The ansatz for the wavefunction (ground state) is given by $$ \begin{equation*} \vert \Psi\rangle = \vert \Psi_{CC}\rangle = e^{\hat{T}} \vert \Phi_0\rangle = \left( \sum_{n=1}^{A} \frac{1}{n!} \hat{T}^n \right) \vert \Phi_0\rangle, \end{equation*} $$ where \( A \) represents the maximum number of particle-hole excitations and \( \hat{T} \) is the cluster operator defined as $$ \begin{align*} \hat{T} &= \hat{T}_1 + \hat{T}_2 + \ldots + \hat{T}_A \\ \hat{T}_n &= \left(\frac{1}{n!}\right)^2 \sum_{\substack{ i_1,i_2,\ldots i_n \\ a_1,a_2,\ldots a_n}} t_{i_1i_2\ldots i_n}^{a_1a_2\ldots a_n} a_{a_1}^\dagger a_{a_2}^\dagger \ldots a_{a_n}^\dagger a_{i_n} \ldots a_{i_2} a_{i_1}. \end{align*} $$