In earlier studies, we have considered the exchange energy density epsilon(x)(r) in terms of the Dirac density matrix rho(1)(r,r(')) for the nonrelativistic limit of large atomic number Z in (i) the Be-like series with configuration (1s)(2)(2s)(2) and (ii) the Ne-like series with closed K+L shells. Subsequently the work of Della Sala and Gorling [J. Chem. Phys. 115, 5718 (2001)] has appeared, in which an integral equation for the exchange potential v(x)(r) is given in terms of the idempotent Dirac density matrix, based on the admittedly drastic approximation that the Hartree-Fock and the Kohn-Sham determinants are equal. Here a formally exact generalization of the integral equation is set up and an approximate solution is presented for the Be series at large Z. (C) 2003 American Institute of Physics.