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E-raamat: Jahn-Teller Effect in C60 and Other Icosahedral Complexes

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  • Formaat: 221 pages
  • Ilmumisaeg: 09-Feb-2021
  • Kirjastus: Princeton University Press
  • Keel: eng
  • ISBN-13: 9780691225340
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Jahn-Teller Effect in C60 and Other Icosahedral ComplexesSuurem pilt
  • Formaat: 221 pages
  • Ilmumisaeg: 09-Feb-2021
  • Kirjastus: Princeton University Press
  • Keel: eng
  • ISBN-13: 9780691225340
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Because of the high symmetry involved, the Jahn-Teller effect is the natural starting point for considering electron-phonon (or vibronic) interactions in icosahedral molecules. This work is the first comprehensive theoretical analysis of the Jahn-Teller interaction in C60 and other icosahedral complexes. The importance of this research derives in part from the increasing, widespread interest in C60 and other molecular clusters and their application in science and industry. The electrical and spectroscopic properties of fullerene and fulleride compounds depend intimately on the coupling between the electronic and vibrational modes of these systems, and this book addresses the fundamental theoretical questions. In particular, a chapter is devoted to the connection between the theory and experimental observations, such as ESR (electron spin resonance) effects and molecular spectra.

Earlier books have discussed the theory of Jahn-Teller interactions in lower symmetry structures (cubic, tetrahedral, tetragonal, trigonal,...); this is the first that focuses on the new icosahedral systems, whose most famous example is Buckminsterfullerene, C60. The book's authors have over fifty years of combined research experience into the theoretical aspects of the Jahn-Teller effect.

Arvustused

"This is an important book for scientists involved in the rapidly expanding research on fullerenes, including C60, (C60)in- and (C60)+, which has stimulated research on other icosahedral species... an excellent reference to the fascinating aspects of icosahedral symmetry."--Australian & New Zealand Physicist

