Stability, bonding, and geometric structure of ${\mathrm{Ti}}_8$${\mathrm{C}}_{12}$, ${\mathrm{Ti}}_8$${\mathrm{N}}_{12}$, ${\mathrm{V}}_8$${\mathrm{C}}_{12}$, and ${\mathrm{Zr}}_8$${\mathrm{C}}_{12}$

We investigate the stability, bonding, and geometric structure of recently discovered metallocarbohedrenes by the use of density-functional calculations. It is found that the previously proposed ${\mathit{T}}_{\mathit{h}}$ dodecahedron structure is dynamically unstable. Instead, a new, stable, and more strongly bound structure with ${\mathit{D}}_{2\mathit{d}}$ symmetry is found. We find strong interactions between C-C and strong Ti-C covalent bonding. The stability of the ${\mathit{D}}_{2\mathit{d}}$ structure has been verified by calculating vibrational frequencies. The infrared spectrum of the ${\mathrm{Zr}}_8$ ${\mathrm{C}}_{12}$ cluster is predicted.