Unlike the CI theory, which is a linear theory, Mean-Field (MF) Theories are necessarily nonlinear. In particular their Hamiltonian depends on their eigenstates. To this end, these equations can be solved by a Self-Consistent Field (SCF) algorithm. In theory, MF approach to "electronic structure" attempts to solve the equilibrium electrostatic distribution, In practice, the MF equations also orthogonalize the atomic-centric Basis-Set-Ansatz.