orbitals at the two sites. The ionic-covalent chemical bond can be approximated by such a dimer when the two sites correspond to the atomic orbitals, and we have the Heitler-London state [@Fulde; @Soos], which is denoted by $| \Psi _{c} \rangle$ in this manuscript, for the covalent limit. The ionic state $| \Psi _{i} \rangle$ may become dominant in the hetero-diatom bond, in which we shall consider different on-site energies introduced in the ionic Hubbard model [@Kampf; @Buzatu].

The Bloch states [@Fulde; @Grosso; @Grafenstein] are important to construct the quasiparticle orbitals, including the plane-wave ones for the nearly free carriers in crystals. Such states can be introduced based on the mean-field methods such as the Hartree-Fock (HF) approach, which yields the self-consistent-field (SCF) solutions [@Fulde; @Grafenstein; @Stoyanova]. It has been discussed in the literature how to include the correlation energy beyond the HF approach by considering the coupled-cluster corrections such as those due to coupled-cluster doubles (CCDs) [@Fulde; @Grafenstein; @Stoyanova; @Doll; @Talukdar]. In addition, my group [@Huang1] has used the AF part of the extended Bogoliubov-BCS quasiparticles to construct the energy form of the one-bond system by considering [@Prasad] $$\begin{aligned}
| \Psi _{b} \rangle = \alpha _{i} | \Psi _{i} 