Computational study of the anion photoelectron spectra of fexn (x = 0, s and n = 3, 4) clusters

PES photoelectron spectroscopyRASPT2 restricted active space second order perturbation theory RASSCF restricted active space self-consistent field RE relative energy RHF restricted Hartr

CELESTIJNENLAAN 200F BOX 2404 B-3001 HEVERLEE, BELGIUM

Computational Study of the

(X = O, S and n = 3, 4) Clusters

Van Tan Tran

Dissertation presented in partial fulfilment of the requirements for the degree of Doctor in Chemistry

December 2013 Promoter:

Prof Dr Marc Hendrickx

Computational Study of the Anion Photoelectron Spectra of FeXn

(X = O, S and n = 3, 4) Clusters

Van Tan Tran

Jury:

Prof Dr Arnout Ceulemans, chair

Prof Dr Marc Hendrickx, promotor

Prof Dr Luc Van Meervelt

Prof Dr Minh Tho Nguyen

Prof Dr Ewald Janssens

Prof Dr Paul Geerlings

(Vrije Universiteit Brussel)

Dissertation presented in partialfulfilment of the requirements forthe degree of Doctor in Chemistry

December 2013

Alle rechten voorbehouden Niets uit deze uitgave mag worden vermenigvuldigden/of openbaar gemaakt worden door middel van druk, fotocopie, microfilm,elektronisch of op welke andere wijze ook zonder voorafgaande schriftelijketoestemming van de uitgever.

All rights reserved No part of the publication may be reproduced in any form byprint, photoprint, microfilm or any other means without written permission fromthe publisher

D/2013/10.705/83

ISBN 978-90-8649-668-6

mysterious It is the fundamental emotion which stands

at the cradle of true art and true science.”

ALBERTEINSTEIN

This work would not have been possible without the help from many wonderful people who gave their support in different ways To them I would like to express my deepest gratitude and sincere appreciation.

First and foremost, I would like to express my gratitude to my supervisor, Prof Marc Hendrickx, for his patient guidance and enthusiastic encouragement during my PhD.

I am especially grateful to Prof Tran Thanh Hue at the Hanoi National University of Education in Vietnam for introducing me to the world of computational chemistry and for his advice and assistance in keeping my progress on schedule.

I would like to send special thanks to Prof Minh Tho Nguyen and Prof Thierry Verbiest for the courses during my first year of my doctoral studies I’m really benefited from the material offered.

I would like to thank the jury members for taking time reading my thesis Their suggestions and corrections really improve my the thesis.

Many thanks I would like to send to my colleagues at Dong Thap University who provided all the convenient conditions for me to study abroad Especially, I would like

to thank Dr Tran Quoc Tri who does a lot of teaching work when I disappear from the university.

i

I am deeply grateful to financial supports from the 322 Scholarship Foundation of Vietnamese Government and from the KU Leuven Without these financial supports, I could not have a chance to finish the thesis.

I would like to thanks Rita Jungbluth for all her kind help for the administration of

my study in Leuven Also, I would wish to thank Hans Vansweevelt for his support concerning all possible computing difficulties I encountered during my PhD.

I am indebted to all my friends here in Leuven, thank you for your understanding and encouragement in my many moments of crisis Your friendship makes my life a wonderful experience.

Lastly, I dedicate this thesis to my parents, my wife and my son who supported and encouraged me to keep going to finalize this thesis.

Van Tan Tran

Leuven, December 2013

Hoofdstuk 1 geeft een overzicht van de technieken die in de experimentelestudies aangewend worden Hieruit blijkt dat anionfoto-elektronspectroscopieonmiskenbaar één van de belangrijkste methoden is voor het bestuderen van destructurele en elektronische eigenschappen van kleine clusters die een transitieme-taalcentrum bevatten Inderdaad, in de literatuur kan een groot aantal spectra voordeze soort clusters teruggevonden worden, die weliswaar waardevolle informatiebevatten betreffende verschillende spectroscopische parameters maar niet steedseen eenduidige conclusie toelaten aangaande de onderliggende geometrische enelektronische structuur Tot heden is de interpretatie van de foto-elektronspectravooral uitgevoerd op DFT-niveau, zodat heel wat vragen onbeantwoord bleven.

iii

Het volgende hoofdstuk beschrijft in detail de basisprincipes van spectroscopie en de aangewende kwantumchemische technieken De elektronischeselectieregels die nodig zijn voor de interpretatie van de spectra worden in detailafgeleid Ook het Franck–Condonprincipe dat in dit werk wordt toegepast om dewaargenomen vibrationele progressies te simuleren, wordt eveneens gẹntroduceerd.Alle aangewende computationele kwantumchemische methoden, zoals DFT,CASPT2, RASPT2 en RCCSD(T) worden op een kwalitatieve wijze omschreven.Het derde hoofdstuk toont aan hoe deze computationele technieken wordenaangewend om de elektronische structuur van de FeO3 en FeO3 − clusters teonderzoeken Meer specifiek, geometrieën van alle relevante spinmultipliciteitenwerden zonder enige symmetriebeperkingen geoptimaliseerd op het BP86/QZVP-niveau en verder verfijnd met de CASPT2- en RCCSD(T)-methoden Beidebevestigen dat alle laaggelegen elektronische toestanden die relevant zijn voor debeschrijving van het foto-elektronspectrum overeenkomen met of sterk gelijken

foto-elektron-op een vlakke D 3h-structuur zonder bindingen tussen de drie zuurstofionen.Afhankelijk van de gebruikte rekenmethode, kan de grondtoestand van hetFeO3−-anion ofwel 2E00 of 4A02 zijn CASPT2 berekent het 4A02 als de laagsteenergietoestand, terwijl RCCSD(T) het 2E00 als grondtoestand voorspelt Detwee laagste bindingsenergiebanden van de foto-elektronspectrum van FeO3−kunnen zonder twijfel alleen worden toegeschreven aan één-elektron ionisatiesvanuit de2E00-toestand De eerste band is het resultaat van een overgang naar

de 1A01-grondtoestand van FeO3, terwijl de tweede band afkomstig is van deeerste aangeslagen 3E00-toestand Uit een harmonische vibrationele analysevan de symmetrische stretching mode bleek dat de waargenomen vibrationeleprogressies van deze twee banden in het experimentele foto-elektronspectrumook in overeenstemming zijn met de RCCSD(T)-assignatie Een moleculaireorbitaalanalyse leidde overduidelijk tot de conclusie dat de elektronische structuurvan de grondtoestanden van de anionische en neutrale clusters respectievelijkovereenkomen met een oxidatietoestand +5 en +6 voor ijzer

De relatieve stabiliteit van alle laaggelegen isomeren van de FeO4−/0-clusters werdenbestudeerd in hoofdstuk 4 Voor zowel de anionische en neutrale clusters, bleekhet bepalen van de meest stabiele structuur een veeleisende taak Zowel DFTals CASPT2 plaatsen de doublettoestand van het tetrặdrische O4Fe-isomeer datopgebouwd is uit vier onafhankelijke O2−atomaire liganden, aanzienlijk lager, tot

SAMENVATTING V

0,81 eV, dan de doublettoestand van hetη2-(O2)FeO2− Dit laatste isomeer bezitslechts twee atomaire O2−-liganden en één moleculair O22−-ligand dat zijdelings aanhet ijzerkation is gebonden De RCCSD(T)-methode reduceert dit energieverschiltot minder dan 0,01 eV Enkel deze gelijke stabiliteit van de grondtoestanden van

