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Asymptotic Behavior of Exact Exchange for Slabs: Beyond the Leading Order

Center for Scientific Computing, J. W. Goethe-Universität Frankfurt, Max-von-Laue-Str. 1, D-60438 Frankfurt/Main, Germany
Computation 2018, 6(2), 35;
Received: 26 February 2018 / Revised: 19 April 2018 / Accepted: 21 April 2018 / Published: 29 April 2018
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
PDF [317 KB, uploaded 3 May 2018]


Far outside the surface of slabs, the exact exchange (EXX) potential v x falls off as 1 / z , if z denotes the direction perpendicular to the surface and the slab is localized around z = 0 . Similarly, the EXX energy density e x behaves as n / ( 2 z ) , where n is the electron density. Here, an alternative proof of these relations is given, in which the Coulomb singularity in the EXX energy is treated in a particularly careful fashion. This new approach allows the derivation of the next-to-leading order contributions to the asymptotic v x and e x . It turns out that in both cases, the corrections are proportional to 1 / z 2 in general. View Full-Text
Keywords: density functional theory; exact exchange; slabs; asymptotic behavior density functional theory; exact exchange; slabs; asymptotic behavior
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Engel, E. Asymptotic Behavior of Exact Exchange for Slabs: Beyond the Leading Order. Computation 2018, 6, 35.

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