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Pierre-Francois Loos 2019-10-02 22:11:23 +02:00
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Data/DNA.dat Normal file
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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
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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Data/DNA_G0W0PBE0_def2SVP.dat
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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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C 71-30-7 -7.971438 -1.309683725056005E-002 -1.554126377782151E-002 -8.067 -8.287 -8.449
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Manuscript/GW-srDFT.tex
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urlcolor=blue, urlcolor=blue,
citecolor=blue citecolor=blue
} }
\urlstyle{same}
\newcommand{\alert}[1]{\textcolor{red}{#1}} \newcommand{\alert}[1]{\textcolor{red}{#1}}
\definecolor{darkgreen}{HTML}{009900} \definecolor{darkgreen}{HTML}{009900}
\usepackage[normalem]{ulem} \usepackage[normalem]{ulem}
@ -176,6 +178,8 @@
% \centering % \centering
% \includegraphics[width=\linewidth]{TOC} % \includegraphics[width=\linewidth]{TOC}
%\end{wrapfigure} %\end{wrapfigure}
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.
Here, we propose a density-based basis set correction which significantly speed up the convergence of energetics towards the complete basis set limit.
\end{abstract} \end{abstract}
\maketitle \maketitle
@ -362,30 +366,31 @@ Unless otherwise stated, in the remaining of this paper, the {\GOWO} QP energies
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} 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}
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 $\Z{p}(\eGW{p})$. 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 $\Z{p}(\eGW{p})$.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Basis Set Correction} %\subsection{Basis Set Correction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The present basis set correction is a two-level correction. %The present basis set correction is a two-level correction.
First, one has to correct the neutral excitations $\Om{x}$ from the RPA calculation. %First, one has to correct the neutral excitations $\Om{x}$ from the RPA calculation.
The corrected matrix elements read %The corrected matrix elements read
\begin{align} %\begin{align}
\label{eq:RPA} %\label{eq:RPA}
\tA_{ia,jb} & = \A{ia,jb} + (ia|\fc|jb), % \tA_{ia,jb} & = \A{ia,jb} + (ia|\fc|jb),
& % &
\tB_{ia,jb} & = \B{ia,jb} + (ia|\fc|bj), % \tB_{ia,jb} & = \B{ia,jb} + (ia|\fc|bj),
\end{align} %\end{align}
where the elements $\A{ia,jb}$ and $\B{ia,jb}$ are given by Eq.~\eqref{eq:RPA}. %where the elements $\A{ia,jb}$ and $\B{ia,jb}$ are given by Eq.~\eqref{eq:RPA}.
\begin{equation} %\begin{equation}
\fc(\br{1},\br{2})= \frac{\delta^2 \Ec}{\delta n(\br{1})\delta n(\br{2})} % \fc(\br{1},\br{2})= \frac{\delta^2 \Ec}{\delta n(\br{1})\delta n(\br{2})}
\end{equation} %\end{equation}
In a second time, we correct the GW energy %In a second time, we correct the GW energy
\begin{equation} %\begin{equation}
\tSigC{p} = \SigC{p} + (p|\Vc|p) % \tSigC{p} = \SigC{p} + (p|\Vc|p)
\end{equation} %\end{equation}
with %with
\begin{equation} %\begin{equation}
\Vc(\br{}) = \fdv{\Ec}{n(\br{})} % \Vc(\br{}) = \fdv{\Ec}{n(\br{})}
\end{equation} %\end{equation}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
\section{Computational details} \section{Computational details}
\label{sec:compdetails} \label{sec:compdetails}
@ -396,6 +401,37 @@ with
\label{sec:res} \label{sec:res}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
%%% TABLE I %%%
\begin{table*}
\caption{
IPs (in eV) of the five canonical nucleobases computed at various levels of theory.
\label{tab:DNA}
}
\begin{ruledtabular}
\begin{tabular}{llddddd}
& & \mc{5}{c}{IPs of nucleobases (eV)} \\
\cline{3-7}
Method & Basis & \tabc{Adenine} & \tabc{Cytosine} & \tabc{Thymine} & \tabc{Guanine} & \tabc{Uracil} \\
\hline
{\GOWO}@PBE\fnm[1] & def2-SVP & 7.27 & 7.53 & 6.95 & 8.02 & 8.38 \\
{\GOWO}@PBE+srLDA\fnm[1] & def2-SVP & 7.60 & 7.95 & 7.29 & 8.36 & 8.80 \\
{\GOWO}@PBE+srPBE\fnm[1] & def2-SVP & 7.64 & 8.06 & 7.34 & 8.41 & 8.91 \\
{\GOWO}@PBE\fnm[2] & def2-TZVP & 7.75 & 8.07 & 7.46 & 8.49 & 9.02 \\
{\GOWO}@PBE+srLDA\fnm[1] & def2-TZVP & & & & & \\
{\GOWO}@PBE+srPBE\fnm[1] & def2-TZVP & & & & & \\
{\GOWO}@PBE\fnm[2] & def2-QZVP & 7.98 & 8.29 & 7.69 & 8.71 & 9.22 \\
{\GOWO}@PBE\fnm[3] & def2-TQZVP & 8.15 & 8.45 & 7.87 & 8.87 & 9.38 \\
\hline
CCSD(T)\fnm[4] & def2-TZVPP & 8.33 & 9.51 & 8.03 & 9.08 & 10.13 \\
Experiment\fnm[5] & & 8.48 & 8.94 & 8.24 & 9.2 & 9.68 \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{This work.}
\fnt[2]{Unpublished data taken from \url{https://gw100.wordpress.com}.}
\fnt[3]{Extrapolated values obtained from the def2-TZVP and def2-QZVP values.}
\fnt[4]{Reference \onlinecite{Krause_2015}.}
\fnt[5]{Experimental values taken from Ref.~\onlinecite{Maggio_2017}.}
\end{table*}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
@ -409,7 +445,10 @@ with
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
\begin{acknowledgements} \begin{acknowledgements}
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}. PFL would like to thank Fabien Bruneval for technical assistance. He also would like to thank Arjan Berger and Pina Romaniello for stimulating discussions.
This work was performed using HPC resources from GENCI-TGCC (Grant No.~2018-A0040801738) and CALMIP (Toulouse) under allocation 2019-18005.
Funding from the \textit{``Centre National de la Recherche Scientifique''} is acknowledged.
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''}.
\end{acknowledgements} \end{acknowledgements}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%

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Notebooks/GW100.nb
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