Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces

Journal Article · · Physical Review B
 [1];  [2];  [3];  [4];  [5]
  1. Temple Univ., Philadelphia, PA (United States); Univ. of Pennsylvania, Philadelphia, PA (United States); DOE/OSTI
  2. Princeton Univ., NJ (United States)
  3. Univ. of Western Ontario, London, ON (Canada)
  4. Rice Univ., Houston, TX (United States)
  5. Temple Univ., Philadelphia, PA (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)
+ Show Author Affiliations
Recently, Tao and Mo developed a semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density-matrix expansion corrected to reproduce the fourth-order gradient expansion of the exchange energy in the slowly-varying-density limit, while the correlation part is based on the Tao-Perdew-Staroverov-Scuseria (TPSS) correlation functional, with a modification for the low-density limit. In this work, the Tao-Mo (TM) functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, seven cohesive energies, and jellium surface exchange and correlation energies for the density parameter rs in the range from 2 to 3 bohr. Our calculations show that the TM approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors (MAEs) of 0.025 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and 35 erg / cm2 for surface exchange-correlation energies. The MAE in band gaps is larger than that of TPSS, but slightly smaller than the errors of the local spin-density approximation, Perdew-Burke-Ernzerhof generalized gradient approximation, and revised TPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the Heyd-Scuseria-Ernzerhof nonlocal screened hybrid functional.
Research Organization:
Rice Univ., Houston, TX (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0001474
OSTI ID:
1535827
Alternate ID(s):
OSTI ID: 1339183
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 3 Vol. 95; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (71)

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals journal July 2007
Low temperature elastic constants of potassium journal February 1965
Compression of MgS TO 54 GPa journal May 1994
Ab initio study of high pressure phase transition in GaN journal November 1994
Chlorine adsorption on the Cu(111) surface journal February 2000
Predicting Energetics of Supramolecular Systems Using the XDM Dispersion Model journal August 2015
Predicting Band Gaps with Hybrid Density Functionals journal October 2016
Performance of meta-GGA Functionals on General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions journal November 2012
Bulk Properties of Transition Metals: A Challenge for the Design of Universal Density Functionals journal August 2014
Prediction Uncertainty of Density Functional Approximations for Properties of Crystals with Cubic Symmetry journal December 2014
Low‐Temperature Elastic Moduli of Aluminum journal February 1964
Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional journal November 2005
Improved hybrid functional for solids: The HSEsol functional journal January 2011
Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors journal April 2012
Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals journal January 1985
Dynamical screening of van der Waals interactions in nanostructured solids: Sublimation of fullerenes journal April 2015
Communication: Accurate higher-order van der Waals coefficients between molecules from a model dynamic multipole polarizability journal January 2016
Rungs 1 to 4 of DFT Jacob’s ladder: Extensive test on the lattice constant, bulk modulus, and cohesive energy of solids journal May 2016
Performance of a nonempirical density functional on molecules and hydrogen-bonded complexes journal December 2016
Elastic Constants of Magnesium Oxide journal February 1971
A density functional study of lithium bulk and surfaces journal January 1999
Elastic Constants of LiF from 4.2°K to 300°K by Ultrasonic Methods journal June 1957
Elastic Constants of Silver and Gold journal August 1958
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Elastic Constants of the Alkali Halides at 4.2°K journal September 1967
Finite Elastic Strain of Cubic Crystals journal June 1947
Temperature Variation of the Elastic Constants of Cubic Elements. I. Copper journal May 1955
Exchange holes in inhomogeneous systems: A coordinate-space model journal April 1989
Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole journal May 1991
Temperature and pressure dependence of the single-crystal elastic constants of Li 6 and natural lithium journal December 1977
Elastic constants of palladium and β -phase palladium hydride between 4 and 300 K journal August 1979
Calculated elastic constants and deformation potentials of cubic SiC journal August 1991
Quantum-mechanical calculation of the solid-state equilibrium MgO+α- Al 2 O 3 ⇄ MgAl 2 O 4 (spinel) versus pressure journal May 1994
Theoretical investigation of Na adsorption on the Al(111) surface journal July 1995
Gradient expansion of the exchange energy from second-order density response theory journal December 1996
Influence of polytypism on thermal properties of silicon carbide journal July 1996
Influence of electron correlations on ground-state properties of III-V semiconductors journal February 1997
Gaussian-basis LDA and GGA calculations for alkali-metal equations of state journal May 1998
Linear-scaling density-functional theory with Gaussian orbitals and periodic boundary conditions: Efficient evaluation of energy and forces via the fast multipole method journal June 2000
Jellium surface energy beyond the local-density approximation: Self-consistent-field calculations journal January 2001
Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model journal May 2001
Reply to “Comment on ‘Energy and pressure versus volume:  Equations of state motivated by the stabilized jellium model’ ” journal January 2003
Tests of a ladder of density functionals for bulk solids and surfaces journal February 2004
Structural and dynamical properties of zinc-blende GaN, AlN, BN, and their (110) surfaces journal May 2005
Meta-generalized gradient approximation for the exchange-correlation hole with an application to the jellium surface energy journal May 2006
Performance on molecules, surfaces, and solids of the Wu-Cohen GGA exchange-correlation energy functional journal March 2007
Quantum Monte Carlo calculations of the surface energy of an electron gas journal July 2007
Erratum: Tests of a ladder of density functionals for bulk solids and surfaces [Phys. Rev. B 69 , 075102 (2004)] journal December 2008
Calculation of the lattice constant of solids with semilocal functionals journal February 2009
Assessing the performance of recent density functionals for bulk solids journal April 2009
Van der Waals density functionals applied to solids journal May 2011
Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method journal July 2011
Lattice constants from semilocal density functionals with zero-point phonon correction journal January 2012
Ice phases under ambient and high pressure: Insights from density functional theory journal June 2013
Construction of a general semilocal exchange-correlation hole model: Application to nonempirical meta-GGA functionals journal September 2013
Quantum Monte Carlo applied to solids journal December 2013
Accurate surface energies from first principles journal March 2015
Accurate van der Waals coefficients between fullerenes and fullerene-alkali atoms and clusters: Modified single-frequency approximation journal August 2016
Density-Matrix Expansion for an Effective Nuclear Hamiltonian journal May 1972
High-Level Correlated Approach to the Jellium Surface Energy, without Uniform-Gas Input journal January 2008
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces journal April 2008
Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry journal July 2009
Engineering the Electronic Band Structure for Multiband Solar Cells journal January 2011
Hydrogen Bonds and van der Waals Forces in Ice at Ambient and High Pressures journal October 2011
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry journal August 2016
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Generalized Gradient Approximation Made Simple journal October 1996
Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids journal September 2003
Increasing Solar Absorption for Photocatalysis with Black Hydrogenated Titanium Dioxide Nanocrystals journal January 2011
Long-Range van der Waals Interaction journal July 2013

