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BSE-PES.bib
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BSE-PES.bib
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2020-01-26 20:27:20 +0100
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%% Created for Pierre-Francois Loos at 2020-01-28 17:57:57 +0100
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%% Saved with string encoding Unicode (UTF-8)
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@ -17,7 +17,8 @@
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Pages = {114111},
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Title = {High-Accuracy Extrapolated ab Initio Thermochemistry. III. Additional Improvements and Overview},
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Volume = {128},
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Year = {2008}}
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Year = {2008},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.2835612}}
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@article{dalton,
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Author = {Aidas, Kestutis and Angeli, Celestino and Bak, Keld L. and Bakken, Vebj{\o}rn and Bast, Radovan and Boman, Linus and Christiansen, Ove and Cimiraglia, Renzo and Coriani, Sonia and Dahle, P{\aa}l and Dalskov, Erik K. and Ekstr{\"o}m, Ulf and Enevoldsen, Thomas and Eriksen, Janus J. and Ettenhuber, Patrick and Fern{\'a}ndez, Berta and Ferrighi, Lara and Fliegl, Heike and Frediani, Luca and Hald, Kasper and Halkier, Asger and H{\"a}ttig, Christof and Heiberg, Hanne and Helgaker, Trygve and Hennum, Alf Christian and Hettema, Hinne and Hjerten{\ae}s, Eirik and H{\o}st, Stinne and H{\o}yvik, Ida-Marie and Iozzi, Maria Francesca and Jans{\'\i}k, Branislav and Jensen, Hans J{\o}rgen Aa. and Jonsson, Dan and J{\o}rgensen, Poul and Kauczor, Joanna and Kirpekar, Sheela and Kj{\ae}rgaard, Thomas and Klopper, Wim and Knecht, Stefan and Kobayashi, Rika and Koch, Henrik and Kongsted, Jacob and Krapp, Andreas and Kristensen, Kasper and Ligabue, Andrea and Lutn{\ae}s, Ola B. and Melo, Juan I. and Mikkelsen, Kurt V. and Myhre, Rolf H. and Neiss, Christian and Nielsen, Christian B. and Norman, Patrick and Olsen, Jeppe and Olsen, J{\'o}gvan Magnus H. and Osted, Anders and Packer, Martin J. and Pawlowski, Filip and Pedersen, Thomas B. and Provasi, Patricio F. and Reine, Simen and Rinkevicius, Zilvinas and Ruden, Torgeir A. and Ruud, Kenneth and Rybkin, Vladimir V. and Sa{\l}ek, Pawel and Samson, Claire C. M. and de Mer{\'a}s, Alfredo S{\'a}nchez and Saue, Trond and Sauer, Stephan P. A. and Schimmelpfennig, Bernd and Sneskov, Kristian and Steindal, Arnfinn H. and Sylvester-Hvid, Kristian O. and Taylor, Peter R. and Teale, Andrew M. and Tellgren, Erik I. and Tew, David P. and Thorvaldsen, Andreas J. and Th{\o}gersen, Lea and Vahtras, Olav and Watson, Mark A. and Wilson, David J. D. and Ziolkowski, Marcin and {\AA}gren, Hans},
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@ -216,10 +217,10 @@
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@article{Li_2019,
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Author = {J. Li and N. D. Drummond and P. Schuck and V. Olevano},
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Date-Added = {2020-01-04 20:07:34 +0100},
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Date-Modified = {2020-01-04 20:07:34 +0100},
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Date-Modified = {2020-01-28 17:57:51 +0100},
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Doi = {10.21468/SciPostPhys.6.4.040},
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Journal = {SciPost Phys.},
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Number = {040},
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Pages = {040},
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Title = {Comparing many-body approaches against the helium atom exact solution},
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Volume = {6},
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Year = {2019},
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@ -9506,7 +9507,6 @@
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Date-Added = {2019-10-23 10:00:45 +0200},
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Date-Modified = {2020-01-26 11:17:42 +0100},
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Journal = {arXiv:1912.06459},
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Pages = {},
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Title = {Robust Analytic Continuation Approach to Many-Body GW Calculations},
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Year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5090605}}
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43
BSE-PES.tex
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BSE-PES.tex
@ -440,7 +440,9 @@ Additional graphs for other basis sets can be found in the {\SI}.
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\begin{table*}
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\caption{
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Equilibrium distances (in bohr) of the ground state of diatomic molecules obtained at various levels of theory and basis sets.
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The reference CC3 and corresponding BSE@$G_0W_0$@HF data are highlighted in black and red bold for visual convenience, respectively.}
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The reference CC3 and corresponding BSE@$G_0W_0$@HF data are highlighted in black and red bold for visual convenience, respectively.
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SI stands for singlet instability.
