, R. Otto, P. Hlavenka, M. Weidem¨uller, R. Wester, J. Chem. Phys. 134, 104306 (2011)
− − • F + CH3I → FCH3 + I Reaction Dynamics. Nontraditional Atomistic Mechanisms and Formation of a Hydrogen-Bonded Complex J. X. Zhang, J. Mikosch, S. Trippel, R. Otto, M. Weidem¨uller, R. Wester, W. L. Hase, Journal of Physical Chemistry Letters 1, 2747 (2010)
• Kinematically complete chemical reaction dynamics S. Trippel, M. Stei, R. Otto, P. Hlavenka, J. Mikosch, C. Eichhorn, U. Lour- deraj, J. X. Zhang, W. L. Hase, M. Weidem¨uller, R. Wester, Journal of Physics: Conference Series (ICPEAC 2009) 194, 012046 (2009).
• Imaging Nucleophilic Substitution Dynamics J. Mikosch, S. Trippel, C. Eichhorn, R. Otto , U. Lourderaj, J. X. Zhang, W. L. Hase, M. Weidem¨uller, R. Wester, Science 319, 183 (2008).
• Kinematically complete reaction dynamics of slow ions J. Mikosch, S. Trippel, R. Otto, C. Eichhorn, P. Hlavenka, M. Weidem¨uller, R. Wester, Journal of Physics: Conference Series (ICPEAC 2007) 88, 012025 (2007). III
• Inverse temperature dependent lifetimes of transient SN 2 ion-dipole complexes J. Mikosch, R. Otto, S. Trippel, C. Eichhorn, M. Weidem¨uller, R. Wester, J. Phys. Chem. A 112, 10448 (2008).
• Evaporation of trapped anions studied with a 22-pole ion trap in tandem time- of-flight configuration J. Mikosch, U. Fr¨uhling, S. Trippel, R. Otto, P. Hlavenka, D. Schwalm, M. Weidem¨uller, R. Wester, Phys. Rev. A 78, 023402 (2008). IV
Abstract: The study of microsolvated anions allows us to bridge the gap between two extreme environments: the gas phase with isolated free moving particles on the one side, and the liquid phase where strong interactions with the solvent molecules occur on the other side. In this thesis we study absolute photode- tachment cross sections of microsolvated anions in a cryogenic multipole ion trap. Near threshold we use this technique to detect internal cooling of the trapped clusters. Furthermore we study the reaction dynamics of microsolvated − OH (H2O)n clusters with methyl iodide, using crossed beam ion imaging. To prepare the clusters at well defined internal energies, we combine the crossed beam setup with a multipole trap. Various reaction channels can be observed for different cluster sizes. For a nucleophilic displacement reaction we find that the number of observed reaction mechanisms decreases with increasing ion sol- vation. Quantum chemical calculations support that this is caused by steric restrictions in the system. For a proton transfer reaction the dynamics change from forward scattering in the unsolvated system to backward scattering in the monosolvated system at high energies. A suppression for solvated products is observed, although they are energetically preferred. This can be understood with an unfavorable rearrangement in an intermediate reaction complex. V
Zusammenfassung: Die Untersuchung von mikrosolvatisierten Anionen erm¨oglicht es, eine Verbindung zwischen zwei extremen Umgebungen herzustellen: der Gasphase, mit isolierten und frei beweglichen Teilchen einerseits, und der fl¨ussigen Phase, mit starken Wechselwirkungen zwischen L¨osemittelmolek¨ulen andererseits. In dieser Arbeit untersuchen wir absolute Photodetachment Wirkungsquerschnitte von mikrosolvatisierten Anionen in einer Tieftemperatur Multipol-Ionenfalle. Nahe an der Schwelle k¨onnen wir so die K¨uhlung der internen Freiheits- grade der gespeicherten Cluster detektieren. Desweiteren untersuchen wir die − Reaktionsdynamik von OH (H2O)n Clustern und Methyliodid mithilfe von geschwindigkeitsabbildender Streuung. Um die Cluster bei wohl definierten in- ternen Energien zu pr¨aparieren, haben wir einen Kreuzstrahlaufbau mit einer Multipol-Ionenfalle kombiniert. Unterschiedliche Reaktionskan¨ale werden f¨ur verschiedene Clustergr¨oßen beobachtet. Bei einer Nucleophilen Substitutions- reaktion beobachten wir, dass die Anzahl der auftretenden Reaktionsmechanis- men mit zunehmender Solvatisierung der Ionen abnimmt. Quantenchemische Rechnungen zeigen, dass dieser Effekt auf sterische Einschr¨ankungen w¨ahrend der Reaktion zur¨uckzuf¨uhren ist. Bei einer Protonentransfer-Reaktion ¨andert sich die Dynamik von Vorw¨artsstreuung im unsolvatisierten System hin zu R¨uckw¨artsstreuung bei hohen Stoßenergien bei einfacher Solvatation. Eine Unterdr¨uckung von solvatisierten Reaktionsprodukten wird beobachtet, obwohl deren Herstellung energetisch beg¨unstigt ist. Dies kann ¨uber eine ung¨unstige Umordnung der Teilchen erkl¨art werden, die in einem Reaktionszwischenkom- plex stattfinden muss. VI Contents
1 Introduction 1
2 Microsolvation 5
3 A multipole trap setup with improved mass resolution 11 3.1 A pulsed discharge ion source for complex molecules ...... 13 3.2 Bendinganddetectingions...... 13 3.3 Thetemperaturevariable22-poleiontrap ...... 16 3.4 Improvingthetime-of-flightresolution ...... 19
4 Absolute photodetachment cross sections studied in a 22-pole trap 25 4.1 Absolute photodetachment cross sections of O− and OH− ...... 26 4.1.1 Photodetachmentvia2Dtomography ...... 26 4.1.2 O− -thereferenceanion ...... 28 4.1.3 OH− - Temperature dependence far above threshold? . . . . . 33 4.1.4 OH− -Thermometryclosetothreshold ...... 34 4.2 Photodetachmentofcoldsolvatedanions ...... 39 4.3 How can a 22-pole ion trap exhibit 10 minima in the effective potential? 44 4.3.1 Tomographyofthetrappingpotential...... 44 4.3.2 Modeling trapping potentials of realistic multipoles ...... 48
5 Combining an Ion Trap with Crossed Beam Imaging 53 5.1 Ionproductionandmassselection ...... 56 5.2 Characterizationoftheoctupoleiontrap ...... 57 5.3 Theneutralbeamsource ...... 63 5.4 Ionimaging-VMIandSMI ...... 67
VII VIII CONTENTS
5.4.1 Themeasurementprocedure ...... 71
− 6 Reactive scattering of cold OH (H2O)n with CH3I 75 6.1 Energydependentbranchingratios ...... 76 − 6.1.1 The unsolvated reaction: OH + CH3I...... 76 − 6.1.2 The monosolvated reaction: OH (H2O) + CH3I...... 79 6.1.3 Temperature dependence close to threshold...... 83
6.2 A microsolvated SN2reaction ...... 86 6.2.1 Imagingdifferentreactionmechanisms ...... 86 6.2.2 Modeling reaction pathways and steric constraints ...... 92 6.3 Switching mechanisms in a solvated proton transfer reaction . . . . . 102 6.4 Whyareunsolvatedproductspreferred? ...... 110
7 Summary 117
8 Outlook 119
A Accuracy of the photodetachment cross section measurements 123
B Density-to-flux Correction 125
Bibliography 128
Acknowledgements 139 Chapter 1
Introduction
The intrinsic properties and interactions of atomic and molecular systems are exten- sively studied in gas phase experiments. High precision spectroscopic methods on isolated particles provide detailed insight into energetic properties, like rotational and vibrational structures, spin-orbit interactions and spectroscopic resonances, but also on the geometric structures of molecules. High accuracy experiments on funda- mental systems provide a test case for the capability of state-of-the-art theoretical methods to describe and predict the measured values [1]. The dynamical features of chemical reaction are studied on a great level of detail. To investigate molecular systems in the gas phase two major techniques are applied in many experiments: trapping of ionic or neutral particles and studying collisions in free jets and molecular beams. For neutral particles trapping of selected atoms can be achieved using the force of light in laser cooling techniques [2]. Few molecules like ND3 or OH that feature a special internal structure can be trapped in specially designed AC traps, taking advantage of the Stark shift in the molecules [3]. Also trapping of these molecules in special storage rings has been demonstrated [4]. For charged species ion traps offer the possibility to store atomic and molecular ions over timescales ranging from seconds up to many months [5]. For atomic cations like Mg+ or Ca+ laser cooling in quadrupole ion traps is available, which offers exciting applications in quantum information processing [6, 7] and ultracold collision studies [8]. There are, however, some major drawbacks on this technique. First, the cooling scheme strongly depends on the energetic structure of the atomic ions and is therefore only applicable to few
1 2 CHAPTER 1. INTRODUCTION
selected species. Laser cooled ions have successfully been used to sympathetically cool molecular ions [9], but the cooling of the internal degrees of freedom has been found to be a problem [10]. All experiment are so far restricted to cationic species, since atomic anions normally do not feature the excited electronic states necessary for laser cooling. A notable exception is the negatively charged osmium isotope 192Os−, which seemed to be a prosperous candidate for laser cooling of an anion. However, recent spectroscopic results on the strength of the electronic transition that has to be employed are quite discouraging [11]. A more general cooling method which is not restricted to the charge or internal structure of the molecules is the thermalization of an ionic ensemble with a cold bath of inert buffer gas. Using the buffer gas cooling technique, radiofrequency ion traps at cryogenic temperatures offer a way to cool the external and internal degrees of freedom of complex systems down to a few Kelvin. They therefore provide ideal tools to prepare molecular ensembles in only few quantum states. The temperature variable 22-pole ion trap described in chapter 3 represents such a device. Ion molecule reactions have been extensively studied over a wide range of inter- nal temperatures and collisional energies using various molecular beam techniques. Guided ion beam studies are powerful tools to reveal detailed information on energy dependent reaction cross sections up to several eV. The product branching ratios that can be measured give direct insight into different reaction channels [12]. Ther- mal rate coefficients of ion molecule reactions have been measured using flow tube and ion drift tube experiments [13] and in supersonic expansions [14]. Unfortunately none of these methods can give insight into the steric properties and dynamics of chemical reactions. The most detailed insight into reaction dynamics can be gained from crossed molecular beam studies. In this technique two beams of reactant species, often cooled in a supersonic expansion, are brought to collision in a small interaction volume. In neutral neutral reactions the products are ionized after the collision and subsequently detected. Moveable detector systems allow to measure product translational energies as well as the distribution of scattering angles of the reaction
products. A famous example is the reaction F + H2 → HF + H, which represents one of the best studied chemical reactions, both experimentally [15] and theoretically [16]. With the invention of ion imaging [17] and the pioneering work on velocity map 3
imaging [18] a new technique has emerged which allows to study reaction dynamics in a kinematically complete fashion at an increased data acquisition speed. In our group we extended this technique for the first time to a crossed beam study of slow atomic ions (e.g. Ar+, Cl−, F−) reacting with cold molecules from a supersonic jet [19, 20]. A key step here was the development of a pulsed field velocity map imaging spectrometer where the lens system performing the imaging process is switched to high operating voltages on extremely short time scales. One of the big challenges is to maximize the energy resolution that can be achieved, in order to track down state-to-state reaction dynamics. With a newly designed imaging spectrometer in combination with a full three dimensional ion detection scheme we recently suc- ceeded in resolving single vibrational levels in the product states of the benchmark + + charge transfer reaction Ar + N2 → Ar + N2 , thereby confirming recent high level calculations on the reaction [21]. In this thesis we address another big quest in the field of reaction dynamics, which is the increase of complexity of the systems under study. In the investigation of reactions of larger molecular ions one of the fascinating questions is, whether quantum effects like scattering resonances play a role in the reaction dynamics of complex systems and to which extent it will be possible to track down and under- stand different reaction mechanisms. However, one has to keep in mind that the wealth of rotational and vibrational degrees of freedom found in larger molecules pose a new challenge to the experiments. The internal energy that is carried by a classical N-atomic system Eint ≈ 3N · kT/2 limits the energetic resolution that can be achieved. No insight into state-to-state reaction dynamics will be possible if too many levels are populated. It is therefore desirable to prepare the molecules in only a few quantum states with a well defined internal state distribution prior to collision. For the neutral reactants this can be achieved by expanding them in a supersonic jet, which cools them to typically below 10K. At these temperatures the molecules are populating only the lowest rovibrational states. Many techniques are available today, to produce molecular ions in the gas phase, like plasma discharges, matrix-assisted laser desorption/ionization (MALDI) or elec- trospray ionization (ESI). However none of these techniques is capable of bringing large ionic molecules in the gas phase with low internal energies [22, 23]. A multi- pole ion trap as it is used in the trap setup described in chapter 3 has been shown to be an ideal tool to cool down the internal degrees of freedom of large molecules 4 CHAPTER 1. INTRODUCTION
(see section 4.2). It therefore seems a logical step to combine the two techniques of ion trapping and a crossed beam experiment in order to study reaction dynamics on complex molecular systems that have been prepared at low temperatures before- hand. The unique combination of a cryogenic multipole ion trap and a crossed beam imaging apparatus has been realized for the first time in this thesis. The thesis is organized as follows. A short introduction into microsolvated re- action systems is given in the next section. A new experimental setup is described (chapter 3) which combines a cryogenic 22-pole ion trap with a multicycle reflectron. This combination provides a very high mass resolution, while at the same time a compact design offers excellent optical access to the trap. We use this new setup to study absolute photodetachment cross sections via a laser tomography method (section 4.1). Photodetachment is demonstrated as a tool to access information on internal temperatures of trapped molecular anions (section 4.2) and to probe the effective trapping potential of a multipole ion trap (section 4.3). In chapter 5 we describe how an octupole ion trap has been successfully combined with a crossed beam imaging setup to act as a source for pre-cooled molecular ions. In chapter 6 − we use this setup to investigate the reaction dynamics of cold OH (H2O)n clusters reacting with methyl iodide. Chapter 2
Microsolvation
Chemical reactions occur in two distinctly different realms: in the gas phase where long-range interactions between free-moving reactants are important and in liquid phase where forces between nearby solute and solvent molecules dominate. On the one side gas phase reactions play a major role for all chemical processes occurring in our atmosphere, as well as for the synthesis of molecules in interstellar clouds. They are of big interest in engineering for the understanding of combustion processes and technical plasmas. On the other side solvent phase chemistry is essential for all biological processes in a world in which almost everything is surrounded by water. In addition almost all processes in chemical industry, like the production of paints, acids, organic solvents, or fertilizers, but also the synthesis of pharmaceutical substances take place in the solvent phase. The study of gas-phase chemical reactions enables us to unravel the intrinsic properties of molecular reaction systems under solvent free conditions. It has be- come possible to understand steric effects by aligning molecules in space prior to reaction [24]. Gas phase studies of chemical reactions have shown, that the outcome of molecular reactions can strongly depend on the vibrational and rotational state of the reactants [25]. Modern experimental techniques allow to selectively prepare reaction partners in single quantum states prior to collisions and open up new per- spectives to study reactions with translationally cold molecular ensembles [26, 27] for a very exclusive class of small neutral molecules. In comparison, much less is known about the dynamical features of chemical re- actions in solution. Under solvent conditions the reactant particles are surrounded
5 6 CHAPTER 2. MICROSOLVATION
by an environment that strongly affects many of their gas phase properties, as well as their interactions. As the complex environment makes dynamical studies on a single molecule level impossible, most of our knowledge is restricted to thermodynami- cal properties of chemical reactions. Although we know, that the solvent particles influence the interaction potential between the reactants and therefore change the thermodynamic characteristics of a reactive process, the way the reaction dynamics are affected remains unknown. And although the thermodynamic framework is es- sential to interpret the kinetic properties of chemical reactions it has to be expected that dynamical and steric effects that occur in collisions between reactive species may be at least equally important. In order to bridge the gap between gas phase experiments and reactions that take place in solution, experiments started to focus on microsolvated systems. Although the term microsolvation can also be found in the context of noble gas clusters like − − X (Ar)n we use it here for the so called hydrogen bonded clusters like X (NH3)n − or X (H2O)n. With the stepwise addition of solvent molecules to the bare reac- tant species microsolvation offers a bottom up approach to learn more about the transition of chemical reactions from gas to liquid phase. As in the gas phase the − production of selectively solvated species like OH (H2O)n can be easily achieved, the chemistry of these systems can now be studied as a function of solvation number. The majority of studies focus on water as a solvent, being the most prevalent and important environment for chemical reactions on earth. Early experiments dealt with the growth of charged water cluster species in a water vapor environment [28] and derived rate coefficients for the reaction
+ + H (H2O)n + H2O+M → H (H2O)n+1 +M
where M is a third body in the collisional process. The binding energies of sol- vated ions were measured extensively using different techniques like high pressure mass spectrometry [29], collision induced dissociation [30] or ion cyclotron reso- nance (ICR) spectroscopy [31]. In section 4.2 we present photodetachment as a tool to measure binding energies with high accuracy. Photodetachment studies have also been extensively used to gain structural information on solvated ions [32]. Recently + spectral information on vibrational levels in H (H2O)n has been gained via infrared photodissociation spectroscopy [33, 34]. One of the remarkable observations when going from gas-phase to liquid chem- 7
ion rateconstant[cm3s−1] OH− (1.0 ± 0.2) x 10−9 − −10 OH ·(H2O) (6.3 ± 2.5) x 10 − −12 OH ·(H2O)2 (2 ± 1) x 10 − −13 OH ·(H2O)3 < 2 x 10 − −25 a OH ·(H2O)∞ 2.3 x 10
− Table 2.1: Room temperature rate constant for the SN2 reaction OH + CH3Br measured for various degrees of hydration. Values taken from [38]. aIn aqueous solution. istry is the decreased reactivity of many systems. Rate constants of gas-phase chem- ical reactions exceed those in aqueous solutions by up to 16 orders of magnitude [35]. Experiments on microsolvated reactions have verified the trend of rapidly decreasing reaction rates at increasing stages of ion solvation [35, 36, 37, 38]. The change in reactivity can thereby already be observed for a small number of solvent molecules. − As an example the rate constants for the 300K reaction OH ·(H2O)n + CH3Br with n = 0 − 3 are listed in table 2.1. Here, the reaction rates measured in a flow tube setup decreased by almost four orders of magnitude upon adding only three water molecules to the reactant ion. Interestingly, thermochemistry still predicts an exoergic behavior for these reactions. Most of the reaction studies carried out have focused on the bimolecular nucle- ophilic substitution (SN2) reaction. It is of the type
− − X + CH3Y → XCH3 + Y and represents one of the most significant reaction types in organic chemistry. The classical mechanism of an SN2 reaction has been successfully described as proceeding along a potential with two minima [39], associated with an ion-dipole bound pre- − − reaction (X ··· CH3Y) and a post-reaction (XCH3 ··· Y ) complex, which are − separated by a central barrier transition state ([X··· CH3 ··· Y] ). An early qualitative model proposed by Brauman et al. [40] tries to give an ex- planation for the decreasing reaction efficiency at the transition from pure gas phase to the liquid phase. According to this model, the free reactant particles are stabi- 8 CHAPTER 2. MICROSOLVATION
Figure 2.1: In the transition from the gas-phase to the liquid phase the energy of the separated reaction partners is stabilized to a much greater extent than that of intermediate structures. This creates a barrier along the reaction pathway.
lized by solvent molecules, which lowers their potential energy. This stabilization effect is much smaller for the transition state of the reaction, where the reactants form a complex with a delocalized charge distribution. As can be seen in Fig. 2.1 this leads to an increasing barrier that hinders the reaction. However, there are open questions that extend beyond this illustrative picture. A transition to a ligand switching mechanism has been reported upon ion solvation starting with the first water molecule [41]
− − Cl (H2O) + CH3Br → Cl (CH3Br) + H2O
which questions the importance of the SN2 mechanism itself to form products. Fur- thermore, it appears to be a general trend, that the formation of unsolvated products is preferred, although thermochemistry dictates a higher stability of solvated pro- ducts [36, 38, 37, 41]. As an example Fig. 2.2 shows a cross section measurement 9
− Figure 2.2: Reaction cross section measurement for the system OH (H2O) +
CH3Cl as a function of collision energy. Taken from [36].
on the reaction − OH (H2O) + CH3Cl → products carried out in a tandem mass spectrometer [36]. As can be seen from the graph, the solvated products are suppressed by more than one order of magnitude. It has been proposed, that the solvent molecules are not efficiently transferred to the products due to steric hindrance. We will give an answer to this question in section 6.4. This example illustrates, that the description of a chemical process by simple evaluation of the characteristics of the potential energy landscape, like reaction enthalpies or minimum energy pathways (see Fig. 2.1), can be highly misleading. Detailed insight into the complex dynamics and the restrictions that may arise from steric effects is necessary in order to understand the mechanisms that govern the reaction. 10 CHAPTER 2. MICROSOLVATION Chapter 3
A multipole trap setup with improved mass resolution
A new experimental setup has been developed for the investigation of complex re- action networks, isotope exchange reactions and photodetachment experiments in- volving water clusters in a cryogenic multipole radiofrequency ion trap. To achieve the necessary mass resolution in the experiment the ion trap was combined with a multicycle reflectron. In this novel approach a mass resolution of m/∆m > 5000 is achieved which makes cluster experiments accessible where high adjacent masses have to be distinguished. At the same time, the new compact design provides excellent optical access to the trapping volume for spectroscopic applications. A schematic view of the trap setup is shown in Fig. (3.1). In the following sections we will describe the parts of the new setup in detail.
