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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Excitons in conjugated polymers: wavefunctions, symmetries, and quantum numbers
William Barford1, Nattapong Paiboonvorachat
1Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom. william.barford@chem.ox.ac.uk
The Journal of Chemical Physics
|December 3, 2008
Summary
We developed a new method to map electronic excitations (excitons) from molecular orbitals to real space. This approach allows us to describe excitons using quantum numbers, similar to hydrogen atoms, revealing their properties in materials like polyacetylene.
Area of Science:
- Quantum Chemistry
- Condensed Matter Physics
- Materials Science
Background:
- Configuration interaction singles (CIS) methods use molecular orbitals to describe electronic excitations.
- Real-space descriptions of excitons are crucial for understanding their behavior in materials.
Purpose of the Study:
- To establish a mapping between configuration interaction singles wavefunctions and real-space exciton wavefunctions.
- To introduce a quantum mechanical description of excitons using quantum numbers.
- To investigate excitons in conjugated polymers.
Main Methods:
- Mapping particle-hole excitations between Hartree-Fock molecular orbitals and localized Wannier functions.
- Representing exciton wavefunctions in terms of center-of-mass (R) and relative (r) coordinates.
- Utilizing quantum numbers (n, j) for exciton characterization.
- Analyzing particle-hole symmetry and parity in relevant models.
Main Results:
- Developed a direct mapping from abstract CIS wavefunctions to physically intuitive real-space exciton wavefunctions.
- Established an analogy between 2D exciton wavefunctions and 1D hydrogenlike wavefunctions.
- Introduced quantum numbers for describing exciton properties based on their center-of-mass and relative motion.
- Demonstrated the method's applicability to conjugated systems like trans-polyacetylene and poly(para-phenylene).
Conclusions:
- The developed mapping provides a powerful tool for understanding exciton behavior in real space.
- The quantum mechanical description offers new insights into exciton properties and their relationships.
- This approach facilitates the study of excitons in various material systems.
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