A generalized Kohn-Sham scheme in which the correlation energy disappears is presented. Therefore, exchange energy has to be determined instead of the exchange-correlation energy and it can be calculated very accurately. Contrary to the standard density functional theory, in the generalization presented here the density can change by a constant factor: rho(zeta)(r) = rho(r)/zeta proposed by Chan and Handy a couple of years ago. Making use of the method a simple approximate relation for the correlation energy of the original Kohn-Sham scheme is derived. (c) 2005 Elsevier B.V. All rights reserved.