  Exact conditions have long been used to guide the construction of density
functional approximations. But hundreds of empirical-based approximations
tailored for chemistry are in use, many of which neglect these conditions in
their design. We analyze well-known conditions and revive several obscure ones.
Two crucial distinctions are drawn: that between necessary and sufficient
conditions, and between all electronic densities and the subset of realistic
Coulombic ground states. Simple search algorithms find that many empirical
approximations satisfy many exact conditions for realistic densities and
non-empirical approximations satisfy even more conditions than those enforced
in their construction. The role of exact conditions in developing
approximations is revisited.

Chemical Physics;Computational Physics