A general penalty method for density‐to‐potential inversion

@article{Kumar2020AGP,
title={A general penalty method for density‐to‐potential inversion},
author={Ashish Kumar and Manoj K. Harbola},
journal={arXiv: Atomic Physics},
year={2020}
}
• Published 7 April 2020
• Physics
• arXiv: Atomic Physics
A general penalty method is presented for the construction of of Kohn-Sham system for given density through Levy's constrained-search. The method uses a functional $S[\rho]$ of one's choice. Different forms of $S[\rho]$ are employed to calculate the kinetic energy and exchange-correlation potential of atoms, jellium spheres, and Hookium and consistency among results obtained from them is shown.
3 Citations

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References

SHOWING 1-10 OF 66 REFERENCES

Variational method for inverting the Kohn-Sham procedure (7 pages)

A procedure based on a variational principle is developed for determining the local Kohn-Sham (KS) potential corresponding to a given ground-state electron density. This procedure is applied to

Density-inversion method for the Kohn-Sham potential: Role of the screening density.

• Geology
The Journal of chemical physics
• 2020
This work presents a method to invert a given density and find the Kohn-Sham potential in Density Functional Theory that shares the density and demonstrates the applicability of the method by inverting both local and non-local densities.

A simple algorithm for the Kohn–Sham inversion problem applicable to general target densities

• Physics
Theoretical Chemistry Accounts
• 2018
A simple algorithm for the Kohn–Sham inversion problem is presented. The method is found to converge toward a nearby $$\nu$$ν-representable Kohn–Sham density irrespective of the fact whether the

A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities

• Chemistry
• 2003
A direct optimization method is developed for the computation of the Kohn–Sham kinetic energy density functional Ts from a given electron density and the exchange–correlation potential vxc if this

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

• Mathematics
Journal 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

Kohn-Sham potentials and wave functions from electron densities.

• Görling
• Chemistry
Physical review. A, Atomic, molecular, and optical physics
• 1992
A method is introduced that allows the determination of the Kohn-Sham effective potential and the corresponding Kohn-Sham orbitals belonging to an arbitrary electron density with boundary conditions

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

Construction of exact Kohn-Sham orbitals from a given electron density.

• WangParr
• Mathematics
Physical review. A, Atomic, molecular, and optical physics
• 1993
This paper prescribes an orbital construction of the exact local effective potential in the Kohn-Sham self-consistent equations, so that from a given electron density the corresponding exact

Algorithm to derive exact exchange-correlation potentials from correlated densities in atoms

• Chemistry
• 2003
A simple algorithm is presented to derive accurately the exchange-correlation potential in the density functional theory (DFT) from the electron density. The method, which can be used with any