Quantum chemical studies of niobium and vanadium doped gold clusters

For example, contrary to the particular inertness of gold bulk, in the form of nano-scale or finely dispersed on metal oxide surfaces, gold exhibits unique catalytic activities for many

Quantum Chemical Studies of Niobium and Vanadium-doped Gold Clusters

PHAM VU NHAT

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

in Chemistry

Promotor:

Prof Minh Tho Nguyen

Members of the Jury:

Prof Luc Van Meervelt

Prof Marc Hendrickx

Prof Tatjana Vogt

Prof Frank De Proft

Prof Ewald Janssens

December 2012

© 2012 Faculteit Wetenschappen, Geel Huis, Arenberg Doctoraatsschool, Kasteelpark Arenberg 11, B-3001 Heverlee, België

Alle rechten voorbehouden Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotokopie, microfilm, elektronisch of

op welke andere wijze ook zonder voorafgaandelijke schriftelijke toestemming van de uitgever

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

ISBN 978-90-8649-576-4

D/2012/10.705/93

to my parents, my wife, and my daughter

Buồn trông phong cảnh quê người, đầu cành quyên nhặt, cuối trời nhạn thưa

Strange landscapes met the mournful eyes,

on trees cuckoos galore, at heaven's edge some geese

Kieu Story, Nguyen Du

Members of the Jury

Prof Dr Luc Van Meervelt (Chair)

Department of Chemistry, KU Leuven

Prof Dr Marc Hendrickx

Department of Chemistry, KU Leuven

Prof Dr Tatjana Vogt

Department of Chemistry, KU Leuven

Prof Dr Frank De Proft

Faculty of Sciences, Vrije Universiteit Brussel (VUB)

Prof Dr Ewald Janssens

Department of Physics and Astronomy, KU Leuven

Prof Dr Minh Tho Nguyen (Promoter)

Department of Chemistry, KU Leuven

Acknowledgments

This work has been carried out during the period of January 2009 – December 2012 at the Department of Chemistry, University of Leuven, Belgium My journey to this point turned out to be much less difficult than I expected as it has been accompanied and supported by many people Now is a pleasant opportunity

to express my gratitude for all of them

First and foremost, I would like to thank my supervisor Prof Minh Tho Nguyen for his endless patience and enthusiasm, along with his understanding and motivating guidance during my Ph.D studies I have really been fortunate that I have come to know him in my life

I also would like to send special thanks to Prof Arnout Ceulemans, Prof Marc Hendrickx, Prof Paul Geerlings (VUB) and Prof Frank De Proft (VUB) I did benefit much from their excellent knowledge and teaching on quantum chemistry Besides, I am grateful to all members of the Jury for their valuable comments, suggestions and corrections that greatly enrich my work I in addition appreciate the timely helps from Mrs Rita Jungbluth and Dr Hans Vansweevelt I always got the right answers whenever knocking their doors I thank also Prof Marc Hendrickx and Drs Pieter Kelchtermans for the translation of the “Samenvatting”

I am also indebted to Profs Peter Lievens and Ewald Janssens for valuable discussion on clusters, Dr Andre Fielicke from the Fritz-Haber Institute in Berlin, Germany, for providing me the original plots of his experimental IR spectra on Nb clusters, and Prof Jerzy Leszczynski for his support during my visit to the Jackson State University, Mississippi, USA

Financial support from the KU Leuven Research Council and the Can Tho University is gratefully acknowledged

How sad and tough would it be to live far from the family and home without friends Thus, I am truly thankful to all my colleagues in the Division of Quantum Chemistry for the friendly working atmosphere, and to all my Vietnamese friends in Leuven for the numerous nice non-scientific meetings

Finally, the greatest thanks go to my parents, my wife and my daughter They stand beside me all the time and bring the sunshine to me in the most difficult moments I dedicate this thesis to them

This thesis is based on the following publications:

1) A New Look at the Structure and Vibrational Spectra of Small Niobium Clusters and Their Ions

Pham Vu Nhat, Vu Thi Ngan and Minh Tho Nguyen, J Phys Chem C, 2010, 114,

4) Structures, Spectra, and Energies of Niobium Clusters from Nb13 to Nb20

Pham Vu Nhat and Minh Tho Nguyen, J Phys Chem A, 2012, 116, 7405–7418

5) Trends in Structural, Electronic and Energetic Properties of Bimetallic Vanadium–gold Clusters Aun V with n = 1–14

Pham Vu Nhat and Minh Tho Nguyen, Phys Chem Chem Phys., 2011, 13, 16254–

16264

6) Theoretical Study of Aun V-CO, n = 1 – 14: The Dopant Vanadium Enhances CO

Adsorption on Gold Clusters

Pham Vu Nhat, Truong Ba Tai and Minh Tho Nguyen, J Chem Phys., 2012, 137,

164312–164324

7) The Icosahedral Evolution in Bimetallic Clusters Aun V, with n = 12 – 20

Pham Vu Nhat and Minh Tho Nguyen, J Chem Phys., 2012, (submitted)

8) Structural Evolution, Vibrational Signatures and Energetics of Small Niobium Clusters

Pham Vu Nhat and Minh Tho Nguyen, Coord Chem Rev., 2012, (to be submitted)

Other publications:

9) Structure and Stability of Aluminum-doped Lithium Clusters (LinAl0/+, n = 1–8): A

Case of The Phenomenological Shell Model

Truong Ba Tai, Pham Vu Nhat and Minh Tho Nguyen, Phys Chem Chem Phys.,

2010, 12, 11477–11486

10) Electronic Structure and Thermochemical Properties of Small Neutral and Cationic Lithium Clusters and Boron-Doped Lithium Clusters: Lin0/+ and LinB0/+ (n =

1–8)

Truong Ba Tai, Pham Vu Nhat, Minh Tho Nguyen, Shenggang Li, and David A

Dixon, J Phys Chem A, 2011, 115, 7673–7686

11) Theoretical Study of Manganese Hydrides and Halides, MnXn with X = H, F, Cl,

Br, n = 1 – 4

Pham Vu Nhat, Ngo Tuan Cuong, Pham Khac Duy and Minh Tho Nguyen,

Chemical Physics, 2012, 400, 185

we ook het effect van dopering onderzocht op bepaalde eigenschappen van deze clusters De meeste berekeningen werden uitgevoerd in het kader van functionaaldensiteitstheorie met behulp van pseudo-potentiaal basissets In de volgende paragrafen geven we aan hoe het doctoraatproefschrift is onderverdeeld in hoofdstukken

