Exchange and correlation Kohn–Sham functionals for the helium atom: locality and homogeneity

The locality and homogeneous nature of the exchange and correlation functionals for the ground state of the helium atom, in the Kohn–Sham formulation, are revisited. Our analysis is focused on the integrands of both functionals, although the integrated quantities are compared with previous results. Both functionals are not local, and the correlation functional is not homogeneous. To study the non-locality, a set of dependences on the derivatives of the density, compatible with the more general constraints that must be fulfilled, is selected. We are not able to explain the non-local nature of the functionals.