Assessing the Structural\nDiversity of Form II Red\nPhosphorus via Stepwise Crystal Structure Search

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