The exchange-correlation (XC) potential is the key element in Kohn-Sham density functional theory (KS-DFT) and fully determines a system's electronic structure. We are developing new methods to obtain reliable XC potentials in challenging systems. Our method lies in the framework of hybrid DFT, which mixes the local density approximation (LDA) XC functional with the exact exchange (EXX). 

We have developed a novel method [1] to fully determine the parameter for mixing the LDA and EXX potentials in real space. The spatially dependent mixing parameter is derived based on the derivative discontinuity of electron density and is first-principle. Our work shows that the derivative discontinuity of electron density is a very promising constraint for constructing high-quality XC potentials. The immediate applications of our method is the study of systems with unpaired charge carriers, such as electron/hole distributions (i.e., polarons) and charge transfer, for which conventional XC functionals are often not reliable due to the localization/delocalization error. 

This new method is illustrated in the right figures. Figure 1 shows the mixing parameter of the CO molecule. The mixing parameter approaches one in carbon's vacuum region, which is the expected asymptotic behavior for the exact XC potential. One way to assess the quality of the XC potential is to study the ionization energies. Figure 2 shows that the new method corrects EXX's overestimation of the ionization energies. We are also evaluating the performance of this new method on several challenging systems, such as, charge transfer systems. Additionally, we are extending this method to degenerate systems. Work in these directions is in progress.

[1] C. Huang, J. Chem. Phys. 161, 084103 (2024)