Hoofdstuk 1 bevat een volledig overzicht van de bestudeerde clusters Verder geeft dit hoofdstuk ook het belang weer van de dergelijke nanopartikels vanuit wetenschappelijk en technologisch standpunt Recentelijke ontwikkelingen betreffende de studie van transitiemetaalclusters worden eveneens besproken Bovendien wordt de aandacht gevestigd op het belang van de d-valentie-elektronen,

de lanthanidecontractie en de relativistische effecten voor de beschrijving van vele eigenschappen van deze clusters Dit was onze belangrijkste motivatie om deze moeilijk te berekenen type van clusters te bestuderen op theoretisch vlak We kunnen inderdaad opmerken dat, niettegenstaande er meer en meer experimentele resultaten beschikbaar komen, de kwantitatieve interpretatie ervan grotendeels ontbreekt

Hoofdstuk 2 bevat een kritische analyse van de performantie van de huidige DFT-technieken en hun mogelijke toepassingen in het domein van de transitiemetaalchemie Hoewel DFT-berekeningen een onmisbaar instrument zijn geworden voor de berekening van de elektronische structuren en de daarmee samenhangende eigenschappen, blijkt toch dat elke functionaal zijn voordelen en nadelen heeft voor welbepaalde systemen Deze analyse diende als een eerste en nuttige leidraad betreffende de keuze van een geschikte functionaal ter berekening

van bepaalde parameters van een specifiek systeem Tot op zekere hoogte presteren functionalen met een lage HF-bijdrage gewoonlijk beter dan de standaard hybridemethoden ter berekening van de moleculaire eigenschappen van clusters die uitsluitend transitiemetalen bevatten We moeten echter tot de conclusie komen dat geen enkele functionaal geschikt is voor alle structurele en energetische parameters Daarom is het van cruciaal belang om een zorgvuldige analyse uit te voeren aangaande de toepasbaarheid van de verschillende computationele opties voor elk nieuw type van verbinding Hiertoe wordt een systematische vergelijking gemaakt van de berekende resultaten met de experimentele gegevens of met hoogwaardige MO-methoden

In hoofdstuk 3 onderzoeken we systematisch de structurele evolutie, vibrationele progressies en energetische eigenschappen van Nbn clusters (n = 2 − 20),

in zowel neutrale als geladen toestand Verscheidene fundamentele energetische eigenschappen van clusters, inclusief elektronaffiniteiten, ionisatie-energieën, bindingsenergie per atoom en stapsgewijze dissociatie-energieën worden berekend en vergeleken met gemeten waarden De vibrationele (IR) spectra van systemen kleiner dan Nb13 werden bestudeerd samen met de waargenomen ver-IR karakteristieken Hoewel de experimentele IR-spectra voor grotere clusters tot op heden nog niet beschikbaar zijn, presenteren we hier voorspellingen die toelaten de voorgestelde evenwichtsstructuren te verifiëren, van zodra de relevante spectroscopische informatie beschikbaar komt Gebaseerd op de theoretische en experimentele bevindingen vermelden we tot slot een enkele algemene en belangrijke punten omtrent de bestudeerde Nbn-clusters

Een ander project van dit proefschrift behelst een uitgebreid onderzoek naar het groeigedrag, de energetische eigenschappen en CO-affiniteit van vanadium-gedopeerde goudclusters Aun V met n = 1 – 20 Hoofdstuk 4 bestudeert in detail hoe

pure goudsystemen beïnvloed worden door het doperingsatoom vanadium Er valt duidelijk waar te nemen dat de structurele evolutie en gerelateerde eigenschappen van goudclusters sterk veranderen door de introductie van een vanadiumatoom We vinden dat een dergelijke substitutie in clusters met oneven aantal atomen de

thermodynamische stabiliteit aanzienlijk verhoogt, maar deze bij oneven clusters significant verlaagt Vrij algemeen wordt CO-adsorptie versterkt na dopering

Dieper inzicht in de elektronische, geometrische en energetische eigenschappen van transitiemetaalclusters zijn erg belangrijk voor de verdere ontwikkeling van corresponderende nanomaterialen en nanostructuurtechnologieën Dit verklaart de noodzaak van een gedetailleerd theoretisch inzicht van zulke systemen De resultaten die in deze thesis worden gerapporteerd kunnen dus hun dienst bewijzen in toekomstige experimentele en theoretische studies betreffende metaalclusters Verscheidene vraagstukken blijven echter onopgelost en motiveren dus verdergaand onderzoek

Hoewel DFT-methoden ons redelijk wat informatie kunnen verstrekken over allerlei eigenschappen van de grondtoestand van deze clusters, houden ze nog steeds een aanzienlijke rekenkost in Daarom is tot op heden het computationele studiegebied beperkt tot systemen met een klein aantal atomen, en konden maar enkele berekeningen naar eigenschappen van geëxciteerde toestanden uitgevoerd worden In de komende jaren hopen we op doorbraken in termen van zowel methodologie als rekencapaciteit waardoor theoretisch onderzoek op grotere clusters van metalen en halfgeleiders haalbaar en betrouwbaar wordt We kijken ook uit naar bijkomende spectroscopische data van verscheidene experimenten die onze voorspellingen kunnen bevestigen Hierop zou een geconcerteerde studie op grotere systemen kunnen volgen

De toepassingen van transitiemetaalclusters in collọdale chemie, katalyse, geneeskunde, elektronische industrie, enzovoort, bieden ook interessante en veelbelovende perspectieven Daarom is een theoretische studie van opto-elektronische en magnetische eigenschappen, agregatie-eigenschappen, interacties met industriële gassen (H2, CO, NO, CH4, .), organische en biomoleculaire verbindingen (van eenvoudige alcoholen, aminozuren tot DNA-basen, …) noodzakelijk Dit onderzoek kan de weg plaveien om kwantumchemische theorieën hun essentiële rol te laten spelen, namelijk het met grote zekerheid voorspellen van chemische fenomenen

