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% \centering
% \includegraphics[width=\linewidth]{TOC}
%\end{wrapfigure}
Similar to other electron correlation methods, many-body perturbation theory methods, such as the so-called $GW$ approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set.
This displeasing feature is due to lack of explicit electron-electron terms modeling the infamous ``Kato'' cusp (at the electron-electron coalescence points) and the correlation Coulomb hole around it.
Here, we propose a computationally efficient density-based basis set correction based on short-range correlation density functionals which significantly speed up the convergence of energetics towards the complete basis set limit.
Similar to other electron correlation methods, many-body perturbation theory methods based on Green functions, such as the so-called $GW$ approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set.
This displeasing feature is due to lack of explicit electron-electron terms modeling the infamous Kato's electron-electron cusp and the correlation Coulomb hole around it.
Here, we propose a computationally efficient density-based basis set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics towards the complete basis set limit.
The performance of this density-based correction is illustrated by computing the ionization potentials of the twenty smallest atoms and molecules of the GW100 test set at the perturbative $GW$ (or $G_0W_0$) level using increasingly large basis sets.
We also compute the ionization potentials of the five canonical nucleobase (adenine, cytosine, thymine, guanine and uracil) and show that, here again, a significant improvement is obtained.
We also compute the ionization potentials of the five canonical nucleobase (adenine, cytosine, thymine, guanine, and uracil) and show that, here again, a significant improvement is obtained.
\end{abstract}
\maketitle
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\section{Introduction}
\label{sec:intro}
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The purpose of many-body perturbation theory (MBPT) is to solve the formidable many-body problem by adding the electron-electron Coulomb interaction perturbatively starting from an independent-particle model. \cite{MarReiCep-BOOK-16}
In MBPT, the \textit{screening} of the Coulomb interaction is an essential quantity that is responsible for a rich variety of phenomena that would be otherwise absent (such as quasiparticle satellites and lifetimes). \cite{Aryasetiawan_1998, Onida_2002, Reining_2017}
The purpose of many-body perturbation theory (MBPT) based on Green functions is to solve the formidable many-body problem by adding the electron-electron Coulomb interaction perturbatively starting from an independent-particle model. \cite{MarReiCep-BOOK-16} In this approach, the \textit{screening} of the Coulomb interaction is an essential quantity that is responsible for a rich variety of phenomena that would be otherwise absent (such as quasiparticle satellites and lifetimes). \cite{Aryasetiawan_1998, Onida_2002, Reining_2017}
The so-called {\GW} approximation is the workhorse of MBPT and has a long and successful history in the calculation of the electronic structure of solids. \cite{Aryasetiawan_1998, Onida_2002, Reining_2017}
{\GW} is getting increasingly popular in molecular systems \cite{Blase_2011, Faber_2011, Bruneval_2012, Bruneval_2015, Bruneval_2016, Bruneval_2016a, Boulanger_2014, Blase_2016, Li_2017, Hung_2016, Hung_2017, vanSetten_2015, vanSetten_2018, Ou_2016, Ou_2018, Faber_2014} thanks to efficient implementation relying on plane waves \cite{Marini_2009, Deslippe_2012, Maggio_2017} or local basis functions. \cite{Blase_2011, Blase_2018, Bruneval_2016, vanSetten_2013, Kaplan_2015, Kaplan_2016, Krause_2017, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b}