The algebraic expression
$$
\begin{align*}
\overline{H}_{ij}^{ab} &= \langle ab\vert V\vert ij\rangle + P(ab)\sum_c f_c^bt_{ij}^{ac} - P(ij)\sum_k f_j^k t_{ik}^{ab} \\
&+ {1\over 2} \sum_{cd} \langle ab\vert V\vert cd\rangle t_{ij}^{cd}+ {1\over 2} \sum_{kl} \langle kl\vert V\vert ij\rangle t_{kl}^{ab} + P(ab)P(ij)\sum_{kc} \langle kb\vert V\vert cj \rangle t_{ik}^{ac} \\
&+ {1\over 2} P(ij)P(ab)\sum_{kcld} \langle kl\vert V\vert cd\rangle t_{ik}^{ac}t_{lj}^{db}
+ {1\over 2} P(ij)\sum_{kcld} \langle kl\vert V\vert cd\rangle t_{ik}^{cd}t_{lj}^{ab}\\
&+ {1\over 2} P(ab)\sum_{kcld} \langle kl\vert V\vert cd\rangle t_{kl}^{ac}t_{ij}^{db}
+ {1\over 4} \sum_{kcld} \langle kl\vert V\vert cd\rangle t_{ij}^{cd}t_{kl}^{ab} .
\end{align*}
$$