CLOSED-FORM EXPRESSION RELATING THE 2ND-ORDER COMPONENT OF THE DENSITY-FUNCTIONAL THEORY CORRELATION-ENERGY TO ITS FUNCTIONAL DERIVATIVE

For helping to improve approximations to the density-functional exchan ge-correlation energy, E-xc[n], and its functional derivative, the dif ference between the second-order component of the correlation energy, E-c((2))[n], and the integral integral drv(c)((2))([n];r)n(r), involvi ng its functional derivative, v(c)((2))([n];r), is given in terms of o nly the occupied Kohn-Sham orbitals and the exchange potential. The qu antity 2E(c)((2))[n] is especially significant because it is the initi al slope in the adiabatic connection formula for E-xc[n]. The analytic expression for 2E(c)((2))[n] -integral drv(c)((2))([n];r)n(r) is obta ined for any spherically symmetric two-electron test density. Numerica l examples are presented. (C) 1998 American Institute of Physics. [S00 21-9606(98)02135-7].