\rangle + \alpha _{c} | \Psi _{c} \rangle.\end{aligned}$$ Here $| \Psi _{b} \rangle$ denotes the bonding wavefunction of the half-filled ionic-covalent bond, and the complex numbers $ \alpha _{i}$ and $\alpha _{c}$ are the bonding coefficients satisfying $| \alpha _{i}| ^{2} +|\alpha _{c}| ^{2} =1$. In this manuscript, the AF model is generalized for the compound in which the chemical bonds are identical to the red one in Fig. 1 (a). To include the bonding correlation, the extended AF density matrix $$\begin{aligned}
\rho _{ea} =  \left[
\begin{array}{c} 
\rho  \text{ \ \ }   \Delta   \\  \Delta  \text{ \ \ } \rho   
\end{array}
\right] \end{aligned}$$ is introduced to construct the correlation operators $$\begin{aligned}
\begin{cases} 
d ^{(1)} = ( \sqrt{2} -1) [ \rho ^{(1)} \rho ^{(2)} ( I - \rho ^{(1)}) +   ( I - \rho ^{(1)}) \rho ^{(2)} \rho ^{(1)} ]   \\  
d ^{(2)} =  ( I - \rho ^{(1)})  \rho ^{(2)}  ( I - \rho ^{(1)}) \text{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }
\end{cases}\end{aligned}$$ for the electron pair in the bonding region $\Omega$. Here $\rho$ and $\Delta$ are 