Band to correlated crossover in alternating Hubbard and Pariser-Parr-Pople chains: Nature of the lowest singlet excitation of conjugated polymers

The evolution with increasing Coulomb correlations of a semiconductor to a magnetic insulator is related to an excited-state crossover in π-electron models for conjugated polymers. We associate strong fluorescence with a lowest singlet excitation ${\mathit{S}}_1$ that is dipole allowed, on the band side, while ${\mathit{S}}_1$ becomes two-photon allowed on the correlated side. ${\mathit{S}}_1$/${\mathit{S}}_2$ crossovers in Hubbard, Pariser-Parr-Pople, or other chains with electron-hole symmetry and alternating transfer integrals t(1±δ) are based on exact results at δ=0 and 1, on molecular exciton theory at large δ, and on oligomer calculations up to twelve sites.