Table of Contents

Chapter 1 Introduction 1

Chapter 2 Theoretical backgrounds 13

2.1 Introduction 14

2.2 Functional classification 15

2.3 DFT applications in transition metal compounds 20

2.3.1 Geometries 20

2.3.2 Spin-state splitting 24

2.3.3 Energetic properties 26

2.4 Some concluding remarks 32

Chapter 3 Niobium clusters 43

3.1 Introduction 44

3.2 Computational methods 47

3.3 Results and discussion 50

3.3.1 Equilibrium structures and vibrational spectra 51

3.3.2 Energetic properties 86

3.3.3 Thermodynamic properties 91

3.4 Concluding remarks 99

Chapter 4 Vanadium-doped gold clusters 107

4.1 Introduction 108

4.2 Computational methods 110

4.3 Results and discussion 114

4.3.1 Growth pattern of Au n V 114

4.3.2 Thermodynamic stabilities of Au n V clustuers 126

4.3.3 CO adsorption on Au n V clustuers 133

4.4 Concluding remarks 155

Chapter 5 General conclusions and outlook 165

5.1 General conclusions 166

5.2 Outlook 170

Chapter 1 Introduction

A brief overview of the metal

clusters studied

In chemistry, a cluster is usually defined as an aggregate of bound atoms

whose size lies between those of an atom and a bulk solid The notion was introduced

by F A Cotton in the early 1960’s to refer to binuclear compounds containing two metal atoms each surrounded by a number of ligands Another type of clusters1includes polynuclear compounds of two or more metal atoms in which direct and substantial metal-metal bonding is present, without the benefit of stabilizing ligands

The study in metal clusters has grown exponentially since late 1970’s, motivated by both academic and industrial concerns.2,3 In the age of miniaturization

of electronic devices, increasing interest has been placed, among other things, in the evolution of structures and related properties of materials with dimension of nanometers In this field, the knowledge on atomic and electronic structures of elemental clusters provides fundamental information for the design of new nano-materials implemented in the modern and future technologies In a recent paper, Loth and co-workers4 revealed that anti-ferromagnetic nanostructures, composed of just two rows of six iron atoms, might become a new generation of memory chips and disk drives Such nanoparticle-supported devices are expected not only to have greater capabilities and flexibilities but also to be significantly less power-consuming than the current silicon-based equipments Currently, most of common magnetic storage systems still need millions of atoms in order to store a digital 1 or 0

Nano-scale particles and compounds also have potential applications in colloidal chemistry, medical science, and particularly in catalysis.3,5 Owing to a variety of oxidation states, transition metals are considered to be perfect candidates for catalytic processes because they are willing to donate as well to accept electrons during the chemical transformations In recent time, small clusters of transition metals have drawn considerable attention in the extensive search for the promising alternatives for currently used catalysts These nano-catalysts are expected to improve the activity, the selectivity, and the recoverability as compared to the traditional catalysts Nano-particles appear to exhibit a more effective catalytic performance owing to the novel characteristics derived from their nano-structures, such as (i) high surface to volume ratio, (ii) availability of active absorption and reactions sites, (iii)

wide range of coordination number, and (iv) easy migration and atomic rearrangements facilitating the chemical bond breaking and forming

Until recently, the structural assignment for metal clusters, particularly for those of transition elements, constituted great challenges for both experimental and theoretical approaches Actually, experimental observations become more and more available owing to the use of modern spectrometric techniques, and thereby theoretical steps can be taken for the understanding and interpretation of the observed findings Nevertheless, a set of simple rules assisting the prediction of the stable structures for metal clusters, as either in molecules or in solids, does not exist yet In addition, relatively little is known about the complex and subtle relationships between structure, both electronic and atomic, with stability and reactivity Generally, one may only expect that the physical and chemical properties of small and medium-sized clusters, containing no more than a few hundred atoms (diameters of 1–3 nm),6strongly depend on either their sizes or shapes, and differ considerably from both individual atoms or molecules and bulk As compared to bulk materials, clusters have

a much larger fraction of atoms on the surface, in such a way that different and additional properties can be introduced For example, contrary to the particular inertness of gold bulk, in the form of nano-scale or finely dispersed on metal oxide surfaces, gold exhibits unique catalytic activities for many gas-phase reactions such as

CO oxidation, propylene epoxidation, NO reduction, water-gas shift and methanol synthesis7–9…

Up to the early 1980s, the most carefully studied clusters were indeed very small, containing utmost about a dozen atoms, as much larger particles were primarily believed to be essentially bulk-like and the surface was thought to scatter electrons randomly.2 The bias was however changed since Knight et al.10 produced and detected clusters of alkali metals containing up to 100 atoms, and certain sizes were found to be much more abundant than others For the sodium clusters produced, large peaks on the mass spectra correspond to systems containing 8, 20, 40, 58, and 92 atoms A widely accepted explanation for such phenomenon is based on the strong

delocalization of the external s electrons.11,12 Thus they can be treated as particles moving around a spherical pseudo-potential composed of the inner electrons along

with the nuclei This highly delocalized behavior of valence electrons brings about the main characteristics of simple metal clusters: the formation of electronic shells and the occurrence of shell closing effects are somewhat similar to those in free atoms In other words, the electronic structure of these clusters appears to reflect that of a spherical potential well Accordingly, the clusters in which the number of valence electrons matched the spherical shell closures, namely 1S/1P/1D/2S/1F/2P/ , are produced more abundantly as compared to the ones immediately following, and are

known as “magic” clusters

Electronic shell effects in clusters of coinage metals (Cu, Ag, Au) also exist,

similarly to those observed for alkali clusters because the d states of these elements

are almost completely occupied.13,14 It was well-established in the literature15 that

Agn, Cun and Aun clusters exhibiting an outstanding stability are found at n = 3, 9,

21, 35, 41, 59, while the negatively charged counterparts are exceptionally abundant

at n = 7, 19, 33, 39, 57, and so on Because the clusters considered are in singly

charged states, those cations and anions virtually contain 2, 8, 20, 34, 40, 58, electrons, which reproduce the same electron shell closing numbers of the alkali

clusters By assuming that the electrons on fulfilled d orbitals are highly localized and the external s electrons are mobile, such experimental observations can be explained

using the same model applied for alkali clusters Clusters of noble metals thus have often been considered to be similar to those of the alkalis However, it should be

attentive to several real differences between coinage elements arising from the sp–d

hybridization, and the relativistic effects that are very crucial in heavy atoms like gold.16,17 Indeed, although an effective core potential basis set with one valence electron can be applied for silver and copper clusters, either 11 or 19 valence electrons per atom should be taken into account for those of gold.18,19

