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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. Its accuracy is largely hindered by the self-interaction error. We are developing a novel method, termed spatial mixing of model potentials (SMMP), to reduce the self-interaction error in XC potentials. The method is formulated within the hybrid DFT framework. The XC potentials are constructed by mixing the local density approximation (LDA) and exact exchange (EXX) potentials, with the spatially dependent mixing parameters derived from the piecewise linearity conditions of both the total energy and electron density.[1,2] These two conditions greatly reduce the self-interaction error. SMMP holds strong promise for predicting electronic structures in challenging systems, such as charge-transfer systems, systems having unpaired electrons (e.g., radicals, anions, and polarons), and mixed-valence systems. The SMMP method is illustrated with the following figures.
[1] C. Huang, J. Chem. Phys. 161, 084103 (2024)
[2] C. Huang, J. Chem. Phys. 163, 154104 (2025)
The figure shows the contour plot of the mixing parameter for the CO molecule. SMMP produces a mixing parameter with the correct asymptotic behavior (approaching one) in carbon's vacuum region (where CO's HOMO dominates). In the oxygen's vacuum region and in the bond region, HOMO overlaps with these low-energy orbitals, leading to a mixing parameter less than one. A smaller mixing parameter indicates stronger electronic screening.
The figure shows the Kohn-Sham correlation potentials of the Be atom calculated from different methods. The atom is at x = 0 Bohr. SMMP can semi-quantitatively reproduce the shell structure of the Kohn-Sham correlation potential, a very challenging task for approximate XC functionals. The shell structure is largely determined by the mixing parameter (lower subplot). This confirms that the linearity condition of electron density is a promising constraint for building high-quality XC potentials.
HOMO eigenvalues of various molecules, radicals, and anions, predicted by SMMP, compared to the ionization energies from the CCSD(T) results. Exact exchange generally overestimates HOMO eigenvalues, while SMMP systematically improves the EXX results.
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