advances in quantum chemistry - gbv · advances in quantum chemistry manifestations of vibronic...

ADVANCES IN

QUANTUM CHEMISTRYMANIFESTATIONS OF VIBRONIC COUPLING

IN CHEMISTRY AND PHYSIC S

JOHN R. SABIN

ERKKI BRANDA S

VOLUME 44

Contributors

xvi i

Preface

xxii i

Obituary

xxvi i

Anniversary

xxxiii

I . General Theor y

A unique Jahn-Teller Mechanism of all the Symmetry Breaking sin Molecular Systems and Condensed Matter

1Isaac B . Bersuker

1. Introduction

22. Jahn-Teller, Renner-Teller, and pseudo-Jahn-Teller symmetr y

breaking

33. Chemical bonding as a particular case of the Jahn-Teller effect :

rigorous formulation of the JT theorem

64. Jahn-Teller induced symmetry breakings in structural phase transitions ,

melting, vaporization, and enantiomer formation

85. General formulations

1 0Acknowledgements

1 2References

1 2

Icosahedral Quarks

1 3B. R. Judd and Edwin Lo

1. Introduction

1 32. Gains

1 43. The irreducible representation G

1 54. Quasispin

1 65. The icosahedral h shell

1 76. Generalizations

1 8Acknowledgements

1 9References

19

Antilinear Particle-Hole Conjugation Operators in Jahn-Teller Theory 2 1

E . D . Savage and G . E. Stedman

1. Introduction

222. States and jm symbols

243. Tensor formulation

254. Quasispin and quasi-Kramers' symmetries

275. Ceulemans' selection rules

3 36. The connection between the 1984 and 1994 selection rules

3 97. Conclusion

42Acknowledgements

42References

42

Renner-Teller Interaction Matrices and Green's Function Formalism

4 5

Giuseppe Bevilacqua, Liana Martinelli and Giuseppe Pastori Parravicin i

1. Introduction

452. Renner-Teller electron-phonon matrices

463. Renner-Teller matrices by symmetry only requirements

5 04. Model p-like Hamiltonian and calculation procedure

5 2

5. Conclusions

5 6Acknowledgements

5 7References

5 7

Tunneling in Jahn-Teller Systems and Multidimensional WK BApproximation

5 9

Victor Polinge r

1. Introduction

5 92. Symmetry properties of tunneling states in JT systems

623. Tunneling splitting in a two-level system with pseudo-Jahn-Teller coupling

664. The junction rule for probability flux

705. Jahn-Teller tunneling in three dimensions : the T0 t2 case

736. The crossover problem in the icosahedral H ® h case

8 07. Concluding remarks and discussion

8 4Acknowledgements

8 6References

8 7

Tunneling Path and Ground State Crossover in Linear T ® (e ® t2 )

and Quadratic G ®(g ®h) Jahn-Teller Systems

8 9

Huanming Li, Victor Z . Polinger, Janette L . Dunn and Colin A . Bate s

1. Introduction

8 92. The WKB approximation approach to Jahn-Teller problems

9 13. Crossover and tunneling paths in the linear T ® (e ® t2 ) system

934. Crossover and tunneling paths in the quadratic G ®(g ®h) JT system

955. Conclusions

10 1References

101

The Electronic Non-Adiabatic Coupling Terms: On the Connectionbetween Molecular Physics and Field Theory

10 3

M. Baer, A. Vibök, G . Haldsz and D . J . Kour i

1. Introduction

10 42. The treatment of atom-atom systems

10 53. The treatment of poly-atomic systems - the time-independent approach

10 64. The treatment of poly-atomic systems - the time-dependent approach

11 25. Conclusions

11 6References

11 7

Nonadiabatic Coupling : General Features and Relation toMolecular Properties

11 9Eugene S . Kryachko

1. Introduction

11 92. Nonadiabatic coupling : key properties

12 13. Orthogonal transformation and two-state problem

1244. `Equation of motion' and diabatic `smoothness' of molecular property

1265. Molecular properties and two-state diabatization

1276. `Smoothness' of the electronic dipole moment and the generalized

Mulliken-Hush approach

1287. Summary

12 9Acknowledgements

13 0References

13 0

Jahn-Teller Effect in the Excited State: Anomalous TemperatureDependence of the Zero-Phonon Line

13 5V. Hizhnyakov, V . Boltrushko, H . Kaasik and I . Sildo s

1. Introduction

1352. Strong Jahn-Teller effect : optical A i -E transition

13 83. Zero-phonon line : position and width

13 94. Application to A i -E transition

1455. Experimental

1466. Conclusions

148Acknowledgements

148References

14 8

Critical Dependence of Multiphonon Transitions on Interactio nStrength and Temperature

