Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method

Muratahan Aykol, Jeff W. Doak, C. Wolverton*

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We evaluate the energetic stabilities of white, red, and black allotropes of phosphorus using density functional theory (DFT) and hybrid functional methods, van der Waals (vdW) corrections (DFT+vdW and hybrid+vdW), vdW density functionals, and random phase approximation (RPA). We find that stability of black phosphorus over red-V (i.e., the violet form) is not ubiquitous among these methods, and the calculated enthalpies for the reaction phosphorus (red-V)→phosphorus (black) are scattered between -20 and 40 meV/atom. With local density and generalized gradient approximations, and hybrid functionals, mean absolute errors (MAEs) in densities of P allotropes relative to experiments are found to be around 10%-25%, whereas with vdW-inclusive methods, MAEs in densities drop below ∼5%. While the inconsistency among the density functional methods could not shed light on the stability puzzle of black versus red phosphorus, comparison of their accuracy in predicting densities and the supplementary RPA results on relative stabilities indicate that opposite to the common belief, black and red phosphorus are almost degenerate, or the red-V (violet) form of phosphorus might even be the ground state.

Original languageEnglish (US)
Article number214115
JournalPhysical Review B
Volume95
Issue number21
DOIs
StatePublished - Jun 28 2017

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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