11 CHAPTER 3. A MULTIPOLE TRAP SETUP WITH IMPROVED MASS 12 RESOLUTION p offers an ideal environment to cool and es have to be distinguishable. At the same time the volume. e combination of this trap with a multicycle reflectron now Schematic view of the new 22-pole setup. The multipole rf tra localize complex ionic species likeopens cluster up ions. the pathway The tocompact uniqu experiments design where provides good high optical adjacent access mass to the trapping Figure 3.1: 3.1. A PULSED DISCHARGE ION SOURCE FOR COMPLEX MOLECULES 13
3.1 A pulsed discharge ion source for complex molecules
A detailed description of the working principle of our ion source can be found in [42] and only a brief summary of the ion production is given here. Positive and negative ions are created from a pulsed supersonic expansion in a plasma ion source and mass analyzed using a Wiley-McLaren time-of-flight mass spectrometer [43]. While this design is well established in different experiments in our group, the ions were so far only produced using electron impact ionization from a 1-2keV electron beam. In the new setup the ion production scheme has been extended to a pulsed plasma discharge ion source. This discharge source was developed for photodetachment − experiments on carbon chain anions CnH that we carried out recently in this new setup. A supersonic gas jet from a suitable precursor gas mixture is expanded into a vacuum chamber with a background pressure of 1·10−5 mbar using a home-built piezo electric valve. At a distance of 2mm after the nozzle the jet travels through a ring electrode which is switched to 500V for typically 10 s to ignite a plasma in the gas. In order to stabilize the moment of ignition a 1 s pulse from an electron gun is shot into the plasma region. A 10kΩ resistor restricts the current over the ring electrode once the plasma starts to burn. Monitoring the voltage drop over this resistor allows to characterize the gas pulse length and to optimize the position of the electron beam with respect to the plasma region. The source is located in a separated vacuum chamber pumped by a 500l turbo molecular pump. The ions leave the source chamber through a 10mm aperture which allows for differential pumping. The whole source region can be separated from the rest of the setup via a pneumatically driven gate valve.
3.2 Bending and detecting ions
All ions produced in the source are mass selected using a Wiley-McLaren mass spectrometer and detected on a micro channel plate (MCP) detector located 1.2m downstream the ion source (detector 1). Using this detector a first optimization of the ion signal is performed. The trap axis is arranged perpendicularly to this initial ion beam path. Once the ion source is tuned to stable operating conditions CHAPTER 3. A MULTIPOLE TRAP SETUP WITH IMPROVED MASS 14 RESOLUTION
we deflect the ion beam by 90 degrees to load it into the trap. This is achieved using a static quadrupole deflector which is depicted in Fig. 3.2. The quadrupole unit consists of four electrodes, each in the shape of a quarter of a circular rod of 17.5mm radius. Two opposing electrodes are connected to the same potential. Additional einzellenses are used to focus the ion beam upon entering and leaving the quadrupole. The quadrupole section resides in a separate vacuum chamber which is pumped by a 150l turbo molecular pump. This is mainly necessary to protect the detector located behind the quadrupole but also to introduce another differential pumping stage between the source region and the high vacuum ion trap section. The ion beam now travels perpendicular to its initial direction and passes the 22-pole trap. Behind the trap a second MCP detector is placed (detector 2) in an off-axis configuration to maintain the optical access to the trap volume. On this detector the ion package that has been deflected by the quadrupole is detected and the quadrupole can be tuned to its optimal settings. After the ion signal is optimized the ion package is trapped (see next section). Due to a very short flight distance to the trap the mass resolution of detector 2 is restricted to m/∆m = 10 for extracted ion species (the mass resolution is about 100 for ions arriving from the source). However this resolution is sufficient in the first step of optimizing the ion trapping signal. The detector can be further used in experiments where only a single ion species is involved and no new ion species are created in the trap during storage time. If a higher mass resolution is necessary, the ions are extracted back in the direction of the quadrupole deflector where they are deflected again to enter the multicycle reflectron (see section 3.4). Once all ions entered this device the quadrupole is switched off using fast HV-switches. Mass analyzed ion packages coming from the reflectron can now be detected on detector 1. 3.2. BENDING AND DETECTING IONS 15
Figure 3.2: Schematic view of the static quadrupole deflector. Shown are SIMION trajectory simulations of an ion beam that is deflected by 90 degrees to load the ions into the trap. If the multicycle reflectron is used for mass analysis after the ions are extracted from the trap the deflector is switched off once the ions enter the reflectron. They are then extracted on detector 1. CHAPTER 3. A MULTIPOLE TRAP SETUP WITH IMPROVED MASS 16 RESOLUTION
3.3 The temperature variable 22-pole ion trap
The central part of the experiment is a 22-pole radiofrequency (rf) ion trap, shown in Fig. 3.3. A detailed description of this device is given in [44, 45]. Stored ions are confined in radial direction by an oscillating rf field. In axial direction cylindri- cal endcaps prevent the ions from leaving the trap. The 22 rf rods are surrounded by static ring electrodes (shaping electrodes) that can be used to manipulate the position of the ion ensemble during storage time. Whereas stable confinement of a single ion in the oscillating quadrupole field of a Paul trap can be precisely pre- dicted by solving the Mathieu differential equations that describe the ion motion, this is different for oscillating high order multipole fields, where the equations of motion have no analytical solution [45]. However, the movement of the ions in a fast oscillating rf-field leads to the concept of an effective trapping potential, based on the separation of the ion motion into a smooth drift and a rapid oscillation, called micromotion [46]. This micromotion is predominant close to the rf electrodes at the outer turning point of the trapped ions. The effective potential can be expressed as
1 (qE ( r))2 V ∗( r)= + qΦ (3.1) 4 mΩ2 0 where E ( r) denotes the electric field at the point r, m is the mass of a test particle
with charge q in an electric field oscillating on frequency Ω and Φ0 is a non-oscillating DC potential (e.g. the static endcaps and the platform potential of the trap). For an ideal cylindrical multipole of the order n this effective potential can be expressed as 2 2 2n−2 ∗ 1 n (qV0) r V (r)= 2 2 (3.2) 4 mΩ r0 r0
where V0 denotes the amplitude of the oscillating rf-field. For a high order multipole field (n =11 for the 22-pole trap) this creates an almost box-like trapping volume with steep walls and a large field free region in the center. Due to the shape of such a potential the region where the trajectories of stored ions are dominated by micromotion is minimized. This is especially important, since collisions with the inert buffer gas in the regions of increased micromotion lead to a heating of the ion ensemble (so called rf-heating) and finally to a loss of the trapped ions [44]. How well suited the equations given above are to predict the shape of the effective potential will be discussed in section 4.3. 3.3. THE TEMPERATURE VARIABLE 22-POLE ION TRAP 17
Figure 3.3: The 22-pole ion trap forms the central element of the new ion trap setup. It is mounted on a helium cryostat and can be cooled to temperatures between 8 – 300K. The base plate of a 50K thermoshield can be seen, which reduces the heat input on the trap housing caused by blackbody radiation. The 22 rf electrodes are surrounded by five electrostatic ring electrodes, which can be used to shift the stored ions inside the trap. Cylindrical endcaps are used to confine the ions in axial direction. CHAPTER 3. A MULTIPOLE TRAP SETUP WITH IMPROVED MASS 18 RESOLUTION
The trap is operated in a tandem time-of-flight configuration, where time-of- flight mass analysis is used twice, for loading only selected ions into the trap, and after ion storage for mass analyzing the extracted ion ensemble [44]. This approach offers many important advantages:
• The stability of the ion source can be monitored during normal operation
• A full mass spectrum (e.g. the ionic products of a chemical reaction) can be recorded at once after ion extraction
• Ionic products are detected with high efficiency
The ions have typical kinetic energies of 470eV when they leave the source region. The trap itself resides on a platform potential that matches this kinetic energy so the ions are decelerated on their way into the trapping volume. Since all ionic species arrive at the trap after different flight times, we can use the static endcaps to mass-selectively load the desired ion species into the trap. The switching of the cylindrical endcaps is done in less than 50ns using homebuilt MOSFET switches in push-pull configuration. Once the ions are in the trap a short intense pulse of buffer gas is used to finally stop them. The entire trapping device is mounted on a closed cycle helium cryostat and can be cooled down to temperatures between 8 – 300K. The thermalization of the ions occurs via collisions with an inert buffer gas, which can be applied at different densities into the trap housing [45] using high precision sapphire valves. Additional reactive gases can be led in the trap at well controlled densities to study chemical reactions between the stored ions and neutral molecules at variable temperatures [45, 47, 42]. The pressure of all the gases in the trap is measured using a gas type independent capacitance gauge (Pfeiffer CMR 275) which is directly connected to the trapping volume. After variable storage times, the ions are extracted from the trapping volume by switching one of the static endcaps from a repulsive to an attractive potential. This drags all the ions out of the trap and accelerates them towards one of the detectors. Loss rates of stored ions can be measured by detecting the ion signal as a function of storage time. Measuring this rate as a function of the buffer gas density allows to determine reaction rate coefficients with high accuracy as a function of temperature. 3.4. IMPROVING THE TIME-OF-FLIGHT RESOLUTION 19
3.4 Improving the time-of-flight resolution
In general the mass resolution that can be achieved in a time-of-flight configuration strongly depends on the length of the flight path. The mass resolution that can be achieved after extraction from the trap1, using all components described so far is only in the order of m/∆m = 10. This resolution is fair in experiments where no new ion species are created in the trap during storage. However, for the investigation of complex reaction networks, isotope exchange reactions or experiments involving larger clusters it is insufficient. To enhance this mass resolution, a multicycle re- flectron was installed in the beam path directly after the ion source as shown in Fig. 3.1. A schematic drawing of this device is shown in Fig. 3.4. The multicycle reflectron consists of two coaxial electrostatic mirrors that are 460mm apart. Ions that travel in this device at a certain kinetic energy are reflected back and forth be- tween these mirrors. Each mirror consists of a stack of seven cylindrical electrodes.
Five of these electrodes are put on potentials V1,V2,V3,V4,VL, the other electrodes are grounded, as depicted in Fig. 3.4. The potentials V1 –V4 form a field ramp, whereas VL provides an ion lens that is used to tune the focal length of the whole ion mirror. The most stable operating conditions are achieved, when the focal point of each mirror lies exactly in the opposite mirror. The device is then in analogy with an optical resonator in a confocal configuration. The geometry as well as the optimum voltages of the design were optimized using SIMION 8.0 [48]. One strategy in designing the electrodes was to maintain the cylindrical symmetry by reducing field distortions caused by the mount of the electrodes or the surrounding vacuum chamber. To achieve this all electrodes were provided with a cylindrical shielding, a concept already successfully implemented and tested in the velocity map imaging spectrometer, described in chapter 5. The shape of the potential is tailored in a way that the ion beam is refocused with every reflection to prevent the ion packages from spreading apart. A good time-of-flight resolution was achieved in the simulations with a set voltages which was later also used in the experiment: V1 = -577 V, V2 = -470 V, V3 = -163 V, V4
= -79 V, VL = -303V. Shown in Fig. 3.5 is a measured time-of-flight mass spectrum for O− and OH−. After one cycle the FWHM of the OH− peak is 800ns at a flight
1In an earlier version of the setup the ion trap was placed between two collinear time-of-flight sections [44]. In this configuration a mass resolution of m/∆m = 50-100 could be achieved. CHAPTER 3. A MULTIPOLE TRAP SETUP WITH IMPROVED MASS 20 RESOLUTION
Figure 3.4: Schematic view of the multicycle reflectron. The device consists of two electrostatic mirrors, each formed by seven cylindrical electrodes. Ions can be reflected back and forth between the mirrors if an appropriate set of voltages is applied to these electrodes.
Figure 3.5: A typical time-of-flight trace acquired for O− and OH− ions that are mass analyzed using the multicycle reflectron. The left trace shows the two species still close together after one cycle. In the right trace the species are well separated and only OH− is visible here. 3.4. IMPROVING THE TIME-OF-FLIGHT RESOLUTION 21
time of 42.3 s, which corresponds to a mass resolution of m/∆m = t/2∆t = 20. After only twenty cycles a resolution of 200 is achieved. Due to the compact design of the setup, the reflectron can be used for preselecting a desired ion species prior to the storage in the rf trap as well as for mass analysis after ion extraction. The need to open and close the entrance mirror of the reflectron to load the arriving ions into this device restricts the range of masses that can be analyzed at once. For most applications, however, this does not limit us, since we use this tool to distinguish few adjacent masses. In addition a coarse mass analysis can be performed using only the back mirror in a normal single reflection configuration. The mass resolution of the reflectron increases with the number of reflections the ions undergo. As the roundtrip time between the two mirrors is different for ion species of different masses, the lighter particles will overtake the heavier ones after a given number of cycles, which has to be taken into account in the analysis. The time the ions can remain in between the two mirrors is limited by collisions with residual background gas. In the current design the reflectron tube does not feature an individual vacuum pump. The vicinity of the reflectron to the ion source leads to an increased background pressure in between the mirrors, which is in the order of 10−6 mbar. Collisions with the background gas restrict the lifetime of the ions in the resonator to about 1ms, which limits the mass resolution to m/∆m ≈ 1000 at 10Hz repetition rate of the ion source. However, since the number of cycles employed is variable, we extract the ions from the reflectron as soon as the desired mass resolution is achieved, which can already be the case after only a few cycles. The ion loss in the reflectron does not influence the decay measurements carried out in the 22-pole trap, since for a fixed number of cycles in the reflectron the ion signal decays by a constant factor. To test the mass resolution that can be achieved, we performed a test run where the source was operated at much lower repetition rates, resulting in a reduced back- ground pressure in the reflectron. In this measurement a mass resolution of 10000 could be achieved. The installation of an additional pumping stage in the reflectron region is intended for the future and only represents a minor change in the setup. While the multicycle reflectron is used in our setup to enhance the time-of-flight resolution, this ion resonator is used in an increasing number of research laboratories as a real trapping device [49, 50]. In this so called ”Zajfman trap” storage times of hundreds of seconds can be achieved under optimal conditions. In cryogenic setups CHAPTER 3. A MULTIPOLE TRAP SETUP WITH IMPROVED MASS 22 RESOLUTION
where a background pressure of < 10−13 mbar can be achieved the lifetime is finally restricted due to geometrical imperfections in the setup and the stability of the em- ployed voltage supplies [51].
To illustrate the broad range of applications of this setup, two examples of an- ion molecule reactions, that we studied in this ion trap are briefly discussed. The first example is the proton transfer reaction
− − NH2 + H2 → NH3 + H
where we observed a strongly suppressed reaction probability at room temperature and a negative temperature dependence of the rate coefficient (see Fig. 3.6). This temperature dependence could be described using phase space theory, a statistical model based on a RRKM approach (dashed line in Fig. 3.6). A detailed description of this experiment including the statistical modeling is given in [52]. At a tem- perature of 20K we found an unexpected maximum in the rate coefficient which is not predicted by the model and could point to a reaction resonance. However, the − phenomena can still be observed in the deuterated reaction NH2 + D2 → NH2D + D−. A final explanation for this observation is still lacking. With this experiment we reached the lowest temperature at which an anion molecule reaction has been studied so far [53]. In the second example we used the 22-pole trap to measure the rate coefficients of the reaction − − D + H2 → H + HD at very low temperatures. The energy landscape of this system is dominated by a large intermediate barrier that separates the reactants from the products. Guided ion beam experiments measured the cross section of this system and revealed a barrier height of 330meV [54]. Measuring the formation rate of H− ionic products at very low temperatures we observed a revival of the upper reaction occurring at an extremely small rate coefficient of k ≈ 5 · 10−19cm3s−1 [55], which points to a tunneling process through the large barrier. The measurements of such slow processes require storage times of many minutes at very high gas densities in the trapping volume and are therefore extremely challenging. 3.4. IMPROVING THE TIME-OF-FLIGHT RESOLUTION 23
0.12 - NH2 + H2 0.1 - NH2 + D2 0.08
0.06 Reaction probability
0.04
0.02
0 0 50 100 150 200 250 300 Temperature K
− Figure 3.6: Reaction probability, defined as the ratio k/kLangevin, for NH2 + H2 − and NH2 + D2 as a function of temperature. The dashed line shows a phase space theory calculation of the reaction with H2, which is based on a capture rate that is scaled down by a factor of 12 from the Langevin rate to match the measured value at 300 K. CHAPTER 3. A MULTIPOLE TRAP SETUP WITH IMPROVED MASS 24 RESOLUTION Chapter 4
Absolute photodetachment cross sections studied in a 22-pole trap
The photodetachment of a weakly bound electron from a neutral molecular core rep- resents a fundamental light-matter interaction. Detached photoelectrons can reveal information on the energy levels in both the anion and the neutral. Comparisons of relative photodetachment cross sections near threshold with Wigner’s law allow for precise studies of the long-range electron neutral interaction [56, 57]. Absolute photodetachment cross sections are needed to model the formation and destruction pathways of anions in various plasma environments [58]. The recent detection of negative molecular ions in interstellar clouds [59] emphasizes the need for experimental data to understand the role anions play in interstellar chemistry [60, 61]. In such cold and low density environments, anions are expected to be formed by radiative attachment. Photodetachment by stellar and cosmic radiation is likely to be the most efficient destruction channel in photon dominated regions. In this chapter we describe photodetachment experiments carried out in the 22- pole trap setup. A laser tomography technique is presented which allows to measure absolute photodetachment cross sections and thereby does not rely on calibration to known standards. The systems we studied cover the area from basic atomic ions over a diatomic molecule with a simple internal structure to a hydrated cluster anion. Furthermore this technique is used to image the effective trapping potential of the 22-pole trap, revealing an interesting substructure.
25 CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 26 IN A 22-POLE TRAP
4.1 Absolute photodetachment cross sections of O− and OH−
4.1.1 Photodetachment via 2D tomography
In this section we describe a scheme to measure absolute photodetachment cross sections of trapped anions1. This technique is completely model independent and does not rely on recalibration against known systems. Given the appropriate light source at hand it is applicable to every anionic species that can be brought in the gas phase and stored in the 22-pole trap. The technique is based on using the photodetachment process to induce an ion loss from the trap, as the anion emits an electron upon absorption of a photon. The anions are depleted by a laser beam propagating parallel to the symmetry axis of the trap. A schematic of the technique is shown in Fig. 4.1. The rate equation that describes the number of trapped ions is then given by dN = −[k (x,y) − Γ] N (4.1) dt pd
where kpd(x,y) is the loss rate of the trapped ions due to the photodetachment laser, depending on its radial position through the trap. Γ denotes a background loss rate, e.g. due to residual gas collisions. This equation is solved by an exponential decay
with a decay rate kpd(x,y) + Γ given by the term in square brackets, which is the quantity that can be measured experimentally. The detachment rate depends on the following factors: large cross sections will cause a large loss rate; a large photon flux will also increase the ion loss; finally the overlap of the laser beam and the ion cloud determines the strength of the interaction. These dependencies can be expressed as
kpd(x,y)= σpd · FL · ρ(x,y) (4.2)
where σpd is the total cross section for photodetachment at the employed laser wavelength, Φ is the photon flux density of the laser, which is taken to be constant along the laser beam parallel to the z-axis and ρ(x,y) is a single particle density which describes the probability to find a single ion at a position (x,y). Using that this probability must be unity when integrating over the entire trapping volume one
1Essential parts of this section have been published in [62]. 4.1. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS OF O− AND OH−27
Figure 4.1: Schematic of the photodetachment tomography technique. Anions are stored in the 22-pole ion trap and are depleted via photodetachment induced by a laser beam propagating parallel to the symmetry axis of the trap. The position of the laser beam can be scanned over the trapping volume using a moveable lens, which is mounted on a 2D translation stage. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 28 IN A 22-POLE TRAP
obtains
kpd(x,y)dxdy = σpd · FL · ρ(x,y)dxdy = σpd · FL (4.3) The integral on the left-hand side is obtained from a full two-dimensional tomo- graphy of the trapped ions. By scanning the photodetachment laser through the distribution of trapped ions and measuring at each laser position (x,y) the decay
rate kpd(x,y), which is proportional to ρ(x,y) according to Eq. 4.2, one directly obtains the photodetachment cross section
1 σpd = kpd(x,y)dxdy (4.4) FL
The tomography scan is performed using a thin convex lens (f = 1000mm) mounted on a step-motor driven two-axis translation stage, which images the laser beam to any (x,y) position in the trap (see Fig. 4.1). The two-dimensional tomography scans are performed on a mesh with 0.25mm point spacing. The mesh points are traversed in random order to avoid systematic drifts. A calibrated silicon power meter is used to determine the laser power in front of the vacuum window and after transmission through the vacuum setup. This test measurement is performed before and after each experimental cycle. Inside the vacuum chamber the beam propagates without further losses. A small fraction of the beam is projected onto a photodiode to monitor the fluctuation of laser power during the experiment. The loss rate of the stored ions is measured as described in chapter 3.