In the case of clusters of transition metals with incomplete d shells, atomic

arrangements could play a more important role than the electronic shells, even with the relatively small sizes.20 Clusters of typical transition elements usually do not exhibit clear shell effects as in coinage metal clusters because the electrons on

unfilled d orbitals are significantly less delocalized than s and p electrons.15Nevertheless, these d electrons also are an integral part in the formation of chemical

bonding, and thus are expected to induce certain effects on the properties of the corresponding clusters The simple model of particles in a potential well or the

“jellium model”11 are apparently not sufficient for describing such systems Consequently, clusters of many transition metals are still covered by a large number

of unexpected, amazing and even exotic properties that make their studies quite challenging but extremely exciting

In this doctoral study, we investigated the clusters of niobium (Nb) and gold (Au), in both pure and doped forms These are two representative elements for which

experimental results are available Both niobium and gold clusters have been the subject of numerous experimental investigations as the early studies on clusters were carried out on the dissociation energy of the dimers Au2 and Nb2.21,22 However, relatively little information on the geometric and electronic structures of Nb clusters

is reported in the literature so far and the identity of several Nbn species remains a matter of debate Similarly, our knowledge about structural and electronic properties

of bimetallic gold-vanadium systems is still very limited, in contrast to the developed understanding of pure gold clusters Hence, the purpose of the current work is twofold The first part is an assignment of the relevant structures and to rationalize available experimental spectroscopic data for systems containing from 2 to

well-20 Nb atoms The second part is an examination of the inherent effects of the dopant

V atom on some basic properties of host gold clusters including the structural growth mechanism, the energetics and the CO adsorption affinities

When studying the clusters of transition metal elements, a particular

attention should be paid to the presence of d electrons The participation in the bonding of these fermions can be seen experimentally via cohesive energy of the bulk materials Indeed, the experimental cohesive energy Ec of Sc amounts to 3.90 eV/atom, then it increases for Ti and attains a maximum value for V After this maximum, it decreases reaching a bottom for Mn (2.92 eV/atom) and then increases, having a broad maximum for Fe, Co, and Ni, and finally it decreases again, approaching another valley at Cu.15,23 Earlier, Morse24 pointed out that the 4s orbitals

of the first transition metal series have more significant contribution to the chemical

bonding than the 3d orbitals because the latter are more contracted than the former

Moving down in the Periodic Table, the d orbitals tend to expand, while the s orbitals

are getting contracted.25 Hence, the nd and (n + 1)s orbitals of the second and third transition metal series become nearly comparable in size, thereby facilitating the d

bonding This may result in a greater stabilization of compounds containing heavier transition metals, as compared with those of the first-row metal elements, even though the relation remains not linear In fact, the bond dissociation energies of V2 and Nb2are determined to be 2.75 ± 0.0126 and 6.20 ± 0.05 eV,27 respectively, while that of

Ta2 is predicted to be in the range from 4.96 to 5.40 eV.28

For gold-containing compounds, it should be noticed that a crucial factor making their properties unique is the relativistic effect,17 rather than the “lanthanoid contraction” as mentioned above Actually, the relativistic maximum of gold, which was initially pointed by Pyykkö,16 leads to many unusual molecular properties of gold compounds For example, while the ground state structure of Cu7– and Ag7– are three dimensional (3D), that of Au7– is planar, separated from the optimal 3D isomer by 0.5

eV.29 The propensity of neutral gold clusters to favor planar structures continues up to surprisingly large sizes, being likely up to 13 atoms.30 The strong relativistic effects in

addition enhance the d–d interaction, leading to a stabilization of Au-Au bond.31,32 As

a result, the gold–gold distance in metal is even shorter than the corresponding silver–silver distance (2.884 versus 2.889 Å).33 The similar phenomenon also appears in dimers, in which the bond dissociation energy of Au2 (2.29 ± 0.02 eV) is significantly larger than those of Ag2 (1.65 ± 0.03 eV) and Cu2 (1.98 ± 0.04 eV).24 Without

relativistic effects, the interactions between fulfilled d orbitals become insignificant;

thereby the bond strength between gold atoms were weaker than that between silver

counterparts because the s orbital shrinks down the group Also due to the strong relativistic effects, Au(I) compounds tend to aggregate (polymerize) via formation of

weak gold-gold bonds with a length of ~ 3.0 Å and a strength of ~ 7-12 kcal.mol–1

Such striking phenomenon is known by the terms of aurophilicity or aurophilic

attraction.34

By combining various classical and modern analytical techniques, a large numbers of properties on size-selected clusters, especially for those of transition elements, have been investigated and reported To obtain insights into the stability of

a certain cluster, mass spectroscopy and laser spectroscopy approaches are often employed, while atomic and molecular methods are used to probe their chemical reactivities Besides, other experimental techniques widely used in cluster science include ion mobility, optical absorption spectroscopy, photoelectron spectroscopy,20… However, very little information about the geometry (atomic arrangement) of clusters could directly be received from these endeavors, though as stated above the molecular structure of clusters is of fundamental importance to understand and interpret their behaviors Optical (UV-VIS) and photoelectron (PES) spectroscopies allow us to probe the electronic structure following excitation and ionization, which is strongly influenced by geometric arrangements Thus these spectrometric techniques can give indirect information on the atomic structure Several techniques that are capable of determining the structure of clusters include trapped ion electron diffraction, scanning tunneling microscopy, and transmission electron microscopy,… but their applications to the clusters considered in this work are still limited

Recently, a more direct and more effective way of obtaining structural information is the use of vibrational spectrometry, because the molecular vibrations are determined by the forces between atoms and thereby reflects their internal positions within a molecular system.35 Nonetheless, in order to interpret vibrational

spectra, such experiments need to be carried out in concert with ab initio calculations

Indeed, in spite of all inherent shortcomings, density functional theory has been shown to be quite successful in reproducing the vibrational signatures of several transition metal clusters whose spectroscopic information were recorded.35–39 Then, systematic comparisons between the calculated harmonic and measured vibrational (IR, FIR) spectra could allow the energetically preferred structure to be assigned However, due to the experimental difficulties in creating the vapor phase, and the limited selection of analytical techniques, the far-infrared absorption spectra with good resolution of only a limited number of transition metal clusters were experimentally obtained so far For the case of niobium clusters, the experimental far-

IR spectra of small neutral and cationic niobium clusters containing five to twelve Nb

atoms were already recorded by Fielicke et al.,37,40 and by comparing the

experimental data to computational results, we were able in recent works to elucidate their growth pattern and electronic properties.41

