System-independent functional giving fundamental gaps of molecules and solids
In plain words
Standard functionals underestimate the energy needed to add or remove an electron, which sets how well a material conducts or absorbs light. Fixes exist but each must be retuned for each material.
Precise statement
Find a generalized Kohn-Sham functional with no system-specific tuning that gives the fundamental gap $I - A$ ($I = \text{ionization energy}, A = \text{electron affinity}$) of molecules (the GW100 set of ionization potentials and electron affinities and similar sets) and the band gap of semiconductors and insulators (Si to LiF) with mean absolute error below $0.2\,\mathrm{eV}$. An answer is such a functional or an argument that tuning-free accuracy at this level requires orbital-dependent nonlocal terms of a specified type.
What would settle it
Benchmark against experimental and many-body (GW, coupled-cluster) gaps across molecules and solids with a single parameter set.