ON THE CONJOINT GRADIENT CORRECTION TO THE HARTREE-FOCK KINETIC AND EXCHANGE ENERGY DENSITY FUNCTIONALS

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.