atoms in the considered bond, as shown in Fig. 4. We can construct these site orbitals by considering the linear combinations of the atomic orbitals after truncating the tails outside the bonding region $\Omega$ and performing suitable orthogonalization to have the zero overlap integral [@Levine]. Let $ \mathbb{C} ^{2} _{\Omega} $ be the vector space composed of the linear combinations of $| A \rangle$ and $|B \rangle$. The space $ \mathbb{C} ^{2} _{\Omega} $ is isomorphic to $ \mathbb{C} ^{2} $, and is a subspace of the Hilbert space $ L^{2} _{\Omega} $ composed of the square-integrable functions which equal zero outside $\Omega$. The Heitler-London correlated state $| \Psi _{c} \rangle = \frac{1}{ \sqrt{2} } ( c_{A \uparrow} ^{\dag} c_{B \downarrow} ^{\dag} +  c_{B \uparrow} ^{\dag} c_{A \downarrow} ^{\dag}) | 0 \rangle $, a linear combination of the AF states $c_{A \uparrow} ^{\dag} c_{B \downarrow} ^{\dag} | 0 \rangle $ and $c_{B \uparrow} ^{\dag} c_{A \downarrow} ^{\dag} | 0 \rangle $, has been taken into account in the covalent limit [@Fulde; @Soos] when the 4-level bond is half-filled. To include the ionic part, we may consider the ionic Hubbard model [@Kampf; @Buzatu] and modify $H _{t-U}$ as the one-bond Hamiltonian 