Fit of Pariser-Parr-Pople and Hubbard model Hamiltonians to charge and spin states of polycyclic aromatic hydrocarbons

Total energies of charge and spin states of a specifically designed target molecule 2,5,8-trihydro-phenalenyl (3H-C13H9 from here on), calculated by means of multiconfigurational self-consistent-field (MCSCF) and density-functional-theory-B3LYP methods, have been fitted by means of interacting Pariser-Parr-Pople (PPP) (intrasite and intersite Coulomb interactions) and Hubbard Hamiltonians for pi electrons. Numerically exact many-body solutions for these models were obtained by a variant of the Lanczos algorithm. Our calculation shows that the combination MCSCF-PPP with a hopping integral t=-2.63 eV and a local Coulomb repulsion U=10.51 eV produces the best results. Both model parameters are close to values frequently used in the literature, sometimes just for the Hubbard model. The fit of MCSCF energies by the Hubbard model is not as satisfactory (root-mean-square deviation is larger and t=-4.83 eV and U=21.27 eV parameters are far from common values). Neither of both models is able to accurately reproduce B3LYP energies. On the other hand, the value of the ratio vertical bar U/t vertical bar is always close to 4 indicating the proximity to a magnetic phase transition in extended systems. Additionally, we find that Lieb's theorem for the Hubbard model on bipartite lattices applies to neutral 3H-C13H9 since all ab initio methods and model Hamiltonians predict a fivefold spin-degenerate ground state.