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Conjugated system have complex behaviors when increasing the number ofmonomers, which is one of the reasons that makes long oligomers hard to becharacterized by numerical methods. An ex- ample of this are fused-azulene, amolecule that has been reported to displays an increasing magnetic moment withsystem size. A similar system composed of symmetric fused-benzene rings isreported to be always no magnetic. Instead of the empiric parametrizedPariser-Parr-Pople (PPP) Hamiltonian, a standard model for conjugatedmolecules, we consider the Hubbard Hamiltonian to explore a range of lowelectronic correlation by means of perturbation theory (PT). We show that asimple second-order perturbation treatment of electronic correlations by meansof Rayleigh-Schroedinger PT allow to accurately infer about the magnetic stateof these long complex {\pi}-conjugated molecules. For fused-azulene our resultssupports the hypothesis that the high-spin ground state on azulene oligomerscomes from the frustrated geometry of these chains. We validate this approachusing Density Matrix Renormalization Group (DMRG) calculations. Our procedureprocedure could be helpful to describe the magnetic ground state of a largerset of conjugated molecules.

Second order perturbation theory to determine the magnetic state of finite size aromatic hydrocarbons molecules