Learnings from exchange-correlation potentials

Exchange-correlation potentials Vxc(r) can be obtained (within an additive constant) from high-quality ab initio electron densities of atoms and small molecules. These potentials show qualitative features not captured by popular density functionals, and highlight unappreciated aspects of electron densities and density functionals. While Vxcs generally scale with ρ1/3 except at very long or short range, the proportionality is more similar to that of hydrogenic systems than to that of the homogeneous electron gas. The Fermi–Amaldi long-range approximation works well into the valence region. The size and location of the large feature at the valence–core transition is system-dependent. This qualitative information can guide the search for improved density functionals.