diff --git a/Manuscript/SRGGW.bib b/Manuscript/SRGGW.bib index f16f32a..1fc760b 100644 --- a/Manuscript/SRGGW.bib +++ b/Manuscript/SRGGW.bib @@ -78,14 +78,12 @@ date-added = {2023-01-30 22:12:16 +0100}, date-modified = {2023-01-30 22:12:32 +0100}, doi = {10.1021/acs.jctc.9b00353}, - eprint = {https://doi.org/10.1021/acs.jctc.9b00353}, journal = {J. Chem. Theory Comput.}, number = {8}, pages = {4399-4414}, title = {Improving the Efficiency of the Multireference Driven Similarity Renormalization Group via Sequential Transformation, Density Fitting, and the Noninteracting Virtual Orbital Approximation}, volume = {15}, - year = {2019}, - bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b00353}} + year = {2019}} @article{ChenyangLi_2021, author = {Li,Chenyang and Evangelista,Francesco A.}, @@ -106,28 +104,24 @@ date-added = {2023-01-30 22:09:49 +0100}, date-modified = {2023-01-30 22:10:02 +0100}, doi = {10.1021/acs.jctc.1c00980}, - eprint = {https://doi.org/10.1021/acs.jctc.1c00980}, journal = {J. Chem. Theory Comput.}, number = {12}, pages = {7666-7681}, title = {Analytic Energy Gradients for the Driven Similarity Renormalization Group Multireference Second-Order Perturbation Theory}, volume = {17}, - year = {2021}, - bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.1c00980}} + year = {2021}} @article{Wang_2023, author = {Wang, Meng and Fang, Wei-Hai and Li, Chenyang}, date-added = {2023-01-30 22:07:40 +0100}, date-modified = {2023-01-30 22:07:50 +0100}, doi = {10.1021/acs.jctc.2c00966}, - eprint = {https://doi.org/10.1021/acs.jctc.2c00966}, journal = {J. Chem. Theory Comput.}, number = {1}, pages = {122-136}, title = {Assessment of State-Averaged Driven Similarity Renormalization Group on Vertical Excitation Energies: Optimal Flow Parameters and Applications to Nucleobases}, volume = {19}, - year = {2023}, - bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.2c00966}} + year = {2023}} @misc{Scott_2023, author = {Scott, Charles J. C. and Backhouse, Oliver J. and Booth, George H.}, @@ -166,7 +160,6 @@ date-added = {2023-01-30 15:45:22 +0100}, date-modified = {2023-01-30 15:45:39 +0100}, doi = {10.1021/acs.jctc.7b00586}, - eprint = {https://doi.org/10.1021/acs.jctc.7b00586}, journal = {J. Chem. Theory Comput.}, number = {10}, pages = {4765-4778}, @@ -386,14 +379,12 @@ date-added = {2023-01-30 13:59:42 +0100}, date-modified = {2023-01-30 14:00:00 +0100}, doi = {10.1021/acs.jctc.2c00617}, - eprint = {https://doi.org/10.1021/acs.jctc.2c00617}, journal = {J. Chem. Theory Comput.}, number = {12}, pages = {7570-7585}, title = {Benchmark of GW Methods for Core-Level Binding Energies}, volume = {18}, - year = {2022}, - bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.2c00617}} + year = {2022}} @incollection{CsanakBook, author = {Csanak, Gy and Taylor, HS and Yaris, Robert}, @@ -471,50 +462,42 @@ bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0009261494011834}, bdsk-url-2 = {https://doi.org/10.1016/0009-2614(94)01183-4}} -@article{Frosini_2022c, - author = {M. Frosini and T. Duguet and J.