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Title: Understanding band gaps of solids in generalized Kohn–Sham theory

Abstract

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. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

Authors:
 [1];  [2];  [3];  [4];  [5];  [6];  [7];  [7];  [8];  [9];  [9];  [10];  [11];  [11]
+ Show Author Affiliations
  1. Temple Univ., Philadelphia, PA (United States). Dept. of Physics, and Dept. of Chemistry
  2. Duke Univ., Durham, NC (United States). Dept. of Chemistry
  3. Univ. of California, Irvine, CA (United States). Dept. of Chemistry, and Dept. of Physics
  4. Temple Univ., Philadelphia, PA (United States). Dept. of Physics; Microsystem and Terahertz Research Center, Chengdu, Sichhuan (China)
  5. Max-Planck Inst. für Mikrostrukturphysik, Halle (Germany)
  6. 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.
  7. Rice Univ., Houston, TX (United States). Dept. of Chemistry, and Dept. of Physics and Astronomy
  8. Fritz-Haber-Inst. der Max-Planck-Gesellschaft, Berlin (Germany)
  9. Temple Univ., Philadelphia, PA (United States). Dept. of Physics
  10. Univ. of Texas, El Paso, TX (United States). Dept. of Physics
  11. Friedrich-Alexander Univ. Erlangen-Nürnberg (Germany). Dept. of Chemistry and Pharmacy
Publication Date:
Research Org.:
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 Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); Humboldt Foundation; German Research Foundation (DFG)
OSTI Identifier:
1388554
Alternate Identifier(s):
OSTI ID: 1595131
Grant/Contract Number:  
SC0012575; FG02-08ER46496
Resource Type:
Accepted Manuscript
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 114; Journal Issue: 11; Related Information: CCDM partners with Temple University (lead); Brookhaven National Laboratory; Drexel University; Duke University; North Carolina State University; Northeastern University; Princeton University; Rice University; University of Pennsylvania; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; catalysis (heterogeneous); solar (photovoltaic); energy storage (including batteries and capacitors); hydrogen and fuel cells; defects; mechanical behavior; materials and chemistry by design; synthesis (novel materials); band gaps; solids; density-functional theory; Kohn-Sham theory; generalized Kohn-Sham theory

Citation Formats

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, and Görling, Andreas. Understanding band gaps of solids in generalized Kohn–Sham theory. United States: N. p., 2017. Web. doi:10.1073/pnas.1621352114.
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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. Understanding band gaps of solids in generalized Kohn–Sham theory. United States. https://doi.org/10.1073/pnas.1621352114
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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, and Görling, Andreas. Mon . "Understanding band gaps of solids in generalized Kohn–Sham theory". United States. https://doi.org/10.1073/pnas.1621352114. https://www.osti.gov/servlets/purl/1388554.
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@article{osti_1388554,
title = {Understanding band gaps of solids in generalized Kohn–Sham theory},
author = {Perdew, John P. and Yang, Weitao and Burke, Kieron and Yang, Zenghui and Gross, Eberhard K. U. and Scheffler, Matthias and Scuseria, Gustavo E. and Henderson, Thomas M. and Zhang, Igor Ying and Ruzsinszky, Adrienn and Peng, Haowei and Sun, Jianwei and Trushin, Egor and Görling, Andreas},
abstractNote = {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. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.},
doi = {10.1073/pnas.1621352114},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 11,
volume = 114,
place = {United States},
year = {Mon Mar 06 00:00:00 EST 2017},
month = {Mon Mar 06 00:00:00 EST 2017}
}
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https://doi.org/10.1073/pnas.1621352114
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