Abstract of the talk// The non-interacting kinetic energy functional plays a fundamental role in Density Functional Theory (DFT), yet its explicit form remains unknown for general N-representable electron densities. While it can, in principle, be evaluated through a constrained optimization problem, the associated adjoint problem is not always well posed; even when it is, the corresponding adjoint operator may be singular. To the best of our knowledge, no existing approach in the literature determines the non-interacting kinetic energy functional exactly for a given N-representable density.

Dharamveer will introduce a variational framework for computing an extension of the non-interacting kinetic energy functional using an exact trigonometric reparametrization of the density. This formulation eliminates the need to solve an adjoint equation. He presents a proof-of-concept numerical validation of the variational principle for the special case of one-dimensional Kohn–Sham systems. The approach is general and provides a systematic foundation for computing the non-interacting kinetic energy functional in higher dimensions. This framework may serve as a basis for the development of improved kinetic energy functionals in density functional theory.