4.1.2 O− - the reference anion
Photodetachment cross sections have been investigated experimentally and theoret- ically for a large number of anions. These are - with only few exceptions [63, 64, 65] - relative measurements that have to be calibrated against a known standard. In the majority of experiments this calibration is directly or indirectly traceable to the O− anion, thereby relying on only two cross section measurements of Branscomb et al. [66] and Lee and Smith [67]. In the former experiment an absolute cross section was obtained by crossing an ion beam with light from a 30 ampere carbon arc discharge using an arrangement of several optical filters to tune the optical wavelength. Note that the laser was not invented yet! The latter measurement was carried out with a selected ion drift tube using normalization to D−. 4.1. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS OF O− AND OH−29
Atomic anions are ideal systems for testing the progress in theoretical predic- tions of photodetachment cross sections, which still represent a major challenge. The most recent ab-initio calculations performed for the atomic anion O− by Zatsarinny and Bartschat [68] succeeded to reproduce the wavelength dependent shape of the measured O− photodetachment cross section. However, on an absolute scale the cal- culated cross sections disagreed by ∼35% with the experimental results. Based on this finding the authors questioned the validity of the old measurement of Ref. [66] and suggested to revise the calibration scale. As this affects a huge amount of ex- perimental data another independent measurement of the O− cross section is highly desirable. We have carried out a series of precise and independent measurements of the O− absolute photodetachment cross section using the method described above to contribute to this discussion2. Most importantly, our method does not rely on a calibration procedure to any former measurement. Two different continuous-wave lasers were employed for the current measure- ments, a free-running diode laser at 661.9nm (Mitsubishi ML1J27, 100mW, spec- tral width 0.7nm FWHM) and a single-mode frequency-doubled Nd:YAG laser at 532nm (Coherent Verdi, attenuated to 58mW). The laser beams were imaged to 2 any (x,y) position in the trap with a 1/e waist of ω0 = 350, 210 and 120 m, respectively. With a distance from the lens to the trap center of 1104(5)mm, the wavelength-dependent magnification of the image position in the trap with respect to the lens position is calculated. A calibrated silicon power meter (Coherent OP2- VIS) is used to determine the laser power in front of the the AR-coated vacuum window (99.2%transmission) before and after each measurement. Inside the vac- uum chamber the beam propagates without further losses. A photodiode monitors the fluctuation of laser power during the experiment. An electro-mechanical shutter interrupts the laser beam during the trap injection, cooling and extraction phases. Atomic O− was produced in the plasma discharge ion source described in section 5.1 using normal air as precursor gas. The experiment runs at 10Hz repetition rate. With each cycle a bunch of ∼1000 ions was mass-selected and loaded into the trap. Helium was used as buffer gas at a typical density of 1014 cm−3 in the experiment. In order to ensure that the ions are fully thermalized before they interact with the laser, a storage period of 200ms was inserted before the laser beam was switched
2The absolute cross section measurements on O− and OH− presented in this section have been carried out in an earlier version of the 22-pole setup, described in [44]. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 30 IN A 22-POLE TRAP
Figure 4.2: Histogram of the measured photodetachment rate for O− as a function of the transverse position of the laser light in the ion trap. Each bin represents an individual decay measurement at a given position. The graph reflects the ion density distribution in the 22-pole trap, as the ion column density is proportional to the detachment rate. The insets show two examples for individual loss rate measurements with laser light induced ion loss. 4.1. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS OF O− AND OH−31
on. The number of ions that survived the interaction with the laser were detected as a function of storage time. For each laser position the photodetachment rate was obtained in a storage time interval of 0.2-2s from the difference of the fitted loss rate with and without the laser. At 300K the background ion loss rate of about 0.25s−1 needs to be taken into account. It is mainly caused by evaporation of ions out of the trap [69]. For lower temperatures it decreases by orders of magnitude and therefore becomes insignificant. To ensure that the laser beam can be scanned through the entire ion distribu- tion without clipping at the end electrodes, the trap was operated at an increased radiofrequency amplitude of V0 = 150V (under normal operating conditions about 30V are sufficient to trap the ions). According to Eq. 3.2 this results in a more nar- row effective potential and therefore pushes the ion cloud towards the trap center. One-dimensional scans have been carried out at different rf amplitudes in the hor- izontal and vertical direction to control that we can access all ions. The data were averaged over typically 4 – 8 scans thereby traversing the mesh points in random order to avoid systematic drifts. We have carried out the measurements of the absolute photodetachment cross section at different buffer gas temperatures. A two dimensional laser tomography scan at 300K is shown in Fig. 4.2. The two insets show the individual detachment rate measurements at two selected mesh points. The photodetachment loss rate for a given position is proportional to the ion column density at that point. Hence, Fig. 4.2 also represents the column density of trapped O− in the 22-pole trap. It resolves several interesting features that have not been observed previously. In the center, the ion distribution is relatively uniform. Near the maximum radius of the distribution it increases slightly and shows ten equally spaced maxima as a function of angle. These unexpected details of the distribution will be discussed in section 4.3. For the total cross section measurements, however, the actual shape of the ion distribution is not important. Following Eq. 4.4, the absolute photodetachment cross section for O− is obtained by discrete integration of the distribution and subsequent division by the photon flux. Two measurements at 662nm, carried out at 300 and 170K buffer gas −18 2 temperature, revealed values of σ =5.7(2)stat(2)syst and 5.9(1)stat(2)syst × 10 cm . The estimation of the statistical and systematic accuracies (a detailed description is given in Appendix A), shows that these two values agree with each other. At −18 2 532nm we obtain σ =6.3(1)stat(2)syst × 10 cm , measured at 170K. The results CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 32 IN A 22-POLE TRAP
Figure 4.3: Measured cross section of O− as a function of the photon energy. Our data (large full circles) is compared with the relative measurements of Ref. [70, 67] (squares and small triangles), which were calibrated to hydrogen anion measurements. The dashed line shows the ab-initio calculation of Ref. [68].
from both wavelength measurements are shown in Fig. 4.3 together with the only two previous measurements [66, 67] and a theoretical calculation [68]. These results − 2 2 pertain to O in a mixture of the two P3/2 and P1/2 spin-orbit state, which are spaced by 177.13cm−1 [71]. To disentangle the contributions of the two different spin-orbit states will be subject to a future study at low temperatures. Our values are in excellent agreement with the two previous, many decades-old experiments. Our measurements hence validate the reliability of the previous O− cross section used as a normalization standard [66, 67] and improve the accuracy of future calibrations to O−. Recent ab-initio calculations give values for the absolute cross section that are about 35% too high [68]. Considering the high accuracy of our new measurements this deviation clearly asks for an explanation. 4.1. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS OF O− AND OH−33
4.1.3 OH− - Temperature dependence far above threshold?
While O− serves as an important benchmark system, the photodetachment of molec- ular anions yields much more dynamical information. The molecular anion for which the most detailed cross section studies exist is the hydroxyl anion OH−. Detailed studies are available for the relative photodetachment cross section of OH− in the threshold region using photoelectron spectroscopy. They serve as a precise test of the long-range electron-dipole interaction [56]. Relative cross sections have also been measured for state-specific transitions [57, 72, 73]. Two absolute cross sec- tion measurements have been carried out independently by Branscomb [74] and Lee and Smith [67]. Both measurements were scaled to H− and D− cross sections and disagree significantly. For OH− we carried out absolute cross section measurements for two different laser wavelengths, using a diode laser at 662nm3 and a 5mW helium neon laser at 632.8nm. The measurement with the 20× weaker HeNe laser is normalized against the column density distribution that we obtained from the 662nm tomography. The cross section is calculated from the measured decay rate at the trap center kHeNe(x =0,y = 0) and known density ρ(0, 0) = k662(0, 0)/ k(x,y)ds and is hence subject to a larger error. The temperature was varied betwee n 8 – 300K. The results shown in Fig. 4.4 reveal no change of the OH− photodetachment cross section in this temperature range at the employed wavelengths. The temperature-averaged cross sections are −18 2 σpd(662nm) = 8.5(1)stat(3)syst × 10 cm and −18 2 σpd(632nm) = 8.1(1)stat(7)syst × 10 cm
The cross section at 662nm agrees within two standard deviations with both pre- vious values of 9.8(9)×10−18 cm2 [74] and 7.3(5)×10−18 cm2 [67] and thereby some- what reconciles the latter two values. The data for different temperatures prove that within the error bar the cross section stays constant in the temperature range from 8 to 300K. Since the thermal population of rotational states in OH− changes strongly in this range, this is evidence for a rotational state-independent cross section for J between zero and about five, given by the temperature at which we carried out the
3see previous section CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 34 IN A 22-POLE TRAP
Figure 4.4: Measured photodetachment cross sections of OH− at 662 nm (solid symbols) and 632.8nm (open symbols) at different temperatures. The data points for 632.8nm are slightly shifted horizontally for clarity. The horizontal lines rep- resent the temperature-averaged values. The values of Ref. [67] are marked by the triangles and the values of Ref. [74], obtained at unknown internal temperature, are indicated by the arrows.
experiment. This is in agreement with the assumption that all H¨onl London fac- tors for s-wave detachment sum up to unity for detachment energies far above the threshold (where all dipole allowed transitions are energetically accessible as well).
4.1.4 OH− - Thermometry close to threshold
In a second set of experiments, we measured the photodetachment cross section close to the threshold as a function of the laser wavelength. The aim in these experiments was to use photodetachment to resolve the rotational structure of a small molecule and to establish a method that uses anion photodetachment as a tool to study internal distributions of stored ion ensembles. For this purpose the OH− molecule provides an excellent test system, as it has a relatively simple and well known spectrum with well spaced rotational levels in the vibrational ground state. 4.1. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS OF O− AND OH−35
In a simple picture this diatomic molecule can be described as a two-dimensional rotor. Its energy levels are given by
E = J(J + 1) · B with the rotational quantum number J and the rotational constant B, which in the case of OH− accounts for B = 18.7352 cm−1 [73]. The experiment is carried out between 10 - 50K, so only the first few rotational levels will be significantly populated. Shown in Fig. 4.5 are the energy levels of the first rotational states of OH− and OH. The arrows in the picture mark possible rotational branches, indicat- ing the change of the total angular momentum in the transition. The levels in OH 2 are split due spin-orbit couplings into the two fine structure components Π3/2 and 2 −1 2 Π1/2 that are separated by about 100cm in energy. Only the lower lying Π3/2 is accessed in the present experiments. In addition the OH levels are split due to orbit-rotation interactions. These so called Λ-doublets are scaled up by a factor of 50 in Fig. 4.5 and can not be resolved for the transitions studied in this experiment. In this respect the OH− provides us an ideal toy model to study the properties of the quantum mechanical 2D rotor. In the experiment we used a grating stabilized diode laser system, operating around 680nm. A detailed description of the experimental setup is given in [75]. Shown in Fig. 4.6 is the measured photodetachment cross section as a function of photon energy close to threshold. The two datasets repre- sent measurements at two different trap temperatures of 50K (red points) and 23K (blue points). As can be seen from the image, we are able to resolve the different rotational branches as they open up with increasing photon energy. The spacing between the different thresholds nicely confirms the predicted position of the energy levels in the 2D rotor. The data of the single branches was fitted with a power law
(ǫ − EA)p (4.5) where ǫ is the photon energy and EA denotes the electron affinity of the pho- todetachment threshold of a specific branch. The exponent p describes the long range interaction of the outgoing electron with the remaining neutral. In the case of p = 1/2 the expression is known as Wigner threshold law4. A modified
4In general Wigner’s law is written as (ǫ − EA)l+1/2, where l denotes the orbital angular momentum of the outgoing electron. In the case of OH− we find an s-wave electron and therefore l = 0 CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 36 IN A 22-POLE TRAP
Figure 4.5: The energy levels of OH− and OH for the first rotational states. The arrows indicate dipole allowed transitions from the first three rotational levels.
version proposed by Engelking [76], which takes into account interactions of the outgoing electron with the dipole of the neutral molecule, yields a coefficient of p = 0.28 which was used in the fits in Fig. 4.6. The threshold energies of the P,Q and R branches of EA(P ) = 14628.70(10) cm−1, EA(Q) = 14703.60(10) cm−1 and EA(R) = 14740.96(10) cm−1 were taken from [56]. In a next step we can now try to derive an internal temperature of the molecules from the measured signal. This can be done, since the relative population of a single rotational level must be directly proportional to its contribution in the photodetach- ment process. In the proportional constant we have to consider the H¨onl-London factors, that determine the transition strength of a single rotational level [73]. As- suming a Boltzmann distribution for the population of the levels, we can now derive internal energies for the stored ion ensembles. The temperatures of the ion ensemble
for the two datasets in Fig. 4.6 are calculated to be 55.9(0.7)stat(6.5)syst)Kelvin for
the 50K measurement and 31.9(0.7)stat(0.9)syst)Kelvin for the 23K measurement [75]. The reason for the slightly enhanced temperature with respect to the temper- ature of the trap housing is not known at the moment. The most likely explanation 4.1. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS OF O− AND OH−37
for this effect is, that the surfaces of the trap suffer from coating with oxide layers caused by experiments on carbon chain anions and cluster growth reactions using water vapor. This coating can cause patch fields that disturb the trapping potential and lead to heating. Dismantling the ion trap and cleaning all surfaces should solve these problems. With these experiments we have demonstrated, that photodetachment measure- ments close to threshold can be used to determine internal state populations of small molecular ensembles. As the photodetachment process is extremely fast using high power laser diodes, this method can especially be employed to study time dependent processes, like the repopulation of rotational levels after depletion or even excitation to higher lying states. This offers valuable clues to cooling efficiencies of buffer gas collisions and timescales of energy redistribution in small molecules. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 38 IN A 22-POLE TRAP
Figure 4.6: Measured OH− photodetachment cross sections at threshold. The datasets show measurements at two different trap temperatures. Different rotational branches open up with increasing photon energy. The single branches have been fitted with the relation (ǫ − EA)0.28 which represents a modified Wigner threshold law [76]. From the relative contribution of the branches we can derive an internal temperature of the molecule assuming a Boltzmann distributed population of the levels. 4.2. PHOTODETACHMENT OF COLD SOLVATED ANIONS 39
4.2 Photodetachment of cold solvated anions
In this section we will extend our method to use anion photodetachment as a thermometer for the internal state distribution of molecular ensembles to a larger − molecule: the monosolvated OH (H2O). In the only previous photodetachment mea- surement on this cluster close to the threshold [77] the authors determined a thresh- old energy of ET = (420±20)nm. A more precise value for the detachment threshold can be inferred from the binding energy of the cluster of Ebind = (1.18 ± 0.05) eV (compare table 6.5). Together with the known electron affinity of the OH− molecule − we can derive an electron affinity for OH (H2O) of EA = (3.01 ± 0.05)eV, which leads to a photodetachment threshold of ET = (412±7)nm. We measured the pho- − todetachment cross section of the OH (H2O) cluster close to the threshold at wave- lengths between 406 and 414nm. The shift of the threshold towards shorter wave- lengths compared to the bare OH− anion (threshold at ∼680nm) reflects the sta- bilization by the water molecule (compare Fig. 4.7). Fortunately this wavelength range can be accessed using cheap Blu-ray laser diodes, that are available with up to 200mW of laser power. − Photodetachment of the OH (H2O) anion leads into a dissociative state, since the neutral OH··· H2O immediately decays into fragments. Additionally the solva- tion of the OH− with a single water molecule also changes the energetic properties − of the system. From a structure calculation of the OH (H2O) cluster (see chapter 6.2.2) we find rotational constants of 10.3, 0.303 and 0.301cm−1, so that we can approximately describe the system as an oblate symmetric top molecule. The rota- tional level structure is now too closely spaced to be resolvable in our experiment. However, the lowest lying vibrational states are found at 132 and 215cm−1 and belong to a torsional mode that is split due to tunneling between two symmetric equivalent structures on the Born-Oppenheimer surface [78]. While at 30K we only expect 0.1% of all molecules to be found in the lowest excited vibrational state, at 85K already 11% of all ions populate one of the two lowest vibrational modes. Will we still be able to see a temperature effect in the threshold behavior of the molecule?
The cross section measurements presented here were carried out at buffer gas tem- peratures between 25 and 300K. For each temperature a full tomography scan was carried out to obtain an absolute cross section value at one wavelength. The data CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 40 IN A 22-POLE TRAP
− Figure 4.7: Electron affinities of the OH (H2O)n clusters. The stabilization of the cluster with increasing solvation leads to a shift of the threshold to shorter wavelengths. Values taken from [79].
taken at the other wavelengths could subsequently be calibrated against this value using the now known ion density distribution. Shown in Fig. 4.8 are the mea- − sured absolute photodetachment cross sections of OH (H2O) at a photon energy of 24410 cm−1 for various trap temperatures between 30 and 205K. As can be seen, the cross section strongly increases with increasing temperature. At room temperature, where we were not able perform a full tomography scan due to the extension of the ion cloud, we extrapolate our data to a cross section of 1.5±0.5Mbarn. This value is still small compared to the cross section of 8.5Mbarn that we measured for OH− at a comparable energy above threshold. This indicates, that the internal structure of the molecule plays an important role in defining the value of the cross section.
The photodetachment cross section has been measured as a function of photon energy for different temperatures of the ion trap. The results are plotted in Fig. 4.9. For all trap temperatures we observe a nearly linear increase in the cross section above threshold. The linear threshold behavior strongly differs from a σ ∼ E1/2 threshold behavior predicted by Wigner’s threshold law for an s-wave electron, as 4.2. PHOTODETACHMENT OF COLD SOLVATED ANIONS 41
− Figure 4.8: Absolute photodetachment cross sections of the solvated OH (H2O) measured at different temperatures. Each point represents a full two dimensional tomography scan at 24410 cm−1.
it is observed for OH− and would therefore also be expected here5. To explain the observed deviation from the Wigner behavior we have to keep in mind that the rotational level spacing is too close to be resolved in our experiment. As the photodetachment leads into a dissociative state, the Franck-Condon factors for the vibrational transition are expected to determine the shape of the cross section. A detailed analysis of this effect is currently carried out in our group. Lacking a complete model for the moment, we describe our data with a linearly increasing cross section close to threshold. A significant change can be observed for the slope of the measurements carried out at different trap temperatures. This change must result from a cooling of the internal degrees of freedom of the trapped clusters. Due to the close spacing of the rotational levels, all dipole allowed transitions are energetically allowed as well at a given photon energy above threshold. This is very different from the OH− case where the rotational branches only open up at a certain energy due to the large level spacing and the angular momentum selection rules. As the H¨onl-London factors for
5The closed-shell water molecule clustered to the OH− does not change the angular momentum for the photodetachment transition. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 42 IN A 22-POLE TRAP
all transitions of a specific rotational state are assumed to sum up to unity, a change in the rotational population due to cooling can not affect the photodetachment cross section. This implies that the change has to be caused by cooling of the vibrational modes of the cluster6. In consequence the photodetachment cross section must depend on the vibrational states of the molecule. A linear extrapolation of all datasets with the same intercept at the energy axis yields a threshold energy of 23995cm−1. The intercept has been optimized to give the best χ2 values for all datasets. We assign its value to the electron affinity of the − OH (H2O) system, which is then EA = 2.98eV. Since we can energetically treat the photodetachment process as
− − − EA[OH (H2O)] = EA[OH ]+Ebind[OH (H2O)]
we can calculate a binding energy of the cluster using the known electron affinity of OH−, EA[OH−] = 1.83eV. From a conservative error estimation we find the threshold between 23500 and 24100cm−1, which gives us a value for the binding +0.01 energy of the cluster of Ebind = 1.15 −0.07 eV. While we are now able to observe internal cooling of the cluster, the next step will be to model the shape of the cross section in order to derive a temperature. The thermometry measurements presented in this section demonstrate the thermaliza- tion of molecular clusters in a multipole ion trap and link the experiments presented in this chapter with the crossed beam studies, we will present in chapter 6.
6This does not mean, that no rotational cooling occurs. The photodetachment process is simply not sensitive to it in this special system. 4.2. PHOTODETACHMENT OF COLD SOLVATED ANIONS 43
2.0
1.6
1.2
0.8 Cross section (MBarn)
0.4
0.0 23900 24100 24300 24500 24700 Photon Energy (wavenumbers)
− Figure 4.9: Energy dependent photodetachment cross sections of OH (H2O) mea- sured close to threshold. The different datasets have been taken at temperatures of 30, 85, 130, 205 and 300 K from bottom to top respectively. Each dataset is calibrated using the absolute measurements shown in Fig. 4.8. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 44 IN A 22-POLE TRAP
4.3 How can a 22-pole ion trap exhibit 10 minima in the effective potential?
Multipole radiofrequency ion traps, in particular the 22-pole ion trap, are versatile devices used in laser spectroscopy [80, 81, 82] and investigations of chemical reaction processes of atomic and molecular ions [83, 53]. High order multipole traps offer a large field free region in the trap center, and therefore provide a reduced interaction time of the ions with the oscillating electric field compared to a quadrupole trap. The number of trapped ions that can be excited with radiation depends on the local density of ions in the interaction volume with the light field. In experiments with trapped Ba+ ions in an octupole trap the density has been imaged by spatially resolving the fluorescence signal [84]. In this section we use the tomography method presented in section 4.1.1 to image the density distribution of the trapped ions7. This can be done since according to Eq. 4.3 the position dependent loss rate k(x,y) is directly proportional to the local ion column density ρ(x,y). Thus, a full two- dimensional tomography scan of the trapped ions can be used to map the entire ion column density in the trap.
