Asymptotic behavior of the exchange-correlation energy density and the Kohn-Sham potential in density functional theory: exact results and strategy for approximations

Density functional theory (DFT) is 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 constructed from first principles by satisfying known properties of the exact functional. In this talk I focus on two such exact properties: the asymptotic behavior of the xc energy density per particle, e_xc(r), and the asymptotic behavior of the Kohn-Sham potential, v_KS(r), in finite many-electron systems. It is shown that these two properties are independent: fulfillment of one does not guarantee the other. Furthermore, none is equivalent to the self-interaction freedom requirement. In this process, I discuss a different quantity – the xc hole response function, η_xc(r; r”|r’). It is the response of the averaged xc hole, n_xc(r”|r’) to a density change at point r. Several properties of this response function are deduced and its exact exchange part is analytically derived. A strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested [1].

[1] E. Kraisler, Isr. J. Chem., Isr. J. Chem. 60, 805 (2020)