Cited By (11)

A meta-GGA level screened range-separated hybrid functional by employing short range Hartree–Fock with a long range semilocal functional journal January 2018
Long-range corrected density functional through the density matrix expansion based semilocal exchange hole journal January 2018
Screened hybrid meta-GGA exchange–correlation functionals for extended systems journal January 2019
Efficient lattice constants and energy bandgaps for condensed systems from a meta-GGA level screened range-separated hybrid functional journal September 2018
Assessing the performance of the Tao-Mo semilocal density functional in the projector-augmented-wave method journal July 2018
Assessing the performance of the recent meta-GGA density functionals for describing the lattice constants, bulk moduli, and cohesive energies of alkali, alkaline-earth, and transition metals journal October 2018
Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: Tests on solids journal October 2018
Accurate lattice geometrical parameters and bulk moduli from a semilocal density functional journal September 2018
Local atomic arrangement in LaCuAl 3 and LaAuAl 3 by NMR and density functional theory journal July 2019
Nonlocal van der Waals functionals for solids: Choosing an appropriate one journal June 2019
Long-range dispersion-corrected density functional for noncovalent interactions journal October 2019

Similar Records

Semilocal exchange hole with an application to range-separated density functionals
Journal Article · Sun Mar 12 20:00:00 EDT 2017 · Physical Review. B · OSTI ID:1535883
First-principles calculations of the electronic and structural properties of GaSb
Journal Article · Sat Oct 15 00:00:00 EDT 2016 · Semiconductors · OSTI ID:22649696
Performance of a nonempirical density functional on molecules and hydrogen-bonded complexes
Journal Article · Sun Dec 18 19:00:00 EST 2016 · Journal of Chemical Physics · OSTI ID:1474133

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
crystal structures
density functional theory
elastic modules
electronic structure
materials science
physics