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 th
e choice of basis functions in this time-dependent theory. The resulti
ng equations of motion include electronic-vibrational couplings. Expli
cit analysis of the simplest model leads to coupling between the highe
st frequency longitudinal vibrational mode and the electrons.