diff --git a/Manuscript/SRGGW.tex b/Manuscript/SRGGW.tex index 1781b45..ddf67d7 100644 --- a/Manuscript/SRGGW.tex +++ b/Manuscript/SRGGW.tex @@ -736,6 +736,21 @@ Also, SRG-qs$GW^\TDA$ is better than qs$GW^\TDA$ in the three cases of Fig.~\ref However, it is not a general rule. Therefore, it seems that the effect of the TDA cannot be systematically predicted. + +%%%%%%%%%%%%%%%%%%%%%% +\subsection{Statistical analysis} +\label{sec:SRG_vs_Sym} +%%%%%%%%%%%%%%%%%%%%%% + +%%% FIG 4 %%% +\begin{figure*} + \includegraphics[width=\linewidth]{fig4.pdf} + \caption{ + Histogram of the errors (with respect to $\Delta$CCSD(T)) for the first ionization potential calculated using HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. + \label{fig:fig4}} +\end{figure*} +%%% %%% %%% %%% + \begin{table*} \caption{First ionization potential (left) and first electron attachment (right) in eV calculated using $\Delta$CCSD(T) (reference), HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. The statistical descriptors are computed for the errors with respect to the reference. \ANT{Maybe change the values of SRG with the one for s=1000}} \label{tab:tab1} @@ -744,28 +759,28 @@ Therefore, it seems that the effect of the TDA cannot be systematically predicte Mol. & \mcc{$\Delta\text{CCSD(T)}$} & \mcc{HF} & \mcc{$G_0W_0$@HF} & \mcc{qs$GW$} & \mcc{SRg-qs$GW$} & \mcc{$\Delta\text{CCSD(T)}$} & \mcc{HF} & \mcc{$G_0W_0$@HF} & \mcc{qs$GW$} & \mcc{SRg-qs$GW$} \\ & \mcc{(Reference)} & & \mcc{$\eta=\num{e-3}$} & \mcc{$\eta=\num{e-1}$} & \mcc{$s=\num{e2}$} & \mcc{(Reference)} & & \mcc{$\eta=\num{e-3}$} & \mcc{$\eta=\num{e-1}$} & \mcc{$s=\num{e2}$} \\ \hline - \ce{He} & 24.54 & 24.98 & 24.59 & 24.58 & 24.54 \\ - \ce{Ne} & 21.47 & 23.15 & 21.46 & 21.83 & 21.59 \\ - \ce{H2} & 16.40 & 16.16 & 16.49 & 16.45 & 16.45 \\ - \ce{Li2} & 5.25 & 4.96 & 5.38 & 5.40 & 5.37 \\ - \ce{LiH} & 8.02 & 8.21 & 8.22 & 8.25 & 8.15 \\ - \ce{HF} & 16.15 & 17.69 & 16.25 & 16.45 & 16.34 \\ - \ce{Ar} & 15.60 & 16.08 & 15.71 & 15.61 & 15.63 \\ - \ce{H2O} & 12.69 & 13.88 & 12.90 & 12.98 & 12.88 \\ - \ce{LiF} & 11.47 & 12.91 & 11.40 & 11.75 & 11.58 \\ - \ce{HCl} & 12.67 & 12.98 & 12.78 & 12.77 & 12.72 \\ - \ce{BeO} & 9.95 & 10.45 & 9.74 & 10.32 & 10.18 \\ - \ce{CO} & 13.99 & 15.11 & 14.80 & 14.34 & 14.33 \\ - \ce{N2} & 15.54 & 16.68 & 17.10 & 15.93 & 15.91 \\ - \ce{CH4} & 14.39 & 14.83 & 14.76 & 14.67 & 14.63 \\ - \ce{BH3} & 13.31 & 13.59 & 13.68 & 13.62 & 13.59 \\ - \ce{NH3} & 10.91 & 11.69 & 11.21 & 11.18 & 11.10 \\ - \ce{BF} & 11.14 & 11.04 & 11.34 & 11.19 & 11.17 \\ - \ce{BN} & 12.05 & 11.55 & 11.76 & 11.89 & 11.90 \\ - \ce{SH2} & 