It is shown that the product of the gradient of the density functional correlation potential and the charge density and the product of the gradient of the sum of the exchange and Hartree potentials and the charge density integrate to zero. The integral of the product of the charge density and the gradient of exchange potential is equal to an integral expression of a product of occupied Kohn-Sham orbitals and the gradient of the mutual Coulomb interaction. It is also shown that the expectation value of the gradient of the mutual Coulomb interaction is zero for the ground state of a many-electron system. (C) 2003 American Institute of Physics.