Singlet-triplet gap (EOM-SF-CCSD/cc-pVTZ) between the lowest states in Molecule 1 is 0.077 eV. This gap is reproduced exactly by Bloch's and des Cloizeaux's effective Hamiltonians. The contribution of the ionic configurations and the validity of Hubbard's model are revealed by the magnitudes of the matrix elements of effective Hamiltonians. The truncated (inexact) effective Hamiltonian to open-shell determinants (Figure ) gives the singlet-triplet gap of 0.084 eV. This observation can be also rationalized from perturbative arguments: the effective direct exchange splits the open-shell states in the first order of degenerate perturbation theory. The indirect exchange from the ionic configurations comes only from the second-order perturbation, having a magnitude of 0.1 2 /4 = 2.5 • 10 -3 eV, which is by one order of magnitude smaller that the direct exchange. These observations reveal the nature of interaction of open-shell configurations in this system: the singlet-triplet gap primarily comes from the effective direct exchange rather from the interaction with the ionic configurations. To accommodate this physics, Hubbard's Hamiltonian can be extended to include direct exchange contribution, as was done, for example, in Ref. . This is likely due to some degree of spin contamination of the EOM-SF-CCSD states used to build effective Hamiltonians. Spin contamination is especially significant for the highest ionic states: the corresponding S 2 values are 1.06 and 1.17. This degree of spin contamination can deteriorate the quality of energy, resulting in somewhat higher energies of the corresponding ionic configurations: 6.5 and 6.3 eV. We note that there are several spin-contaminated electronic states with lower energies that are not represented well by the model space; these states were not included in the effective Hamiltonian.