Van Tan Tran FACULTY OF SCIENCE DEPARTMENT OF CHEMISTRY DIVISION OF QUANTUM CHEMISTRY AND PHYSICAL CHEMISTRY CELESTIJNENLAAN 200F BOX 2404 B-3001 HEVERLEE, BELGIUM ARENBERG DOCTORAL SCHOOL FACULTY OF SCIENCE COMPUTATIONAL STUDY OF THE ANION PHOTOELECTRON SPECTRA OF FeXn (X = O, S AND n = 3, 4) CLUSTERS Computational Study of the Anion Photoelectron Spectra of FeXn (X = O, S and n = 3, 4) Clusters Van Tan Tran December 2013 Promoter: Prof Dr Marc Hendrickx Dissertation presented in partial fulfilment of the requirements for the degree of Doctor in Chemistry December 2013 Computational Study of the Anion Photoelectron Spectra of FeXn (X = O, S and n = 3, 4) Clusters Van Tan Tran Jury: Dissertation presented in partial Prof Dr Arnout Ceulemans, chair fulfilment of the requirements for Prof Dr Marc Hendrickx, promotor the degree of Doctor in Chemistry Prof Dr Luc Van Meervelt Prof Dr Minh Tho Nguyen Prof Dr Ewald Janssens Prof Dr Paul Geerlings (Vrije Universiteit Brussel) December 2013 © Katholieke Universiteit Leuven – Faculty of Science Celestijnenlaan 200F box 2404, B-3001 Heverlee (Belgium) Alle rechten voorbehouden Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotocopie, microfilm, elektronisch of op welke andere wijze ook zonder voorafgaande schriftelijke toestemming van de uitgever All rights reserved No part of the publication may be reproduced in any form by print, photoprint, microfilm or any other means without written permission from the publisher D/2013/10.705/83 ISBN 978-90-8649-668-6 Preface “The most beautiful experience we can have is the mysterious It is the fundamental emotion which stands at the cradle of true art and true science.” A LBERT E INSTEIN 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 II P REFACE 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 Samenvatting In dit proefschrift worden de structurele en elektronische eigenschappen van FeXn −/0 ( X = O, S en n = 3–4 ) clusters onderzocht door gebruik te maken van verschillende computationele kwantumchemische methoden Deze clusters zijn relevant om een beter begrip op te bouwen in allerlei sterk uiteenlopende domeinen zoals onder andere diverse industriële katalytische processen en tal van biochemische processen Vanwege de ingewikkelde elektronische structuur van dit soort van clusters, wat meestal het geval is voor transitiemetaalverbindingen, is gebleken dat enkel een combinatie van verschillende elektroncorrelatiemethoden zoals DFT, CASPT2 en RCCSD(T) toelaat een afdoende beschrijving te geven van de bestudeerde verbindingen Hierbij wordt elke computationele methode gebruikt ter berekening van die eigenschappen waarvoor ze het best geschikt is Op deze wijze was het mogelijk om de onderliggende ionisaties zoals die optreden in de beschikbare experimentele anionfoto-elektronspectra, te identificeren Omgekeerd was het eveneens mogelijk deze experimentele gegevens te gebruiken om de kwaliteit van de rekenmethoden in te schatten Hoofdstuk geeft een overzicht van de technieken die in de experimentele studies aangewend worden Hieruit blijkt dat anionfoto-elektronspectroscopie onmiskenbaar één van de belangrijkste methoden is voor het bestuderen van de structurele en elektronische eigenschappen van kleine clusters die een transitiemetaalcentrum bevatten Inderdaad, in de literatuur kan een groot aantal spectra voor deze soort clusters teruggevonden worden, die weliswaar waardevolle informatie bevatten betreffende verschillende spectroscopische parameters maar niet steeds een eenduidige conclusie toelaten aangaande de onderliggende geometrische en elektronische structuur Tot heden is de interpretatie van de foto-elektronspectra vooral uitgevoerd op DFT-niveau, zodat heel wat vragen onbeantwoord bleven iii S AMENVATTING IV Het volgende hoofdstuk beschrijft in detail de basisprincipes van foto-elektronspectroscopie en de aangewende kwantumchemische technieken De elektronische selectieregels die nodig zijn voor de interpretatie van de spectra worden in detail afgeleid Ook het Franck–Condonprincipe dat in dit werk wordt toegepast om de waargenomen vibrationele progressies te simuleren, wordt eveneens geïntroduceerd 