1 Introduction to conjugated polymers .......................... 1
2 π-electron theories of conjugated polymers ................... 7
2.1 Introduction ............................................ 7
2.2 The many body Hamiltonian ............................... 7
2.3 The Born-Oppenheimer approximation ...................... 8
2.4 Second quantization of the Born-Oppenheimer
Hamiltonian ............................................ 10
2.5 spn hybridization ...................................... 12
2.6 π-electron models ...................................... 14
2.7 Electron-nuclear coupling .............................. 17
2.8 Summary of π-electron models ........................... 19
2.9 Symmetries and quantum numbers ......................... 22
3 Noninteracting electrons .................................... 26
3.1 Introduction ........................................... 26
3.2 The noninteracting (Hiickel) Hamiltonian ............... 26
3.3 The ethylene dimer ..................................... 27
3.4 Undimerized chains ..................................... 30
3.5 Dimerized chains ....................................... 33
3.6 The ground state and electron-hole excitations ......... 36
3.7 Symmetries ............................................. 38
3.8 Bond order ............................................. 41
4 Electron-nuclear coupling I: Noninteracting electrons ....... 44
4.1 Introduction ........................................... 44
4.2 The Peierls model ...................................... 45
4.3 The dimerized ground state ............................. 46
4.4 Self-consistent equations for {Δn} ..................... 48
4.5 Solitons ............................................... 50
4.6 Soliton-antisoliton pair production .................... 54
4.7 Nondegenerate systems .................................. 57
4.8 The continuum limit of the Su-Schrieffer-Heeger model .. 59
4.9 Polarons ............................................... 61
4.10 Dynamics of the Su-Schrieffer-Heeger model ............. 62
4.11 Self-trapping .......................................... 63
4.12 Concluding remarks ..................................... 63
5 Interacting electrons ....................................... 65
5.1 Introduction ........................................... 65
5.2 The weak-coupling limit ................................ 70
5.3 The strong-coupling limit .............................. 71
5.4 The phase diagram of the undoped Pariser-Parr-Pople
model .................................................. 74
5.5 The valence bond method ................................ 75
6 Excitons in conjugated polymers ............................. 78
6.1 Introduction ........................................... 78
6.2 The weak-coupling limit ................................ 79
6.3 The strong-coupling limit .............................. 93
6.4 The intermediate-coupling regime ...................... 96
6.5 Concluding remarks ..................................... 98
7 Electron-nuclear coupling II: Interacting electrons ........ 101
7.1 Introduction .......................................... 101
7.2 The Pariser-Parr-Pople-Peierls model .................. 102
7.3 Dimerization and optical gaps ......................... 103
7.4 Excited states and soliton structures ................. 107
7.5 Polarons .............................................. 113
7.6 Extrinsic dimerization ................................ 113
7.7 Quantum phase transition .............................. 114
7.8 Concluding remarks .................................... 118
8 Linear polyenes and trans-polyacetylene .................... 120
8.1 Introduction .......................................... 120
8.2 Predictions from the Pariser-Parr-Pople-Peierls
model ................................................. 123
8.3 Role of nuclear zero-point fluctuations ............... 128
8.4 Character of the excited states of
trans-polyacetylene ................................... 129
8.5 Other theoretical approaches .......................... 131
9 Light emitting polymers .................................... 132
9.1 Introduction .......................................... 132
9.2 Poly(para-phenylene) .................................. 137
9.3 Poly(para-phenylene vinylene) ......................... 150
9.4 Other theoretical approaches .......................... 152
9.5 Exciton binding energies .............................. 158
9.6 The excited states of light emitting polymers ......... 159
9.7 Electronic coupling to nuclear degrees of freedom ..... 161
10 Exciton localization in disordered polymers ................ 168
10.1 Introduction .......................................... 168
10.2 Definition of the exciton conjugation length .......... 169
10.3 Origins of disorder ................................... 170
10.4 Localization of vertical excitations .................. 171
10.5 Dynamical localization ................................ 184
10.6 Concluding remarks .................................... 189
11 Optical processes in conjugated polymers ................... 192
11.1 Introduction .......................................... 192
11.2 Linear optical processes .............................. 193
11.3 Evaluation of the transition dipole moments ........... 194
11.4 Nonlinear optical processes ........................... 204
11.5 Size-dependencies of χ(n) .............................. 210
11.6 Photophysical processes in conjugated polymers ........ 211
12 Excitonic processes in conjugated polymers ................. 212
12.1 Introduction .......................................... 212
12.2 Exciton transfer ...................................... 212
12.3 Exciton diffusion in the condensed phase .............. 226
12.4 Excited molecular complexes ........................... 231
12.5 Second order dispersion interactions .................. 232
13 Epilogue ................................................... 240
Appendix A Dirac bra-ket operator representation of
one-particle Hamiltonians ..................................... 242
A.l The Hückel Hamiltonian ................................. 242
A.2 The Frenkel exciton Hamiltonian ........................ 243
Appendix В Electron-hole symmetry and average occupation
number ..................................................... 245
Appendix С Single-particle eigensolutions of a periodic
poly-mer chain ............................................. 247
C.l Dimerized chain ........................................ 248
C.2 Poly(para-phenylene) ................................... 249
Appendix D The Holstein model ................................ 250
D.l The model .............................................. 251
D.2 General solutions ...................................... 253
D.3 Variational calculation ................................ 254
D.4 Optical intensities .................................... 254
Appendix E Derivation of the effective-particle Schrödinger
equation ................................................... 257
Appendix F Hydrogenic solutions of the effective-particle
exciton models ............................................. 262
F.l The weak-coupling limit ............................... 262
F.2 The strong-coupling limit ............................. 265
Appendix G Valence-bond description of benzene ............... 267
Appendix H Derivation of the Frenkel exciton Hamiltonian ..... 270
Appendix I Evaluation of the electronic transition dipole
moments .................................................... 277
1.1 The weak-coupling limit ............................... 277
1.2 The strong-coupling limit ............................. 280
Appendix J Spin-orbit coupling in π-conjugated polymers ...... 281
J.l Spin-orbit coupling of π-electrons .................... 281
J.2 Symmetry restrictions on spin-orbit coupling .......... 282
J.3 Spin-orbit coupling and spatial wavefunctions ......... 283
Appendix К Derivation of the line dipole approximation ....... 284
Appendix L Direct configuration interaction-singles
calculations for the Pariser-Parr-Pople model .............. 287
L.l Hartree-Fock Solutions ................................ 287
L.2 Direct Cl-singles method .............................. 288
Appendix M Density matrix renormalization group method ....... 289
M.l Introduction to the real-space method .................. 289
M.2 Local Hilbert space truncation ......................... 293
References .................................................... 294
Index ......................................................... 302
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