In addition to atomic arrangements (structure), theoretical studies provide crucial information on the electronic structure, fragmentation behavior (stability), magnetic properties, thermochemical parameters, as well as chemical reactivities of clusters… Even before clusters could be prepared in the laboratory, simulations could already be done to predict their structures, using for example tight-binding molecular dynamics methods based on empirical potentials.20 So far, many studies still use such techniques, although they seem rather oversimplified However, this kind of semi-empirical approaches has intrinsic limitations in the description of energetic properties Currently, first-principle calculations within the framework of density functional theory, along with Gaussian-type or plane-wave basis sets become central

in the cluster studies Except for very small systems, they compete well in accuracy with most post-HF wave-function methods, while the computational cost is substantially less expensive.42 Furthermore, many quantitative definitions of chemical notions including electronegativity, softness, hardness, and the electronic origins of chemical bonding and reactivity… could be defined and understood more clearly within the framework of density functional theory.43

In Chapter 2, a concise description of DFT methods and their performance in transition metal clusters will be presented Then the applications of these methodologies on the study of Nb and Au clusters are discussed thoroughly in Chapter 3 and Chapter 4, respectively Finally, we summarize in Chapter 5 the main results obtained in the thesis and suggest some related works in the future, as well as some perspectives in the theoretical approaches for cluster studies

5 M.A Hayat, Colloidal Gold: Principles, Methods, and Applications, Academic

Press, San Diego, 1991

6 F Baletto and R Ferrando, Rev Mod Phys., 2005, 77, 371

7

M Haruta, Catal Today, 1997, 36, 153

8 M Valden, X Lai and D W Goodman, Science, 1998, 281, 1647

9 A Sanchez, S Abbet, U Heiz, W.D Schneider, H Haekkinen, R.N Barnett and U

Landman, J Phys Chem A, 1999, 103, 9573

10

W D Knight, , K Clemenger, W A de Heer, W A Saunders, M Y Chou and M

L Cohen, Phys Rev Lett., 1984, 52, 2141

11 W A de Heer, W D Knight, M Y Chou and M L Cohen, Solid State Phys.,

1987, 40, 93

12 J A Alonso and N H March, Electrons in Metals and Alloys; Academic: London,

1989

13 I Katakuse, T Ichihara, Y Fujita, T Matsuo, T Sakurai and H Matsuda, Int J

Mass Spectrom Ion Processes, 1985, 67, 229

14 I Katakuse, T Ichihara, Y Fujita, T Matsuo, T Sakurai and H Matsuda, Int J

Mass Spectrom Ion Processes, 1986, 74, 33

15 J A Alonso, Chem Rev., 2000, 100, 637

16 P Pyykkö, Chem Rev., 1988, 88, 563

17 P Schwerdtfeger, M Dolg, W H E Schwarz, G A Bowmaker and P D W

Boyd, J Chem Phys., 1989, 91, 1762

18 H Akeby, I Panas, L G M Petterson, P Siegbahn and U Wahlgren, J Phys

21 P Schissel, J Chem Phys., 1957, 26, 1276

22 S K Gupta and K A Gingerich, J Chem Phys., 1979, 70, 5350

23 C Kittel, Introduction to Solid State Physics; Wiley: New York, 1976

24 M D Morse, Chem Rev., 1986, 86, 1049

25

P.Schwerdtfeger, P D Boyd, G A Bowmaker, H G Mack and H Oberhammer,

J Am Chem Soc., 1989, 111, 15

26 E M Spain and M D Morse, J Phys Chem., 1992, 96, 2479

27 M B Knickelbein and S Yang, J Chem Phys., 1990, 93, 5760

28

A C Borin and J P Gobbo, Int J Quant Chem., 2011, 111, 1306

29 H Häkkinen, Michael Moseler and Uzi Landman, Phys Rev Lett., 2002, 89,

32 P Schwerdtfeger, Heteroatom Chem., 2002, 13, 578

33 M Bardají and A Laguna, J Chem Ed., 1999, 76, 201

34

H Schmidbaur, Gold Bulletin, 2000, 33, 1

35 C Ratsch, A Fielicke, A Kirilyuk, J Behler, G V Helden, G Meijer and M

Scheffler, J Chem Phys., 2005, 122, 124302

36 A Fielicke, A Kirilyuk, C Ratsch, J Behler, M Scheffler, G V Helden and G

Meijer, Phys Rev Lett., 2004, 93, 023401

37 A Fielicke, C Ratsch, G V Helden, and G Meijer, J Chem Phys., 2007, 127,

234306

38

P Gruene, D M Rayner, B Redlich, A F G van der Meer, J T Lyon, G Meijer

and A Fielicke, Science, 2008,321, 674

39

L Lin, P Claes, P Gruene, G Meijer, A Fielicke, M T Nguyen and P Lievens,

ChemPhysChem, 2010, 11, 1932

40 A Fielicke and G Meijer, J Phys Chem A, 2011, 115, 7869

41 (a) P V Nhat, V T Ngan, M T Nguyen, J Phys Chem C, 2010, 114, 13210; (b)

P V Nhat, V T Ngan, T B Tai and M T Nguyen, J Phys Chem A, 2011, 115,

3523 (c) P V Nhat, V T Ngan, T B Tai and M T Nguyen, J Phys Chem A,

2011, 115, 14127

42 C J Cramer and D G Truhlar, Phys Chem Chem Phys., 2009, 11, 10757

43 P Geerlings, F De Proft and W Langenaeker, Chem Rev., 2003, 103, 1793

12

Chapter 2 Theoretical Backgrounds

The performance of density

functional theory for transition metal compounds

2.1 Introduction

To some extent, the Hartree–Fock model, a fundamental step in treatment of many-electron systems, provides good descriptions for a number of chemical observables including equilibrium geometries and energetics of several kinds of known chemical compounds and their reactions However, such an approximation naturally leads to overestimation of the repulsion energy between electrons The electronic energy calculated by the Hartree–Fock (HF) method even with a complete basis set is thus typically larger (more positive) than the energy resulted from an exact solution of the Schrödinger equation Therefore, a number of techniques going beyond the HF theory have been developed to reduce the difference between the HF

energy and the exact Schrödinger energy, well known as the correlation energy

In the first approach based on the molecular orbitals, the HF wave function

or a Slater determinant corresponding to the electronic ground state is expanded by a linear combination of wave functions describing several excited states This leads to the methods of configuration interaction (CI) or multi-configuration (MC) The

second approach is now commonly known as density functional theory (DFT),

which describes an electronic state of the many-electron systems in terms of the

three-dimensional electronic density ρ(r), rather than a 3N-three-dimensional anti-symmetric

wave function for an N-electron system as in molecular orbital theory (MO, or wave function theory, WFT).1 This alternative makes DFT of great interest because it significantly lowers the computational costs as compared to any post-HF method