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 worden aangewend om de elektronische structuur van de FeO3 en FeO3 − clusters te onderzoeken Meer specifiek, geometrieën van alle relevante spinmultipliciteiten werden zonder enige symmetriebeperkingen geoptimaliseerd op het BP86/QZVPniveau en verder verfijnd met de CASPT2- en RCCSD(T)-methoden Beide bevestigen dat alle laaggelegen elektronische toestanden die relevant zijn voor de beschrijving van het foto-elektronspectrum overeenkomen met of sterk gelijken op een vlakke D 3h -structuur zonder bindingen tussen de drie zuurstofionen Afhankelijk van de gebruikte rekenmethode, kan de grondtoestand van het FeO3 − -anion ofwel E of A2 zijn CASPT2 berekent het A2 als de laagste energietoestand, terwijl RCCSD(T) het E als grondtoestand voorspelt De twee laagste bindingsenergiebanden van de foto-elektronspectrum van FeO3 − kunnen zonder twijfel alleen worden toegeschreven aan één-elektron ionisaties vanuit de E -toestand De eerste band is het resultaat van een overgang naar de A1 -grondtoestand van FeO3 , terwijl de tweede band afkomstig is van de eerste aangeslagen E -toestand Uit een harmonische vibrationele analyse van de symmetrische stretching mode bleek dat de waargenomen vibrationele progressies van deze twee banden in het experimentele foto-elektronspectrum ook in overeenstemming zijn met de RCCSD(T)-assignatie Een moleculaire orbitaalanalyse leidde overduidelijk tot de conclusie dat de elektronische structuur van de grondtoestanden van de anionische en neutrale clusters respectievelijk overeenkomen met een oxidatietoestand +5 en +6 voor ijzer De relatieve stabiliteit van alle laaggelegen isomeren van de FeO4 −/0 -clusters werden bestudeerd in hoofdstuk Voor zowel de anionische en neutrale clusters, bleek het bepalen van de meest stabiele structuur een veeleisende taak Zowel DFT als CASPT2 plaatsen de doublettoestand van het tetraëdrische O4 Fe-isomeer dat opgebouwd is uit vier onafhankelijke O2− atomaire liganden, aanzienlijk lager, tot S AMENVATTING V 0,81 eV, dan de doublettoestand van het η2 -(O2 )FeO2 − Dit laatste isomeer bezit slechts twee atomaire O2− -liganden en één moleculair O2 2− -ligand dat zijdelings aan het ijzerkation is gebonden De RCCSD(T)-methode reduceert dit energieverschil tot minder dan 0,01 eV Enkel deze gelijke stabiliteit van de grondtoestanden van O4 Fe− en η2 -(O2 )FeO2 − leidt tot een volledige assignatie van de experimentele foto-elektronspectra van FeO4 − De laagste bindingsenergieband (X-band) wordt toegeschreven aan de ionisatie A1 naar A1 van het η2 -(O2 )FeO2 − , terwijl de eerstvolgende hogere energieband (A-band) het gevolg is van de overgang van E naar A1 tussen de O4 Fe−/0 -conformaties Voor een specifiek isomeer, berekent CASPT2 de beste ionisatie-energieën De hoogste piek in de A-band met de zwakste intensiteit, kan eventueel worden toegeschreven aan de overgang van A2 naar A2 van η2 -(O2 )FeO2 Beide progressies in het experimentele spectrum zijn het resultaat van ionisaties vanuit de antibindende orbitalen met overheersend ijzer-3d-karakter Een Franck–Condonsimulatie van de waargenomen vibrationele progressies zoals deze werd uitgevoerd met BPW91, bevestigde de voorgestelde assignaties Geometrische structuren van FeS3 en FeS3 − met spinmultipliciteiten variërend van singlet tot octet werden in hoofdstuk geoptimaliseerd op het B3LYPniveau, waardoor twee laaggelegen isomeren voor deze clusters konden worden geïdentificeerd Het planaire isomeer bezit een D 3h -symmetrie en bevat drie S2− -atomaire liganden (S3 Fe−/0 ), terwijl de C 2v structuur, naast een atomair S2− -ligand een S2 2− -ligand bevat dat zijdelings gebonden is aan het ijzerkation: een η2 -(S2 )FeS isomeer Vervolgens werden de energieverschillen tussen de verschillende toestanden van deze twee isomeren geschat door het uitvoeren van geometrie-optimalisaties met de multireferentie CASPT2-methode Verschillende concurrerende structuren voor de grondtoestand van de anionische cluster werden herkend op dit niveau De relatieve stabiliteiten werden ook geschat door singlepoint RCSSD(T)-berekeningen uitvoeren op de B3LYP-geometrieën Het B2 werd