-P. Ebran and B. Bally and H. Hergert and T. R. Rodr{\'{\i}}guez and R. Roth and J. M. Yao and V. Som{\`{a}}}, - date-added = {2023-01-20 09:45:17 +0100}, - date-modified = {2023-01-20 09:45:37 +0100}, - doi = {10.1140/epja/s10050-022-00694-x}, - journal = {Eur. Phys. J. A}, - month = apr, - number = {4}, - publisher = {Springer Science and Business Media {LLC}}, - title = {Multi-reference many-body perturbation theory for nuclei}, - url = {https://doi.org/10.1140/epja/s10050-022-00694-x}, - volume = {58}, - year = {2022}, - bdsk-url-1 = {https://doi.org/10.1140/epja/s10050-022-00694-x}} - -@article{Frosini_2022b, - author = {M. Frosini and T. Duguet and J.-P. Ebran and B. Bally and H. Hergert and T. R. Rodr{\'{\i}}guez and R. Roth and J. M. Yao and V. Som{\`{a}}}, - date-added = {2023-01-20 09:44:49 +0100}, - date-modified = {2023-01-20 09:45:46 +0100}, - doi = {10.1140/epja/s10050-022-00694-x}, - journal = {Eur. Phys. J. A}, - month = apr, - number = {4}, - publisher = {Springer Science and Business Media {LLC}}, - title = {Multi-reference many-body perturbation theory for nuclei}, - url = {https://doi.org/10.1140/epja/s10050-022-00694-x}, - volume = {58}, - year = {2022}, - bdsk-url-1 = {https://doi.org/10.1140/epja/s10050-022-00694-x}} +@article{Frosini_2022, + title = {Multi-Reference Many-Body Perturbation Theory for Nuclei}, + author = {Frosini, M. and Duguet, T. and Ebran, J.-P. and Som{\`a}, V.}, + year = {2022}, + journal = {Eur. Phys. J. A}, + volume = {58}, + number = {4}, + pages = {62}, + issn = {1434-601X}, + doi = {10.1140/epja/s10050-022-00692-z} +} @article{Frosini_2022a, - author = {M. Frosini and T. Duguet and J.-P. Ebran and V. Som{\`{a}}}, - date-added = {2023-01-20 09:44:22 +0100}, - date-modified = {2023-01-20 09:45:43 +0100}, - doi = {10.1140/epja/s10050-022-00692-z}, - journal = {Eur. Phys. J. A}, - month = apr, - number = {4}, - publisher = {Springer Science and Business Media {LLC}}, - title = {Multi-reference many-body perturbation theory for nuclei}, - url = {https://doi.org/10.1140/epja/s10050-022-00692-z}, - volume = {58}, - year = {2022}, - bdsk-url-1 = {https://doi.org/10.1140/epja/s10050-022-00692-z}} + title = {Multi-Reference Many-Body Perturbation Theory for Nuclei}, + author = {Frosini, M. and Duguet, T. and Ebran, J.-P. and Bally, B. and Mongelli, T. and Rodr{\'i}guez, T. R. and Roth, R. and Som{\`a}, V.}, + year = {2022}, + journal = {Eur. Phys. J. A}, + volume = {58}, + number = {4}, + pages = {63}, + issn = {1434-601X}, + doi = {10.1140/epja/s10050-022-00693-y} +} + +@article{Frosini_2022b, + title = {Multi-Reference Many-Body Perturbation Theory for Nuclei}, + author = {Frosini, M. and Duguet, T. and Ebran, J.-P. and Bally, B. and Hergert, H. and Rodr{\'i}guez, T. R. and Roth, R. and Yao, J. M. and Som{\`a}, V.}, + year = {2022}, + journal = {Eur. Phys. J. A}, + volume = {58}, + number = {4}, + pages = {64}, + issn = {1434-601X}, + doi = {10.1140/epja/s10050-022-00694-x} +} + @misc{Tolle_2022, archiveprefix = {arXiv}, @@ -1920,8 +1903,7 @@ pages = {6203-6210}, title = {Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation}, volume = {12}, - year = {2021}, - bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.1c01723}} + year = {2021}} @article{Scuseria_2013, author = {Scuseria,Gustavo E. and Henderson,Thomas M. and Bulik,Ireneusz W.