Advances in Quantum Chemistry

686 Pages·2003·9.105 MB·English

by  Per Olov Lowdin

Contents
Contributors xvii
Preface xxiii
Obituary xxvii
Anniversary xxxiii
I.General Theory
AuniqueJahn–Teller Mechanismofall the Symmetry Breakings
inMolecular Systems and Condensed Matter 1
Isaac B. Bersuker
1. Introduction 2
2. Jahn–Teller,Renner–Teller,andpseudo-Jahn–Tellersymmetry
breaking 3
3. ChemicalbondingasaparticularcaseoftheJahn–Tellereffect:
rigorousformulationoftheJTtheorem 6
4. Jahn–Tellerinducedsymmetrybreakingsinstructuralphasetransitions,
melting,vaporization,andenantiomerformation 8
5. Generalformulations 10
Acknowledgements 12
References 12
Icosahedral Quarks 13
B. R. Judd and Edwin Lo
1. Introduction 13
2. Gains 14
3. TheirreduciblerepresentationG 15
4. Quasispin 16
5. Theicosahedralhshell 17
6. Generalizations 18
Acknowledgements 19
References 19
v
vi CONTENTS
Antilinear Particle–HoleConjugation Operators inJahn–Teller Theory 21
E. D.Savage andG. E. Stedman
1. Introduction 22
2. Statesandjmsymbols 24
3. Tensorformulation 25
4. Quasispinandquasi-Kramers’symmetries 27
5. Ceulemans’selectionrules 33
6. Theconnectionbetweenthe1984and1994selectionrules 39
7. Conclusion 42
Acknowledgements 42
References 42
Renner–Teller Interaction MatricesandGreen’s Function Formalism 45
GiuseppeBevilacqua,Liana Martinelli and GiuseppePastori Parravicini
1. Introduction 45
2. Renner–Tellerelectron–phononmatrices 46
3. Renner–Tellermatricesbysymmetryonlyrequirements 50
4. Modelp-likeHamiltonianandcalculationprocedure 52
5. Conclusions 56
Acknowledgements 57
References 57
Tunneling inJahn–Teller Systems and MultidimensionalWKB
Approximation 59
Victor Polinger
1. Introduction 59
2. SymmetrypropertiesoftunnelingstatesinJTsystems 62
3. Tunnelingsplittinginatwo-levelsystemwithpseudo-Jahn–Tellercoupling 66
4. Thejunctionruleforprobabilityflux 70
5. Jahn–Tellertunnelinginthreedimensions:theT^t case 73
2
6. ThecrossoverproblemintheicosahedralH^hcase 80
7. Concludingremarksanddiscussion 84
Acknowledgements 86
References 87
Tunneling Path and Ground State Crossover inLinear T^ðe%t Þ
2
and Quadratic G^ðg%hÞ Jahn–Teller Systems 89
HuanmingLi, Victor Z. Polinger,Janette L.Dunn and Colin A.Bates
1. Introduction 89
2. TheWKBapproximationapproachtoJahn–Tellerproblems 91
3. CrossoverandtunnelingpathsinthelinearT^ðe%t Þsystem 93
2
4. CrossoverandtunnelingpathsinthequadraticG^ðg%hÞJTsystem 95
5. Conclusions 101
References 101
CONTENTS vii
The Electronic Non-Adiabatic Coupling Terms: Onthe Connection
between MolecularPhysics and Field Theory 103
M. Baer, A.Vibo´k,G. Hala´sz and D.J.Kouri
1. Introduction 104
2. Thetreatmentofatom–atomsystems 105
3. Thetreatmentofpoly-atomicsystems–thetime-independentapproach 106
4. Thetreatmentofpoly-atomicsystems–thetime-dependentapproach 112
5. Conclusions 116
References 117
Nonadiabatic Coupling:General Featuresand Relation to
Molecular Properties 119
Eugene S. Kryachko
1. Introduction 119
2. Nonadiabaticcoupling:keyproperties 121
3. Orthogonaltransformationandtwo-stateproblem 124
4. ‘Equationofmotion’anddiabatic‘smoothness’ofmolecularproperty 126
5. Molecularpropertiesandtwo-statediabatization 127
6. ‘Smoothness’oftheelectronicdipolemomentandthegeneralized
