The Jahn-Teller Effect: Fundamentals and Implications for Physics and Chemistry PDF
Preview The Jahn-Teller Effect: Fundamentals and Implications for Physics and Chemistry
SpringerSeriesin chemical physics 97 SpringerSeriesin chemical physics SeriesEditors: A.W.Castleman,Jr. J.P.Toennies K.Yamanouchi W.Zinth The purpose of this series is to provide comprehensive up-to-date monographs inbothwellestablisheddisciplinesandemergingresearchareaswithinthebroad fieldsofchemicalphysicsandphysicalchemistry.Thebooksdealwithbothfun- damentalscienceandapplications,andmayhaveeitheratheoreticaloranexperi- mentalemphasis.Theyareaimedprimarilyatresearchersandgraduatestudents inchemicalphysicsandrelatedfields. For further volumes: http://www.springer.com/series/676 Horst Köppel David R. Yarkony Heinz Barentzen (Eds.) (cid:32)(cid:84)(cid:104)(cid:101)(cid:32)(cid:74)(cid:97)(cid:104)(cid:110)(cid:45)(cid:84)(cid:101)(cid:108)(cid:108)(cid:101)(cid:114)(cid:32)(cid:69)(cid:102)(cid:102)(cid:101)(cid:99)(cid:116) (cid:70)(cid:117)(cid:110)(cid:100)(cid:97)(cid:109)(cid:101)(cid:110)(cid:116)(cid:97)(cid:108)(cid:115)(cid:32)(cid:97)(cid:32) (cid:110)(cid:100)(cid:32) (cid:73)(cid:109)(cid:112)(cid:108)(cid:105)(cid:99)(cid:97)(cid:116)(cid:105)(cid:111)(cid:110)(cid:115) (cid:102)(cid:111)(cid:114)(cid:32) (cid:80)(cid:104)(cid:121)(cid:115)(cid:105)(cid:99)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32) (cid:32) (cid:67)(cid:104)(cid:101)(cid:109)(cid:105)(cid:115)(cid:116)(cid:114)(cid:121) With 350 Figures 123 Pro fesso r Horst Köppel Pro fesso r Heinz Barentzen Universität Heidelberg MPI für Festkörperforschung Theoretische Chemie Heisenbergstr. 1 Im Neuenheimer Feld 229 70569 Stuttgart 69120 Heidelberg Germany Germany E-mail: [email protected] E-Mail:[email protected] Pro fesso r David R. Yarkony Johns Hopkins University Department of Chemistry 3400 N. Charles Street Baltimore MD 21218 USA E-Mail:[email protected] SeriesEditors: ProfessorA.W.Castleman,Jr. DepartmentofChemistry,ThePennsylvaniaStateUniversity 152DaveyLaboratory,UniversityPark,PA16802,USA ProfessorJ.P.Toennies Max-Planck-Institutfu¨rStro¨mungsforschung Bunsenstrasse10,37073Go¨ttingen,Germany ProfessorK.Yamanouchi UniversityofTokyo,DepartmentofChemistry Hongo7-3-1,113-0033Tokyo,Japan ProfessorW.Zinth Universita¨tMu¨nchen,Institutfu¨rMedizinischeOptik O¨ttingerstr.67,80538Mu¨nchen,Germany ISSN0172-6218 ISBN 978-3-642-03431-2 e-ISBN 978-3-642-03432-9 DOI 10.1007/978-3-642-03432-9 SpringerHeidelberg Dordrecht LondonNewYork Library of Congress Control Number: 2009938946 © Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. 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Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface TheJahn–Teller(JT)effectcontinuestobeaparadigmforstructuralinstabilitiesand dynamicalprocessesinmoleculesandinthecondensedphase.Whilethebasictheo- rem,firstpublishedin1937,hadtoawaitexperimentalverificationfor15years,the interveningyearssawrapiddevelopment,initiallyinthetheoreticalarena,followed increasingly by experimental work on molecules and crystals. The International Jahn–TellerSymposiumwasestablishedinthemid-1970s,tofostertheexchangeof ideasbetweenresearchersinthefield.Amongthemanyimportantdevelopmentsin thefield,wementioncooperativephenomenaincrystals,thegeneralimportanceof pseudo-Jahn–Teller(PJT) couplingsfor symmetry-loweringphenomenain molec- ular systems, nonadiabatic processes at conical intersections of potential energy