Table of Contents

Introduction     1
The fullerene hypothesis     2
From hypothesis to experimental fact     5
The need for a systematic theory     9
What this book contains     10
References and notes     12
Fullerene cages     15
Fullerene polyhedra     15
Fullerene duals     17
The Coxeter construction     18
Fullerene graphs     22
The spiral conjecture     23
The spiral algorithm     27
How many fullerenes are there?     31
A fullerene without a spiral     35
Concluding remarks     39
References and notes     41
Electronic structure     43
Qualitative molecular orbital theory     44
Open, closed, and pseudo-closed shells     47
Icosahedral fullerenes     50
The leapfrog transformation     51
Carbon cylinders     59
Sporadic closed shells     62
Conclusion     65
References and notes     66
Steric strain     68
Steric strain and rehybridization     69
The isolated-pentagon rule     73
Pentagon indices forlower fullerenes     75
Hexagon indices for higher fullerenes     80
Steric strain in leapfrogs and carbon cylinders     84
Selected higher fullerene examples     88
References and notes     93
Symmetry and spectroscopy     95
The fullerene point groups     95
Topological coordinates     101
Symmetry assignment     105
[superscript 13]C NMR spectra     111
IR and Raman spectra     113
References and notes     118
Fullerene isomerization     120
The Stone-Wales rearrangment     120
Symmetry aspects     125
Chirality and the Stone-Wales transformation     129
Isomerization maps     131
The C[subscript 60] Stone-Wales map     141
Isomer distributions     145
References and notes     147
Carbon gain and loss     149
C[subscript 2] insertion and extrusion     150
Symmetry aspects of C[subscript 2] processes     153
Insertion/extrusion maps     157
References and notes     163
The Spiral computer program     165
Atlas tables     177
General fullerene isomers C[subscript 20] to C[subscript 50]     180
Isolated-pentagon isomers C[subscript 60] to C[subscript 100]     254
Index     389