LIST OF FIGURES
ix(2)
LIST OF TABLES
xi(2)
GLOSSARY OF SYMBOLS
xiii
1. Introduction
3(10)
1.1 From Past to Present
3(1)
1.2 Definition and History
4(1)
1.3 The EXXXBeta (1) Interaction
5(2)
1.4 The Berry Phase
7(2)
1.5 Icosahedral Complexes
9(4)
1.5.1 C(60)-Based Materials
9(2)
1.5.2 Other Icosahedral Clusters
11(2)
2. Icosahedral Symmetry and Its Effects
13(18)
2.1 Icosahedral Symmetry
13(1)
2.2 Geometry of C(60) and the Group I(h)
13(3)
2.3 Irreducible Representations of I(h)
16(3)
2.3.1 Spin Representations: The Double Group
19(1)
2.4 Electron-Phonon Interactions
19(3)
2.5 Vibrational Modes and Their Symmetries
22(3)
2.6 Ham Reduction Factors
25(2)
2.7 Icosahedral Jahn-Teller Systems
27(4)
2.7.1 T XXX h and P(n) XXX h
27(1)
2.7.2 G XXX(g XXX h)
28(1)
2.7.3 H XXX(g XXX h)
28(3)
3. T XXX h and P(n) XXX h
31(36)
3.1 Introduction
31(1)
3.2 The Potential Energy Surfaces
32(7)
3.2.1 Rotational Symmetry of T(1) XXX h
32(3)
3.2.2 The Shape of the Distorted Molecule
35(1)
3.2.3 "Warping" of the Lowest-APES
36(2)
3.2.4 Modification for T(2) XXX h 3.2.4 Modification for T(2) XXX h
38(1)
3.3 The Ground States at Strong Coupling
39(8)
3.3.1 The Ground States in the Adiabatic Approximation
39(2)
3.3.2 The Ham Factors in T(1) XXX h
41(1)
3.3.3 The Ham Factors in T(2) XXX h
42(1)
3.3.4 The Ground State with Warping
43(4)
3.4 Intermediate Coupling Strength
47(3)
3.5 Multiple Occupation of T(1) Orbitals
50(11)
3.5.1 The Configurations P(2) and P(4)
51(3)
3.5.2 The Configuration P(3)
54(3)
3.5.3 Numerical Work on p(n)
57(1)
3.5.4 Term Splittings and Energy Ordering
58(3)
3.6 Optical Absorption Spectra
61(3)
3.6.1 Molecular Spectra
61(2)
3.6.2 Absorption Bands in Solids: The Cluster Model
63(1)
3.7 The Introduction of Spin-Orbit Coupling
64(3)
3.7.1 XXX XXX E(JT)
64(1)
3.7.2 XXX Comparable to or Larger than E(JT)
65(2)
4. Electronic Quartets and GXXX(g XXX h)
67(24)
4.1 Introduction
67(1)
4.2 G XXX g
68(9)
4.2.1 The Method of Opik and Pryce
68(3)
4.2.2 Biharmonic Parametrization of the G Bases
71(2)
4.2.3 The Geometry of the Ground States
73(2)
4.2.4 Numerical Phase Tracking
75(1)
4.2.5 The Ham Factors in G XXX g
76(1)
4.3 Symmetry and the Two Phase Spaces
77(1)
4.4 G XXX h
78(3)
4.4.1 Phase Tracking and the Ground States
79(2)
4.4.2 The Ham Factors in G XXX h
81(1)
4.5 G XXX (g XXX h)
81(6)
4.5.1 G XXX (g XXX h)(eq) and SO(4) Symmetry
83(3)
4.5.2 The Ham Factors
86(1)
4.5.3 Other Relative Coupling Strengths
86(1)
4.6 Broad Band Spectra
87(3)
4.7 An Overview of G XXX (g XXX h)
90(1)
5. Electronic Quintets and HXXX(g XXX h)
91(20)
5.1 Introduction
91(1)
5.2 H XXX h(4)
92(3)
5.3 H XXX h in General
95(5)
5.4 H XXX h(2)
100(5)
5.4.1 Bases and the Hamiltonian
100(1)
5.4.2 Rotational Symmetry of H XXX h(2)
100(2)
5.4.3 The Ground States at Strong Coupling
102(3)
5.5 H XXX g
105(1)
5.6 H XXX (g XXX h(4)(eq)
106(1)
5.7 H XXX (g XXX h(4) XXX h(2))(eq)
107(3)
5.7.1 The Ham Reduction Factors
108(2)
5.8 H XXX (g XXX h)
110(1)
6. Bridge to Experiment
111(46)
6.1 Multimode Effects: Cluster Models
111(10)
6.1.1 A Cluster Model for the Low Energy States
112(8)
6.1.2 A Cluster for Optical Absorption
120(1)
6.2 Electron Spin Resonance
121(18)
6.2.1 Jahn-Teller Interactions in the Spin Representations of the Group I
122(1)
6.2.2 The Spin Hamiltonian
123(1)
6.2.3 The g Factors
124(6)
6.2.4 The Spin Hamiltonian for Spin Triplet States
130(2)
6.2.5 Esr on C(60): Experiment and Theory
132(7)
6.3 Energy Levels in C(60)(n-)
139(3)
6.3.1 C(60) Vibrational Modes and Their Coupling
139(1)
6.3.2 Configuration Interaction in C(60)(n-)
140(2)
6.4 Molecular Spectra
142(3)
6.4.1 Symmetry-Lowering Distortions
142(1)
6.4.2 Allowed Transitions
143(1)
6.4.3 Experimental Evidence
144(1)
6.5 C(60)(-) Spectra
145(2)
6.6 C(60)(+) Spectra
147(4)
6.7 Superconductivity in the Fullerides
151(6)
6.7.1 C(60): Molecular Crystal
151(1)
6.7.2 Superconducting Fullerides
151(1)
6.7.3 p(3) XXX h
152(4)
Appendixes 157(42)
A. Adiabatic Approximation
157(4)
A.1 Corrections to the Adiabatic Approximation
159(2)
B. Quantum Tunneling Energies
161(8)
B.1 Introduction
161(1)
B.2 One-Dimensional Potentials
161(3)
B.3 Higher Dimensionality
164(1)
B.4 The WKB Approximation and Its Applications
165(4)
B.4.1 One-Dimensional Application
166(1)
B.4.2 WKB in More Dimensions
167(2)
C. E XXX
169(4)
D. The Group I
173(2)
E. Jahn-Teller Interaction Matrices and Their Bases
175(4)
E.1 Basis States
175(4)
E.1.1 L equal to 1 and L equal to 2 Bases
175(1)
E.1.2 Bases from L equal to 3 and Upwards
176(1)
E.1.3 Interaction Matrices
177(2)
F. Transformations
179(4)
F.1 Parametrizations of the h Modes
179(1)
F.2 Rotations to Diagonalize H XXX h(2)
180(1)
F.3 Rotations to Diagonalize T XXX h
181(1)
F.4 Representation of a Rotating Quadrupole
181(2)
G. Parameters of the Jahn-Teller Minima and Other Stationary Points
183(6)
H. Cited References and Bibliography
189(10)
H.1 Cited References
189(5)
H.2 Bibliography
194(5)
H.2.1 Molecular Quantum Mechanics
194(1)
H.2.2 Group Theory and Techniques
194(1)
H.2.3 The Icosahedral Group
195(1)
H.2.4 The Jahn-Teller Effect
195(1)
H.2.5 Icosahedral Systems
195(1)
H.2.6 The Berry Phase
196(1)
H.2.7 Spin Resonance
196(1)
H.2.8 Numerical Methods
197(1)
H.2.9 Superconductivity in the Fullerides
198(1)
H.2.10 Molecular Spectra
198(1)
INDEX 199
C. C. Chancey is Professor of Physics at Purdue University. M. C. M. O'Brien is a lecturer in theoretical physics at Oxford University.
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