4.3.1 Tomography of the trapping potential
The measurements have been carried out using OH− which can be easily produced and trapped at different trap temperatures. The tomography scans are performed in the same fashion as described in section 4.1. Shown in Fig. 4.10a is a tomo- graphy scan of OH− anions in the 22-pole trap at 300K with the rf amplitude set to 160V. The figure also contains the sketched arrangement of the trap’s copper housing mounted on the helium cryostat, the position of the 22 rf electrodes and the axial end electrodes. Fig. 4.10b is a zoom of the scan which more clearly shows the measured ion density distribution. Every pixel of the histogram here represents a fitted photodetachment depletion rate k(x,y) (see previous section) and is propor- tional to the single-particle probability density ρ(x,y) along a column parallel to the z-axis. As can be seen the ion distribution as a first approximation can be considered circularly symmetric and constant in the center region of the trap, whereas it drops to zero when the ions reach the outer regions of the trapping volume. Note that this
7Essential parts of this section have been published in [85] 4.3. HOW CAN A 22-POLE ION TRAP EXHIBIT 10 MINIMA IN THE EFFECTIVE POTENTIAL? 45
Figure 4.10: a) Measured density distribution of trapped OH− ions at 300K buffer gas temperature with the rf amplitude set to 160V. The sketched geometry shows the layout of the ion trap, viewed along its symmetry axis. It includes the copper housing, the 22 rf electrodes (end-on), a surrounding shaping electrode, and the end electrodes. b) Zoom into the measured ion density distribution, each pixel represents an individual decay rate measurement. c) One-dimensional cut through the density distribution along the horizontal axis. d) Effective potential derived from the density distribution by assuming a Boltzmanm distribution of the trapped ions at 300 K. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 46 IN A 22-POLE TRAP
happens for smaller radii than the end electrode (solid line in Fig. 4.10b), indicating that clipping of the laser at the end electrode is not affecting the measured density distribution. For smaller rf amplitudes the ion density distribution would extend to larger radii and could not be fully probed by the photodetachment tomography. For this reason we have restricted ourselves to large enough rf amplitudes in this study. In Fig. 4.10c a horizontal cut through the ion distribution is shown, which follows the dashed line in Fig. 4.10b. While in the center the distribution is relatively uniform, the population is locally enhanced by up to 40% near the edge of the ion distribution. Such a behavior has already been observed in previous measurements [65]. To study this here in more detail, the effective potential V (x,y) is extracted from the local ion density ρ(x,y) assuming a Boltzmann distribution for the ions in the trap 1 ρ(x,y)= exp(−V (x,y)/k T ), (4.6) Z B where T is the absolute temperature, kB is Boltzmann’s constant, and Z is the partition function. Since only the column density is measured, the resulting potential V (x,y) is an average over the z-direction. Fig. 4.10d shows a cut through the obtained effective potential for the distribution of Fig. 4.10c. Overall this potential compares well with the calculated potential of an ideal 22-pole potential (solid line), obtained without any free parameters from Eq. (3.2). Closer inspection reveals interesting features in the potential that deviate from the ideal multipole. While the potential is relatively flat in the center, it shows a distinct minimum of about 12meV near the left edge of the ion distribution and a weaker minimum of about 5meV near its right edge. It can be excluded that this change of the distribution is caused by space charge effects, because the experiments are performed with only a few hundred ions in a trap volume of about 1cm3. The same features of the effective potential are observed in measurements at a lower trap temperature. Fig. 4.11a shows a tomography scan at 170K at the same rf amplitude as above. The ion distribution again looks circular symmetric with a distinct cutoff when the ions reach the steep walls of the trapping potential. A horizontal cut through the effective potential, obtained in the same fashion as Fig. 4.10d, is shown in Fig. 4.11b. The same minima as for 300K are observed in the effective potential. At this lower temperature the two minima are better resolved and appear similar in depth on the left side and slightly deeper on the right side of the potential as compared to the 4.3. HOW CAN A 22-POLE ION TRAP EXHIBIT 10 MINIMA IN THE EFFECTIVE POTENTIAL? 47
Figure 4.11: a) Ion density distribution at 170K with an rf amplitude of 160V. It shows a substructure of ten clearly distinct maxima. b) Cut through the effective potential, derived from the the density distribution. Overall, the potential is in accordance with the effective potential of an ideal 22-pole (solid line).
300 K tomography. Further substructure becomes visible in the 170K density distribution. Ten clearly separated maxima in the density distribution appear almost equally spaced in angle at a radial position of about 3mm. According to Eq. (4.6) they correspond to ten localized minima in the trapping potential at this radius with a typical depth of 10meV. These minima have not been significant in the 300K ion distribution at 160V rf amplitude. They become visible, however, for larger amplitudes, as according to Eq. 3.1 the features scale with the square of the electric field. Fig. 4.12a shows a 300K ion distribution for an rf amplitude of 270V. It reveals the same ten density maxima and respective potential minima that could only be resolved at lower temperature at 160V. We have studied the dependence of the depth of the ten potential minima on the rf amplitude at 300K. The depth of the deepest minimum is plotted in Fig. 4.12b. Since the effective potential is expected to depend quadratically on the rf amplitude, a fit with only a constant and a quadratic term is applied to the data (solid line in Fig. 4.12b). It yields an rf-independent offset of about 11meV, which is attributed to the static potential of the end electrodes of the ion trap. These end electrodes produce a radially repulsive potential inside the trap, as discussed in Ref. [65, 86]. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 48 IN A 22-POLE TRAP
Figure 4.12: a) Ion density distribution at 300K with an rf-amplitude of 270 V. The histogram shows ten distinct maxima, which correspond to minima in the effective potential. b) The depth of the deepest minimum shows a strong increase as a function of the applied rf-amplitude. The solid line shows a polynomial fit with only a constant and a quadratic term.
It compares well with simulations, as shown in the next section. The ten “pockets” in the potential, however, reveal a more complex deviation from the ideal multipole description of Eq. (3.2).
4.3.2 Modeling trapping potentials of realistic multipoles
The effective potential of a 2n-pole has a 2n-fold rotational symmetry. The ap- pearance of the ten observed potential minima is therefore a clear indication for a breaking of the ideal symmetry. To investigate this effect further, the effective potential of the employed 22-pole trap has been modeled using a numerical simula- tion package based on a fast multipole solver [87] for the boundary element problem in combination with accurate field evaluation in free space. With this method the electric field E(r) can be calculated at any location inside the trap. It is converted into the effective trapping potential using Eq. (3.1). We have verified that the simu- lation of the trapping potential of an ideal 22-pole structure reproduces the effective potential of Eq. (3.2) on the numerical level of accuracy. Different assumptions have been tested as origin of the observed ten potential minima, such as the influence of the shape and position of the end electrodes and of the copper housing around the 4.3. HOW CAN A 22-POLE ION TRAP EXHIBIT 10 MINIMA IN THE EFFECTIVE POTENTIAL? 49
Figure 4.13: a) Depth of the deepest potential minimum as a function of the tilt angle of the rf electrodes with a potential applied to the end electrodes (upper points) and without any potential on the end electrodes (lower points). The solid lines show quadratic fits without a linear term. The inset shows the geometry of the 22-pole ion trap, viewed in the direction onto the coldhead (see Fig. 4.10a). The right wall of the trap together with the 11 implanted rf electrodes has been tilted by an angle of 1.0◦. b) Calculated ion density distribution for 300K in the effective potential of 270V rf amplitude and -2V static end electrode potential. A tilt angle of 0.15◦ is chosen, which leads to a good agreement with the measured density distribution shown in Fig. 4.12a.
trap electrodes, without showing a measurable effect on the potential. This suggests that imperfections of the trap geometry itself may be responsible. To simulate these imperfections a breaking of the ideal symmetry is introduced by displacing one half of the 22 radiofrequency electrodes by a small angle (see inset in Fig. 4.13a). Such a small tilt of one set of electrodes against the others occurs to be the most likely displacement during the trap assembly. Upon tilting one set of electrodes by only a few tenths of a degree the calculated effective potential of a 22-pole trap at 160V rf amplitude and -2V on the end electrodes immediately shows ten potential minima. In Fig. 4.13a the dependence of the maximum pocket depth on the tilt angle, as obtained from a series of simulations, is plotted. These simulations have been car- ried out for 160V rf amplitude. Here, an imperfection in the parallelity of only 0.2◦ causes a pocket depth of 5meV. The pocket depth is calculated at each angle with CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 50 IN A 22-POLE TRAP
and without a potential of -2V applied to the static end electrodes. The end elec- trode voltage produces an overall quadrupole potential that pushes the ion ensemble towards larger radii in the trap in addition to the tilt-induced pockets. Both data sets with and without end electrode potential are described by the same quadratic increase. For the simulations with end electrode potential a constant offset of about 9meV is obtained, in fair agreement with the experiment value of about 11meV. From the measured depths of the potential minima (Fig. 4.12b) a value of be- tween 3 and 5meV is extracted for an rf amplitude of 160V, after subtracting the influence of the static end electrode (see Fig. 4.12b). Such an rf-induced pocket depth is obtained in the simulation for a tilt angle of between 0.15◦ and 0.2◦ (see Fig. 4.13a). Fig. 4.13b shows a simulated density distribution for a tilt angle of 0.15◦. Following Eq. (4.6), the simulation has been performed for OH− ions that are stored at 300K in the 22-pole trap with 270V rf amplitude and -2V poten- tial on the end electrodes. This simulated density distribution agrees well with the measured distribution of Fig. 4.12a, which has been obtained with the same trap parameters. A larger tilt angle was found to already overestimate the ten potential minima. Note that it is preferable to compare graphs of the density distributions of simulation and experiment instead of effective potentials, because the experimental potential is obtained by a logarithm of the density distribution which suppresses the fine details in the images. In searching for an explanation for the observed ten minima, we have extended the electric field simulations to multipoles of different order n. These calcula- tions have shown that the number of minima observed in the effective potential of a distorted multipole ion trap is directly connected to the multipole order as
Nminima = n − 1. Based on this finding an illustrative explanation can be given for the origin of the pockets. The simple model given here has been validated us- ing electric field simulations. Fig. 4.14a shows a sketch of an extremely distorted hexapole (n=3) where all rf rods are in a linear arrangement. In this configuration the hexapole can be interpreted as two quadrupoles stacked onto each other that share the two middle electrodes. The effective potential is expected to be a com- bination of the two quadrupole potentials so that it consequently consists of two potential minima, indicated by the concentric circles in Fig. 4.14a. This scheme can be extended to higher order multipoles. Fig. 4.14b shows a 10-pole (n=5) which, in this linear configuration, is an arrangement of four quadrupoles and therefore 4.3. HOW CAN A 22-POLE ION TRAP EXHIBIT 10 MINIMA IN THE EFFECTIVE POTENTIAL? 51
Figure 4.14: Simplified picture why an imperfect n-pole features n-1 potential minima. a) A hexapole (n=3) in this configuration can be seen as two stacked quadrupoles. Each quadrupole has a potential minimum in the center of the four rods. b) This scheme can be extended to higher order multipoles. For n=5 one expects to find four pockets. c) When the transition is made from the linear con- figuration to a real multipole with all rods on a circle the pockets remain. d) If the ideal multipole has slight geometrical imperfections this symmetry breaking will cause the appearance of the minima. CHAPTER 4. ABSOLUTE PHOTODETACHMENT CROSS SECTIONS STUDIED 52 IN A 22-POLE TRAP
shows four potential minima. If the geometrical arrangement of the rf-electrodes is shifted from the linear to a circular configuration (Fig. 4.14c) these minima change their position but remain visible. Only in a perfectly circular symmetric arrange- ment of the rf-electrodes the minima vanish as the contributions from all electrodes cancel out exactly. Slight distortions, however, will immediately induce the pockets (Fig. 4.14d). Furthermore the simulations show, that the depth of the pockets is asymmetric with respect to the position of the rf electrode which is breaking the symmetry as indicated in Fig. 4.14d. When the 22-pole trap was assembled the strong influence of small displacements of the rf electrodes on the effective potential was not known. A tilt of one set of rf electrodes by a tenth of a degree can therefore not be excluded for our trap. Such small tilt angles already come close to the mechanical tolerances for the assembly of a 22-pole trap in the presently used design. Our measurements show the need to significantly improve the precision in the course of the rf electrode assembly process when trapping potentials are desired, where the pocket depths are suppressed to the range of eV or less. One approach to increase the precision of the manufacturing process is to circumvent the assembly process of the trapping electrodes itself. In a recent publication Asvany et al. [86] reported on a new 22pole trap design which used the most modern machinery techniques to construct the trap from as few parts as possible. To avoid mutual tilts of the 22 rf electrodes they were wire eroded out of one stainless steel cylinder. With this technique the authors avoid the need to implant single rods into drilled holes. A tomography scan of the trapping potential could evaluate the improvement of this new manufacturing method. Chapter 5
Combining an Ion Trap with Crossed Beam Imaging
To study the reaction dynamics of atoms and molecules, crossed beam experiments have been established as a standard method for many years now [88, 89, 15, 90]. Collisions at low kinetic energies provide insight in the quantum dynamics of gas phase chemistry. The technique of velocity map imaging pioneered by Eppink and Parker in 1997 [18], allows the kinematically complete detection of reaction products. As the scattered products into all angular directions are recorded for each scattering event, the data acquisition occurs at an increased rate compared to setups with moveable detector systems. In our group we successfully extended the crossed beam imaging technique for the first time to slow ion-neutral collisions with the development of a pulsed velocity map imaging spectrometer [19, 91, 20, 42]. The recent combination of a newly designed imaging stack with full three dimensional particle detection allowed us to study vibrationally resolved reaction dynamics [92].
53 54CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING maging spectrometer offers the possibility cold ions. The combination of a multipole rf ion trap and a velocity map i to carry out crossed molecular beam studies with internally Figure 5.1: 55
All the reactions we studied with this existing setup so far were restricted to the use of atomic ions. In these cases a suitable precursor gas was chosen such, that only the desired ion species was produced (e.g. Cl− from electron impact on
CCl4). These experiments also profit from the fact that the atomic ions do not + 2 feature an internal structure (electronic finestructure effects like in Ar ( P3/2) and + 2 Ar ( P1/2) are a notable exception). However, this method is not applicable to the more complex cluster ions, as they were studied in the course of this thesis. In this chapter the development of a multipole rf trap as an ion source for an existing velocity map imaging spectrometer will be described. This unique combination of an ion trap with crossed beam scattering offers many appealing advantages
• Ions produced in discharges may carry lots of internal energy. The internal state distribution, however, is mostly unknown. A multipole ion trap using the buffer gas cooling technique allows to cool the internal degrees of freedom of complex ionic systems. In the system described here, we cooled down the ion trap to 100K using a liquid nitrogen reservoir.
• Varying the internal temperature of the reactant ions allows to study the internal energy dependence of collisional processes.
• The ion trap enables us to mass select the ionic species prior to reaction. This aspect is crucial in experiments with cluster ions that are produced in a large progression of masses, e.g. from a plasma discharge.
• Ions that are only producible in small quantities can be accumulated in the trap using a multiple loading scheme1. Accumulating ions is also advantageous for studying processes with small cross sections that occur at very low rates.
• It has been observed [93] that the ion beam coming from our ion source ex- periences a slow up-and-down drift (probably due to small instabilities in the gas jet) which makes experiments in which long-time perfect beam overlap is necessary quite demanding. The ion trap offers a good angular acceptance for loading and therefore decouples this drifting behavior. Even for very large
1The repetition rate of the crossed beam machine is currently restricted to 20Hz due to the CCD camera image processing. The ion source however can be operated at up to 1kHz, so that the trap can be loaded 50 times per experiment cycle. 56CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
drifts trapping the ions translates a spatial fluctuation into an intensity fluc- tuation of the ion beam, which is less problematic since we measure events one by one.
• Extracting cold ions from a small trapping volume promises an improved ki- netic energy resolution.
An overview over the new setup is depicted in Fig. 5.1. The ions are produced in a plasma discharge ion source, mass selected using time-of-flight and stored in a temperature variable octupole ion trap. After a suitable storage time the ions are extracted from the trap with a typical kinetic energy distribution of ∆E = 100meV (see section 5.2). Entering the imaging spectrometer the ions are decelerated to tunable kinetic energies between 0.1 - 5eV before they are crossed with a supersonic molecular beam. This setup will be described and characterized in the following sections.
5.1 Ion production and mass selection
The ion production takes place in a separate vacuum chamber to allow for differential pumping between the source region and the ion trap and imaging setup. The design of the ion source employed in this setup is comparable to that of the source in the ion trap setup described in chapter 3.1. A schematic of the ion source is depicted in Fig. 5.2. Ions are produced from a pulsed plasma discharge in a supersonic gas jet. The moment of ignition of the plasma is stabilized using a short electron pulse out − of a homebuilt electron gun. For the production of OH (H2O)n clusters, which have been used in the experiments described in chapter 6, different gas mixtures have
been tested (e.g. ambient air, H2O/Ar mixture). Stable plasma conditions, where
clusters from n = 0 − 5 are efficiently formed, have been achieved using 10% NH3 in 90% Ar which is bubbled through a 30% ammonia solution. From this mixture
negative ions are produced via secondary electron attachment of NH3. The desired OH− is generated in a subsequent reaction with water
− + − − Ar + efast → Ar +eslow +efast
− − NH3 +eslow → NH2 + H 5.2. CHARACTERIZATION OF THE OCTUPOLE ION TRAP 57
− − NH2 + H2O → NH3 + OH (5.1)
In the high density region of the gas jet water clusters are formed in three body processes. A typical mass spectrum obtained from the source is shown in the top panel of Fig. 5.2. The progression of water clusters with increasing size is clearly visible. By changing the voltage and the duration of the plasma pulse we can tweak the size of the clusters that are preferably produced (see [94]). An example is shown as two different traces of a mass spectrum in the image. The ions in the gas jet travel between the field plates of a Wiley-McLaren time- of-flight mass spectrometer. The lowest plate features a curtain-like shielding with small entrance holes. This shielding adopts the concept we successfully use in the imaging spectrometer and also in the multicycle reflectron to avoid field distortions due to external electrodes, here the electric fields from the plasma region or the electron gun. The four plates of the Wiley-McLaren are switched to 250 V, 220 V, 100V and 0V respectively to accelerate the ions perpendicularly out of the jet. A set of simulated ion trajectories is shown together with the assembly in Fig. 5.2. For the simulation, carried out in SIMION 8.0, the ions are assumed to be created in an extended volume with a spread of σx = 4mm along the direction of the pulsed jet and σy = 0.5mm perpendicular to it. As can be seen from the picture the Wiley- McLaren field plates create a spatial focus at a short distance after the last electrode. An arrangement of six cylindrical ion lenses is used to smoothly recollimate the ion beam. A pair of deflectors is used to steer the beam in horizontal and vertical direction. The ions are mass selected according to their flight time and decelerated before they enter the trap.
5.2 Characterization of the octupole ion trap
In order to accumulate and cool ionic clusters before the scattering process we store them in a multipole radiofrequency ion trap. In contrast to the 22-pole trap setup described in chapter 3, here we employ an octupole ion trap. According to Eq. 3.2 6 the effective potential of this trap with multipole order n = 4 scales with Veff ∼ r . The octupole trap design was chosen as, on the one hand, it features a more narrow confinement of the ion cloud than the 22-pole trap. On the other hand it still 58CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
Figure 5.2: The ion source consists of a pulsed piezoelectric valve which creates a supersonic expansion. Ions are created in a plasma discharge which is stabilized by a pulse from an electron gun. The ions are accelerated and mass selected using a Wiley-McLaren type mass spectrometer. A set of simulated trajectories is plotted together with the parts. A typical time of flight spectrum for the production of − OH (H2O)n clusters is shown in the top panel. By changing the duration and the voltage of the plasma pulse different cluster sizes can be favored (compare red and black line). 5.2. CHARACTERIZATION OF THE OCTUPOLE ION TRAP 59
offers the good cooling properties of a multipole ion trap [86]. The assembly of the octupole is depicted in Fig. 5.3. The trap consists of eight cylindrical rods with a diameter of d =2.5mm that are planted alternatingly into two copper sideplates. They have an inscribed diameter of D =7.5mm, so that they fulfill the relation
D =(n − 1)d to approximate a hyperbolic potential [46]. With a total trap length of 36mm the trapping volume is comparable in size to the 22-pole trap. As the assembly uses larger diameter rf rods it should be more robust against misarrangement of single electrodes and therefore avoid distortions of the effective potential (see section 4.3). In addition we tried to minimize mutual tilts during the assembly by locking each rod in the opposite copper side plate using a ceramic sleeve. The sideplates are connected to the two opposite phases ±V0 cos(ωt) of a homebuilt rf generator [95]. A typical frequency of 8MHz is applied with up to 150V rf amplitude. The rf rods are surrounded by three electrostatic ring electrodes (shaping electrodes) which allow to apply a DC offset potential inside the ion trap to push the ion cloud towards one end of the trap. Axial confinement is achieved using cylindrical endcaps that are switched from an attractive potential (ions enter the trap) to a repulsive potential (ions are inside the trap). The whole trap resides on a platform potential (≈ 230 V) that matches the kinetic energy the ions have when they leave the source region. Hence, approaching the trap decelerates the ions to 1-2eV, and a short and intense buffer gas pulse is applied into the trap volume to finally stop the arriving ions. At a 20Hz experiment cycle the length of this pulse provides enough buffer gas over the whole ion storage time (typically 10-20ms). Additional cw buffer gas can be introduced for longer storage times via a high precision sapphire valve. In the same way reactant gases can be led into the trap, e.g. to induce cluster growth or chemical conversion of stored ions. The ion trap is mounted on a dewar tube which is filled with liquid nitrogen to cool the entire trap assembly. In equilibrium between the heat transport through the dewar’s stainless steal base plate and the heat input (mainly due to blackbody radiation, but also caused by thermal contact with wires) we achieve a trap tem- perature of 100K, which is measured independently by several PT100 sensors on the trap housing. The volume of the dewar contains enough nitrogen to keep the 60CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
Figure 5.3: Sketch of the 8-pole rf ion trap. Pulsed buffer gas can be applied into the trapping volume via an opening in the base plate of the trap housing.
