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Manuscript/SRGGW.tex

@@ -767,7 +767,6 @@ Therefore, it seems that the effect of the TDA cannot be systematically predicte
   \includegraphics[width=\linewidth]{fig5.pdf}
   \caption{
     Histogram of the errors (with respect to $\Delta$CCSD(T)) for the first ionization potential of the GW50 test set calculated using HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$.
-    \PFL{Add MAE and MSE values to each figure.}
     \label{fig:fig4}}
 \end{figure*}
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@@ -890,7 +889,6 @@ On the other hand, the imaginary shift regularizer acts equivalently on intruder
   \includegraphics[width=\linewidth]{fig7.pdf}
   \caption{
     Histogram of the errors (with respect to $\Delta$CCSD(T)) for the first electron attachment of the GW50 test set calculated using HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$.
-   \PFL{Add MAE and MSE values to each figure.}
    \label{fig:fig6}}
 \end{figure*}
 %%% %%% %%% %%%
@@ -924,16 +922,21 @@ This new qs$GW$ approximation is referred to as SRG-qs$GW$.
 In addition, to this new static form we also explained how to use the SRG formalism to cure discontinuity problems (which are also due to intruder states).
 This gave a first-principle rationale for the SRG-inspired regularizer introduced in Ref.~\onlinecite{Monino_2022}.
 
-The flow parameter dependence of SRG-qs$GW$ principal ionization potentials has been studied for a few test cases.
-It has been shown that the IP gradually evolves from the HF one to a plateau value for $s\to\infty$ that is much closer to the reference than the starting point.
-For small values of the flow parameter the SRG-qs$GW$ IPs are actually worst than their starting point so one should always use a value of $s$ as large as possible.
+The flow parameter dependence of the SRG-qs$GW$ IPs has been studied for a few test cases.
+It has been shown that the IPs gradually evolves from the HF starting point at $s=0$ to a plateau value for $s\to\infty$ that is much closer to the reference than the HF initial value.
+For small values of the flow parameter the SRG-qs$GW$ IPs are actually worst than their starting point.
+Therefore, in practice one should always use a value of $s$ as large as possible.
+This is similar to qs$GW$ calculations where one need to use the smallest possible $\eta$.
 
-As a second stage to this study, the SRG-qs$GW$ performance has been statistically gauged for a test set of 50 atoms and molecules (referred to as $GW$50).
+The second stage of this study was to statistically gauge the accuracy of the SRG-qs$GW$ IP for a test set of 50 atoms and molecules (referred to as $GW$50).
 It has been shown that in average SRG-qs$GW$ is slightly better than its traditional qs$GW$ counterpart for principal ionization energies.
 Note that while the accuracy improvement is quite small, it comes with no additional computational cost and its really fast to implement as one just need to change the static self-energy expression.
 In addition, the SRG-qs$GW$ can be converged in a much more black-box fashion than traditional qs$GW$ thanks to its intruder-state free nature.
 
-
+Finally, the EA have been investigated as well.
+It has been found that the performance of the two qs$GW$ flavours for the $GW$50 set are quite similar.
+However, there is a caveat because most of the anions of the $GW$50 set are actually resonance states and their associated physcis can not be accurately described.
+A test set of molecules with bound anions and a benchmark of accurate reference values would certainly valuable to many-body perturbation theory community.
 
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 \acknowledgements{