Reassessing the role of exact conditions in density functional theory

Exact conditions have long been used to guide the construction of density functional approximations. Nowadays hundreds of approximations are in common use, many of which neglected these conditions in their design. Such approximations yield extremely accurate results on comprehensive molecular benchmarks and are often more accurate than their more constrained counterparts. To resolve this paradox, we carefully parse the logic of exact conditions, finding that many enforced conditions are too strong for real matter. A computational scanning procedure finds violations, coupled with the construction of corresponding reasonable (but not realistic) densities. Half a dozen exact conditions and hundreds of approximate functionals are analyzed. Several forgotten conditions are revived and analyzed, while even well-known conditions yield surprising new twists. The role of exact conditions in density functional development is revisited.