surfacesandextensionsofthebasictheoryinrelationtothediscoveryoffullerenes andothericosahedralsystems. Itistheobjectiveofthisvolumetoprovidetheinterestedreaderwithacollection oftutorialreviewsbyleadingresearchersinthefield.Thesereviewsprovideacom- prehensive overview of the current status of the field, including important recent developments.Thisvolumeistargetedatboththenon-expertscientistaswellasthe expertwhowantsto expandhis/herknowledgein allied areas.Itis intendedto be acomplementtotheexistingexcellenttextbooksinthefield.Guidedbytheideaof tutorialreviews,weprovidehereshortintroductoryremarkstothevarioussections, astheyappearinthetableofcontents.Thesearefollowedbyabriefcharacterization oftheindividualpaperstomaketheirbasiccontents,aswellastheirinterrelation, moretransparent. 1.Jahn–TellerEffectandVibronicInteractions:GeneralTheory Thefirstsetofreviewsdealswithgeneralformalaspectsofthetheory,itsrangeof applicationandimplementation.While the originalformulationof theJT theorem applies to orbitally degenerate electronic states, it was later recognized that simi- larmechanismsforstructuralinstabilitiesareoperativealsoinnondegeneratestates (PJT effect).Inthefirstpaperofthisvolume,Bersukeremphasizestheevenmore generalimplicationsoftheJTandrelatedcouplings,bydemonstratingthattheymay affect ground state structural properties, even when operative in the excited state manifold(hiddenJTeffect).Thismaybeassociatedwithspin-crossovereffectsand orbitaldisproportionation.Thefollowingtwopapers(byCeulemansandLijnen,and v vi Preface byBreza)addressgrouptheoreticalaspects.Adesirehassometimesbeenexpressed togainmoreinsightintothenatureoftheJTtheoremthanisaffordedbytheorigi- nalproof(whichconsistsinenumeratingalltopologicallydistinctrealizationsofall molecularpointgroups).Thisgoalisindeedachievedinthe article byCeulemans andLijnen.PoluyanovandDomckeadvocatetheuseofthemicroscopicBreit-Pauli operator for the spin–orbit coupling rather than the phenomenologicalform often adopted.Theypointoutthattheresultingdependenceofthespin–orbitcouplingon thenuclearcoordinatescanleadtonoveleffects,ofrelevancetomolecularspectra. Satoandcoworkerspresentaschemeforanalyzingvibroniccouplingconstantsin termsofdensities,whichallowsthemtoinvestigatetheirlocalpropertiesandvisu- alizetheirelectronicorigin.Finally,anefficientmethodtocomputemultimodeJT couplingconstantswith densityfunctionaltheoryispresentedbyZlatar etal. The approach uses information from the JT distorted structure, which is decomposed intocontributionsfromthevariousrelevantnormalmodes. 2.ConicalIntersectionsandNonadiabaticDynamicsinMolecularProcesses Conical intersections can be considered generalizations of the JT intersections in lesssymmetriccases,thelatterbeingalsoconicalinshapeowingtothepresenceof the linear couplingtermspredictedby the JT theorem.In molecularphysics,con- ical intersections have emerged in the past one or two decades as paradigms for nonadiabaticexcited-statedynamics,triggeringaplethoraofstudiesofelementary photophysicalandphotochemicalprocesses.ThearticlebyBlancafortetal.reports onmoderndevelopmentsinthecharacterizationofconicalintersectionsbyabini- tiotechniques.Theirsecond-orderanalysisshows,forexample,howtodistinguish betweenminimaandsaddlepointsinthesubspaceofelectronicdegeneracyandto identifyphotochemicallyactivecoordinates.ThepaperbyBouaklineetal.presents aquantumdynamicalanalysisofthesmallestJTactivesystem,triatomichydrogen. This prototypical reactive scattering system is subject to geometric phase effects