\begin{equation}
\mathbf{f}=\mathbf{C}^{\dagger}\cdot\mathbf{S}_{AO}\cdot \left[ \mathbf{D}^{C}_{AO}\cdot\mathbf{F}^{D}_{AO}+\sum_{O\in\mathcal{O}}f_{O}\cdot\mathbf{D}^{O}_{{AO}}\cdot ( \mathbf{F}^{D}_{{AO}}+(a_{O}-1)\mathbf{Q}^{V,O}_{{AO}} ) \right] \mathbf{C}
\end{equation}