In quantum chemical calculations, the electron density ρ(r) is a function of

the coordinate r that specifies the position of electrons inside a small volume dr In

molecules, regions of electron density are usually found around the heavy hydrogen) atoms, and the chemical bonds Indeed, X-ray crystallography locates atoms by identifying vicinities of high electron density Besides, an electron density surface can be employed to reveal the location of bonds between atoms The density

(non-ρ(r) is so readily visualized and a quantum theory can be put in terms of it.2 In fact, energies and other related properties of a molecular system can be calculated from its

electron density ρ(r)

P Hohenberg and W Kohn (1964) proved for molecules with a

non-degenerate ground state that the electronic energy E is a functional of ρ(r), namely E

= E[ρ(r)].3 Their theoretical proof then became a practical tool in condensed-matter physics, computational physics, and computational chemistry when W Kohn and L

J Sham (1965) devised a feasible method for finding ρ(r) and then for finding Efrom

ρ(r).4

Accordingly, one can compute the optimal energy of a many-body system by varying the Kohn–Sham orbitals θiKS, which are introduced to determine ρ(r), thereby

to minimize the functional E[ρ(r)]

Even though different versions of DFT were applied to study solids with considerable success since the 1970s, they were not considered reliable enough for molecular systems until the 1990s This theory is now among the most popular methods in computational chemistry Except for very small systems and for parameters involving the excited states, DFT competes well with most WFT approaches, in terms of accuracy/cost performance This is especially true for transition metal compounds as the number of valence electrons is normally very large More importantly, it is empirically observed that DFT is surprisingly trustworthy in computing the non-dynamic electron correlation,5 which is crucial in treatment of compounds containing transition metals but very difficult to be included in a well balanced way in MO-WFT calculations (through MC methods).6 Within the usual terminology, the non-dynamic correlation is considered as the long-range correlation,7

which can be included into DFT via exchange functional.8 This part can further be

corrected via the combination of a GGA exchange functional in DFT with the HF

exchange integral by using a standard error function.9,10 Furthermore, we can make use of DFT for quantitative definitions of chemical parameters including the electro-negativity, softness, hardness, and for the interpretations of the electronic origins of chemical bonding and reactivity.2,11

2.2 Functional classification

The wave function and the electron density are functions as they are

prescriptions for producing numbers from a set of variables (coordinates), while the

energy computed from the wave function or the electron density is called functional

The aim of DFT is to devise a tool that quantitatively accounts for the relations between the electron density and the energy This tool is popularly called as energy functional

It was well established in the quantum chemistry textbooks that the energy functional is approximated as a sum of four terms, T[ρ], Ene[ρ], Eee[ρ], and Exc[ρ] T[ρ] is the kinetic energy of a system of non-interacting electrons with the same spin densities as the real system, Ene[ρ] the attraction energy between nuclei and electrons,

Eee[ρ] the classical Coulomb energy of the spin densities interacting with each other and with themselves The first three terms T[ρ], Ene[ρ] and Eee[ρ] can be computed from the Kohn–Sham orbitals θiKS, which are introduced to obtain an approximate electron density of the fictitious non-interacting system, and also constitute the main contributions to the energy of a molecular system

In contrast, the fourth term Exc[ρ], which corrects the first three terms, is relatively small but difficult to accurately be evaluated This also represents the beauty and challenge of DFT as all of the mathematical and conceptual complexity is hidden in this small term In principle, if the exact Exc[ρ] is known, the total energy including the electron correlation can be calculated exactly However, no one knows exactly what the correct functional Exc[ρ] is, therefore various approximations have been developed in the last three decades to derive suitable formulas for the exchange–correlation term

The simplest method to obtain a density functional is now called the local

density approximation (LDA), in which the density ρ is assumed to vary extremely

slowly with position and thus can be treated as a uniform electron gas Mathematically, the exchange–correlation term Exc[ρ] is usually written as a sum of separate exchange (x) and correlation (c) parts, Ex[ρ] and Ec[ρ] Within such approach, these parts depend only on the scalar value of the electron density at a given point in space For open-shell systems, when the spin densities are not equal, the local density approximation is normally replaced by the local spin density approximation (LSDA) In the LSDA, paired electrons with opposite spins are located

in different spatial Kohn–Sham orbitals θiαKS and θiβKS Although the electron density

in a molecule cannot be treated locally, this type of treatment is surprisingly reliable

in predicting molecular constants including equilibrium geometries, vibrational frequencies, and dipole moments However, for some thermochemical properties such

as dissociation, atomization, ionization and affinity energies, LSDA calculations often yield significant deviations from experiment More sophisticated functionals going beyond the LSDA are needed to account for the latter parameters

The next improvements over LSDA approach, which are still local but make the electron density dependent on coordinates, are normally known as gradient

corrected methods or generalized gradient approximations (GGA) A large variety of

GGA exchange and correlation functionals are actually available In most cases, the authors of a specific functional aimed to improve a certain chemical or spectroscopic property It is not our intention to give here the detailed formulation of these functionals (which requires several books with full of mathematical formulas!), but

we would rather briefly mention the currently available ones John Perdew, a pioneer

in the functional development from Tulane University, New-Orleans, predicted in the late 1990‟s the emergence of a “Functionals Zoo” It is just hard for a non-frequent visitor to appreciate the value and the beauty of each animal!