Figure 5.4: Lifetime measurement of OH− ions in the new octupole ion trap. An exponential fit yields a lifetime of τ = 1400 s. The inset shows an increasing ion signal for short storage times which is associated with phase space cooling of initially hot ions. After 1ms the ions are thermalized. 5.2. CHARACTERIZATION OF THE OCTUPOLE ION TRAP 61
low temperature for about 5hours. An automatic refill system was installed which connects the dewar with a 100l tank. This system allows to cool the trap for many days. The storage times that can be achieved with the new ion trap are in the order of hundreds of seconds. Shown in Fig. 5.4 is a lifetime measurement carried out at a temperature of 100K where we observed lifetimes in the trap of τ = 1400s. This implies that there are virtually no ion losses during the 20ms storage time used in the present experiments. In order to let the initially hot ions thermalize we estimate that a minimum storage time of 1ms is necessary. This can be deduced from the phase space cooling behavior of initially hot ions for very short storage times [52], as shown in the inset in Fig. 5.4. The derived timescale is also in good agreement with −4 −1 a collision rate k of the trapped ions with the buffer gas k = n·kLangevin =1·10 s assuming a buffer gas density of n =1·1013cm−3 and a Langevin rate coefficient [96] −9 3 −1 of kLangevin =1 · 10 cm s . This implies that about ten collisions are required for the thermalization. The long storage times also make it possible to use slow chemical conversion processes to create the desired ion species. Furthermore it makes the ion trap a suitable tool for studying chemical reactions in the way the 22-pole trap is used. In order to extract the stored ions the static exit electrode is switched from a repulsive to an attractive potential to drag the ions out of the trapping volume. The ions leave the trapping region with the kinetic energy of the trap platform potential and are guided towards the velocity map imaging stack where the ions are decelerated to tunable kinetic energies between 0.1 and 5eV. To determine the velocity distribution of the ions, the decelerated ion package is directly mapped onto the imaging detector. Due to the length of the package of about 15 – 20mm this mapping has to be done sequentially by shifting the time delay when the field plates are switched on. The ion velocity distribution is then reconstructed from the single pictures of this scan. Shown in Fig. 5.5 is a typical velocity measurement for OH− ions, which have been extracted form the trap and decelerated to a kinetic energy of about 100meV. Energy resolutions of ∆E = 50meV (FWHM) can be achieved. To minimize the velocity spread it turned out to be advantageous to use the shaping electrodes to compress the ion cloud towards the exit side of the trap. In this way the ions are confined in a smaller spatial region which in turn results in a reduced energy spread during the extraction process. The energy resolution that 62CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
Figure 5.5: Kinetic energy distribution of an ion package extracted from the octupole trap and decelerated to 0.09eV. An energy resolution of ∆E = 50 meV (FWHM) can be achieved.
can finally be achieved is restricted by the phase space that has to be conserved. It is therefore not possible to focus the ion ensemble that started from an extended space volume (the ion trap) into a small interaction volume for the scattering process without increasing the energy spread. In that sense, small apertures along the ion’s flight path could be used to tailor more narrow energy distributions. Since cooling the ion trap further reduces the spatial extension of the ion cloud due to the shape 6 of the effective potential (Veff ∼ r ), the kinetic energy spread could be further reduced by going to lower temperatures. This would also further reduce the internal temperature of the stored ion ensemble. To achieve this, the liquid nitrogen dewar could be replaced by a coldhead, which can cool the trap below 10K. A technical problem here that has to be kept in mind is the low frequency oscillations of the coldhead that could rhythmically displace the ion trap and therefore increase the energy spread again. 5.3. THE NEUTRAL BEAM SOURCE 63
5.3 The neutral beam source
In our crossed beam setup neutral molecular beams are created from a separate molecular beam source, described in [42]. A pulsed gas jet is produced from a supersonic expansion using a homebuilt piezoelectric valve. For the experiments described in this work we expanded a mixture of 10% methyl iodide in 90% Helium at a stagnation pressure of 0.8bar. The jet was skimmed using a 300 m skimmer. Although it is well known, that with Helium as a carrier gas it is problematic to achieve low jet temperatures it was chosen here to avoid that clustering of CH3I occurs in the jet during the expansion. The same holds for the quite low stagnation pressure of the expansion. A (2+1) REMPI scheme ionizing CH3I with a pulsed dye laser at around 304.5nm was used to verify that no clustering occurs in the jet. Details of this measurement technique are given in [93]. In addition the valve was heated to a temperature of 330K to avoid clogging of the nozzle by the methyl iodide. In order to measure the velocity of the neutral gas jet we ionize the molecules in the scattering region using a short 1-2keV electron pulse from a homebuilt electron gun that is mounted close to the imaging spectrometer. In the case of methyl iodide we produced negatively charged I− ions that are formed in the process
− + − − He + efast → He +eslow +efast
− ∗− − CH3I+eslow → CH3I → I + CH3 (5.2) and detected them using the imaging spectrometer. Alternatively it is also possible to detect positive I+ ions. However, for the experiments carried out on negative ions this detection involves inverting all voltages on the spectrometer to be able to detect the positive ion. In order to compare the velocity distributions we obtain from the positive and negative ions, we performed two consecutive measurements with identical beam parameters on both ions. The results are shown in Fig. 5.6. Interestingly the velocity image of the I+ signal shows a much more narrow distri- bution than the negative ions at an identical jet velocity. In addition, the I− signal features an interesting ring-like substructure which we attribute to a process linked with the ionization process itself. The center of the two distributions, however, is identical in both cases. From the measured velocity distribution we find a jet velo- 64CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
city of 900m/s with a sigma of 88m/s as is shown in Fig. 5.7. This velocity spread
gives us a measure for the translational temperature, since σv = kBT/m. For the employed beam conditions we find a temperature of about 130K, which shows, as
expected, that the CH3I is not completely thermalized. We estimate the rotational temperature to be in equilibrium with the translational temperature. For the vibra- tional temperature the nozzle temperature poses an upper limit, so that we expect it to be found between 130 and 330K.
In order to maximize the scattering rate it is crucial to optimize the overlap of the ion package and the neutral beam in time and space. The spatial position of the jet can be determined in two ways. The vertical position can be measured via laser ionization of the gas jet as described above. Using a moveable lens the focus of the laser beam can be scanned over the neutral beam to measure its position as a function of the ionization signal. In Fig. 5.8 such a vertical scan is shown. A beam diameter of 1.4mm (FWHM) in the scattering region can be derived. A second method uses the VMI spectrometer in a spatially resolving mode (SMI- mode) to directly map the position of the beam. Switching to this mode simply requires changing the applied voltages in the VMI1 - 5 imaging electrodes. No further changes in the electrode assembly has to be made. In Fig. 5.9 such a spa- tially resolved image of the neutral beam is shown. The magnification factor for the projected image is simulated using SIMION 8.0 [48] and depends on the em- ployed set of voltages. For the settings we used here (VMI1=3000 V, VMI2=2800 V, VMI3=2600 V, VMI4=1400 V, VMI5=0 V) it accounts for
R = −3.1 · r (5.3)
where R is the position on the detector plane and r is the source position in the scattering plane. The negative magnification reflects that the imaging inverts the picture in the given mode. A cut through the spatial distribution of the neutral beam is shown in the right panel of Fig. 5.9. A beam diameter of 1.6mm can be derived which is in good agreement with the result obtained via the laser scan. As the position of the ion beam can be mapped in the same fashion this spatial mode offers perfect diagnostics for the overlap of the two crossed beams. 5.3. THE NEUTRAL BEAM SOURCE 65
+ − Figure 5.6: Comparison of the I and I velocity distributions of the ionized CH3I neutral gas jet. The substructure in the I− distribution is caused by the ionization process.
+ Figure 5.7: Velocity distrubtion of the I ions, ionized from a jet of 10% CH3I seeded in 90% Helium. The distribution is derived from the rotated two dimensional distribution shown in the left panel of Fig. 5.6. The velocity of the jet is found to
be about 900m/s at a velocity spread of σv = 88m/s. 66CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
Figure 5.8: Vertical profile of the neutral methyl iodide beam. A pulsed dye laser is used to ionize the molecules and is scanned over the gas jet using a moveable lens. A beam diameter of 1.4mm can be derived.
Figure 5.9: Beam profile measurement of the neutral methyl iodide jet using a spatially resolving mode of the VMI spectrometer setup. 5.4. ION IMAGING - VMI AND SMI 67
5.4 Ion imaging - VMI and SMI try to give a generalized picture to describe the ion imaging process. This picture allows us to understand how a specific imaging setup can be used to resolve different phase space properties of an ion ensemble, like its position or velocity. We start with a particle of mass m that can be initially described by its properties (r,z,vr,vz,m), where r is the horizontal position in the scattering plane (we assume cylindrical symmetry of the imaging apparatus), z is the vertical position and vr and vz are the velocities of the particle in the respective directions. The ion imaging process can be described as mapping of the vector (r,z,vr,vz)m onto a detector event (R,T ) which is recorded on the detector surface at radial position R (using the CCD-camera) after a flight time T of the particle (using the PMT + TDC setup described below). We treat the mass as parameter that is fixed during one measurement. The geometry and voltages of the imaging lens system define the transfer (r,z,vr,vz)m → (R,T ) which can be approximated in the first order as
∂R ∂T ∂r ∂r ∂R ∂T ∂z ∂z R =(r,z,vr,vz)m · ∂R , T = T0 + (r,z,vr,vz)m · ∂T (5.4) ∂vr ∂vr ∂R ∂T ∂vz ∂vz
The time offset T0 denotes the flight time of a particle starting from a position
(r = 0,z = 0) with an initial velocity (vr = 0,vz = 0). The requirements of the experiment dictate which properties of the particle distribution should be reflected in the ion image. If the lens system is used for pure mass analysis it is desirable to resolve the value of m, ideally without dependence of the initial starting point (r, z) in the spectrometer and its velocity distribution (vr,vz). An electrode arrangement optimized for this purpose is known as Wiley-McLaren mass spectrometer. The quantity that is measured here is the flight time T . Since the R component is typically neglected in these type of experiments, the detector can be a channeltron or even a Faraday cup.
If the position of the particle in the spectrometer is of interest, (r, z)m would be mapped to (R,T ). We use this spatially resolving mode (SMI = spatial map imaging) as a tool for beam characterics, e.g. to overlap the neutral and the ion beam. The mass of the particles is encoded in the flight time. If we restrict ourselves to detecting single species, however, we can treat it as a parameter. We are currently 68CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
investigating this SMI mode in detail to learn more about the ultimate spatial resolution that can be achieved. A full characterization of the SMI mode will be given in [97]. The most interesting imaging mode for our experiments provides a mapping of
the particle’s velocity (vr,vz)m onto (R,T ) and is known as velocity map imaging (VMI). The spatial extension (r, z) of the ion cloud that is mapped can be estimated to be about (2-4mm)3 for ions that are extracted 1-2 s after an ion package has crossed with the neutral jet and that travel with a product velocity of 1000m/s. The VMI mode is ideally independent of the spatial extension of the ion cloud. Field simulations of our imaging spectrometer have shown, that this is fulfilled to a very good extent [93]. We have extended these simulation in order to express the properties of our VMI spectrometer in terms of the matrix given above. For the settings employed in the present experiments using m = 127 (I−) Eq. 5.4 becomes
0.017 1 · 10−4 0 −4.3 · 10−5 R =(r,z,vr,vz)m · , T = 12.36+(r,z,vr,vz)m · − (5.5) 9.8 8.4 · 10 4 0 −0.1
It can be seen that to a good approximation R and T only depend on vr and vz respectively. Although velocity map imaging is a widespread technique which is used in many labs, most VMI experiments do not record the flight time T , so the only
information that can be extracted is the radial velocity vr. If the velocity distribution is spherically symmetric, like it is the case in photofragmentation or photoelectron experiments, it is possible to reconstruct the initial velocity distribution using an Abel inversion scheme [98]. Especially in photoelectron spectroscopy studies, where it is not possible to measure the extremely short flight times of the photoelectrons, this method has to be applied. The velocity map imaging (VMI) spectrometer is described in great detail in [93, 99, 100] and only a brief summary will be given here. The spectrometer consists of six cylindrical field plates (VMI1 - VMI6) that are stacked onto each other as shown in Fig. 5.10. To improve the resolution and to minimize stray fields from ion optics close to the imaging region each of the plates features a curtain like shielding [93, 101]. The second electrode has cylindrical holes through which the molecular beam can pass into the interaction region. In order to decelerate arriving ions to 5.4. ION IMAGING - VMI AND SMI 69
tunable velocities, the whole VMI stack resides on a variable platform potential. A specially designed lens system is used to minimize the spatial spread of the ion package during the deceleration (see Fig. 5.1). After the ion package has crossed the neutral beam the VMI field plates are switched to their working potential. The switching is done in typically 20ns using Behlke HV-switches (Behlke HTS 31(61)- 03-GSM). Synchronizing the switching times for the different electrodes is crucial [42] to provide a homogeneous field ramp for the ions. All ions are now accelerated towards a position sensitive detector system consisting of a double MCP in chevron configuration and a phosphor screen. The impact position on the detector surface is recorded using a CCD-camera. In addition the flight time of each ion is measured using a photomultiplier tube (PMT) together with a time-to-digital converter (TDC) unit to detect the arrival time at the detector surface. The start trigger for the TDC is provided by a Quantum Composers 9520 TTL pulse generator that triggers the entire experiment. The stop trigger comes from the PMT. Overall time resolutions of 140ps are achieved. The correct assignment of the TDC events to the camera data relies on single reaction events per cycle. Cycles with two or more events are discarded. The combination of velocity mapping with simultaneous detection of the flight time allows us to reconstruct the full three dimensional velocity distribution of each scattering event [92, 101]. The most dominant advantage over the previously used time slice imaging2 is that it speeds up the data acquisition since no data has to be discarded due to the slicing process. Moreover all product channels of a chemical reaction leading to different product ion species can be recorded in the same measurement as different product masses can be distinguished according to their flight time. Shown in Fig. 5.11 is a typical time-of-flight spectrum which we acquired from the − reaction OH (H2O) + CH3I. In the inset we show the flight times obtained from a Gaussian fit to the peaks in the spectra versus the square root of the assigned masses. A linear fit to the data yields a relation of
t = (0.22+1.102 · m1/2) s between the flight time t and a product masses m. The offset in the fit reflects fixed time delays in the setup.
2In this technique the detector is switched on for a short time period to cut out the center slice of the three dimensional velocity distribution [102]. 70CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
Figure 5.10: The arrangement of the velocity map imaging electrodes. Each electrode features a curtain like shielding to avoid field distortions due to close by electrodes outside the spectrometer. 5.4. ION IMAGING - VMI AND SMI 71
Figure 5.11: Time-of-flight spectrum showing the product ions resulting from the − − − − reaction OH (H2O) + CH3I. The masses are assigned as I , CH2I , I (H2O) and − CH2I (H2O) from left to right. A linear fit of the square root of assigned masses to their respective flight time is shown in the inset. The offset of 220ns reflects time delays in the setup.
5.4.1 The measurement procedure
In order to acquire a set of data for reactive collisions at a certain relative energy we applied the following measurement procedure
• The desired ion species was created in a plasma discharge in the ion source region. Time-of-flight mass analysis was used to separately load the mass in the octupole ion trap, where they were stored for 20ms to achieve thermalization with the buffer gas.
• The ions were extracted from the trap and accelerated towards the VMI spec- trometer. The ion’s kinetic energy was measured using the method describe in section 5.2. The spectrometer’s platform potential was tuned such, that the arriving ions feature the desired kinetic energy necessary for the collision 72CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
energy we aimed at. The available ion optics were used to minimize the energy spread of the ion package.
• The velocity of the neutral beam was determined via ionization of the jet using an electron gun as described in section 5.3.
• As the scattering products are detected using single ion detection with high MCP voltages, the detector is now turned off during the arrival time of the reactant ion beam. The detection time window is shifted to the arriving time of the product ions instead.
• Starting from an initially weak scattering signal the beam overlap of the neutral jet and the ion beam is optimized. This is achieved by a) varying the time delay between the neutral jet and the ion package and b) using static deflectors in front of the imaging stack to shift the position of the ion beam (see Fig. 5.12). In this case the energy of the ion package was checked again.
• The data acquisition is started. The conditions we were able to establish (especially the stability of the octupole trap as an ion source) allowed us to acquire data over 8 – 12h. Depending on the scattering rate ∼1·105 scattering events could be collected in this time.
• A cross check measurement of the velocities of the ion beam and the neutral jet carried out after each measurement revealed if any drifts occurred during the data acquisition. If the ion energy had shifted by more than 0.1eV the entire measurement was discarded (normal drifts of the ion energy were in the order of 0.01eV).
A typical velocity image is an average of 2 to 10 independently calibrated single measurements and contains up to 5·105 scattering events. For each event the differ- 3 ential cross section d σ is measured by recording the three dimensional velocity dvxdvydvz information (vx,vy,vz)m of the scattering products. To evaluate the data the prod- uct species is isolated in the mass spectra and the position and time information is transformed into product velocity vectors in the center-of-mass frame. In addi- tion the distribution is rotated such, that the relative vectors align horizontally in the images (compare Fig. 5.13). The differential cross section is best expressed in 5.4. ION IMAGING - VMI AND SMI 73
Figure 5.12: In order to maximize the scattering rate the overlap of the ion package and the neutral beam can be tuned in time and space. The vertical position of the ion beam is manipulated with an electrostatic deflector before the ions are decelerated. The left panel shows the scattering rate as a function of this deflector’s voltage. The right panel shows the scattering rate as a function of delay between the ion package and the neutral jet.
3 cylindrical coordinates d σ , with the collision axis oriented along v 3. Due to vrdvxdvzdθ x the cylindrical symmetry of the scattering process about the relative velocity axis, the differential cross sections depend only on vx and vr, so that the full informa- tion on the velocity magnitude and angle-differential cross section is displayed in a two-dimensional way. Consequently all velocity images are up-down symmetric with respect to the relative velocity axis. In addition, each event is weighted with 1/vr so that the distributions shown can be interpreted as small slices through a three dimensional velocity distribution. It has to be taken into account, that although products can be symmetrically ejected from a point in the center-of-mass frame they have different velocities in the lab frame. Particles with high lab frame velocities will eventually leave the spectrometer before they can be detected, so their contribution is underestimated in the images. An example is given in Fig. 5.14. All events have been corrected for this effect (so called density-to-flux correction). Details of this procedure are given in Appendix B.
3 Note that vr is not to be mixed up with the radial position r we used earlier to describe a position in the imaging plane. 74CHAPTER 5. COMBINING AN ION TRAP WITH CROSSED BEAM IMAGING
Figure 5.13: Newton diagram for a scattering event. The scattering process is cylindrically symmetric with respect to the relative velocity axis. The outer ring marks the kinematical cutoff, given by the maximum product velocity that can occur taking into account the energy and momentum conservation.
Figure 5.14: Uncorrected product velocity distribution in the lab frame. Although the scattering process is cylindrically symmetric with respect to the relative velocity axis, the picture is highly asymmetric. This is caused by a decreased detection efficiency at high velocities in the lab frame, denoted by the numbers at the circles. Chapter 6
Reactive scattering of cold − OH (H2O)n with CH3I
Experiments on microsolvation effects in chemical reaction dynamics have so far been restricted to detecting reaction products and measuring total reaction cross sections, which does not allow one to identify and visualize different reaction mech- anisms. In our group we have realized for the first time kinematically complete imaging of reactive scattering of ion-molecule reactions [19, 20, 103]. This has made it possible to directly observe the rich dynamics of SN2 reactions of atomic anions re- acting with methyl iodide, including the observation of previously unknown reaction mechanisms. In this chapter we present how this technique in combination with mass-selected and thermalized cluster ions makes it possible to study microsolvated reaction dy- namics. We carried out high resolution crossed molecular beam studies on the microsolvated reaction systems
− OH + CH3I −→ products (6.1)
− OH (H2O) + CH3I −→ products (6.2)
− OH (H2O)2 + CH3I −→ products (6.3) using full three-dimensional velocity map imaging. The OH− anions are stepwise solvated with n=0,1,2 water molecules to study the transition from a pure gas phase reaction towards microsolvated reaction dynamics. The microhydrated OH− cluste- rions are extracted from an octupole radiofrequency ion trap (see chapter 5), which
75 − 76 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
is cooled to 100K and filled with helium buffer gas to pre-cool all external and in- ternal degrees of freedom of the reactant cluster ions. Reaction channels leading to different ionic product species are observed and their fractional contribution to the overall scattering signal is studied in detail as a function of relative collision energy. By changing the temperature of the trap we can heat the molecular ensemble to well defined internal temperatures and study the influence of this heating on endother- mic processes close to threshold. In the second part we use the two dimensional velocity distributions of the product ions to unravel different reaction mechanisms in a nucleophilic displacement and a proton transfer reaction.
6.1 Energy dependent branching ratios
For reaction (6.1)-(6.3) different product channels can be observed as a function of collision energy. In this section we study their fractional contribution to the overall scattering signal. For this we can restrict our analysis to the time-of-flight information which is recorded for each event. The fractional contribution of each channel is evaluated by fitting the area under each peak in the mass spectra. The sum of all contributions is subsequently normalized to unity.
− 6.1.1 The unsolvated reaction: OH + CH3I
Shown in Fig. 6.1 is a typical TOF trace for reaction (6.1) obtained for a collision energy of 2.0eV. The fractional contribution of each channel is obtained by a Gaus- sian fit of each peak. The branching ratios of the different product channels is shown in Fig. 6.2. In the mass spectra for reaction (6.1) three reaction channels can be identified. The two most prominent peaks are assigned to a nucleophilic displacement reaction − − channel forming I product ions and a proton transfer reaction forming CH2I pro- ducts. Both reactions are exothermic, as can be seen from the reaction enthalpies listed in Table 6.1. At the lowest collision energies we studied in this experiment (0.15eV) reaction cross sections of σ ≈ 150 A˚2 have been measured for the related − − reaction systems OH + CH3Br and OH + CH3Cl using a tandem mass spectrom- eter [36]. This value corresponds to a high reaction efficiency of ∼80%. The authors find that the proton transfer becomes slightly more dominant than the nucleophilic 6.1. ENERGY DEPENDENT BRANCHING RATIOS 77
− Figure 6.1: Time-of-flight mass spectrum obtained for the reaction OH + CH3I at 2.0eV collision energy. The different masses stem from a nucleophilic displacement − − reaction forming I and a proton transfer reaction that leads to CH2I products. − The formation of the solvated I (H2O) involves a break-up of the neutral CH3OH product molecule.
