Is it possible to construct excited-state energy functionals by splitting k-space?

We show that our procedure of constructing excited-state energy functionals by splitting k-space, employed so far to obtain exchange energies of excited-states, is quite general. We do so by applying the same method to construct modified Thomas-Fermi kinetic energy functional and its gradient-expansion up to the second order for the excited-states. We show that the resulting kinetic energy functional has the same accuracy for the excited-states as the ground-state functionals do for the ground-states.