}, @@ -1945,9 +1927,7 @@ pages = {012809}, title = {Hydrogen-molecule spectrum by the many-body $GW$ approximation and the Bethe-Salpeter equation}, volume = {103}, - year = {2021}, - bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.103.012809}, - bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.103.012809}} + year = {2021}} @article{Vitale_2020, author = {Vitale, Eugenio and Alavi, Ali and Kats, Daniel}, @@ -2192,7 +2172,7 @@ note={Gaussian Inc. Wallingford CT} title = {Coupled-Cluster Techniques for Computational Chemistry: {{The CFOUR}} Program Package}, author = {Matthews, Devin A. and Cheng, Lan and Harding, Michael E. and Lipparini, Filippo and Stopkowicz, Stella and Jagau, Thomas-C. and Szalay, P{\'e}ter G. and Gauss, J{\"u}rgen and Stanton, John F.}, year = {2020}, - journal = {The Journal of Chemical Physics}, + journal = {J. Chem. Phys.}, volume = {152}, number = {21}, pages = {214108}, @@ -14955,7 +14935,7 @@ note={Gaussian Inc. Wallingford CT} author = {Surj{\'a}n, P. R. and Szabados, {\'A}.}, doi = {10.1063/1.471814}, issn = {0021-9606}, - journal = {The Journal of Chemical Physics}, + journal = {J. Chem. Phys.}, number = {9}, pages = {3320--3324}, title = {Damping of Perturbation Corrections in Quasidegenerate Situations}, @@ -16464,7 +16444,7 @@ note={Gaussian Inc. Wallingford CT} author = {{Ismail-Beigi}, Sohrab}, doi = {10.1088/1361-648X/aa7803}, issn = {0953-8984}, - journal = {Journal of Physics: Condensed Matter}, + journal = {J. Phys. Cond. Mat.}, number = {38}, pages = {385501}, title = {Justifying Quasiparticle Self-Consistent Schemes via Gradient Optimization in {{Baym}}\textendash{{Kadanoff}} Theory}, @@ -16476,7 +16456,7 @@ note={Gaussian Inc. Wallingford CT} author = {Bruneval, Fabien and Marques, Miguel A. L.}, doi = {10.1021/ct300835h}, issn = {1549-9618}, - journal = {Journal of Chemical Theory and Computation}, + journal = {J. Chem. Theory Comput.}, number = {1}, pages = {324--329}, title = {Benchmarking the {{Starting Points}} of the {{GW Approximation}} for {{Molecules}}}, @@ -17127,7 +17107,6 @@ note={Gaussian Inc. Wallingford CT} @article{Tiago_2006, author = {Tiago, Murilo L. and Chelikowsky, James R.}, doi = {10.1103/PhysRevB.73.205334}, - file = {/Users/loos/Zotero/storage/3YTWEDNW/Tiago_2006.pdf}, issn = {1098-0121, 1550-235X}, journal = {Phys. Rev. B}, language = {en}, @@ -17135,8 +17114,8 @@ note={Gaussian Inc. Wallingford CT} number = {20}, title = {Optical Excitations in Organic Molecules, Clusters, and Defects Studied by First-Principles {{Green}}'s Function Methods}, volume = {73}, - year = {2006}, - bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.73.205334}} + year = {2006} + } @article{Ou_2016, author = {Ou, Qi and Subotnik, Joseph E.