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Manuscript/SRGGW.tex

@@ -364,20 +364,7 @@ Indeed, the $GW$ quasiparticle equation is equivalent to the diagonalization of
 %  \boldsymbol{\epsilon},
 \end{equation}
 %where $\boldsymbol{\epsilon}$ is a diagonal matrix collecting the quasiparticle and satellite energies, 
-where the 2h1p and 2p1h matrix elements are
+
-\begin{subequations}
-  \begin{align}
-    C^\text{2h1p}_{i\nu,j\mu} & =  \left(\epsilon_i - \Omega_\nu\right)\delta_{ij}\delta_{\nu\mu},
-    \\
-    C^\text{2p1h}_{a\nu,b\mu} & = \left(\epsilon_a + \Omega_\nu\right)\delta_{ab}\delta_{\nu\mu},
-  \end{align}
-\end{subequations}
-and the corresponding coupling blocks read [see Eq.~(\ref{eq:GW_sERI})]
-\begin{align}
-  W^\text{2h1p}_{p,i\nu} & = W_{pi}^{\nu},
-  &
-    W^\text{2p1h}_{p,a\nu} & = W_{pa}^{\nu}.
-\end{align}
 The usual $GW$ non-linear equation can be obtained by applying L\"owdin partitioning technique \cite{Lowdin_1963} to Eq.~\eqref{eq:GWlin} yielding \cite{Bintrim_2021} 
 \begin{equation}
   \begin{split}