A method for constructing effective Hamiltonians using the information contained in the ground state reduced single-electron density matrices for many-electron systems is proposed and applied to trans-polyacetylene oligomers C 2 n H 2 n + 2 with n = 4-24. The resulting effective Hamiltonians for π electrons, expanded in the basis set of natural atomic orbitals (NAOs) with nearest neighbor transfer integrals, reproduce accurately the Hartree-Fock ground state density matrices.