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Manuscript/GW-srDFT.bib
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@ -1,20 +1,43 @@
%% 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 2019-10-24 20:30:56 +0200 %% Created for Pierre-Francois Loos at 2019-10-26 21:05:44 +0200
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@article{Adler_2007,
Author = {T. B. Adler and G. Knizia and H.-J. Werner},
Date-Added = {2019-10-26 20:55:14 +0200},
Date-Modified = {2019-10-26 20:56:31 +0200},
Journal = {J. Chem. Phys.},
Keywords = {10.1063/1.2817618},
Pages = {221106},
Title = {A Simple and Efficient {{CCSD(T)-F12}} Approximation},
Volume = {127},
Year = {2007}}
@article{Kim_2013,
Author = {{Min-Cheol} Kim and Eunji Sim and Kieron Burke},
Date-Added = {2019-10-26 20:51:36 +0200},
Date-Modified = {2019-10-26 20:52:31 +0200},
Doi = {10.1103/PhysRevLett.111.073003},
Journal = {Phys. Rev. Lett.},
Pages = {073003},
Title = {Understanding and Reducing Errors in Density Functional Calculations},
Volume = {111},
Year = {2013},
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.111.073003}}
@article{Dunning_1989, @article{Dunning_1989,
Author = {Thom H. Dunning}, Author = {Thom H. Dunning},
Date-Added = {2019-10-24 20:22:40 +0200}, Date-Added = {2019-10-24 20:22:40 +0200},
Date-Modified = {2019-10-24 20:22:47 +0200}, Date-Modified = {2019-10-26 21:03:53 +0200},
Journal = {J. Chem. Phys.}, Journal = {J. Chem. Phys.},
Pages = {1007}, Pages = {1007},
Title = {Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen}, Title = {Gaussian Basis Sets For Use In Correlated Molecular Calculations. I. The Atoms Boron Through Neon And Hydrogen},
Volume = {90}, Volume = {90},
Year = {1989}} Year = {1989}}
@ -197,13 +220,13 @@
@article{Toulouse_2004, @article{Toulouse_2004,
Author = {J. Toulouse and F. Colonna and A. Savin}, Author = {J. Toulouse and F. Colonna and A. Savin},
Date-Added = {2019-10-24 20:10:53 +0200}, Date-Added = {2019-10-24 20:10:53 +0200},
Date-Modified = {2019-10-24 20:19:46 +0200}, Date-Modified = {2019-10-26 21:03:16 +0200},
Journal = {Phys. Rev. A}, Journal = {Phys. Rev. A},
Keywords = {density functional theory; wave functions; exchange interactions (electron); electron correlations}, Keywords = {density functional theory; wave functions; exchange interactions (electron); electron correlations},
Number = {6}, Number = {6},
Pages = {062505}, Pages = {062505},
Publisher = {APS}, Publisher = {APS},
Title = {Long-range--short-range separation of the electron-electron interaction in density-functional theory}, Title = {Long-Range--Short-Range Separation Of The Electron-Electron Interaction In Density-Functional Theory},
Volume = {70}, Volume = {70},
Year = {2004}} Year = {2004}}
@ -238,11 +261,11 @@
@article{Ferte_2019, @article{Ferte_2019,
Author = {Anthony Fert\'e and Emmanuel Giner and Julien Toulouse}, Author = {Anthony Fert\'e and Emmanuel Giner and Julien Toulouse},
Date-Added = {2019-10-24 20:05:01 +0200}, Date-Added = {2019-10-24 20:05:01 +0200},
Date-Modified = {2019-10-24 20:12:16 +0200}, Date-Modified = {2019-10-26 21:02:51 +0200},
Doi = {10.1063/1.5082638}, Doi = {10.1063/1.5082638},
Journal = {J. Chem. Phys.}, Journal = {J. Chem. Phys.},
Pages = {084103}, Pages = {084103},
Title = {Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density}, Title = {Range-Separated Multideterminant Density-Functional Theory With A Short-Range Correlation Functional Of The On-Top Pair Density},
Volume = {150}, Volume = {150},
Year = {2019}, Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}} Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}}
@ -302,10 +325,10 @@
@article{Giner_2018, @article{Giner_2018,
Author = {Emmanuel Giner and Barth\'elemy Pradines and Anthony Fert\'e and Roland Assaraf and Andreas Savin and Julien Toulouse}, Author = {Emmanuel Giner and Barth\'elemy Pradines and Anthony Fert\'e and Roland Assaraf and Andreas Savin and Julien Toulouse},
Date-Added = {2019-10-24 19:59:35 +0200}, Date-Added = {2019-10-24 19:59:35 +0200},
Date-Modified = {2019-10-24 19:59:43 +0200}, Date-Modified = {2019-10-26 21:03:25 +0200},
Journal = {J. Chem. Phys.}, Journal = {J. Chem. Phys.},
