  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.
