One-dimensional excitons in organic molecular crystals

• Main Author: Montgomery, Charles Gray
• Format: Others
• Published: 1965
• Online Access: https://thesis.library.caltech.edu/1403/1/Montgomery_c_1965.pdf; Montgomery, Charles Gray (1965) One-dimensional excitons in organic molecular crystals. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4DXJ-K303. https://resolver.caltech.edu/CaltechETD:etd-04172003-110815 <https://resolver.caltech.edu/CaltechETD:etd-04172003-110815>

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A number of organic molecular crystals contain topologically linear chains of interacting molecules, coupled relatively weakly to the rest of the crystal lattice. The hamiltonian operators for several systems of this sort are represented as quadratic forms in Bose or Fermi creation and annihilation operators. A theorem is presented which permits the diagonalization of these forms by linear canonical transformations of the operators. This method is applied to the study (using a quasi-boson approximation) of the low-lying energy states of a chain of [...] with the hamiltonian [...] where [...]. The effects of anisotropic coupling and of an external magnetic field are included. Qualitative agreement with existing experimental data on crystals containing such chains is good. When...], the system is the Heisenberg antiferromagnet; the results obtained in this limit are in good quantitative agreement with theoretical treatments of that system. A fermion representation of the electronic states of certain linear-chain molecular crystals is developed. The method of canonical transformations can then be applied to crystals with strong intermolecular interactions due to dispersion forces or to intermolecular charge transfer. The treatment of dispersion interactions extends the Davydov singlet exciton theory into the range of strong coupling, where the elementary excitations of the system may have unusually small energies and are associated with distributed ferroelectric type electronic polarization. Change transfer effects in linear chains of alternating donor and acceptor molecules are treated, with cooperative Coulomb effects included in a self-consistent field approximation. The energy spectrum of the current-carrying elementary excitations is calculated. The calculation is also applicable to the problem of the electronic states of N/2 mobile electrons on a regular linear array of N molecules.