Mulliken–Hushapproach 128
7. Summary 129
Acknowledgements 130
References 130
Jahn–Teller Effect in the ExcitedState:Anomalous Temperature
Dependence of the Zero-Phonon Line 135
V.Hizhnyakov, V.Boltrushko, H.Kaasik and I.Sildos
1. Introduction 135
2. StrongJahn–Tellereffect:opticalA –Etransition 138
1
3. Zero-phononline:positionandwidth 139
4. ApplicationtoA –Etransition 145
1
5. Experimental 146
6. Conclusions 148
Acknowledgements 148
References 148
Critical Dependence ofMultiphonon Transitionson Interaction
Strengthand Temperature 151
V.Hizhnyakov and H.Kaasik
1. Introduction 151
2. Relaxationofalocalizedvibrationalmode 152
3. Temperaturedependenceofnon-radiativetransitions 160
4. Conclusions 167
References 167
viii CONTENTS
Non-CondonCorrection toFranck–Condon Values of Second-order
Reduction Factors:The Cubic T Term 169
Faten Al-Hazmi, VictorZ. Polinger, Janette L. Dunn, ColinA. Bates,
Elie A.Moujaes and Michel Abou-Ghantous
1. Introduction 170
2. GeneralbackgroundtocubicT^tJTsystems 171
3. Definitionsofsecond-ordervibronicRFs 172
4. ThebasisoftheFCapproximation 174
5. EvaluationoftheRFsKð2ÞðT ^T ÞfortheT^tJTsystemusing
M 1 1
theFCapproximation 174
6. Non-CondoncorrectionsoftheFCvalues 176
7. Discussion 181
Acknowledgements 181
References 182
Embeddingof the K Graph on aSurface with Seven Cross-caps
10
and the Icosahedral H^2h Jahn–Teller Surface 183
Erwin Lijnen andArnout Ceulemans
1. Introduction 184
2. Thepolyhedralrepresentation 184
3. Whyapolyhedralrepresentationisuseful 186
4. TheinterconversionpathsonthelinearH^ðg%2hÞJTsurface 187
5. Polyhedralembeddingoftheinterconversiongraphsforthetrigonalminima 189
6. Discussionandconclusions 196
Acknowledgements 197
AppendixA:Embeddingsofthecomplementthatkeeptheequivalence
ofthetenvertices 197
References 198
II. MolecularSystems: Hydrocarbons
Combined Jahn–Teller and Pseudo-Jahn–Teller Effects inthe Benzene
Radical Cation 199
H.Ko¨ppel, I.Baˆldea andP. G. Szalay
1. Introduction 200
2. Theoreticalframework 201
3. Themulti-modeJTeffectintheXX~2E state 204
1g
4. SimultaneousJTandPJTinteractionsintheDD~ 2E (cid:3)EE~2B system 210
1u 2u
5. Concludingremarks 215
Acknowledgements 216
References 216
CONTENTS ix
Symmetry Aspects ofDistortivity inpSystems 219
P. W. Fowler
1. Introduction 219
2. TheHeilbronnermodel 221
3. CountingHeilbronnermodes 222
4. SymmetryandHeilbronnermodes 225
5. Heilbronnermodesinpolyhedra 227
6. Heilbronnermodesandthelinegraphs 229
7. Whendoesdistortionoccur? 232
8. Distortionandaromaticity 234
References 236
Jahn–Teller Effect in Circulenes 239
Tohru Sato, YasutakaKuzumoto, Ken Tokunaga, HideakiTanaka
and Hiroshi Imahori
1. Introduction 240
2. Jahn–Tellereffect 242
3. Experimental 243
4. Methodofcalculation 243
5. Resultsanddiscussion 244
6. Summary 253
Acknowledgements 254
References 255
VibronicInteractions and Jahn–Teller Effects
inCharged Hydrocarbons 257
TakashiKato andKazuyuki Hirao
1. Introduction 257
2. Optimizedstructures 258
3. Electron–phononcouplinginthemonoanionsofacene-and
phenanthrene-edge-typehydrocarbons 260
4. PossibleT Sforthemonoanionsofacene-andphenanthrene-edge-type
c
hydrocarboncrystals 264
5. PossibleT Sforthemonoanionsofcoroneneandcorannulene 266
