Invited
The exchange-correlation potential in density-functional theory: exact asymptotic behavior and strategy for advanced approximations
Density functional theory (DFT) is nowadays the leading theoretical framework for quantum description of materials from first principles. The predictive power of DFT critically depends on an accurate approximation to the generally unknown exchange-correlation (xc) energy functional. Approximations to the xc functional can be and many times are constructed from first principles, by satisfying known properties of the exact functional. In this talk I focus on the behavior of the exact xc potential, vxc(r), and the exact xc energy-density-per-particle, exc(r) for very large r -- far away from a finite, many-electron system. Sereval aspects of the behavior of the aforementioned quantities are presented. First, it is shown that the asymptotic form of vxc(r) and exc(r) is independent: correct behavior of one does not guarantee the other. The relation between the two is via the xc hole response function, whose properties are discussed and its exact exchange part is analytically derived [1]. Furthermore, it is shown that the asymptotic behavior of vxc(r) is not a direct consequence of the infamous self-interaction problem in DFT [2]. These are two separate issues to be addressed in the design of xc approximations. Second, the importance of reconstructing the sharp steps in the KS potential for an accurate prediction of the fundamental gap and the correct distribution of charge in complex systems is emphasized. The relationship between the derivative discontinuity and steps in stretched systems is exposed [3]. Third, the asymptotic behavior of the exact Pauli potential, an essential ingredient in orbital-free DFT, is presented [4]. Based on these findings, a strategy for development of advanced approximations for exchange and correlation with correct asymptotics is suggested.
[1] E. Kraisler, Isr. J. Chem., accepted. https://doi.org/10.26434/chemr
[2] T. Schmidt, E. Kraisler, L. Kronik and S. Kümmel, Phys. Chem. Chem. Phys. 16, 14357 (2014)
[3] M.J.P. Hodgson, E. Kraisler, A. Schild, E.K.U. Gross, J. Phys. Chem. Lett. 8 5974-5980 (2017)
[4] E. Kraisler, A. Schild, submitted. https://doi.org/10.26434/chemrxiv.9902582.v1
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