We will now approximate the cluster operator \( \hat{T} \) to include only \( 2p-2h \) correlations. This leads to the so-called CCD approximation, that is $$ \hat{T}\approx \hat{T}_2=\frac{1}{4}\sum_{abij}t_{ij}^{ab}a^{\dagger}_aa^{\dagger}_ba_ja_i, $$ meaning that we have $$ \vert \Psi_0 \rangle \approx \vert \Psi_{CCD} \rangle = \exp{\left(\hat{T}_2\right)}\vert \Phi_0\rangle. $$