The coupled cluster wavefunction is now given by $$ \begin{equation*} \vert \Psi_{CC}\rangle = e^{\hat{T}_1 + \hat{T}_2} \vert \Phi_0\rangle \end{equation*} $$ where $$ \begin{align*} \hat{T}_1 &= \sum_{ia} t_{i}^{a} a_{a}^\dagger a_i \\ \hat{T}_2 &= \frac{1}{4} \sum_{ijab} t_{ij}^{ab} a_{a}^\dagger a_{b}^\dagger a_{j} a_{i}. \end{align*} $$