Despite the simple and universal structure of the nonrelativistic Hamiltonian for N interacting electrons, it produces a broad spectrum of physical and chemical phenomena that are difficult to conceptualize within the full N-electron theory. Starting with the work of Hartree [162] in the early years of quantum mechanics, it was found to be very rewarding to develop a model of electrons that interact only indirectly with each other, through a self-consistent mean field. A deeper motivation lies in the fact that the relativistic quantum field theory of electrons is explicitly described by a field operator that corresponds more closely to a oneparticle model wave function than to that of the Schrödinger N-electron theory. The fundamental characterization of this electron field by Fermi–Dirac statistics is directly applicable to the mean-field theory, using concepts of statistical occupation numbers determined by effective one-electron orbital energy values. The variational theory appropriate to such independent-electron models is developed in this chapter.