Pages = {194301}, Pages = {194301},
Title = {Curing basis-set convergence of wave-function theory using density-functional theory: A systematically improvable approach}, Title = {Curing Basis-Set Convergence Of Wave-Function Theory Using Density-Functional Theory: A Systematically Improvable Approach},
Volume = {149}, Volume = {149},
Year = {2018}} Year = {2018}}
@ -444,22 +467,22 @@
@article{Krause_2015, @article{Krause_2015,
Author = {K. Krause and M. E. Harding and W. Klopper}, Author = {K. Krause and M. E. Harding and W. Klopper},
Date-Added = {2019-10-08 22:05:00 +0200}, Date-Added = {2019-10-08 22:05:00 +0200},
Date-Modified = {2019-10-08 22:07:43 +0200}, Date-Modified = {2019-10-26 21:04:13 +0200},
Journal = {Mol. Phys.}, Journal = {Mol. Phys.},
Keywords = {10.1080/00268976.2015.1025113}, Keywords = {10.1080/00268976.2015.1025113},
Pages = {1952}, Pages = {1952},
Title = {Coupled-cluster reference values for the GW27 and GW100 test sets for the assessment of GW methods}, Title = {Coupled-Cluster Reference Values For The Gw27 And Gw100 Test Sets For The Assessment Of Gw Methods},
Volume = {113}, Volume = {113},
Year = {2015}} Year = {2015}}
@article{Teke_2019, @article{Teke_2019,
Author = {N. K. Teke and F. Pavosevic and C. Peng and E. F. Valeev}, Author = {N. K. Teke and F. Pavosevic and C. Peng and E. F. Valeev},
Date-Added = {2019-10-08 21:02:47 +0200}, Date-Added = {2019-10-08 21:02:47 +0200},
Date-Modified = {2019-10-08 21:04:04 +0200}, Date-Modified = {2019-10-26 21:04:55 +0200},
Doi = {10.1063/1.5090983}, Doi = {10.1063/1.5090983},
Journal = {J. Chem. Phys.}, Journal = {J. Chem. Phys.},
Pages = {214103}, Pages = {214103},
Title = {Explicitly correlated renormalized second-order Green's function for accurate ionization potentials of closed-shell molecules}, Title = {Explicitly Correlated Renormalized Second-Order Green's Function For Accurate Ionization Potentials Of Closed-Shell Molecules},
Volume = {150}, Volume = {150},
Year = {2019}, Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1063/1.5090983}} Bdsk-Url-1 = {https://doi.org/10.1063/1.5090983}}
@ -467,11 +490,11 @@
@article{Johnson_2018, @article{Johnson_2018,
Author = {C. M. Johnson and A. E. Doran and S. L. Ten-no and S. Hirata}, Author = {C. M. Johnson and A. E. Doran and S. L. Ten-no and S. Hirata},
Date-Added = {2019-10-08 20:59:18 +0200}, Date-Added = {2019-10-08 20:59:18 +0200},
Date-Modified = {2019-10-09 11:44:29 +0200}, Date-Modified = {2019-10-26 21:05:11 +0200},
Doi = {10.1063/1.5054610}, Doi = {10.1063/1.5054610},
Journal = {J. Chem. Phys.}, Journal = {J. Chem. Phys.},
Pages = {174112}, Pages = {174112},
Title = {Monte Carlo explicitly correlated many-body Green's function theory}, Title = {Monte Carlo Explicitly Correlated Many-Body Green's Function Theory},
Volume = {149}, Volume = {149},
Year = {2018}, Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1063/1.5054610}} Bdsk-Url-1 = {https://doi.org/10.1063/1.5054610}}
@ -3330,6 +3353,7 @@
@article{Krause_2017, @article{Krause_2017,
Author = {Krause, Katharina and Klopper, Wim}, Author = {Krause, Katharina and Klopper, Wim},
Date-Modified = {2019-10-26 21:04:20 +0200},
Doi = {10.1002/jcc.24688}, Doi = {10.1002/jcc.24688},
File = {/Users/loos/Zotero/storage/4XKBP9ZQ/Krause_2016.pdf}, File = {/Users/loos/Zotero/storage/4XKBP9ZQ/Krause_2016.pdf},
Issn = {01928651}, Issn = {01928651},
@ -3338,7 +3362,7 @@
Month = mar, Month = mar,
Number = {6}, Number = {6},
Pages = {383--388}, Pages = {383--388},
Title = {Implementation of the {{Bethe}}-{{Salpeter}} Equation in the {{TURBOMOLE}} Program}, Title = {Implementation Of The {{Bethe}}-{{Salpeter}} Equation In The {{Turbomole}} Program},
Volume = {38}, Volume = {38},
Year = {2017}, Year = {2017},
Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.24688}} Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.24688}}
@ -3479,6 +3503,7 @@
@article{Ohnishi_2016, @article{Ohnishi_2016,
Author = {Ohnishi, Yu-ya and Ten-no, Seiichiro}, Author = {Ohnishi, Yu-ya and Ten-no, Seiichiro},
Date-Modified = {2019-10-26 21:01:47 +0200},
Doi = {10.1002/jcc.24468}, Doi = {10.1002/jcc.24468},
File = {/Users/loos/Zotero/storage/6QF6TQIF/Ohnishi_2016.pdf}, File = {/Users/loos/Zotero/storage/6QF6TQIF/Ohnishi_2016.pdf},