O4Fe−enη2-(O2)FeO2−leidt tot een volledige assignatie van de experimentelefoto-elektronspectra van FeO4− De laagste bindingsenergieband (X-band) wordttoegeschreven aan de ionisatie 2A1 naar 1A1 van het η2-(O2)FeO2−, terwijl deeerstvolgende hogere energieband (A-band) het gevolg is van de overgang van2Enaar1A1tussen de O4Fe−/0-conformaties Voor een specifiek isomeer, berekentCASPT2 de beste ionisatie-energieën De hoogste piek in de A-band met de zwaksteintensiteit, kan eventueel worden toegeschreven aan de overgang van2A2naar3A2vanη2-(O2)FeO2 Beide progressies in het experimentele spectrum zijn het resultaatvan ionisaties vanuit de antibindende orbitalen met overheersend ijzer-3d-karakter.Een Franck–Condonsimulatie van de waargenomen vibrationele progressies zoalsdeze werd uitgevoerd met BPW91, bevestigde de voorgestelde assignaties

Geometrische structuren van FeS3en FeS3−met spinmultipliciteiten variërendvan singlet tot octet werden in hoofdstuk 5 geoptimaliseerd op het B3LYP-niveau, waardoor twee laaggelegen isomeren voor deze clusters konden worden

geïdentificeerd Het planaire isomeer bezit een D 3h-symmetrie en bevat drie

S2−-atomaire liganden (S3Fe−/0), terwijl de C 2v structuur, naast een atomair

S2−-ligand een S22−-ligand bevat dat zijdelings gebonden is aan het ijzerkation:een η2-(S2)FeS isomeer Vervolgens werden de energieverschillen tussen deverschillende toestanden van deze twee isomeren geschat door het uitvoeren vangeometrie-optimalisaties met de multireferentie CASPT2-methode Verschillendeconcurrerende structuren voor de grondtoestand van de anionische cluster werdenherkend op dit niveau De relatieve stabiliteiten werden ook geschat door single-point RCSSD(T)-berekeningen uitvoeren op de B3LYP-geometrieën Het5B2werdondubbelzinnig aangeduid als de grondtoestand van het neutrale complex De aardvan de grondtoestand van het anion daarentegen is aanzienlijk minder zeker De

14B2-, 24B2-,4B1- en6A1-toestanden werden allemaal gevonden als laaggelegen

η2-(S2)FeS−-toestanden Ook het4B2van S3Fe−heeft een vergelijkbare energie Hiermee in tegenstelling, plaatsen B3LYP en RCCSD(T) gezamenlijk deze

CASPT2-S3Fe−toestand op een veel hogere energie Energetisch, kunnen op het niveau alle banden van de foto-elektronspectra van FeS3 −gereproduceerd wordenals ionisaties vanuit ofwel de4B - of de6A -toestand van hetη2-(S )FeS− Echter,

CASPT2-uit de Franck–Condonsimulaties, die verkregen werden door een harmonischevibrationele analyse uit te voeren op het B3LYP niveau, blijkt dat alleen deionisatie van4B2naar5B2, waarbij de structuur η2-(S2)FeS behouden blijft, debeste overeenkomst-qua vibrationele progressie bezit met de X-band van hetexperimentele foto-elektronspectrum.

De B3LYP, CASPT2 en RCCSD(T) computationele methoden werden eveneens inhoofdstuk 6 succesvol aangewend voor de interpretatie van de foto-elektronspectravan de FeS4−-stoichiometrie door het berekenen van de geometrische structurenvan alle mogelijke laaggelegen FeS4 −/0-isomeren De 4B1g-toestand van het(η2-(S2))2Fe−-isomeer met twee S22−-moleculaire liganden zijdelings gebonden op

een D 2h-wijze aan het centrale ijzer(III)kation, wordt eenduidig als grondtoestandvan de anionische cluster voorspeld en de experimentele foto-elektronspectrawerden met CASPT2 toegewezen als afkomstig van dit isomeer De complexevibrationele structuur van de laagste energie X-band is het resultaat van ionisa-tietransities naar de3B3g-,5B1u- en5B1g-toestanden van de neutrale cluster, dieenergetisch erg dicht bij elkaar gelegen zijn Een analyse van de CASSCF-orbitalengeeft een quasi ontaarding aan van de niet-bindende 3d-orbitalen van het ijzerkation

en deπ∗-valentie-orbitalen van het moleculaire S22−-ligand Alle experimenteelwaargenomen hogere ionisatie-energiebanden kunnen theoretisch toegekendworden als zijnde afkomstig van de voorgestelde anionische grondtoestand dooronthechting van een elektron uit één van deze ijzer(III)- of ligandorbitalen

ADE adiabatic detachment energy

ANO atomic natural orbital

CASPT2 complete active space second order perturbation theory

CASSCF complete active space self-consistent field

CC coupled-cluster

CCSD coupled-cluster with single and double excitations

CCSD(T) coupled-cluster with single and double and

perturbative triple excitations

CCSDT coupled-cluster with single, double, and triple excitations

CISD configuration interaction including single and double excitations

CISDT configuration interaction including single, double,

and triple excitations

CSF configuration state function

DFT density functional theory

FCF Franck–Condon factor

GGA generalized gradient approximation

GTF Gaussian type function

GTO Gaussian type orbital

HF Hartree–Fock

LDA local-density approximation

LSDA local-spin density approximation

MCSCF multi-configuration self-consistent field

meta-GGA meta-generalized gradient approximation

MPn Møller–Plesset perturbation theory of order n

MRCI multi-reference configuration interaction

vii

PES photoelectron spectroscopy

RASPT2 restricted active space second order perturbation theory

RASSCF restricted active space self-consistent field

RE relative energy

RHF restricted Hartree–Fock

ROHF restricted open-shell Hartree–Fock

RCCSD(T) restricted coupled-cluster with single and double and

perturbative triple excitations

UHF unrestricted Hartree–Fock

VDE vertical detachment energy

ZPE zero-point energy

2 Photoelectron spectroscopy and computational approach 15

2.1 Basic principles of photoelectron spectroscopy 15

2.2 The photoelectron spectrometer 16

2.3 Interpretation of photoelectron spectra 17

2.4 Selection rules 19

2.5 Electronic selection rules 20

2.6 Vibrational selection rules 22

2.7 Interpretation of the spectra: electron binding energy 25

2.8 Interpretation of the spectra: Franck–Condon simulations 26

2.9 The Schrödinger equation 27

2.10 Wave functions for many-electron systems 28

2.11 The Hartree–Fock method 30

2.12 Electron correlation 31

2.13 Coupled-cluster theory 32

2.14 CASSCF, RASCSF, CASPT2, and RASPT2 methods 33

2.15 Density functional theory 36

ix

2.16 Basis sets 37

3 In search for the ground state of FeO3− 43 3.1 Introduction 43

3.2 Computational methods 45

3.3 Results and discussion 46

3.4 Conclusion 62

4 Which is the most stable isomer of FeO4 −? 67 4.1 Introduction 67

4.2 Computational methods 70

4.3 Results and discussion 72

4.4 Conclusion 87

5 Nearly degenerate low-lying electronic states of FeS3− 91 5.1 Introduction 91

5.2 Computational methods 93

5.3 Results and discussion 95

5.4 Conclusion 110

6 Unraveling the complex X band of the photoelectron spectra of FeS4− 115 6.1 Introduction 115

6.2 Computational methods 116

6.3 Results and discussion 119

6.4 Conclusion 132

7 General conclusions and perspectives 137

A Supplements to chapter 5 149

B Supplements to chapter 6 151 List of publications 153

List of Figures

2.1 The principal components of a photoelectron spectrometer 172.2 Photoelectron spectrum of FeO3−as recorded with 4.66 eV photonenergy 182.3 Potential energy curves of diatomic molecules illustrating the vibra-tional structure of photoelectron spectra 232.4 Illustration of the CASSCF and RASSCF wave function 35