ondubbelzinnig aangeduid als de grondtoestand van het neutrale complex De aard van de grondtoestand van het anion daarentegen is aanzienlijk minder zeker De 14 B2 -, 24 B2 -, B1 - en A1 -toestanden werden allemaal gevonden als laaggelegen η2 -(S2 )FeS− -toestanden Ook het B2 van S3 Fe− heeft een vergelijkbare CASPT2energie Hiermee in tegenstelling, plaatsen B3LYP en RCCSD(T) gezamenlijk deze S3 Fe− toestand op een veel hogere energie Energetisch, kunnen op het CASPT2niveau alle banden van de foto-elektronspectra van FeS3 − gereproduceerd worden als ionisaties vanuit ofwel de B2 - of de A1 -toestand van het η2 -(S2 )FeS− Echter, S AMENVATTING VI uit de Franck–Condonsimulaties, die verkregen werden door een harmonische vibrationele analyse uit te voeren op het B3LYP niveau, blijkt dat alleen de ionisatie van B2 naar B2 , waarbij de structuur η2 -(S2 )FeS behouden blijft, de beste overeenkomst-qua vibrationele progressie bezit met de X-band van het experimentele foto-elektronspectrum De B3LYP, CASPT2 en RCCSD(T) computationele methoden werden eveneens in hoofdstuk succesvol aangewend voor de interpretatie van de foto-elektronspectra van de FeS4 − -stoichiometrie door het berekenen van de geometrische structuren van alle mogelijke laaggelegen FeS4 −/0 -isomeren − (η -(S2 ))2 Fe -isomeer met twee S2 2− De B1g -toestand van het -moleculaire liganden zijdelings gebonden op een D 2h -wijze aan het centrale ijzer(III)kation, wordt eenduidig als grondtoestand van de anionische cluster voorspeld en de experimentele foto-elektronspectra werden met CASPT2 toegewezen als afkomstig van dit isomeer De complexe vibrationele structuur van de laagste energie X-band is het resultaat van ionisatietransities naar de B3g -, B1u - en B1g -toestanden van de neutrale cluster, die energetisch erg dicht bij elkaar gelegen zijn Een analyse van de CASSCF-orbitalen geeft een quasi ontaarding aan van de niet-bindende 3d-orbitalen van het ijzerkation en de π∗ -valentie-orbitalen van het moleculaire S2 2− -ligand Alle experimenteel waargenomen hogere ionisatie-energiebanden kunnen theoretisch toegekend worden als zijnde afkomstig van de voorgestelde anionische grondtoestand door onthechting van een elektron uit één van deze ijzer(III)- of ligandorbitalen Abbreviations 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 140 G ENERAL CONCLUSIONS AND PERSPECTIVES By analyzing the structural properties of the most stable isomers of the FeXn −/0 (X = O, S; n = 3–4) clusters, we observed that, for the same stoichiometric cluster, sulfur has more tendency to form the S2 2− molecular ligand while oxygen prefers to remain as atomic O2− ligand when combines with iron center As a result, the central iron atom in the oxide clusters usually has higher formal oxidation states than in the corresponding sulfide clusters Particularly, the most stable isomers of FeO3 −/0 have triangle D 3h structures with three atomic O2− ligands, and therefore the central iron atom has an oxidation state of +5 or +6 In contrast, the FeS3 −/0 clusters have a stable C 2v structure with one atomic S2− ligand and one molecular S2 2− ligand, and therefore the oxidation state of iron is +3 or +4 The same conclusion could be made for the FeO4 −/0 and FeS4 −/0 clusters The two FeO4 − isomers with the same stability, as calculated at RCCSD(T) level, are the tetrahedral FeO4 − and η2 -(O2 )FeO2 − in which two O2− ligands in the former isomer are replaced by one O2 2− ligand in the latter isomer The resulting oxidation states of Fe in these anionic oxide isomers are +7 and +5, respectively In the corresponding two neutral isomers of FeO4 , iron has an oxidation state of +6 and +4, respectively For the FeS4 −/0 clusters, the most stable isomers (η2 -(S2 ))2 Fe−/0 have both two S2 2− molecular ligands, and therefore oxidation states of +3 and +4 for iron The much easier formation of the S2 2− than the O2 2− ligand in the studied clusters can be explained based on their electronic structures By exploring the CASSCF molecular orbitals of the lowest energy state of the D 3h FeO3 − , the tetrahedral FeO4 − , and the D 3h FeS3 − clusters as shown in Figures 3.5, 4.4, and 5.4, we