Effective tight-binding models for excitons in branched conjugated molecules.

Effective tight-binding models have been introduced to describe vertical electronic excitations in branched conjugated molecules. The excited-state electronic structure is characterized by quantum particles (excitons) that reside on an irregular lattice (graph) that reflects the molecular structure. The methodology allows for the exciton spectra and energy-dependent exciton scattering matrices to be described in terms of a small number of lattice parameters which can be obtained from quantum-chemical computations using the exciton scattering approach as a tool. We illustrate the tight-binding model approach using the time-dependent Hartree-Fock computations in phenylacetylene oligomers. The on-site energies and hopping constants have been identified from the exciton dispersion and scattering matrices. In particular, resonant, as well as bound states, are reproduced for a symmetric quadruple branching center. The capability of the tight-binding model approach to describe the exciton-phonon coupling and energetic disorder in large branched conjugated molecules is briefly discussed.