3.1 (a) Choice of the coordination system for the CASPT2 calculations.(b) Qualitative orbital energy scheme for the valence d orbitals 453.2 Structures (bond distances in Ångstroms and bond angles in degrees)and relative energies (eV) of FeO3 and FeO3 − as obtained byBP86/QZVP calculations M is the spin multiplicity with even valuesfor the anions and odd values for neutral clusters 473.3 Structures (bond distances in Ångstroms and bond angles in degrees)and relative energies (eV) for the low lying states of FeO3and FeO3−

as obtained by CASPT2 geometry optimizations 493.4 CASPT2 (using small ANO-RCC basis sets) potential energy curves of

the symmetric Fe–O bond stretch (D 3hsymmetry) 503.5 Pseudonatural molecular orbital plots and their occupation numbersfor the4B2state (FeO3 −) as calculated by CASSCF (small ANO-RCCbasis sets) 53

xi

3.6 Photoelectron spectrum of FeO3− taken from ref 10 Abscissa:binding energies in electronvolts Ordinate: relative electron intensities 573.7 Simulated vibrational progression on the basis of harmonic Franck–Condon factors for the symmetric stretch of the three lowest energyelectron detachment processes Peak positions derived from CASPT2energies, BP86/QZVP zero-point energies, and CASPT2 symmetricstretch frequencies Abscissa: binding energy in eV Ordinate: relativetransition probabilities 61

4.1 Coordinate systems for FeO4−/0as employed during the CASPT2 andRCCSD(T) calculations 714.2 Structures, symmetries, and relative energies of FeO4−/0as calculated

at the BPW91/aug-cc-pVTZ level M is the spin multiplicity with evenvalues for the anions and odd values for neutral clusters 744.3 Potential energy curves for the ground states of O4Fe−/0calculated

at the CASPT2 level for the symmetric stretching mode of the Fe–O

bond in T dsymmetry 76

4.4 CASSCF pseudo-natural orbitals of the active space for the2A1state

of O4Fe−and their occupation numbers in parentheses 794.5 CASSCF pseudo-natural orbitals of the active space for the2A2state

ofη2-(O2)FeO2−and their occupation numbers in parentheses 804.6 Franck–Condon simulations by using the harmonic vibrationalfrequency analyses at the BPW91 level (a) Simulation of the X bandstarting at 3.30 eV, (b) simulation of the intense peaks of the A bandstarting at 3.84 eV, and (c) single peak, that is, tentative assigned as thehighest energy peak of the A band Abscissa: vibrational frequency in

cm−1 Ordinate: relative transition probabilities 834.7 Photoelectron spectrum of FeO4−as recorded with 4.66 eV photonenergy (taken from Ref 7) On the abscissa, the binding energies aregiven in eV and arbitrary units for the intensity in the ordinate 84

LIST OF FIGURES XIII

5.1 Choice of coordinate systems for the CASPT2 and RCCSD(T) lations and qualitative orbital energy schemes for the valence 3dorbitals as derived from the CASPT2 results for (a) S3Fe−/0and (b)

calcu-η2-(S2)FeS−/0 945.2 Calculated structures for the relevant low-energy spin multiplicities

of FeS3and FeS3−at the B3LYP/QZVP level and their relative energies

in electronvolts M is the spin multiplicity with even values for theanions and odd values for neutral clusters 965.3 Photoelectron spectrum of FeS3 −taken from ref 11 as recorded usinglaser detachment photons of 193 nm Arrows indicate the calculatedCASPT2 vertical detachment energies expressed in electronvolts 1025.4 CASSCF natural orbitals for the4B2state of the S3Fe−isomer classifiedaccording to their symmetry and natural occupation numbers inparentheses The type of predominant iron 3d orbitals is alsoindicated 1045.5 CASSCF natural orbitals for the4B2initial state of theη2-(S2)FeS−isomer classified according to their symmetry and natural occupationnumbers in parentheses The type of predominant iron 3d orbitals isalso indicated 1065.6 Calculated Franck–Condon factors at the B3LYP level for theη2-(S2)FeSisomer Relative transition probabilities (in arbitrary units) for the (a)

4B2A5B2and (b)6A1A5B2ionizations The inset in panel a depictsthe experimental vibrational progression of the X band as obtainedwith 355-nm detachment photons in ref 11 109

6.1 Coordinate systems of D 2h (a) and D 2d(b) structures of (η2-(S2))2Fe−/0,

and C 2vstructure ofη2-(S3)FeS−/0(c) as used in the DFT, CASPT2 andRCCSD(T) calculations 1186.2 Qualitative orbital diagram showing the state average CASSCFpseudo-natural orbitals of the4B1gground state of the (η2-(S2))2Fe−cluster The occupation of the orbitals refers to the leading configura-tion of this state 123

6.3 Photoelectron spectra of FeS4−as recorded at 193 nm (a) and 355 nm(b) photon energies.[14] Abscissa: binding energies in electronvolts.Ordinate: relative electron intensities Arrows represent the verticaldetachment energies (VDE) calculated at the CASPT2 level 1266.4 Qualitative state diagram explaining the origin of the X, A and F bands.Because of the small exchange energy between the metal 3d orbitalsand theπ∗orbitals, there is a small splitting between the3B1uand

5B1ustates The original larger splitting between the5B1g on theone hand and the3B1gand3B3g(3d exchange energy) is reduced byconfiguration interaction 1306.5 B3LYP Franck–Condon factor simulations for the4B3gA3B3g(a),

4B3gA5B1u(b),4B3gA5B1g(c) ionizations starting at 3.20, 2.99,and 3.19 eV, respectively Abscissa: vibrational frequency in cm−1.Ordinate: relative transition probabilities Displacement vectors ofthe vibrational modes responsible for the corresponding calculatedvibrational progressions are depicted as insets 131

A.1 CASPT2 optimized structures and relative energies in eV of the lying states of FeS3−/0 149

low-B.1 State-average CASSCF pseudo-natural orbitals and the electronoccupation numbers in the active space of the 6A1 state of D 2d

(η2-(S2))2Fe−cluster with two S2ligands perpendicular together 151B.2 State-average CASSCF pseudo-natural orbitals and the electronoccupation numbers in the active space of the6A1state ofη2-(S3)FeS−cluster 152

