First-principles calculations of structural and electronic properties of Ta-doped Si clusters, wires, and bulk systems

Recent experiments have shown that Ta@Si${}_{16}{}^{+}$ is a very stable cation from which it should be possible to create Si-based cluster assembled materials. In this paper we have studied, by means of first-principles spin-dependent generalized gradient approximation calculations, the structural and electronic properties of the following systems: (i) Ta@Si${}_{n}{}^{+}$ clusters in the range $n=14\ensuremath{-}18$; (ii) (Ta@Si${}_{16}$F)${}_{m}$ aggregates with sizes $m=1\ensuremath{-}8$ formed by Ta@Si${}_{16}$F molecules; (iii) infinite wires formed by stacking triangular (Ta@Si${}_{16}$F)${}_{3}$ aggregates twisted 60${}^{\ifmmode^\circ\else\textdegree\fi{}}$ to each other along the vertical axis; and (iv) the fcc phase of bulk Ta@Si${}_{16}$F. The minimum-energy Ta@Si${}_{16}{}^{+}$ cluster shows ${C}_{3v}$ symmetry, having 40 meV smaller total energy than a fullerenelike ${D}_{4d}$ isomer. However, the molecule Ta@Si${}_{16}$F formed with that ${D}_{4d}$ isomer is 40 meV more stable than that formed with the ${C}_{3v}$ one. We have optimized several [Ta@Si${}_{16}$F]${}_{n}$ aggregates ($n=1\ensuremath{-}8$) which contain the Ta@Si${}_{16}$ unit with ${D}_{4d}$ symmetry. The more bound (Ta@Si${}_{16}$F)${}_{6}$ aggregate is formed by stacking vertically two triangular (Ta@Si${}_{16}$F)${}_{3}$ aggregates which are twisted 60${}^{\ifmmode^\circ\else\textdegree\fi{}}$ to each other. The infinite wire formed with that (Ta@Si${}_{16}$F)${}_{6}$ aggregate as the unit cell has a cohesive energy 1.88 eV and a small highest occupied molecular orbital--lowest occupied molecular orbital gap. We have optimized also a metastable fcc bulk phase having the Ta@Si${}_{16}$F supermolecule as the unit cell. A Birch-Murnaghan fit to that phase produces a cohesive energy 0.84 eV at lattice constant 12.27 \AA{}, with bulk modulus 7.55 GPa and a phase stability to isotropic compression smaller than 0.75 GPa. That phase is nonmagnetic and shows a band gap of 0.20 eV. Using the values of hardness of Ta@Si${}_{16}$F molecules, we estimated a correction enhancement factor $~$3 to that small band gap. For that metastable solid we performed a 13.5-ps run of first-principles molecular dynamics annealing at 300 K and constant volume, and we found that the Ta@Si${}_{16}$F supermolecule in the fcc cell becomes severely distorted after the first 5 ps.