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still working on the introduction

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Pierre-Francois Loos 2019-10-09 15:35:14 +02:00
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17
Manuscript/GW-srDFT.tex
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@ -31,7 +31,7 @@
\newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}} \newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}}
\newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}} \newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}}
\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} \newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}}
\newcommand{\AS}[1]{\toto{(\underline{\bf TOTO}: #1)}} \newcommand{\AS}[1]{\toto{(\underline{\bf AS}: #1)}}
\usepackage{hyperref} \usepackage{hyperref}
\hypersetup{ \hypersetup{
@ -227,11 +227,13 @@ The simplest and most popular variant of $GW$ is perturbative $GW$, or {\GOWO}.
Although obviously starting-point dependent, it has been widely used in the literature to study solids, atoms and molecules. \cite{Bruneval_2012, Bruneval_2013, vanSetten_2015, vanSetten_2018} Although obviously starting-point dependent, it has been widely used in the literature to study solids, atoms and molecules. \cite{Bruneval_2012, Bruneval_2013, vanSetten_2015, vanSetten_2018}
For finite systems such as atoms and molecules, partially or fully self-consistent $GW$ methods have shown great promise. \cite{Ke_2011, Blase_2011, Faber_2011, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b, Koval_2014, Hung_2016, Blase_2018, Jacquemin_2017} For finite systems such as atoms and molecules, partially or fully self-consistent $GW$ methods have shown great promise. \cite{Ke_2011, Blase_2011, Faber_2011, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b, Koval_2014, Hung_2016, Blase_2018, Jacquemin_2017}
Similarly to other electron correlation methods, MBPT methods suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. Similar to other electron correlation methods, MBPT methods suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set.
Pioneered by Hyllerras \cite{Hyl-ZP-29} in the 1930's and popularized in the 1990's by Kutzelnigg and coworkers \cite{NogKut-JCP-94,KutMor-ZPD-96,Kut-TCA-85,KutKlo-JCP-91} (and subsequently others \cite{KonBisVal-CR-12, HatKloKohTew-CR-12, TenNog-WIREs-12, GruHirOhnTen-JCP-17}), this can be tracked down to the lack of explicit electron-electron terms modeling the infamous electron-electron coalescence points also known as Kato cusp. \cite{Kat-CPAM-57} This can be tracked down to the lack of explicit electron-electron terms modeling the infamous electron-electron coalescence point (also known as Kato cusp \cite{Kat-CPAM-57}) and, more specifically, the Coulomb correlation hole around it.
Pioneered by Hyllerras \cite{Hyl-ZP-29} in the 1930's and popularized in the 1990's by Kutzelnigg and coworkers \cite{Kut-TCA-85, NogKut-JCP-94, KutKlo-JCP-91} (and subsequently others \cite{KonBisVal-CR-12, HatKloKohTew-CR-12, TenNog-WIREs-12, GruHirOhnTen-JCP-17}), the so-called F12 methods overcome this slow convergence by employing geminal basis functions that closely resemble the correlation holes in electronic wave functions.
F12 methods are now routinely employed in computational chemistry and provide robust tools for electronic structure calculations where small basis sets may be used to obtain near complete basis set (CBS) limit accuracy. \cite{TewKloNeiHat-PCCP-07}
The basis-set correction presented here follow a different avenue, and relies on the range-separated density-functional theory (RS-DFT) formalism to capture, thanks to a short-range correlation functional, the missing part of the short-range correlation effects. \cite{GinPraFerAssSavTou-JCP-18, LooPraSceTouGin-JPCL-19} The basis-set correction presented here follow a different avenue, and relies on the range-separated density-functional theory (RS-DFT) formalism to capture, thanks to a short-range correlation functional, the missing part of the short-range correlation effects. \cite{GinPraFerAssSavTou-JCP-18}
As we shall illustrate later on in this manuscript, it significantly speeds up the convergence of energetics towards the complete basis set (CBS) limit. As shown in recent studies on both ground- and excited-state properties, \cite{LooPraSceTouGin-JPCL-19, GinSceTouLoo-JCP-19} similar to F12 methods, it significantly speeds up the convergence of energetics towards the CBS limit while avoiding the usage of large auxiliary basis sets.
Explicitly correlated F12 correction schemes have been derived for second-order Green's function methods (GF2) \cite{SzaboBook, Casida_1989, Casida_1991, Stefanucci_2013, Ortiz_2013, Phillips_2014, Phillips_2015, Rusakov_2014, Rusakov_2016, Hirata_2015, Hirata_2017, Loos_2018} by Ten-no and coworkers \cite{Ohnishi_2016, Johnson_2018} and Valeev and coworkers. \cite{Pavosevic_2017, Teke_2019} Explicitly correlated F12 correction schemes have been derived for second-order Green's function methods (GF2) \cite{SzaboBook, Casida_1989, Casida_1991, Stefanucci_2013, Ortiz_2013, Phillips_2014, Phillips_2015, Rusakov_2014, Rusakov_2016, Hirata_2015, Hirata_2017, Loos_2018} by Ten-no and coworkers \cite{Ohnishi_2016, Johnson_2018} and Valeev and coworkers. \cite{Pavosevic_2017, Teke_2019}
However, to the best of our knowledge, a F12-based correction for $GW$ has not been designed yet. However, to the best of our knowledge, a F12-based correction for $GW$ has not been designed yet.
@ -556,8 +558,9 @@ IPs (in eV) of the 20 smallest molecule of the GW100 set computed at the {\GOWO}
%%% FIG 1 %%% %%% FIG 1 %%%
\begin{figure*} \begin{figure*}
\includegraphics[width=0.49\linewidth]{IP_G0W0HF_H2O} \includegraphics[width=0.45\linewidth]{IP_G0W0HF_H2O}
\includegraphics[width=0.49\linewidth]{IP_G0W0PBE0_H2O} \hspace{1cm}
\includegraphics[width=0.45\linewidth]{IP_G0W0PBE0_H2O}
\caption{ \caption{
IPs (in eV) of the water molecule computed at the {\GOWO} (black circles), {\GOWO}+srLDA (red squares) and {\GOWO}+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) with two different starting points: HF (left) and PBE0 (right). IPs (in eV) of the water molecule computed at the {\GOWO} (black circles), {\GOWO}+srLDA (red squares) and {\GOWO}+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) with two different starting points: HF (left) and PBE0 (right).
The thick black line represents the CBS value obtained by extrapolation (see text for more details). The thick black line represents the CBS value obtained by extrapolation (see text for more details).

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Manuscript/biblio.bib
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@ -1,13 +1,22 @@
%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2019-10-09 11:44:04 +0200 %% Created for Pierre-Francois Loos at 2019-10-09 15:35:04 +0200
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@article{GinSceTouLoo-JCP-19,
Author = {E. Giner and A. Scemama and J. Toulouse and P. F. Loos},
Date-Added = {2019-10-09 15:28:44 +0200},
Date-Modified = {2019-10-09 15:31:02 +0200},
Journal = {J. Chem. Phys.},
Title = {Chemically Accurate Excitation Energies With Small Basis Sets},
Volume = {in press},
Year = {2019}}
@article{LooPraSceTouGin-JPCL-19, @article{LooPraSceTouGin-JPCL-19,
Author = {P. F. Loos and B. Pradines and A. Scemama and J. Toulouse and E. Giner}, Author = {P. F. Loos and B. Pradines and A. Scemama and J. Toulouse and E. Giner},
Date-Added = {2019-10-08 22:09:00 +0200}, Date-Added = {2019-10-08 22:09:00 +0200},