Green's-function study of optical properties of polymers: Charge-transfer exciton spectra of polydiacetylenes

The visible optical spectrum of two typical polydiacetylene (PDA) crystals, $\mathrm{poly}[2,4-\mathrm{h}\mathrm{e}\mathrm{x}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{y}\mathrm{n}\mathrm{e}-1,6-\mathrm{d}\mathrm{i}\mathrm{o}\mathrm{l}-\mathrm{b}\mathrm{i}\mathrm{s}-(p-\mathrm{t}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{u}\mathrm{l}\mathrm{f}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{e}\left)\right]$ (PTS) with an acetylene-like structure and poly[5,7-dodecadiyne-1,2-diol-bis-(phenylurethane)] (TCDU) with a butatriene-like structure, is investigated with the use of a first-principles Green's-function formalism of charge-transfer exciton theory. The energy-band structures of the ground state are calculated first at the Hartree-Fock level with nonlocal exchange and they are corrected afterward for electron correlation effects using the electron-polaron model of Toyozawa. The electron-hole interaction ${\hat{H}}_{e,h}$ is treated by first-order perturbation theory in the framework of the Lax-Koster-Slater resolvent method as proposed by Takeuti. The influence of screening on ${\hat{H}}_{e,h}$ is also investigated with the help of an $\overrightarrow{\mathrm{r}}$-dependent static dielectric function. The results show that correlation corrections play an important role in the calculation of the optical spectrum since they substantially modify the Green's function of the host crystal as well as ${\hat{H}}_{e,h}$. Both the singlet and triplet excitons are found to be delocalized with a radius of 25-30 Å in PDA's: the Frenkel exciton contributes only ∼30% of the binding energy. The calculations predict the first-singlet absorption maximum for PTS at 2.1-2.2 eV and for TCDU at 1.7-1.8 eV, with an exciton bandwidth of ∼2.9 and ∼3.5 eV, respectively. The exciton binding energy is found to be ∼0.4 eV for both systems. Triplet levels are located at 0.8-0.9 eV below the singlets at $K=0\mathrm{}$ and they form relatively flat bands. The theoretical ionization potentials are 5.7 and 5.0 eV for PTS and TCDU crystals, respectively.