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.

The effects of interchain coupling on vibration modes localized around a polaron in polyacetylene of finite length are investigated. It is shown that the eight localized modes found in an isolated finite chain are delocalized between chains due to the interchain coupling. New modes of lattice vibration emerge because of the delocalization of the charged polaron. The well-known Goldstone zero-frequency mode becomes pinned by the chain ends for sufficiently short chains. Our results can qualitatively account for the frequency shifts observed recently in Raman scattering and infrared absorption spectra.

Localized modes of lattice vibration in polythiophene are investigated numerically by considering a chain of finite length. th the periodic boundary condition, we find three even-parity and four odd-parity modes. One of the even modes due to the sulfur heteroatom in the heterocycle is believed to be re-sponsible for what is observed around 700 cm. in the Raman spectrum of polythiophene. With the free-end boundary condition, several modes from the highest optical branch become localized near the surface. These modes may be identified as the high-frequency modes observed in infrared-active vibra-tion and resonant. Raman. scattering absorption experiments.

On the basis of a model similar to that of Su, Schrieffer, and Heeger, we investigate transitions be-tween bipolaron and polaron states In doped heterOCyCle polymers such as polypyrrole, polythlophene, and polyselenophene. The dopant impurity is assumed to be located between chains, and the interchain oupling is due to the electron hopping which is assumed to be confined to nearest-neighboring carbon groups around the counterion. The electron-electron interaction described by a Hubbard-type Hamil-tonian is also included in our calculation. It is shown that the system may be in a bipolaron state or a state of polaron pair of triplet triplet (singlet) nature. We find：that the interchain couping has litthstate of a polaron pair of spin triplet singlet nature We find that the interchain coupling has little influence on the stability of a bipolaron. Transitions from a bipolaron to a pair of polarons can be in-duced 0y a strong electron-electron Interactmn. WnlCn IS also responsible tor the energy dlfierence be-tween the singlet and triplet polarons states.

with a local site-impurity potential in the framework of the su, schrieffer, and Heeger (SSH) model, both the dopant dependence and the chain-length dependence of the vibrational modes related to charged solitons in a finite trans-polyacetylene chain have been studied. The numerical calcultions showed that the well-known Goldstone mode will be pinned by the dopant potentials as well as by the chhain ends. Two localized modes were found in the acoustic-frequency branch. The results are in agree-ment with the infrared- active vbibrational modes also observed in lightly doped polyacetylene cases. A comparison with the phtoexcitation measurements has been given.