List of Tables

3.1 Relative energies (RE), harmonic vibrational frequencies (cm−1), andintensities (km/mol) for the two studied isomers of FeO3and FeO3 −

at the BP86/QZVP level 483.2 Vertical detachment energies (VDE) from the4B2state as calculated

by CASPT2 with small ANO-RCC basis sets 503.3 Vertical detachment energies (VDE) from the2A2state as calculated

by (a) CASPT2 with small ANO-RCC basis sets and (b) CASPT2 withlarge ANO-RCC basis sets 513.4 Relative CASPT2 energies for the iron trioxides FeO3and FeO3 − (a)CASPT2 single point calculations with small ANO-RCC basis sets atBP86/QZVP geometries (b) CASPT2 geometry optimizations withsmall ANO-RCC basis sets (c) CASPT2 single point calculation withlarge ANO-RCC basis sets at geometries (b) 523.5 Mulliken population analysis charges for low-lying states of the FeO3and FeO3−clusters as obtained from the CASPT2 wave functions 553.6 Relative energies (eV) of the low-lying states of O3Fe−/0as calculatedwith RCCSD(T) 59

4.1 Relative energies (RE) and frequencies of O4Fe−/0 calculated atBPW91/aug-cc-pVTZ level (a) Calculated from the doublet of O4Fe−,(b) calculated from the doublet ofη2-(O2)FeO2 −, and (c) calculatedfrom the doublet ofη1-(O2)FeO2− 73

xv

4.2 Estimated CASPT2 adiabatic and vertical detachment energies (a)Relative energies with respect to the2E (2A1,2A2) state of O4Fe−asobtained by using the BPW91 optimized structures For a specificspin multiplicity of a particular conformation the lowest energydifference represents an estimate for the adiabatic detachment energy.(b) Ditto (a) but calculated from the2A2state ofη2-(O2)FeO2− (c)Vertical detachment energies from the2E (2A1,2A2) ground state of

O4Fe− (d) Vertical detachment energies from the2A2ground state of

η2-(O2)FeO2− 784.3 Basis set influence on the calculated relative energies (eV) for variousstates RCCSD(T) results obtained for the triple (3-ζ), quadruple (4-ζ),

and quintuple (5-ζ) zeta basis sets by using the corresponding BPW91

equilibrium structures 85

5.1 Relative energies (REs) and harmonic vibrational frequencies for theconsidered spin multiplicities of FeS3and FeS3 −as calculated at theB3LYP/QZVP level 975.2 Relative energies (REs) and harmonic frequencies for the totallysymmetric vibrational modes of the low-lying states of FeS3−/0asobtained by CASPT2 geometry optimizations 995.3 RCCSD(T) relative energies (eV) with respect to the4B2state of

η2-(S2)FeS− for relevant low-lying states of FeS3−/0 (a) For thesmallest basis set (aug-cc-pVTZ) only the valence electrons of iron(3d and 4s) and sulfur (3s and 3p) are correlated, whereas for the twolarger basis sets, aug-cc-pwCVTZ and aug-cc-pwCVQZ, the outer core

of iron (3s and 3p) is also correlated (b) Calculation did not convergebecause of persistent oscillations 1005.4 Vertical relative energies (VREs) for the lowest one-electron ion-izations as calculated for the4B2state (upper part) and2B1state(lower part) of the S3Fe−isomer by multistate (two-root) CASPT2 (a)Denotes the molecular orbital that is ionized for the specific electron-detachment process (b) Relative energy with respect to2A2at thegeometry of2B 103

LIST OF TABLES XVII

5.5 Vertical detachment energies (VDEs) for the lowest one-electronionizations as calculated for the6A1state (upper part) and the4B2state (lower part) of theη2-(S2)FeS−isomer by multistate (four-state)CASPT2 (a) Denotes the molecular orbital that is ionized for thespecific electron-detachment process with its predominant character

in parentheses (b) Calculated as an average of two states (c)Calculated as an average of six states (d) Calculated as an average ofeight states 107

6.1 B3LYP relative energies (RE) and structural parameters of low-lyingstates for different isomers of the FeS4−/0stoichiometries 1206.2 Relative energies (RE) and structural parameters of low-lying states of(η2-(S2))2Fe−/0andη2-(S3)FeS−/0as calculated by CASPT2 geometryoptimizations (a) single-point calculations employing the B3LYPgeometry 1226.3 Relative energies (RE) and structural parameters for low-lying states

of (η2-(S2))2Fe−/0andη2-(S3)FeS−/0as calculated with RCCSD(T) (a)Geometry optimization with the triple-ζ basis sets without iron outer-

core correlation, (b) single-point calculations with the quadruple-ζ

basis sets including iron outer-core correlation 1246.4 Vertical detachment energies (VDEs) of (η2-(S2))2Fe−as calculatedwith CASPT2 (a) Orbitals from which an electron is removed duringthe ionization process from the4B1gground state 128

Chapter 1

Introduction

Transition metal-containing compounds are very important for our modern society.The presence of these compounds is found in industrial catalysis, medicine, andbiological storage and transport.[1–3] According to the periodic table, transitionmetals are all the elements of the d-block, including groups 3 to 12 In compounds,

these metals have an ability to lose multiple electrons from their valence nd and (n + 1)s orbitals to create cations which usually have open-shell electronic

configurations Because of their rather exceptional electronic structures, includingelectronic near-degeneracy effects, transition metal compounds have a wide range

of physical and chemical applications However, a detailed investigation of theelectronic structures of these rather large molecular systems represents an extremelyimportant challenge for understanding their properties On the other hand, thesmaller sized transition metal-containing compounds in the gas phase such as

MCn−/0, MOn−/0and MSn−/0, which contain one transition metal center, have beenextensively investigated by theoretical and experimental techniques.[4–18] Sincethese compounds are synthesized by clusterification processes, they are frequentlydenoted in the literature as clusters Further, because they are stable chemicalidentities in the gas phase, it is also acceptable to describe them as molecules ormore specifically as transition metal complexes In spite of their small sizes, theseclusters are of importance because they represent fundamental building blocks forlarger clusters Therefore, getting an insight into the electronic structures of small

1

clusters could be beneficial for understanding the properties of larger transitionmetal compounds.

Experimentally, these small clusters are generated in plasma reactions of laserablated pure transition metals that are mixed with a helium carrier gas containing

a suitable gas, or are produced by laser vaporization of solid targets of variouscomposition.[5, 6, 9, 12–18] In particular, in order to create iron oxide clusters [6, 13,14], an intense pulsed laser beam is concentrated onto a pure iron target to produce

a plasma containing iron atoms and ions A helium carrier gas with 0.5% O2is mixedwith the plasma to produce FexOy−/0clusters Otherwise, iron sulfide clusters[16]are produced by laser vaporization of a mixed Fe/S target (10/1 ratio) in the presence

of a helium carrier gas Transition metal carbides FexCy−/0clusters[9, 17, 18] areformed either by plasma reactions between laser-ablated metal atoms or ions and ahelium carrier gas containing 5% CH4or by laser vaporization of a transition metalcarbide target Generally, as a result of these uncontrollable clusterification reactions,different uncharged and charged clusters containing a different number of atoms areobserved Additionally, each specific stoichiometric cluster is able to have severalisomers of almost the same stability Therefore, in subsequent steps a particularstoichiometric cluster is selected and its structural and electronic properties can beprobed by an appropriate experimental technique

In the experiments that we will consider in this work, only singly charged anionicclusters containing a single transition metal center are selected, which can beachieved by using a time-of-flight mass spectrometer.[15, 19–21] During this massselection, all equally charged anionic clusters are accelerated by an electrostatic field

to have equally kinetic energies These clusters are then allowed to move through the

free-flight drift tube towards the detector Depending on the mass-to-charge (m/z)

ratio, different clusters strike on the detector at different times Clusters with smallermass-to-charge ratio will fly faster and reach the detector first, while clusters withlarger mass-to-charge ratio will arrive later Measuring the time needed for a cluster

to fly to the detector in a very accurate way, usually in the rage of nanoseconds (ns),allows to separate clusters with different mass-to-charge ratios

