saving work

Manuscript/SRGGW.tex

@@ -636,7 +636,7 @@ Note that, after this transformation, the form of the regularizer is actually cl
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 % Reference comp det
-Our set is composed by 50 closed-shell organic molecules, displayed in Fig.~\ref{fig:mol}, with singlet ground states.
+Our set is composed by closed-shell organic molecules that correspond to the 50 smallest atoms and molecules of the $GW$100 benchmark set. \cite{vanSetten_2015}
 Following the same philosophy as the \textsc{quest} database for neutral excited states, \cite{Loos_2020d,Veril_2021} their geometries have been optimized at the CC3 level \cite{Christiansen_1995b,Koch_1997} in the aug-cc-pVTZ basis set using the \textsc{cfour} program. \cite{CFOUR}
 The reference CCSD(T) principal ionization potentials (IPs) and electron affinities (EAs) have been obtained using Gaussian 16 \cite{g16} with default parameters, that is, within the restricted and unrestriced HF formalism for the neutral and charged species, respectively.
 
@@ -648,6 +648,7 @@ We use (restricted) HF guess orbitals and energies for all self-consistent $GW$
 The maximum size of the DIIS space \cite{Pulay_1980,Pulay_1982} and the maximum number of iterations were set to 5 and 64, respectively.
 In practice, one may achieve convergence, in some cases, by adjusting these parameters or by using an alternative mixing scheme.
 However, in order to perform a black-box comparison, these parameters have been fixed to these default values.
+\titou{The $\eta$ value used in the convetional $G_0W_0$ and $qsGW$ calculations corresponds to the largest value where one succesfully converges all systems.}
 
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 \section{Results}
@@ -821,20 +822,18 @@ Therefore, it seems that the effect of the TDA cannot be systematically predicte
 \end{figure*}
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-The test set considered in this study is made of the 50 smallest atoms and molecules of the $GW$100 benchmark set. \cite{vanSetten_2015}
-%This set has been augmented with the MgO and O3 molecules (which are part of GW100 as well) because they are known to possess intruder states. \cite{vanSetten_2015,Forster_2021}
-
 Table \ref{tab:tab1} shows the principal IP of the 50 molecules considered in this work computed at various levels of theory.
-As mentioned previously the HF IPs are overestimated with a mean signed error (MSE) of \SI{0.64}{\electronvolt} and a mean absolute error (MAE) of \SI{0.74}{\electronvolt}.
-Performing a one-shot $G_0W_0$ calculation on top these mean-field results allows to divided by more than two the MSE and MAE, \SI{0.26}{\electronvolt} and \SI{0.32}{\electronvolt}, respectively.
-However, there are still outliers with quite large errors, for example the IP of the dinitrogen is overestimated by \SI{1.56}{\electronvolt}.
-Self-consistency can mitigate the error of the outliers as the maximum error at the qs$GW$ level is now \SI{0.56}{\electronvolt} and the standard deviation error (SDE) is decreased from \SI{0.39}{\electronvolt} for $G_0W_0$ to \SI{0.18}{\electronvolt} for qs$GW$.
-In addition, the MSE and MAE (\SI{0.24}{\electronvolt}/\SI{0.25}{\electronvolt}) are also slightly improved with respect to $G_0W_0$@HF.
+As mentioned previously the HF approximation overestimates the IPs with a mean signed error (MSE) of \SI{0.64}{\eV} and a mean absolute error (MAE) of \SI{0.74}{\eV}.
+Performing a one-shot $G_0W_0$ calculation on top of this mean-field starting point, $G_0W_0$@HF, reduces by more than a factor two the MSE and MAE, \SI{0.26}{\eV} and \SI{0.32}{\eV}, respectively.
+However, there are still outliers with large errors. 
+For example, the IP of \ce{N2} is overestimated by \SI{1.56}{\eV}.
+Self-consistency can mitigate the error of the outliers as the maximum error at the qs$GW$ level is now \SI{0.56}{\eV} and the standard deviation of the error (SDE) is decreased from \SI{0.39}{\eV} for $G_0W_0$ to \SI{0.18}{\eV} for qs$GW$.
+In addition, the MSE and MAE (\SI{0.24}{\eV} and \SI{0.25}{\eV}, respectively) are also slightly improved with respect to $G_0W_0$@HF.
 
 Now turning to the new results of this manuscript, \ie the alternative self-consistent scheme SRG-qs$GW$.
-Table~\ref{tab:tab1} shows the SRG-qs$GW$ values for $s=100$.
-The statistical descriptors corresponding to the alternative static self-energy are all improved with respect to qs$GW$.
-Of course these are slight improvements but this is done with no additional computational cost and can be implemented really quickly just by changing the form of the static approximation.
+Table \ref{tab:tab1} shows the SRG-qs$GW$ values for $s=100$.
+The statistical descriptors corresponding to this alternative static self-energy are all improved with respect to qs$GW$.
+Of course, these are slight improvements but this is done with no additional computational cost and can be implemented really easily by changing the form of the static approximation.
 The evolution of the statistical descriptors with respect to the various methods considered in Table~\ref{tab:tab1} is graphically illustrated by Fig.~\ref{fig:fig4}.
 The decrease of the MSE and SDE correspond to a shift of the maximum toward zero and a shrink of the distribution width, respectively.