Note how with this definition, the first term on the right-hand side of Eq (6) integrates to the KS kinetic energy of the systems, while the Laplacian part, which allows local regions of space to have negative energy densities, integrates to zero. Whereas there exists several other definitions for the kinetic energy density, our choice of Eq. ( ) is necessary to provide the exact same electron energy density 𝛸(𝒓) as with Eq. ( ) used previously for molecules (See Fig. ).