A combination of electronic-structure calculations from density-functional theory (DFT) through a tight-binding (TB) model to analytic bond-order potentials (BOPs) has been used to investigate the structural trend of the ${\text{TM}}_5{\text{Si}}_3$ compounds across the early transition metals (TM). First of all, the formation energies of ${\text{TM}}_5{\text{Si}}_3$, whose ground states adopt the competing $\text{D}{8}_8$, $\text{D}{8}_l$, or $\text{D}{8}_m$ structure types, have been calculated by using DFT (TM is Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, or W). In agreement with experiments the DFT results predict the observed $\text{D}{8}_8\to \text{D}{8}_m$ structural trend across the $3d$ series and the $\text{D}{8}_8\to \text{D}{8}_l\to \text{D}{8}_m$ trend across the $4d$ and $5d$ series. A $p\text{−}d$ canonical TB model is then shown to reproduce these trends, thereby providing a valid basis for the application of BOP theory. By performing a moment analysis within the BOP formalism, we conclude that up to the fifth moment of the density of states is required to explain the structural trend across the $3d$ series whereas up to the ninth moment is required for the $4d$ and $5d$ series.

• Received 20 July 2010

DOI:https://doi.org/10.1103/PhysRevB.82.184104