Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 921

Electronic Structure and Core-HoleDynamics of Ozone

Synchrotron-radiation based studies and ab-initiocalculations

BY

KAROLINE WIESNER

ACTA UNIVERSITATIS UPSALIENSISUPPSALA 2003

Dissertation at Uppsala University to be publicly examined in Haggsalen, Angstrom Laboratory,Saturday, January 24, 2004 at 10:15 for the Degree of Doctor of Philosophy. The examinationwill be conducted in English

AbstractWiesner, K. 2003. Electronic Structure and Core-Hole Dynamics of Ozone. Synchrotron-radiationbased studies and ab-initio calculations. Acta Universitatis Upsaliensis. Comprehensive Summariesof Uppsala Dissertations from the Faculty of Science and Technology 921. 47 pp. Uppsala.ISBN 91-554-5842-4

The electronic structure of the ozone molecule (O3) has been studied with spectroscopy techniquesand computations. The investigation was focused on O3 in a core-hole state. The electronicconfiguration and the nuclear dynamics have been found to be highly correlated.

This electron correlation is mapped out for the two chemically different sites in the molecule:the central and the terminal oxygen. The energy difference between the corresponding coreorbitals is 4.58 eV, which allows for site-selective core ionization and core excitation.

The influence of the core-hole site on the electronic structure is substantial, which is shownwith ion and electron spectroscopy data and ab-initio quantum chemical computations. Moreover,the induced nuclear motion differs considerably for the two core-hole sites.

One of the core-excited states is proven to be ultra-fast dissociative. An analysis of the datawith a formalism for two-body dissociation disclosed the localized character of core excitation.The symmetry-equivalent terminal-oxygen core orbitals do have very little overlap, so that adelocalized model for the core excitation becomes inadequate.

Moreover, core-excitation opens up a decay channel to a valence-ionized state that has notbeen observed with photoionization. The reason for this state to have low cross section forphotoionization is illuminated with a CASSCF computation of the electronic configuration.The configuration of the state was found to be very distinct from the ground state configuration.

Another effect of configuration-interaction was found in MRCI computations of the core-ionized states. Several local minima with distinct electronic configurations could be identified.

Keywords: ozone, electronic structure, core-hole dynamics, resonant Auger decay,photoionization, electron spectroscopy, ion spectroscopy, ab initio computation

Karoline Wiesner, Department of Electronic Publishing. Uppsala University. Villavagen 14,SE-752 36 Uppsala, Sweden

c© Karoline Wiesner 2003

ISBN 91-554-5842-4ISSN 1104-232Xurn:nbn:se:uu:diva-3914 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3914)

Meiner Familie

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List of Papers

This thesis is based on the following papers which will be referred to in thetext by their roman numerals:

I Femtosecond dissociation of ozone studied by the Auger Doppler effectL. Rosenqvist, K. Wiesner, A. Naves de Brito, M. Bassler, R. Feifel, I. Hjelte,C. Miron, H. Wang, M. N. Piancastelli, S. Svensson, O. Bjorneholm,S. L. Sorensen,J. Chem. Phys. 115 (2001) 3614-3620.

II Experimental study of photoionization of ozone in the 12 to 21 eV re-gionA. Mocellin, K. Wiesner, F. Burmeister, O. Bjorneholm, A. Naves de Brito,J. Chem. Phys. 115 (2001) 5041-5046.

III The dynamic Auger-Doppler effect in HF and DF: control of fragmentvelocities in femtosecond dissociation through photon energy detuningK. Wiesner, A. Naves de Brito, S. L. Sorensen, F. Burmeister, M. Gissel-brecht, S. Svensson, O. Bjorneholm,Chem. Phys. Lett. 354 (2002) 382-388.

IV Valence photoionization and resonant core excitation of ozone – exper-imental and theoretical study of the C-state of O+

3K. Wiesner, R. F. Fink, S. L. Sorensen, M. Andersson, R. Feifel, I. Hjelte,C. Miron, A. Naves de Brito, L. Rosenqvist, H. Wang, S. Svensson, O. Bjorne-holm,Chem. Phys. Lett. 375 (2003) 76-83.

V Core excitation in O3 localized to one two symmetry-equivalent chemi-cal bondsK. Wiesner, A. Naves de Brito, S. L. Sorensen, O. Bjorneholm,submitted to Phys. Rev. Lett.

VI Core-ionized ozone – Electronic-structure calculations and experimentK. Wiesner, S. Svensson, O. Bjorneholm, K. J. Børve,in manuscript.

VII Derivation of Peak-Shape Functions for Ion-Ion Coincidence Data fromTwo-Body DissociationK. Wiesner,in manuscript.

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VIII Electronic States and Fragmentation of Core-Excited OzoneK. Wiesner, O. Bjorneholm, F. Burmeister, R. R. T. Marinho, A. Mocellin,L. Rosenqvist, S. L. Sorensen, A. Naves de Brito,in manuscript.

IX Selected Dissociation of Ozone Probed by Coincidence Measurementsbetween Energy-Selected Photoelectrons and Fragment IonsA. Mocellin, K. Wiesner, S. L. Sorensen, C. Miron, K. LeGuen, D. Ce-olin, M. Simon, P. Morin, A. Bueno Machado, O. Bjorneholm, A. Naves deBrito,in manuscript.

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Contents

1 Popular Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1 Molecular earthquake in ozone . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Molekylar jordbavning i ozon . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Introduction – “Good” and “bad” ozone . . . . . . . . . . . . . . . . . . . . . . 73 Ozone – Summary of the main results . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 The ground state of O3

CONFIGURATION INTERACTION RIGHT FROM THE START . . . . 113.2 Electronic states inaccessible via absorption

CONFIGURATION INTERACTION, THE SECOND . . . . . . . . . . . . . 123.3 Stable valence-ionized states

SOMETIMES OZONE IS STABLE . . . . . . . . . . . . . . . . . . . . . . . . . 133.4 Nuclear dynamics of core-ionized states

DOES SITE MATTER? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4.1 Electronic structure computation

CONFIGURATION INTERACTION GOING WILD . . . . . . . . . 163.4.2 Core-hole site-dependent fragmentation

SITE DOES MATTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 Nuclear dynamics of core-excited states

VISITOR FROM THE CORE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5.1 Ultra-fast dissociation

FLYING CORE HOLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5.2 Core-excitation localized to one chemical bond

WHAT ABOUT EQUIVALENT SITES? . . . . . . . . . . . . . . . . . 243.5.3 Core-hole site-dependent fragmentation

SITE ALWAYS MATTERS . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Electron spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Electron-ion-ion coincidence spectroscopy . . . . . . . . . . . . . . . . . 284.3 Energy-selected electron-ion coincidence . . . . . . . . . . . . . . . . . . 304.4 Generation of pure ozone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 Comments on My Own Participation . . . . . . . . . . . . . . . . . . . . . . . . 43

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Preface

Over the almost five years I spent as a graduate student in the group of SvanteSvensson and Olle Bjorneholm, I have received an education much more di-verse than I had expected. I started in the belief I would get trained in molec-ular physics and possibly in creative thinking. Well, I have – but not only inthese disciplines. I have been trained in working hard, not giving up but givingin – from time to time. I got an education in team work and computer work.As a graduate student I was not only being trained, I was allowed to simplyexplore. I discovered my own strengths and weaknesses. I was free to find outwhat I wanted (and if you read this in two senses, you are right). I am verygrateful for this time, which gave room for forming me as a person and as ascientist. And I am not able to tell which of these formations was dominatingbut I am sure they are correlated.

My special thanks go to Svante Svensson and Olle Bjorneholm. Both havedone their best to provide me with all the resources I needed to become anemancipated person and scientist. Both in their own wonderful way. I wouldn’twant other advisers.

They haven’t been my only advisers. Other senior scientists have accompa-nied me. I am especially grateful to Stacey Sorensen in Lund. She became ascientific and personal role model, a colleague and a friend.

