Effects of polarons on static polarizabilities and second order hyperpolarizabilities of conjugated polymers

According to the one-dimensional tight-binding SuSchrieffer–Heeger model, we have investigated the effects of charged polarons on the static polarizability, \alpha_xx, and the second order hyperpolarizabilities, \gamma_xxxx, of conjugated polymers. Our results are consistent qualitatively with previous ab initio and semi-empirical calculations. The origin of the universal growth is discussed using a local-view formalism that is based on the local atomic charge derivatives. Furthermore, combining the Su–Schrieffer–Heeger model and the extended Hubbard model, we have investigated systematically the effects of electron–electron interactions on \alpha_xx and \gamma_xxxx of charged polymer chains. For a fixed value of the nearest-neighbour interaction V, the values of \alpha_xx and \gamma_xxxx increase as the on-site Coulomb interaction U increases for U<U_c and decrease with U for U >U_c, where U_c is a critical value of U at which the static polarizability or the second order hyperpolarizability reaches a maximal value of \alpha_max or \gamma_max. It is found that the effect of the e–e interaction on the value of \gamma_xx is dependent on the ratio between U and V for either a short or a long charged polymer. Whereas, that effect on the value of \gamma_xxxx is sensitive both to the ratio of U to V and to the size of the molecule.