Density-functional study of the evolution of the electronic structure of oligomers of thiophene: Towards a model Hamiltonian

We present density-functional and time-dependent density-functional studies of the ground, ionic, and excited states of a series of oligomers of thiophene. We show that, for the physical properties, the most relevant highest occupied and lowest unoccupied molecular orbitals develop gradually from monomer molecular orbitals into occupied and unoccupied broad bands in the large length limit. We show that band gap and ionization potentials decrease with size, as found experimentally and from empirical calculations. This gives credence to a simple tight-binding model Hamiltonian approach to these systems. We demonstrate that the length dependence of the experimental excitation spectra for both singlet and triplet excitations can be very well explained with an extended Hubbard-like Hamiltonian, with a monomer on-site Coulomb and exchange interaction and a nearest-neighbor Coulomb interaction. We also study the ground and excited-state electronic structures as functions of the torsion angle between the units in a dimer, and find almost equal stabilities for the transoid and cisoid isomers, with a transition energy barrier for isomerization of only 4.3 kcal/mol. Fluctuations in the torsion angle turn out to be very low in energy, and therefore of great importance in describing even the room-temperature properties. At a torsion angle of 90 degrees the hopping integral is switched off for the highest occupied molecular orbital levels because of symmetry, allowing a first-principles estimate of the on-site interaction minus the next-neighbor Coulomb interaction as it enters in a Hubbard-like model Hamiltonian.