}, diff --git a/Manuscript/SRGGW.tex b/Manuscript/SRGGW.tex index ac95647..2086708 100644 --- a/Manuscript/SRGGW.tex +++ b/Manuscript/SRGGW.tex @@ -44,7 +44,9 @@ showstringspaces=false, showtabs=false, tabsize=2 -} + } + + \newcolumntype{d}{D{.}{.}{-1}} \lstset{style=mystyle} @@ -134,7 +136,7 @@ In particular, we focus here on the possibility of curing the qs$GW$ convergence The SRG formalism has been developed independently by Wegner \cite{Wegner_1994} and Glazek and Wilson \cite{Glazek_1993,Glazek_1994} in the context of condensed matter systems and light-front quantum field theories, respectively. This formalism has been introduced in quantum chemistry by White \cite{White_2002} before being explored in more detail by Evangelista and coworkers in the context of multi-reference electron correlation theories. \cite{Evangelista_2014b,ChenyangLi_2015, ChenyangLi_2016,ChenyangLi_2017,ChenyangLi_2018,ChenyangLi_2019a,Zhang_2019,ChenyangLi_2021,Wang_2021,Wang_2023} The SRG has also been successful in the context of nuclear structure theory, where it was first developed as a mature computational tool thanks to the work of several research groups. -\cite{Bogner_2007,Tsukiyama_2011,Tsukiyama_2012,Hergert_2013,Hergert_2016,Frosini_2022a,Frosini_2022b,Frosini_2022c} +\cite{Bogner_2007,Tsukiyama_2011,Tsukiyama_2012,Hergert_2013,Hergert_2016,Frosini_2022,Frosini_2022a,Frosini_2022b} See Ref.~\onlinecite{Hergert_2016a} for a recent review in this field. The SRG transformation aims at decoupling an internal (or reference) space from an external space while incorporating information about their coupling in the reference space. @@ -500,15 +502,6 @@ It is worth noting the close similarity of the first-order elements with the one \subsection{Second-order matrix elements} % ///////////////////////////% -%%% FIG 1 %%% -\begin{figure*} - \includegraphics[width=0.8\linewidth]{fig1.pdf} - \caption{ - Functional form of the qs$GW$ self-energy (left) for $\eta = 1$ and the SRG-qs$GW$ self-energy (right) for $s = 1/(2\eta^2) = 1/2$. - \label{fig:plot}} -\end{figure*} -%%% %%% %%% %%% - The second-order renormalized quasiparticle equation is given by \begin{equation} \label{eq:GW_renorm} @@ -529,8 +522,8 @@ with elements \label{eq:SRG-GW_selfenergy} \begin{split} \widetilde{\bSig}_{pq}(\omega; s) - &= \sum_{i\nu} \frac{W_{p,i\nu} W_{q,i\nu}}{\omega - \epsilon_i + \Omega_{\nu} - \ii \eta} e^{-(\Delta_{pi\nu}^2 + \Delta_{qi\nu}^2) s} \\ - &+ \sum_{a\nu} \frac{W_{p,a\nu}W_{q,a\nu}}{\omega - \epsilon_a - \Omega_{\nu} + \ii \eta}e^{-(\Delta_{pa\nu}^2 + \Delta_{qa\nu}^2) s}. + &= \sum_{i\nu} \frac{W_{p,i\nu} W_{q,i\nu}}{\omega - \epsilon_i + \Omega_{\nu}} e^{-(\Delta_{pi\nu}^2 + \Delta_{qi\nu}^2) s} \\ + &+ \sum_{a\nu} \frac{W_{p,a\nu}W_{q,a\nu}}{\omega - \epsilon_a - \Omega_{\nu}}e^{-(\Delta_{pa\nu}^2 + \Delta_{qa\nu}^2) s}. \end{split} \end{equation} @@ -546,6 +539,16 @@ which can be solved by simple integration along with the initial condition $\bF^ \times \qty[1 - e^{-(\Delta_{pr\nu}^2 + \Delta_{qr\nu}^2) s}]. \end{multline} +%%% FIG 1 %%% +\begin{figure} + \centering + \includegraphics[width=\linewidth]{flow} + \caption{ + \ant{Schematic} evolution of the quasiparticle equation as a function of the flow parameter $s$ in the case of the dynamic SRG-$GW$ flow (magenta) and the static SRG-qs$GW$ flow (cyan). \ANT{Maybe we should replace dynamic by full?