Figure 6.2: Branching ratio of the different product channels of the reaction OH−
+ CH3I as a function of collision energy. The contribution of each reaction channel is determined by fitting the area under the time-of-flight peaks (see Fig. 6.1) for − each energy. The endothermic I (H2O) channel shows a threshold at 1.2eV. − 78 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
− − Figure 6.3: Sketched energy landscape of the OH + CH3I → I (H2O) + CH2
reaction. The break-up of the CH3OH represents an intermediate barrier along the reaction pathway.
displacement at energies above 1eV. We can derive the same trend for the OH− +
CH3I reaction. At collisional energies above 1.2eV reaction channels that lead to fragmentation
of the CH3OH products become energetically accessible. The energies needed for
decomposing CH3OH into fragments are listed in Table 6.2. Since we are restricted to detecting ionic products we have no direct way to resolve these channels. However, − a third channel that forms I (H2O) products can be observed in the mass spectra at collision energies above 1eV. From a stoichiometric point of view this channel can
only be explained in terms of a break-up process of the neutral CH3OH products leading to a water fragment. The channel features a threshold behavior which is characteristic for an endothermic process. To describe this threshold behavior we fit the data with the relation [96]
E σ ∝ 1 − , ET >E (6.4) ET
which gives us a value for the threshold energy of ET = 1.2eV in contrast to an en- dothermicity of 0.7eV expected from the products heat of formation. Interestingly, from the value of the threshold energy we can infer that the reaction must occur in 6.1. ENERGY DEPENDENT BRANCHING RATIOS 79
the sequential process
− − OH + CH3I −→ CH3OH+I +2.78eV (6.5)
CH3OH −→ CH2 + H2O − 3.92eV (6.6)
− − I + H2O −→ I (H2O)+0.44eV (6.7) in which the first two steps have to be overcome before the product clusters can form. A sketch of the energetics of the reaction is shown in Fig. 6.3. The measured threshold of 1.2eV is in very good agreement with a barrier along the pathway assigned with the break-up of CH3OH located 1.14eV above the reactants. − The overall contribution of the I (H2O) channel never accounts for more than 3% of the entire scattering signal. If we assume this channel to be representative for other CH3OH fragmentation channels, we can conclude that these channels only play a minor role in reaction (6.1).
− 6.1.2 The monosolvated reaction: OH (H2O) + CH3I
If a single water molecule is attached to the reactant anion many more product − species are observed. Here we mass select OH (H2O) clusters and cool them in our 100K ion trap before we let them collide with methyl iodide. We can exclude that 35 − − impurities of Cl are mixed with the OH (H2O) signal, since we do not detect a mass 37Cl− peak in the ion time-of-flight spectra that would occur due to the natural 3:1 mixture of the two isotopes. A typical mass spectrum at a collision energy of 0.35eV is shown in Fig. 6.4. Pos- sible reaction channels together with their respective calculated reaction enthalpies are summarized in Table 6.3. Shown in Fig. 6.5 are the branching ratios of the differ- ent channels we investigated. For every channel, each point in the image represents an individual measurement. As in the OH− case, the formation of I− products is the dominant process over the whole energy range studied in this experiment. In the monosolvated system the reaction is less exoergic, which reflects the binding energy of the water molecule − − to the reactant OH ion. In the OH (H2O) reaction the nucleophilic displacement − − reaction can now lead to two different ionic products, I and I (H2O). The formation of the solvated product is stronger exoergic by 0.5eV due to the stabilization energy − 80 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
products ∆ H0 [eV] − OH + CH3I 0
− I + CH3OH -2.78 − CH2I + H2O -0.17 ± 0.07 − I (H2O) + CH2 +0.7
− Table 6.1: Enthalpies of reaction ∆ H0 taken from [104] for I products. For − 0 CH2I the enthalpies have been calculated from enthalpies of formation ∆f H of − CH2I [105] and the corresponding electron affinity [106]. The I (H2O) value is
derived from the CH2 + H2O fragmentation channel given in Table 6.2 and the − binding energy of the I (H2O) cluster of 450meV [79].
products ∆ H0 [eV]
CH3OH 0
CH2 + H2O +3.92
CH3 +OH +3.99
CH3O+H +4.55
CH2OH+H +4.18 a CH2O + H2 +0.79
Table 6.2: Reaction enthalpies for the decomposition of CH3OH into fragments. aTo access this hydrogen abstraction channel a barrier of 3.9 eV has to be overcome. Values are taken from [107]. 6.1. ENERGY DEPENDENT BRANCHING RATIOS 81
− Figure 6.4: Typical time of flight trace for the reaction OH (H2O) + CH3I ob- tained at a collision energy of 0.35eV. The dominant reaction channel at this energy yields I− product ions. The inset shows a zoom in the TOF trace, where a mass at 14.6 s becomes visible. The peak vanishes at collision energies above 0.5 eV and − could point to a CH2I (H2O)2 reaction complex.
of the water molecule. However, although energetically favorable the formation of − − I (H2O) products is 20 fold suppressed compared to unsolvated I products, as can be seen from the branching ratios. This implies that despite a lower exoergicity the reaction shows a clear preference for unsolvated product formation. We try to give an explanation for this behavior in section 6.4. Two more reaction channels are observed in the mass spectra. The first can − be clearly identified as a proton transfer reaction leading to unsolvated CH2I pro- ducts. The second channel can be interpreted either as a proton transfer reaction − forming solvated CH2I (H2O) products or as a ligand switching mechanism that − − forms OH (CH3I) products (further we excluded this channel to be I (CH3OH) for reasons given below). Note that from the mass of the species alone, we would not be able to resolve the structure. A more detailed discussion will be given in section 6.3. − 82 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
Figure 6.5: Branching ratio of the different product channels of the reaction − OH (H2O) + CH3I as a function of collision energy. Fitting the threshold be-
havior of the endothermic CH2I channel yields a threshold energy of 1.11eV. A fit − on the CH2I (H2O) channel yields an energy of 0.38eV.
− In the case of the CH2I formation, going from reaction (6.1) to reaction (6.2), i.e. solvating the reactant OH− ion, completely changes the energetics of the proton transfer from a slightly exoergic to a clearly endoergic process. Both proton transfer channels we observe here show a clear threshold behavior which was fitted using Eq. − 6.4. Threshold energies of 1.11eV and 0.38eV can be derived for the CH2I and − the CH2I (H2O) channel respectively. We estimate an accuracy for these values of 0.1eV due to the uncertainties in the relative collisions energies. The clear signature of an endoergic process was the crucial aspect for excluding the channel with mass − 159amu to be the formation of I (CH3OH) which would be a strongly exoergic process. − While the unsolvated CH2I channel keeps increasing with rising energy, we − observe a maximum in the yield of CH2I (H2O) products at around 1.5 - 2eV. Using the two dimensional velocity distributions we identify a switch over in the 6.1. ENERGY DEPENDENT BRANCHING RATIOS 83
underlying reaction mechanism at this energy in section 6.3. At low collision energies another peak has been observed in the mass spec- − tra, shown in the inset in Fig. 6.4. We assigned this peak to be CH2I (H2O)2 − or I (CH3OH)(H2O). The formation of this product species must involve a third particle to carry away the reaction’s excess energy, since the lifetime of a highly excited collision complex is only in the order of picoseconds[47], which would make it undetectable in our setup. It is therefore fair to assume that here this complex is stabilized by collisions with the supersonic jet in the collision region of the VMI spectrometer. As its fractional contribution to the entire ion signal is only 10−3 it is not shown in Fig. 6.5. The channel is no longer observable at collision energies − above 0.5eV. This could point to a CH2I (H2O)2 structure which finally breaks up − to form CH2I (H2O) as soon as this channel becomes energetically accessible. For technical reasons we restricted our studies to products that arrive at later − − flight times than the OH (H2O) reactant ions and hence did not detect possible OH products together with the other products discussed here. The studies by Hierl et al. on CH3Cl and CH3Br show that this collision induced dissociation channel
− − OH (H2O) + CH3X −→ OH + H2O + CH3X becomes dominant at energies above 1eV. Fair agreement of the threshold energies for this channel was found by the authors [36].
6.1.3 Temperature dependence close to threshold
One of the charming features of the new combination of an octupole ion trap with a crossed beam apparatus is the possibility to change the internal temperature of the ion ensemble prior to reaction. To illustrate this possibility we performed the scattering experiment of reaction (6.2) described in the previous sections at an el- evated temperature. The same procedure as described above is used to map out the branching ratios of the different product channels. Shown in Fig. 6.6 are the product branchings for the 300K measurement (closed symbols) together with the − 100K data (open symbols) for comparison. The I (H2O) channel is omitted for clarity. The threshold energies of the two endoergic proton transfer channels are fitted using Eq. 6.4. We determine the threshold energies of the two channels to − − be 0.73eV for CH2I and 0.24eV for CH2I (H2O). Both energies differ significantly − 84 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
products ∆ H0 [eV] − OH (H2O) + CH3I 0
− I + CH3OH + H2O -1.6 ± 0.11 − I (H2O) + CH3OH -2.1 ± 0.11 − CH2I + 2 H2O +1.0 ± 0.08 − a CH2I (H2O) + H2O +0.5 ± 0.11 − b OH (CH3I) + H2O +0.5 ± 0.11
− c OH + H2O + CH3I +1.25 ± 0.3
Table 6.3: Enthalpies of Reaction ∆ H0 calculated from enthalpies of formation 0 − − a ∆f H at 0K [94] for the I and CH2I product channels. The hydration energy − of I (H2O) (∆H = 0.45eV [79]) was used to estimate the binding energy of H2O − b − with CH2I . The binding energy of Cl (CH3I) (∆H = 0.43eV [79]) was used to − c − estimate the binding energy of OH with CH3I. OH (H2O) binding energy taken from [79]
from the 100K thresholds of 1.11eV and 0.38eV. In order to explain this effect we − consider the difference in internal energy of the OH (H2O) cluster at 100K and 300K. Classically the molecule consisting of N=5 atoms carries 3 E = E + E = kT +9kT rot vib 2 of internal energy. Since the vibrational spacing in the cluster is large and only few levels are populated at low temperatures, we assume that the maximum difference
in internal energy going from 100K to 300K accounts for ∆Eint = Eint(300K) −
Eint(0K) ≈ 170meV. If we further assume that translational and internal energy are equally suited to promote the reaction, we would expect the energy thresholds to be shifted by this amount of energy towards lower collision energies. While this simple − classical model nicely reproduces the observed shifting of the CH2I (H2O) threshold, − it cannot explain the large shift in the CH2I product channel. At this point we − can only speculate that certain vibrational levels in the OH (H2O) cluster that are stronger populated at higher energies might promote the reaction in an unusual way, 6.1. ENERGY DEPENDENT BRANCHING RATIOS 85
Figure 6.6: The closed symbols show the product branchings of reaction (6.2) for an ion trap temperature of 300K. The threshold behavior of the two endoergic − proton transfer channels is fitted using Eq. 6.4 yielding 0.24eV for CH2I and − 0.73 eV for CH2I (H2O). The open symbols show the 100K data for comparison.
− e.g. by helping to break up the OH ··· H2O bond. Further investigations of the temperature dependence of the thresholds will shed light on this topic. − 86 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
6.2 A microsolvated SN2 reaction
As discussed in the previous section, a wealth of different product channels can be
observed for the reactions (6.1)-(6.3). In this section we focus on the SN2 reaction channel of the microsolvated reactions
− − OH + CH3I −→ CH3OH+I +2.8eV (6.8)
− − OH (H2O) + CH3I −→ CH3OH+I + H2O+1.6eV (6.9)
− − OH (H2O)2 + CH3I −→ CH3OH+I + 2 H2O+0.8eV (6.10)
and discuss possible reaction mechanisms in detail. While in the previous sections we restricted our analysis to the time-of-flight information to derive branching ratios of the different product channels, we now take into account the full three dimensional information v(x,r,φ) of each scattering event that leads to product anions.
6.2.1 Imaging different reaction mechanisms
A comparison of the velocity distributions we obtained for the I− product channel − of the reactions OH (H2O)n=0,1,2 + CH3I is presented in Fig. 6.7. For each system the I− differential cross sections are shown at four different relative collision energies
between Erel = 0.5eV and 2.0eV. Already a first coarse observation of the images reveals, that the microsolvation of the reactant OH− anions results in a strong change of the reaction dynamics of the system as the gross features of the distributions are completely different for different stages of ion solvation. For the unsolvated reaction (6.8) we find the dominant feature at all energies to be scattering into the forward hemisphere, shifting from forward to sideways scattering at high collision energies (top row of Fig. 6.7). For reaction (6.9), where a single water molecule is bound to the ionic species, the measured velocity distribution becomes almost isotropic at low energies and is only slightly stretched along the relative velocity axis (center row of Fig. 6.7). Backward-scattering, represented by the lobe on the right side of the distribution, dominates at collision energies above 1eV. Adding a second water molecule to the reactant ion suppresses all angle-dependent features in the cross section for reaction (6.10) and leads to isotropically distributed products with small absolute velocities for all collision energies (bottom row of Fig. 6.7). 6.2. A MICROSOLVATED SN2 REACTION 87 I at four different collision 3 + CH 2 , 1 , =0 n O) 2 (H − ng plane are derived from the measured three-dimensional products of reaction OH − Velocity distribution of the I Figure 6.7: energies. The shown velocityvelocity distributions distributions. in the scatteri − 88 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
Figure 6.8: The observed sideways scattering for reaction (6.8) could be caused by the OH− attacking the C–I bond of methyl iodide. The I− products would be ejected perpendicularly to the relative velocity axis.
None of these effects can be revealed by experiments that are restricted to a mere detection of product species. We identify the reaction mechanisms that are relevant for reactions (6.8)-(6.10) from the features observed in the two dimensional velocity distributions. In the measured cross section for reaction (6.8) three distinct reaction mechanisms are observed: forward- (including sideways-) and backward- scattering as well as the formation of low kinetic energy reaction products. The fractional abundance of the different mechanisms as a function of collision energy is listed in Table 6.4. In order to derive the fractional contributions, one has to keep 3 in mind, that the images represent the angle differential cross section d σ , that vrdvxdvrdθ only depends on vr and vx, and therefore all points in the images have to be weighted
with vr (see section 5). How the exact assignment of the different features in the images to the mechanisms is performed will be described below. Forward scattering is predominant and accounts for nearly two thirds of the total product flux at all energies. The forward scattering of the products indicates large impact parameters + which points to a stripping mechanism that transfers the CH3 sub-unit. Above 1eV the forward scattering transforms into sideways scattering into the forward hemisphere. A plausible mechanism would be the OH− attacking the C–I bond that is oriented perpendicular to the relative velocity axis, as depicted in Fig. 6.8. A smaller fraction of the product flux is backward-scattered with a shape that
represents the direct nucleophilic displacement (SN2) mechanism which we found in − earlier experiments for the Cl + CH3I reaction [20]. An even smaller part of the product flux is found to lead to low energy products. As this implies highly excited neutral product molecules it indicates that the reaction is mediated by a collision 6.2. A MICROSOLVATED SN2 REACTION 89
mechanism collision energies [eV] 0.5 1.0 1.5 2.0 low energy 0.06 0.06 0.05 0.07 n=0 forward 0.66 0.61 0.6 0.63 backward 0.29 0.33 0.35 0.31 low energy 0.62 0.41 0.29 0.19 n=1 backward 0.38 0.59 0.72 0.81
Table 6.4: Average contribution of the different reaction mechanisms to the total − product flux for the reaction OH (H2O)n=0,1 + CH3I as a function of collision energy. complex where the translational energy of the collision is efficiently channeled into internal degrees of freedom of the reaction products. A similar mechanism was found − − for the Cl and F reactions with CH3I [20, 108]. It is noteworthy in this context that the F− is furthermore isoelectronic to the OH− anion and is also comparable in terms of mass and nucleophilicity.
While the direct (SN2) mechanism is of minor importance in the unsolvated reac- tion it undergoes a remarkable revival in the monosolvated reaction (6.9). Overall, only two different reaction mechanisms are found. The low energy mechanism occurs at all collision energies and is only slightly shifted towards forward scattering above 1 eV. Backward-scattering of the iodide, which is identified with the direct nucleophilic displacement mechanism, emerges above 1eV and becomes the domi- nant feature in the monosolvated reaction above 1.5eV. In this respect our results − − for the OH (H2O) system are comparable to that of the Cl + CH3I reaction, where a large contribution of the nucleophilic displacement was found as well. Note that, again, there is a strong similarity for both ionic reactants in terms of their mass.
In reaction (6.10) there is no evidence for the direct SN2-mechanism at all. Here, for all collision energies an isotropic scattering with low product translational en- ergies is found, which implies that the low energy mechanism that has also been identified in reactions (6.8) and (6.9) is the dominant mechanism in this reaction. The circles in the images of Fig. 6.7 represent spheres of the same translational energy, spaced at 1.0eV intervals. The outermost circle marks the maximum amount − 90 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
of translational energy available given by the relative translational energy plus the exoergicity ∆H of the reaction. Therefore the structure in the images reflects the internal energy distribution of the neutral products due to conservation of energy and momentum during the scattering process. For all the systems, a large fraction of the available energy is partitioned to internal energy of the products. The sharp − − velocity cutoff observed for the features in the OH and OH (H2O) reaction points to a well defined amount of internal product excitation. Transfer of collisional energy into vibrational modes or three body break-up processes of the cluster ions might serve as an explanation. At the highest internal excitations new pathways that lead
to fragmentation of the CH3OH product molecules become energetically allowed (see − Table 6.2). One of this pathways that leads to I (H2O) products has been described in the previous section. For a quantitative analysis of the high internal excitation we calculate the inter- nal energy distributions of the reaction mechanisms identified above. The criteria for assigning the channels of reaction (6.8) to different product velocity classes are depicted in the left panel of Fig. 6.9. The separations are defined such, that they follow minima in the differential cross section to optimally distinguish between the mechanisms. Events with absolute product velocities |v| < 350m/s are assigned to
the low energy mechanism, events with vx > 200m/s and |v| > 350m/s are as- signed to the backward mechanism. All other events are attributed to the forward mechanism as indicated by the gray lines in the two dimensional velocity distribu- tion. The identical criteria have been used to distinguish the mechanisms for all collision energies. Summing up the contributions from the different channels leads to the values listed in Table 6.4. The internal energy distributions of all reactions, separated according to the identified mechanisms are depicted in Fig. 6.10. The arrangement of the panels matches the one of the velocity distributions shown in Fig. 6.7. For reaction (6.8) a coarse comparison of the distributions reveals no significant change in the shape for the different collision energies. In particular, there is no change in the fractional contributions from the three reaction mechanisms (compare Table 6.4). The internal energy, however, grows more or less linearly with the collision energy, namely by the same amount that this one is increased. In the velocity distributions (Fig. 6.7) this is reflected by a cutoff region that barely shifts when the energy is changed. We performed the same analysis to obtain the internal energy distributions for 6.2. A MICROSOLVATED SN2 REACTION 91
Figure 6.9: Assignment of the different reaction mechanisms as described in the text to different classes of velocity vectors for reaction (6.8) and (6.9). The sep- arations are defined empirically to follow minima in the differential cross section to optimally separate the different contributions. For reaction (6.8) all events with absolute product velocities v < 350m/s are assigned to the low energy mecha-
nism, events with vx > 200 m/s and v > 350m/s are assigned to the backward mechanism. All other events are attributed to the forward mechanism as indicated by the gray lines in the two dimensional velocity distribution. The identical criteria have been used to distinguish the mechanisms for all collision energies. Summing up the contributions from the different channels leads to the values listed in Table
6.4. For reaction (6.9) products with a velocity v < 530m/s centered around vx = -320m/s (indicated by the gray circle in the two dimensional velocity distribution) are attributed to the backward, all other events to the low energy mechanism. − 92 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
reaction (6.9). Shown in the right panel of Fig. 6.9 are the criteria used to distinguish between the low energy and the backward mechanism. Products with a velocity
|v| < 530m/s centered around vx = -320m/s (indicated by the gray circle in the two dimensional velocity distribution) are attributed to the former, all other events to the latter mechanism. Unlike in the OH− reaction, for the monosolvated reaction the fractional contri- butions from the two channels change drastically as a function of collision energy. While at 0.5eV the reaction predominantly produces low energy products the backward mechanism is four times stronger at 2.0eV. If we compare the cutoff re- − − gion in the OH and the OH (H2O) system we find, that the cutoff is even steeper in the monosolvated reaction.
