Bib

Manuscript/srDFT_SC.bib

@@ -1,7 +1,7 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2019-12-13 10:13:42 +0100 
+%% