Theory of even-parity states and two-photon spectra of conjugated polymers

Abstract

The two-photon absorption (TPA) spectrum of interacting \ensuremath{\pi} electrons in conjugated polymers is shown to be qualitatively different from any single-particle description, including the Hartree-Fock limit. Alternating transfer integrals t(1\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}) along the backbone lead to a weak TPA below the one-photon gap ${\mathit{E}}_{\mathit{g}}$ for arbitrarily weak correlations at \ensuremath{\delta}=0, for intermediate correlations at \ensuremath{\delta}=0.07 in polyenes, and for strong correlations at any \ensuremath{\delta}1. More intense TPA is derived from two-electron transfer across ${\mathit{E}}_{\mathit{g}}$; this even-parity state shifts from 2${\mathit{E}}_{\mathit{g}}$ in single-particle theory to ${\mathit{E}}_{\mathit{g}}$ in the limit of strong correlations in Hubbard models and is around 1.5${\mathit{E}}_{\mathit{g}}$ for Pariser-Parr-Pople (PPP) parameters. The PPP model, which accounts for one- and two-photon excitations of finite polyenes, is extended to even-parity states in polydiacetylenes (PDA's), polyacetylene (PA), and polysilanes (PS's). Previous experimental data for PDA and PS support both the strong TPA above ${\mathit{E}}_{\mathit{g}}$ and weak TPA slightly below ${\mathit{E}}_{\mathit{g}}$ for \ensuremath{\delta}=0.15 in PDA and above ${\mathit{E}}_{\mathit{g}}$ for \ensuremath{\delta}\ensuremath{\sim}0.3 in PS. The strong TPA expected around 1.5${\mathit{E}}_{\mathit{g}}$ in isolated PA strands shifts to \ensuremath{\sim}${\mathit{E}}_{\mathit{g}}$ due to interchain \ensuremath{\pi}-electron dispersion forces. TPA intensities in correlated states are shown to reflect both ionicity and mean-square charge separation. The even-parity states of conjugated polymers, like those of polyenes, show qualitatively different features associated with electron-electron correlations.