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}
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\label{tab:Req}
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\begin{ruledtabular}
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@ -451,7 +453,7 @@ The reference CC3 and corresponding BSE@$G_0W_0$@HF data are highlighted in blac
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\hline
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CC3 & cc-pVDZ & 1.438 & 3.043 & 3.012 & 2.435 & 2.114 & 2.166 & 2.444 & 2.740 \\
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& cc-pVTZ & 1.403 & 3.011 & 2.961 & 2.413 & 2.079 & 2.143 & 2.392 & 2.669 \\
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& cc-pVQZ &\bb{1.402} &\bb{3.019} & 2.963 & 2.403 & 2.075 & 2.136 & 2.390 & 2.663 \\
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& cc-pVQZ &\bb{1.402} &\bb{3.019} &\bb{2.963} &\bb{2.403} &\bb{2.075} &\bb{2.136} &\bb{2.390} &\bb{2.663} \\
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CCSD & cc-pVDZ & 1.438 & 3.044 & 3.006 & 2.433 & 2.101 & 2.149 & 2.435 & 2.695 \\
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& cc-pVTZ & 1.403 & 3.012 & 2.954 & 2.409 & 2.064 & 2.126 & 2.382 & 2.629 \\
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& cc-pVQZ & 1.402 & 3.020 & 2.953 & 2.398 & 2.059 & 2.118 & 2.118 & 2.621 \\
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& cc-pVTZ & 1.393 & 3.004 & 2.968 & 2.405 & 2.095 & 2.144 & 2.383 & 2.636 \\
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& cc-pVQZ & 1.391 & 3.008 & 2.970 & 2.395 & 2.091 & 2.137 & 2.382 & 2.634 \\
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BSE@{\GOWO}@HF & cc-pVDZ & 1.437 & 3.042 & 3.000 & 2.454 & 2.107 & 2.153 & 2.407 & 2.700 \\
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& cc-pVTZ & 1.404 & 3.023 & glitch & 2.410 & 2.068 & & glitch & glitch \\
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& cc-pVQZ &\rb{1.399} &\rb{3.017} & & & & & & \\
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& cc-pVTZ & 1.404 & 3.023 & glitch & 2.410 & 2.068 & 2.116 & glitch & glitch \\
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& cc-pVQZ &\rb{1.399} &\rb{3.017} &\rb{} &\rb{} &\rb{} &\rb{} &\rb{} &\rb{} \\
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RPA@{\GOWO}@HF & cc-pVDZ & 1.426 & 3.019 & 2.994 & 2.436 & 2.083 & 2.144 & 2.403 & 2.691 \\
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& cc-pVTZ & 1.388 & 3.013 & glitch & 2.408 & 2.065 & & glitch & glitch \\
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& cc-pVTZ & 1.388 & 3.013 & glitch & 2.408 & 2.065 & 2.114 & glitch & glitch \\
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& cc-pVQZ & 1.382 & 3.013 & & & & & & \\
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RPAx@HF & cc-pVDZ & 1.428 & 3.040 & 2.998 & 2.424 & 2.077 & 2.130 & 2.417 & NaN \\
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& cc-pVTZ & 1.395 & 3.003 & 2.971 & 2.400 & <2.060 & & <2.420 & \\
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RPAx@HF & cc-pVDZ & 1.428 & 3.040 & 2.998 & 2.424 & 2.077 & 2.130 & 2.417 & SI \\
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& cc-pVTZ & 1.395 & 3.003 & 2.971 & 2.400 & <2.050 & 2.110 & <2.420 & \\
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& cc-pVQZ & 1.394 & 3.011 & & & & & & \\
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RPA@HF & cc-pVDZ & 1.431 & 3.021 & 2.999 & 2.424 & 2.083 & 2.134 & & 2.623 \\
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& cc-pVTZ & 1.388 & 2.978 & 2.939 & 2.396 & <2.060 & & 2.416 & \\
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& cc-pVQZ & 1.386 & 2.994 & & & & & <2.420 & \\
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RPA@HF & cc-pVDZ & 1.431 & 3.021 & 2.999 & 2.424 & 2.083 & 2.134 & 2.416 & 2.623 \\
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& cc-pVTZ & 1.388 & 2.978 & 2.939 & 2.396 & <2.050 & 2.110 & <2.420 & \\
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& cc-pVQZ & 1.386 & 2.994 & & & & & & \\
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% FROZEN CORE VERSION
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% Method & Basis & \ce{H2} & \ce{LiH}& \ce{LiF}& \ce{N2} & \ce{CO} & \ce{BF} & \ce{F2} & \ce{HCl}\\
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% \hline
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@ -528,11 +530,14 @@ Additional graphs for other basis sets and within the frozen-core approximation
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\end{figure*}
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%%% %%% %%%
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The cases of \ce{LiF} and \ce{HCl} (see Fig.~\ref{fig:PES-LiF-HCl}) are interesting as they corresponds to a strongly polarized bond towards the halogen atoms which are much more electronegative than the first row elements.
