DNA + abstract
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Data/DNA.dat
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A 73-24-5 -7.265806 -1.211220672617561E-002 -1.385783048793831E-002 -7.748 -7.975 -8.15 -8.33 -8.48
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C 71-30-7 -7.527844 -1.546006861838614E-002 -1.940117174135618E-002 -8.067 -8.287 -8.449 -9.512 -8.94
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G 73-40-5 -6.951933 -1.225096955803263E-002 -1.413179166956595E-002 -7.461 -7.691 -7.872 -8.034 -8.24
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T 65-71-4 -8.019884 -1.231951892771176E-002 -1.437665931379063E-002 -8.489 -8.708 -8.866 -9.081 -9.2
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U 66-22-8 -8.379481 -1.561024372083486E-002 -1.963262364674972E-002 -9.017 -9.223 -9.382 -10.125 -9.68
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@ -1,5 +0,0 @@
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A 73-24-5 -7.619669 -1.188807989121034E-002 -1.347846624909449E-002 -7.748 -7.975 -8.15
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T 65-71-4 -8.430762 -1.213173859277770E-002 -1.403130444037225E-002 -8.489 -8.708 -8.866
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G 73-40-5 -7.314073 -1.205464000600519E-002 -1.378918997228398E-002 -7.461 -7.691 -7.872
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C 71-30-7 -7.971438 -1.309683725056005E-002 -1.554126377782151E-002 -8.067 -8.287 -8.449
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U 66-22-8 -8.814516 -1.240474844370148E-002 -1.441015016892908E-002 -9.017 -9.223 -9.382
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@ -15,6 +15,8 @@
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urlcolor=blue,
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citecolor=blue
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}
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\urlstyle{same}
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\newcommand{\alert}[1]{\textcolor{red}{#1}}
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\definecolor{darkgreen}{HTML}{009900}
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\usepackage[normalem]{ulem}
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@ -176,6 +178,8 @@
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% \centering
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% \includegraphics[width=\linewidth]{TOC}
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%\end{wrapfigure}
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Similarly 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 functions due to the lack of explicit electron-electron terms modeling the infamous electron-electron cusp.
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Here, we propose a density-based basis set correction which significantly speed up the convergence of energetics towards the complete basis set limit.
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\end{abstract}
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\maketitle
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@ -362,30 +366,31 @@ Unless otherwise stated, in the remaining of this paper, the {\GOWO} QP energies
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In the case of {\evGW}, the QP energy, $\eGW{p}$, are obtained via Eq.~\eqref{eq:QP-G0W0}, which has to be solved self-consistently due to the QP energy dependence of the self-energy [see Eq.~\eqref{eq:SigC}]. \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011}
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At least in the weakly correlated regime where a clear QP solution exists, we believe that, within {\evGW}, the self-consistent algorithm should select the solution of the QP equation \eqref{eq:QP-G0W0} with the largest renormalization weight $\Z{p}(\eGW{p})$.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Basis Set Correction}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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The present basis set correction is a two-level correction.
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First, one has to correct the neutral excitations $\Om{x}$ from the RPA calculation.
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The corrected matrix elements read
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\begin{align}
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\label{eq:RPA}
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\tA_{ia,jb} & = \A{ia,jb} + (ia|\fc|jb),
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&
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\tB_{ia,jb} & = \B{ia,jb} + (ia|\fc|bj),
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\end{align}
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where the elements $\A{ia,jb}$ and $\B{ia,jb}$ are given by Eq.~\eqref{eq:RPA}.
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\begin{equation}
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\fc(\br{1},\br{2})= \frac{\delta^2 \Ec}{\delta n(\br{1})\delta n(\br{2})}
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\end{equation}
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In a second time, we correct the GW energy
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\begin{equation}
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\tSigC{p} = \SigC{p} + (p|\Vc|p)
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\end{equation}
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with
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\begin{equation}
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\Vc(\br{}) = \fdv{\Ec}{n(\br{})}
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\end{equation}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\subsection{Basis Set Correction}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%The present basis set correction is a two-level correction.
