where ε r = 2 is the relative dielectric constant, as relevant to organic media. The PPP Hamiltonian can be written on the so-called real space (RS) basis, comprising all states obtained by distributing the n π-electrons on the N atoms. In the valence bond (VB) approach, the basis states are combined, following the Pauling rules, to be eigenstates of the total spin operator, Ŝ2 , so that the Hamiltonian factorizes in subspaces having the same S value. The VB approach is extremely efficient as it allows to work with comparatively small matrices, but the VB basis is non-orthogonal and hence difficult to manage. On the other hand, in the RS representation, the basis states are selected as eigenstates of the z-component spin operator, Ŝz . The RS subspaces are therefore much larger than the VB subspaces, but the basis set is orthogonal. For closed shell systems, as discussed here, diagonalizing the PPP Hamiltonian in the S z = 0 and 1 subspaces, allows to single out triplet (and higher spin) states as those states that are present in both subspaces. The dimension of the RS basis grows fast with N , leading to very large Hamiltonian matrices, that however are very sparse. Exploiting specific algorithms for the storage and diagonalization of sparse matrices, the PPP Hamiltonian for the 2T-N and 2T-7N molecules in Fig. can be diagonalized numerically, in spite of a basis that in the S z = 0 subspace contains 2,944,656 states.