During my stays in Campinas in Brazil, I had the privilege to work withArnaldo Naves de Brito, a very skilled scientist. And I was lucky to meethis family Maria de Lourde and Gabriel who made my stays in Brazil such awonderful time.

My goal was to get trained in both experiment and theory. Many peoplewere laughing at me, when I started. I am therefore especially grateful andobliged to those who didn’t laugh but instead tucked up and helped. ReinholdFink never got tired of explaining the principles of quantum chemical compu-tation to me. Knut Børve was my remote ”quantum chemistry buddy”. FromBergen he managed to steer my understanding of quantum chemistry throughthe stormy waters of the ozone molecule. He cleared up my fuzzy picture ofelectronic structure with a patience and an expertise that are unique.

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I was privileged to work with Leif Sæthre from Bergen, Paul Morin, CatalinMiron amd Marc Simon from Paris, Darrah Thomas from Corvalis and TomCarroll from Keuka Park. They added a special facet to my education, both asexcellent scientists and great people.

Carla Puglia, Pia Thorngren Engblom and Ulla Tengblad were my “womenin physics bodies”. Gunnel Ingelog and Asa Andersson were my “administra-tion buddies”. Martin Agback, Magnus Jansson and Mikael Wirde were my”Linux buddies”. Gunnar Ohrwall was my ”molecular physics buddy”. Com-plex systems are my obsession and hopefully my future. Hans Karlsson andJohan Aberg deliberately discussed my ideas about complex quantum chem-istry. Jim Crutchfield didn’t hesitate to support my ideas and let me take part inhis great expertise in chaotic and complex systems during my stay at the SantaFe Institute.

The people that made work every day a pleasure are my graduate-studentcolleagues, former and present, here and abroad. Achim, Alexander, Alexan-dra, Alf, Anders, Andreas L., Andreas L., Annika, Cecilia, Elisabeth, Emma,Erik, Florian, Henrik, Ingela, Jan, Jo, Johan, John, Jorgen, Katharina, Larsa,Liselott, Linda, Lucia, Magnus, Marcus, Maria, Maria, Micke, Oksana, Patrick,Per-Erik, Raimund, Ricardo, Stefan, Stina, Tor, Torbjorn, Velaug, Ylvi, Zuo.

Sincere thanks are also given to Anders E., Anders S. Anne, Annemieke,Annika K., Birgitt, Carla, Cedric, Charlie, Denis, Dimitri, Hans S., Hakan, In-ger, Janne, Joachim, Jonathan, Karl-Einar, Leif K., Lidia, Lizzy, Loa, Margit,Maria Novella, Mathieu, Maxim, Paul, Teddy. The staff at MAX-lab, espe-cially Ann, Helena and Stefan, and at the LNLS have been extremely support-ive.

Christof Isopp deserves standing ovations for the wonderful layout of thecover. Sincere thanks are given to Anne Wiesner, Anne Krueger, Emma Col-bridge, Andreas Lindblad and Torbjorn Rander for reviewing and translatingthe chapter on popular science. For proof reading I thank my advisers, Ingela,Katharina, John, Gunnar and Denis. The magnetism group is gratefully ac-knowledged for the supply of a such a fine cappuccino machine and Svante forthe continuous supply of Uppsala Sacher bakery during the finish.

Remote but always close – This thesis is dedicated to my family. They onlyget some lines here but fill so much more space in my heart.

Uppsala, December 5, 2003

KAROLINE WIESNER

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Popular Science

1.1 Molecular earthquake in ozoneIn mid-summer the ozone hole is a hot topic in the media. The lack of ozonein the atmosphere is dangerous for us because, high up in the atmosphere,the ozone molecule absorbs part of the sunlight, the so-called ultraviolet solarradiation (UV-light). UV-light is harmful to humans, it destroys skin and otherdeeper tissues. At a height of about 30 km, ozone acts like a pair of sunglassesthat absorbs this harmful part of the sunlight.

The ozone molecule consists, like any other molecule, of electrons and nu-clei. When the molecule absorbs radiation, like UV-light, the radiation getsstuck in the molecule. Thus, ozone prevents the harmful UV-part of solar radi-ation from getting down to the earth’s surface. Radiation is energy. The elec-trons inside the ozone molecule are responsible for taking up the major partof that energy. They use it for restructuring themselves. This is what makesthe “ozone sunglasses” work. My work therefore focused on the restructuringmechanism of the electrons in the ozone molecule.

To get a better view of what the electrons actually do, I enforced a kind ofmolecular earthquake deep inside the molecule. I shone light on the moleculesthat is a hundred times more energetic than UV-light. While absorbing the lightthe ozone molecule kicks out an electron from deep down inside the molecule.This molecular earthquake causes an almost hysterical reaction among theother electrons that sit on top of the hole that the missing electron left be-hind. One or several more electrons are ejected. These ejected electrons carryinformation about what actually happened inside the molecule: Which elec-trons got kicked out, has the molecule broken apart, how fast did the electronscalm down again after the quake? It was this information that I extracted frommy measurements.

Further I computed the effects of the molecular earthquake. Using existingcomputer programs I predicted the energy of the kicked out electrons and com-pared these to the ones I have measured. If they agreed, the computer programgave me more details about how the electrons restructured.

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My measurements and computations showed that the electrons in the ozonemolecule have a variety of ways to restructure. I was able to specify some ofthese restructuring paths. In some cases the electrons restructure extremelyfast. The variety of paths makes the ozone molecule as a whole very fragile.Every path opens a way to react with another molecule and be destroyed. Thisis why agressive molecules from air pollution destruct the ozone layer. At thesame time the variety of paths makes ozone very flexible. It can absorb a widerange of the UV-radiation. The flexibility in the restructuring makes ozone anexcellent pair of “sunglasses”.

1.2 Molekylar jordbavning i ozonI Midsommartider ar ozonhalet ett amne som far mycket uppmarksamhet ivara medier. Eftersom ozon absorberar de ultravioletta delarna av solljuset, saar bristen pa ozon pa hog hojd i atmosfaren direkt farlig for oss manniskor.Ultraviolett (UV) forstor huden och aven mer djupliggande vavnader. Ozon paca 30 km hojd fungerar ungefar som ett par solglasogon som filtrerar bort deskadliga delarna av solljuset.

Ozonmolekylen bestar, som alla andra molekyler, av elektroner och atom-karnor. Nar molekylen absorberar stralning (t.ex. UV-ljus) sa ”fastnar” dennastralning i molekylen. Saledes forhindrar ozonet det skadliga UV-ljuset fran attna jordytan. Stralning ar en form av energi, elektronerna inuti ozonmolekylenfangar upp merparten av denna stralningsenergi och anvander den for att omfor-dela sig. Det ar denna omfordelning som far ”ozonsolglasogonen” att fungera.Darfor har jag valt att studera omfordelningsmekanismen for elektronerna iozon i mitt arbete.

For att bilda mig en uppfattning vad elektronerna egentligen har for sigsa skapade jag ett slags molekylar jordbavning djupt inuti molekylen. Foratt astadkomma detta belyste jag molekylerna med en lampa som ar hundraganger mer energirik an UV-ljus. Da molekylen upptar all denna energi frigorsen elektron djupt i molekylens inre. Denna molekylara jordbavning skapar etthal dar elektronen tidigare satt. De andra elektronerna, som sitter ovanpa halet,reagerar nastan hysteriskt pa denna forandring. En eller flera av dem frigors,och bar med sig information om vad som egentligen hande inuti molekylen;vilka elektroner frigjordes, har molekylen gatt sonder, hur snabbt lugnade elek-tronerna ner sig efter jordbavningen? Det ar bl.a. denna information jag fickut fran mina matningar.

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Jag beraknade aven effekterna av den molekylara jordbavningen. Jag an-vande redan befintliga datorprogram for att forutsaga energin hos de frigjordaelektronerna och jamforde sedan dessa energier med de jag hade uppmatt. Omde overensstamde sa gav datorprogrammet mig annu fler detaljer om hur elek-tronerna omfordelar sig.

Mina matningar och berakningar visade att elektronerna i ozonmolekylenkan omfordela sig pa en mangd olika satt. Jag kunde bestamma nagra av dessaomfordelningsvagar, i nagra fall sa sker denna omfordelning extremt snabbt.Den rika floran av omfordelningsvagar for ozonmolekylen gor den valdigtskor, eftersom varje sadan vag oppnar en mojlighet for en reaktion med en an-nan molekyl. Det ar darfor aggressiva molekyler fran luftfororeningar forstorozonlagret. Samtidigt sa gor den stora mangden satt att omfordela elektronernaozonmolekylen valdigt flexibel, pa sa satt att den kan fanga in en stor del avljuset i UV-omradet. Denna flexibilitet gor ozonmolekylen till ett utmarkt par”solglasogon”.

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Introduction – “Good” and “bad” ozone

Ozone was discovered by C. F. Schonbein in the middle of the 19th century;he also was first to detect ozone in air [Sch40, Sch54]. Schonbein suggestedthe presence of an atmospheric gas having a peculiar odor (the Greek word for“to smell” is ozein). Spectroscopic studies in the late 19th century showed thatozone is present at higher mixing ratios in the upper atmospheric layers thanclose to the ground. Whereas stratospheric ozone is essential for screeningof solar ultraviolet radiation, ozone at ground level can, at elevated concen-trations, lead to respiratory failure in humans. This paradoxical dual role ofozone in the atmosphere has, on occasion, led to the dubbing of stratosphericozone as “good” ozone and tropospheric ozone as “bad” ozone.

Absorption of radiation by gases is one of the most important aspects ofboth global meteorology and atmospheric chemistry. The solar spectrum isradically altered by absorption as the radiation transverses the atmosphere. Itis important to note that the molecules that are responsible for the most pro-nounced absorption of both solar and terrestrial radiation are the minor con-stituents of the atmosphere, not N2. The most significant absorbing gases inthe atmosphere are O2, O3, H2O, and CO2. The minute amount of ozone in theatmosphere can be appreciated by the fact that if all the atmosphere’s ozonewas brought down to the Earth’s surface at standard temperature and pressure,it would produce a layer only about 3 mm thick. Yet, ozone exerts a profoundinfluence on the atmosphere and on life on Earth.

Most of the Earth’s atmospheric ozone (about 90 %) is found in the strato-sphere where it plays a critical role in absorbing ultraviolet radiation emittedby the Sun. The peak in ozone molecular number density (concentration) oc-curs in the region of 20 to 30 km. The so-called stratospheric ozone layerabsorbs virtually all of the solar ultraviolet radiation of wavelengths between240 and 290 nm. Such radiation is harmful to unicellular organisms and to sur-face cells of higher plants and animals. Photolysis of ozone produces O + O2

with practically unit efficiency at wavelengths shorter than 300 nm. In addi-tion, ultraviolet radiation in the wavelength range 290 to 320 nm, so-calledUV-B, is biologically active. A reduction in stratospheric ozone leads to in-creased levels of UV-B at the ground, which can lead to increased incidence ofskin cancer in susceptible individuals.

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Why molecules absorb in particular regions of the spectrum can be deter-mined only by quantum chemical calculations. Which regions they absorb inand what the effects are can be determined with spectroscopic methods. Com-bining the theoretical with the experimental approach provides a powerful toolto explore molecular absorption. The question “why a molecule absorbs” canbe answered in very much detail. The absorption mechanism is studied throughchanges in electronic structure and through nuclear dynamics.

A highly developed experimental technique is electron spectroscopy. Ifthe photon energy is high enough the absorption is followed by ionization. Theenergies are above the molecular ionization energies of a few eV and upwards.Those energies are a magnitude higher than ultraviolet radiation. This methodis still very useful, since space- and energy-resolved electron spectroscopy re-veals a variety of information about the effect of radiation on electronic struc-ture. The use of synchrotron radiation opens up the deeper lying electroniclevels, which are not accessible with ultraviolet radiation. The picture of theelectronic structure gets more complete.

It is important to notice the time scale to which an experimental techniqueis sensitive. Electron spectroscopy is sensitive to the time scale of electronemission which, in small molecules, takes place within a few femtosecondsafter irradiation. Electron spectroscopy data are blind for what happens afterelectron emission. Notice that there always are exceptions to the rule.

Ion spectroscopy is sensitive to the time scale of dissociation. A few nanosec-onds is a good estimate for the time after which a molecule is dissociated (keepthe exceptions in mind). The electron emission has happened “long” time ago.Ion spectroscopy is blind for what happens after a microsecond. It is alsoblind for the details of electron emission since that time scale is much shorter.Quantum chemistry calculations on the other hand don’t have a time scale. Theelectronic structure can be computed at any time of the process. Which timescale is meaningful to investigate is not ordinated by the computer but needsto be thought out by the investigator. After a microsecond one enters the timescale of chemical reactions to which all my methods are blind.

The here presented thesis on the ozone molecule is based on electronand ion spectroscopic methods and ab-initio quantum-chemical calculations.Having the different time scales in mind which these methods are sensible to,their combination is expected to be very powerful. A combined experimentaland theoretical approach is mutually profitable. In the center of this thesis isthe core-hole state. And, although atmospheric ozone never is in a core-holestate (it isn’t even ionized), this approach enabled me to look at the electronicstructure “from inside”. I caused a perturbation (core hole) deep down insideelectronic structure. The effect of this perturbation on the whole electronicstructure and on the nuclear dynamics is a key to understand the interrelationof structure and dynamics.

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Why then is there “good” and “bad” ozone? The electronic structureof the ozone molecule is unusual. In its ground state the molecular wavefunction is dominated by two electronic configurations. In all the results Ipresent here, this “configuration interaction” plays a critical role in the absorp-tion and following electron emission and dissociation. It returns in differentways over and over again. And whenever configuration interaction is in theplay the nuclear dynamics become interesting. There is a connection betweenconfiguration interaction and “good” and “bad” ozone. Configuration interac-tion makes the electronic structure very flexible and opens up a large windowfor radiation absorption. Thanks to this large absorption window stratosphericozone is “good” ozone. On the other hand does the electronic structure becomevery fragile, since configuration interaction opens up ways to react with othermolecules. For example does the high reactivity cause respiratory failure whenozone comes in contact with our lungs, which is why ozone on the ground levelis called “bad” ozone. In the following I summarize results on the correlationbetween electronic structure and nuclear dynamics.

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Ozone – Summary of the main results

In this chapter I briefly review the results of my experimental and computa-tional investigations of the core-hole dynamics of ozone. I do not follow theordering of the publications but group together results whenever they are con-nected. The central connection is the site of the core hole. It turns out that thesite of the core hole is critical for the core-hole dynamics. The correspondingchanges in electronic structure reflect the influence of the core-hole site.

3.1 The ground state of O3

CONFIGURATION INTERACTION RIGHT FROM THE START

A sketch of the ozone molecule (O3) is shown in Fig. 3.1.

The two inequivalent oxygen sites, the central (OC, 1) and the terminalatoms (OT , 2 and 3) are indicated. between the central and the two terminalatoms are equivalent. The two terminal oxygens have no bond inbetween them.The equilibrium geometry of the neutral ground state is 116.81◦ bond angle θ(OT−OC−OT ) and r of 1.2746 A bond length (OC−OT ) [VI], [Her66, TM70].

The orbitals of ground state O3 are shown in Fig. 3.2.

The electronic ground state is a closed-shell singlet 1A1. It has been pointedout in the literature that there are two configurations that dominate the groundstate wave function: The configuration with lowest energy in the one-electron(Hartree Fock) picture interacts with a bi-excited configuration, which is a veryunusual phenomenon.

1s core orbitals 1a1 (OC), 2a1, 1b1, (OT )

2s-like inner valence orbitals 3a1, 4a1, 2b1

valence orbitals, of σ and lone-pair character 5a1, 3b1, 4b1, 6a1

valence orbitals of π character 1b2 (π), 1a2 (n), 2b2 (π∗)

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Figure 3.1: A schematic view of the ozone molecule in the ground state. Ter-minal and central oxygens are indicated.

