Fate of density functional theory in the study of high-pressure solid hydrogen

Sam Azadi and W. M. C. Foulkes
Phys. Rev. B 88, 014115 – Published 31 July 2013

Abstract

This paper investigates some of the successes and failures of density functional theory in the study of high-pressure solid hydrogen at low temperature. We calculate the phase diagram, metallization pressure, phonon spectrum, and proton zero-point energy using three popular exchange-correlation functionals: the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, and the semilocal Becke-Lee-Yang-Parr (BLYP) functional. We focus on the solid molecular P63/m, C2/c, Cmca-12, and Cmca structures in the pressure range from 100<P<500 GPa over which phases I, II, and III are observed experimentally. At the static level of theory, in which proton zero-point energy is ignored, the LDA, PBE, and BLYP functionals give very different structural transition and metallization pressures, with the BLYP phase diagram in better agreement with experiment. Nevertheless, all three functionals provide qualitatively the same information about the band gaps of the four structures and the phase transitions between them. Going beyond the static level, we find that the frequencies of the vibron modes observed above 3000 cm1 depend strongly on the choice of exchange-correlation functional, although the low-frequency part of the phonon spectrum is little affected. The largest and smallest values of the proton zero-point energy, obtained using the BLYP and LDA functionals, respectively, differ by more than 10 meV/proton. Including the proton zero-point energy calculated from the phonon spectrum within the harmonic approximation improves the agreement of the BLYP and PBE phase diagrams with experiment. Taken as a whole, our results demonstrate the inadequacy of mean-field-like density functional calculations of solid molecular hydrogen in phases I, II, and III and emphasize the need for more sophisticated methods.

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  • Received 5 April 2013
  • Corrected 12 September 2013

DOI:https://doi.org/10.1103/PhysRevB.88.014115

©2013 American Physical Society

Corrections

12 September 2013

Erratum

Authors & Affiliations

Sam Azadi and W. M. C. Foulkes

  • The Thomas Young Centre and the Department of Physics, Imperial College, Exhibition Road, London SW7 2AZ, United Kingdom

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Issue

Vol. 88, Iss. 1 — 1 July 2013

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