Hydrodynamic Tensor-DFT with correct susceptibility

In a previous work we developed a family of orbital-free tensor equations for DFT [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equations hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work we assumed that the cumulants vanish above a certain order (N). Here we show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a non-perturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained while the Thomas Fermi and von-Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate our previous assertion that as the order of the theory is increased, new additional transverse sound modes appear mimicking the RPA transverse dispersion region.