Communication: Testing and using the Lewin-Lieb bounds in density functional theory

2014/10/31 by David Feinblum, David V. Feinblum, John Kenison +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Atom (system on chip) #Chemistry #Complement (music) #Computer science #Density functional theory #Mathematical analysis #Mathematical physics #Mathematics #Metal-Organic Frameworks: Synthesis and Applications #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Upper and lower bounds #cond-mat.other #physics.chem-ph

paper · pdf · doi:10.1063/1.4904448

arxiv created 2014/12/06 · openalex publication_date 2014/12/23 · arxiv updated 2014/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding them usually less strict than the Lieb-Oxford bound. However, we also show that, if a generalized gradient approximation is to guarantee satisfaction of the new bounds for all densities, new restrictions on the exchange-correlation enhancement factor are implied.

Citations

• Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
• Atomic correlation energies and the generalized gradient approximation
• Generalized Gradient Approximation Made Simple
• Perspective: Fifty years of density-functional theory in chemical physics
• Condition on the Kohn–Sham kinetic energy and modern parametrization of the Thomas–Fermi density
• Improved Lieb-Oxford exchange-correlation inequality with a gradient correction

Cited by

• Gradient-dependent upper bound for the exchange-correlation energy and application to density functional theory