} + \label{fig:flow}} +\end{figure} +%%% %%% %%% %%% + At $s=0$, the second-order correction vanishes, hence giving \begin{equation} \lim_{s\to0} \widetilde{\bF}(s) = \bF^{(0)}. @@ -563,13 +566,12 @@ Therefore, the SRG flow continuously transforms the dynamical self-energy $\wide As illustrated in Fig.~\ref{fig:flow}, this transformation is done gradually starting from the states that have the largest denominators in Eq.~\eqref{eq:static_F2}. %%% FIG 2 %%% -\begin{figure} - \centering - \includegraphics[width=\linewidth]{flow} +\begin{figure*} + \includegraphics[width=0.8\linewidth]{fig1.pdf} \caption{ - Evolution of the quasiparticle equation as a function of the flow parameter $s$ in the case of the dynamic SRG-$GW$ flow (magenta) and the static SRG-qs$GW$ flow (cyan). - \label{fig:flow}} -\end{figure} + Functional form of the qs$GW$ self-energy (left) for $\eta = 1$ and the SRG-qs$GW$ self-energy (right) for $s = 1/(2\eta^2) = 1/2$. + \label{fig:plot}} +\end{figure*} %%% %%% %%% %%% %///////////////////////////% @@ -717,9 +719,9 @@ Therefore, it seems that the effect of the TDA can not be systematically predict \caption{First ionization potential 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:tab1} \begin{ruledtabular} - \begin{tabular}{lccccc} - Mol. & $\Delta$CCSD(T) & HF & $G_0W_0$@HF & qs$GW$ & SRG-qs$GW$ \\ - & & & $\eta=\num{e-3}$ & $\eta=\num{e-1}$ & $s=\num{e2}$ \\ + \begin{tabular}{lddddd} + Mol. & \multicolumn{1}{c}{$\Delta\text{CCSD(T)}$} & \multicolumn{1}{c}{HF} & \multicolumn{1}{c}{$G_0W_0$@HF} & \multicolumn{1}{c}{qs$GW$} & \multicolumn{1}{c}{SRg-qs$GW$} \\ + & & & \multicolumn{1}{c}{$\eta=\num{e-3}$} & \multicolumn{1}{c}{$\eta=\num{e-1}$} & \multicolumn{1}{c}{$s=\num{e2}$} \\ \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 \\ @@ -785,65 +787,119 @@ Of course these are slight improvements but this is done with no additional comp 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. +%%% FIG 5 %%% +\begin{figure} + \centering + \includegraphics[width=\linewidth]{fig5.pdf} + \caption{ + Temporary figure about convergence + \label{fig:fig5}} +\end{figure} +%%% %%% %%% %%% + In addition to this improvement of the accuracy, the SRG-qs$GW$ scheme is also much easier to converge than its qs$GW$ counterpart. -Indeed, up to $s=10^3$ self-consistency of the SRG-qs$GW$ scheme can be converged without any problems. -For $s=10^4$, convergence could not be attained for the following molecules \ANT{waiting for calculation}. -On the other hand, the qs$GW$ convergence is much more erratic. +Indeed, up to $s=10^3$ self-consistency can be attained without any problems (mean and max number of iterations = n for s=100). +For $s=10^4$, convergence could not be attained for 12 molecules out of 22, meaning that some intruder states were included in the static correction for this value of $s$. +This is illustrated in the case of \ce{H2O} in the