We present the case for the nonempirical construction of density functional approximations for the exchange-correlation energy by the traditional method of “constraint satisfaction” without fitting to data sets, and present evidence that this approach has been successful on the first three rungs of “Jacob’s ladder” of density functional approximations [local spin-density approximation (LSD), generalized gradient approximation (GGA), and meta-GGA]. We expect that this approach will also prove successful on the fourth and fifth rungs (hyper-GGA or hybrid and generalized random-phase approximation). In particular, we argue for the theoretical and practical importance of recovering the correct uniform density limit, which many semiempirical functionals fail to do. Among the beyond-LSD functionals now available to users, we recommend the nonempirical Perdew–Burke–Ernzerhof (PBE) GGA and the nonempirical Tao–Perdew–Staroverov–Scuseria (TPSS) meta-GGA, and their one-parameter hybrids with exact exchange. TPSS improvement over PBE is dramatic for atomization energies of molecules and surface energies of solids, and small or moderate for other properties. TPSS is now or soon will be available in standard codes such as GAUSSIAN, TURBOMOLE, NWCHEM, ADF, WIEN, VASP, etc. We also discuss old and new ideas to eliminate the self-interaction error that plagues the functionals on the first three rungs of the ladder, bring up other related issues, and close with a list of “do’s and don’t’s” for software developers and users.
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8 August 2005
Research Article|
August 17 2005
Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits
John P. Perdew;
John P. Perdew
Department of Physics and Quantum Theory Group,
Tulane University
, New Orleans, Louisiana 70118
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Adrienn Ruzsinszky;
Adrienn Ruzsinszky
Department of Physics and Quantum Theory Group,
Tulane University
, New Orleans, Louisiana 70118
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Jianmin Tao;
Jianmin Tao
Department of Physics and Quantum Theory Group,
Tulane University
, New Orleans, Louisiana 70118
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Viktor N. Staroverov;
Viktor N. Staroverov
Department of Chemistry,
Rice University
, Houston, Texas 77005
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Gustavo E. Scuseria;
Gustavo E. Scuseria
Department of Chemistry,
Rice University
, Houston, Texas 77005
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Gábor I. Csonka
Gábor I. Csonka
Department of Inorganic Chemistry,
Budapest University of Technology and Economics
, H-1521 Budapest, Hungary
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J. Chem. Phys. 123, 062201 (2005)
Article history
Received:
August 18 2004
Accepted:
March 17 2005
Citation
John P. Perdew, Adrienn Ruzsinszky, Jianmin Tao, Viktor N. Staroverov, Gustavo E. Scuseria, Gábor I. Csonka; Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits. J. Chem. Phys. 8 August 2005; 123 (6): 062201. https://doi.org/10.1063/1.1904565
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