Abstract
The response part of the exchange-correlation potential of Kohn–Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Cotar, G. Friesecke, C. Klüppelberg, Comm. Pure Appl. Math. 66, 548 (2013)
M. Lewin, Semi-classical limit of the Levy–Lieb functional in density functional theory, arXiv:1706.02199 (2017)
C. Cotar, G. Friesecke, C. Klüppelberg, Smoothing of transport plans with fixed marginals and rigorous semiclassical limit of the hohenberg-kohn functional, arXiv:1706.05676 (2017)
M. Seidl, Phys. Rev. A 60, 4387 (1999)
M. Seidl, P. Gori-Giorgi, A. Savin, Phys. Rev. A 75, 042511/12 (2007)
P. Gori-Giorgi, G. Vignale, M. Seidl, J. Chem. Theory Comput. 5, 743 (2009)
G. Buttazzo, L. De Pascale, P. Gori-Giorgi, Phys. Rev. A 85, 062502 (2012)
F. Malet, P. Gori-Giorgi, Phys. Rev. Lett. 109, 246402 (2012)
F. Malet, A. Mirtschink, J. C. Cremon, S. M. Reimann, P. Gori-Giorgi, Phys. Rev. B 87, 115146 (2013)
C.B. Mendl, F. Malet, P. Gori-Giorgi, Phys. Rev. B 89, 125106 (2014)
L.O. Wagner, P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)
H. Bahmann, Y. Zhou, M. Ernzerhof, J. Chem. Phys. 145, 124104 (2016)
S. Vuckovic, P. Gori-Giorgi, J. Phys. Chem. Lett. 8, 2799 (2017)
M.A. Buijse, E.J. Baerends, J.G. Snijders, Phys. Rev. A 40, 4190 (1989)
C.J. Umrigar, X. Gonze, Phys. Rev. A 50, 3827 (1994)
O. Gritsenko, R. van Leeuwen, E.J. Baerends, J. Chem. Phys. 101, 8955 (1994)
C. Filippi, X. Gonze, C.J. Umrigar, Generalized gradient approximations to density functional theory: comparison with exact results, in Recent developments and applications in modern DFT, edited by J.M. Seminario (Elsevier, Amsterdam, 1996), pp. 295–321
E.J. Baerends, O.V. Gritsenko, Phys. Rev. A 54, 1957 (1996)
O.V. Gritsenko, R. van Leeuwen, E.J. Baerends, J. Chem. Phys. 104, 8535 (1996)
E.J. Baerends, O.V. Gritsenko, J. Phys. Chem. A 101, 5383 (1997)
D.G. Tempel, T.J. Martínez, N.T. Maitra, J. Chem. Theory. Comput. 5, 770 (2009)
N. Helbig, I.V. Tokatly, A. Rubio, J. Chem. Phys. 131, 224105 (2009)
R. Cuevas-Saavedra, P.W. Ayers, V.N. Staroverov, J. Chem. Phys. 143, 244116 (2015)
R. Cuevas-Saavedra, V.N. Staroverov, Mol. Phys. 114, 1050 (2016)
S.V. Kohut, A.M. Polgar, V.N. Staroverov, Phys. Chem. Chem. Phys. 18, 20938 (2016)
M.J.P. Hodgson, J.D. Ramsden, R.W. Godby, Phys. Rev. B 93, 155146 (2016)
Z.J. Ying, V. Brosco, G.M. Lopez, D. Varsano, P. Gori-Giorgi, J. Lorenzana. Phys. Rev. B 94, 075154 (2016)
A. Benítez, C.R. Proetto, Phys. Rev. A 94, 052506 (2016)
I.G. Ryabinkin, V. Kohut, R. Cuevas-Saavedra, P.W. Ayers, V.N. Staroverov, J. Chem. Phys. 145, 037101 (2016)
M.J.P. Hodgson, E. Kraisler, A. Schild, E.K.U. Gross, J. Phys. Chem. Lett. 8, 5974 (2017)
S. Giarrusso, S. Vuckovic, P. Gori-Giorgi, Response potential in the strong-interaction limit of dft: Analysis and comparison with the coupling-constant average, arXiv:1804.09001 (2018)
G. Hunter, Int. J. Quant. Chem. 9, 237 (1975)
G. Hunter, Int. J. Quant. Chem. 9, 311 (1975)
M. Levy, J.P. Perdew, V. Sahni, Phys. Rev. A 30, 2745 (1984)
A. Abedi, N.T. Maitra, E. KU Gross, Phys. Rev. Lett. 105, 123002 (2010)
A. Schild, E. Gross, Phys. rev. lett. 118, 163202 (2017)
R. van Leeuwen, O. Gritsenko, E.J. Baerends, Z. Phys. D 33, 229 (1995)
R.V. Meer, O. Gritsenko, E. Baerends, J. Chem. Theory Comput. 10, 4432 (2014)
O.V. Gritsenko, L.M. Mentel, E.J. Baerends, J. Chem. Phys. 144, 204114 (2016)
O.V. Gritsenko, E.J. Baerends, Phys. Rev. A 54, 1957 (1996)
S. Vuckovic, M. Levy, P. Gori-Giorgi, J. Chem. Phys. 147, 214107 (2017)
M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)
M. Colombo, L. De Pascale, S. Di Marino, Canad. J. Math. 67, 350 (2015)
M. Seidl, S. Di Marino, A. Gerolin, L. Nenna, K.J. Giesbertz, P. Gori-Giorgi, The strictly-correlated electron functional for spherically symmetric systems revisited. arXiv:1702.05022 (2017)
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.
Rights and permissions
Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Giarrusso, S., Gori-Giorgi, P. & Giesbertz, K.J.H. Sum-rules of the response potential in the strongly-interacting limit of DFT. Eur. Phys. J. B 91, 186 (2018). https://doi.org/10.1140/epjb/e2018-90301-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2018-90301-8