upper panel Fig. +However, this is not a problem as the MAE is already well converged before the intruder states are added to the SRG-qs$GW$ static self-energy (lower panel). + +On the other hand, the qs$GW$ convergence with respect to $\eta$ is more difficult to evaluate. The whole set considered in this work could be converged for $\eta=0.1$. -However, if we decrease $\eta$ then self-consistency could not be attained for the whole set of molecules using the black-box convergence parameters (see Sec.~\ref{sec:comp_det}). -Unfortunately, the convergence of the IP is not as tight as in the SRG case because for $\eta=0.01$ the values of the IP that could be converged can vary between $10^{-3}$ and $10^{-1}$ with respect to $\eta=0.1$. +However, as soon as we decrease $\eta$ self-consistency could not be attained for the whole set of molecules using the black-box convergence parameters (see Sec.~\ref{sec:comp_det}). +Unfortunately, the convergence of the IP is not as tight as in the SRG case. +The values of the IP that could be converged for $\eta=0.01$ can vary between $10^{-3}$ and $10^{-1}$ with respect to $\eta=0.1$. -We will now gauge the effect of the TDA for the screening on the accuracy of the various methods considered previously. +% \begin{table} +% \caption{First ionization potential in eV calculated using $G_0W_0^{\text{TDA}}$@HF, qs$GW^{\text{TDA}}$ and SRG-qs$GW^{\text{TDA}}$. The statistical descriptors are computed for the errors with respect to the reference.} +% \label{tab:tab1} +% \begin{ruledtabular} +% \begin{tabular}{lddd} +% Mol. & \multicolumn{1}{c}{$G_0W_0^{\text{TDA}}$@HF} & \multicolumn{1}{c}{qs$GW^{\text{TDA}}$} & \multicolumn{1}{c}{SRG-qs$GW^{\text{TDA}}$} \\ +% & \multicolumn{1}{c}{$\eta=\num{e-3}$} & \multicolumn{1}{c}{$\eta=\num{5e-2}$} & \multicolumn{1}{c}{$s=\num{e2}$} \\ +% \hline +% \ce{He} & 24.45 & 24.48 & 24.39 \\ +% \ce{Ne} & 20.85 & 21.23 & 20.92 \\ +% \ce{H2} & 16.53 & 16.46 & 16.50 \\ +% \ce{Li2} & 5.45 & 5.50 & 5.46 \\ +% \ce{LiH} & 8.14 & 8.17 & 8.05 \\ +% \ce{HF} & 15.64 & 15.79 & 15.66 \\ +% \ce{Ar} & 15.60 & 15.42 & 15.46 \\ +% \ce{H2O} & 12.42 & 12.40 & 12.31 \\ +% \ce{LiF} & 10.75 & 11.02 & 10.85 \\ +% \ce{HCl} & 12.70 & 12.65 & 12.59 \\ +% \ce{BeO} & 9.33 & 10.21 & 10.05 \\ +% \ce{CO} & 14.60 & 13.82 & 13.84 \\ +% \ce{N2} & 17.36 & 15.15 & 15.21 \\ +% \ce{CH4} & 14.67 & 14.50 & 14.47 \\ +% \ce{BH3} & 13.66 & 13.57 & 13.54 \\ +% \ce{NH3} & 10.91 & 10.75 & 10.68 \\ +% \ce{BF} & 11.38 & 11.11 & 11.12 \\ +% \ce{BN} & 11.85 & 12.05 & 12.04 \\ +% \ce{SH2} & 10.47 & 10.44 & 10.38 \\ +% \ce{F2} & 15.55 & 15.23 & 15.22 \\ +% \ce{MgO} & 8.10 & 7.76 & 7.58 \\ +% \ce{O3} & 13.68 & 12.22 & 12.22 \\ +% \hline +% MSE & 0.07 & -0.12 & -0.18 \\ +% MAE & 0.37 & 0.22 & 0.25 \\ +% SDE & 0.55 & 0.26 & 0.27 \\ +% Min & -0.72 & -0.63 & -0.63 \\ +% Max & 1.82 & 0.26 & 0.22 \\ +% \end{tabular} +% \end{ruledtabular} +% \end{table} -Part on approximation and correction for W: -TDHF G0W0 not that bad in GW100 but bad in GW22, qsGW TDHF even worse even with SRG, -Maybe that would be nice to add SRG G0W0 to see if it