Application of partition density-functional theory to model systems

Elliott et al.\footnote{P. Elliott, K. Burke. M. H. Cohen and A. Wasserman, Phys. Rev. A {\bf 82}, 024501 (2010)} have introduced a method called partition density-functional theory (PDFT) for expressing the Kohn-Sham charge density as a sum of overlapping fragment densities, which promises accuracy and efficiency along with a framework for developing and testing useful approximations for kinetic-energy functionals, T[n]. They illustrate their method using results obtained for non-interacting electrons in a one-dimensional model potential. Following their approach, we apply PDFT to similar models which examine its usefulness in developing approximations for T. We also discuss how PDFT compares with the self-consistent atomic deformation\footnote{L. L. Boyer, H. T. Stokes, M. M. Ossowski and M. J. Mehl, Phys. Rev. B {\bf 78}, 045121 (2008)} method.