O3

C

TT

3.2 Electronic states inaccessible via absorptionCONFIGURATION INTERACTION, THE SECOND

Already the electronic structure of the ground state is complicated. Can weinvestigate the valence electronic structure upon ionization? Both direct pho-toionization and resonant core excitation lead to valence-ionized final states,see Fig. 3.3.

However, the process by which the final states are created has an influenceon the relative intensities in the final-state spectrum. In the case of ozone an ex-treme case of intensity redistribution was observed in the final state spectrum.A state showed up in the decay spectrum at an energy position that coincidedwith no state in the photoionization spectrum [IV], see Fig. 3.4. A computationof the final-state spectrum after core-hole decay showed that a valence-ionizedstate around that energy, with a wave function dominated by two configura-tions very different from the other states should have considerable intensity.The doubly excited configuration of the ground state [1a0

2 2b02] is preserved in

the first ionized states of O3. The state that appeared in the decay soectrumand which we call C-state, since it is the fourth ionized state, has the followingwave function:

ψC−state = 0.73 · |1a22 4b2

1 6a01 2b1

2〉 +0.60 · |1a22 4b0

1 6a21 2b1

2〉The wave function of the C-state has, similar to the first three ionized states,

weight in two configurations, though with about about equal coefficients. Itis characterized by a bi-excitation from the 4b1 into the 6a1 orbital, whichmakes it dark in direct photoionization. The ionization cross section becomessignificant first after core-excitation of a state, that presumably has dominatingconfiguration |1s−1

T 1a22 4b2

1 6a21 2b1

2〉. The higher electron density in the 2b2

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Figure 3.2: Molecular orbitals of O3

1a1 2a1 1b1 3a1

2b1 4a1 3b1 5a1

1b2 1a2 4b1 6a1

2b2 7a1 5b1

orbital opens up the decay channel to the C-state. The equilibrium geometryof the C-state is at 73.1◦ and 1.3A [SCR+91]. The observation of the C-stateis therefore a very good example for the influence of the highly correlatedelectronic structure of O3 on the absorption behaviour.

3.3 Stable valence-ionized statesSOMETIMES OZONE IS STABLE

What happens to the ozone after core ionization? The bonding and anti-bonding character of valence orbitals is reflected in the dissociation patternwhich can be observed with ion spectroscopy. The onset of ion productionscanning the photon energy can be correlated to the ionization threshold ofan electronic state. The corresponding fragmentation pattern then reveals thedissociation behaviour. Some of the first ionic states in O3 were found to bepossibly dissociative, if not in the vibrational ground state at least in highervibrational states [II]. Though, especially the first two ionic states, 12A1 and12B2 were confirmed to be stable. “Stable” in the present context means thatthe molecules don’t dissociate on the timescale of microseconds, and undervacuum conditions.

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Figure 3.3: A wave packet on potential curves of a diatomic molecule illus-trates direct photoionization and resonant Auger excitation leadingto the same valence-ionized final states.

(2)

(1)

(3)(1) direct photoionization

(2) resonant photoexcitation

(3) Auger decay

Energy

Internuclear distance

3.4 Nuclear dynamics of core-ionized statesDOES SITE MATTER?

In contrast to valence orbitals, the core orbitals of adjacent atoms hardly over-lap. The core orbitals do hence not participate in the bonding. What happensupon removal of a core electron? Does it matter on which site ionization takesplace? Core-ionized O+

3 can be studied site-selectively taking advantage ofthe difference in ionization energy between the the terminal (OT ) and centraloxygen (OC) 1s orbital of 4.58 eV. Although the observed vibrational broad-ening is large, they are spectroscopically well separated, as seen in the O1sphotoelectron spectrum of ozone in Fig. 3.5 [VI].

The ionization energies of the central and terminal oxygen are 541.61 eV(OT 1s) and 546.19 eV (OC1s), which agrees well with the latest values re-ported by Stranges and co-workers [SAFD01]. The ionization energy of OC1sis the highest measured in the series of bound and unbound oxygen atoms.

The nuclear dynamics in the two core-ionized states proved to be very dif-ferent. Although studied with different techniques and therefore on differenttimescales, the data always show a fingerprint of differences in the nuclear dy-namics in these two states. The effect of the core-hole site is observable longafter the core-hole lifetime of a few femtoseconds. Fig. 3.6 illustrates the influ-ence of a core hole on the valence electronic structure. The 2b2 valence orbitalis shown for the two core-hole sites. plot has been generated from a Gaussiancalculation. It shows the contraction of the wave function around the core-holesite.

The experimental observations together with the calculations give a consis-tent picture of the electronic structure and the nuclear dynamics of core-ionizedO+

3 .

14

Figure 3.4: (a) The photoelectron spectrum measured with 100 eV photons.(b) RAE spectrum after excitation of the OT 1s−12b1

1 resonance.(c) Calculated final states for OT 1s−12b1

2 excitation, convolutedwith a Voigt function corresponding to the life-time and experi-mental broadening.

500

400

300

200

100

02624222018161412

Transitionrate(µau)

Binding Energy (eV)

Intensity(arbitraryunits)

24222018161412Binding Energy (eV)

I

IIIII

IV

V

VI

VII

VIII IX

026

024222018161412

Intensity(arbitraryunits)

Binding Energy (eV)

1

2

3

45 6 7

89 10 11

26

(a)

(c)

(b)

15

Figure 3.5: The O1s photoelectron spectrum of ozone (circles), measured withmonochromatized synchrotron radiation using a photon energy of570 eV [VI].

0

550 549 548 547 546 545 544 543 542 541 540

Intensity[arbitraryunits]

Binding Energy [eV]

FWHM = 0.75 eV

FWHM = 0.63 eV

OC1s OT1s

3.4.1 Electronic structure computationCONFIGURATION INTERACTION GOING WILD

The main features of the O1s photoelectron spectrum shown in Fig. 3.5 are thelack of any vibrational structure, and a 20% larger line width for the OC1s linecompared to the OT 1s line. The experimental resolution was around 170 meV,which is well below the smaller line width of 630 meV, and therefore canbe almost neglected. Using ab-initio computational methods we were able tomap out the nuclear dynamics of the two core-excited states [VI]. The reasonfor the broad, unstructured lines was explained with a dissociative characterof the core-ionized states. Moreover, the computations reproduced the linewidth which is 20% larger for the OC1s line compared to the OT 1s line. Eachline width is caused by a different dominating vibrational normal mode. Thethree normal vibrational modes of O3 are illustrated in Fig. 3.7. The nucleardynamics of OT 1s-ionized O+

3 are dominated by the asymmetric stretch mode.The mode is strong enough to dissociate the molecule. The nuclear dynamicsof OC1s-ionized O+

3 are dominated by two vibrational modes, the symmetricstretch and the bending mode. Though, the bending mode is only excited aftera short while, which leaves the symmetric stretching mode to be responsiblefor the large line width of the OC1s line. The wave functions of the groundstate and the two ionized states at vertical geometry are given in Tab. 3.1.

16

Table 3.1: Wave functions and energies at ground-state equilibrium geometry.

