The electron-electron interaction in trans-${\left(\mathrm{CH}\right)}_x$ is considered with a Hubbard repulsion term, and the electron-lattice coupling vibrational modes are calculated to test the effects of the $e-e$ interaction on the localized modes. The results show that all five localized modes survive after turning on the $e-e$ interaction, but their localizations are changed and the frequencies move slightly.

• Received 4 February 1986

DOI:https://doi.org/10.1103/PhysRevB.33.8772