The maximin principle of pi-radical packings

A two-term model is proposed for hydrocarbon and N-containing pi-radicals which are in close contact with one another. The first term is attractive (due to partially occupied frontier pi-orbitals), and the second, repulsive (due to hard-core repulsion between close-lying atoms). This model is applied to dimers where intermolecular contacts are closer than <0.95 x the sum of the atomic van der Waals radii. The maximin principle is proposed. The maximin principle states that the lowest energy conformation maximizes overlap of the frontier orbitals while simultaneously minimizing intermolecular contacts. A Hückel Hamiltonian, the mu(2)-Hamiltonian, which contains the above attractive and repulsive terms, is applied. The interaction surfaces of two pi-hydrocarbon radical cations were calculated for the three systems known crystallographically to contain cations in close contact: naphthalene, fluoranthene, and pyrene. The global minima of these surfaces correspond to the experimentally determined structures. The mu(2)-Hamiltonian energy surfaces of the naphthalene cation dimer are qualitatively similar to those calculated at the RHF/6-311G(d,p) and MP2/6-311G(d,p) levels. The maximin principle is applied to N-containing pi-radicals. Except in the case of tetracyanoethene, the maximin principle correctly predicts the most common dimer crystal packing. (MgPc)(NO(3)).0.5THF and (MgPc)(ReO(4)).1.5THF (Pc = phthalocyanine) were prepared: both new crystal structures follow the maximin principle. The maximin principle is used to suggest the dimer cation ground state of oligoacenes, cations important as organic hole-based semiconductors.