15 1

V. Hizhnyakov and H . Kaasik

1. Introduction

15 12. Relaxation of a localized vibrational mode

15 23. Temperature dependence of non-radiative transitions

1604. Conclusions

167References

167

Non-Condon Correction to Franck-Condon Values of Second-orde rReduction Factors : The Cubic T Term

I fi g

Eaten Al-Hazmi, Victor Z . Polinger, Janette L . Dunn, Colin A . Bates ,Ehe A. Moujaes and Michel Abou-Ghantou s

1. Introduction

17 02. General background to cubic T ®t JT systems

17 13. Definitions of second-order vibronic RFs

17 24. The basis of the FC approximation

1745. Evaluation of the RFs K,v»(Ti ® Ti ) for the T ® t JT system usin g

the FC approximation

1746. Non-Condon cor rections of the FC values

17 67. Discussion


18 1References

18 2

Embedding of the Kw Graph on a Surface with Seven Cross-cap sand the Icosahedral H ® 2h Jahn-Teller Surface

I 8 3

Erwin Lijnen and Arnout Ceulemans

1. Introduction

1842. The polyhedral representation

18 43. Why a polyhedral representation is useful

18 64. The interconversion paths on the linear H ® (g 2/i) JT surface

18 75. Polyhedral embedding of the interconversion graphs for the trigonal minima

18 96. Discussion and conclusions

196Acknowledgements

197Appendix A : Embeddings of the complement that keep the equivalenceof the ten vertices

19 7References

198

11 . Molecular Systems : Hydrocarbons

Combined Jahn-Teller and Pseudo-Jahn-Teller Effects in the Benzen eRadical Cation

19 9

H. Koppel, I . Bäldea and P. G. Szala y

1. Introduction

20 02. Theoretical framework

20 13. The multi-mode JT effect in the X 2E I , state

2044. Simultaneous JT and PJ'l' interactions in the D 2 E1 „ - E 2 B 2 ,, system

21 05. Concluding remarks


21 6References

216

Symmetry Aspects of Distortivity in zr Systems

21 9

P. W. Fowler

1. Introduction

21 92. The Heilbronner model

22 13. Counting Heilbronner modes

22 24. Symmetry and Heilbronner modes

22 55. Heilbronner modes in polyhedra

22 76. Heilbronner modes and the line graphs

22 97. When does distortion occur?

23 28. Distortion and aromaticity

234References

23 6

Jahn-Teller Effect in Circulenes

23 9

Tohru Sato, Yasutaka Kuzumoto, Ken Tokunaga, Hideaki Tanak aand Hiroshi Imahori

1. Introduction

2402. Jahn-Teller effect

2423. Experimental

2434. Method of calculation

2435. Results and discussion

24 46. Summary


25 4References

25 5

Vibronic Interactions and Jahn-Teller Effectsin Charged Hydrocarbons

257

Takashi Kato and Kazuyuki Hirao

1. Introduction

2572. Optimized structures

25 83. Electron-phonon coupling in the monoanions of acene- and

phenanthrene-edge-type hydrocarbons

2604. Possible TE S for the monoanions of acene- and phenanthrene-edge-type

hydrocarbon crystals

2645. Possible Tc S for the monoanions of coronene and corannulene

2666. Concluding remarks

269Acknowledgements

270References

27 0

The Spin Hamiltonian Effective Approach to the Vibroni cEffects - Selected Cases

273F. Cimpoesu, K . Hirao, N . Stanica and V . Chihai a

1. Introduction

27 32. The spin Hamiltonian and its generalization

274

3. A Jahn-Teller system modeled through generalized spinHamiltonian : the H3 molecule

27 6

4. A pseudo-Jahn-Teller system modeled through generalized spi nHamiltonian : the C4H4 molecule

27 95. The comparison with C 6 H6 - The vibronic perspective on resonanc e

stabilization and aromaticity

28 26. Conclusion


287

References

28 8

III . Molecular Systems : Fullerenes

Jahn-Teller Distortions and Excitation Energies in C«

28 9

Martin Lüders and Nicola Manin i

1. Introduction

28 92. The model Hamiltonian

29 1

3. The adiabatic calculations

2934. Vertical excitation energies

2975. Non-adiabatic corrections

297

6. Discussion and conclusions

299Acknowledgements

30 0Appendix A

30 1

References

303

Many Electron- and Hole Terms of Molecular Ions at

30 5

A. V . Nikolaev and K . II . Michel

Acknowledgements

31 2

References

31 2

Cage Structure Distortion of Fullerenes

31 3

Tatsuhisa Kato

References

31 6

Multiple Occupancy of Triply Degenerate States i nIcosahedral Symmetry

31 9S. S . Sookhun, C . A. Bates, J . L . Dunn and W . Diery

1. Introduction

32 02. J'E interaction matrices

32 13. Adiabatic potential energy surfaces (APES)

