2025/06/30 by Kumar, Dharamveer, Amuthan A. Ramabathiran, Ramabathiran, Amuthan A.
Chemistry · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Chemical Physics (physics.chem-ph) #Crystallography and molecular interactions #FOS: Physical sciences #Machine Learning in Materials Science #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2507.00321
openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The non-interacting kinetic energy functional, TKS(ρ), plays a fundamental role in Density Functional Theory (DFT), but its explicit form remains unknown for arbitrary N-representable densities. Although it can, in principle, be evaluated by solving a constrained optimization problem, the associated adjoint problem is not always well-posed; moreover, even when it is, the corresponding adjoint operator may be singular. To the best of our knowledge, none of the existing approaches in the literature precisely determines the non-interacting kinetic energy functional for a given N-representable electron density, ρ. In this work, we present a variational framework for computing an extension of TKS(ρ) using an exact trigonometric reparametrization of the density that eliminates the need for an adjoint equation. We present a proof-of-concept numerical validation of the variational principle for the special case of one-dimensional Kohn-Sham systems. Our method, however, is general and provides a systematic foundation for computing TKS(ρ) in higher dimensions too, paving the way for improved kinetic energy functionals in DFT.