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

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.

Authors:
 [1];  [1];  [1]
  1. Northwestern Univ., Evanston, IL (United States). Dept. of Materials Science and Engineering
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1544385
DOE Contract Number:  
FG02-07ER46433; AC02-05CH11231
Resource Type:
Journal Article
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 21; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English

Citation Formats

Aykol, Muratahan, Doak, Jeff W., and Wolverton, C. Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.95.214115.
Aykol, Muratahan, Doak, Jeff W., & Wolverton, C. Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method. United States. doi:10.1103/PhysRevB.95.214115.
Aykol, Muratahan, Doak, Jeff W., and Wolverton, C. Thu . "Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method". United States. doi:10.1103/PhysRevB.95.214115.
@article{osti_1544385,
title = {Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method},
author = {Aykol, Muratahan and Doak, Jeff W. and Wolverton, C.},
abstractNote = {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.},
doi = {10.1103/PhysRevB.95.214115},
journal = {Physical Review B},
issn = {2469-9950},
number = 21,
volume = 95,
place = {United States},
year = {2017},
month = {6}
}

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