Ti₁₂C₆₈: A stable T _h -symmetry hollow cage

A stable T _h -symmetry Ti₁₂C₆₈ cage was systemically investigated using density functional theory. The structure of Ti₁₂C₆₈ is a hollow cage with twelve TiC₁₃ subunit of three pentagons and one hexagon. The calculated frequencies are in the range 95.1 cm^-1-1423.9 cm^-1. There are no imaginary frequencies, showing its kinetic stability. Ab initio molecular dynamics simulations demonstrate that the topological structure of cage-like Ti₁₂C₆₈ cluster was well maintained when the effective temperature is up to 1139 K. The natural bond orbitals analysis shows that the d orbit of Ti atoms form four σ bonds with the neighboring four carbon atoms in each TiC₁₃ subunit playing an important role in the cluster stability. The molecular frontier orbitals analysis indicates that Ti₁₂C₆₈ cage has a narrow HOMO-LUMO gap with metal-like property. It would be expected to enrich the species of hollow metal carbide clusters.