orbitals, as an example. For convenience, I parameterize these bonds by the integer parameter $j=1 \sim N$ and denote the bonding region of the $j$-th bond as $\Omega _{j}$, where $N$ is the total number of the bonds. Each bond in the compound is a 4-level dimer just as the one-bond system in Fig. 1 (a). Assume that there exists the one-to-one mapping ${\bf R} _{j}$ to relate any position ${\bf r} _{j} \in \Omega _{j}$ in the $j$-th bond to ${\bf r} \in \Omega$ in Fig. 1 (a) by ${\bf R} _{j} ({\bf r}) = {\bf r} _{j}$ and ${\bf R} _{j} ^{-1} ({\bf r} _{j}) = {\bf r}$ such that the distance $|{\bf r}_{1}-{\bf r} _{2}|$ between ${\bf r}_{1}$ and ${\bf r}_{2} \in \Omega$ equals $|{\bf R} _{j} ( {\bf r} _{1} )- {\bf R} _{j}({\bf r} _{2})| $ for all $j$. Therefore, every ionic-covalent chemical bond in the compound is identical to that in Fig. 1 (a). Let $| A, j \rangle $ and $| B, j \rangle $ as the kets mapped from $| A \rangle $ and $| B \rangle $ under ${\bf R}_{j}$, respectively. The space $\mathbb{C} ^{2} _{ \Omega _{j} }$ spanned by 