Density functional theory promises exact solutions to quantum mechanics if you know the exact functional — but you don't, and no one does. Every practical DFT calculation uses an approximation, and developing better approximations is a central activity in computational chemistry.
The authors (arXiv:2603.23466) present a systematic protocol for pushing these approximations to their limits. The strategy: combine constraint enforcement (physics the functional must obey), flexible functional forms (mathematical freedom within those constraints), and modern optimization (fitting to broad benchmarks). Applied to the range-separated hybrid meta-GGA framework, this produces the COACH functional.
COACH improves accuracy and transferability over the leading alternatives, including ωB97M-V, across broad molecular benchmarks. But the interesting finding is the saturation analysis. After optimizing everything that can be optimized within this mathematical framework, the remaining errors reveal a ceiling — a performance limit inherent to the rung of Jacob's Ladder the functional sits on.
Further improvement requires genuinely nonlocal information — correlations between electrons at different points in space that the current mathematical form cannot capture. This isn't a fitting problem or an optimization problem. It's a structural limitation of the functional's mathematical expressiveness.
The through-claim: there's a ceiling for each level of DFT approximation, and the ceiling is measurable. COACH is close to it. The remaining error isn't noise or insufficient fitting — it's the information the functional's form can't encode. Progress requires climbing to a higher rung, not polishing the current one.