DOI: 10.1063/1.2085170. Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

10.1063/1.2085170

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 Å for HSE vs 0.047 Å for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0–1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations.

Bibliography

Heyd, J., Peralta, J. E., Scuseria, G. E., & Martin, R. L. (2005). Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional. The Journal of Chemical Physics, 123(17).

Authors 4

Jochen Heyd (first)
Juan E. Peralta (additional)
Gustavo E. Scuseria (additional)
Richard L. Martin (additional)

References 68 Referenced 1,789

10.1103/PhysRev.140.A1133 / Phys. Rev. (1965)
10.1002/qua.560300314 / Int. J. Quantum Chem. (1986)
10.1103/PhysRevLett.77.3865 / Phys. Rev. Lett. (1996)
10.1103/PhysRevLett.91.146401 / Phys. Rev. Lett. (2003)
10.1063/1.1626543 / J. Chem. Phys. (2003)
10.1103/PhysRevB.69.075102 / Phys. Rev. B (2004)
10.1103/PhysRevB.30.3460 / Phys. Rev. B (1984)
10.1103/PhysRevB.44.943 / Phys. Rev. B (1991)
10.1103/PhysRevB.48.16929 / Phys. Rev. B (1993)
10.1103/PhysRevB.52.R5467 / Phys. Rev. B (1995)
10.1016/S0081-1947(08)60248-9 / Solid State Phys. (2000)
10.1063/1.464304 / J. Chem. Phys. (1993)
10.1063/1.473182 / J. Chem. Phys. (1997)
10.1063/1.1668634 / J. Chem. Phys. (2004)
{'first-page': '335', 'volume-title': 'Solid State Physics', 'year': '1976', 'key': '2023080103162836900_c15'} / Solid State Physics (1976)
10.1002/qua.560560407 / Int. J. Quantum Chem. (1995)
10.1063/1.1564060 / J. Chem. Phys. (2003)
10.1063/1.1760074 / J. Chem. Phys. (2004)
{'volume-title': 'Elementary Excitations in Solids', 'year': '1999', 'key': '2023080103162836900_c19'} / Elementary Excitations in Solids (1999)
10.1016/0009-2614(96)00280-1 / Chem. Phys. Lett. (1996)
10.1080/00268979650026037 / Mol. Phys. (1996)
{'first-page': '327', 'volume-title': 'Recent Developments and Applications of Modern Density Functional Theory', 'year': '1996', 'key': '2023080103162836900_c22'} / Recent Developments and Applications of Modern Density Functional Theory (1996)
10.1063/1.1383587 / J. Chem. Phys. (2001)
10.1103/PhysRevB.53.3764 / Phys. Rev. B (1996)
10.1063/1.478401 / J. Chem. Phys. (1999)
10.1063/1.478522 / J. Chem. Phys. (1999)
10.1016/0038-1098(75)90618-3 / Solid State Commun. (1975)
10.1063/1.472933 / J. Chem. Phys. (1996)
10.1063/1.464913 / J. Chem. Phys. (1993)
{'key': '2023080103162836900_c30'}
10.1063/1.1953427 / J. Chem. Phys. (2005)
{'key': '2023080103162836900_c32'}
10.1103/PhysRevB.71.155112 / Phys. Rev. B (2005)
10.1103/PhysRevB.72.035101 / Phys. Rev. B (2005)
10.1016/j.cplett.2004.06.011 / Chem. Phys. Lett. (2004)
10.1103/PhysRevB.41.7868 / Phys. Rev. B (1990)
See EPAPS https://www.scitation.org/doi/suppl/10.1063/1.2085170 for our detailed results for experimental and optimized structures, as well as calculated bandgaps and basis sets used. This document can be reached via a direct link in the online article’s HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
{'volume-title': 'Gaussian Development Version, Revision C.01', 'year': '2004', 'key': '2023080103162836900_c38'} / Gaussian Development Version, Revision C.01 (2004)
10.1103/PhysRevB.61.16440 / Phys. Rev. B (2000)
10.1063/1.472627 / J. Chem. Phys. (1996)
10.1126/science.274.5284.51 / Science (1996)
10.1016/0003-4916(74)90333-9 / Ann. Phys. (1974)
10.1103/PhysRevA.32.756 / Phys. Rev. A (1985)
10.1103/PhysRevA.33.3742 / Phys. Rev. A (1986)
10.1063/1.1851973 / J. Chem. Phys. (2005)
10.1103/PhysRevA.47.143 / Phys. Rev. A (1993)
10.1063/1.1305880 / J. Chem. Phys. (2000)
{'edition': '2nd', 'volume-title': 'Semiconductors-Basic Data', 'year': '1996', 'key': '2023080103162836900_c48'} / Semiconductors-Basic Data (1996)
10.1103/PhysRevB.58.10326 / Phys. Rev. B (1998)
10.1088/0022-3719/19/34/016 / J. Phys. C (1986)
10.1143/JJAP.33.2453 / Jpn. J. Appl. Phys., Part 1 (1994)
10.1103/PhysRevB.8.5711 / Phys. Rev. B (1973)
10.1103/PhysRevB.43.14142 / Phys. Rev. B (1991)
10.1103/PhysRevB.10.676 / Phys. Rev. B (1974)
10.1103/PhysRevB.50.8433 / Phys. Rev. B (1994)
{'volume-title': 'Semiconductor Parameters', 'year': '1996', 'key': '2023080103162836900_c56'} / Semiconductor Parameters (1996)
10.1103/PhysRevB.69.115216 / Phys. Rev. B (2004)
10.1103/PhysRevB.50.10780 / Phys. Rev. B (1994)
10.1088/0268-1242/12/8/007 / Semicond. Sci. Technol. (1997)
10.1103/PhysRevLett.85.1552 / Phys. Rev. Lett. (2000)
10.1103/PhysRevB.64.113203 / Phys. Rev. B (2001)
10.1002/pssb.200301889 / Phys. Status Solidi B (2003)
10.1063/1.363714 / J. Appl. Phys. (1996)
10.1103/PhysRevB.50.16232 / Phys. Rev. B (1994)
10.1103/PhysRevB.49.15341 / Phys. Rev. B (1994)
10.1103/PhysRevB.32.4066 / Phys. Rev. B (1985)
10.1103/PhysRevB.50.12318 / Phys. Rev. B (1994)
10.1103/PhysRev.111.113 / Phys. Rev. (1958)

Dates

Type	When
Created	19 years, 9 months ago (Oct. 26, 2005, 6:13 p.m.)
Deposited	2 years ago (July 31, 2023, 11:16 p.m.)
Indexed	5 hours, 3 minutes ago (Aug. 22, 2025, 12:46 a.m.)
Issued	19 years, 9 months ago (Oct. 28, 2005)
Published	19 years, 9 months ago (Oct. 28, 2005)
Published Online	19 years, 9 months ago (Oct. 28, 2005)
Published Print	19 years, 9 months ago (Nov. 1, 2005)

Funders 0

None

BibTeX

@article{Heyd_2005, title={Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional}, volume={123}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2085170}, DOI={10.1063/1.2085170}, number={17}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Heyd, Jochen and Peralta, Juan E. and Scuseria, Gustavo E. and Martin, Richard L.}, year={2005}, month=oct }

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      "first-page": "6791",
      "DOI": "10.1088/0022-3719/19/34/016",
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      "first-page": "14142",
      "DOI": "10.1103/PhysRevB.43.14142",
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