  The Matrix Product method (MPM) has been used in the past to generate
variational ansatzs of the ground state (GS) of spin chains and ladders. In
this paper we apply the MPM to study the GS of conjugated polymers in the
valence bond basis, exploiting the charge and spin conservation as well as the
electron-hole and spin-parity symmetries. We employ the $U-V-\delta$
Hamiltonian which is a simplified version of the PPP Hamiltonian. For several
coupling constants $U$ and $V$ and dimerizations $\delta$ we compute the GS
energy per monomer which agrees within a $2%-4%$ accuracy with the DMRG
results. We also show the evolution of the MP-variational parameters in the
weak and strong dimerization regimes.
