Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits

2005/08/08 by John P. Perdew, Adrienn Ruzsinszky, Jianmin Tao +3 · 10 citations
Physics and Astronomy · Materials Science · Chemical Engineering · Mathematics · #Advanced Chemical Physics Studies #Machine Learning in Materials Science #Catalysis and Oxidation Reactions #Constraint (computer-aided design) #Hybrid functional #Density functional theory #Gaussian #Limit (mathematics) #Local-density approximation #Statistical physics #Mathematics #Physics #Computer science #Applied mathematics #Quantum mechanics #Mathematical analysis #Geometry

paper · doi:10.1063/1.1904565

openalex publication_date 2005/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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• Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
• Performance of a nonempirical meta–generalized gradient approximation density functional for excitation energies
• Nonempirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound
• Established DFT methods calculation of conjugation disturbed in the\n presence of torsional hyperconjugation
• Intracule densities in the strong-interaction limit of density functional theory
• Role of Exchange in Density Functional Theory for Weakly-Interacting Systems: Quantum Monte Carlo Analysis of Electron Density and Interaction Energy
• Rungs 1 to 4 of DFT Jacob’s ladder: Extensive test on the lattice constant, bulk modulus, and cohesive energy of solids
• Mitigating error cancellation in density functional approximations via machine learning correction
• Density functional theory [wikipedia]