International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'

September 26, 2017 to September 29, 2017
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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Analytically inverted non-additive kinetic potential functional at small density overlaps

Mojdeh Banafsheh

Coauthor(s) : T.A. Wesolowski


In density-dependent embedding methods [1], non-additive kinetic potential plays an important role. This functional is a bi-functional depending on a pair of electron densities ρA and ρB. We report here the first time use of the numerical inversion procedure to generate reference non-additive kinetic potentials for weakly overlapping ρA and ρB. To obtain exact quantity of non-additive kinetic potential, analytically inverted procedure is proposed [2]. It is especially suited for small overlap cases and it is applicable only for a special case of ρA being a two-electron density. The procedure requires particular constraint on the choice of pair of electron densities to assure their admissibility as well as the smallness of the overlap between ρA and ρB. The constraint is applied over total density to provide the pair of electron densities. Mathematical challenge of this preparation and the accuracy of the pair electron densities will be presented in detail. All reported are obtained using basis set free numerical solver of Kohn-Sham equation for diatomic systems [3]. The non-additive kinetic potential at small overlap is constructed for different systems of four electrons (LiHe+, BeHe2+, LiH and BeH+). The exact potential was calculated for a chosen four electron system changing interatomic distance. For all investigated systems, the non-additive kinetic potentials derived by means of the proposed analytical inversion method was compared to the potential obtained using the common approximations to the density functional of the kinetic energy. We showed that exact potential is smooth in overlap region for all system and a system with different interatomic distances.


[1] T.A. Wesolowski, S. Shedgen, X. Zhou. Chem. Rev. 115 5891 (2015).
[2] M. Banafsheh, T.A. Wesolowski T. Int J Quanum Chem. 2017;e25410 , “In press”.
[3] A. Makmal, S. Kummel, L. Kronik, J. Chem. Theory Comput. 5 1731 (2009).