Understanding band gaps of solids in generalized Kohn–Sham theory

Perdew, John P.; Yang, Weitao; Burke, Kieron; Yang, Zenghui; Gross, Eberhard K.  U.; Scheffler, Matthias; Scuseria, Gustavo E.; Henderson, Thomas M.; Zhang, Igor Ying; Ruzsinszky, Adrienn; Peng, Haowei; Sun, Jianwei; Trushin, Egor; Görling, Andreas

doi:10.1073/pnas.1621352114

Understanding band gaps of solids in generalized Kohn–Sham theory

Journal Article · Sun Mar 05 23:00:00 EST 2017 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.1621352114· OSTI ID:1388554

Perdew, John P. ^[1]; Yang, Weitao ^[2]; Burke, Kieron ^[3]; Yang, Zenghui ^[4]; Gross, Eberhard K. U. ^[5]; Scheffler, Matthias ^[6]; Scuseria, Gustavo E. ^[7]; Henderson, Thomas M. ^[7]; Zhang, Igor Ying ^[8]; Ruzsinszky, Adrienn ^[9]; Peng, Haowei ^[9]; Sun, Jianwei ^[10]; Trushin, Egor ^[11]; Görling, Andreas ^[11]

Temple Univ., Philadelphia, PA (United States). Dept. of Physics, and Dept. of Chemistry
Duke Univ., Durham, NC (United States). Dept. of Chemistry
Univ. of California, Irvine, CA (United States). Dept. of Chemistry, and Dept. of Physics
Temple Univ., Philadelphia, PA (United States). Dept. of Physics; Microsystem and Terahertz Research Center, Chengdu, Sichhuan (China)
Max-Planck Inst. für Mikrostrukturphysik, Halle (Germany)
Fritz-Haber-Inst. der Max-Planck-Gesellschaft, Berlin (Germany); Univ. of California, Santa Barbara, CA (United States). Dept. of Chemistry and Biochemistry, and Materials Dept.
Rice Univ., Houston, TX (United States). Dept. of Chemistry, and Dept. of Physics and Astronomy
Fritz-Haber-Inst. der Max-Planck-Gesellschaft, Berlin (Germany)
Temple Univ., Philadelphia, PA (United States). Dept. of Physics
Univ. of Texas, El Paso, TX (United States). Dept. of Physics
Friedrich-Alexander Univ. Erlangen-Nürnberg (Germany). Dept. of Chemistry and Pharmacy

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn–Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. Finally, a linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

View Accepted Manuscript (DOE)

Research Organization:: Energy Frontier Research Centers (EFRC) (United States). Center for the Computational Design of Functional Layered Materials (CCDM); Univ. of California, Irvine, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Humboldt Foundation; German Research Foundation (DFG)

Grant/Contract Number:: SC0012575; FG02-08ER46496

OSTI ID:: 1388554

Alternate ID(s):: OSTI ID: 1595131

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 11 Vol. 114; ISSN 0027-8424