Vertical Geometry Energy

θ = 116.81◦, rCT = 1.2746 A [Hartree]

ψgs 0.87 · |1a22 4b2

1 6a21 2b0

2〉 + 0.34 · |1a02 4b2

1 6a21 2b2

2〉 -225.068850

ψT 0.90 · |1a22 4b2

1 6a21 2b0

2〉 + 0.23 · |1a02 4b2

1 6a21 2b2

2〉ψC 0.78 · |1a2

2 4b21 6a2

1 2b02〉 + 0.54 · |1a0

2 4b21 6a2

1 2b22〉

Table 3.2: Wave Functions and energies relative to energy at vertical geometryof OC1s−1 at selected geometries

Wave Function Energy

[Hartree]

vertical geometry rC∗T = 1.2746 A, θ = 116.81◦

0.78 · |1a22 4b2

1 6a21 2b0

2〉 + 0.54 · |1a02 4b2

1 6a21 2b2

2〉 0.000000

local minimum (1) rC∗T = 1.434 A, θ = 114.94◦

0.72 · |1a22 4b2

1 6a21 2b0

2〉 + 0.61 · |1a02 4b2

1 6a21 2b2

2〉 -0.026772

local minimum (2) rC∗T = 1.4786 A, θ = 59.89◦

0.92 · |1a22 4b0

1 6a21 2b2

2〉 + 0.20 · |1a22 4b2

1 6a01 2b2

2〉 -0.040323

asymptotic geometry rC∗T = 4.0000 A, rT T = 1.1151 A

0.66 · |1a02 3b2

1 4b01 6a2

1 7a21 2b2

2〉 + 0.66 · |1a22 3b0

1 4b22 6a2

1 7a21 2b2

2〉 -0.191664

18

Figure 3.8: Scan of the OC1s−1 PES along the bending (left) and the symmet-ric stretch (right) normal coordinate. (left) The bond length is op-timized for every point. The PES for frozen and relaxed electronicconfigurations illustrates the curve crossing inbetween the mini-mum (1) and (2), see Tab. 3.2 and text. The position of minima (1)and (2) are indicated. (right) The PES for relaxed electronic con-figuration. The bond length between oxygen 2 and 3 is optimizedfor every point.

Bond angle [degree]

Energy[Hartree]

OC1s-1 PESfrozen and relaxed configuration

Bond distance [Å]

Energy[Hartree]

OC1s-1 PESrelaxed congfiguration

configuration minimum (1)configuration minimum (2)relaxed configuration

-173.10

-173.05

-173.00

-172.95

11010090807060

minimum (1)

vertical geometry

minimum (2)

-173.25

-173.20

-173.15

-173.10

4.03.53.02.52.01.5

minimum (1)

vertical geometry

19

Figure 3.10: A sketch of the Auger Doppler effect in fragment Auger electronsfor detection in two angles with respect to the light vector.

e- e-

e-e-

molecular decay fragment decay

3.5 Nuclear dynamics of core-excited statesVISITOR FROM THE CORE

Core-excited states can be investigated on two different timescales. ResonantAuger electron spectroscopy (RAE) probes the electronic structure directlyafter core-hole decay and electron emission, i. e. on the timescale of fem-toseconds, ordinated by the life time of the core hole. Ion spectroscopy, on theother hand, investigates the consequence of core-excitation on the timescale ofmicroseconds, since the majority of the fragmentation happens long after thecore-hole decay. Still, the fragmentation pattern contains a finger print of thecore-excited state.

3.5.1 Ultra-fast dissociationFLYING CORE HOLE

The resonant Auger decay spectra of O3 core-excited to OT 1s−17a11 exhibits

the peculiarity of two superimposed spectra, see Fig. 3.11 [I]. The decay spec-trum of core-excited O∗

3 is superimposed by the decay spectrum of core-excitedO∗. However, no atomic oxygen is in the sample and the ozone is stable un-der the experimental conditions until it is irradiated. Consequently, the O∗ isgenerated from core-excited O∗

3. The observation of electronic decay of O∗

implies that the dissociation of O∗3 into O∗ and presumably O2 happens dur-

ing the core-hole lifetime which is a few femtoseconds. Consequently, thenuclear dynamics are on the femtosecond timescale. Dissociation on the fem-tosecond timescale is called “ultra-fast dissociation”. It has been observed forseveral molecules, such as HBr [MN86], HF [III], O2 [SCKJM93, CSKJM93].The ultra-fast dissociation of HF and DF has been investigated closer [III].In the HF and DF decay spectra nuclear dynamics have been observed whichwe called “dynamic Auger-Doppler effect”. When monitoring the kinetic en-

21

Figure 3.11: Resonant Auger decay spectra of O∗3 core excited to the

OT 1s−17a11 state. The atomic electronic states show up as split

lines for detection in plane of the polarization direction of thelight (upper spectrum). For detection perpendicular to the polar-ization and the propagation direction of the light the atomic statesshow up as single lines, due to the Doppler effect.

Intensity[arbitraryunits]

Kinetic Energy [eV]520510500490480

22

ergy of the fragments while detuning photon energy it was observed that thefragment kinetic energy is transfered to the Auger electrons. photon energy isdetuned, the lacking or redundant energy is found in the fragment kinetic en-ergy. This is purely due to energy conservation, since the electronic excitationand deexcitation is constant in energy. Any deviation can only be compensatedfor by the kinetic energy of the fragments.

Ultra-fast dissociation in O∗3 [I] has been identified through the Auger Doppler

effect [GHS98, BBA+00]. When measuring the fragment Auger electrons intwo different angles with respect to the light vector, the peak shape in thedecay spectrum changes, as illustrated in Fig. 3.10 for a σ resonance of a di-atomic [VII] . The cause for the OT 1s−17a1

1 state to exhibit such extremely fastnuclear dynamics is the strongly anti-bonding character of the populated 7a1

orbital which is highly repulsive. Frankly said, the molecule “explodes”.

One obvious question is if also for core excitation of the central oxygenthe OC1s−17a1

1 state is ultra-fast dissociative. The experiment does not exhibitany sign of ultra-fast dissociation for the population of this state. No decayspectrum of O∗ is superimposed onto the O∗

3 decay spectrum. Still the samerepulsive 7a1 orbital is populated. And the reason for the OC1s−17a1

1 state notto be ultra-fast dissociative lies in the core-hole dynamics.

The position of the core hole influences the electron density in the valenceorbitals (otherwise there would be no wit in doing site-selective core excita-tion), see Fig 3.6. The dynamics for different core-hole sites has been dis-cussed for core-ionized O+

3 . A similar influence is expected for core-excitedO∗

3. As a first approximation a one-to-one comparison of core ionization andcore excitation helps understanding the nuclear dynamics of core-excited O∗

3.In a one-to-one comparison, core-excited O∗

3 in the OT 1s−17a11 state is mainly

excited in the asymmetric stretch mode. This mode preferentially breaks oneof the two bonds, see Fig. 3.7. Whereas excitation of the symmetric stretch, ina dissociative state, tends to break both bonds. To answer the question fromthe beginning why the OT 1s−17a1

1 is ultra-fast dissociative and the OC1s−17a11

is only dissociative we compare the nuclear motion for the two excited normalmodes shown in Fig. 3.7. The asymmetric stretching mode elongates bond 1-3and contracts bond 1-2, whereas the symmetric stretching mode elongates bothbonds. Thus, the distance between the core-excited atom increases faster in thecase of terminal core excitation than in the case of central core excitation. Theeffect is a faster dissociation in the first case.

In conclusion, the experimental observation of ultra-fast dissociation forthe OT 1s−17a1

1 state sheds light on the core-hole dynamics, which are verydifferent for the two core-hole sites. It is another example of the interrelationof electronic structure and nuclear dynamics.

23

Kinetic Energy [eV]

Intensity[arb.units]

OT1s� 7a1

a1 + b1 peak shape

σ peak shape

3800

3600

3400

3200

476.0475.0474.0473.0

Figure 3.12: RAE spectrum of O3 (circles) excited to OT 1s−17a11. The solid

line is the convoluted profile function for σ transition. The dottedline is the convoluted profile function for a1+b1 transition.