10.39 & 10.49 & 10.51 & 10.50 & 10.45 \\ - \ce{F2} & 15.81 & 18.15 & 16.35 & 16.27 & 16.22 \\ - \ce{MgO} & 7.97 & 8.75 & 8.40 & 8.54 & 8.36 \\ - \ce{O3} & 12.85 & 13.29 & 13.56 & 13.34 & 13.27 \\ + \ce{He} & 24.54 & 24.98 & 24.59 & 24.58 & 24.54 & 2.66 & 2.70 & 2.66 & 2.66 & 2.66 \\ + \ce{Ne} & 21.47 & 23.15 & 21.46 & 21.83 & 21.59 & 5.09 & 5.47 & 5.25 & 5.19 & 5.19 \\ + \ce{H2} & 16.40 & 16.16 & 16.49 & 16.45 & 16.45 & 1.35 & 1.33 & 1.28 & 1.28 & 1.28 \\ + \ce{Li2} & 5.25 & 4.96 & 5.38 & 5.40 & 5.37 & -0.34 & 0.08 & -0.17 & -0.18 & -0.21 \\ + \ce{LiH} & 8.02 & 8.21 & 8.22 & 8.25 & 8.15 & 0.29 & -0.20 & -0.27 & -0.27 & -0.27 \\ + \ce{HF} & 16.15 & 17.69 & 16.25 & 16.45 & 16.34 & 0.66 & 0.81 & 0.71 & 0.70 & 0.70 \\ + \ce{Ar} & 15.60 & 16.08 & 15.71 & 15.61 & 15.63 & 2.55 & 2.97 & 2.68 & 2.64 & 2.65 \\ + \ce{H2O} & 12.69 & 13.88 & 12.90 & 12.98 & 12.88 & 0.61 & 0.80 & 0.68 & 0.65 & 0.66 \\ + \ce{LiF} & 11.47 & 12.91 & 11.40 & 11.75 & 11.58 & -0.35 & -0.29 & -0.33 & -0.32 & -0.33 \\ + \ce{HCl} & 12.67 & 12.98 & 12.78 & 12.77 & 12.72 & 0.57 & 0.79 & 0.64 & 0.63 & 0.63 \\ + \ce{BeO} & 9.95 & 10.45 & 9.74 & 10.32 & 10.18 & -2.17 & -1.80 & -2.28 & -2.10 & -2.13 \\ + \ce{CO} & 13.99 & 15.11 & 14.80 & 14.34 & 14.33 & 1.57 & 1.80 & 1.66 & 1.61 & 1.62 \\ + \ce{N2} & 15.54 & 16.68 & 17.10 & 15.93 & 15.91 & 2.37 & 2.20 & 2.10 & 2.10 & 2.10 \\ + \ce{CH4} & 14.39 & 14.83 & 14.76 & 14.67 & 14.63 & 0.65 & 0.79 & 0.70 & 0.68 & 0.68 \\ + \ce{BH3} & 13.31 & 13.59 & 13.68 & 13.62 & 13.59 & 0.09 & 0.81 & 0.46 & 0.29 & 0.30 \\ + \ce{NH3} & 10.91 & 11.69 & 11.21 & 11.18 & 11.10 & 0.61 & 0.80 & 0.68 & 0.66 & 0.66 \\ + \ce{BF} & 11.14 & 11.04 & 11.34 & 11.19 & 11.17 & 0.80 & 1.06 & 0.90 & 0.87 & 0.87 \\ + \ce{BN} & 12.05 & 11.55 & 11.76 & 11.89 & 11.90 & -3.02 & -2.97 & -3.90 & -3.41 & -3.44 \\ + \ce{SH2} & 10.39 & 10.49 & 10.51 & 10.50 & 10.45 & 0.52 & 0.76 & 0.60 & 0.58 & 0.59 \\ + \ce{F2} & 15.81 & 18.15 & 16.35 & 16.27 & 16.22 & -0.32 & 1.71 & 0.53 & -0.10 & -0.07 \\ + \ce{MgO} & 7.97 & 8.75 & 8.40 & 8.54 & 8.36 & -1.54 & -1.40 & -1.64 & -1.72 & -1.71 \\ + \ce{O3} & 12.85 & 13.29 & 13.56 & 13.34 & 13.27 & -1.82 & -1.32 & -2.19 & -2.22 & -2.17 \\ \ce{C2H2} & & & & & & & & & & \\ \ce{NCH} & & & & & & & & & & \\ \ce{B2H6} & & & & & & & & & & \\ @@ -798,29 +813,15 @@ Therefore, it seems that the effect of the TDA cannot be systematically predicte & \mcc{$\Delta\text{CCSD(T)}$} & \mcc{HF} & \mcc{$G_0W_0$@HF} & \mcc{qs$GW$} & \mcc{SRg-qs$GW$} & \mcc{$\Delta\text{CCSD(T)}$} & \mcc{HF} & \mcc{$G_0W_0$@HF} & \mcc{qs$GW$} & \mcc{SRg-qs$GW$} \\ & \mcc{(Reference)} & & \mcc{$\eta=\num{e-3}$} & \mcc{$\eta=\num{e-1}$} & \mcc{$s=\num{e2}$} & \mcc{(Reference)} & & \mcc{$\eta=\num{e-3}$} & \mcc{$\eta=\num{e-1}$} & \mcc{$s=\num{e2}$} \\ \hline - MSE & & 0.64 & 0.26 & 0.24 & 0.17 \\ - MAE & & 0.74 & 0.32 & 0.25 & 0.19 \\ - SDE & & 0.71 & 0.39 & 0.18 & 0.15 \\ - Min & & -0.50 & -0.29 & -0.16 & -0.15 \\ - Max & & 2.35 & 1.56 & 0.56 & 0.42 \\ + MSE & & 0.64 & 0.26 & 0.24 & 0.17 & & -0.30 & -0.02 & 0.00 & 0.00 \\ + MAE & & 0.74 & 0.32 & 0.25 & 0.19 & & 0.32 & 0.19 & 0.11 & 0.12 \\ + SDE & & 0.71 & 0.39 & 0.18 & 0.15 & & 0.43 & 0.31 & 0.17 & 0.17 \\ + Min & & -0.50 & -0.29 & -0.16 & -0.15 & & -2.03 & -0.85 & -0.22 & -0.25 \\ + Max & & 2.35 & 1.56 & 0.56 & 0.42 & & 0.17 & 0.88 & 0.41 & 0.42 \\ \end{tabular} \end{ruledtabular} \end{table*} -%%%%%%%%%%%%%%%%%%%%%% -\subsection{Statistical analysis} -\label{sec:SRG_vs_Sym} -%%%%%%%%%%%%%%%%%%%%%% - -%%% FIG 4 %%% -\begin{figure*} - \includegraphics[width=\linewidth]{fig4.pdf} - \caption{ - Histogram of the errors (with respect to $\Delta$CCSD(T)) for the first ionization potential calculated using HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. - \label{fig:fig4}} -\end{figure*} -%%% %%% %%% %%% - 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 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. @@ -900,45 +901,45 @@ The values of the IP that could be converged for $\eta=0.01$ can vary between $1 % \end{ruledtabular} % \end{table} -\begin{table} - \caption{First electron attachment in eV calculated using $\Delta$CCSD(T) (reference), HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. The statistical descriptors are computed for the errors with respect to the reference.} - \label{tab:tab2} - \begin{ruledtabular} - \begin{tabular}{lddddd} - Mol. & \mcc{$\Delta\text{CCSD(T)}$} & \mcc{HF} & \mcc{$G_0W_0$@HF} & \mcc{qs$GW$} & \mcc{SRg-qs$GW$} \\ - & & & \mcc{$\eta=\num{e-3}$} & \mcc{$\eta=\num{e-1}$} & \mcc{$s=\num{e2}$} \\ - \hline - \ce{He} & 2.66 & 2.70 & 2.66 & 2.66 & 2.66 \\ - \ce{Ne} & 5.09 & 5.47 & 5.25 & 5.19 & 5.19 \\ - \ce{H2} & 1.35 & 1.33 & 1.28 & 1.28 & 1.28 \\ - \ce{Li2} & -0.34 & 0.08 & -0.17 & -0.18 & -0.21 \\ - \ce{LiH} & 0.29 & -0.20 & -0.27 & -0.27 & -0.27 \\ - \ce{HF} & 0.66 & 0.81 & 0.71 & 0.70 & 0.70 \\ - \ce{Ar} & 2.55 & 2.97 & 2.68 & 2.64 & 2.65 \\ - \ce{H2O} & 0.61 & 0.80 & 0.68 & 0.65 & 0.66 \\ - \ce{LiF} & -0.35 & -0.29 & -0.33 & -0.32 & -0.33 \\ - \ce{HCl} & 0.57 & 0.79 & 0.64 & 0.63 & 0.63 \\ - \ce{BeO} & -2.17 & -1.80 & -2.28 & -2.10 & -2.13 \\ - \ce{CO} & 1.57 & 1.80 & 1.66 & 1.61 & 1.62 \\ - \ce{N2} & 2.37 & 2.20 & 2.10 & 2.10 & 2.10 \\ - \ce{CH4} & 0.65 & 0.79 & 0.70 & 0.68 & 0.68 \\ - \ce{BH3} & 0.09 & 0.81 & 0.46 & 0.29 & 0.30 \\ - \ce{NH3} & 0.61 & 0.80 & 0.68 & 0.66 & 0.66 \\ - \ce{BF} & 0.80 & 1.06 & 0.90 & 0.87 & 0.87 \\ - \ce{BN} & -3.02 & -2.97 & -3.90 & -3.41 & -3.44 \\ - \ce{SH2} & 0.52 & 0.76 & 0.60 & 0.58 & 0.59 \\ - \ce{F2} & -0.32 & 1.71 & 0.53 & -0.10 & -0.07 \\ - \ce{MgO} & -1.54 & -1.40 & -1.64 & -1.72 & -1.71 \\ - \ce{O3} & -1.82 & -1.32 & -2.19 & -2.22 & -2.17 \\ - \hline - MSE & & -0.30 & -0.02 & 0.00 & 0.00 \\ - MAE & & 0.32 & 0.19 & 0.11 & 0.12 \\ - SDE & & 0.43 & 0.31 & 0.17 & 0.17 \\ - Min & & -2.03 & -0.85 & -0.22 & -0.25 \\ - Max & & 0.17 & 0.88 & 0.41 & 0.42 \\ - \end{tabular} - \end{ruledtabular} -\end{table} +% \begin{table} +% \caption{First electron attachment in eV calculated using $\Delta$CCSD(T) (reference), HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. The statistical descriptors are computed for the errors with respect to the reference.} +% \label{tab:tab2} +% \begin{ruledtabular} +% \begin{tabular}{lddddd} +% Mol. & \mcc{$\Delta\text{CCSD(T)}$} & \mcc{HF} & \mcc{$G_0W_0$@HF} & \mcc{qs$GW$} & \mcc{SRg-qs$GW$} \\ +% & & & \mcc{$\eta=\num{e-3}$} & \mcc{$\eta=\num{e-1}$} & \mcc{$s=\num{e2}$} \\ +% \hline +% \ce{He} & 2.66 & 2.70 & 2.66 & 2.66 & 2.66 \\ +% \ce{Ne} & 5.09 & 5.47 & 5.25 & 5.19 & 5.19 \\ +% \ce{H2} & 1.35 & 1.33 & 1.28 & 1.28 & 1.28 \\ +% \ce{Li2} & -0.34 & 0.08 & -0.17 & -0.18 & -0.21 \\ +% \ce{LiH} & 0.29 & -0.20 & -0.27 & -0.27 & -0.27 \\ +% \ce{HF} & 0.66 & 0.81 & 0.71 & 0.70 & 0.70 \\ +% \ce{Ar} & 2.55 & 2.97 & 2.68 & 2.64 & 2.65 \\ +% \ce{H2O} & 0.61 & 0.80 & 0.68 & 0.65 & 0.66 \\ +% \ce{LiF} & -0.35 & -0.29 & -0.33 & -0.32 & -0.33 \\ +% \ce{HCl} & 0.57 & 0.79 & 0.64 & 0.63 & 0.63 \\ +% \ce{BeO} & -2.17 & -1.80 & -2.28 & -2.10 & -2.13 \\ +% \ce{CO} & 1.57 & 1.80 & 1.66 & 1.61 & 1.62 \\ +% \ce{N2} & 2.37 & 2.20 & 2.10 & 2.10 & 2.10 \\ +% \ce{CH4} & 0.65 & 0.79 & 0.70 & 0.68 & 0.68 \\ +% \ce{BH3} & 0.09 & 0.81 & 0.46 & 0.29 & 0.30 \\ +% \ce{NH3} & 0.61 & 0.80 & 0.68 & 0.66 & 0.66 \\ +% \ce{BF} & 0.80 & 1.06 & 0.90 & 0.87 & 0.87 \\ +% \ce{BN} & -3.02 & -2.97 & -3.90 & -3.41 & -3.44 \\ +% \ce{SH2} & 0.52 & 0.76 & 0.60 & 0.58 & 0.59 \\ +% \ce{F2} & -0.32 & 1.71 & 0.53 & -0.10 & -0.07 \\ +% \ce{MgO} & -1.54 & -1.40 & -1.64 & -1.72 & -1.71 \\ +% \ce{O3} & -1.82 & -1.32 & -2.19 & -2.22 & -2.17 \\ +% \hline +% MSE & & -0.30 & -0.02 & 0.00 & 0.00 \\ +% MAE & & 0.32 & 0.19 & 0.11 & 0.12 \\ +% SDE & & 0.43 & 0.31 & 0.17 & 0.17 \\ +% Min & & -2.03 & -0.85 & -0.22 & -0.25 \\ +% Max & & 0.17 & 0.88 & 0.41 & 0.42 \\ +% \end{tabular} +% \end{ruledtabular} +% \end{table} %%% FIG 6 %%% \begin{figure*}