which,however,almostcompletelycanceloutintheintegralcrosssection.Onthe otherhand,strongnonadiabaticcouplings/geometricphaseeffectsgoverntheupper- coneresonances(Rydbergstates)ofthesystem.ThepapersbyFarajietal.andby ReddyandMahapatrapresentmultimodequantumdynamicaltreatmentsofJTand PJTsystemswithmorethantwointersectingpotentialenergysurfaces.Pronounced effectsofthecouplingsinthespectralintensitydistributionandinfemtosecond(fs) internal conversion processes are identified. A systematic dependenceof the phe- nomenaonthe(fluoro)substituentsaswellastheimportanceforthephotostability ofhydrocarbonsisdemonstrated.InthearticlebyMcKinlayandPaterson,similar phenomena,includingnonadiabaticphotodissociationprocessesandfspump-probe spectroscopy,arediscussedfortransitionmetalcomplexes,thusprovidingabridge betweentheJTeffectandphotochemistry. 3.Impurities;SpectroscopyofTransitionMetalComplexes Transitionmetalcomplexeshaverepresented,foralongtime,thearchetypicalsys- tem for which the JT effect plays a crucial role, especially with regard to crystal field splitting and spin–orbit interaction (Ham effect). This affects optical as well Preface vii as EPR spectra of 3d group ions, for example. In the review by Brik and Avram thesearestudiedforvariouscoordinationsitesusinganeffectiveHamiltonianfor- malism. Useful relations for the Ham reduction factors are derived, and the JT parameters obtained from the Ham effect are compared with those obtained from theJT-distortedminimaofthepotentialenergysurfaces.Tregenna-PiggottandRiley presentintheirreviewa verypedagogicintroductionto theExeJT effect,andthe Ham effect as one of its consequences. Applications to various types of spectra of different transition metal complexes underline the usefulness of the theoretical concepts.Garcia-Fernandezetal. addressthequestionofstructuralinstabilitiesof dopedmaterialsandtheirtypeandorigin.Theyargue,andpresentconvincingevi- dence, that these are frequently not due to differencesin atomic sizes (as is often assumed in the literature) but rather to vibronic coupling, that is, the PJT effect. Finallyintheirreview,ReinenandAtanasovanalyzeintheirreview,theeffectsof JT couplingonthechangesfroma high-spinto alow-spinelectronicgroundstate in hexacoordinate fluoride complexes of Mn(III), Co(III), Ni(III) and Cu(III), an aspect which is frequently ignored in the literature on spin-crossover systems. In particular,the strong links to coordinationand solid state chemistry are set out in thiscontribution. 4.FullerenesandFullerides In the mid 1980sand subsequentyears, the discoveryof C and other fullerenes 60 openeda route to the analysisof JT systems with higherthan threefolddegenera- cies (G and H irreducible representations). This led to substantial developments fromthepointofviewofpuretheoryaswellasapplications.Thisvolumeincludes twoimportantpapersinthisarea.Structuralaspectsoffulleridesalts,i.e.fullerene anionsinvariouschargestatesinthesolidstate,arecoveredbyKluppandKamaras. Evidence,basedmostlyoninfraredspectroscopy,isusedtodiscussissuesincluding staticvs.dynamicJTeffect,unusualphases,andrelationtoconductivity.Thereview byHandsetal.addressesthefurthercomplicationoffullerenesbeingadsorbedon surfaces.Theloweringinsymmetryduetothesurfaceinteractionsisconsidered,as wellastheratherslowtime-scaleoftheexperimentaltechniqueofscanningtunnel- ing microscopy proposed. Detailed simulations of the correspondingimages shed usefullightontheirpossiblesignificanceinestablishingthepresenceandshapeof JTdistortions. 