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

摘要

The kinetic and the exchange energy functionals are expressed in the form T[rho] = C(TF)integral dr rho(5/3)(r)f(T)(s) and K[rho] = C-D integral 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, respectively, 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) and f(K)(s) in terms of their generalized gradient expansion approximations. It is shown that f(K)(s) approximate to f(T)(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. (C) 1996 John Wiley & Sons, Inc. [References: 15]