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Issue 29, 2020

Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

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Abstract

The exact energy functional of density functional theory (DFT) is well known to obey various constraints. Three conditions that must be obeyed by the exact energy functional, but may or may not be obeyed by approximate ones, are often pointed out as important in general and for accurate computation of spectroscopic observables in particular. These are: (1) piecewise linearity as a function of the fractional particle number, (2) freedom from one-electron self-interaction, and (3) for a finite system, the functional derivative with respect to the density results in an asymptotic −1/r potential (in Hartree atomic units), where r is the distance from the system center. In this overview, we explain what these conditions are, what they address, and why each one is of importance for spectroscopy. We then show, using specific examples from the literature, that these three properties are related, but are not equivalent and need to be assessed individually.

Graphical abstract: Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

Article information


Submitted
11 May 2020
Accepted
01 Jul 2020
First published
01 Jul 2020

Phys. Chem. Chem. Phys., 2020,22, 16467-16481
Article type
Perspective

Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

L. Kronik and S. Kümmel, Phys. Chem. Chem. Phys., 2020, 22, 16467 DOI: 10.1039/D0CP02564J

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