3.5.2 Core-excitation localized to one chemical bondWHAT ABOUT EQUIVALENT SITES?

The ozone molecule contains two equivalent OT sites. Are the core orbitalsbest described as delocalized over the two sites, or are the two orbitals ratherindependent? To investigate this, a closer analysis of the OT 1s−17a1

1 state [V]has been based on a formalism for calculating peak shapes of electronic decayspectra [V]. The peak shapes depend on the symmetry of the excitation preced-ing the decay. The formalism has originally been developed for ion spectra, buthas been modified to be applicable to fragment Auger electron spectra. Usingthis formalism predicted peak shapes for C2ν molecules (the symmetry groupof O3) have been compared to the experimental peak shape of the fragmentAuger electron, see Fig. 3.12. The two peak shapes, however, were not com-patible. We looked for an explanation in a localized/delocalized descriptionof the core excitation. A delocalized description is inherent in a representa-tion of the molecule in C2ν symmetry. The core-excitation is modeled as anexcitation out of the delocalized molecular orbitals that are formed by the twoterminal 1s orbitals. A localized model of the core excitation reduces the tri-atomic molecule with two bonds and delocalized molecular core orbitals toa molecule with one bond and localized core orbitals. The above mentionedformalism yields a peak shape for this case that is equal to that of diatomicmolecules. The orientation of the bond close to the core hole determines theexcitation probability which the peak shape depends on. And this peak shapeagrees with the experimental peak shape. We draw the conclusion that excita-tion of the terminal core electrons is localized to one site of the molecule. Thesymmetrization that quantum mechanics requires for the two cases of “left”

24

core hole and “right” core hole is obtained through an equal treatment of thetwo. The difference is that the symmetrization is not done with “left” and“right” excitation in one molecule but with one molecule “left” excited andone molecule “right” excited. The latter treatment becomes the correct one forlarge bond distances between the symmetric sites. The distance between theterminal atoms in ozone is 2.2 A, which might serve as a rule of thumb fromwhich point on an oxygen system has to be described in a localized model. Theobservation of localized core excitation in ozone as a small, triatomic moleculeis unexpected. Though, it delivers a case study for core excitation of larger freeand adsorbed molecules. The latter are usually treated in the localized model.The observation and explanation of the effect in ozone explains the success ofthat model for large molecules.

3.5.3 Core-hole site-dependent fragmentationSITE ALWAYS MATTERS

Leaving the timescale of core excitation we go over to the microsecond timescaleagain and the fragmentation pattern of core-excited ozone. Similar to what wefound for core-ionized ozone [IX] , the fragmentation pattern of core-excitedozone is different for different core-hole sites [VIII]. Moreover, we observeddifferences depending on the symmetry of the core-excited state for the samecore-hole site. The phenomenon of ultra-fast dissociation known from the elec-tron spectroscopy data was manifested in the ion data as well. This illustratesthat the ion data contain a finger print of the core-excited state that precededthe decay and dissociation. The main feature of the fragmentation patternis the difference between the terminal and central-excited molecules. OT 1s-excited O∗

3 dissociates mainly to O+2 and an O fragment, which can be neutral

or charged. Whereas OC1s-excited O∗3 dissociates mainly to O+ O+ and neu-

tral O. The effect would probably be even more pronounced if the core-excitedstates didn’t overlap with each other. Which valence orbital is populated obvi-ously plays a minor role compared to the influence of the core-hole site. Thesymmetry of the core-excited states was analyzed using the formalism from[VII] . The formalism allowed for the characterization of overlapping core-excited states. The effect of localized core excitation, which had been observedwith electron spectroscopy [V] was confirmed in the ion data.

25

26

Experimental Details

This chapter gives a short overview over the experimental resources I had at mydisposal. I briefly review the three synchrotron-radiation laboratories, whereI conducted the experiments and I summarize the experimental techniques.The development of a generator for pure ozone stood at the beginning of myresearch and will be reviewed in some detail.

4.1 Electron spectroscopyMAX-lab, Lund, Sweden

The MAX-II storage ring of the Swedish National Synchrotron Radiation Lab-oratory MAX-lab in Lund, Sweden is a 3rd-generation synchrotron radiationsource. The ring of 90 m circumference stores electrons at an energy of1.5 GeV. The electrons circulate in bunches with a full width at half maximum(FWHM) of 20 ps. As a 3rd-generation ring, MAX-II is equipped with sev-eral undulators. The undulator at beam line I411 covers a photon energy rangeof 50-1500 eV. The radiation is linearly polarized (≤ 99%) in the horizontalplane. The soft X-ray beam line I411 [BFB+99, BAJ+01] has been operationalsince January 1999. The beam line contains a modified Zeiss SX-700 planegrating monochromator, focusing mirrors and further optical elements. It isdesigned for high-resolution electron spectroscopic studies of gases, clusters,liquids and solid samples. The end station [SFS+96] is stationary equippedwith a Scienta SES-200 electron analyzer [MBB+94].

Electron spectroscopy

Fig. 4.1 shows a schematic view of the Scienta electron analyzer.The angle between analyzer and electrical vector in a plane perpendicular

to the photon beam can be set between 0-90◦ with precision of 0.2◦. Thedifferentially pumped chamber for gas-phase studies is not separated by anywindow from the storage ring.

They leave the field-free interaction region through an exit hole in the gascell and enter the analyzer. The analyzer spatially resolves the electrons bytheir kinetic energy in a radial electromagnetic field. The energy resolution is

27

Figure 4.1: A schematic figure of the Scienta electron analyzer, mounted atbeam line I411, MAX-lab, Sweden.

Gas/synchrotroninteraction region

Electron lensElectrostaticalhemispheres

Detector

dependent on the entrance slit size and pass energy. At 10 eV pass energy and0.5 mm curved slit it is ∆E =15 meV.

4.2 Electron-ion-ion coincidence spectroscopyLNLS, Campinas, BrazilThe Laboratorio Nacional de Luz Sincrotron (LNLS) in Campinas, Brazil iscurrently being updated to a 3rd-generation facility. The electron energy is1.3 GeV. The SGM (spherical grating monochromator) and the TGM (toroidalgrating monochromator) beam line are fed with linearly polarized bending-magnet radiation with an estimated 95% degree of polarization. The SGMbeam line operates in the VUV- and soft X-ray regime (250-1000 eV) withan energy resolution of E/∆E = 2000. The TGM beam line, equipped with 3toroidal gratings, operates in the UV- and VUV-regime (12-300 eV) with anenergy resolution of E/∆E =400-1000, depending on the grating.

28

Figure 4.2: A principle sketch of the experimental chamber and the ion time-of-flight spectrometer, developed at LNLS, Brazil.

Electron-ion-ion coincidence spectroscopy

The set-up of an experimental chamber and an ion time-of-flight spectrome-ter is non-stationary. It has been installed temporarily at beam line SGM andTGM. This home-made equipment is described and characterized by Burmeis-ter and co-workers [BCM+]. The upper kinetic-energy limit of the 4π detectionof electrons and ions is characterized in [BCM+]

The ion time-of-flight spectrometer is mounted with the axis parallel to thepolarization direction and perpendicular to the propagation direction of thesynchrotron light. The gas/synchrotron-light interaction region is designed af-ter Wiley-McLaren focusing conditions. The electrons are accelerated towarda multi-channel plate, which induces a start signal that opens a time windowof 3000 ns for ion detection. The ions are accelerated toward a field-free tube.This so-called time-of-flight tube separates the ions after their mass/charge ra-tio based on their flight time. In the time window all charged ions are correlatedto one ionization event.

29

Figure 4.3: A principle sketch of the double-toroidal electron analyzer and theion time-of-flight spectrometer, developed at LURE, France.

4.3 Energy-selected electron-ion coincidenceLURE, Orsay, FranceThe SuperAco at the Laboratoire pour Utilization du Rayonment Electromag-netique (LURE) synchrotron laboratory is an 800 MeV 2nd-generation storagering. Beam Line SA22 operates with linearly polarized wiggler radiation in theVUV- and soft X-ray regime (100-900 eV). The energy resolution of the plane-grating monochromator is E/∆E =5000 [Del95]. Our measurements weredone with the non-stationary EPICEA II end station [MSLM97, Mir97, Ceo03]which was installed temporarily at beam line SA22.

