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

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Density Functional Theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
• A key component of DFT is the Kohn-Sham (KS) potential, which is typically unknown and must be approximated.
• Inverting the KS equations to find the potential from a given density is a challenging but important problem.

Purpose of the Study:

• To present a novel method for inverting electron densities to determine the corresponding Kohn-Sham (KS) potential in DFT.
• To ensure the inverted KS potential exhibits correct asymptotic behavior and is smooth.
• To demonstrate the method's utility in mitigating self-interaction errors in DFT.

Main Methods:

• The proposed method utilizes the concept of a 'screening density' which is constrained during the inversion process.
• The procedure is applied to invert both local and non-local (Hartree-Fock and coupled cluster) densities.
• Constraints on the screening density are employed to address self-interaction effects.

Main Results:

• The method successfully inverts given densities to yield accurate KS potentials.
• The resulting potentials demonstrate correct asymptotic behavior.
• The approach effectively mitigates self-interaction errors when applied to common DFT potentials.

Conclusions:

• The developed inversion method provides a reliable way to obtain KS potentials from electron densities.
• This technique enhances the accuracy of DFT calculations by providing correct potentials and reducing self-interaction errors.
• The method is versatile and applicable to various types of densities and DFT potentials.