  The relationship between the exact kinetic energy density in a quantum system
in the frame of Density Functional Theory and the semiclassical functional
expression for the same quantity is investigated. The analysis is performed
with Monte Carlo simulations of the Kohn-Sham potentials. We find that the
semiclassical form represents the statistical expectation value of the quantum
nature. Based on the numerical results, we propose an empirical correction to
the existing functional and an associated method to improve the Orbital-Free
results.
