Let us begin by inspecting the pure mean-field terms (A 0 and B 0 ). If we neglect all other contributions, the matrix elements of the zero-order Hamiltonian can be written as follows, where we insert the explicit definition of the Fock matrix: H i j (0) = h i j + ⟨ik|| jk⟩ + A 0 ⟨ik|| jk⟩