can reach the following conclusion The CASSCF molecular orbitals of η2 -(O2 )FeO2 − and η2 -(S2 )FeS− in Figures 4.5 and 5.5 present six orbitals for the X2 2− ligand, which are the σ, π(×2), π∗ (×2), and σ∗ orbitals Among these orbitals, the anti-bonding σ∗ orbital is formally empty while the remaining orbitals are always doubly occupied The same conclusion can be drawn for η2 -(S2 )2 Fe− where the two anti-bonding σ∗ orbitals of the two S2 2− ligands are unoccupied Because oxygen has a much higher electronegativity (3.44) than sulfur (2.58), it has a tendency to attract more electrons from iron And as a result, the partial electron occupation number of the σ∗ orbital of O2 2− is larger than that of S2 2− Because of the anti-bonding effect of the σ∗ orbital, the O–O bond will become much weaker than the S–S bond, and in some case, it breaks into two separate O2− ligands by getting two more electrons from the iron center G ENERAL CONCLUSIONS AND PERSPECTIVES 141 Overall, it is proven in this thesis that the combination of the DFT, CASPT2, and RCCSD(T) computational methods is a good choice to study the structural and electronic properties of small open shell transition metal-containing clusters Therefore, this approach can be applied to a large number of this kind of clusters, for which the photoelectron spectra are available in the literature but not fully understood Besides the clusters presented in this thesis, calculations were found to also provide satisfactory assignments for the photoelectron spectra of FeO2 − [1] and of small sized transition metal-carbon clusters such as MC2 − (M = Mn, Cr)[2, 3] Otherwise, as can be seen in Chapter 1, a huge number of photoelectron spectra of transition metal-oxygen, -carbon, and -sulfur clusters have been reported so far which provide valuable spectroscopic information for further detailed computational work One type of topic that needs to be studied at the wave function level of computation in the future is the electronic structure of the first row transition metal MC3 −/0 (M = Sc, V, Cr, Mn, Fe, Co, and Ni) clusters Their anion photoelectron spectra MC3 − were recorded by Wang and coworkers with the photon energies of 532 nm and 355 nm.[4] Density functional theory was applied to explore their electronic structures and to propose assignments for some of these clusters.[5–11] Moreover, due to the strong multi-reference wavefuntions, the CASPT2 method was applied to ScC3 −/0 [12] and FeC3 −/0 [13] clusters Additionally for the ScC3 −/0 clusters, the corresponding anion photoelectron spectra were interpreted at the MRCI level.[14] For the other clusters in the series, it would be quite interesting to investigate their electronic structures with the wave function methods used in the current computational study As another extension of this thesis an investigation of the electronic structures of vanadium oxides could be considered Indeed these compounds are related to important compounds in field of heterogeneous catalysis.[15–18] The structural and electronic properties of small vanadium oxide clusters have been extensively studied by photoelectron spectroscopy and quantum chemistry.[19–28] Here, we would like to focus on the vanadium dioxide and its anion because these clusters exhibit very complicated electronic structures as a result of the unsaturated d shell of vanadium Previous calculations on the neutral cluster show that there is a near degeneracy of the A1 and B1 states, which are split from the linear D 2h ∆g state under the Renner–Teller effect.[19–21, 29] By using the CASSCF, BPW91, B1LYP, and CCSD(T) methods, the A1 has been calculated as the neutral ground state.[20, 142 G ENERAL CONCLUSIONS AND PERSPECTIVES 21, 29] Contradictory, the B3LYP functional predicts the B1 as the lowest energy state.[19] For the anionic cluster there is also a near degeneracy of the A1 and B1 states, which are two components of the linear D 2h ∆g state.[20, 21] Both the BPW91 and B3LYP functionals compute the A1 as the anionic ground states,[19, 20] while this state is calculated to be 0.06 and 0.19 eV less stable than the B1 by the B1LYP functional and CCSD(T)[21] The photoelectron spectra of VO2 − have been recorded with photon energies of 532 nm, 355 nm, 266 nm, and 193 nm.