Excited states of branched conjugated molecules using the exciton scattering approach

The exciton scattering (ES) approach assumes that an excited state in a conjugated system can be treated as a quantum quasiparticle, i.e., exciton, propagating and scattering in a graph which represents the molecular structure. The resultant standing wave like pattern can be formulated mathematically as exciton scattering equations by using transition frequency dependent scattering matrices and exciton dispersion relation. By solving the ES equations, the exciton wavefunctions and transition energies can be obtained. Since conjugated systems can be decomposed into linear segments linked by various branching centers, the knowledge of exciton behavior of the repeat unit composing the linear segments (exciton propagation) and branching centers (exciton scattering) can fully characterize the collective exciton properties through the exciton scattering equations. Both the TDDFT and the TDHF methods have been used to extract information to set up the scattering matrices and the dispersion relation. Then the properties of characterized molecular building blocks (linear segments and branching centers) can be transferred directly to solving molecules of the same composition but with different geometric structures. The numerical effort depends on the number of linear segments rather than the number of orbitals. The approach is asymptotic exact as the ratio of the exciton's size to the length of linear segments decreases, and the results are generally accurate (within several meV comparing to quantum-mechanical methods) and even more reliable for larger molecules.