- Title Pages
- Preface
- Acknowledgements
- Dedication
- 1 Introduction to conjugated polymers
- 2 <i>π</i>-electron theories of conjugated polymers
- 3 Noninteracting electrons
- 4 Electron-nuclear coupling I: Noninteracting electrons
- 5 Interacting electrons
- 6 Excitons in conjugated polymers
- 7 Electron-nuclear coupling II: Interacting electrons
- 8 Linear polyenes and <i>trans</i>-polyacetylene
- 9 Light emitting polymers
- 10 Exciton localization in disordered polymers
- 11 Optical processes in conjugated polymers
- 12 Excitonic processes in conjugated polymers
- 13 Epilogue
- Appendix ADirac bra-ket operator representation of one-particle Hamiltonians
- Appendix BElectron-hole symmetry and average occupation number
- Appendix CSingle-particle eigensolutions of a periodic polymer chain
- Appendix DThe Holstein model
- Appendix EDerivation of the effective-particle Schrödinger equation
- Appendix FHydrogenic solutions of the effective-particle exciton models
- Appendix GValence-bond description of benzene
- Appendix HDerivation of the Frenkel exciton Hamiltonian
- Appendix IEvaluation of the electronic transition dipole moments
- Appendix J Spin-orbit coupling in <i>π</i>-conjugated polymers
- Appendix KDerivation of the line dipole approximation
- Appendix LDirect configuration interaction-singles calculations for the Pariser-Parr-Pople model
- Appendix MDensity matrix renormalization group method
- Bibliography
- Index

# Electron-nuclear coupling I: Noninteracting electrons

# Electron-nuclear coupling I: Noninteracting electrons

- Chapter:
- (p.44) 4 Electron-nuclear coupling I: Noninteracting electrons
- Source:
- Electronic and Optical Properties of Conjugated Polymers
- Author(s):
### William Barford

- Publisher:
- Oxford University Press

The effect of electron-nuclear coupling in π‐conjugated systems is described in the limit of noninteracting electrons. The Peierls mechanism that leads to a semiconducting behaviour and to bond alternation is explained. Next, the fundamental excitations, e.g. solitons and mid-gap states – that are associated with reversals of the bond alternation – are described. Charge-polarons are also described with the aid of the Holstein model.

*Keywords:*
electron-nuclear coupling, Peierls transition, bond alternation, solitons, polarons, Holstein model

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- Title Pages
- Preface
- Acknowledgements
- Dedication
- 1 Introduction to conjugated polymers
- 2 <i>π</i>-electron theories of conjugated polymers
- 3 Noninteracting electrons
- 4 Electron-nuclear coupling I: Noninteracting electrons
- 5 Interacting electrons
- 6 Excitons in conjugated polymers
- 7 Electron-nuclear coupling II: Interacting electrons
- 8 Linear polyenes and <i>trans</i>-polyacetylene
- 9 Light emitting polymers
- 10 Exciton localization in disordered polymers
- 11 Optical processes in conjugated polymers
- 12 Excitonic processes in conjugated polymers
- 13 Epilogue
- Appendix ADirac bra-ket operator representation of one-particle Hamiltonians
- Appendix BElectron-hole symmetry and average occupation number
- Appendix CSingle-particle eigensolutions of a periodic polymer chain
- Appendix DThe Holstein model
- Appendix EDerivation of the effective-particle Schrödinger equation
- Appendix FHydrogenic solutions of the effective-particle exciton models
- Appendix GValence-bond description of benzene
- Appendix HDerivation of the Frenkel exciton Hamiltonian
- Appendix IEvaluation of the electronic transition dipole moments
- Appendix J Spin-orbit coupling in <i>π</i>-conjugated polymers
- Appendix KDerivation of the line dipole approximation
- Appendix LDirect configuration interaction-singles calculations for the Pariser-Parr-Pople model
- Appendix MDensity matrix renormalization group method
- Bibliography
- Index