The vibrational properties of strongly coupled one-dimensional electron-lattice systems are dis-tinct form those of weakly coupled ones. While the weakly coupled systems have only four localized modes around the soliton and there is overlap between acoustic and optical phonon branches, the strongly coupled systems can possess more localized modes, and no overlap exists. In terms of the coupling constant λ, the boundary beween strong and weak coupling is λe=0.2119. The number of localized modes depends on λ, and each localized mode can only exist for a certain region of λ. Then the whole rane [0.2/π] of λ can be divided into seven regions, each of which has a charac-teristic disposition of the localized modes.

The stabilities of solitons, polarons and bipolmns in divalent-doped frompolyacerylene have been shldied by considering the impurity Coulomb confinement as well as the eleetron-electron interactions in the framework of the tight-binding PeierlsHubbard model. It was found that transitions between bipolarons and solitons and between bipolarons and polarons will rake place under cert3in conditions. The calculated values of the energy msitions agree well with the experimental results in the dilute Ca2+-doped trans-polyaceiylene material. The stability of excitations with respect to the impurity confinement and the electron4edron interactions have been discussed.

Single-photon excitation in a charged π-conjugated oligomer is studied theoretically. An apparent reverse polarization is obtained through single-photon excitation, which is different from that obtained through a double-photon excitation. The polarizability is calculated and it is found that a maximum reverse polarization will appear at a suitable conjugation length. In addition, we indicate that the reverse polarization is a nonlinear behavior with the induced electric field. Effects of nondegenerate confinement and interchain interactions on the reverse polarization are also discussed.

Several boundary conditions have been proposed to stabilize the dimerized structures of finite-length Peierls–Hubbard chains. The effects of different boundary conditions on the lattice structures and the electronic energy spectra have been analysed. It was found that the natural or the fixed-end boundary conditions are more suitable to describe polymer chains with very short lengths than the periodic boundary condition. The competition of electron–electron interactions with electron–phonon interactions in finite-length chains has also been studied.

In the framework of the tight-binding model, the effects of longitudinal as well as transverse coupling between polyacetylene chains with different lengths and the electron–electron interactions on excitations have been studied. A new spinless charged polaronic excitation (q=±e; s=0) was obtained due to the transverse interchain coupling, which is different from the general magnetic polaron (q=±e; s=1/2) obtained in the perfect one-dimensional model. Due to its end positioning, a polaron is more easily stimulated energetically in a longer chain than in a shorter one, and it can hop to the longer chains nearby via either transverse or longitudinal interchain coupling. In addition, the transverse coupling decreases the energy of creation of a polaron. Considering the strong electron–electron interactions and the end positioning of chains in actual materials, we concluded that the one-dimensional model of conducting polymers is fairly appropriate in certain circumstances.