  Searches for low-energy tetrahedral polymorphs of carbon and silicon have
been performed using density functional theory computations and the ab initio
random structure searching (AIRSS) ap- proach. Several of the hypothetical
phases obtained in our searches have enthalpies that are lower or comparable to
those of other polymorphs of group 14 elements that have either been
experimentally synthesized or recently proposed as the structure of unknown
phases obtained in experiments, and should thus be considered as particularly
interesting candidates. A structure of P bam symmetry with 24 atoms in the unit
cell was found to be a low energy, low-density metastable polymorph in carbon,
silicon, and germanium. In silicon, Pbam is found to have a direct band gap at
the zone center with an estimated value of 1.4 eV, which suggests applications
as a photovoltaic material. We have also found a low-energy chiral framework
structure of P 41 21 2 symmetry with 20 atoms per cell containing fivefold
spirals of atoms, whose projected topology is that of the so-called Cairo-type
two- dimensional pentagonal tiling. We suggest that P41 21 2 is a likely
candidate for the structure of the unknown phase XIII of silicon. We discuss
Pbam and P41 21 2 in detail, contrasting their energetics and structures with
those of other group 14 elements, particularly the recently proposed P42 /ncm
structure, for which we also provide a detailed interpretation as a network of
tilted diamond-like tetrahedra.
