Exact-exchange energy density in the gauge of a semilocal density-functional approximation

2007/10/31 by Jianmin Tao, Viktor N. Staroverov, Gustavo E. Scuseria +1 · 4 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #cond-mat.mtrl-sci

paper · pdf · doi:10.1103/physreva.77.012509

9 pages, 10 figures. This is a revised version

arxiv created 2007/12/04 · openalex publication_date 2008/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The exact-exchange energy density and energy density of a semilocal density-functional approximation are two key ingredients for modeling the static correlation, a strongly nonlocal functional of the electron density, through a local hybrid functional. Because energy densities are not uniquely defined, the conventional (Slater) exact-exchange energy density e_x^ex(conv) is not necessarily well suited for local mixing with a given semilocal approximation. We show how to transform e_x^ex(conv) in order to make it compatible with an arbitrary semilocal density functional, taking the nonempirical meta-generalized-gradient approximation of Tao, Perdew, Staroverov, and Scuseria as an example. Our additive gauge transformation function integrates to zero, satisfies exact constraints, and is most important where the density is dominated by a single orbital shape. We show that, as expected, the difference between semilocal and exact-exchange energy densities becomes more negative under bond stretching in He₂⁺ and related systems. Our construction of e_x^ex(conv) by a resolution-of-the-identity method requires uncontracted basis functions.

Citations

• Generalized Gradient Approximation Made Simple
• Spin-density gradient expansion for the kinetic energy
• Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis
• Density-functional thermochemistry. III. The role of exact exchange
• Self-Consistent Equations Including Exchange and Correlation Effects

Cited by

• Restoring the Point-and-Charge Gradient Expansion for the Strong Interaction Density Functionals
• Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
• Collapse of the Electron Gas to Two Dimensions in Density Functional Theory
• Kohn-Sham kinetic energy density in the nuclear and asymptotic regions: Deviations from the von Weizsäcker behavior and applications to density functionals

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• Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density