Generalized gradient approximation for the fermion kinetic energy as a functional of the density

Abstract

The kinetic energy T s [ n] for noninteracting electrons of density n( r) has a generalized gradient approximation (GGA) ∫ d 3 rnt s ( nΦ( s), where t s(n) = 3ℏ 2k 2 F 10m , k F= (3π 2n) 1 3 , and s = |▿ n|/2 k F n. The function Φ( s) may be constructed a priori by two different methods (real-space cutoff of the second-order gradient expansion for the exchange hole, and convergent resummation of a subseries of the sixth-order expansion) which yield closely similar results: Φ ≈ 1 + 5s 2 27 . Thus it appears that the second-order gradient expansion for the kinetic energy is almost equal to its own generalized gradient approximation; a significantly better Φ( s) can probably not be found. For completeness, the GGA for the kinetic energy of interacting electrons is also presented.