Comparison of μ2‐scaled Hückel theory and Hartree–Fock theory of boranes and carboranes

The Maximin Principle of π-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.

STRUCTURAL DIVERSITY IN SOLID STATE CHEMISTRY:A Story of Squares and Triangles

▪ Abstract  A simple method for calculating the electronic energy of extended solids is discussed in this review. This method is based on the Hückel or tight-binding theory in which an explicit pairwise repulsion is added to the generally attractive forces of the partially filled valence electron bands. An expansion based on the power moments of the electronic density of states is discussed, and the structural energy difference theorem is reviewed. The repulsive energy is found to vary linearly with the second power moment of the electronic density of states. These results are then used to show why there is such a diversity of structure in the solid state. The elemental structures of the main group are rationalized by the above methods. It is the third and fourth power moments (which correspond in part to triangles and squares of bonded atoms) that account for much of the elemental structures of the main group elements of the periodic table. This serves as an introduction to further rationalizations of transition for noble metal alloy, binary and ternary telluride and selenide, and other intermetallic structures.Thus a cohesive picture of both covalent and metallic bonding is presented in this review, illustrating the importance of atomic orbitals and their overlap integrals.