We propose an approach to perform the global search for low-lying crystal structures from first principles, by combining the artificial force induced reaction (AFIR) method and the periodic boundary conditions (PBCs). The AFIR method has been applied extensively to molecular systems to elucidate the mechanism of chemical reactions such as homogeneous catalysis. The present PBC/AFIR approach found 274 local minima for carbon crystals in the ${\mathrm{C}}_8$ unit cell described by the generalized gradient approximation–Perdew-Burke-Ernzerhof functional. Among many newly predicted structures, three low-lying structures, which exhibit somewhat higher energy compared with those previously predicted, such as $\mathrm{Cco}-{\mathrm{C}}_8$ ($Z$-carbon) and $M$-carbon, are further discussed with calculations of phonon and band dispersion curves. Furthermore, approaches to systematically explore two- or one-dimensional periodic structures are proposed and applied to the ${\mathrm{C}}_8$ unit cell with the slab model. These results suggest that the present approach is highly promising for predicting crystal structures.

• Received 16 February 2017
• Revised 29 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.184110