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

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Density functional theory (DFT) relies on a unique mapping between electron densities and external potentials.
• Inverse Kohn-Sham (iKS) methods are essential for understanding and verifying this fundamental relationship in DFT.
• iKS methods aid in developing accurate exchange-correlation functionals and density-based embedding techniques.

Purpose of the Study:

• To investigate the fundamental and practical challenges of numerical iKS problems.
• To analyze the performance of constrained-optimization methods, specifically Wu-Yang (WY) and PDE-CO, on finite basis sets.
• To propose novel strategies for improving the tractability and reliability of iKS calculations.

Main Methods:

• Systematic analytical and numerical comparison of factors affecting iKS method performance.
• Focus on constrained-optimization techniques: Wu-Yang (WY) and partial differential equation constrained optimization (PDE-CO).
• Evaluation of iKS problem behavior within finite basis set approximations.

Main Results:

• Numerical iKS problems are inherently ill-posed and prone to instability.
• Finite basis sets introduce significant limitations for WY and PDE-CO methods.
• Identified key factors influencing the stability and accuracy of iKS calculations.

Conclusions:

• The study highlights the limitations imposed by finite basis sets in current iKS methodologies.
• Introduced new conceptual approaches to enhance the feasibility of iKS calculations.
• Provided a strategic framework for numerical density-to-potential inversions and outlined future research directions.