  Since the seminal works of Thomas and Fermi, researchers in the
Density-Functional Theory (DFT) community are searching for accurate electron
density functionals. Arguably, the toughest functional to approximate is the
noninteracting Kinetic Energy, $T_s[\rho]$, the subject of this work. The
typical paradigm is to first approximate the energy functional, and then take
its functional derivative, $\frac{\delta T_s[\rho]}{\delta \rho(r)}$, yielding
a potential that can be used in orbital-free DFT, or subsystem DFT simulations.
Here, this paradigm is challenged by constructing the potential from the
second-functional derivative via functional integration. A new nonlocal
functional for $T_s[\rho]$ is prescribed (which we dub MGP) having a density
independent kernel. MGP is constructed to satisfy three exact conditions: (1) a
nonzero "Kinetic electron" arising from a nonzero exchange hole; (2) the second
functional derivative must reduce to the inverse Lindhard function in the limit
of homogenous densities; (3) the potential derives from functional integration
of the second functional derivative. Pilot calculations show that MGP is
capable of reproducing accurate equilibrium volumes, bulk moduli, total energy,
and electron densities for metallic (BCC, FCC) and semiconducting (CD) phases
of Silicon as well as of III-V semiconductors. MGP functional is found to be
numerically stable typically reaching selfconsistency within 12 iteration of a
truncated Newton minimization algorithm. MGP's computational cost and memory
requirements are low and comparable to the Wang-Teter (WT) nonlocal functional
or any GGA functional.
