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2018 A numerical study of the extended Kohn–Sham ground states of atoms
Eric Cancès, Nahia Mourad
Commun. Appl. Math. Comput. Sci. 13(2): 139-188 (2018). DOI: 10.2140/camcos.2018.13.139


In this article, we consider the extended Kohn–Sham model for atoms subjected to cylindrically symmetric external potentials. The variational approximation of the model and the construction of appropriate discretization spaces are detailed together with the algorithm to solve the discretized Kohn–Sham equations used in our code. Using this code, we compute the occupied and unoccupied energy levels of all the atoms of the first four rows of the periodic table for the reduced Hartree–Fock (rHF) and the extended Kohn–Sham X α models. These results allow us to test numerically the assumptions on the negative spectra of atomic rHF and Kohn–Sham Hamiltonians used in our previous theoretical works on density functional perturbation theory and pseudopotentials. Interestingly, we observe accidental degeneracies between s and d shells or between p and d shells at the Fermi level of some atoms. We also consider the case of an atom subjected to a uniform electric field. For various magnitudes of the electric field, we compute the response of the density of the carbon atom confined in a large ball with Dirichlet boundary conditions, and we check that, in the limit of small electric fields, the results agree with the ones obtained with first-order density functional perturbation theory.


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Eric Cancès. Nahia Mourad. "A numerical study of the extended Kohn–Sham ground states of atoms." Commun. Appl. Math. Comput. Sci. 13 (2) 139 - 188, 2018.


Received: 7 February 2017; Revised: 25 February 2018; Accepted: 25 March 2018; Published: 2018
First available in Project Euclid: 6 July 2018

zbMATH: 06950006
MathSciNet: MR3819575
Digital Object Identifier: 10.2140/camcos.2018.13.139

Primary: 35P30 , 35Q40 , 65Z05 , 81V45

Keywords: density functional theory , electronic structure of atoms , extended Kohn–Sham model , Stark effect

Rights: Copyright © 2018 Mathematical Sciences Publishers


Vol.13 • No. 2 • 2018
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