The coupled-cluster wave function model

Most generally, the coupled cluster wave function is written as an exponential wave function model: \[\begin{equation} \require{physics} \ket{CC(\vb{t})} % = \exp\qty(\hat{T}(\vb{t})) \ket{\text{HF}} % \thinspace , \end{equation}\] in which \(\ket{\text{HF}}\) is the Hartree-Fock reference determinant and \(\hat{T}(\vb{t})\) is the cluster operator, which depends on the amplitudes \(\vb{t}\): \[\begin{equation} \hat{T}(\vb{t}) = \hat{T}_1 + \hat{T}_2 + \cdots % \thinspace . \end{equation}\] Here, \(\hat{T}_1\) is a single-excitation cluster operator: \[\begin{equation} \hat{T}_1 % = \sum_I^N \sum_{A=N+1}^M % t_I^A \hat{E}_{AI} \end{equation}\] and similarly \(\hat{T}_2\) is a double-excitation cluster operator.