6.2.2 Modeling reaction pathways and steric constraints
Overall, several distinct reaction mechanisms are observed to contribute to the total product flux, which become progressively suppressed with increasing ion solvation. In order to perform a detailed analysis on on this behavior, we have performed quantum chemical calculations to determine the energetics and geometrical struc- tures of intermediate species along possible reaction pathways. The structures were optimized on the MP2/ECP/d level of theory [109] using the GAUSSIAN 03 [110] software package. To obtain more reliable energetic values single point energies were determined using a higher level CCSD(T)/ECP/d calculation. The calculated en- ergies of stationary points of reactions (6.8)-(6.10) are shown in Fig. 6.11. Some of the calculated structures are depicted in Fig. 6.12 and the reaction enthalpies are again summarized in Table 6.5. The association of the OH− with a single water molecule stabilizes the anion by 1.2eV with respect to the unsolvated OH−. A second water molecule further stabi- lizes the anion by 0.8eV. These calculated binding energies and the reaction enthalpy of reaction (6.8) are in good agreement with previous experimental and theoretical results, as summarized in Table 6.5. The endoergicity of the proton transfer chan- nels discussed in the previous section can now be compared to these calculations. The results from the experimental data of ∆H = +1.11eV and ∆H = +0.38eV are in good agreement with the calculated reaction enthalpies of ∆H = +1.06eV and − − ∆H = +0.28eV for the CH2I and the CH2I (H2O) channel respectively. 6.2. A MICROSOLVATED SN2 REACTION 93 isms (blue). The ) all events have been low energy 6.10 (red) and . For reaction ( 6.9 backward ) as a function of collision energy. The internal 6.10 ntribution of each mechanisms is extracted from the )-( (green), + ∆H, which takes into account the relative translational fined in Fig. 6.8 ′ rel f the reaction, respectively. The different reaction mechan - E forward rel = E int mechanism. low energy Internal energy distributions for reaction ( sum of all contributionsdata is by depicted considering by subclasses the of the black velocity line. vectors as The de co explained in the text are depicted in three colors: assigned to the Figure 6.10: energy is determined for eachenergies event before using and after E collision and the exothermicity o − 94 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
single point energies [eV]
species CCSD(T)/ECP/d MP2/ECP/d expt
− OH + CH3I 000 − a OH (H2O) + CH3I -1.17 -1.26 (-1.18±0.05) − a OH (H2O)2 + CH3I -2.10 -2.12 (-2.01±0.32) − b I + CH3OH -2.66 -2.54 -2.78 − CH2I + H2O -0.11 -0.04 -
− OH (H2O) + CH3I 0 0 0 − a+b I + CH3OH + H2O -1.49 -1.28 (-1.6±0.05) − a+b+c I (H2O) + CH3OH -1.95 -1.92 (-2.05±0.06) − d CH2I + 2 H2O 1.06 1.22 (1.1±0.1) − d CH2I (H2O) + H2O 0.28 0.48 (0.38±0.05) − d OH (CH3I) + H2O 0.32 0.2 (0.38±0.05)
− OH (H2O)2 + CH3I 0 0 0 − a+b I + CH3OH + 2 H2O -0.4 -0.42 (-0.77±0.32) − a+b+c I (H2O) + CH3OH + H2O -1.02 -1.06 (-1.22±0.32) − a+b+c I (H2O)2 + CH3OH - -1.54 (-1.65±0.32)
− Table 6.5: Calculated single point energies in the OH (H2O)n=0,1 + CH3I reaction system. The experimental values are taken from a refs. [111, 112], b ref. [104], c using − d the I (H2O)n binding energy given in [79], this work. 6.2. A MICROSOLVATED SN2 REACTION 95 ed using the MP2/ECP/d gher accuracy CCSD(T)/ECP/d cal- hown are the sum of electronic and thermal ts demonstrate possible intermediate steps of the different h structure. The entrance channel complex geometries of the I and the energy levels marked with dashed lines are calculat 3 + CH 2 , 1 , =0 n ]. The levels depicted with solid lines are obtained using hi O) 2 109 Calculated stationary points along the reaction pathway. S (H − Figure 6.11: enthalpies including zero point energyreaction corrections OH for eac culations. The dotted linesreaction connecting channels. the stationary poin level of theory [ − 96 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I . All geometries have 6.11 ts shown in Fig. Calculated geometrical structures of some stationary poin Figure 6.12: been optimized on the MP2/ECP/d level of theory. 6.2. A MICROSOLVATED SN2 REACTION 97
With the calculated structures of the water clusters at hand, we use geometric considerations to explain the solvation-induced suppression of reaction mechanisms. For understanding the reaction dynamics of solvated OH− we assume the entrance channel dynamics to play the decisive role. This assumption is supported by the finding, that the calculated entrance channel energies are all very similar for the − OH (H2O)n cluster investigated here. Accordingly, the large differences in the reac- tion dynamics can not be explained with simple energetic considerations, but have to take into account the geometrical differences of the distinct systems. − − For the OH + CH3I reaction a hydrogen-bonded OH ··· HCH2I pre-reaction − complex instead of the traditional OH ··· CH3I ion-dipole complex has been found. − Also a corresponding [HO ··· HCH2I] transition state could be identified. Similar − structures have been found in the F + CH3I reaction [108] which is comparable to the OH− system as mentioned above. Shown in Fig. 6.13 is the potential energy − surface for the OH ··· CH3I attack, plotted as a function of the O – C distance and the O – C – I angle. In these coordinates a collisional encounter with a straight trajectory in cartesian coordinates describes a bound trajectory as sketched in the upper left panel. For large distances the reactants approach under 180 degrees, while the impact parameter of the collision is found under 90 degrees. The hydro- gen bonded entrance channel complex is found at an O – C – I angle of about 120 degrees. Although there are no barriers that hinder a direct collinear attack of the OH− under 180 degrees, the PES is curved towards larger angles. This implies that − the system is pulled towards the OH ··· HCH2I entrance channel minimum, as denoted by the sketched trajectory shown in the image. Once the system reaches this configuration a transition state at an angle of 150 degrees has to be overcome before the deep valley that marks the SN2 reaction pathway is accessed at short O – C distances. This results in backscattered I− products. The observed forward scattering at small angles further implies large impact parameters. These collisions could cause a stripping of the methyl group. − 98 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I ) is identified at 6.12 ) (compare Fig. 6.8 or each point. All energies are single point energy oint energy corrections. The zero in energy corresponds I attack as a function of the O – C distance and the O lex of reaction ( 3 CH ··· − Potential energy surface for the OH – C – Icalculations angle. on the The MP2/ECP/d remaining level ofto coordinates theory the have without asymptotic been zero free p optimized reactants. f The entrance channel comp Figure 6.13: an O – C – I angle of about 120 degrees. 6.2. A MICROSOLVATED SN2 REACTION 99
− On the exit channel side no classical SN2 ion-dipole complex (XCH3 ··· Y ) is found. However, our calculations reveal a complex, where the iodide is hydrogen − bonded to the OH group in a CH3OH··· I configuration, as shown in Fig. 6.12.A similar complex was found in high level trajectory calculations on the reaction OH− − + CH3F → CH3OH+F . Here the authors find, that a small fraction of all reaction − events proceeds via the formation of a CH3OH··· F post-reaction complex, in which the F− is bound to the OH group on the opposite side from where it is leaving the methanol molecule [113]. In this indirect reaction pathway a large amount of the available energy is transferred into internal excitation of the product molecule. To reach this geometry implies that the ejected ion migrates around the methanol (or that the methanol turns around) to bind on its opposite side. The authors find this indirect mechanism to contribute with less than 10% to the total product flux, although it represents the deepest minimum in the exit channel of the reaction1. In order to understand the exit channel dynamics in the present case, we calculated the − potential energy surface for the fragmentation of the I and the CH3OH, as shown in Fig. 6.14. The energies along the surface have been calculated as a function of the I – C distance and the I – C – O angle. The deep potential minimum associated with the exit channel complex can be found at an angle of 60 degrees. The large available energy in the exit channel leads to a rapid separation of the reaction products. As the curvature of the energy landscape is rather flat over a wide range of angles, only very weak forces pull the iodide towards the potential minimum (trajectory B). If we further assume this exit channel complex of the reaction to be responsible for the complex mediated formation of low energy products, we expect that for the major part of all reactive encounters the system decays into products without crossing the exit channel complex (trajectory A) as in the case of F−. This is nicely confirmed by the observed small contribution of the low energy mechanism (see Table 6.4).
1See the movie under http://monte.chem.ttu.edu/group/animations/ani-dirindir.html − 100 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I ) (compare 6.8 imized for each point. All energies are single point t zero point energy corrections. The zero in energy bonded exit channel complex of reaction ( OH dissociation plotted as a function of the I – C distance 3 CH ··· − Potential energy surface for the I ) is identified at an I – C – O angle of about 60 degrees. 6.12 and the I – Cenergy – calculations O angle. on The thecorresponds remaining MP2/ECP/d to coordinates level the have of been asymptotic opt free theory reactants. withou The hydrogen Figure 6.14: Fig. 6.2. A MICROSOLVATED SN2 REACTION 101
− In the reaction of OH (H2O) we identify two possible structures for the entrance channel complex from our calculations. These are labeled as complex A and B in Fig. 6.12. While in complex A the OH− is localized in an almost collinear fashion with the C – I axis it is localized outside the CH3 umbrella in complex B. The two structures can also be understood in terms of an identity flip of the OH− in − the OH (H2O) system. As the geometry of the structures supports, that complex A favors direct encounters of the reactants, we assume structure B to be of minor importance for the discussed SN2 channel. Furthermore, the spatial extension of the − − OH (H2O) cluster in the entrance channel is larger than that of OH the cluster effectively hinders free propagation of forward-scattered iodide products. These effects are assumed to be the cause for the suppression of the stripping mechanism.
Interestingly, the SN2 mechanism is not suppressed by the addition of one water molecule, but even becomes the dominant reaction mechanism above 1.0eV. We attribute this remarkable revival of the SN2 mechanism in the monosolvated reaction to reactive encounters where the water molecule is sheared off upon the formation of the C–O bond, as also described in ref. [114]. − In reactive collisions of CH3I with OH (H2O)2 clusters, the geometry of the entrance channel complex, depicted in Fig. 6.11, fixes the central OH− anion further − away from the CH3I than for OH (H2O). One could argue, that the two water molecules are mainly arranged around the oxygen-side of the OH− which presents the hydrogen side unshielded. However, collisions with the hydrogen atom oriented towards the CH3 umbrella will not lead to the formation of methanol products. In any case the water molecules have to be pushed aside or rearranged in a collision complex before the OH− can attack the nucleophile. This explains why neither a direct nucleophilic displacement mechanism nor a stripping mechanism occurs, in accordance with our experimental data for this system. It is also fair to assume that in such reactive events a major part of the collision energy is transferred into internal energy, which explains the measured high excitation in the product molecules. − Our experimental investigation of the OH (H2O)n+ CH3I reaction has unraveled remarkable changes in the differential scattering cross sections when a nucleophilic substitution reaction occurs under the influence of microsolvation with already one or two water molecules. All reactions under study are strongly exothermic and have only a small intermediate barrier below the energy of the entrance channel, despite the microsolvation of the reactant ion. Using ion imaging of angle differential cross − 102 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
sections allows us here to identify individual reaction mechanisms and an increasing steric hindrance with increasing ion solvation. Our findings therefore give a plausible scenario for the decreasing reaction cross sections with increasing ion solvation, that has been identified in many systems in earlier experiments.
6.3 Switching mechanisms in a solvated proton transfer reaction
Proton transfer reactions are among the most important chemical and biological processes [115]. For example acid-base reactions can be understood in terms of a proton transfer from a donor (acid) to an acceptor (base). In this section we discuss the proton transfer reaction channels
− − OH + CH3I −→ CH2I + H2O+0.11eV (6.11)
− − OH (H2O) + CH3I −→ CH2I + 2 H2O − 1.1eV (6.12)
− − OH (H2O) + CH3I −→ CH2I (H2O) + H2O − 0.4eV (6.13)
for the unsolvated reaction (6.1) and its monosolvated counterpart in detail. As in the previous section we prepared the OH− water cluster at 100K internal energy prior to reaction. Shown in Fig. 6.15 are velocity distributions for reaction (6.11) − where CH2I products are formed in an exothermic process. At the lowest collision energy of 0.15eV the velocity of the products is almost isotropically distributed with only a slight preference for forward scattering. As explained earlier such a distribution points to mechanism where a collision complex is formed, in which the kinetic energy is partitioned among all internal degrees of freedom available. If this complex lives longer than a rotational period reaction products will fly apart with no preferred angular direction. As we increase the collision energy a transition can be observed from this complex mediated to a direct mechanism where products are scattered into a small cone of angles. Such a sharp angular distribution generally implies that the reaction process proceeds on a time scale that is much shorter than the rotational period of transient reaction complexes. The small scattering angles (close to 0◦) point to collisions with large impact parameters where the proton is transferred in a direct stripping mechanism, as sketched in the top image in Fig. 6.3. SWITCHING MECHANISMS IN A SOLVATED PROTON TRANSFER REACTION 103
6.15. Such a behavior is typical for exothermic proton transfer reactions (see e.g. [116] and references therein). − The proton transfer from CH3I to the OH (H2O) cluster shows a different be- − havior. In Fig. 6.16 the velocity distributions for the CH2I channel is shown for six different collision energies between 0.5eV and 3.0eV. Although the energetics of the reaction would dictate that this channel is only accessible at energies above 1eV we still observe a minor contribution in the scattering signal up to 1eV (compare Fig. 6.5). Although we can not measure reaction cross sections in the present setup, we see from the branching ratios shown in Fig. 6.5 that the fraction of this channel is far below 10% of the entire signal at this collision energies. To understand this contribution we have to explain an excitation of about 0.6eV in the lowest collision energy data shown in Fig. 6.16. A possible contribution could stem from reactions of a small fraction of high kinetic energy reactants in the ion beam. From the typical energy distribution of the decelerated ions (see Fig. 5.5) we estimate that less than 10% of all ions differ by more than 0.1eV from the mean ion energy. We checked that the fraction of ions that are about 0.5eV higher in energy is < 10−4. The collision energy is assumed to be known up to 0.1eV taking into account all angle uncertainties in the collision and the broadenings of the two beams. We can exclude − that ions beside OH (H2O) are extracted from the trap, that could be responsi- − ble for the reaction. Thermal excitation of the OH (H2O) cluster can account for about 0.05eV taking into account excitation of the lowest lying vibrational modes.
The temperature of the CH3I jet can be responsible for another 0.05-0.1eV. Even summing up all these contributions2 it is still problematic to explain the observed signals. The velocity distribution for the lowest collision energy is almost isotropic, point- ing to a collision complex mediated mechanism. A possible reaction pathway could − therefore lead via the formation of the [OH··· H2O··· CH3I] entrance channel com- plex of the SN2 channel, shown in Fig. 6.11. With increasing collision energy the distribution is shifted towards forward scattering, as in the case of reaction (6.11). A part of the product flux, however, is always found isotropically distributed at low kinetic energies. An interesting feature of the velocity distributions at higher ener- gies is the small satellite peak found in forward direction. From the circles in the
2The estimated errors assume a worst case scenario in order to explain the observed signals. In deed we estimate our energy uncertainty to be about 0.1eV − 104 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
Figure 6.15: Product velocity distributions for the proton transfer reaction (6.11). The movie on top shows a direct stripping mechanisms that is responsible for the narrow cone of forward scattered products at the high collision energies. 6.3. SWITCHING MECHANISMS IN A SOLVATED PROTON TRANSFER REACTION 105
images that are spaced by 1eV intervals we can infer that this satellite structure is about 1.3eV shifted in energy with respect to the main peak that is found in forward direction. The two structures clearly indicate two distinct reaction mechanisms in this system. As in the nucleophilic displacement reaction two different products can arise from the proton transfer in the monosolvated system. In section 6.1.2 we observed − that the reaction leading to CH2I (H2O) products can be interpreted either as sol- − vated proton transfer or as a ligand switching mechanism that leads to OH (CH3I) products. As can be inferred from the calculated geometries shown in Fig. 6.12 the structures of the two complexes are remarkable similar. The major difference is given by the position of the shared proton, that is closer located towards the OH− in − − − the CH2I (H2O) structure, while it is closer to the CH2I in the OH (CH3I) com- − plex. We calculated the energy of the [HO··· H··· CH2I] structure as a function of the position of the shared proton, as shown in Fig. 6.17. As can be seen from the − energy landscape, the OH (CH3I) structure is only slightly higher in energy (about − 100meV) and is separated from the CH2I (H2O) by a small intermediate barrier of about 100meV. Therefore we assume that the system can convert between the two structures. Without further information on the complex, in the following we refer − to the structure as CH2I (H2O), as this one is slightly lower in energy. − As shown in the upper left graph in Fig. 6.19 the contribution of the CH2I (H2O) channel starts rising from a threshold at ≈0.3eV up to an energy of about 1.5 - 2eV where it starts to decrease again. Below this panel we show the velocity distribu- − tions of the CH2I (H2O) products at increasing collision energies. The distribution for the lowest collision energies is very isotropic, a feature we have observed for the other proton transfer channels, too. Above 1.0eV we can observe an increasing trend towards forward scattering. On a molecular level this can again be explained with a stripping-type mechanism that occurs at large impact parameters. Unex- pectedly however, at 2.0eV a second mechanism comes into play which leads to backward scattered products. At 2.5eV only a small contribution from the forward scattered signal remains. At 3.0eV this mechanism dies off and backscattering be- comes the dominant process. The pictogram on the right side of Fig. 6.19 shows what this means on molecular level. The new backward scattered feature points to a mechanism with small impact parameters, where the methyl iodide hits the − OH (H2O) cluster in a nearly collinear fashion. The heavy CH3I is bounced off − 106 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
Figure 6.16: Product velocity distributions for the proton transfer reaction (6.12). 6.3. SWITCHING MECHANISMS IN A SOLVATED PROTON TRANSFER REACTION 107
Figure 6.17: Potential energy surface describing the motion of the shared proton − − between the HO ··· HCH2I and HOH··· CH2I structure. The position of the proton has be scanned, while the rest of the structure has been kept frozen in − an initial CH2I (H2O) configuration. The energies have been calculated at the MP2/ECP/d level.
the water cluster after an OH− group is transferred. Due to momentum conserva- tion the remaining neutral water flies away with a huge amount of kinetic energy. − As the drop in the efficiency to form CH2I (H2O) products occurs at the same energies where the backscattering is observed, we assume that these two features are connected. To understand this behavior we extended our quantum chemical calculations for the nucleophilic substitution reaction to determine the geometrical structures of the stationary points along the reaction pathway of reaction (6.13).
We assume that the reaction proceeds via the same ion-dipole complex as the SN2 reaction, which is depicted in Fig. 6.11. We identified two possible geometric con- figurations for this entrance channel complex, that are shown in Fig. 6.12 and in the top row of Fig. 6.18. In the left picture (Fig. 6.18a) we find the OH− in a − hydrogen-bonded position, similar to the OH ··· CH3I complex (entrance channel complex B in Fig. 6.12). The water molecule is located close to the CH3 umbrella. In this arrangement the reaction most likely proceeds via transferring the proton − to the hydrogen bonded OH . This newly formed H2O molecule could then leave − 108 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
Figure 6.18: We identified two possible geometries in the entrance channel com- plex of reaction (6.13) using quantum chemical calculations. The two complexes could lead to different abstraction mechanisms of the water molecule which can be
identified using deuterated CD3I reactants.
the complex, while the remaining water molecule close to the umbrella forms the − − CH2I (H2O) complex. In picture Fig. 6.18b the OH is located close to the umbrella
while the H2O sits on the outside of the complex (entrance channel complex A in Fig. 6.12). A possible reaction scenario here is that this water molecule is sheared − − off and the OH forming H2O in the proton transfer remains in the CH2I (H2O). In the present experiment we have no way to differentiate between the two geometries and can therefore not judge which mechanism actually occurs. If the experiments
are repeated, however, with CD3I the two pathways suddenly become distinguish- − able, as in case a) a CD2I (H2O) product molecule will be detected, whereas in case − b) it would be CD2I (DHO). Also the question wether the observed products are produced via ligand switching could be answered, since this mechanism is likely to proceed via case b). It will be interesting to learn, how the change in the reaction mechanisms discovered above is related to this question. 6.3. SWITCHING MECHANISMS IN A SOLVATED PROTON TRANSFER REACTION 109 ) increases up to an energy of 1.5eV, where 6.13 rgies above 1.5eV. Whereas the systems shows forward m exhibits backward scattering (mechanism II). aneously, in the velocity distributions we observe a switch The fractional contribution of the products of reaction ( the signal starts to decreaseover to again a (top new left reaction graph).scattering mechanism for Simult that low occurs energies at (mechanism collision I) ene this new mechanis Figure 6.19: − 110 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
6.4 Why are unsolvated products preferred?
− The nucleophilic displacement reaction channel in the system OH (H2O) + CH3I can either form solvated or unsolvated product ions
− − OH (H2O) + CH3I −→ CH3OH+I + H2O+1.6eV (6.14)
− − OH (H2O) + CH3I −→ CH3OH+I (H2O)+2.04eV (6.15)
Both reaction pathways are observed in the experiment (see section 6.1.2). But although favorable in energy, the cross section for solvated product formation is suppressed by a factor of ≈20 compared to the unsolvated products, as can be seen in Fig. 6.5. In order to understand the preference of the system to form unsolvated products, we analyze the two dimensional velocity distributions of reaction (6.15). These are shown in Fig. 6.20 for relative collision energies up to 1.5eV. The rough binning of the images reflects the small amount of data we were able to collect due to strong suppression of this channel. For all energies we find that low energy reaction products are formed that are isotropically distributed around zero. As we already inferred for different reaction channels earlier, such a behavior points to the formation of a long lived reaction complex in which all available energy is randomized before the system decays into products. − A trajectory calculation study on the related reaction OH (H2O) + CH3Cl re- veals a mechanism, where the water passes over the methyl group to form solvated − Cl (H2O) products [114]. Shown in Fig. 6.22a is an illustration on how this would like in the case of methyl iodide. If the reaction proceeds like shown in this example, the iodide must stick long enough to the methanol to accept the water molecule, before both of them can bond together and leave. A completely different mechanism was found in high level trajectory calculations − − on the reaction OH + CH3F → CH3OH + F . Here the authors find, that for − a small fraction the reaction proceeds via the formation of a CH3OH··· F post- reaction complex [113], as explained in section 6.2.2. For our system the quantum − chemical calculations carried out in section 6.2 reveal an [H2O··· CH3OH··· I ] exit − channel complex as well, where the I and the H2O are hydrogen bonded to the OH group, shown in Fig. 6.12. In this exit channel complex the iodide and the − water molecule are close enough to form the I (H2O) product cluster and leave the methanol. The whole scenario is depicted in Fig. 6.22b. In the case of the 6.4. WHY ARE UNSOLVATED PRODUCTS PREFERRED? 111
− Figure 6.20: Product velocity distributions for solvated I (H2O) products of the nucleophilic displacement reaction (6.15). − 112 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
− − reaction with bare OH we found a similar CH3OH··· I exit channel complex, which we attributed to be responsible for the formation of low energy products (see
section 6.2.2). To understand the role of the exit channel complex in the H2O- − − CH3OH··· I system we calculated the potential energy landscape of the I ···
CH3OH(H2O) dissociation as a function of the I – C distance and the I – C – O − angle, as depicted in Fig. 6.21. Compared the dissociation of the I ··· CH3OH system shown in Fig. 6.14 we find a much stronger curvature of the landscape towards larger angles. This implies, that the ejected iodide is pulled much stronger into the exit channel configuration. This can be understood to be caused by the additional water molecule, which catches the outgoing I− efficiently. We can assume that this exit channel complex plays a decisive role in reaction (6.9) where it is involved in the formation of the low energy I− products. Once the system reaches the configuration of the exit channel complex, the iodide is very closely located to the loosely bound water molecule. We therefore assume, that the − formation of I (H2O) products is mediated by this complex as well. In order to support this assumption, we derive how many of the reactive encounters lead to the formation of the exit channel complex. We define the fractional abundance of the − − solvated channel as the ion yield for I (H2O) divided by that of the sum of the I − and I (H2O) channels as we can extract it from the time-of-flight spectra. Likewise we define the fractional abundance of the I− low energy mechanism as the ion yield for this mechanism as it is listed in Table 6.4 divided by that of the sum of − − the I and I (H2O) channels. In Fig. 6.23 we plot these fractional abundances as a function of relative collision energy. The energy dependency can be described by the empirical formula 0 f(E)= f exp(−E/E0) which has been found to describe the abundance of solvated products in different reaction systems as well [36]. In this relation f 0 is the abundance at zero kinetic
energy and E0 is the energy increase which causes the fractional abundance to de- crease by 1/e. From a fit to our data in Fig. 6.23 we derive values of f 0 = 0.9 and − E0 =1.3eV for the I low energy mechanism (upper curve in Fig. 6.23). We fixed − 0 the value for E0 in the fit to the I (H2O) abundance and find f = 0.04 in this case(lower curve in Fig. 6.23). 6.4. WHY ARE UNSOLVATED PRODUCTS PREFERRED? 113 ] without zero point energy 117 gen atom and the oxygen of the methanol has O) dissociation plotted as a function of the I – C 2 ining coordinates have been optimized for each point. /MidiX+ level of theory [ ic free reactants. OH(H 3 CH ··· − Potential energy surface for the I distance and the Ibeen – kept C constant at – the OAll bond energies angle. length are in single The the point distance cluster. energy between The calculations one rema on hydro the MP2 Figure 6.21: corrections. The zero in energy corresponds to the asymptot − 114 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
Figure 6.22: Schematic of possible reaction pathways that could lead to solvated ionic products. In case a) the water molecule has to be passed over the methyl group in order to bind to the iodide. In case b) a post-reaction complex is formed, which can decay in either unsolvated or solvated products.
