# Building Kohn–Sham Potentials for Ground and Excited States

@article{Garrigue2022BuildingKP, title={Building Kohn–Sham Potentials for Ground and Excited States}, author={Louis Garrigue}, journal={Archive for Rational Mechanics and Analysis}, year={2022} }

. We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density ρ , there exist potentials having k th bound mixed states which densities are arbitrarily close to ρ . The state can be chosen pure in dimension d = 1 and without interactions, and we provide numerical and theoretical evidence consistently leading us to conjecture that the same pure representability result holds for d = 2 , but that the set of…

## 5 Citations

Complete solution to the inverse Kohn-Sham problem: From the density to the energy

- MathematicsPhysical Review C
- 2022

A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground…

Geometry of Degeneracy in Potential and Density Space

- Mathematics
- 2022

In a previous work [J. Chem. Phys. 155 , 244111 (2021)], we found counterexamples to the fundamental Hohenberg– Kohn theorem from density-functional theory in ﬁnite-lattice systems represented by…

Nuclear energy density functionals from empirical ground-state densities

- Physics
- 2021

A model is developed, based on the density functional perturbation theory and the inverse KohnSham method, that can be used to improve relativistic nuclear energy density functionals towards an exact…

Some Properties of the Potential-to-Ground State Map in Quantum Mechanics

- MathematicsCommunications in Mathematical Physics
- 2021

We analyze the map from potentials to the ground state in static many-body quantum mechanics. We first prove that the space of binding potentials is path-connected. Then we show that the map is…

DFTK: A Julian approach for simulating electrons in solids

- Materials ScienceJuliaCon Proceedings
- 2021

Density-functional theory (DFT) is a widespread method for simulating the quantum-chemical behaviour of electrons in matter. It provides a first-principles description of many optical, mechanical and…

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