32 24. Rotational coordinates

32 4

5. The states

32 66. Energy evaluations

328

7. Discussion

33 18. Conclusion

33 2References

33 3

Vibronic-induced Shifts in the Optical Spectra of Doped Fullerenes

335

I . D . Hands, J . L . Dunn and C. A. Bates

1. Introduction

33 62. Vibronic coupling in C60

337

3. Experimental coupling constants

33 94. Doping effects in the optical spectra of fullerides

34 15. Force constant models for C60

344

6. Charge transfer-induced mode shifts

3507. Conclusions and discussion

350Acknowledgements

352References

352

IV. Molecular Systems : Main-Group and Transition Elements

A DFT Based Parameterization of the Vibronic Mixing between TwoNon-degenerate Electronic States and the Application to s 2 -lone Pairs

35 5

M. Atanasov and D . Reinen

1. Introduction

3562. A new recipe for calculating Eg , Ee and N using DFT

3593. Computational details

3604. Applications

3605. Conclusions

365Appendix

366References

368

The Ab Initio Analytical Approach of Vibronic Quantities : Applicationto Inorganic Stereochemistry

36 9

F. Cimpoesu and K. Hira o

1. Introduction

37 02. Principle and formal background

37 13. The orbital approach to pseudo-Jahn-Teller effect . A new concept :

the vibronic orbitals

37 24. Results and discussion

37 55. Conclusion


38 5Appendix A

38 5References

387

Vibronic Interactions in High Nuclearity Clusters

38 9

Serguei A. Borshch

1. Introduction

38 92. Hexanuclear rhenium chalcohalide clusters

39 0

3. Delocalization of excitations in decatungstate cluster

39 5

4. Conclusions


39 9References

39 9

On the Jahn-Teller Origin of the Phosphorus Molecule P 4 Activationby One- and Two-Electron Reduction

40 1

I . Ya . Ogurtsov and V. Mirzac

1. Introduction

4 022. Computational methods

402

3. Electronic structure of the P4 (q = 0, -1, -2) molecular systems

40 3

4. Discussions of the results

40 8

5. Conclusions

41 2

Acknowledgements

41 2

References

41 2

Magnetic Properties of a Low-Symmetry d5 Complex: An AdiabaticPseudo-Jahn-Teller Problem

41 3

Kim R. Dunbar, Eric J . Schelter, Boris S . Tsukerblat, Andrei V . Palii,Sergei M . Ostrovsky, Vadim Yu . Mirovitskii and Sophia I . Klokishner

1. Introduction

41 4

2. The model

41 4

3. Matrix representation of the main interactions

41 5

4. Energy pattern for a d 5 complex in a static model

41 8

5. g-Factors and TIP in the 2 T2 ® (e + SO + V tr; g ) pseudo-IT vibronic problem

42 0

6. Concluding remarks


42 8

References

428

Pseudo-Jahn-Teller Origin of the Metastable States in Sodiu mNitroprusside

429

E. Coronado, S . Klokishner, O . Reu and B . Tsukerbla t

1. Introduction

4292. The model

43 1

3. Ground adiabatic potential sheet

43 4

4. Qualitative discussion : concluding remarks

442

Acknowledgements

443

References

444

V. Impurity Systems

Jahn-Teller Ions in Cubic Crystals Explored ThroughDFT Calculations

445

J . A. Aramburu, M . T. Barriuso, P. Garcia Fern'andez and M . Moreno

1. Introduction

44 62. Analysis of the model-Hamiltonian

44 7

3. DFT calculations for RhClb in NaCl : evaluation of parameters

45 14. Other Jahn-Teller systems explored through DFT


45 8References

45 8

Analysis of the EPR and Raman Scattering of Copper(II) doped CaO

46 1

Philip L . W. Tregenna-Piggot t

1. Introduction

46 22. Theory

46 33. Analysis of the experimental data obtained for CaO :Cu 2+ and MgO :Cu 2+

46 84. Suggested experiments for the characterization of the low energ y

vibronic structure

47 55. Conclusion


47 9Appendix

47 9References

48 1

The Mechanisms of Jahn-Teller Complex Reorientations

48 3

Yurii V . Yablokov, Maria A . Augustyniak-Jablokow ,Michael Hitchman and Dirk Reinen

1. Introduction

48 32. The experimental results and discussion

4843. Conclusions


49 6References

49 6

Diffusion in Concentrated Jahn-Teller Systems

49 7

A. Ya . Fishman, M . A. Ivanov, T . E. Kurennykh, A . S . Lahtin ,L . L . Surat and V. B. Vykhodet s

1. Introduction

4972. Experimental : samples and methods

4993. Experimental results

50 34. Theory

5055. Conclusions

506Acknowledgements

507References

507

Spectral Intensities in Cubic Stoichiometric Elpasolites :The Cs2NaSmC16 and Cs2 NaEuC16 Systems