Alternatively, following the mass selection, the electronic structures of the selectedanionic clusters and of the corresponding neutral clusters can be investigated

by using photoelectron spectroscopy.[15, 21–23] In this step, a specific anioniccluster is irradiated by a laser beam which induces ionization By collecting the

INTRODUCTION 3

detached electrons and measuring their kinetic energies, a photoelectron spectrum

is recorded which typically contains a series of peaks and bands In the mostsimple interpretation, each band in a photoelectron spectrum corresponds to aremoval of one electron from a particular orbital The starting point position ofeach band is usually interpreted as the adiabatic electron detachment energy ofthe corresponding band High resolution photoelectron spectra are observed bylowering the energy of the photons of the detachment laser beam, while higherionization energies are accessible by increasing the photon energy

More specifically, anion photoelectron spectroscopy is widely used to investigate theelectronic structure of neutral transition metal compounds Indeed, an electron can

be detached from any molecular orbital of the anionic ground state, provided thatthe photon energy of the beam is high enough Therefore, some low-lying electronicstates of the neutral cluster are seen in the photoelectron spectrum Moreover,when the structural difference between the initial anionic and final electronicstate is large enough, vibrational progressions are additionally observed, whichare usually the result of transitions between the vibrational ground state of theanionic electronic ground state and several vibrational levels of the neutral finalstate In these circumstances the vibrational frequencies of the final neutral stateare measurable In some spectra hot bands at the low energy side of a band are seen.Since these arise from a detachment out of an excited vibrational level, they affordvibrational frequencies for the initial state of the anionic cluster

As a conclusion it is possible to state that anion photoelectron spectra provideinformation about the electron affinity, the relative energies of low-lying statesand vibrational frequencies of the anionic and neutral cluster However, suchinformation is not sufficient for a clear understanding of the geometric andelectronic structures of the compounds studied For instance, it is not possible

to determine with absolute certainty which isomers of the cluster contribute tothe spectra Therefore, quantum chemical calculations are needed to obtain thestructural, electronic, and vibrational properties of the considered clusters

In addition to photoelectron spectroscopy, the vibrational properties of smallclusters have also been investigated by infrared matrix isolation spectroscopy.[4, 5,

8, 11] All products formed in the reactions between laser-ablated metal atoms and anoble gas carrier containing a second suitable gas, are trapped within a solid matrix

of the noble gas at very low temperatures In this way vibrational absorption bands

of different clusters have been recorded by infrared spectroscopy This technique isvery useful for studying clusters because it isolates different isomers into the frozenmatrix, prevents them from further chemical interaction, and therefore rendersevidence for the existence of different isomers as they are produced during theformation process Also, frequencies of asymmetric vibrational modes, which cannot

be recorded by photoelectron spectroscopy, can be observed By employing thisinfrared matrix isolation spectroscopy to investigate the reaction between ironatoms and oxygen molecules, the existence of the side-on and the end-on bounddioxygen-iron dioxide complexes, which are respectively denoted asη1-(O2)FeO2andη2-(O2)FeO2, was proposed.[5, 7, 8] Otherwise, the reactions between smallsized sulfur molecules with laser-ablated iron atoms were also studied with thesame technique, and allowed to identify theη2-(S2)2Fe cluster, which contains two

S2ligands side-on bound to iron.[11] For this identification the comparison of theobserved vibrational frequencies with density functional theory results proved to bevery helpful.[7, 8, 11]

As already mentioned, computational chemistry, which uses quantum mechanics todirectly calculate many different molecular properties, represents a very valuabletool to investigate the electronic structures of small transition metal-containingclusters.[7, 11, 18, 24–27] Geometric and electronic structures, potential energysurfaces, harmonic vibrational frequencies, and ionization energies are a fewexamples of what computational chemistry can predict The calculated resultshave the potential to assign the recorded photoelectron spectra It is very well-known that clusters containing transition metals still remain as a difficult challengefor quantum chemists, because of the complex electron correlation effects in thiskind of systems Qualitatively, the correlation energy is divided into the dynamicalcorrelation which arises from the correlated motion of each electron with everyother electron, and a non-dynamical (static) part which originates from a certainnumber of frontier molecular orbitals that are quasi-degenerate The latter effectoccurs frequently in transition metal complexes

In order to recover a sufficient amount of dynamical correlation energy, electroncorrelation methods such as perturbation theory (MP2, MP3, ), configuration in-teraction (CISD, CISDT, ), or coupled-cluster theory (CCSD, CCSD(T), CCSDT, )must be used These methods are usually called post-Hartree–Fock methods becausethey use a single reference Hartree–Fock wave function as a starting point In spite

The non-dynamical correlation is best dealt with by using the multi-configurationself-consistent field (MCSCF) method In order to include the dynamical correlationenergy, a second-order perturbation treatment or a single and double excitationconfiguration interaction step will be included in the calculations by using theMCSCF wave function as a reference, which results in the so-called CASPT2(complete active-space self-consistent field second-order perturbation theory) orMRCI (multi-reference configuration interaction) method, respectively.[24–26, 29–33] However, because MRCI is very time-consuming, even for diatomic clusters, itsapplication to transition metal compounds is limited In contrast, the CASPT2method, which has the ability to calculate all low-lying electronic states in anacceptable computational time, has been successfully applied to study the electronicstructure of clusters from small to medium size.[24–26, 32–36] It should be notedthat the success of the CASPT2 method depends very much on the choice of theactive space orbitals In principle, larger active spaces will give better results,but there are no absolute rules for selecting a good active space, and thereforedifferent kinds of active spaces must be tested for a specific chemical system.Nowadays, most of the computer installations allow CASPT2 calculations with amaximum around 17 active space orbitals In those cases that would require alarger active space, RASPT2 -restricted active space self-consistent field (RASSCF)followed by a second-order perturbation theory calculation- represents a promisingcomputational instrument.[36–38]

Another electron correlation technique, which is very popular for studying transitionmetal compounds due to its low computational cost, is density functional theory[5, 11, 18, 39, 40] in all its forms (DFT) These methods are applicable to a largeamount of chemical systems containing from a few to more than a hundred atoms.However, the problem that makes it less sufficient than other electron correlationmethods is that the exact form of the exchange-correlation functional is not known,

and therefore, the use of different approximate functionals may lead to differentresults.[39–41] This problem becomes more crucial when density functional theory

is applied to small transition metal compounds because the prediction of the lowestelectronic state and the most stable isomer appear to be very sensitive to the choice

of the functional This means that by changing the functional, the ground electronicstate or even the most stable isomer of a specific stoichiometry may vary Therefore,

it is very important to always verify whether a functional is appropriate for a specificproperty such as harmonic vibrational frequency, geometry, or relative energies ofthe considered chemical systems, before drawing final conclusions