[22] The highest resolution 532 nm spectrum shows three features, i.e., a X band at 2.03 eV with a vibrational progression of 970 cm−1 composed of three sharp peaks and two vibrational unresolved features, X and X , at 1.90 eV and 1.72 eV, respectively The remaining spectra also reveal A, B, and C bands at 2.60, 4.00, and 4.60 eV By using theoretical data for the neutral cluster from previous computational results, the authors predict the A1 with a closed shell electronic configuration as the anionic ground state.[22, 29] Consequently, the X, A, B, and C bands in the spectra were explained by using this singlet as an initial state, while the X and X features are believed to be the result of ionizations from low-lying excited anionic states However, this assignment is in contradiction to the more recent computational results in which the ground state of the anionic cluster was calculated as the A1 or the B1 state.[19–21] Overall, due to the complicated electronic structures as can be seen from the photoelectron spectroscopy and computational results, we feel that it is necessary to perform calculations to derive the relative energy order of the low-lying states of VO2 −/0 with the computational model proposed in this work and possibly to propose novel assignments for the anion photoelectron spectra Further computational work in the field could be the study of the electronic structure of the second-row transition metal-containing clusters In this respect the small sized mono-niobium carbide clusters represent an interesting choice because they are considered as the building blocks for new materials such as metallocarbohedrenes (met-cars) and metallofullerenes.[30] Especially, for the NbC2 −/0 clusters, previous density functional theory (DFT) and multireference configuration interaction (MRSDCI) calculations found a B1 of C 2v cyclic isomer, in which niobium binds side-on to C2 , as the neutral ground state.[31] More recently, DFT and symmetry adapted cluster configuration interaction (SAC-CI) results showed a triplet (DFT) or quintet (SAC-CI) of the cyclic isomer as the lowest states of NbC2 − [32] In the G ENERAL CONCLUSIONS AND PERSPECTIVES 143 same work, the C ∞v linear isomer in which niobium binds end-on to C2 was also studied From these results it was concluded that the photoelectron spectra, as reported by Wang and coworkers[33], could only be explained by using both the quintet state of the cyclic isomer and the triplet state of linear isomer as initial states This interpretation of the photoelectron spectra of NbC2 − sharply contrasts the previous assignment in which the low-lying features in the photoelectron spectra were predicted to correspond exclusively to ionizations from the initial A2 anionic ground state of the cyclic isomer.[33] Due to the difficulty to predict the most stable anionic isomer and the nature of its ground state, the investigation of the electronic structures of NbC2 −/0 still remains as a challenging task for the future Additionally, assignments for the photoelectron spectra of dinuclear transition metal-containing clusters such as Cu2 On − (n = 1–4)[34], Fe2 On − (n = 2–5)[35, 36], V2 On − (n = 3–7)[37], Cr2 On − (n = 1–7)[38], Ti2 O4 − [39], and Cr2 O6 − [40] should be considered as an extension of our work The structural and electronic properties of the larger clusters have been investigated so far by density functional theory [19, 23, 41–54], while the multi-configuration and coupled-cluster methods have been much applied to the smaller systems[40, 43–45, 53, 55] In particular, for the V2 O4 −/0/+ clusters, the multi-reference averaged coupled-pair functional (MRACPF) method with an active space including 10 orbitals was utilized to study the electronic structures and to calculate the corresponding ionization energies.