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%First, one has to correct the neutral excitations $\Om{x}$ from the RPA calculation.
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%The corrected matrix elements read
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%\begin{align}
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%\label{eq:RPA}
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% \tA_{ia,jb} & = \A{ia,jb} + (ia|\fc|jb),
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% &
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% \tB_{ia,jb} & = \B{ia,jb} + (ia|\fc|bj),
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%\end{align}
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%where the elements $\A{ia,jb}$ and $\B{ia,jb}$ are given by Eq.~\eqref{eq:RPA}.
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%\begin{equation}
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% \fc(\br{1},\br{2})= \frac{\delta^2 \Ec}{\delta n(\br{1})\delta n(\br{2})}
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%\end{equation}
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%In a second time, we correct the GW energy
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%\begin{equation}
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% \tSigC{p} = \SigC{p} + (p|\Vc|p)
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%\end{equation}
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%with
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%\begin{equation}
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% \Vc(\br{}) = \fdv{\Ec}{n(\br{})}
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%\end{equation}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Computational details}
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\label{sec:compdetails}
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@ -396,6 +401,37 @@ with
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\label{sec:res}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%% TABLE I %%%
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\begin{table*}
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\caption{
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IPs (in eV) of the five canonical nucleobases computed at various levels of theory.
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\label{tab:DNA}
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}
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\begin{ruledtabular}
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\begin{tabular}{llddddd}
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& & \mc{5}{c}{IPs of nucleobases (eV)} \\
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\cline{3-7}
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Method & Basis & \tabc{Adenine} & \tabc{Cytosine} & \tabc{Thymine} & \tabc{Guanine} & \tabc{Uracil} \\
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\hline
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{\GOWO}@PBE\fnm[1] & def2-SVP & 7.27 & 7.53 & 6.95 & 8.02 & 8.38 \\
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{\GOWO}@PBE+srLDA\fnm[1] & def2-SVP & 7.60 & 7.95 & 7.29 & 8.36 & 8.80 \\
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{\GOWO}@PBE+srPBE\fnm[1] & def2-SVP & 7.64 & 8.06 & 7.34 & 8.41 & 8.91 \\
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{\GOWO}@PBE\fnm[2] & def2-TZVP & 7.75 & 8.07 & 7.46 & 8.49 & 9.02 \\
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{\GOWO}@PBE+srLDA\fnm[1] & def2-TZVP & & & & & \\
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{\GOWO}@PBE+srPBE\fnm[1] & def2-TZVP & & & & & \\
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{\GOWO}@PBE\fnm[2] & def2-QZVP & 7.98 & 8.29 & 7.69 & 8.71 & 9.22 \\
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{\GOWO}@PBE\fnm[3] & def2-TQZVP & 8.15 & 8.45 & 7.87 & 8.87 & 9.38 \\
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\hline
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CCSD(T)\fnm[4] & def2-TZVPP & 8.33 & 9.51 & 8.03 & 9.08 & 10.13 \\
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Experiment\fnm[5] & & 8.48 & 8.94 & 8.24 & 9.2 & 9.68 \\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{This work.}
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\fnt[2]{Unpublished data taken from \url{https://gw100.wordpress.com}.}
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\fnt[3]{Extrapolated values obtained from the def2-TZVP and def2-QZVP values.}
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\fnt[4]{Reference \onlinecite{Krause_2015}.}
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\fnt[5]{Experimental values taken from Ref.~\onlinecite{Maggio_2017}.}
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\end{table*}
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%%%%%%%%%%%%%%%%%%%%%%%%
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@ -409,7 +445,10 @@ with
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%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{acknowledgements}
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This work was performed using HPC resources from GENCI-TGCC (Grant No.~2018-A0040801738), CALMIP (Toulouse) under allocation 2019-18005 and the Jarvis-Alpha cluster from the \textit{Institut Parisien de Chimie Physique et Th\'eorique}.
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PFL would like to thank Fabien Bruneval for technical assistance. He also would like to thank Arjan Berger and Pina Romaniello for stimulating 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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\end{acknowledgements}
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%%%%%%%%%%%%%%%%%%%%%%%%
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