Toward routine Kohn-Sham inversion using the "Lieb-response" approach.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Kohn-Sham (KS) inversion is crucial for understanding exact density functional theory (DFT) and developing new approximations.
• Despite theoretical advances, practical KS inversion, especially in finite basis sets, remains challenging.
• Existing methods often lack efficiency or compatibility with standard computational chemistry tools.

Purpose of the Study:

• To present a novel, efficient, and practical KS inversion method.
• To enable routine inversion of challenging KS systems.
• To provide outputs suitable for embedding schemes and machine learning of DFT approximations.

Main Methods:

• Introduction of the "Lieb-response" approach for KS inversion.
• Integration with existing Fock-matrix DFT infrastructure in finite basis sets.
• Analysis of the impact of finite basis sets on KS inversion.

Main Results:

• The Lieb-response method is numerically efficient and directly yields relevant matrix and energy quantities.
• The approach is applicable to both pure-state and ensemble systems.
• Demonstrated routine inversion of difficult KS systems across various applications.

Conclusions:

• The Lieb-response method overcomes practical limitations of KS inversion.
• This technique facilitates the development of advanced density functional approximations.
• The method's outputs are valuable for embedding and machine learning applications in DFT.