Gradient expansion of the kinetic energy density functional: Local behavior of the kinetic energy density

Calculations with Hartree—Fock electron densities for the rare gas atoms He through Xe show that the gradient expansion for the kinetic energy functional, T] = T₀] + T₂] + T₄] + … = ∫t() dτ, approximates the kinetic energy by averaging over the shell structure present in the true local kinetic energy density, t(), and that the accuracy of the gradient expansion improves with increasing atomic number. Components of t(), t₀(), t₂() and t₄(), are exhibited and discussed. The defined function t() is everywhere positive.