Energy-selected electron-ion coincidenceThe heart of the EPICEA II end station is a double-toroidal electron energyanalyzer which is operated in coincidence with an energy-resolving ion time-of-flight detector. The analyzer is rotatable in a plane perpendicular to thepropagation direction of the light. In any orientation the electron acceptanceangle is 5% of 4π. At a pass energy of 160 eV the electron kinetic-energyresolution is ∼1.2 eV. The ion time-of-flight spectrometer is mounted in thesame plane perpendicular to the propagation direction of the light and par-allel to the polarization direction. It has ∼4π acceptance angle for the ions.The gas/synchrotron-light interaction region is field free until an electron is

30

Figure 4.4: A schematic view of the ozone generation set-up.

Oxygen

p

t

MnO2

pump

pressure gage

gas/synchrotron-lightinteraction region

valve

temperaturecontrol

spectrometerglass reservoire

glass U-tube,distillation

pump protection

ozonegenerator

liquidnitrogen

Ozone-generation set-up

detected, to preserve its energy resolution. The electrons pass through thedeflecting plates of the analyzer before hitting multi-channel plates that aremounted before a position-sensitive detector. The electron-induced signal trig-gers a pulsed exctration field to the interaction region and opens a window forion detection. Such, all charged fragments are correlated to one electron en-ergy, and can in the limit of resolution be assigned to an electronic final state.

4.4 Generation of pure ozoneThe home-made ozone generating system was central for this thesis. It shouldbe noted that the purity of the ozone sample achieved with the generation pro-cess was between 95 and 99%. A sketch of the set-up is shown in Fig. 4.4. Acommercial ozone generator [ozo] produced a gas mixture of 10% ozone and90% oxygen. A distillation process purified the mixture in a system consistingmainly of glass and PTFE components. The use of these materials is crucialto the efficiency of the purification process and the lifetime of the generatedozone. Stainless steel proved to be sufficiently inert to to prevent ozone fromdissociating during the inlet into the experimental chamber.

In the continuously pumped system, the gas mixture was liquefied in a glasstube surrounded with liquid nitrogen, which trapped both ozone and oxygen.The liquid was heated up to a point in-between the boiling point of ozone(161.1 K) and oxygen (90.2 K). At this point the oxygen had evaporated andcould be pumped out. The remaining ozone liquid had a purity of up to 99%[VI]. The purified ozone liquid was filled into a glass reservoir, which was con-nected to the spectrometer. The pumps had been protected by MnO2 granulesacting as a catalyst to break the ozone molecules and, in addition, by liquid

31

nitrogen traps. The most important precaution to be taken in order to avoidexplosions is to keep the pressure in the system as low as possible. The ozoneliquid has to be cooled down continuously with liquid nitrogen. Only in orderto refill the glass reservoir the connection to the pumps was shut and the liquidwas heated up, while monitoring the pressure. It is recomendable to surroundthe glass U-tube containing the liquid ozone with a Plexiglass box. Explosionscan never be excluded and the Plexiglass box prevents pieces of glass to harmanybody. Since ozone is sensible to visible and UV-light, covering the wholeinlet system with non-transparent foil increases the lifetime of the liquid andgaseous sample.

32

Computational Details

We performed calculations of the Resonant Auger electron spectrum with acode developed by R. F. Fink [Fin95]. The decay (autoionization) of the coreexcited molecule leads to the final ionic states of O+

3 and a continuum elec-tron. In principle all states of the ion – that means a huge number of electronicstates – can be reached by autoionization. We accounted for a sufficientlylarge portion of them by using electronic states that can be represented withthe valence orbitals of the O3 molecule. We used valence CI wave functionsfor the ground, intermediate and final states. For this purpose the followingvalence orbitals were constructed in a cc-vTZP basis set of Dunning [Dun89]:The strongly occupied orbitals of ozone were obtained by a CAS SCF calcu-lation using two electrons in the two partially occupied orbitals 1a2 and 2b1.Two further valence orbitals (7a1 and 5b2) were determined according to themodified improved virtual orbital technique described in Ref. [FSdB+00]. Ac-cording to their character we designate the latter as σ∗ orbitals. The groundstate was represented by a CI wave function containing up to two electrons inthe σ∗ orbitals and all possible occupations of the strongly occupied orbitals.For the intermediate state one hole was required to be in either the symmetricor the antisymmetric linear combination of the OT 1s orbitals and again up totwo electrons were allowed in the σ∗ orbitals. For the final states however onlyone electron could be included in the σ∗ orbitals. The Auger transition rateswere obtained according to the one-center approximation [SAK75, ASW75].

In order to aid interpretation of the vibrational structures in the core pho-toionization spectrum, high-level ab initio calculations were carried out for theneutral molecule as well as for the two core-hole states. The calculations wereperformed with the MOLCAS set of quantum chemistry programs [ABB+02],with atomic natural-orbital bases [PDWR95] chosen as 7s 5p 3d contractedfunctions. All valence electrons were correlated in terms of the multi-referenceconfiguration interaction (MRCI) method [Sie80], with orbitals generated bythe CASSCF method [RTS80]. The MRCI energies were corrected for un-linked clusters according to the Davidson scheme [LD74]. Molecular geome-tries were optimised based on energy evaluations only.

33

For the ground state, the active space in the CASSCF calculations consistedof 1b2 (π), 1a2 (n), 2b2 (π∗), with four electrons, and only two reference stateswere used in the subsequent MRCI.

For core-ionized ozone, a considerable effort was made at exploring how thecomputed potential energy surfaces change with the choice of active space andnumber of reference states. Near the equilibrium geometry of the ground statea small active space and fairly few reference states (5-8 references) suffice,while the multiconfigurational nature of the wave functions naturally becomesmore pronounced as covalent bonds are stretched significantly.

For the ionized states, we adopted a simplified approach in which the core ofthe ionized atom is described in terms of an effective core potential (ECP). Tothis end we used the oxygen ECP devised by Huzinaga et al. [SLZK87], albeitscaled to account for only 1 electron in the 1s shell. Relative to the original ex-pressions, this implies that the M1 coefficients have been scaled by 0.5*(6/7),the 1s orbital energy is doubled to maintain valence-core orthogonality, andthe effective charge of the core is increased from 6 to 7. It is important to notethat the ECP approach is not that of the equivalent core approximation, ratherit closer to a frozen-core description. This approach is previously used withgood results in a number of studies [KB00, KSB+01, KBS+02, SBB+01].

34

Concluding Remarks

A main aim of the study has been to shed light on the electronic structureof the ozone molecule, which exhibits unusually strong configuration interac-tion. The main result of the study is that electronic configuration interaction issubstantial in most electronic states: the ground state, valence-ionized states,core-ionized and core-excited states. Moreover, the nuclear motion is corre-lated to changes in electronic structure. We found considerable differences inthe excitation of vibrational modes depending on the electronic state that hadbeen created. The tool of site-selective core excitation has proven to be veryuseful for mapping out the correlation between electronic states and nucleardynamics.

On the other hand, ozone is a peculiar molecule consisting of only oneatomic species, and with an unusually complicated electronic structure. Wediscovered phenomena that are of interest to molecular physics in general, suchas the localized character of specific core excitations. The variety of techniquescontributed to a broad range of studied phenomena. Results found with onemethod could be confirmed or explained with another.

In conclusion, ozone is a system worth studying from several points ofviews. This thesis hopefully provides a comprehensive overview over a partof the electronic structure and the connection between electronic structure andnuclear dynamics.

35

36

Glossary

Active orbital Orbital with varying occupancies for different configurations,see also virtual orbital, inactive orbital, CASSCF.

Adiabatic ionization energy The difference in energy between the initial statein the vibrational ground state and the final state in the vibrational groundstate. It is found experimentally as the first peak in a vibrational pro-gression a photoelectron band. Adiabatic transitions are weak for verydifferent equilibria of initial and final state. See also vertical ionizationenergy.

Auger Doppler effect The kinetic energy of the fragment is transfered to theAuger electron emitted from the fragment. Electrons from forward andbackward directed fragments with respect to the detector obtain a shiftin opposite direction (Fig. 3.10), see also dynamic Auger Doppler effect.

Autoionization Any ionization following an electronic excitation. See alsoresonant and normal Auger decay, shake-off.

