Speaker: Vebjørn Hallberg Bakkestuen
Title: Kohn–Sham Inversion with Error Bounds
Abstract: Density-functional theory (DFT) serves as a crucial tool for efficient calculations in chemistry, materials science, and solid-state physics. Despite being exact in principle, a key quantity, the universal density functional, remains unknown and has to be approximated. Typically, DFT calculations focus on obtaining the ground-state density of a system, most commonly using the well-studied Kohn–Sham approach. Although significantly less studied, the inverse Kohn–Sham problem—determining the non-interacting potential from an exact ground-state density—is fundamentally important and may ultimately advance the development of approximate functionals. In this talk, I will introduce a Kohn–Sham inversion procedure within a Moreau–Yosida regularised formulation of DFT, in which the elusive exchange-correlation potential is obtained as a strict mathematical limit. In a recent work [1], we demonstrated the performance of the inversion scheme for three bulk materials, specifically bulk silicon, gallium arsenide, and potassium chloride. Moreover, this Moreau–Yosida based inversion scheme is particularly suited for deriving rigorous error bounds, which we have been now demonstrated in practical calculations. This approach enhances the understanding of Kohn–Sham inversion and may ultimately further the development of approximate functionals.
[1] Herbst, M. F., Bakkestuen, V. H. & Laestadius, A. Kohn-Sham inversion with mathematical guarantees 2025. arXiv: 2409.04372 [physics.chem-ph]. https://arxiv.org/abs/2409.04372.