It is shown that, in general, Gaussian basis set xOEP methods cannot yield the HF total energy because, in general, products of occupied and unoccupied orbitals are effectively linearly dependent. xOEP methods can yield the HF total energy only if the quality of the employed orbital basis set is insufficient with respect to the computational accuracy. Furthermore it is shown that the basic equation underlying the xOEP method can be obtained via a weighted minimization of the difference between the occupied-virtual block of the xOEP and the HF exchange matrix, with weight factors given by inverse orbital eigenvalue differences. (C) 2008 Elsevier B.V. All rights reserved.