Two-Point Approximate Orbital-Free Kinetic Energy Functionals

4 TWO-POINT APPROXIMATE ORBITAL-FREE KINETIC ENERGY FUNCTIONALS 

The functionals considered in Section 1.3 are all semilocal the local kinetic energy at the point r depends only on the electron density and its derivatives at the point r. Improved models for the kinetic energy require considering how the electron density at other points r affects the local kinetic energy at the point r. Without including these effects, the oscillations in electron density that are essential for modeling the shell structure of atoms and differentiating between core and valence electrons in molecules cannot be recovered. 

Most nonlocal functionals aim to reproduce the Kohn-Sham linear response function 

The Kohn-Sham linear response predicts long-range and short-range density oscillations in the nearly uniform electron gas in particular, it captures how the electron density becomes nonuniform when the Kohn-Sham potential is changed by an external perturbation, 

For the uniform electron gas, the response function depends only on the distance between the perturbation and the point at which the density change is measured 

---