Density functionals for exchange and correlation energies: Exact conditions and comparison of approximations

A set of exact conditions is compiled for the purpose of developing and testing approximations for the exchange‐correlation energy as a functional of the electron density. Special emphasis is placed upon recently developed density‐scaling relationships. Commonly used generalized gradient approximations are compared against several of these conditions. A direct tabular comparison of these functionals (not of calculated properties) with one another is also made.