  An excitonic method proper to study conjugated oligomers and polymers is
described and its applicability tested on the ground state and first excited
states of trans-polyacetylene, taken as a model. From the Pariser-Parr-Pople
Hamiltonian, we derive an effective Hamiltonian based on a local description of
the polymer in term of monomers; the relevant electronic configurations are
build on a small number of pertinent local excitations. The intuitive and
simple microscopic physical picture given by our model supplement recent
results, such as the Rice and Garstein ones. Depending of the parameters, the
linear absorption appears dominated by an intense excitonic peak.
