A quick tour of Coupled Cluster theory
The energy is given by
$$
\begin{equation*}
E_{\mathrm{CC}} = \langle\Phi_0\vert \overline{H}\vert \Phi_0\rangle,
\end{equation*}
$$
where \( \overline{H} \) is a similarity transformed Hamiltonian
$$
\begin{align*}
\overline{H}&= e^{-\hat{T}} \hat{H}_N e^{\hat{T}} \\
\hat{H}_N &= \hat{H} - \langle\Phi_0\vert \hat{H} \vert \Phi_0\rangle.
\end{align*}
$$