Nonempirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

2009/03/31 by Mariana M. Odashima, K. Capelle · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Correlation #Coulomb #Density functional theory #Electron #Geometry #Hybrid functional #Mathematics #Photochemistry and Electron Transfer Studies #Physics #Quantum mechanics #Representation (politics) #Simple (philosophy) #Spectroscopy and Quantum Chemical Studies #Statistical physics #cond-mat.mtrl-sci #physics.atom-ph #physics.chem-ph

paper · pdf · doi:10.1103/physreva.79.062515

published as Phys. Rev. A 79, p. 062515 (2009) · v2: Major revison. Added information on relation to the gradient expansion and to local hybrids, improved discussion of size consistency and of performance relative to other functionals

arxiv created 2009/05/08 · openalex publication_date 2009/06/30 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully nonempirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.

Citations

• Generalized Gradient Approximation Made Simple
• Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals
• Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
• Rationale for mixing exact exchange with density functional approximations
• Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids
• Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits
• Density-functional thermochemistry. III. The role of exact exchange
• Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation

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• Perspective: Fifty years of density-functional theory in chemical physics