\(\phi_{\text{AB}}^{part-A}\left(\mathbf{r}\right)=\sum_{I\in A}{\phi^{I}\left(\mathbf{r}\right)}+\sum_{I<J\in A}{{\phi}^{\text{IJ}}\left(\mathbf{r}\right)}+\sum_{\alpha\in A}\frac{Z_{\alpha}}{\left|\mathbf{r}-\mathbf{R}_{\alpha}\right|}+\frac{1}{2}\sum_{I\in A}{\sum_{J\in B}{{\phi}^{\text{IJ}}(\mathbf{r})}},\) (6)
\(\phi_{\text{AB}}^{part-B}\left(\mathbf{r}\right)=\sum_{I\in B}{\phi^{I}(\mathbf{r})}+\sum_{I<J\in B}{{\phi}^{\text{IJ}}\left(\mathbf{r}\right)}+\sum_{\alpha\in B}\frac{Z_{\alpha}}{|\mathbf{r}-\mathbf{R}_{\alpha}|}+\frac{1}{2}\sum_{I\in A}{\sum_{J\in B}{{\phi}^{\text{IJ}}(\mathbf{r})}}.\) (7)