GENERALIZED GRADIENT APPROXIMATION FOR THE FERMION KINETIC-ENERGY AS A FUNCTIONAL OF THE DENSITY

The kinetic energy T(s)[n] for noninteracting electrons of density n(r) has a generalized gradient approximation (GGA) integral d3rnt(s)(n) PHI(s), where t(s)(n) = 3h2k(F)2/10mBAR, k(F) = (3-pi-2n)1/3, and s = \deln\/2k(F)n. The function PHI(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: PHI almost-equal-to 1 + 5s2/27. 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 PHI(s) can probably not be found. For completeness, the GGA for the kinetic energy of interacting electrons is also presented.