Prediction of the Derivative Discontinuity in Density Functional Theory from an Electrostatic Description of the Exchange and Correlation Potential

We propose an approach to approximate the exchange and correlation (XC) term in density functional theory. The XC potential is considered as an electrostatic potential, generated by a fictitious XC density, which is in turn a functional of the electronic density. We apply the approach to develop a correction scheme that fixes the asymptotic behavior of any approximated XC potential for finite systems. Additionally, the correction procedure gives the value of the XC derivative discontinuity; therefore, it can directly predict the fundamental gap as a ground-state property.

Figure 1

KLI electronic density and KLI and LDA XC densities for the beryllium atom. The inset details the asymptotic region, where the KLI XC density shows the correct behavior. The LDA XC density is incorrect in this region, with a positive part that screens the charge in the central region.

Figure 2

CXD-LDA potential for neon. Comparison with the LDA, LB [13], RPP [22], and the exact [16] potentials.

Figure 3

Comparison of the CXD-LDA gap with LDA and available experimental results. The CXD-LDA gap has contributions from the Kohn-Sham (KS) gap and the derivative discontinuity (DD). Result for atoms (top) from H to Kr, experimental values from Ref. 29, and a set of molecules (bottom), experimental values compiled in Ref. 7, except for ${\mathrm{C}}_6{\mathrm{H}}_6$ [29, 37]. (Data in Supplemental Material [14].)

Figure 4

LDA and CXD-LDA ionization energy as a function of the experimental value. Atoms from H to Sr. (Data in Supplemental Material [14].)