Based on the Peierls-extended Hubbard model and breaking the alternative symmetry, we examine the stability of the high-spin ground state on a pi -conjugated hydrocarbon chain with respect to the intersite Coulomb interaction and dimerization of the backbone. We find that the ground state switches from a low-spin to a high-spin state only when the on-site Coulomb interaction approaches a critical value. When increasing the intersite Coulomb interaction or dimerization, the ground state switches from a high-spin to a low-spin state.