Jl. Gazquez et J. Robles, ON THE CONJOINT GRADIENT CORRECTION TO THE HARTREE-FOCK KINETIC AND EXCHANGE ENERGY DENSITY FUNCTIONALS, International journal of quantum chemistry, 57(1), 1996, pp. 3-6
The kinetic and the exchange energy functionals are expressed in the f
orm T[rho] = C(TF)integral dr rho(5/3)(r)f(T)(s) and K[rho] = C-D inte
gral dr rho(4/3)(r)f(K)(s), where C-TF = (3/10)(3 pi(2))(2/3) and C-D
= -(3/4)(3/pi)(1/3) are the Thomas-Fermi and the Dirac coefficients, r
espectively, and s = \V rho(r)\/C-s rho(4/3)(r), with C-s = 2(3 pi(2))
(1/3). These expressions are used to perform a comparison of f(T)(s) a
nd f(K)(s) in terms of their generalized gradient expansion approximat
ions. It is shown that f(K)(s) approximate to f(T)(s) in the range cha
racteristic of the interior regions of atoms and many solids and that
the second-order gradient expansion of the kinetic energy provides a r
ather reasonable approximation to the generalized gradient expansion a
pproximation of both the kinetic and the exchange energy functionals.
(C) 1996 John Wiley & Sons, Inc.