Issn = {01928651}, Issn = {01928651},
@ -3488,7 +3513,7 @@
Number = {27}, Number = {27},
Pages = {2447--2453}, Pages = {2447--2453},
Shorttitle = {Explicitly Correlated Frequency-Independent Second-Order Green's Function for Accurate Ionization Energies}, Shorttitle = {Explicitly Correlated Frequency-Independent Second-Order Green's Function for Accurate Ionization Energies},
Title = {Explicitly Correlated Frequency-Independent Second-Order Green's Function for Accurate Ionization Energies: {{FULL PAPER}}}, Title = {Explicitly Correlated Frequency-Independent Second-Order Green's Function for Accurate Ionization Energies},
Volume = {37}, Volume = {37},
Year = {2016}, Year = {2016},
Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.24468}} Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.24468}}

4
Manuscript/GW-srDFT.tex
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@ -221,7 +221,7 @@ Pioneered by Hylleraas \cite{Hylleraas_1929} in the 1930's and popularized in th
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{Tew_2007} 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{Tew_2007}
The basis-set correction presented here follow a different route, 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{Giner_2018} The basis-set correction presented here follow a different route, 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{Giner_2018}
As shown in recent studies on both ground- and excited-state properties, \cite{Loos_2019, Giner_2019} similar to F12 methods, it significantly speeds up the convergence of energetics towards the CBS limit while avoiding the usage of the large auxiliary basis sets that are used in F12 methods to avoid the numerous three- and four-electron integrals. \cite{Kong_2012, Hattig_2012, Tenno_2012a, Tenno_2012b, Gruneis_2017, Barca_2018} As shown in recent studies on both ground- and excited-state properties, \cite{Loos_2019, Giner_2019} similar to F12 methods, it significantly speeds up the convergence of energetics towards the CBS limit while avoiding the usage of the large auxiliary basis sets that are used in F12 methods to avoid the numerous three- and four-electron integrals. \cite{Kong_2012, Hattig_2012, Tenno_2012a, Tenno_2012b, Gruneis_2017, Barca_2016, Barca_2017, Barca_2018}
Explicitly correlated F12 correction schemes have been derived for second-order Green 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 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.
@ -605,7 +605,7 @@ For example, at the {\GOWO}@PBE0+srLDA/cc-pVQZ level, the MAD is only $0.02$ eV
It is worth pointing out that, for ground-state properties such as atomization and correlation energies, the density-based correction brought a more significant basis set reduction. It is worth pointing out that, for ground-state properties such as atomization and correlation energies, the density-based correction brought a more significant basis set reduction.
For example, we evidenced in Ref.~\onlinecite{Loos_2019} that quintuple-$\zeta$ quality atomization and correlation energies are recovered with triple-$\zeta$ basis sets. For example, we evidenced in Ref.~\onlinecite{Loos_2019} that quintuple-$\zeta$ quality atomization and correlation energies are recovered with triple-$\zeta$ basis sets.
Here, the overall gain seems to be less important. Here, the overall gain seems to be less important.
The potential reasons for this could be: i) potential-based DFT corrections are usually less accurate than the ones based directly on energies, and ii) because the present scheme only corrects the basis set incompleteness error originating from the electron-electron cusp, some incompleteness remains at the HF or KS level. The potential reasons for this could be: i) potential-based DFT corrections are usually less accurate than the ones based directly on energies, \cite{Kim_2013} and ii) because the present scheme only corrects the basis set incompleteness error originating from the electron-electron cusp, some incompleteness remains at the HF or KS level. \cite{Adler_2007}
%%% TABLE III %%% %%% TABLE III %%%
\begin{table*} \begin{table*}