This thesis consists of three investigations into the electronic structure of solid state materials. In each case a semi-empirical method, extended Hueckel (eH) or mu2-Hueckel (mu2) is used for qualitative insight, with LDA-DFT being used to calibrate the semi-empirical calculations.

The first part accounts for two empircal rules of the Nowotny Chimney Ladder phases (NCLs, intermetallic compounds of the form TtEm, T: groups 4-9, E: groups 13-15). The first rule is that for late transition metal NCLs there are 14 valence electrons per T atom. The second is a pseudo-periodicity with a spacing of cpseudo=c/(2t-m), for the stoichiometry TtEm. Both rules accounted are for by viewing the NCLs as constructed from blocks of the RuGa2 structure of thickness c/2, with successive layers rotated 90 degrees relative to each other. Sterically encumbered E atoms are then deleted at the interfaces between layers, followed by relaxation. eH calculations explain the special stability of RuGa2, the parent NCL structure, at 14 electrons per T atom. A gap between filled and unfilled bands arises from the occupation of two Ga-Ga bonding/Ru-Ga nonbonding orbitals plus all five Ru d levels per RuGa2 (7 filled bands for 14 electrons/Ru). We discuss the connections between this 14 electron rule and the 18 electron rule of organometallic complexes.

Second part of this thesis reports the synthesis, crystal structures, and electronic band structures of (pyrene)10-(I3-)4(I2)10, 1, and of [1,3,6,8-tetrakis(methyl- thio)pyrene]3(I3)3-(I2)7, 2. In both structures, the organic molecules form face-to-face cationic stacks which are separated from one another by a polyiodide network. eH Band calculations suggest that the stacks of pyrene molecules in 1 have undergone a Peierls distortion appropriate to a 3/4 filling of the HOMO bands of the stacked pyrene molecules. Band calculations on 2 suggest that it is a Mott insulator. The intermolecular contacts within both the polyiodide networks and the face-to-face stacks of organic cations are rationalized within the frontier orbital framework.

In the final part studies a two-dimensional structure map for AB3 binary transition metal compounds with variables appropriate for direct quantum-mechanical energy calculations: electron count and Delta Hii, the difference in d-orbital Coulombic integrals. The experimental structure map differentiates between the six known AB3 transition metal structure types: Cr3Si, AuCu3, SnNi3, TiAl3, TiCu3 and TiNi3. The theoretical map (based on mu2 calculations) gives good agreement with the experimental map. Further analysis of the mu2 results indicates that the major energetic differences stem from the varying number of three- and four-member rings of bonded atoms.