An extensive theoretical survey of low-density allotropy in silicon

Using a variety of computational approaches, we demonstrate that the energy landscape of low-density silicon (e. g. silicon clathrates) is considerably more complicated than suggested by previous studies and identify several new prospective low-energy silicon allotropes. Many of our new prospective silicon allotropes contain 4-membered rings, previously thought to be incompatible with low-energy structures, while all of them have surprisingly large unit cells. These allotropes are found by identifying minima on the energy landscape of silicon, as described by the Tersoff potential, in two distinctly different ways: (i) via a random search approach and (ii) by optimising sets of four-coordinated nets previously enumerated for silica. The lowest-energy minima found are subsequently refined using periodic density functional theory. We discuss the merits of both approaches and identify the need for robust global optimisation methods that can efficiently explore low-symmetry systems with large numbers of atoms.