Relationship between orbital energy gaps and excitation energies for long-chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time-dependent (TD) density functional theory (DFT) for long-chain systems: all-trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long-range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two-electron interactions between occupied and unoccupied orbitals through the Coulomb-exchange-correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long-range exchange interactions are involved. Spin-flip (SF) TDDFT calculations are then carried out to clarify double-excitation effects in these excitation energies. The calculated SF-TDDFT results indicate that double-excitation effects significantly contribute to the excitations of long-chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP-EA) values and the HOMO-LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least-square fits to estimate the exciton binding energy of infinitely long systems. It is found that long-range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long-range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long-chain systems, while double-excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.