DOI: 10.1063/1.2187006. Screened hybrid density functionals applied to solids

Screened hybrid density functionals applied to solids

10.1063/1.2187006

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.

Bibliography

Paier, J., Marsman, M., Hummer, K., Kresse, G., Gerber, I. C., & ÃngyÃ¡n, J. G. (2006). Screened hybrid density functionals applied to solids. The Journal of Chemical Physics, 124(15).

Authors 6

J. Paier (first)
M. Marsman (additional)
K. Hummer (additional)
G. Kresse (additional)
I. C. Gerber (additional)
J. G. Ángyán (additional)

References 47 Referenced 2,120

{'volume-title': 'Density Functional Theory and its Applications to Materials', 'year': '2001', 'author': 'van Doren', 'key': '2023072408055571600_c1'} / Density Functional Theory and its Applications to Materials by van Doren (2001)
10.1103/PhysRevLett.55.1665 / Phys. Rev. Lett. (1985)
10.1063/1.464304 / J. Chem. Phys. (1993)
10.1063/1.472933 / J. Chem. Phys. (1996)
10.1016/S0009-2614(01)00616-9 / Chem. Phys. Lett. (2001)
10.1103/PhysRevB.61.5194 / Phys. Rev. B (2000)
10.1063/1.1564060 / J. Chem. Phys. (2003)
10.1063/1.1760074 / J. Chem. Phys. (2004)
10.1063/1.2085170 / J. Chem. Phys. (2005)
10.1103/PhysRevLett.91.146401 / Phys. Rev. Lett. (2003)
10.1063/1.1926272 / J. Chem. Phys. (2005)
10.1103/PhysRevB.48.13115 / Phys. Rev. B (1993)
10.1016/0927-0256(96)00008-0 / Comput. Mater. Sci. (1996)
10.1103/PhysRevB.54.11169 / Phys. Rev. B (1996)
10.1103/PhysRevB.34.4405 / Phys. Rev. B (1986)
10.1063/1.478522 / J. Chem. Phys. (1999)
10.1103/PhysRevLett.77.3865 / Phys. Rev. Lett. (1996)
10.1016/S0009-2614(96)01225-0 / Chem. Phys. Lett. (1996)
10.1063/1.1626543 / J. Chem. Phys. (2003)
10.1063/1.1528936 / J. Chem. Phys. (2003)
10.1016/0009-2614(96)00280-1 / Chem. Phys. Lett. (1996)
10.1016/0009-2614(96)00931-1 / Chem. Phys. Lett. (1996)
{'key': '2023072408055571600_c22', 'first-page': '327', 'volume-title': 'Recent Developments and Applications of Modern Density Functional Theory', 'author': 'Seminario', 'year': '1996'} / Recent Developments and Applications of Modern Density Functional Theory by Seminario (1996)
10.1016/S0009-2614(97)00758-6 / Chem. Phys. Lett. (1997)
10.1103/PhysRevB.50.17953 / Phys. Rev. B (1994)
10.1103/PhysRevB.59.1758 / Phys. Rev. B (1999)
{'key': '2023072408055571600_c26'}
10.1088/0953-8984/6/40/015 / J. Phys.: Condens. Matter (1994)
10.1073/pnas.30.9.244 / Proc. Natl. Acad. Sci. U.S.A. (1944)
10.1103/PhysRevB.13.5188 / Phys. Rev. B (1976)
10.1103/PhysRevB.49.16223 / Phys. Rev. B (1994)
{'year': '2001', 'key': '2023072408055571600_c31'} (2001)
10.1016/S0038-1098(99)00577-3 / Solid State Commun. (2000)
10.1103/PhysRevB.69.075102 / Phys. Rev. B (2004)
{'volume-title': 'NIST-JANAF Thermochemical Tables', 'year': '1998', 'author': 'Chase', 'key': '2023072408055571600_c34'} / NIST-JANAF Thermochemical Tables by Chase (1998)
{'volume-title': 'Numerical Data and Functional Relationships in Science and Technology', 'year': '1982', 'author': 'Hellwege', 'key': '2023072408055571600_c35'} / Numerical Data and Functional Relationships in Science and Technology by Hellwege (1982)
10.1103/PhysRevB.5.497 / Phys. Rev. B (1972)
10.1103/PhysRevB.47.2130 / Phys. Rev. B (1993)
10.1016/0038-1098(70)90163-8 / Solid State Commun. (1970)
10.1016/0038-1098(76)90973-X / Solid State Commun. (1976)
10.1103/PhysRevLett.54.142 / Phys. Rev. Lett. (1985)
{'volume-title': 'Optical Properties of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information', 'year': '1999', 'key': '2023072408055571600_c41'} / Optical Properties of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information (1999)
10.1103/PhysRevB.11.5190 / Phys. Rev. B (1975)
10.1103/PhysRevB.69.045111 / Phys. Rev. B (2004)
10.1103/PhysRevB.48.5058 / Phys. Rev. B (1993)
10.1088/0034-4885/61/3/002 / Rep. Prog. Phys. (1998)
10.1007/3-540-09202-1 / Photoemission in Solids II, Case studies by Ley (1979)

Dates

Type	When
Created	19 years, 4 months ago (April 17, 2006, 6:40 p.m.)
Deposited	2 years, 1 month ago (July 24, 2023, 4:06 a.m.)
Indexed	18 hours, 26 minutes ago (Aug. 23, 2025, 9:38 p.m.)
Issued	19 years, 4 months ago (April 19, 2006)
Published	19 years, 4 months ago (April 19, 2006)
Published Online	19 years, 4 months ago (April 19, 2006)
Published Print	19 years, 4 months ago (April 21, 2006)

Funders 0

None

BibTeX

@article{Paier_2006, title={Screened hybrid density functionals applied to solids}, volume={124}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2187006}, DOI={10.1063/1.2187006}, number={15}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Paier, J. and Marsman, M. and Hummer, K. and Kresse, G. and Gerber, I. C. and Ángyán, J. G.}, year={2006}, month=apr }

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