mitigates the outliers of GW20 cf Bruneval 2021, -That would be nice to understand clearly why qsGWTDHF is worse (screening, gap, etc) +Part on EA: +MgO- does not converge yet but when we have it same analysis as Table 1 and Fig 4 but for the EA \begin{table} - \caption{First ionization potential in eV calculated using $G_0W_0^{\text{TDA}x}$@HF, qs$GW^{\text{TDA}}$ and SRG-qs$GW^{\text{TDA}}$. The statistical descriptors are computed for the errors with respect to the reference.} + \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:tab1} \begin{ruledtabular} - \begin{tabular}{lccc} - Mol. & $G_0W_0^{\text{TDA}}$@HF & qs$GW^{\text{TDA}}$ & SRG-qs$GW^{\text{TDA}}$ \\ - & $\eta=\num{e-3}$ & $\eta=\num{5e-2}$ & $s=\num{e2}$ \\ - \hline - \ce{He} & 24.45 & 24.48 & 24.39 \\ - \ce{Ne} & 20.85 & 21.23 & 20.92 \\ - \ce{H2} & 16.53 & 16.46 & 16.50 \\ - \ce{Li2} & 5.45 & 5.50 & 5.46 \\ - \ce{LiH} & 8.14 & 8.17 & 8.05 \\ - \ce{HF} & 15.64 & 15.79 & 15.66 \\ - \ce{Ar} & 15.60 & 15.42 & 15.46 \\ - \ce{H2O} & 12.42 & 12.40 & 12.31 \\ - \ce{LiF} & 10.75 & 11.02 & 10.85 \\ - \ce{HCl} & 12.70 & 12.65 & 12.59 \\ - \ce{BeO} & 9.33 & 10.21 & 10.05 \\ - \ce{CO} & 14.60 & 13.82 & 13.84 \\ - \ce{N2} & 17.36 & 15.15 & 15.21 \\ - \ce{CH4} & 14.67 & 14.50 & 14.47 \\ - \ce{BH3} & 13.66 & 13.57 & 13.54 \\ - \ce{NH3} & 10.91 & 10.75 & 10.68 \\ - \ce{BF} & 11.38 & 11.11 & 11.12 \\ - \ce{BN} & 11.85 & 12.05 & 12.04 \\ - \ce{SH2} & 10.47 & 10.44 & 10.38 \\ - \ce{F2} & 15.55 & 15.23 & 15.22 \\ - \ce{MgO} & 8.10 & 7.76 & 7.58 \\ - \ce{O3} & 13.68 & 12.22 & 12.22 \\ - \hline - MSE & 0.07 & -0.12 & -0.18 \\ - MAE & 0.37 & 0.22 & 0.25 \\ - SDE & 0.55 & 0.26 & 0.27 \\ - Min & -0.72 & -0.63 & -0.63 \\ - Max & 1.82 & 0.26 & 0.22 \\ - \hline + \begin{tabular}{lddddd} + Mol. & \multicolumn{1}{c}{$\Delta\text{CCSD(T)}$} & \multicolumn{1}{c}{HF} & \multicolumn{1}{c}{$G_0W_0$@HF} & \multicolumn{1}{c}{qs$GW$} & \multicolumn{1}{c}{SRg-qs$GW$} \\ + & & & \multicolumn{1}{c}{$\eta=\num{e-3}$} & \multicolumn{1}{c}{$\eta=\num{e-1}$} & \multicolumn{1}{c}{$s=\num{e2}$} \\ + \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} -Part on EA: -MgO- does not converge yet but when we have it same analysis as Table 1 and Fig 4 but for the EA +%%% FIG 6 %%% +\begin{figure*} + \includegraphics[width=\linewidth]{fig6.pdf} + \caption{ + Histogram of the errors (with respect to $\Delta$CCSD(T)) for the first electron attachment calculated using HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. + \label{fig:fig4}} +\end{figure*} +%%% %%% %%% %%% %=================================================================% \section{Conclusion} diff --git a/Manuscript/fig4.pdf b/Manuscript/fig4.pdf index d4200d5..c3faac9 100644 Binary files a/Manuscript/fig4.pdf and b/Manuscript/fig4.pdf differ diff --git a/Manuscript/fig5.pdf b/Manuscript/fig5.pdf new file mode 100644 index 0000000..7c51643 Binary files /dev/null and b/Manuscript/fig5.pdf differ diff --git a/Manuscript/fig6.pdf b/Manuscript/fig6.pdf new file mode 100644 index 0000000..6d5267f Binary files /dev/null and b/Manuscript/fig6.pdf differ