Gradient expansion of the atomic kinetic energy functional

It is demonstrated that the ground-state atomic kinetic energy functional T[?], where ? is the electron density, can be computed to surprising accuracy from the truncated gradient expansion: T[?] = + T₂[?] + T₄[?], with T_o[?] = $\text{3}\text{10}$(3π²)$\text{2}\text{3}$ ∫ ?$\text{5}\text{3}$ d_τ, T₂ [?] = $\text{1}\text{72}$ ∫ (??)²?^?1 d_τ, and T₄ [?] given by the formula of Hodges. Calculations of T₀, T₂ and T₄ are reported for He with ? both the Hartree—Fock and a very accurate density, and for Ne, Ar and Kr with ? the Hartree—Fock density. For Kr, T₀ + T₂ + T₄ is within 0.3% of the exact Hartree—Fock T, with T₂/T₀ = 0.05, T₄/T₂ = 0.17.