In addition to the electronic correlation effect, relativistic effects must be sidered in quantum chemical calculations on the transition metal-containingcompounds.[42] Especially for compounds containing heavy transition metals,the energetic properties, bond lengths, and therefore bond strengths are affectedwhen relativistic effects are included The theoretical basis for relativistic quantumchemistry is the four-component Dirac equations However, because solving theDirac equations is very demanding, the Dirac operator is transformed into a two-component form and then is further reduced By assuming that spin-orbit coupling

con-is small, scalar relativcon-istic effects are easily included in the non-relativcon-istic quantumchemical calculations by adding the Douglas–Kroll–Hess Hamiltonian to the one-electron part of the Hamiltonian [43, 44] In this thesis, the scalar relativistic Douglas–Kroll–Hess Hamiltonian is included in both the CASPT2 and CCSD(T) calculations asimplemented in the MOLCAS[45] and MOLPRO[46] quantum chemistry packages.The structural and electronic properties of small clusters containing transitionmetals and carbon, oxygen, or sulfur have been extensively investigated with thephotoelectron spectroscopy technique Indeed, in the literature a large amount ofstudies about different kinds of anionic clusters can be found For instance, for thetransition metal-carbon clusters, the vibrational resolved spectra of MC2−(M = Sc,

V, Cr, Mn, Fe, and Co) [9, 18], MC3−(M = Sc, V, Cr, Mn, Fe, Co, and Ni) [12, 18], CrCn−

(n = 2–8) [18], NbC n−(n = 2–7) [17], TiC n−(n = 2–5) [47], and FeC n−(n = 2–5) [48]

are available Further, for the transition metal-oxygen clusters, the photoelectronspectra of ScOn−(n = 1–4) [49, 50], TiO n−(n = 1–3) [51], VO n−(n = 1–4) [52], CrO n−(n = 1–5) [53], MnO n−(n = 1–3) [54], FeO n−(n = 1–4) [6, 13, 14], NiO n−(n = 1, 2)

[55], CuOn−(n = 1–6) [15, 56], YO n−(n = 1–5) [50], ZrO2−[57], MOn−(M = Mo, W; n

= 3–5) [58], AuOn−(n = 1,2) [59], and ReO n−(n = 2, 3) [60] were reported Finally, the

INTRODUCTION 7

spectra of transition metal-sulfur clusters, i.e., FeSn−(n = 1–6) [16, 61–63], AgS n−

(n = 1–5) [63], MnS n−(n = 1–10) [64], AuS n−(n = 1, 2) [59], and MS n−(M = Mo,

W; n = 1–12)[65], were also measured in detail Overall, these spectra give very

valuable, yet incomplete information about the underlying structural and electronicproperties To understand these spectra fully, quantum chemical calculations areneeded, which is the reason as to why computational results, mostly at the DFT level,are occasionally included in the publications

The interpretation of these anion photoelectron spectra needs to be performed

at high quantum chemical computational levels because of their complicatedgeometric, electronic, and vibrational properties.[24, 25, 28, 34, 35, 49, 57, 66]

In many cases, each stoichiometric cluster has a few isomers with almost thesame stability, and even within one specific isomer, there are quasi-degenerateelectronic states Such near degeneracy effects makes the identification of thecorrect isomer and initial state of the anionic cluster for the interpretation of thespectra, a difficult task For some anionic clusters, there is even a contribution of twoisomers to the experimental spectra Up to now, most of the spectra of small clustersare interpreted at the DFT and CASPT2 levels However, DFT is not capable ofunambiguously determining the initial states of the spectra, but is more trustworthyfor the calculation of equilibrium geometries and performing harmonic vibrationalfrequency analysis With a sufficient large active space, the CASPT2 method isefficient to calculate the relative energies of the low-lying excited electronic statesand the ionization energies of different bands in the anion photoelectron spectra.The combination of DFT and CASPT2 for getting an insight into the electronicstructure and for the assignment of the anion photoelectron spectra can be seen inthe specific cases of the ScCn−/0(n = 2, 3) [34], FeC n−/0(n = 2, 3) [35], and FeS n−/0(n = 1, 2) [24, 25] clusters Additionally, the CCSD(T) method has been successfully

applied for clusters such as ScO2−/0[49], CrO3−/0[66], ZrO2−/0[57], and AuXn−(X =

O, S; n = 1, 2) to interpret the corresponding anion photoelectron spectra.

In those cases where there are a few ionization processes with comparable ionizationenergies which contribute to several closely spaced bands of the spectra, Franck–Condon simulations can be very helpful to identify the true sequence of theunderlying ionization processes Indeed, the comparison of the experimental andobserved vibrational progressions offers an additional aid for the correct assignment

of the spectra.[50, 57, 66] For the photoelectron spectra of ScO2 −, the vibrational

progression with a frequency of 740 cm−1of the first band starting at 2.32 eV hasbeen successfully reproduced by carrying out a Franck–Condon factor simulationfor the1A1A2B2detachment at the RCCSD(T) level.[49, 50] Moreover, the 266 nmphoton energy photoelectron spectrum of CrO3−shows a vibrational progression of

887 cm−1for the first band located at 3.66 eV, which was calculated to correspondvery well with the Franck–Condon simulation for the2A10A1A10transition of the

planar C sCrO3−/0clusters.[66]

In this thesis we will study the geometric and electronic structures of FeXn−/0

(X = O, S; n = 3, 4) for the purpose to provide reliable assignments for their

anion photoelectron spectra by using quantum chemical methods Situated inthe middle part of the first-row transition metal series with an electron configuration

of [Ar]3d64s2, iron has a high probability to give rise to highly complex shell electronic structures in the studied compounds which therefore representchallenging compounds to study Moreover, although oxygen and sulfur arecongeners (group 16), they have different electronic properties so that, for aspecific type of stoichiometric cluster, they can bind to the central iron in differentways By applying computational quantum chemical methods, we would like toidentify which is the most stable arrangement of atoms in the studied clusters,and compare them mutually The structural and electronic properties of FeXn−

open-(X = O, S; n = 3, 4) were probed intensively by photoelectron spectroscopy as

reported in several works,[13, 14, 16, 62] and computational quantum chemicalcalculations were also applied to study these clusters In particular, for the FeO3 −/0

clusters, the hybrid B3LYP and pure BP86 and BPW91 functionals were used.[67–69] For the FeO4 −/0clusters, a large number of functionals, for instance, BPW91,PBE∗2, TPSS∗2, B3PW91, and B3LYP, were utilized.[67, 69–71] In addition to densityfunctional theory, multi-configuration self-consistent field (MCSCF), singles anddoubles coupled cluster (CCSD) and the configuration interaction (CISD) resultswere also reported for FeO4 −/0.[72] For FeSn−/0(n = 3, 4), only preliminary pure

density functional theory calculations with the generalized-gradient Perdew–Wangexchange-correlation functional were carried out.[16] On the whole, so far most ofthe calculations carried out on the studied clusters are limited to density functionaltheory It goes without saying that the considered clusters are likely to have complexmultireference wave functions because of the open d shell of iron Therefore, morereliable elaborate quantum chemical data, such as CASPT2 and RCCSD(T) results,are clearly needed These computational data will prove to be essentially used to

INTRODUCTION 9

interpret the available anion photoelectron spectra Conversely, the photoelectronspectra in turn will be a key guidance to us to acquire experience about the employedcomputational methods for investigating transition metal-containing compounds.Seven chapters, including this introduction, are presented in this thesis InChapter 2, we provide a more detailed description of the basic principles ofphotoelectron spectroscopy and the applied computational techniques Theselection rules needed for the assignment of the photoelectron spectra are derived.The Franck–Condon principle which is very important to simulate the vibrationalprogressions of photoelectron spectra is introduced Concerning the computationalmodels employed, essentials about the restricted coupled cluster technique, thecomplete active space self-consistent field (CASSCF) and the related second-orderperturbation based CASPT2 methods are presented in this chapter From Chapter 3

to Chapter 6, the geometric and electronic structures of FeO3−/0, FeO4−/0, FeS3−/0,and FeS4−/0clusters are discussed in full detail, respectively These chapters includeDFT, RCCSD(T), and CASPT2 results for the description of the geometric andelectronic structures of the studied clusters The anion photoelectron spectra

of these clusters will be interpreted by calculating the adiabatic and verticaldetachment energies at various levels of computation Further, in specific cases,Franck–Condon simulations will be compared to the vibrational progressions of thelow-lying bands in the vibrationally resolved spectra Finally, Chapter 7 summarizesthe main results as obtained in this thesis

[3] P.J Sadler, Z.J Guo, Pure Appl Chem., 70 (1998) 863–871.

