The Jahn-Teller Effect: Fundamentals and Implications for Physics and Chemistry

911 Pages·2009·21.138 MB·English

by  Isaac B. Bersuker (auth.), Horst Köppel, David R. Yarkony, Heinz Barentzen (eds.)

SpringerSeriesin
chemical physics
97
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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
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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