50 9

R. Acevedo . C. Portillo, G . Navarro and T . Meruan e

I . Introduction

51 02. Experimental section

51 13. Theoretical model

51 24. Vibronic intensity calculations

51 45. Summary


524References

524

Jahn-Teller Effect in Laser Crystal LiCaAlF 6 :Cr 3+

52 7

C . N. Avram, Gh . E. Draganescu and N . M. Avram

1. Introduction

5272. Symmetry and vibration of LiCAF crystal

5283. Low-lying energy levels in static crystal field model

5294. Jahn-Teller effect in the 4T2 . state

53 25. Conclusion


53 4References

53 4

VI. Solid State

Electron Correlation and Jahn-Teller Effectin Alkali-Metal-Doped C 60

53 5

Shugo Suzuki, Tadahiko Chida and Kenji Nakao

1. Introduction

53 52. Basis of electronic structure

53 93. Photoemission spectrum

54 34. Superconductivity

54 85. Summary and open questions


55 3References

55 3

Vibronic Renormalization of Superconductivity Gap sin a Two-Band Model of Cuprates

55 5

N . Kristoffel

Acknowledgements

56 0References

560

Orbital Ordering and the Cooperative Jahn-Teller Effect in Singl eCrystals of the Magnetic Perovskite La 718Sr118 MnO3

56 3

I . Gordon, P . Wagner, V. V. Moshchalkov, Y . Bruynseraede, L . Pinsar dand A. Revcolevschi

1. Introduction

56 42. Experimental

56 63. Structure and transport properties of LSMO

56 64. Influence of the CJT transition on the resistivity

57 05. Influence of the CJT transition on the magnetization

57 36. Summary


577References

577

Low-Temperature Phase Transition and Structure of Ordered Phasein K3H(SO 4) 2 (TKHS)-Family Materials

57 9

S . P. Dolin, A. A. Levin, T . Yu. Mikhailova and M. V. Solin

1. Introduction

57 92. Model Hamiltonian

58 03. Parameters 12 and Ju

58 14. Ground state of localized deuterons

58 25. Thermodynamics of the TKHS family


58 5References

58 6

Cooperative Dynamical Effect in Rhombohedral LaMnO 3

58 7

A. E. Nikiforov and S . E. Popov

1. Introduction

5872. Lattice energy calculation model


5904. Conclusion

597Acknowledgements

597References

598

First-order Phase Transition in UO 2 : the Interplay of the 5f2 -5f2Superexchange Interaction and Jahn-Teller Effect

59 9V. S . Mironov, L . F . Chibotaru and A. Ceulemans

1. Introduction

60 02. Superexchange interaction between U4+ ions in UO2

60 33. Jahn-Teller effect for the ground F5 state of U 4+ ions : calculations of

vibronic coupling constants for the e g, t2g(l) and t2g(2) Jahn-Teller modes

61 14. Discussion : The relationship between the 5f2 - 5f2 superexchang e

interaction and Jahn-Teller effect

61 35. Conclusions and further outlook

615

Acknowledgements

61 6References

61 6

Dynamic Jahn-Teller Character of Manganese(III) Spin-Crossove rComplex [Mn(taa)] (H3taa = tris(1-(2-azolyl)-2-azabuten-4-yl)amine)

61 7

Motohiro Nakano, Gen-etsu Matsuhayashi and Takasuke Matsu o

1. Introduction

61 82. Experimental


61 94. Conclusion

629Acknowledgements

62 9References

629

Ground State of Quantum Jahn-Teller Model : Selftrapping vs.Correlated Phonon-assisted Tunneling

63 1

Eva Majernikovä and S . Shpyrko

1. Introduction

63 22. Extended (lattice) generalized Jahn-Teller model

63 33. Ground state of the lattice model

63 64. Ground state of the local model

64 15. Discussion of the numerical results

6436. Quantum fluctuations in the local model

6457. Conclusion

646Acknowledgements

64 7Appendix A

647References

648

Microscopic Approach to Cooperative Jahn-Teller Effect in Crystal swith Strong Intra-site Vibronic Coupling

64 9

L. F . Chibotar u

1. Introduction

65 02. Effective Hamiltonian for cooperative Jahn-Teller effect

65 03. Low-temperature structural phases in Jahn-Teller hexagonal perovskites

65 64. Conclusions

665Acknowledgements

66 5Appendix A : Derivation of the effective force constants

66 6References

66 7

Index

669

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