The exchange-correlation (XC) potential is the central quantity in Kohn-Sham density functional theory (KS-DFT) and fully determines the accuracy of electronic structure calculations. We are developing a novel method to obtain reliable XC potentials for challenging systems. The method is formulated within the hybrid-DFT framework, and the XC potentials are constructed by mixing the local density approximation (LDA) and exact exchange (EXX) potentials, with spatially dependent mixing parameters derived from the piecewise linearity condition of the electron density. In our latest work [2], we also show how to satisfy the piecewise linearity condition of energy in the construction, which provides the theoretical foundation for reliable predictions of HOMO eigenvalues. 

This new method is illustrated in the following figures. Figure 1 demonstrates the mixing parameter of the CO molecule. The method produces a mixing parameter with the correct asymptotic behavior, that is, it approaches one in carbon's vacuum region (where CO's HOMO dominates). Figure 2 shows that the new method predicts more accurate HOMO eigenvalues for various molecular systems, especially many challenging anions. It is also very exciting to see that this new method can semi-quantitatively reproduce the Kohn–Sham correlation potentials (Figure 3), a very challenging task for XC functionals. This shows that this new method holds strong promise for predicting electronic structures in difficult systems, such as systems with unpaired electrons and mixed-valence systems. 

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

[2] C. Huang, J. Chem. Phys. 163, 154104 (2025)