scholarly journals Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

2020 ◽  
Vol 153 (7) ◽  
pp. 074114
Author(s):  
Aaron D. Kaplan ◽  
Biswajit Santra ◽  
Puskar Bhattarai ◽  
Kamal Wagle ◽  
Shah Tanvir ur Rahman Chowdhury ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Functional Theory ◽  
Atomic Ions ◽  
Exchange And Correlation

scholarly journals Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory

2013 ◽  
Vol 139 (13) ◽  
pp. 134113 ◽  
Author(s):  
Alexandrina Stoyanova ◽  
Andrew M. Teale ◽  
Julien Toulouse ◽  
Trygve Helgaker ◽  
Emmanuel Fromager
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Functional Theory ◽  
Exchange And Correlation

scholarly journals Asymptotic behavior of the Hartree-exchange and correlation potentials in ensemble density functional theory

2019 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis ◽  
Julien Toulouse ◽  
Eli Kraisler ◽  
Leeor Kronik
Keyword(s):  
Density Functional Theory ◽  
Quantum Monte Carlo ◽  
Density Functional ◽  
Outer Region ◽  
Electron Number ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Asymptotic Constant ◽  
Coulomb Potentials ◽  
Exchange And Correlation

We report on previously unnoticed features of the exact Hartree-exchange and correlation potentials for atoms and ions treated via ensemble density functional theory, demonstrated on fractional ions of Li, C, and F. We show that these potentials, when treated separately, can reach non-vanishing asymptotic constant values in the outer region of spherical, spin unpolarized atoms. In the next leading order, the potentials resemble Coulomb potentials created by effective charges which have the peculiarity of not behaving as piecewise constants as a function of the electron number. We provide analytical derivations and complement them with numerical results using the inversion of the Kohn-Sham equations for interacting densities obtained by accurate quantum Monte Carlo calculations. The present results expand on the knowledge of crucial exact properties of Kohn-Sham systems, which can guide development of advanced exchange-correlation approximations.<br><br>

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