Dissociation limit in Kohn–Sham density functional theory. (February 2022)

• Record Type: Journal Article
• Authors: Behr, Sören; Graswald, Benedikt R.
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: Density functional theory -- Analysis of PDE -- Nonlinear analysis -- Mathematical physics; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112633
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the dissociation limit for molecules of the type X 2 in the Kohn–Sham density functional theory setting, where X can be any element with N electrons. We prove that when the two atoms in the system are torn infinitely far apart, the energy of the system converges to min α ∈ [ 0, N ] ( I α X + I 2 N − α X ), where I α X denotes the energy of the atom with α electrons surrounding it. Depending on the "strength" of the exchange this minimum might not be equal to the symmetric splitting 2 I N X . We show numerically that for the H 2 -molecule with Dirac exchange this gives the expected result of twice the energy of a H-atom 2 I 1 H .