Fundamental studies on the structures and properties of some B12-based crystals.

Abstract

The first-principles orthogonalized linear combination of atomic orbitals method has been applied to calculate the electronic structures, total energies, and optical properties of four boron-rich compounds: ${\mathrm{B}}_{12}$${\mathrm{As}}_{2}$, ${\mathrm{B}}_{12}$${\mathrm{P}}_{2}$, ${\mathrm{B}}_{11}$C(CBC) (or ${\mathrm{B}}_{4}$C), and ${\mathrm{B}}_{13}$${\mathrm{C}}_{2}$. The band structures show that ${\mathrm{B}}_{12}$${\mathrm{As}}_{2}$, ${\mathrm{B}}_{12}$${\mathrm{P}}_{2}$, ${\mathrm{B}}_{11}$C(CBC) are semiconductors with indirect band gaps while ${\mathrm{B}}_{13}$${\mathrm{C}}_{2}$ is a metal with an intrinsic hole at the top of the valence band below a semiconductorlike gap. The calculated density of states are resolved into atomic and orbital partial components and the valence-charge distributions are also studied. The natural bonding characteristics in these crystals are illuminated by evaluating the Mulliken effective charges on each atom and overlap populations between pairs of atoms. It is shown that intericosahedral bonding is much stronger than the intraicosahedral bonding. The chain elements in ${\mathrm{B}}_{12}$${\mathrm{As}}_{2}$ and ${\mathrm{B}}_{12}$${\mathrm{P}}_{2}$ donate electrons to the icosahedra while in the other two crystals, they gain a slight amount of charge in forming strong covalent bonds. The bulk moduli of these crystals are estimated by means of total-energy calculation as a function of crystal volume, and are to be considered as upper limits. We have also calculated the interband optical conductivities and the complex dielectric functions in these crystals. Static dielectric constants for the three semiconductors are estimated to be 6.59, 5.49, and 6.35, respectively, which are in good agreement with recent experimental measurements. The bulk plasmon excitations in these four crystals are found to be in the 30--34-eV range.