$d ^{( \text{II} )}$ for the bonding correlation in the quasielectron system of the considered compound. I decompose such a system into the 4-level subsystems shown in Fig. 3 (a), and the energy difference to excite a carrier is obtained in section IV-B by considering the ionized/affinitive process. When the compound forms an ideal crystal following the periodic boundary condition, each subsystem may correspond to a Bloch-type function. Near the ionic limit, as shown in Appendix C, my model can be supported by the coupled-cluster theory. On the other hand, we can see the importance of the bonding coefficients to the excited carrier near the covalent limit under the strong e-e repulsive strength, which is responsible for the Mott insulating behaviors in some AF systems [@Lee1; @Liu]. The Hamiltonian family, which can correspond to the random Schr$\ddot{o}$dinger operators in the random-matrix theory [@Kirsc; @Erdos; @Lee2; @Huang2], is discussed in section V. Actually we may generalize Eq. (2) to include a set of Hamiltonians by constructing the multiple-component quasielectrons. I note that the multiple-component functions can be used to introduce the vector bundles [@Bohm; @Friedman; @Banks] for the gauge theory. The compound system composed of different ionic-covalent dimers are discussed in 