Superhard sp3 carbon allotropes with odd and even ring topologies

Four sp3 carbon allotropes with six, eight, and 16 atoms per primitive cell have been derived using a combination of metadynamics simulations and topological scan. A chiral orthorhombic phase oC16 (C2221) was found to be harder than monoclinic M-carbon and shows excellent stability in the high-pressure range. A second orthorhombic phase of Cmmm symmetry, by \sim 0.028 eV/atom energetically lower than W-carbon, can be formed from graphite at \sim 9 GPa. In general, the mechanical response under pressure was found to depend on the structure topology, which reflects the way rings are formed from an initial graphene layer stacking.