A bottom-up valence bond derivation of excitation energies in 1D-like delocalized systems

Using the chemically relevant parameters hopping integral t(0) and on-site repulsion energy U, the charge gap (lowest dipolarly allowed transition energy) in 1D systems is examined through a bottom-up strategy. The method is based on the locally ionized states, the energies of which are corrected using short-range delocalization effects. In a valence bond framework, these states interact to produce an excitonic matrix which accounts for the delocalized character of excited states. The treatment, which gives access to the correlated spectrum of ionization potentials, is entirely analytical and valid whatever the U/|t(0)| ratio for such systems ruled by Peierls-Hubbard Hamiltonians. This second-order analytical derivation is finally confronted to numerical results of a renormalized excitonic treatment using larger blocks as functions of the U/|t(0)| ratio. The method is applied to dimerized chains and to fused polybenzenic 1D lattices. Such approaches complement the traditional Bloch-function based picture and deliver a conceptual understanding of the charge gap opening process based on a chemical intuitive picture.