On the conjoint gradient correction to the Hartree?Fock kinetic and exchange energy density functionals

Abstract

The kinetic and the exchange energy functionals are expressed in the form T[ρ] = CTF∫ drρ5/3(r)ft(s) and K[ρ] = CD∫ drρ4/3(r)fK(s), where CTF = (3/10)(3π2)2/3 and CD = −(3/4)(3/π)4/3 are the Thomas-Fermi and the Dirac coefficients, respectively, and s = |∇ρ(r)|/Csρ4/3(r), with Cs = 2(3π2)1/3. These expressions are used to perform a comparison of fT(s) and fK(s) in terms of their generalized gradient expansion approximations. It is shown that fκ(s) and is congruent to fT(s) in the range characteristic of the interior regions of atoms and many solids and that the second-order gradient expansion of the kinetic energy provides a rather reasonable approximation to the generalized gradient expansion approximation of both the kinetic and the exchange energy functionals. © 1996 John Wiley & Sons, Inc.