Publisher:: National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites Liu, Chi; Huhn, William; Du, Ke-Zhao Physical Review Letters, Vol. 121, Issue 14 https://doi.org/10.1103/physrevlett.121.146401	journal	October 2018
Assessment of the GLLB-SC potential for solid-state properties and attempts for improvement Tran, Fabien; Ehsan, Sohaib; Blaha, Peter Physical Review Materials, Vol. 2, Issue 2 https://doi.org/10.1103/physrevmaterials.2.023802	journal	February 2018
Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals Elmaslmane, A. R.; Wetherell, J.; Hodgson, M. J. P. Physical Review Materials, Vol. 2, Issue 4 https://doi.org/10.1103/physrevmaterials.2.040801	journal	April 2018
Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators Chen, Wei; Miceli, Giacomo; Rignanese, Gian-Marco Physical Review Materials, Vol. 2, Issue 7 https://doi.org/10.1103/physrevmaterials.2.073803	journal	July 2018
Towards predictive band gaps for halide perovskites: Lessons from one-shot and eigenvalue self-consistent G W Leppert, Linn; Rangel, Tonatiuh; Neaton, Jeffrey B. Physical Review Materials, Vol. 3, Issue 10 https://doi.org/10.1103/physrevmaterials.3.103803	journal	October 2019
Structural, electronic, and magnetic properties of bulk and epitaxial LaCoO 3 through diffusion Monte Carlo Saritas, Kayahan; Krogel, Jaron T.; Okamoto, Satoshi Physical Review Materials, Vol. 3, Issue 12 https://doi.org/10.1103/physrevmaterials.3.124414	journal	December 2019
Ultranonlocality and accurate band gaps from a meta-generalized gradient approximation Aschebrock, Thilo; Kümmel, Stephan Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/physrevresearch.1.033082	journal	November 2019
Many-Body Quantum Monte Carlo Study of 2D Materials: Cohesion and Band Gap in Single-Layer Phosphorene Frank, T.; Derian, R.; Tokár, K. Physical Review X, Vol. 9, Issue 1 https://doi.org/10.1103/physrevx.9.011018	journal	January 2019
Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites W., You,; K. -Z., Du,; V., Blum, The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/v5ra-ar75	text	January 2018
Oganesson Is a Semiconductor: On the Relativistic Band-Gap Narrowing in the Heaviest Noble-Gas Solids Mewes, Jan-Michael; Jerabek, Paul; Smits, Odile R. FID GEO https://doi.org/10.23689/fidgeo-4521	text	January 2019
Transport and Optical Gaps in Amorphous Organic Molecular Materials San-Fabián, Emilio; Louis, Enrique; Díaz-García, María Molecules, Vol. 24, Issue 3 https://doi.org/10.3390/molecules24030609	journal	February 2019
Direct extraction of excitation energies from ensemble density-functional theory Yang, Zeng-hui; Pribram-Jones, Aurora; Burke, Kieron arXiv https://doi.org/10.48550/arxiv.1703.10738	text	January 2017
Assessment of the GLLB-SC potential for solid-state properties and attempts for improvement Tran, Fabien; Ehsan, Sohaib; Blaha, Peter arXiv https://doi.org/10.48550/arxiv.1712.06508	text	January 2017
Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites Liu, Chi; Huhn, William; Du, Ke-Zhao arXiv https://doi.org/10.48550/arxiv.1803.07230	text	January 2018
Understanding the origin of bandgap problem in transition and post-transition metal oxides Tan, Hengxin; Liu, Haitao; Li, Yuanchang arXiv https://doi.org/10.48550/arxiv.1812.11288	text	January 2018
Regularized SCAN functional Bartók, Albert P.; Yates, Jonathan R. arXiv https://doi.org/10.48550/arxiv.1903.01007	text	January 2019
On the calculation of the bandgap of periodic solids with MGGA functionals using the total energy Tran, Fabien; Doumont, Jan; Blaha, Peter arXiv https://doi.org/10.48550/arxiv.1909.00720	text	January 2019
Theoretical Study of Ternary CoSP Semiconductor: a Candidate for Photovoltaic Applications Houari, Abdesalem; Benissad, Fares arXiv https://doi.org/10.48550/arxiv.2003.09864	text	January 2020
Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density Janesko, Benjamin G.; Scalmani, Giovanni; Frisch, Michael J. Taylor & Francis https://doi.org/10.6084/m9.figshare.7232273.v1	text	January 2018

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Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
74 ATOMIC AND MOLECULAR PHYSICS
Kohn-Sham theory
band gaps
catalysis (heterogeneous)
defects
density-functional theory
energy storage (including batteries and capacitors)
generalized Kohn-Sham theory
hydrogen and fuel cells
materials and chemistry by design
mechanical behavior
solar (photovoltaic)
solids
synthesis (novel materials)

Understanding band gaps of solids in generalized Kohn–Sham theory

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