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

The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory