Because the FCI space is very large, i.e. scaling exponentially with the number of electrons, it is computationally intractable for most interesting systems (in chemistry and biochemistry). It is often truncated by excitations or a choice of an Active-Space descriptions, this is beyond the scope of this paper. If the theory is contracted to a single state, this is known as Mean-Field Theory, for the ground state this is the famous Hartree-Fock Theory. Solving the Mean-Field/Hartree-Fock Equation is the first step to solving the FCI equations here.