Inverse Kohn–Sham Density Functional Theory: Progress and Challenges

Inverse Kohn–Sham (iKS) methods are needed to fully understand the one-to-one mapping between densities and potentials on which density functional theory is based. They can contribute construction of empirical exchange–correlation functionals development techniques for density-based embedding. Unlike forward problems, numerical iKS problems ill-posed be unstable. We discuss some fundamental practical difficulties with constrained-optimization finite basis sets. Various factors that affect performance systematically compared discussed, both analytically numerically, a focus two most methods: Wu–Yang method (WY) partial differential equation constrained optimization (PDE-CO). Our analysis WY PDE-CO highlights limitation introduce new ideas make more tractable, provide an overall strategy performing density-to-potential inversions, challenges future directions.