Unified Variational Framework Developed for Inverse Kohn-Sham Problem in Computational Chemistry
A new preprint on arXiv presents a unified optimization-theoretic framework for the inverse Kohn-Sham (KS) problem, which seeks a local effective potential whose noninteracting ground state reproduces a given electron density. The work connects previously disparate inversion formulations—including penalty regularization, response-based iteration, and PDE-constrained optimization—under a single variational structure anchored in the fixed-density noninteracting constrained search. This matters because a coherent theoretical map of inversion approaches clarifies the origins of known numerical difficulties and guides more principled algorithmic design in density functional theory.
The inverse Kohn-Sham problem is a foundational challenge in density functional theory (DFT): given a target electron density, find the local effective potential that reproduces it as the ground state of a noninteracting system. Prior inversion methods have been developed in largely separate theoretical languages, making systematic comparison and improvement difficult. Authors Nan Sheng and collaborators address this by first identifying the fixed-density noninteracting constrained search and its density-potential duality as the natural variational anchor of the problem, in which the KS potential emerges as a Lagrange multiplier enforcing density reproduction. Building on this anchor, they classify major inversion formulations—Wu-Yang, Zhao-Morrison-Parr, and PDE-constrained approaches—according to how the KS state equations and density-reproduction condition are handled within the optimization architecture. The framework makes explicit where known difficulties such as additive-constant ambiguity, asymptotic normalization issues, nonsmooth variational structure, metric choice, and weak-gap instability enter each inversion architecture. The paper, submitted in March 2026 and revised through June 2026, is a preprint and has not yet undergone formal peer review.
What's missing
As a preprint, this work has not yet undergone formal peer review. The paper is primarily theoretical and does not include numerical benchmarks comparing the performance of the classified inversion schemes under the unified framework, leaving open questions about practical computational advantages.
What different sources said
- arXiv physicsCenter
A unified variational framework for the inverse Kohn-Sham problem
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