Theory of unsaturated silicon lattices

Several molecules are known to contain stable silicon double or triple bonds that are sterically protected by bulky side groups. Through first-principles computation, we demonstrate that well-defined $\pi$ bonds can also be formed in two prototypical {\it crystalline} Si structures: Schwarzite Si-168 and dilated diamond. The sp$^2$-bonded Si-168 is thermodynamically preferred over diamond silicon at a modest negative pressure of -2.5 GPa. Ab-initio molecular dynamics simulations of Si-168 at 1000 K reveal significant thermal stability. Si-168 is metallic in density functional theory, but with distinct $\pi$-like and $\pi^*$-like valence and conduction band complexes just above and below the Fermi energy. A bandgap buried in the valence band but close to the Fermi level can be accessed via hole doping in semiconducting Si$_{144}$B$_{24}$. A less-stable crystalline system with a silicon-silicon triple bond is also examined: a rare-gas intercalated open framework on a dilated diamond lattice.