[44] Also, multi-reference configuration interaction (MRCI) with an active space containing 16 orbitals was applied to investigate the electronic structures of Ni2 O2 and Ni2 O2 + [55] The relative energy order of several low-lying electronic states of these clusters were reported in this study Furthermore, the CCSD(T) method was used to describe the electronic structures of the Fe2 O2 [45], Cr2 O6 −/0 [40, 43], and Ti2 O4 −/0 [53] clusters Specifically, for the Cr2 O6 −/0 clusters, the corresponding anionic photoelectron spectra were interpreted at the CCSD(T) level while the multi-dimensional Franck– Condon simulations were performed at the DFT level.[40, 43] Overall, we can see that in order to understand the electronic structures of this kind of clusters, the most accurate quantum chemical methods need to be applied Otherwise, as the number of transition metal centers increases in these clusters, the electronic wave function can become more multireference and this makes it difficult to calculate them with the available quantum chemistry methods Nowadays, the CASPT2 calculations can handle an active space with around 17 orbitals, but this is not enough to cover the important nondynamical correlation energy even in the case of diatomic transition 144 G ENERAL CONCLUSIONS AND PERSPECTIVES metal clusters Particularly for Fe2 −/0 clusters,[56] the CASPT2 and MRCI predict different ground states With an active space of 15 orbitals CASPT2 calculates the ∆g as the lowest energy state In contrast, MRCI with a smaller active space of 12 orbitals predicts the ground state as Σ− u Clearly, in order to reach a more believable conclusion about the ground state of Fe2 − , the active space needs to be increased and this can only be done with the RASPT2 method However, the application of RASPT2 to this kind of clusters is very limited due to convergence problems of RASSCF A RASPT2 investigation on the geometric and electronic structures of dinuclear transition metal-containing clusters would result in a PhD thesis on itself On the whole, because of the large amount of photoelectron spectra that are presently available in the literature, and many more that surely will be published in the near future, a theoretical study of the 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Vancoillie, Hailiang Zhao, Van Tan Tran, Marc F A Hendrickx, and Kristine Pierloot, Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Studies on Mononuclear First-Row TransitionMetal Systems, J Chem Theory Comput., 2011, 7, 3961–3977 Marc F A Hendrickx and Van Tan Tran, On the Electronic and Geometric Structures of FeO2 −/0 and the Assignment of the Anion Photoelectron Spectrum, J Chem Theory Comput., 2012, 8, 3089–3096 Van Tan Tran and Marc F A Hendrickx, A CASPT2 Description of the Electronic Structures of FeO3 −/0 in Relevance to the Anion Photoelectron Spectrum, J Chem Theory Comput., 2011, 7, 310–319 Van Tan Tran and Marc F A Hendrickx, Description of the Geometric and Electronic Structures Responsible for the Photoelectron Spectrum of FeO4 − , J Chem Phys., 2011, 135, 094505 Van Tan Tran and Marc F A Hendrickx, Assignment of the Photoelectron Spectra of FeS3 −/0 by Density Functional Theory, CASPT2, and RCCSD(T) Calculations, J Phys Chem A, 2011, 115, 13956–13964 Van Tan Tran and Marc F A Hendrickx, Molecular Structures for FeS4 −/0 As Determined from an Ab Initio Study of the Anion Photoelectron Spectra, J Phys Chem A, 2013, 117, 3227–3234 153 154 L IST OF PUBLICATIONS Van Tan Tran, Christophe Iftner and Marc F A Hendrickx, Quantum Chemical Study of the Electronic Structures of MnC2 −/0 Clusters and Interpretation of the Anion Photoelectron Spectra, Chem Phys Lett., 2013, 575, 46–53 Van Tan Tran, Christophe Iftner and Marc F A Hendrickx, A New Interpretation of the Photoelectron Spectra of CrC2 − , J Phys Chem A, 2013, 117, 5613–5619 Conferences Van Tan Tran, Marc F A Hendrickx, Unravelling the Electronic Structures of FeO3 −/0 , FeO4 −/0 , and FeS3 −/0 by Assignment of their Anion Photoelectron Spectra, at 10th Quantum Chemistry in Belgium Conference, at Vrije Universiteit Brussel, Belgium, on Feb 10, 2012 (poster presentation) Van Tan Tran, Marc F A Hendrickx, Assignment of the Photoelectron Spectra of FeOn − (n = 1–4) by Ab Initio Methods, at Theoretical and Applications of Computational chemistry, in Pavia, Italy, on Sept 2–7, 2012 (poster presentation)