Testing density functionals for structural phase transitions of solids under pressure: Si, SiO2, and Zr

Bing Xiao, Jianwei Sun, Adrienn Ruzsinszky, Jing Feng, Robin Haunschild, Gustavo E. Scuseria, and John P. Perdew
Phys. Rev. B 88, 184103 – Published 12 November 2013
PDFHTMLExport Citation


We have investigated the structural phase transitions of crystalline Si (insulator-metal), SiO2 (insulator-insulator), and Zr (metal-metal) under pressure, as a test of several density functionals for the exchange-correlation energy. While meta-generalized gradient approximations (meta-GGAs) such as revTPSS (revised Tao-Perdew-Staroverov-Scuseria) are more sophisticated than GGAs such as PBE (Perdew-Burke-Ernzerhof), and are more accurate without empiricism for atomization energies of molecules, lattice constants of solids, and surface energies, we confirm that these meta-GGAs tend to give smaller and less realistic transition pressures than the PBE GGA does. But we also show that the recent functionals of the meta-GGA made simple family (MGGA_MS) behave differently, predicting larger and often more realistic transition pressures. We suggest that further refinement of the meta-GGA can lead to a functional that is more accurate for properties of molecules and solids at equilibrium or under compression. We also show that, contrary to recent suggestions but in line with older ones, an accurate fundamental gap in the noninteracting band structure is not necessary for an accurate prediction of the transition pressure. Unlike the semilocal GGAs and meta-GGAs, and unlike the local density approximation also tested here, the screened hybrid functional HSE06 (Heyd-Scuseria-Ernzerhof) is fully nonlocal and predicts more realistic fundamental gaps. HSE06 is better than the semilocal functionals for the transition pressures of Si and SiO2, but seriously overestimates the transition pressure in Zr. Besides the transition pressures, we report the transition energies and volumes, binding energy curves, and structural parameters at zero and transition pressure. Finally, we discuss how the performance of a functional can reflect its plottable exchange enhancement factor, and why the structural phase transitions are especially challenging for approximate density functionals.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
6 More
  • Received 20 August 2013


©2013 American Physical Society

Authors & Affiliations

Bing Xiao1,*, Jianwei Sun1, Adrienn Ruzsinszky1, Jing Feng2, Robin Haunschild3, Gustavo E. Scuseria3,4,5, and John P. Perdew1

  • 1Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
  • 2School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Department of Chemistry, Rice University, Houston, Texas 77005, USA
  • 4Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
  • 5Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

  • *tuf23889@temple.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Vol. 88, Iss. 18 — 1 November 2013

Reuse & Permissions
Access Options
Physics Next Workshops
March 20, 2017

The American Physical Society is initiating a new series of international workshops. These Physics Next workshops will be aimed at fostering new and emerging areas of physics research, focusing on topics that straddle traditional subject boundaries and are starting to “emerge from the noise.”

The first workshop is titled “Physics Next: Materials Design and Discovery,” and will take place on May 15 -17, 2017. More information.

Authorization Required




Sign up to receive regular email alerts from Physical Review B

Log In



Article Lookup

Paste a citation or DOI

Enter a citation