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}
}
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. 

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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.

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

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

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

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

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

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
...