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For these ionic bond, the performance of BSE@{\GOWO}@HF are terrific with an almost perfect match to the CC3 curve.
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For \ce{LiF}, the two curves starting to deviate a few tenths of bohr after the equilibrium geometry, but they remain tightly ... for much longer in the case of \ce{HCl}.
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The cases of \ce{LiF} and \ce{HCl} (see Fig.~\ref{fig:PES-LiF-HCl}) are interesting as they corresponds to strongly polarized bonds towards the halogen atoms which are much more electronegative than the first row elements.
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For these ionic bonds, the performance of BSE@{\GOWO}@HF are terrific with an almost perfect match to the CC3 curve.
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For \ce{LiF}, the two curves starting to deviate a few tenths of bohr after the equilibrium geometry, but they remain tightly bound for much longer in the case of \ce{HCl}.
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Maybe surprisingly, BSE@{\GOWO}@HF outperforms both CC2 and CCSD, as well as RPAx@HF by a big margin for these two molecules exhibiting charge transfer.
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However, in the case of \ce{LiF}, the attentive reader would have observed a small glitch in the $GW$-based curves very close to their minimum.
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As observed in Refs.~\cite{vanSetten_2015,Maggio_2017,Loos_2018} and explained in details in Refs.~\cite{Veril_2018,Duchemin_2020}, these irregularities, which makes tricky the location of the minima, are due to ``jumps'' between two distinct solutions of the $GW$ quasiparticle equation.
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Including a broadening via the increasing the value of $\eta$ in the $GW$ self-energy and the screened Coulomb operator soften the problem, but does not remove it completely.
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Note that these irregularities would be genuine discontinuities in the case of {\evGW}. \cite{Veril_2018}
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%%% FIG 2 %%%
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\begin{figure*}
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@ -547,8 +552,7 @@ Additional graphs for other basis sets and within the frozen-core approximation
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%%% %%% %%%
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Let us now look at the isoelectronic series \ce{N2}, \ce{CO}, and \ce{BF}, which have a decreasing bond order (from triple bond to single bond).
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In that case again, the performance of BSE@{\GOWO}@HF are outstanding as shown in Fig.~\ref{fig:PES-N2-CO-BF}.
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In that case again, the performance of BSE@{\GOWO}@HF are outstanding, as shown in Fig.~\ref{fig:PES-N2-CO-BF}, and systematically outperforms both CC2 and CCSD.
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%%% FIG 3 %%%
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\begin{figure*}
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@ -564,6 +568,8 @@ Additional graphs for other basis sets and within the frozen-core approximation
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%%% %%% %%%
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The \ce{F2} molecule is a notoriously difficult case to treat due to the relative weakness of its covalent bond (see Fig.~\ref{fig:PES-F2}).
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Similarly to what we have observed for \ce{LiF} and \ce{BF}, there is an irregularities near the minimum of the {\GOWO}-based curves.
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However, BSE@{\GOWO}@HF is the closest to the CC3 curve
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%%% FIG 4 %%%
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\begin{figure}
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@ -576,7 +582,6 @@ Additional graphs for other basis sets and within the frozen-core approximation
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\end{figure}
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%%% %%% %%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{Conclusion}
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%\label{sec:conclusion}
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@ -588,6 +593,7 @@ This shortcoming, which is entirely due to the quasiparticle nature of the under
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We believe that this central issue must be resolved if one wants to expand the applicability of the present methods.
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In the perspective of developing analytical nuclear gradients within the BSE@$GW$ formalism, we are currently investigating the accuracy of the ACFDT@BSE scheme for excited-state PES.
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We hope to be able to report on this in the near future.
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\titou{We hope to have demonstrated that future developments around $GW$ methods are worthwhile.}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Supporting Information}
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@ -596,11 +602,10 @@ See {\SI} for additional potential energy curves with other basis sets and withi
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%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{acknowledgements}
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PFL would like to thank Julien Toulouse for enlightening discussions about RPA.
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XB is indebted to Valerio Olevano for numerous discussions.
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PFL would like to thank Julien Toulouse for enlightening discussions about RPA, and XB is indebted to Valerio Olevano for numerous discussions.
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This work was performed using HPC resources from GENCI-TGCC (Grant No.~2018-A0040801738) and CALMIP (Toulouse) under allocation 2019-18005.
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Funding from the \textit{``Centre National de la Recherche Scientifique''} is acknowledged.
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This work has been supported through the EUR grant NanoX ANR-17-EURE-0009 in the framework of the \textit{``Programme des Investissements d'Avenir''. }
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This work has been supported through the EUR grant NanoX ANR-17-EURE-0009 in the framework of the \textit{``Programme des Investissements d'Avenir''.}
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\end{acknowledgements}
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%%%%%%%%%%%%%%%%%%%%%%%%
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