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 1Acknowledgements
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 5Acknowledgements
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 3Acknowledgements
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
28 6Acknowledgements
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 4Acknowledgements
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 9Acknowledgements
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 6Acknowledgements
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 5Acknowledgements
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 9Acknowledgements
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 5Acknowledgements
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
51 9Acknowledgements
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 3Acknowledgements
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 3Acknowledgements
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
57 6Acknowledgements
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 3Acknowledgements
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
58 83. Results and discussion
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 93. Results and discussion
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