OpenAI paper on Kohn-Sham DFT: a Coulomb ground-state density without ensemble representation

Summary

A few days ago OpenAI released a paper generated by "an internal frontier model" of Navier-Stokes fame titled A Coulomb ground-state density without Kohn-Sham ensemble representation . The model considers a system with 2 nuclei and 3 electrons. It then spends 40 pages (seemingly) proving that for "sufficiently large" internuclear distance, restricted open-shell ensemble KS-DFT cannot describe the ground-state density of this system, no matter the choice of the effective potential. I tried to understand what "sufficiently large" means. Theorem 2.2 suggests that internuclear distance of 200 bohr is necessary but not sufficient. In theorem 1.1 and section 7, the internuclear distance is explicitly set to 2x10 200 bohr, which is 10 163 orders of magnitude larger than the diameter of the observable universe (???). If there are any people here working on analytical foundations of DFT, how significant is this for your field? Does the paper demonstrate any new useful techniques, e.g., for functional inequalities? Can the lower bound on the internuclear distance in this construction be sharpened so it does not involve intergalactic scales? submitted by /u/decelerated_dragon [link] [comments]