From 9268f1e33de468c80211122b1e066682398d94db Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 2 Oct 2019 22:11:23 +0200 Subject: [PATCH] DNA + abstract --- Data/DNA.dat | 5 + Data/DNA_G0W0PBE0_def2SVP.dat | 5 - Manuscript/GW-srDFT.tex | 89 ++-- Notebooks/GW100.nb | 807 +++++++++++++++++++--------------- 4 files changed, 528 insertions(+), 378 deletions(-) create mode 100644 Data/DNA.dat delete mode 100644 Data/DNA_G0W0PBE0_def2SVP.dat diff --git a/Data/DNA.dat b/Data/DNA.dat new file mode 100644 index 0000000..426f30f --- /dev/null +++ b/Data/DNA.dat @@ -0,0 +1,5 @@ +A 73-24-5 -7.265806 -1.211220672617561E-002 -1.385783048793831E-002 -7.748 -7.975 -8.15 -8.33 -8.48 +C 71-30-7 -7.527844 -1.546006861838614E-002 -1.940117174135618E-002 -8.067 -8.287 -8.449 -9.512 -8.94 +G 73-40-5 -6.951933 -1.225096955803263E-002 -1.413179166956595E-002 -7.461 -7.691 -7.872 -8.034 -8.24 +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 diff --git a/Data/DNA_G0W0PBE0_def2SVP.dat b/Data/DNA_G0W0PBE0_def2SVP.dat deleted file mode 100644 index 306785c..0000000 --- a/Data/DNA_G0W0PBE0_def2SVP.dat +++ /dev/null @@ -1,5 +0,0 @@ -A 73-24-5 -7.619669 -1.188807989121034E-002 -1.347846624909449E-002 -7.748 -7.975 -8.15 -T 65-71-4 -8.430762 -1.213173859277770E-002 -1.403130444037225E-002 -8.489 -8.708 -8.866 -G 73-40-5 -7.314073 -1.205464000600519E-002 -1.378918997228398E-002 -7.461 -7.691 -7.872 -C 71-30-7 -7.971438 -1.309683725056005E-002 -1.554126377782151E-002 -8.067 -8.287 -8.449 -U 66-22-8 -8.814516 -1.240474844370148E-002 -1.441015016892908E-002 -9.017 -9.223 -9.382 diff --git a/Manuscript/GW-srDFT.tex b/Manuscript/GW-srDFT.tex index fc720cf..261d506 100644 --- a/Manuscript/GW-srDFT.tex +++ b/Manuscript/GW-srDFT.tex @@ -15,6 +15,8 @@ urlcolor=blue, citecolor=blue } +\urlstyle{same} + \newcommand{\alert}[1]{\textcolor{red}{#1}} \definecolor{darkgreen}{HTML}{009900} \usepackage[normalem]{ulem} @@ -176,6 +178,8 @@ % \centering % \includegraphics[width=\linewidth]{TOC} %\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} \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} 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} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -The present basis set correction is a two-level correction. -First, one has to correct the neutral excitations $\Om{x}$ from the RPA calculation. -The corrected matrix elements read -\begin{align} -\label{eq:RPA} - \tA_{ia,jb} & = \A{ia,jb} + (ia|\fc|jb), - & - \tB_{ia,jb} & = \B{ia,jb} + (ia|\fc|bj), -\end{align} -where the elements $\A{ia,jb}$ and $\B{ia,jb}$ are given by Eq.~\eqref{eq:RPA}. -\begin{equation} - \fc(\br{1},\br{2})= \frac{\delta^2 \Ec}{\delta n(\br{1})\delta n(\br{2})} -\end{equation} -In a second time, we correct the GW energy -\begin{equation} - \tSigC{p} = \SigC{p} + (p|\Vc|p) -\end{equation} -with -\begin{equation} - \Vc(\br{}) = \fdv{\Ec}{n(\br{})} -\end{equation} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\subsection{Basis Set 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. +%The corrected matrix elements read +%\begin{align} +%\label{eq:RPA} +% \tA_{ia,jb} & = \A{ia,jb} + (ia|\fc|jb), +% & +% \tB_{ia,jb} & = \B{ia,jb} + (ia|\fc|bj), +%\end{align} +%where the elements $\A{ia,jb}$ and $\B{ia,jb}$ are given by Eq.~\eqref{eq:RPA}. +%\begin{equation} +% \fc(\br{1},\br{2})= \frac{\delta^2 \Ec}{\delta n(\br{1})\delta n(\br{2})} +%\end{equation} +%In a second time, we correct the GW energy +%\begin{equation} +% \tSigC{p} = \SigC{p} + (p|\Vc|p) +%\end{equation} +%with +%\begin{equation} +% \Vc(\br{}) = \fdv{\Ec}{n(\br{})} +%\end{equation} + %%%%%%%%%%%%%%%%%%%%%%%% \section{Computational details} \label{sec:compdetails} @@ -396,6 +401,37 @@ with \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} -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} %%%%%%%%%%%%%%%%%%%%%%%% diff --git a/Notebooks/GW100.nb b/Notebooks/GW100.nb index bd2fc8d..fc7883f 100644 --- a/Notebooks/GW100.nb +++ b/Notebooks/GW100.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 11159278, 200899] -NotebookOptionsPosition[ 11145906, 200629] -NotebookOutlinePosition[ 11146352, 200647] -CellTagsIndexPosition[ 11146309, 200644] +NotebookDataLength[ 11167020, 201010] +NotebookOptionsPosition[ 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