5.Jahn–TellerEffectandMolecularMagnetism Molecular magnetism concerns the synthesis, characterization and application of molecular-based materials that possess the typical properties of magnets – slow relaxation, quantum tunneling and blocking of the magnetization at low temper- atures (single molecular magnets (SMM)). It is an interdisciplinary research field whichrequiresthecombinedefforts(cooperation)ofchemists,molecularandsolid statephysicists,aswellastheoreticians(quantumchemists).Thisisthepointwhere theJTeffectentersintothegame.ThemagneticpropertiesofSMMsareaffectedby thestructuralinfluencescausedbyvibroniccouplingandtheseinfluencesarefurther manifestedintheopticalbandshapes,theinteractionsbetweenmagneticmolecules viii Preface withdegenerategroundstates(cooperativeJTeffect),andthedynamicalJTandPJT effects (which impactupon the magnetic relaxationand spin coherencetimes). In theirreview,Tsukerblat,KlokishnerandPaliiaddressthesepointsinspin-frustrated systems with threefold symmetry, mixed valence systems, photoswitchable spin systems, andmagneticmoleculeswhich undergotautomerictransformationslead- ing to long-lived(metastable)states. TheJahn–Tellereffectplaysa crucialrolein magnetic clusters built up from magnetic centers in orbitally degenerate ground states. Using a combination of ligand field theory and density functional theory AtanasovandCombashowhowsmallstructuralchangesduetoJahn–Telleractiv- ityand/orstructuralstrainsinduceadramaticloweringofthemagneticanisotropy. The same authors also show for the first time, using cyanide-bridged systems as modelexamples,howonecandeducetheparametersofthespinHamiltonianfrom firstprinciples. 6.TheCooperativeJahn–TellerEffectandOrbitalOrdering It has longbeen recognizedfor JT crystals, i.e., crystalscontaininga JT center in eachunitcell,thattheintrinsicinstabilityofJTcomplexesagainstdistortionsmay give rise to an effectiveinteractionbetweenJT ions, mediatedby the surrounding ligands of the ions. Below a critical temperature, this interaction may lead to the cooperativeJTeffect(CJTE),astructuralphasetransitionwherethewholecrystal distorts. There are two main approachesto the CJTE, differing in the form of the effectiveion–ioninteraction.Kaplan’sreviewispartlybasedonKanamori’streat- ment, who generated this interaction by the transformation from local vibrational modestophonons.Thistreatment,incombinationwiththecanonicalHamiltonian shifttransformationandasubsequentmean-fieldapproximation,isthemostpopu- larapproachtotheCJTE.Althoughthisconcept,alsoreferredtoasvirtualphonon exchange, has led to impressive results for some simpler systems, it cannot be applied to systems characterized by the Exe JT effect because of insurmountable technicaldifficulties. Such systems are convenientlytreated by meansof an alter- nativeapproach,developedbyThomasandco-workersanddescribedinPolinger’s article. This method assumes a bilinear lattice-dynamical interaction between the normalcoordinatesbelongingtonearest-neighborcells.However,themainempha- sisofthisarticleliesinadetailedcomparisonoftheCJTEwiththeorbital-ordering (orKugel-Khomskii)approach.Atypicalexampleoftheorbital-orderingapproach ispresentedinIshihara’sreview.Themainemphasisofthisarticleisontheintrinsic orbitalfrustrationeffect,meaningthatnoorbitalconfigurationexists,wherebythe bondenergiesinallequivalentdirectionsaresimultaneouslyminimized.Itisshown thatthe orbitalfrustrationeffectleadsto severalnontrivialphenomenain strongly