The Jahn-Teller Effect in C60 and Other Icosahedral Complexes

by C. C. Chancey, M. C.M. O'Brien

Overview

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.

Product Details

ISBN-13:	9780691044453
Publisher:	Princeton University Press
Publication date:	12/14/1997
Pages:	225
Product dimensions:	6.30(w) x 9.40(h) x 0.70(d)

About the Author

C. C. Chancey is Professor of Physics at Purdue University. M. C. M. O'Brien is a lecturer in theoretical physics at Oxford University.

Table of Contents

LIST OF FIGURES
LIST OF TABLES
GLOSSARY OF SYMBOLS
1. Introduction
1.1 From Past to Present
1.2 Definition and History
1.3 The EXXXBeta (1) Interaction
1.4 The Berry Phase
1.5 Icosahedral Complexes
1.5.1 C(60)-Based Materials
1.5.2 Other Icosahedral Clusters
2. Icosahedral Symmetry and Its Effects
2.1 Icosahedral Symmetry
2.2 Geometry of C(60) and the Group I(h)
2.3 Irreducible Representations of I(h)
2.3.1 Spin Representations: The Double Group
2.4 Electron-Phonon Interactions
2.5 Vibrational Modes and Their Symmetries
2.6 Ham Reduction Factors
2.7 Icosahedral Jahn-Teller Systems
2.7.1 T XXX h and P(n) XXX h
2.7.2 G XXX(g XXX h)
2.7.3 H XXX(g XXX h)
3. T XXX h and P(n) XXX h
3.1 Introduction
3.2 The Potential Energy Surfaces
3.2.1 Rotational Symmetry of T(1) XXX h
3.2.2 The Shape of the Distorted Molecule
3.2.3 "Warping" of the Lowest-APES
3.2.4 Modification for T(2) XXX h 3.2.4
Modification for T(2) XXX h
3.3 The Ground States at Strong Coupling
3.3.1 The Ground States in the Adiabatic Approximation
3.3.2 The Ham Factors in T(1) XXX h
3.3.3 The Ham Factors in T(2) XXX h
3.3.4 The Ground State with Warping
3.4 Intermediate Coupling Strength
3.5 Multiple Occupation of T(1) Orbitals
3.5.1 The Configurations P(2) and P(4)
3.5.2 The Configuration P(3)
3.5.3 Numerical Work on p(n)
3.5.4 Term Splittings and Energy Ordering
3.6 Optical Absorption Spectra
3.6.1 Molecular Spectra
3.6.2 Absorption Bands in Solids: The
Cluster Model
3.7 The Introduction of Spin-Orbit Coupling
3.7.1 XXX XXX E(JT)
3.7.2 XXX Comparable to or Larger than E(JT)
4. Electronic Quartets and GXXX(g XXX h)
4.1 Introduction
4.2 G XXX g
4.2.1 The Method of Opik and Pryce
4.2.2 Biharmonic Parametrization of the G Bases
4.2.3 The Geometry of the Ground States
4.2.4 Numerical Phase Tracking
4.2.5 The Ham Factors in G XXX g
4.3 Symmetry and the Two Phase Spaces
4.4 G XXX h
4.4.1 Phase Tracking and the Ground States
4.4.2 The Ham Factors in G XXX h
4.5 G XXX (g XXX h)
4.5.1 G XXX (g XXX h)(eq) and SO(4) Symmetry
4.5.2 The Ham Factors
4.5.3 Other Relative Coupling Strengths
4.6 Broad Band Spectra
4.7 An Overview of G XXX (g XXX h)
5. Electronic Quintets and HXXX(g XXX h)
5.1 Introduction
5.2 H XXX h(4)
5.3 H XXX h in General
5.4 H XXX h(2)
5.4.1 Bases and the Hamiltonian
5.4.2 Rotational Symmetry of H XXX h(2)
5.4.3 The Ground States at Strong
Coupling
5.5 H XXX g
5.6 H XXX (g XXX h(4)(eq)
5.7 H XXX (g XXX h(4) XXX h(2))(eq)
5.7.1 The Ham Reduction Factors
5.8 H XXX (g XXX h)
6. Bridge to Experiment
6.1 Multimode Effects: Cluster Models
6.1.1 A Cluster Model for the Low Energy States
6.1.2 A Cluster for Optical Absorption
6.2 Electron Spin Resonance
6.2.1 Jahn-Teller Interactions in the
Spin Representations of the Group
6.2.2 The Spin Hamiltonian
6.2.3 The g Factors
6.2.4 The Spin Hamiltonian for Spin Triplet States
6.2.5 Esr on C(60): Experiment and Theory
6.3 Energy Levels in C(60)(n-)
6.3.1 C(60) Vibrational Modes and Their
Coupling
6.3.2 Configuration Interaction in
C(60)(n-)
6.4 Molecular Spectra
6.4.1 Symmetry-Lowering Distortions
6.4.2 Allowed Transitions
6.4.3 Experimental Evidence
6.5 C(60)(-) Spectra
6.6 C(60)(+) Spectra
6.7 Superconductivity in the Fullerides
6.7.1 C(60): Molecular Crystal
6.7.2 Superconducting Fullerides
6.7.3 p(3) XXX h
Appendixes
A. Adiabatic Approximation
A.1 Corrections to the Adiabatic Approximation
B. Quantum Tunneling Energies
B.1 Introduction
B.2 One-Dimensional Potentials
B.3 Higher Dimensionality
B.4 The WKB Approximation and Its Applications
B.4.1 One-Dimensional Application
B.4.2 WKB in More Dimensions
C. E XXX
D. The Group I
E. Jahn-Teller Interaction Matrices and Their Bases
E.1 Basis States
E.1.1 L equal to 1 and L equal to 2 Bases
E.1.2 Bases from L equal to 3 and Upwards
E.1.3 Interaction Matrices
F. Transformations
F.1 Parametrizations of the h Modes
F.2 Rotations to Diagonalize H XXX h(2)
F.3 Rotations to Diagonalize T XXX h
F.4 Representation of a Rotating Quadrupole
G. Parameters of the Jahn-Teller Minima and Other Stationary Points
H. Cited References and Bibliography
H.1 Cited References
H.2 Bibliography
H.2.1 Molecular Quantum Mechanics
H.2.2 Group Theory and Techniques
H.2.3 The Icosahedral Group
H.2.4 The Jahn-Teller Effect
H.2.5 Icosahedral Systems
H.2.6 The Berry Phase
H.2.7 Spin Resonance
H.2.8 Numerical Methods
H.2.9 Superconductivity in the Fullerides
H.2.10 Molecular Spectra
INDEX

Editorial Reviews

"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

"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

From the Publisher