Borderline cases in density functional theory

We discuss two examples (antiferromagnetic order in transition metal oxides and van der Waals interaction) where density functional theory (DFT) seems to fail in giving an appropriate description of the actual physical situation. We analyze whether or not this failure reflects only a shortcoming of the approximations to the exchange‐correlation functionals that are commonly used. It is shown that the well‐known incapability of DFT to yield the correct antiferromagnetic (AF) moment and insulating properties of CoO and stoichiometric La 2 CuO 4 may be indicative of a more fundamental deficiency, namely, absence of an exact noninteracting V‐representability of the spin densities in AF materials. By enlarging and reducing the self‐consistent DFT spin densities by an appropriate amount and simultaneously keeping the total densities fixed, one can turn CoO and La 2 CuO 4 into insulators with the correct AF moments. We also discuss the ground‐state energy of two noble gas atoms of radius R 0 at a distance R ≫ 2 R 0 , for which situation an exact DFT should yield a 1/ R 6 ‐dependence for the difference between the total energy of the bi‐atom and the two atoms at infinite separation. Even if one improves the local density approximation to the exchange‐correlation energy by gradient corrections, this dependence remains outside the current practical framework of DFT. We report and practically check a simple idea as to how this difficulty can be overcome. The method we develop also might prove useful in actually calculating the above defect spin densities for critical AF materials.