Thus, the coupled-cluster method with the full cluster operator (15) is exponentially expensive, just as FCI. To make progress, we need to make an approximation by truncating the operator. Here, we will use the CCSD (coupled clusters singles doubles) approximation, where
$$ \begin{equation} \tag{17} T \equiv \sum_{ia} t_i^a a^\dagger_a a_i + \frac{1}{4}\sum_{ijab}t_{ij}^{ab} a^\dagger_aa^\dagger_ba_ja_i . \end{equation} $$