Assessing the Structural Diversity of Form II Red Phosphorus via Stepwise Crystal Structure Search

Recently, the long less-known Form II red phosphorus (RP) (viz. Type II RP) was ascertained by the state-of-the-art 3-dimensional electron diffraction technique with a triclinic lattice, completely distinct from other known elemental phosphorus and leaving atomic coordinates not determined. The cell composed of ∼250 atoms might exceed the capacity of current readily available crystal structure search packages, which have been widely applied to systems with several tens of atoms. Besides, mistaking Form II RP for violet phosphorus is still surprisingly common in the studies on allotropic phosphorus due to misinterpretations on JCPDS card #00-044-0906. Herein, by reproducing annealing synthesis and cell relaxation of structures obtained in the literature, we verified two former crystal structures for Form II RP to be wrong and explained how the misinterpretations have occurred. Then, on the basis of experimental lattice data, we provided possible Form II RP models containing atomic positions by a nearly exhaustive high-throughput stepwise crystal structure search approach optimized by molecular mechanics, machine-learned force field, and density functional theory in succession. The energetic stability of Form II RP was found to rank between white phosphorus and black phosphorus, similar to the nanorod modifications.