Systematic search for low-enthalpy sp3 carbon allotropes using evolutionary metadynamics

We present a systematic search for low-energy metastable superhard carbon allotropes by using the recently developed evolutionary metadynamics technique. It is known that cold compression of graphite produces an allotrope at 15-20 GPa. Here we look for all low-enthalpy structures accessible from graphite. Starting from 2H- or 3R-graphite and applying a pressure of 20 GPa, a large variety of intermediate sp(3) carbon allotropes were observed in evolutionary metadynamics simulation. Our calculation not only found all the previous proposed candidates for "superhard graphite," but also predicted two allotropes (X-carbon and Y-carbon) showing unusual types of 5+7 and 4+8 topologies. These superhard carbon allotropes can be classified into five families based on 6 (diamond/lonsdaleite), 5+7 (M-and W-carbon), 5+7 (X-carbon), 4+8 (bct-C-4), and 4+8 (Y-carbon) topologies. This study shows that evolutionary metadynamics is a powerful approach both to find the global minima and systematically search for low-energy metastable phases reachable from given starting materials.