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

@article{Liardi2022CompleteST, title={Complete solution to the inverse Kohn-Sham problem: From the density to the energy}, author={A. Liardi and F. Marino and Gianluca Col{\`o} and Xavier Roca-Maza and E. Vigezzi}, journal={Physical Review C}, year={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 state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified…

## References

SHOWING 1-10 OF 66 REFERENCES

Universal nature of different methods of obtaining the exact Kohn–Sham exchange-correlation potential for a given density

- MathematicsJournal of Physics B: Atomic, Molecular and Optical Physics
- 2019

Finding the external potential or the Kohn–Sham (KS) potential for a given ground state density is a fundamental inverse problem in density functional theory. Furthermore, it is important in…

Numerical methods for the inverse problem of density functional theory

- Mathematics
- 2017

The inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of…

Building Kohn–Sham Potentials for Ground and Excited States

- MathematicsArchive for Rational Mechanics and Analysis
- 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…

Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory

- PhysicsJournal of Physics B: Atomic, Molecular and Optical Physics
- 2019

We propose a way to improve energy density functionals (EDFs) in the density functional theory based on the combination of the inverse Kohn--Sham method and the density functional perturbation…

Inverse Kohn-Sham Density Functional Theory: Progress and Challenges.

- Computer ScienceThe journal of physical chemistry letters
- 2021

New ideas to make iKS problems more tractable, provide an overall strategy for performing numerical density-to-potential inversions, and discuss challenges and future directions are introduced.

Reconstruction of Density Functionals from Kohn-Sham Potentials by Integration along Density Scaling Paths.

- PhysicsJournal of chemical theory and computation
- 2009

If a Kohn-Sham exchange-correlation potential is given explicitly in terms of the electron density and its derivatives, then one can easily reconstruct the parent density functional by evaluating analytically the van Leeuwen-Baerends line integral along a path of (coordinate)-scaled densities.

Communication: Explicit construction of functional derivatives in potential-driven density-functional theory.

- MathematicsThe Journal of chemical physics
- 2010

It is shown that if a model potential v(r) involves no ingredients other than ρ, ∇ρ, and ∇(2)ρ, then the necessary and sufficient condition for v( r) to be a functional derivative is ∂v/∂∇ρ=∇(∂ v/∁∂ ∂∁ρ) and the Integrability conditions can be used to construct functional derivatives without knowing their parent functionals.

Measuring density-driven errors using Kohn-Sham inversion.

- ChemistryJournal of chemical theory and computation
- 2020

This work studies the precision and reliability of several inversion schemes, finding estimates of density-driven errors at a useful level of accuracy in HF-DFT, which is almost as accurate as DFT evaluated on CCSD(T) densities.

Theory of Model Kohn-Sham Potentials and its Applications

- Physics
- 2013

The purpose of Kohn–Sham density functional theory is to develop increasingly accurate approximations to the exchange-correlation functional or to the corresponding potential. When one chooses to…

Nonlocal kinetic energy functionals by functional integration.

- PhysicsThe Journal of chemical physics
- 2018

The MGP functional is found to be numerically stable typically reaching self-consistency within 12 iterations of a truncated Newton minimization algorithm and its computational cost and memory requirements are low and comparable to the Wang-Teter nonlocal functional or any generalized gradient approximation functional.