  Conjugated system have complex behaviors when increasing the number of
monomers, which is one of the reasons that makes long oligomers hard to be
characterized by numerical methods. An ex- ample of this are fused-azulene, a
molecule that has been reported to displays an increasing magnetic moment with
system size. A similar system composed of symmetric fused-benzene rings is
reported to be always no magnetic. Instead of the empiric parametrized
Pariser-Parr-Pople (PPP) Hamiltonian, a standard model for conjugated
molecules, we consider the Hubbard Hamiltonian to explore a range of low
electronic correlation by means of perturbation theory (PT). We show that a
simple second-order perturbation treatment of electronic correlations by means
of Rayleigh-Schroedinger PT allow to accurately infer about the magnetic state
of these long complex {\pi}-conjugated molecules. For fused-azulene our results
supports the hypothesis that the high-spin ground state on azulene oligomers
comes from the frustrated geometry of these chains. We validate this approach
using Density Matrix Renormalization Group (DMRG) calculations. Our procedure
procedure could be helpful to describe the magnetic ground state of a larger
set of conjugated molecules.
