As N grows, the size of the RS basis expands exponentially, reaching 2,944,656 states in the S z = 0.5 subspace for the phenalenyl radicals in Fig. , leading to Hamiltonian matrices that are extremely large and sparse. First few eingestates and eigenvalues are derived using the implicitly restarted Lanczos algorithm as implemented in the ARPACK package. This RS diagonalization yields full-CI results. To facilitate direct comparison with current quantum chemical techniques, we move to the MO picture of the PPP Hamiltonian. Specifically, in the mean-field Hartree-Fock (HF) approximation the PPP Hamiltonian in Eq. 1 boils down to the one-electron Fock operator: