How Interatomic Steps in the Exact Kohn–Sham Potential Relate to Derivative Discontinuities of the Energy

2017/06/02 by M. J. P. Hodgson, Eli Kraisler, E. Kraisler +2 · 1 citation
Chemistry · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Chemistry #Classification of discontinuities #Computational chemistry #Density functional theory #Derivative (finance) #Energy (signal processing) #High-pressure geophysics and materials #Kohn–Sham equations #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #cond-mat.str-el #physics.atom-ph #physics.chem-ph #physics.comp-ph

paper · pdf · doi:10.1021/acs.jpclett.7b02615

published as J. Phys. Chem. Lett. 2017, 8, 24, 5974-5980 · 6 pages, 3 figures, supplementary material included

arxiv created 2017/06/02 · openalex publication_date 2017/11/28 · arxiv updated 2021/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Accurate density functional calculations hinge on reliable approximations to the unknown exchange-correlation (xc) potential. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features in this regard are the spatially uniform shift in the potential, as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form, for example, between the atoms of stretched molecules. Although both aforementioned concepts are well known, the exact relationship between them remained unclear. Here we establish this relationship via an analytical derivation. We support our result by numerically solving the many-electron Schrödinger equation to extract the exact Kohn-Sham potential and directly observe its features. Spatial steps in the exact xc potential of a full configuration-interaction (FCI) calculation of a molecule are presented in three dimensions.

Citations

• Role of electron localization in density functionals
• Exact and approximate Kohn-Sham potentials in ensemble density-functional theory
• Generalized Gradient Approximation Made Simple
• Exact time-dependent density-functional potentials for strongly correlated tunneling electrons
• Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
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• Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields
• Self-Consistent Equations Including Exchange and Correlation Effects
• Origin of static and dynamic steps in exact Kohn-Sham potentials

Cited by

• Accurate real-time evolution of electron densities and ground-state properties from generalized Kohn-Sham theory