c
6. Concludingremarks 269
Acknowledgements 270
References 270
The Spin Hamiltonian Effective Approach tothe Vibronic
Effects – Selected Cases 273
F. Cimpoesu, K.Hirao, N.Stanica andV.Chihaia
1. Introduction 273
2. ThespinHamiltoniananditsgeneralization 274
x CONTENTS
3. AJahn–Tellersystemmodeledthroughgeneralizedspin
Hamiltonian:theH molecule 276
3
4. Apseudo-Jahn–Tellersystemmodeledthroughgeneralizedspin
Hamiltonian:theC H molecule 279
4 4
5. ThecomparisonwithC H – Thevibronicperspectiveonresonance
6 6
stabilizationandaromaticity 282
6. Conclusion 286
Acknowledgements 287
References 288
III. Molecular Systems: Fullerenes
Jahn–Teller Distortions and Excitation Energiesin Cn1 289
60
Martin Lu¨ders andNicolaManini
1. Introduction 289
2. ThemodelHamiltonian 291
3. Theadiabaticcalculations 293
4. Verticalexcitationenergies 297
5. Non-adiabaticcorrections 297
6. Discussionandconclusions 299
Acknowledgements 300
AppendixA 301
References 303
Many Electron- and Hole Terms ofMolecular Ions Cn6 305
60
A.V. Nikolaev andK. H.Michel
Acknowledgements 312
References 312
Cage StructureDistortion ofFullerenes 313
TatsuhisaKato
References 316
MultipleOccupancy ofTriplyDegenerate States in
Icosahedral Symmetry 319
S. S. Sookhun, C. A.Bates, J.L. Dunn andW. Diery
1. Introduction 320
2. JTinteractionmatrices 321
3. Adiabaticpotentialenergysurfaces(APES) 322
4. Rotationalcoordinates 324
5. Thestates 326
6. Energyevaluations 328
CONTENTS xi
7. Discussion 331
8. Conclusion 332
References 333
Vibronic-inducedShiftsin the OpticalSpectra ofDoped Fullerenes 335
I.D. Hands, J.L. Dunn andC. A. Bates
1. Introduction 336
2. VibroniccouplinginC 337
60
3. Experimentalcouplingconstants 339
4. Dopingeffectsintheopticalspectraoffullerides 341
5. ForceconstantmodelsforC 344
60
6. Chargetransfer-inducedmodeshifts 350
7. Conclusionsanddiscussion 350
Acknowledgements 352
References 352
IV. Molecular Systems: Main-Groupand Transition Elements
ADFT Based Parameterization ofthe VibronicMixingbetweenTwo
Non-degenerate ElectronicStatesandthe Application tos2-lonePairs 355
M. Atanasov and D.Reinen
1. Introduction 356
2. AnewrecipeforcalculatingE ,E andN usingDFT 359
g e
3. Computationaldetails 360
4. Applications 360
5. Conclusions 365
Appendix 366
References 368
The Ab Initio Analytical Approach ofVibronic Quantities: Application
toInorganic Stereochemistry 369
F. Cimpoesu and K.Hirao
1. Introduction 370
2. Principleandformalbackground 371
3. Theorbitalapproachtopseudo-Jahn–Tellereffect.Anewconcept:
thevibronicorbitals 372
4. Resultsanddiscussion 375
5. Conclusion 384
Acknowledgements 385
AppendixA 385
References 387
xii CONTENTS
VibronicInteractions inHigh Nuclearity Clusters 389
SergueiA.Borshch
1. Introduction 389
2. Hexanuclearrheniumchalcohalideclusters 390
3. Delocalizationofexcitationsindecatungstatecluster 395
4. Conclusions 399
Acknowledgements 399
References 399
Onthe Jahn–Teller Origin ofthe Phosphorus Molecule P Activation
4
by One- and Two-Electron Reduction 401
I.Ya. Ogurtsov and V.Mirzac
1. Introduction 402
2. Computationalmethods 402
3. ElectronicstructureofthePq ðq¼0;(cid:3)1;(cid:3)2Þmolecularsystems 403
4
4. Discussionsoftheresults 408