[4] S Abramowitz, N Acquista, I.W Levin, Chem Phys Lett., 50 (1977) 423–426 [5] L Andrews, G.V Chertihin, A Ricca, C.W Bauschlicher, J Am Chem Soc., 118

(1996) 467–470

[6] J.W Fan, L.S Wang, J Chem Phys., 102 (1995) 8714–8717.

[7] Y Gong, M.F Zhou, L Andrews, Chem Rev (Washington, DC, U S.), 109 (2009)

[13] H.B Wu, S.R Desai, L.S Wang, J Am Chem Soc., 118 (1996) 7434–7434 [14] H.B Wu, S.R Desai, L.S Wang, J Am Chem Soc., 118 (1996) 5296–5301 [15] H.B Wu, S.R Desai, L.S Wang, J Phys Chem A, 101 (1997) 2103–2111.

[16] H.J Zhai, B Kiran, L.S Wang, J Phys Chem A, 107 (2003) 2821–2828.

[17] H.J Zhai, S.R Liu, X Li, L.S Wang, J Chem Phys., 115 (2001) 5170–5178 [18] H.J Zhai, L.S Wang, P Jena, G.L Gutsev, C.W Bauschlicher, J Chem Phys., 120

(2004) 8996–9008

[19] J.H Gross, Mass Spectrometry: A Textbook, Springer 2011

[20] D.L Pavia, G.M Lampman, G.S Kriz, J.R Vyvyan, Introduction to Spectroscopy,Brooks/Cole, 2009

[21] L.S Wang, H.S Cheng, J.W Fan, J Chem Phys., 102 (1995) 9480–9493.

[22] A.M Ellis, M Feher, T.G Wright, Electronic and Photoelectron Spectroscopy:Fundamentals and Case Studies, Cambridge University Press, 2005

[23] J.M Hollas, Modern Spectroscopy, John Wiley & Sons, 2004

[24] S Clima, M.F.A Hendrickx, Chem Phys Lett., 436 (2007) 341–345.

[25] S Clima, M.F.A Hendrickx, J Phys Chem A, 111 (2007) 10988–10992.

[26] M.F.A Hendrickx, K.R Anam, J Phys Chem A, 113 (2009) 8746–8753.

INTRODUCTION 11

[27] K Pradhan, G.L Gutsev, C.A Weatherford, P Jena, J Chem Phys., 134 (2011) [28] S.G Li, H.J Zhai, L.S Wang, D.A Dixon, J Phys Chem A, 116 (2012) 5256–5271 [29] E Miliordos, A Mavridis, J Phys Chem A, 111 (2007) 1953–1965.

[30] C.N Sakellaris, A Mavridis, J Phys Chem A, 116 (2012) 6935–6949.

[31] C.N Sakellaris, E Miliordos, A Mavridis, J Chem Phys., 134 (2011).

[32] L.M Lawson Daku, F Aquilante, T.W Robinson, A Hauser, J Chem Theory Comput., 8 (2012) 4216–4231.

[33] B.J Persson, B.O Roos, K Pierloot, J Chem Phys., 101 (1994) 6810–6821 [34] M.F.A Hendrickx, S Clima, Chem Phys Lett., 388 (2004) 284–289.

[35] M.F.A Hendrickx, S Clima, Chem Phys Lett., 388 (2004) 290–296.

[36] H.L Zhao, K Pierloot, E.H.G Langner, J.C Swarts, J Conradie, A Ghosh, Inorg Chem., 51 (2012) 4002–4006.

[37] V Sauri, L Serrano-Andres, A.R.M Shahi, L Gagliardi, S Vancoillie, K Pierloot,

J Chem Theory Comput., 7 (2011) 153–168.

[38] P.A Malmqvist, K Pierloot, A.R.M Shahi, C.J Cramer, L Gagliardi, J Chem Phys., 128 (2008) 204109.

[39] C.J Cramer, D.G Truhlar, Phys Chem Chem Phys., 11 (2009) 10757–10816 [40] G.L Gutsev, B.K Rao, P Jena, J Phys Chem A, 104 (2000) 11961–11971 [41] E.L Uzunova, G St Nikolov, H Mikosch, J Phys Chem A, 106 (2002) 4104–4114.

[42] K.G Dyall, K Faegri, Introduction to Relativistic Quantum Chemistry, OxfordUniversity Press, 2007

[43] M Douglas, N.M Kroll, Ann Phys., 82 (1974) 89–155.

[44] B.A Hess, Phys Rev A, 33 (1986) 3742–3748.

[45] F Aquilante, L De Vico, N Ferré, G Ghigo, P.-Å Malmqvist, P Neogrády, T.B.Pedersen, M Pito ˇnák, M Reiher, B.O Roos, L Serrano-Andrés, M Urban, V Veryazov,

R Lindh, J Comput Chem., 31 (2010) 224–247.

[46] MOLPRO, version 2012.1, A Package of Ab Initio Programs, H.-J Werner, P J.Knowles, G Knizia, F R Manby, M Schütz, and others , see http://www.molpro.net/.

[47] X.-B Wang, C.-F Ding, L.-S Wang, J Phys Chem A, 101 (1997) 7699–7701 [48] L.S Wang, Surf Rev Lett., 3 (1996) 423–427.

[49] E.P.F Lee, D.K.W Mok, F.-T Chau, J.M Dyke, J Comput Chem., 30 (2009) 337–

345

[50] H Wu, L.-S Wang, J Phys Chem A, 102 (1998) 9129–9135.

[51] H Wu, L.-S Wang, J Chem Phys., 107 (1997) 8221–8228.

[52] H Wu, L.-S Wang, J Chem Phys., 108 (1998) 5310–5318.

[53] G.L Gutsev, P Jena, H.-J Zhai, L.-S Wang, J Chem Phys., 115 (2001) 7935–7944 [54] G.L Gutsev, B.K Rao, P Jena, X Li, L.-S Wang, J Chem Phys., 113 (2000)

1473–1483

[55] H Wu, L.-S Wang, J Chem Phys., 107 (1997) 16–21.

[56] H Wu, S.R Desai, L.-S Wang, J Chem Phys., 103 (1995) 4363–4366.

[57] D.K.W Moka, F.T Chau, J.M Dyke, E.P.F Lee, Chem Phys Lett., 458 (2008) 11–14 [58] H.-J Zhai, B Kiran, L.-F Cui, X Li, D.A Dixon, L.-S Wang, J Am Chem Soc.,

INTRODUCTION 13

[64] N Zhang, H Kawamata, A Nakajima, K Kaya, J Chem Phys., 104 (1996) 36–41 [65] S Gemming, J Tamuliene, G Seifert, N Bertram, Y.D Kim, G Gantefor, Appl Phys A-Mater Sci Process., 82 (2006) 161–166.

