Structural, bonding, and electronic properties of IIA-IV antifluorite compounds

We have studied the electronic and structural properties of the antifluorite compounds ${\mathrm{Mg}}_2$X (X=Si, Ge, Sn), ${\mathrm{Be}}_2$C, and hypothetical compounds ${\mathrm{Mg}}_2$C and ${\mathrm{Be}}_2$Si using the first-principles pseudopotential total energy method. Five of the compounds are small-gap semiconductors, while ${\mathrm{Be}}_2$Si is a metal. Calculated lattice constants agree well with experiment for the four known compounds, but are consistently a few percent smaller than the reported values. The bulk moduli of this group of materials follow a semiempirical formula for ${\mathit{B}}_0$ to within ∼5%. Bulk moduli calculated from first principles, corrected for the underestimation of the lattice constant, agree well with the available experimental values.