Diagrams 7, 8, and 9 of Fig. xx also need to be factorized.
For diagram number 7, we compute
$$ \begin{align} \chi_{id}^{al}\equiv\sum_{kc} \langle kl\vert V\vert cd\rangle t_{ik}^{ac} \tag{30} \end{align} $$at a cost of \( A^3 n_u^3 \) and then compute
$$ \begin{align} {1\over 2} P(ij)P(ab) \sum_{ld} \chi_{id}^{al} t_{lj}^{db} \tag{31} \end{align} $$at the cost of \( A^3 n_u^3 \).