In 1988, Becke introduced an extensively used (and probably the most successful) exchange functional denoted as B, B88 or Becke88.12 Other widely used gradient-corrected exchange functionals include the PW86 and PW91 proposed by Perdew and Wang.13,14 Various functionals were also suggested for correlation energy, including the Lee, Yang and Parr LYP,15 P8616 and PW91.14 The possible combinations of an exchange functional with a correlation functional bring about numerous GGA functionals such as BP86, BLYP, PW91PW91 and BPW91, etc… Other popular GGA functional is that of Perdew, Burke, and Ernzerhof, denoted as PBE.17

In general, the gradient-corrected functionals yield relatively good results for both molecular constants and a number of energetic properties, such as total energies, atomization energies, structural energy differences, and energy barriers.14,18,19

However, due to the fact that these functionals tend to include exchange and correlation, which have no physical significance, DFT with GGA framework is likely

self-to underestimate the HOMO–LUMO gaps in molecules, or the band gaps in solids.5

In addition, GGA methods typically fail for the van der Waals, weak and bonded interactions.20,21 Hence, more advanced functionals than GGAs have been developed to reduce such shortcomings One of common approaches is to introduce

hydrogen-the Hartree–Fock exchange, giving rise hydrogen-the so-called hybrid functionals The use of

LSDA and GGA methods often leads to significant overestimations of bond energies, while the Hartree–Fock method substantially underbinds them.22 Therefore, a combined hybrid treatment is expected to produce more balanced results for thermochemical parameters, due to a certain mutual cancellation of opposite effects

So far the most popular hybrid functional is still the B3LYP, which was used and present in more than 80% of the total of occurrences of density functionals in the literature for the period 1990-2006.23 Less popular hybrid-GGA functionals are the B3P86, B3PW91, PBE1PBE or PBE024,25 and mPW1PW,26 … Within the hybrid approaches, a certain percentage (normally called X%) of local density functional exchange has been replaced by Hartree–Fock exchange For example, in B3LYP, B3P86 and B3PW91, the Becke 3 parameter exchange functional (B3)27 has X = 20, while both PBE0 and mPW1PW have X = 25 Some functionals with higher values of

X include the BH&HLYP (X = 50), MPW1K (X = 42.8).28 One occasionally finds B3LYP* with X = 12 – 15 adjusted from X = 20 in B3LYP for investigations of iron(II) and iron(III) complexes.29,30 Besides, a number of more sophisticated hybrid GGAs have been developed with an optimized value of X, such as B97-1, B97-2, B97-3 and B98.31–34

Mixing in the Hartree–Fock exchange is not the only way to go beyond the generalized gradient approximations In GGA methods, the exchange–correlation energy is a function of both electron density and its first derivative The more general extension of GGA methods is to make the exchange and correlation functionals dependent not only on the density and the gradient (first derivatives) of the density, but also on the Laplacian (second derivatives) of the density, leading to the so-called

meta-GGA functionals Addition of Hartree–Fock exchange to meta-GGAs yields

hybrid meta-GGA functionals, which are proposed as the most powerful functionals currently available Some of the earliest attempts to include the Laplacian of the

density were performed by Becke et al.35,36 Recently developed meta-GGA functionals are -HCTH (Hamprecht, Cohen, Tozer and Handy),37 VSXC (Voorhis–Scuseria eXchange–Correlation),38 TPSS (Tao, Perdew, Staroverov and Scuseria),39PKZB (Perdew, Kurth, Zupan and Blaha)40 and BtLap.41 Several functionals of this type have been augmented with an amount of Hartree–Fock exchange to produce the hybrid meta-GGA functionals such as -HCTHh,37 and TPSSh.42 These functionals contain only 10 – 15% HF exchange, as compared to 28 – 46% in PW6B9543 and BMK,44 being also hybrid meta-GGAs More recently, functionals including corrections for dispersion have also been proposed

High accuracy calculations not only for transition metals but also for main group elements are especially important in the studies of organometallic and coordination compounds However, at the time being, it is rather hard to find a functional which is good for both, because the description of bonding in transition metal compounds typically requires DFT functionals with low amount of Hartree–Fock exchange, while functionals with high percentage of Hartree–Fock exchange are more appropriate for main-group compounds.22 In 2005, Truhlar and co-workers introduced a hybrid meta functional that was designed to overcome these difficulties, called M05.45 The functional then was re-optimized yielding the M06,46 with X = 27

as compared to X = 28 of M05

Also, by fixing local spin density, its gradient and Laplacian, and Hartree–Fock exchange, these authors published a number of hybrid meta-GGAs, known as M05 and M06 suites of functionals, including M05–2X,47 M06–L,48 M06–2X,46 and M06–HF.49 Such functionals were designed to study coordination compounds, organometallics, non-covalent bonds, chemical kinetics and reaction mechanisms, and charge transfer TD-DFT For example, to examine noncovalent complexes, the M06–2X functional is recommended because it surprisingly provides accurate binding energies even for weak non-covalent bonds,50 which are inaccurately predicted by common functionals.22 More recently, this group proposed the series of M11

functionals in which hundreds of empirical parameters were introduced and fitted.51,52These approaches are likely appropriate for calculations of electronic excitation energies, barrier heights, as well as band gaps of solids.53

2.3 DFT applications in transition metal compounds

DFT calculations have thus become an effective tool for analyzing electronic structures and related properties of transition metal compounds, and are routinely used not only by specialized computational chemists, but also by experimental

groups It should however be noticed that in transition metal chemistry all currently

used functionals are still likely to yield inaccurate results, especially for energetic quantities Commonly, the deviations from experiment for bond energies of modern

GGA, hybrid and meta-GGA functionals are quite large (up to >10 kcal.mol–1) in transition metal compounds, while such errors are extremely rare in main group compounds.22 Furthermore, in general, each functional naturally has its own advantages and disadvantages for specific properties, and the functionals that work well for main group elements are sometimes not reliable for transition metals.54–57Hence, this section briefly considers the performance of current DFT methods when applied for transition metal compounds, which can be served as a useful guidance in choosing functionals for certain properties of a given system

2.3.1 Geometries

In general, most common DFT functionals are sufficient for predicting the lowest-energy structures for small compounds, except for the cases where the potential energy surface is rather flat along a given coordinate In a study for 8 metal dimers, namely Ag2, Cr2, Cu2, CuAg, Mo2, Ni2, V2, and Zr2, Schultz and coworkers54found that the local SPWL and SVWN3 functionals yield the lowest average mean unsigned error (MUE being the average magnitude of the absolute errors in a set of forecasts) in bond lengths (MUE = 0.05 Å) Among GGA methods, BP86, G96LYP and mPWLYP are the most successful (MUE = 0.07 Å), while BB95 is best among the meta-GGAs (MUE = 0.07 Å) In the hybrid GGAs, B97-2 comes first with MUE

= 0.15 Å, as compared to MUE = 0.16 Å obtained by B3LYP Of hybrid meta-GGA functionals considered, the B1B95, TPSSh and TPSS1KCIS give the best results with MUE = 0.14 Å

