Electronic structure methods were used to investigate bonding, metal-atom site preference, magnetic ordering, and crystal structure in ternary and quaternary intermetallic compounds that include arsenic or boron. Computational methods based on density functional theory were used to investigate the electronic structure and properties of hypothetical compounds closely related to the compounds of interest, in order to investigate the origins of properties that have been observed experimentally.

The Ti-M-Ir-B (M = transition metal) system was investigated through density functional theory (DFT) calculations in collaboration with experimental researchers. Compounds with approximate compositions (TixM1–x)3Ir3B3 were identified in two structures: a hexagonal structure for M = V, Cr, Mn, with Ti:M ratios near 1:1, and an orthorhombic structure for M = Mn and heavier transition metals, with Ti-M ratios near 2:1. Calculated lattice parameters for hypothetical “(Ti1/2M1/2)3Ir3B3” and “(Ti2/3M1/3)3Ir3B3” also showed a shift in stability of the hexagonal compounds for M heavier than Mn. Second-moment scaling with the Huckel method showed that the zigzag B4 subunit found in the orthorhombic structure would be, in isolation, more energetically favorable than the trigonal-planar B4 subunit of in the hexagonal structure. Crystal orbital Hamilton population (COHP) analysis suggested that the hexagonal TiCrIr2B2 structure was instead stabilized by Cr–Cr bonding, while the Ti:M ratio of the orthorhombic structures serves to maximize heteroatomic Ti:M bonds.

DFT with a Hubbard U term (DFT+U) was used to investigate the importance of electron-electron correlation in CrMnAs and TmAlB4. In CrMnAs, DFT+U results give a better match for experimental magnetic ordering and metal-atom site preference than results from DFT alone. In TmAlB4, the electronic structure depends significantly on the choice of U, suggesting that previous results using DFT without U might not be accurate. COHP analysis was used to examine a possible Stone-Wales-like transformation mechanism between two related phases in TmAlB4. The strongest B–B bonds in β-TmAlB4 were found to be isolated by weaker B–B bonds, but the strongest B–B bonds in α-TmAlB4 formed chains oriented along the structure’s a axis.