The electron nuclear dynamics (END) approach is developed for a linear chain in a parametrized model inspired by the PPP (Pariser-Parr-Pople) model. Particular attention is given to the model parameters, and the choice of basis functions in this time-dependent theory. The resulting equations of motion include electronic-vibrational couplings. Explicit analysis of the simplest model leads to coupling between the highest frequency longitudinal vibrational mode and the electrons.