Earlier, Barden et al.58 applied the LSDA, BP86, BLYP, B3P86 and B3LYP

functionals to nine homonuclear 3d dimers For bond distances, the BP86 is found to

be the best with MUE = 0.02 Å and the B3LYP the worst functional with MUE = 0.053 Å For vibrational frequencies, the MUE varies from 98 cm–1 (BLYP) to 122

cm–1 (B3P86) Legge et al.59 applied the LSDA, BLYP, BPW91, B3PW91 and B3LYP functionals to molecular geometries, vibrational frequencies and dissociation energies for a large number of coinage-based molecules They obtained the lowest average errors with BPW91 and this functional was also suggested to be the applicable approach for clusters of noble metal atoms These results indicate that non-hybrid methods usually perform better than hybrid functionals in predicting molecular geometries and vibrational spectra of compounds containing only transition elements

However, organometallic compounds seem to be more sensitive with functionals employed as the performance of most functionals delicately depends on the row of the transition metal involved By some measures, it has been found that

geometries of 3d complexes are better described by GGA/meta-GGA functionals, while hybrid functionals are more reliable for 4d and 5d element species For example, in a benchmark study for 50 metal–ligand bond distances in a series of 3d-

complexes,60 non-hybrid functionals in general perform better than the corresponding hybrid methods Of all functionals considered, the meta-GGA functional TPSS was found to come first in terms of performance Equilibrium geometries of 19 second-row transition-metal complexes were also tested using 15 different functionals and compared with measured values obtained from gas phase electron diffraction experiments.61 In this case, the hybrid GGAs always yield better results than the pure counterparts Hybrid functionals PBE0 (PBE1PBE), B3P86 and B3PW91 exhibit the lowest standard deviations from the measured bond lengths Furthermore, following

precise structural data for 25 5d-series complexes in the gas phase, these authors

tested 14 functionals against 41 transition metal–ligand bond distances.62 Again, as in

4d-metal complexes, hybrid functionals are consistently superior to GGAs and

meta-GGAs, except for B3LYP, which is surpassed by PBE, and more or less matched by a number of other standard GGAs such as BPW91 or BP86 The PBE0 functional along

with the B3P86 is judged to be most promising in predicting geometries of 5d-metal

complexes Though the basis sets employed, namely the Stuttgart-Dresden ECP (SDD) for metals and the 6-31G* for ligands, are quite small to obtain quantitative results, the set of compounds chosen cover a broad range of bonding types and could usefully be integrated in future benchmarking studies

In cases where accurate experimental data are not available, some groups tried to use high-level wave-function computations to test out the accuracy of DFT and several discrepancies with DFT were found A unanimous conclusion reached is that the DFT method has actually failed to predict However, in some cases the WFT method used is deficient, either due to the use of small basis sets or to an inadequate description of correlation This is convincingly illustrated by thorough discussions of Siegbahn63 and Rode et al.64

Let us consider a simple case One complex of dinuclear copper(I) can exist

in two forms, i.e isomer A and isomer B, as shown in Figure 2.1 In an extensive ab

initio study by Flock et al.,65 the μ-oxo structure (B) was found to be more stable than

the peroxo (A) by 12.7 kcal.mol–1 at the multi-configurational CASSCF/CASPT2 level, while at the B3LYP level, the isomer A is more stable by 19.9 kcal.mol–1 The CASPT2 result thus contradicts the experimental observations as the complex prefers the peroxo structure.66,67 These authors speculated that the preference of [Cu2(μ-η2:η2-peroxo)]2+ core in several enzymes such as hemocyanin (Figure 2.2), catechol oxidase, and tyrosinase is probably due to the steric or/and solvent effects In addition they suggested that DFT/B3LYP is not capable of treating such systems, and MO based multi-configurational CASSCF/CASPT2 calculations yield more accurate results This complex has then been reinvestigated using multi-reference configuration interaction (MRCI) techniques.64 Accordingly, the peroxo form (A) was found to be more stable by 6 – 8 kcal.mol–1 than the oxo (B), which qualitatively agrees with the B3LYP but is in strong contrast to the CASPT2 prediction It was also suggested that the main part of the discrepancy is likely to come from CASPT2 calculation rather from DFT.68 Nonetheless, although the B3LYP result is in good

agreement with the MRCI, it still overestimates the stability of structure A Reduction

of the amount of exact exchange to 10–15%, it then yields a better agreement between MRCI and DFT.64

A B

Figure 2.1 Two forms of the [Cu2(μ-η2:η2-peroxo)]2+ (A) and [Cu2(μ-oxo)]2+ (B)

complexes with six NH3 ligands

Figure 2.2 X-ray structure of the peroxo form of hemocyanin

2.3.2 Spin-state splittings

Another crucial parameter in testing the accuracy of DFT calculations is the relative energy of different spin states of a given complex In general, this gap is not internally consistent within different functionals because such calculated value in transition metal compounds strongly depends on the amount of Hartee–Fock exchange.69–71 Indeed, a decreasing exact exchange in hybrid functionals usually leads

to lower relative energies for high-spin states compared to low-spin states For example, while the B3LYP functional (X = 20) tends to overestimate high-spin/low-spin energy gaps of Fe(II) complexes in weak ligand fields, a modification of B3LYP

to B3LYP* (X = 15) significantly reduces such differences and yields better agreement between theory and experiment.29,69–72 Moreover, in a study on spin-crossover compounds,73 the complex Fe(phen)2(NCS)2 was predicted to prefer a singlet ground state by BP86 and BLYP, whereas B3LYP yields a quintet ground state The author in addition deduced that although the singlet state is truly the ground state, its stability is still overestimated by GGA functionals, and in this case, the high-spin/low-spin splitting computed by the modified functional B3LYP* with X = 12 is seemingly much more trustworthy

Paulsen and co-workers74 previously performed an extensive investigation

on nine iron(II) spin-crossover complexes and also drawn a similar pattern that the hybrid B3LYP generally favors the high-spin state, while a general feature of GGA functionals BLYP and PW91 is their preference of low-spin states In another study

on metallocenes and bis(benzene) complexes of the first transition metal, Reiher et

al.75 again observed a similar trend

Several comparisons of DFT to highly correlated multi-reference techniques have been reported in the literature For instance, Batista and Martin76 compared CASSCF and B3LYP results in an attempt to clarify the ground state of the binuclear ruthenium blue dimer [(bpy)2(OH2)RuORu(OH2)(bpy)2]4+ Their CASSCF calculations yielded a singlet ground state consistent with both magnetic susceptibility measurements77 and a previous DFT study,78 but inconsistent with a triplet ground state predicted by B3LYP functional Though the CASSCF result is not quantitatively