Coulomb screening and exciton binding energies in conjugated polymers

Abstract

Hartree–Fock solutions of the Pariser–Parr–Pople and MNDO Hamiltonians are shown to give reasonable predictions for the ionization potentials and electron affinities of gas-phase polyenes. However, the energy predicted for formation of a free electron-hole pair on an isolated chain of polyacetylene is much larger than that seen in the solid state. The prediction is 6.2 eV if soliton formation is ignored and about 4.7 eV if soliton formation is included. The effects of interchain interactions on the exciton binding energy are then explored using a model system consisting of one solute and one solvent polyene, that are coplanar and separated by 4 Å. The lowering of the exciton binding energy is calculated by comparing the solvation energy of the exciton state to that of a single hole (a cationic solute polyene) and a single electron (an anionic solute polyene). It is argued that when the relative timescales of charge fluctuations on the solute and solvent chains are taken into account, it is difficult to rationalize the electron–electron screening implicit in the parametrization of a single-chain Hamiltonian to solid-state data. Instead, an electron–hole screening model is developed that includes the time scales of both the electron–hole motion and the solvent polarization. The predicted solvation energies, which are saturated with respect to solute and solvent chain length, are 0.07 eV for the exciton and 0.50 eV for a well separated electron–hole pair. Given this large, 0.43 eV reduction in the exciton binding energy due to interaction with a single chain, it seems likely that interchain interactions play a central role in establishing the solid-state exciton binding energy.