Scaling properties and local forms of the correlation-energy functional

The scaling properties of the exact correlation-energy functional are applied in the study of the general rational, polynomial, and logarithmic local forms (and their combinations) of the correlation-energy functional, which depend on the density. It is concluded that these forms cannot satisfy the uniform and nonuniform scaling properties at the same time; therefore, they would have to be modified to represent exact forms of the correlation-energy density functional, at least in the high- and low-density limits. These results are not affected by the application of the local spin density or the self-interaction correction procedures to the above functionals.