Failure of the Weizsäcker kinetic energy functional for one-, two-, and three-electron distribution functions

Further progress in pair-density functional theory (sometimes called 2-DFT) hinges on the development of computationally facile and quantitatively accurate models for the kinetic energy functional. In this paper we perform computational tests for two of the simplest models, the generalized Weizsäcker kinetic energy functional and its spin-resolved extension. Both of these models perform very poorly for atoms. The higher-order Weizsäcker functionals (based on the three-electron distribution function) perform better, but are still not successful. This suggests that an alternative approach for designing kinetic energy functionals of the pair density is needed.