Do polyacenes, circumacenes, periacenes, nanographenes and graphene nanoribbons show a spin polarized ground state? In this work, we present mono-determinantal (Hartree-Fock and Density Functional Theory types), and multi-determinantal calculations ( Møller-Plesset and Coupled Cluster), for several families of unsaturated organic molecules (n-Acenes, n-Periacenes and n-Circumacenes).All HF calculations and many DFT show a spin-polarized (antiferromagnetic) ground state, in agreement with previous calculations. Nevertheless, the multi-determinantal calculations, carried out with perturbative and variational wavefunctions, show that the more stable state is obtained starting from the unpolarized Hartree-Fock wavefunction.The trend of the stabilisation of wavefunctions (polarized or unpolarized) with respect to exchange and correlation potentials, and to the number of benzene rings, has been analysed. A study of the spin (<Ŝ 2 >) and the spin density on the carbon atoms has also been carried out.