5. Conclusions 412
Acknowledgements 412
References 412
Magnetic Properties ofa Low-Symmetry d5 Complex:An Adiabatic
Pseudo-Jahn–Teller Problem 413
Kim R. Dunbar, Eric J. Schelter,Boris S. Tsukerblat, Andrei V. Palii,
SergeiM. Ostrovsky, Vadim Yu. Mirovitskii and Sophia I. Klokishner
1. Introduction 414
2. Themodel 414
3. Matrixrepresentationofthemaininteractions 415
4. Energypatternforad5 complexinastaticmodel 418
5. g-FactorsandTIPinthe2T ^ðeþSOþV Þpseudo-JTvibronicproblem 420
2 trig
6. Concludingremarks 426
Acknowledgements 428
References 428
Pseudo-Jahn–Teller Origin ofthe Metastable Statesin Sodium
Nitroprusside 429
E. Coronado, S. Klokishner, O.Reu and B. Tsukerblat
1. Introduction 429
2. Themodel 431
3. Groundadiabaticpotentialsheet 434
4. Qualitativediscussion:concludingremarks 442
Acknowledgements 443
References 444
CONTENTS xiii
V. ImpuritySystems
Jahn–Teller Ions in Cubic Crystals Explored Through
DFT Calculations 445
J. A.Aramburu, M. T. Barriuso,P. Garc´ıaFern´andez andM. Moreno
1. Introduction 446
2. Analysisofthemodel-Hamiltonian 447
3. DFTcalculationsforRhCl4(cid:3) inNaCl:evaluationofparameters 451
6
4. OtherJahn–TellersystemsexploredthroughDFT 455
Acknowledgements 458
References 458
Analysisof the EPR and RamanScattering of Copper(II)dopedCaO 461
Philip L.W. Tregenna-Piggott
1. Introduction 462
2. Theory 463
3. AnalysisoftheexperimentaldataobtainedforCaO:Cu2+andMgO:Cu2+ 468
4. Suggestedexperimentsforthecharacterizationofthelowenergy
vibronicstructure 475
5. Conclusion 479
Acknowledgements 479
Appendix 479
References 481
The Mechanisms ofJahn–Teller ComplexReorientations 483
Yurii V.Yablokov, Maria A.Augustyniak-Jabłokow,
Michael Hitchman and Dirk Reinen
1. Introduction 483
2. Theexperimentalresultsanddiscussion 484
3. Conclusions 495
Acknowledgements 496
References 496
Diffusion inConcentrated Jahn–Teller Systems 497
A.Ya. Fishman,M. A.Ivanov, T. E.Kurennykh, A.S. Lahtin,
L. L. Surat and V.B. Vykhodets
1. Introduction 497
2. Experimental:samplesandmethods 499
3. Experimentalresults 503
4. Theory 505
5. Conclusions 506
Acknowledgements 507
References 507
xiv CONTENTS
SpectralIntensities inCubicStoichiometric Elpasolites:
The Cs NaSmCl and Cs NaEuCl Systems 509
2 6 2 6
R. Acevedo, C. Portillo, G.Navarro andT. Meruane
1. Introduction 510
2. Experimentalsection 511
3. Theoreticalmodel 512
4. Vibronicintensitycalculations 514
5. Summary 519
Acknowledgements 524
References 524
Jahn–Teller Effect in Laser Crystal LiCaAlF :Cr3+ 527
6
C. N.Avram, Gh. E. Draganescu and N.M. Avram
1. Introduction 527
2. SymmetryandvibrationofLiCAFcrystal 528
3. Low-lyingenergylevelsinstaticcrystalfieldmodel 529
4. Jahn–Tellereffectinthe4T state 532
2g
5. Conclusion 533
Acknowledgements 534
References 534
VI. Solid State
Electron Correlation and Jahn–Teller Effect
inAlkali-Metal-Doped C 535
60
Shugo Suzuki,Tadahiko Chida and Kenji Nakao
1. Introduction 535
2. Basisofelectronicstructure 539
3. Photoemissionspectrum 543
4. Superconductivity 548
5. Summaryandopenquestions 553
Acknowledgements 553
References 553
VibronicRenormalization ofSuperconductivity Gaps
ina Two-Band Model ofCuprates 555
N.Kristoffel
Acknowledgements 560
References 560