The fact that the energy dependence can in both cases be described with the − same exponential decay factor, justifies our statement that the formation of I (H2O) products as well as the production of low energy I− proceeds via a joint step along the − reaction pathway, which could be the formation of the [H2O··· CH3OH··· I ] com- plex. It is only in the dissociation into products that the system decides whether solvated or unsolvated products are formed. From the ratio of the f 0 values we find that once this complex is formed, in only 1 out of 20 cases the complex decays into solvated products. The overall probability to form the complex at all drops with increasing collision energy, as the nucleophilic displacement mechanism becomes dominant (see section 6.2). This can be understood in terms of faster dissociation − dynamics of the I ··· CH3OH(H2O) system which avoids the exit channel complex − and therefore explains the suppression of the I (H2O) contribution to the total prod- uct yield. As mentioned above, the same energy dependence for solvated products
has been observed in the reaction with CH3Cl and CH3Br [36] where the authors 6.4. WHY ARE UNSOLVATED PRODUCTS PREFERRED? 115
− Figure 6.23: Fractional abundance of the solvated I (H2O) products (lower curve) and of the low energy mechanism (upper curve) of the nucleophilic displacement channel of reaction (6.2) as a function of relative collision energy. The energy 0 dependence is fitted with an exponential decay f(E)= f exp(−E/E0).
0 0 find values of f = 0.25, E0 = 0.4eV and f = 0.1 and E0 = 1.1eV respectively. Taking our data into account, we can establish the following trend for the fractional abundance for solvated products: CH3Cl > CH3Br > CH3I. As this sequence also reflects the proton affinity of the corresponding halogenide anions Cl−, Br− and I− [118], we conclude that this quantity is a good measure for the ability to attract and bind a water molecule in the exit channel of solvated SN2 reactions as well. Interestingly, the proton transfer reactions studied in the previous section do not show the very strong preference for the unsolvated products (solvated/unsolvated ≈1/3 at 2eV). This can be understood by looking at the geometries of the interme- diate reaction complex that has to be passed to form solvated products. Other than − 116 CHAPTER 6. REACTIVE SCATTERING OF COLD OH (H2O)N WITH CH3I
for the SN2 channel, no difficult rearrangement of the molecular structure has to − be undergone for the water molecule to bind to the CH2I since the water already resides on the ”correct” side of the product. This is again a strong support, for our finding that the suppression of solvated products is caused by steric hindrance rather than energetic barriers. Chapter 7
Summary
Microsolvated systems offer a bottom-up approach to explore the wide gap between two distinctly different environments, the gas phase and the liquid phase. In this thesis we have studied molecular systems in the gas phase at the transition from purely unsolvated to microsolvated systems. In the first part we have used a cryogenic 22-pole ion trap, to study molecular anions at temperatures between 8 and 300K. A new setup has been designed and realized, which combines the trap with a multicycle reflectron for an enhanced mass resolution of m/∆m = 10000. The compact arrangement of all components provides an excellent optical access to the trapping volume. The new setup has been used to study absolute photodetachment cross sections of anions using a newly developed two dimensional laser tomography method. This new method does not rely on any calibration to known standard cross sections and is in principle applicable to any anionic system. We have used this method to study the cross section of atomic O−, which is used as a standard reference system in many photodetachment experiments. Our results confirm existing experimental data, questioning recent high-level ab-initio calculations. For molecular OH− we have not observed a temperature dependence in the photodetachment cross section far above the threshold. In energy dependent measurements close to threshold, we have been able to resolve the contribution from single rotational levels. Changes in their relative population due to cooling of the molecules can be directly measured, which establishes photodetachment as a thermometer for internal temperatures of − trapped ions. For the microsolvated system OH (H2O) the more complex structure
117 118 CHAPTER 7. SUMMARY
of the molecule changes the shape of the cross section near threshold. Also for this system we have been able to use photodetachment in order to observe changes in the internal temperature of trapped ions. In addition the tomography technique has been used to visualize details of the effective potential of our trapping device. Ten minima have been found in the trapping potential of our 22-pole ion trap. Electric field simulations have attributed these minima to be caused by imperfections in the electrode arrangement of our trap. An intuitive picture was found which connects the number of minima observed with the multipole order n of the trap. In the second part of this thesis we combined for the first time a radiofrequency ion trap, which acts as a source for internally cold ionic molecules, with an exist- ing crossed beam imaging setup. We studied the dynamics of reactive scattering of solvated OH− molecules with methyl iodide over a wide range of collision energies using full three dimensional velocity map imaging. Several reaction channels like proton transfer and nucleophilic displacement have been observed for different stages of ion solvation. Their branching ratios reveal detailed information on endothermic processes with a clear threshold behavior. An increase of the internal energy of the ionic cluster has been found to have a strong influence on the threshold energies. From the analysis of velocity- and angle-differential cross sections, we identify dif- ferent reaction mechanisms in the nucleophilic displacement channel. We find that the number of different mechanisms that can be observed is damped with increasing stages of ion solvation. Already for two water molecules that are clustered to the OH− reactant anion, only a single reaction mechanism survives. Quantum chemical calculations have been carried out in order to determine geometrical structures and stationary points along the reaction pathways of the increasingly solvated systems. From these calculations we find, that not the energetic, but the steric characteris- tics of the reactions are responsible for an increased damping of the mechanisms. This observation casts a new light on the well known trend of decreasing reaction efficiency at the transition from gas phase chemistry to solution. A preference for unsolvated product formation has been found in all reactions despite unfavorable
energetics. In the case of the SN2 channel we have found evidence for a joint mech- anism that produces unsolvated products with high internal energies or solvated products. From the analysis of the observed proton transfer channels we identify different reaction mechanism as a function of ion solvation. Chapter 8
Outlook
The study of increasingly complex molecular systems in the gas phase has attracted an enormous amount of experimental and theoretical work in the last 40 years. Yet, we are still only beginning to understand all the phenomena that occur at this interface between physics and chemistry. Simplified models like the concept of microsolvated reaction dynamics present a stimulating source for basic concepts and ideas in physical chemistry and chemical physics. The results of this thesis contribute to this. The following projects give an example of the richness of experiments with which we can contribute to the field of molecular dynamics using the concepts described in this work.
Future experiments on microsolvated reaction dynamics The experiments presented in this thesis represent only a first step in the study of reaction dynamics of microsolvated systems. Very briefly a number of future crossed beam experiments is presented
• The influence of isotope effects on the reactions presented in this thesis will be studied. The use of deuterated species changes the internal structure of the reaction partners. A selective and stepwise deuteration of the reactants − − (e.g. OH (D2O)and OD (D2O), but also CH2DI, CHD2I, CD3I) will allow to study the influence of internal energy or to track and identify specific reaction mechanism (compare Fig. 6.18).
• Higher stages of microsolvation with three and more water molecules attached
119 120 CHAPTER 8. OUTLOOK
− Figure 8.1: Calculated structures of two different isomers of the OH (H2O)3 cluster.
to the reactants will be studied. Different isomeric structures of these larger clusters open up a new form of complexity in these systems (see Fig. 8.1). A major challenge in these experiments is the continuously decreasing reac- tion cross section at increasing ion solvation. To overcome the limitations of a decreasing event rate (which makes the data acquisition unpractical), the experimental cycle will be increased. If the data acquisition (e.g. the camera read-out) becomes event-based it should be feasible to run the crossed beam apparatus on a 1kHz repetition rate.
• The temperature dependence of the reaction dynamics and the branching ra- tios will be investigated. If the ion trap is mounted on a cryostat, ion temper- atures below 10K are accessible. On the other hand internal temperatures as high as 700K can already be reached with the existing setup.
− − • Previously studied reactions like Cl + CH3I and F + CH3I can be inves- tigated under the influence of microsolvation. It will be interesting to learn, if the effects observed under increasing ion solvation (e.g. the damping of reaction mechanisms) can be generalized for a broad range of reactions.
Quantum state control of reaction products In our group we are currently setting up a crossed beam experiment, in which the neutral reaction partners will be prepared in a well defined vibrational state prior 121
to collision. The molecules that are cooled to their vibrational ground state in a supersonic jet will be excited with an intense infrared laser pulse. While these experiments have been successfully carried out for neutral-neutral collisions (e.g.
CHD3 + Cl [119]), this will be the first experiment that studies the influence of specific quantum states in ion neutral collisions. It is of specific interest, whether the vibrational excitation actively manipulates the outcome of the reaction, or if some modes simply act as spectators that do not participate at all in the dynamics of the reaction. Another exciting new approach to the molecular beam technique is the use of Stark decelerated slow molecules, that can be prepared in a well known initial quan- tum state [120].
THz spectroscopy on microsolvated clusters − For molecular spectroscopy on large systems like OH (H2O)n, a lack of experimental data exists in the regime of 0.3 – 3THz, which covers the lowest transitions in these systems. These frequencies, that lie in the so called Terahertz gap, have nowadays become accessible with cw terhertz sources, based e.g. on difference frequency mix- ing of two diode laser systems. In an upcoming project we will combine our cryogenic ion trap with cw terahertz spectroscopy. Mass selected molecular ions will be pre- pared at the lowest accessible temperatures in the trap. Due to the extremely long storage times that can be achieved, long interaction times with the light field can be provided. This can be crucial, since the output power even of modern THz sources is usually extremely low. The excitation of a THz transition will be detected in a pump-probe scheme using photodetachment. The internal temperature measure- ments developed in chapter 4 will be a valuable diagnostic tool in these experiments. 122 CHAPTER 8. OUTLOOK Appendix A
Accuracy of the photodetachment cross section measurements
To assess the accuracy of the measured cross sections we consider both statistical and possible systematic errors. The statistical fluctuations of the measured ion intensities amount to about 7%, limited by noise in the microchannel plate detector and shot noise due to the finite number of ions. This leads to an uncertainty of the fitted decay rates of <2% for the majority of the exponential fits. The statistical uncertainty of the integral in Eq. 4.4 is hence estimated to be 1.5%, which is further improved by averaging over several tomography scans. A systematic source of error of the integral is the accuracy of the beam posi- tioning. The translation stage, which carries the imaging lens, can be positioned with micrometer precision. The accuracy of the magnification is determined by the uncertainty of the lens-to-trap distance and the uncertainty of the focal length of the lens. For this we measure a value of below 1%. The overall accuracy of the position is therefore estimated to be 1% for each dimension. The absolute laser power is determined with a power meter before the beam enters vacuum chamber. Taking into consideration the nominal accuracy of the silicon-based power meter and possible clipping of the laser beam on the detector surface the accuracy of the laser power measurement is better than 2%. The vacuum viewport through which the beam is passed into the trap setup is anti reflection-coated with an absorption below the power meter resolution. Possible power changes due to clipping at the entrance electrode of the trap or back-scattering at the exit electrode are estimated
123 APPENDIX A. ACCURACY OF THE PHOTODETACHMENT CROSS SECTION 124 MEASUREMENTS
to lie below 0.3%. Relative fluctuations during a tomography scan are continuously monitored with a power meter behind one port of a beam splitter. To judge the systematic error of the finite discretization of the tomography mesh we performed numerical simulations. They show that for the experimental condi- tions this error is below 0.3%. Measurements with different ion density distributions, created by using different radiofrequency amplitudes, verify that the cross section derivation is not sensitive to the details of the distribution. Accordingly, the overall accuracy for determining the absorption cross section from a tomography scan is given by 1.5% statistical error and 3.5% systematic error, containing 2% for the laser power and 1.5% for the two position coordinates. A larger uncertainty is de- rived for the OH− measurements with the HeNe laser, which is cross-referenced to the 662nm measurement. Appendix B
Density-to-flux Correction
A simple density to flux correction scheme is applied to all scattering events. For this scheme it is necessary to determine a correction function f(vr), that accounts for a velocity dependence in the detection efficiency. As the spectrometer has a rotational symmetry this dependence is a function of the absolute radial velocity component vr. It is assumed that the scattering processes studied here show a cylindrical symmetry with respect to the relative velocity axis of the reactants. It is then possible to derive f(vr) from an asymmetric picture using the following procedure:
1. A point in the two dimensional velocity distribution is chosen at a random po-
sition. This starting point has an intensity N(v1) and is assigned the detection
efficiency f(v1) = N(v1)/N(v1) = 1.
2. The mirror point with respect to the symmetry axis is identified. Although
this point should have the same intensity, it is found to have an intensity N(v2)
and is therefore assigned the detection efficiency f(v2) = N(v2)/N(v1).
3. A random point from the distribution with a velocity v2 is chosen.
4. From its mirror point we find f(v3) = N(v3)/N(v2) f(v2).
The image shown in Fig. B.1 visualizes the procedure. The rings in the image denote areas of the same radial velocity vr. The procedure can now be iterated in order to determine f(vr) for various velocity values. The graph shown in Fig. B.2 is an example how this procedure yields a large number of points for f(vr). The graph is fitted with a linear function. All events in the distribution are weighted with the
125 126 APPENDIX B. DENSITY-TO-FLUX CORRECTION
Figure B.1: Uncorrected product velocity distribution in the lab frame. The procedure described in
the text is used to determine the dependence of the detection efficiency as a function of the velocity vr.
Figure B.2: Detection efficiency f(vr) as a function of the velocity vr in the lab frame. A linear fit to
the data yields f(vr) = 2.3 − 0.001 vr. 127
Figure B.3: Comparison between an uncorrected two dimensional velocity distribution (left) and the
same density-to-flux corrected image (right).
inverse of this function to correct for the asymmetry. Shown in Fig. B.3 is the result of the applied correction scheme. The density-to-flux correction does not depend on the reactant ion velocity, so that once the correction function f(vr) is determined it can be applied to reactions at all relative kinetic collision energies. 128 APPENDIX B. DENSITY-TO-FLUX CORRECTION Acknowledgements
An dieser Stelle m¨ochte allen danken, die mich auf dem Weg zu dieser Arbeit be- gleitet und unterst¨utzt haben. An erster Stelle geb¨uhrt mein wichtigster Dank Roland Wester. Daf¨ur, dass du mich mitgenommen hast auf viele spannende Reisen durch die Physik und dabei stets tolle Ziele vor Augen hast. Du schaffst es stets, eine Freude und Dynamik zu entwickeln, die einen mitreißt und teilhaben lassen m¨ochte an all den spannenden Projekten, die dir im Kopf rumspuken! Danke, dass ich so unglaublich viel bei dir gelernt habe und du f¨ur Ideen stets offen bist. Danke, dass du mir die Freiheit gegeben hast eigene Ziele zu entwickeln und dein Vertrauen in mich gesetzt hast, dass wir diese auch erreichen k¨onnen. Einen großen Dank auch an Matthias Weidem¨uller f¨ur all die Unterst¨utzung. Danke dass du dich stets begeistert hast f¨ur unsere Projekte. Ein besonderer Dank gilt nat¨urlich allen Leuten, die tage- und n¨achtelang mit mir im Labor gegen die T¨ucken der Technik gefochten haben. Ein Riesendank geht an Sebastian Trippel. Die Freude die du austrahlst bei dem was du tust empfand ich immer als ansteckend. Danke f¨ur die vielen Male, in denen du mir gezeigt hast, dass es immer einen ”magic button” gibt. Danke auch f¨ur all die unvergessenen Momente außerhalb der Physik, die wir zusammen verbracht haben. Ein weiterer Dank geht an Thorsten Best. All die R¨atsel die uns begegneten, egal an welchem Projekt, scheinen dich magisch anzuziehen. Danke f¨ur’s mitr¨atseln! Vielen Dank an Jochen Mikosch der die Grundsteine im Labor gelegt hat und auf dessen Spuren wir noch immer wandeln. Danke an Petr Hlavenka f¨ur die tolle Zusammenarbeit an der Falle. Ein besonderer Dank geht an Jonathan Brox, der unerm¨udlich im Labor stand, und dessen Schichtbetrieb auch zu unm¨oglichen Zeiten uns oft gerettet hat! Viel Spaß und ein gutes H¨andchen bei den Herausforderungen in deiner Promotion! Vielen Dank an Martin Stei, der die Riesenaufgabe angetreten ist, die Labore in der neuen Heimat Innsbruck wieder flott zu machen. Ich w¨unsche
129 APPENDIX B. DENSITY-TO-FLUX CORRECTION
dir viel Gl¨uck und Erfolg in deiner Promotion, vielleicht wird ja noch ein echter Tiroler aus dir! Danke an Alexander von Zastrow, Johannes von Vangerow, Stephanie Eisenbach und Anna G¨oritz f¨ur die sch¨onen Momente im Labor und die lustige Zeit am Kicker. Bedanken m¨ochte ich mich bei Sebastien Jezouin, Mackenzie Barton-Rowledge, James Cox und Nathan Morrison die nur kurz bei uns waren, uns aber jederzeit tatkr¨aftigt unterst¨utzt haben. Danke ebenfalls an Christoph Eichhorn der seinen Weg als Ingenieur fortgesetzt hat. Bedanken m¨ochte ich mich auch bei den G¨asten aus Stockholm Wolf Geppert, Mathias Hamberg und Erik Vigren, die mit uns die R¨atsel des Alls erforschen. Danke an Terry Mullins, der immer gut drauf ist, nie friert und ¨uber alles lachen kann. Viel Spaß in Hamburg! Auch den Leuten der ¨ubrigen Projekte m¨ochte ich danken, die immer f¨ur eine tolle Atmosph¨are gesorgt haben und diese Gruppe zu etwas Besonderem gemacht haben: Johannes Deiglmayr, Thomas Amthor, Simone G¨otz,Wenzel Salz- mann, Christian Giese, Markus Reetz-Lamour, Anna Grochola, Karin M¨ortelbauer, Christoph Hofmann, Janne Denskat, Hanna Schempp, Mag- nus Albert, Mark Repp, J¨org Lange, Stephan Kraft, Christian Gl¨uck, Ina Blank und Judith Eng. Vielen Dank an Helga M¨uller, die uns in all den organisatorischen Dingen im- mer tatkr¨aftig unterst¨utzt hat. Ein großer Dank gilt der mechanischen Werkstatt, die uns oft aus der Patsche geholfen hat, wenn mal wieder alles an einem Bauteil hing. Danke auch der elektronischen Werkstatt.
Besonders bedanken m¨ochte ich mich bei meinen Eltern, die mich stets unterst¨utzt haben, und die immer bem¨uht sind, mir den R¨ucken frei zu halten. Der letzte und gr¨oßte Dank geh¨ort dir, Yvonne, f¨ur all die Liebe und Kraft die du mir in all den Jahren geschenkt hast. Auf zum n¨achsten Abenteuer!