A truncation of the Heisenberg Hamiltonian Cl matrix is proposed in order to treat large molecules or clusters. The criterion for the selection of the model space is energetic. To correct the size-inconsistency error due to the truncation of the Cl matrix, the diagonal part is dressed by the spin configurations of the outer space. This correction remains simple despite its self-consistent character and gives accurates energies. Using a geometry-dependent Heisenberg Hamiltonian for conjugated hydrocarbons, it provides reliable geometries at low computational cost. Test calculations on linear polyenes are compared with the results of the full matrix diagonalization, and the large linear polyene C32H34 and the cyclic C32H32 polyene are studied.