[66] H.-J Zhai, S Li, D.A Dixon, L.-S Wang, J Am Chem Soc., 130 (2008) 5167–5177.

[67] G.V Chertihin, W Saffel, J.T Yustein, L Andrews, M Neurock, A Ricca, C.W

Bauschlicher, J Phys Chem., 100 (1996) 5261–5273.

[68] Y Gong, M.F Zhou, J Phys Chem A, 112 (2008) 10838–10842.

[69] G.L Gutsev, S.N Khanna, B.K Rao, P Jena, J Phys Chem A, 103 (1999) 5812–

5822

[70] M Atanasov, Inorg Chem., 38 (1999) 4942–4948.

[71] G.L Gutsev, C.A Weatherford, K Pradhan, P Jena, J Phys Chem A, 114 (2010)

9014–9021

[72] Z Cao, W Wu, Q Zhang, J Mol Struct.-Theochem, 489 (1999) 165–176.

Chapter 2

Photoelectron spectroscopy and

computational approach

2.1 Basic principles of photoelectron spectroscopy

Photoelectron spectroscopy is known as a useful technique for probing the electronicstructure of a large amount of chemical systems from solid state to gas phasemolecules.[1, 2] Two kinds of photoelectron spectroscopic techniques have beendeveloped separately The X-ray photoelectron spectroscopy (XPS) is used tomeasure the core electrons ionization energies of bulks, surfaces, and thin filmsmaterials, while ultraviolet photoelectron spectroscopy (UPS) is appropriate todetermine the valence electrons ionization energies of molecules in the gas phase.Because the photoelectron spectra of small transition metal-containing clusters inthe gas phase are studied in this thesis, our discussion will focus on the latter type ofphotoelectron spectroscopy

Ultraviolet photoelectron spectroscopy, also known as molecular photoelectronspectroscopy, was developed by Turner between 1962 and 1967 to study freemolecules.[3] The term “ultraviolet” means that a high energy beam with photonenergies in the vacuum ultraviolet region from 3 to 124 eV is used to detach electrons.Note that most molecules have their lowest ionization energy around 9 eV, which

is in the region of the ultraviolet, and therefore this type of light has been used as

15

the most common radiation source In particular, HeIα radiation with a photon

energy of 21.2 eV (58.4 nm) is produced when neutral helium atoms relax from theexcited state1P (1s12p1) to the ground state1S (1s2) in a helium resonance lamp.Here, I indicates that the photon is emitted from the neutral helium, whereasα indicates that this radiation is due to the first transition in a series of possible npA

where h ν is the photon energy of the incident radiation, and BE is the binding energy,

i.e the energy difference between the initial state and a final state This equation,after a simple rearrangement, allows us to experimentally determine the bindingenergy In this work, the words ionization energy and electron detachment energyare used as synonyms of binding energy

2.2 The photoelectron spectrometer

The principle components of a photoelectron spectrometer are represented inFigure 2.1.[1, 2, 5, 6] We can see that the studied sample after being generated inplasma reactions, is selected by a time-of-flight mass spectrometer and transferred

to the target chamber where it is bombarded by the photon source, and thereforeejects electrons These electrons pass into the time-of-flight electron kinetic energyanalyzer where they are separated by their velocity energies The electrons, aftergoing out of the electron kinetic energy analyzer, pass onto an electron detector Inthis way the photoelectron spectrum is obtained, which is the number of electronsper unit time as a function of kinetic energy of the photoelectrons or the ionizationenergies Because medium vacuum pressure (≈ 10−2Torr) is required to keep thesample in the gas phase and higher vacuum (≈ 10−5 Torr) is necessary for theoperation of the electron kinetic energy analyzer and detector, different vacuumpumps are used in the photoelectron spectrometer

INTERPRETATION OF PHOTOELECTRON SPECTRA 17

Figure 2.1: The principal components of a photoelectron spectrometer.

In order to observe a high-resolution photoelectron spectrum, which usuallyincludes the vibrational fine structures of the low-lying bands, we must have anappropriate photon source As already mentioned above, the ultraviolet beam

spectroscopy Because of the very high photon energy, this ultraviolet source is onlyused to detach electron from molecules which usually have their lowest ionizationenergies around 9 eV However, the anionic transitional metal-containing clustersthat are studied in this thesis have much smaller ionization energies, from 0.5 eV

to 6 eV Therefore, in all the reported anion photoelectron spectra, a laser beam isused to detach electrons Additionally, due to the high intensity, low divergence,high monochromaticity, and spatial and temporal coherence, a laser beam is quiteappropriate to produce very high-resolution photoelectron spectra In particularfor the studied clusters in this thesis, a Nd:YAG laser, which is a photon source of

532 nm (2.331 eV), 355 nm (3.496 eV), and 266 nm (4.661 eV), is employed.[5–14] Insome cases, in order to record higher values of ionization energies, an ArF excimerlaser producing photons of 193 nm (6.424 eV) are utilized.[6, 12]

2.3 Interpretation of photoelectron spectra

A normal photoelectron spectrum contains a series of peaks or bands, whichcorrespond to a specific ionization process These bands are usually labeled by

X, A, B, C, and so on according to the increasing ionization energy, i.e bindingenergy As an example, in Figure 2.2 we present the photoelectron spectrum of theFeO −cluster, which was recorded at a photon energy of 4.66 eV.[10, 11] This anion

photoelectron spectrum contains two bands, the lowest band (X band) starts at3.26 eV and the A band begins at 3.81 eV For anion photoelectron spectroscopy, the

X band can arise from the ionization from the anionic electronic ground state tothe neutral ground state, while the other higher energy bands are the result of theionizations to the neutral excited electronic states

Depending on the geometrical difference between the initial state and the final state,

an ionization may correspond to one peak or a series of peaks or a broad band Ifthere is a relative large structural difference between theses states, we can obtain anumber of peaks, which are referred to as a vibrational progression or vibrationalfine structure due to the fact that they are the result of transitions from the anionicvibrational ground state to the neutral ground and excited vibrational states Incontrast, if there is no structural difference between the involved states, only onesharp band is observed in the spectrum Figure 2.2 shows that both the X and Abands in the photoelectron spectrum of FeO3 −exhibit vibrational progressions withalmost the same frequency (850 ± 50 cm−1), but the vibrational progression in the Xband is much broader than that of the A band Note that the structure is likely toextensively change when an electron is detached from a bonding or antibondingorbital A detachment of an electron from a nonbonding orbital will not cause muchchange in structure Furthermore, since it is impossible to resolve the rotationalstructure in ordinary photoelectron spectroscopy, the ionization processes dealingwith the rotational states are ignored in theoretical studies

by somewhat different selection rules By applying time-dependent quantummechanics, two types of selection rules are derived for photoelectron spectroscopy,which are known as the electronic selection rules and the vibrational selectionrules.[1, 2, 4]

In quantum mechanics, selection rules are based on the concept of transitionprobabilities between two states The absorption of electromagnetic radiation bymolecules is found, to a good approximation, to be proportional to the square of the

transition dipole moment integral P

in which riare the position vector operators of the electrons

According to the Born–Oppenheimer approximation, the total wave function can besubdivided into its electronic, vibrational, and rotational components:

Ψ = ψ es(r, ms; R).ψ vi b(R).ψ r(R) (2.4)