correlatedsystemswithorbitaldegreesoffreedom.TheinfluenceoftheCJTEand ofJTimpuritiesonmaterialpropertiesiselucidatedinthereviewsbyGudkovand Lucovsky.ThereviewbyGudkovdealsmainlywiththeinfluenceofJTimpurities ontheelasticmoduliandultrasonicwaveattenuationindilutedcrystals.Theelastic- wavetechniquebroadensthefacilitiesofJTspectroscopyinitslow-energypartand providesnew information,mostly about the propertiesof the groundstate and its tunnelingsplitting.ThattheJTeffectevenplaysanimportantroleinsemiconduc- tortechnologyisconvincinglydemonstratedin Lucovsky’sarticle.HeretheCJTE Preface ix manifestsitselfinthegroupIVBtransition-metaloxides,designedasreplacement gatedielectricsforadvancedmetal-oxide-semiconductordevices. 7.Jahn–TellerEffectandHigh-TcSuperconductivity The explanation of high-temperature superconductivity (HTSC) in copper oxides (cuprates) is one of the most difficult problems in modern physics. The undoped cuprates are antiferromagnetic Mott insulators, where the insulating behavior is caused by a strong on-site Coulomb repulsion. HTSC arises upon hole doping, whereupon the originally immobile electrons in the half-filled conduction band becomemobile.Thebasicproblemistofindthepropermechanismfortheformation ofCooperpairs,thenecessaryingredientofallsuperconductors.Therearemainly two antagonistic views on the problem amounting to the question of whether the participationofphononsisindispensableforthepairformationorwhethertheelec- tronsalonecandothejob.ThereviewbyMirandaMenatriestoanswerthisquestion bygatheringallavailableevidenceinfavorofelectron–phononmechanismssuchas (bi)polarons and JT (bi)polarons. Seen in this perspective, the article gives a fair account of the state of the art in HTSCs. A more detailed theory of JT polarons andbipolaronswithapplicationtothefullerenesuperconductorsispresentedinthe articlebyHoriandTakada.Inadditiontoofferingathoroughmathematicalanaly- sis,theauthorsalsomaketheinterestingobservationthat,forstrongercoupling,JT polaronsacquireasmallereffectivemassthantheHolsteinpolaron.Suchareduc- tionofthepolaroneffectivemassisessentialfortheexistenceofsuperconductivity, asthepolaronmassincreaseswithincreasingcouplingsothat,forsufficientlystrong coupling,thepolaronbecomesimmobileandcannotcontributetotheelectriccur- rent.Theseremarksapply,inparticular,toKoizumi’swork,whichproposesthatthe dopedholesbecomesmallpolaronsandnot,asissupposedinallelectron-basedthe- oriesofHTSC,constituentsofZhang-Ricesinglets.Asthemobilityofthepolarons is very limited, a novelmechanism is requiredto facilitate a macroscopicelectric current.Theauthorsolvestheproblembyaloopcurrentgenerationaroundeachspin vortexdueto thespinBerryphase.Themacroscopiccurrentisthenthecollection ofalltheseloopcurrents. This set of tutorial reviews has been created on the occasion of the 19th Inter- national Jahn–Teller Symposium, held in Heidelberg, University Campus, 25–29 August 2008. The volume does not, however, reflect directly the conference con- tents.Fullcoverageofthe46oralpresentationsgivenatthemeeting(plusasimilar numberofposters)wasnotattempted.Conversely,the27paperscollectedherego intoconsiderablymoredepththanwouldbenormalforaproceedingsvolume.We hope that this volume constitutes a valuable reference, for beginners and experts alike. Heidelberg H.Ko¨ppel Stuttgart H.Barentzen Baltimore D.R.Yarkony May2009 Acknowledgments D.R.YarkonyacknowledgesthesupportofNSFgrantCHE-0513952.Theeditors areindebtedtoM.Atanasovforhelpfulcomments. xi
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