Bending magnet radiation Radiation emitted by a relativistic electron expe-riencing radial acceleration as it travels around a circle. The broad an-gular pattern of the radiation – seen in the electron reference frame –is very much compressed upon Lorentz transformation from one frameof reference (that with the moving electron) into another (the laboratoryframe of the observer) leading to a narrow cone of broad-band radiation.

CASSCF Complete Active Space SCF computational method. The active or-bital in the final optimized states have nonintegral occupation.

Chemical shift Difference in ionization/excitation energy for symmetry-inequivalent core-hole states of the same atom in different moleculesor molecular environments.

Configuration interaction Standard model incorporating the effects of dy-namical correlation. The wave function is constructed by a linear com-bination of Slater determinants, see also CASSCF.

Core-hole dynamics Nuclear dynamics caused by creation of a core hole.

37

Coulomb operator The operator Jr represents the Coulombic interaction be-tween electron (1) and electon (2) in the orbital ψr:

Jrψs = 〈ψ∗r (2)

(e2

4πε0r12

)ψr(2)〉ψs(1)

Dipole approximation The transition probability is 〈ψ f |eik·rep |ψi 〉, wherek is the electromagnetic wave vector, e is the polarization direction ofthe light and p is the electron momentum. Expanding the exponentialand retaining only the first term gives the dipole approximation. A con-sequence of the dipole approximation is that the excitation probability isdependent on the angle between polarization direction of the light andtransition polarization.

Dipole moment The transition dipole moment for transitions between statesψi and ψ f 〈ψi|µ|ψ f 〉 with the dipole operator µ.

Dipole operator µ = er governs the selection rules for electric-dipole transi-tions.

Direct photoionization In contrast to autoionization. A photon is absorbedand an electron is ejected into the continuum. The ionization is gov-erned by the dipole operator. See also adiabatic and vertical ionizationenergy, shake-up, vibrational modes.

Dynamic Auger Doppler effect Tuning the photon energy through the reso-nance of an ultra-fast dissociating state changes the kinetic energy ofthe fragments by the same amount of energy, observable with the AugerDoppler effect.

Dynamic core-hole localization Introduced by Domcke and Cederbaum in1977 [DC77]. The mechanism of vibronic coupling leads to a lowersymmetry, which forces a symmetrized, delocalized core hole to local-ize.

Electronic structure Spatial and energetic distribution of electronic wave func-tions.

Fermi’s golden rule The transition probability λi f of an electronic state isproportional to the density of final statesρ f : λi f = 2π

�|Mi f |2 ρ f , where Mi f is the interaction matrix element. See

also lifetime of electronic state.

Hartree Fock approximation The electronic wave function is approximatedby a single configuration of spin orbitals.

Inactive orbital Orbital doubly occupied in all configurations, see also activeorbital, virtual orbital.

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Irreducible representation The orbital basis set that can not simultaneouslybe represented by a linear combination of symmetry operations. Thematrix representative of a symmetry operation is spanned by the orbitalbasis set. If the orbital basis set is the irreducible representation thematrices do have block form. Each irreducible representation has a labelcalled a symmetry species. Orbitals of the same symmetry act as basisfor the same matrix representation. They transform equivalently underthe symmetry operations.

LCAO Linear combination of atomic orbitals. Molecular orbital wave func-tions are conventionally constructed by linear combination of atomicorbital wave functions.

Lifetime broadening Spectral line broadening due to finite lifetime of non-ground electronic state.

Lifetime of electronic state If N0 molecules are in an excited state at time t0,the number of molecules left in this state at time t0 + t is N = N0 e−

t0+tτ .

τ is called the lifetime of the state. Molecular core-hole states havea lifetime of a few femtoseconds. See also Fermi’s golden rule andlifetime broadening.

NEXAFS The electronic states below and above the 1s ionization thresholdconstitute the Near Edge X-ray Absorption Fine Structure. A NEXAFSexperiment scans the photon energy and records the photoabsorption,alternatively the number of emitted electrons (total electron yield) orions (total ion yield).

Normal Auger decay The deexcitation through electron ejection after coreionization.

One-electron picture Freezing all electrons but one (“active” one). Multi-electron processes such as shake-up and configuration interaction areneglected.

Normal modes Vibrations along the normal coordinates of a molecule, seeFig. 3.7.

Nuclear dynamics Motion of the nuclei in a molecule, e. g. bond stretchingor bending, dissociation. Any motion can be expressed in terms of nor-mal modes. The potential energy of a molecule depends on the positionof the nuclei, see also potential energy surface.

Potential energy surface Plot of potential energy vs geometry of an elec-tronic state.

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Resonant Auger decay The deexcitation through electron ejection after reso-nant photoexcitation. The excitation is goverend by the dipole operator.The decay is governed by the Coulomb operator.

SCF Self-Consistent Field. Iterative procedure to optimize Hartree Fock wavefunction.

Selection rules Rules that specify the specific electronic transitions that mayoccur, based on the examination of the transition operator.

Shake-up Excitation of “passive” electrons into bound states due to the cre-ation of an ionized state.

Site-selective excitation Taking advantage of the chemical shift to core-excitea specific atomic site in a molecule.

Synchrotron radiation Radiation generated when relativistic electrons areaccelerated in a magnetic field. There are three types of magnetic struc-tures commonly used to produce synchrotron radiation: bending mag-nets, wigglers and undulators. 3rd generation synchrotrons are equippedwith undulators. Recommended literature [Att99].

Transition polarization Angular transition probability depending on the or-bital symmetry of initial and final state.

Ultra-fast dissociation Dissociation on the timescale of electronic relaxationupon core excitation. When the nuclei move apart so fast that the moleculealready dissociates in the intermediate state we talk about ultra-fast dis-sociation. It is visible in the final electronic state spectrum since it hap-pens on the same timescale as the Auger decay, i.e. on the timescale offemtoseconds. If the molecule dissociates it causes an extreme change ofelectronic configuration, namely towards the configurations of the frag-ments. The final state spectrum becomes a superposition of states fromthe molecule and states from the fragments. This phenomenon has beenobserved in this thesis for O3 [I], for HF and DF [I].

Undulator radiation Radiation emitted by relativistic electrons passing througha periodic magnetic structure. The radiation pattern as observed in thelaboratory frame is relativistically contracted into a narrow radiationcone. For electron motion directed along the z-axis of an undulator withperiodic magnetic fields oriented along the y-axis the generated radiationis polarized in the x-direction. The emitted light interferes constructivelyproducing a harmonic distribution of sharply peaked radiation.

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Vertical ionization energy The difference in energy between the initial statein the vibrational ground state and the final state with nuclear geometryfrozen to the initial-state geometry. It is found experimentally as thepeak of maximum intensity in a vibrational progression a photoelectronband. See also adiabatic ionization energy.

Vibrational modes Molecules have one or more normal modes, such as sym-metric stretch or bending. Normal modes are with few exceptions al-ways excited in connection with electronic transitions.

Vibronic coupling States of different electronic symmetries obtain the sametotal symmetry through a vibrational mode, which allows them to cou-ple. The mechanism of vibronic coupling leads to dynamic core-holelocalization.

Virtual orbital Orbital unoccupied in all configurations, see also active or-bital, inactive orbital.

Wiley-McLaren condition Focusing conditions compensating for the finitesize of the source volume to preserve time resolution. Achieved by ap-propriate choice of geometry and electric fields on time-of-flight massspectrometer [WM55].

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Comments on My Own Participation

The ozone generation set-up has been developed and constructed by me. Thedata acquisition has been carried out by me and my co-workers at the differentsynchrotron radiation laboratories. The calculations were conducted by meunder the supervision of R. F. Fink [IV] and K. J. Børve [VI]. Planning andpreparation of the projects, data analysis and discussion is always team work.For the here presented projects, where my name is first on the author list ofthe publication or manuscript [III, IV, V, VI, VII, VIII], I have been the mainresponsible and been in charge of the manuscript writing.

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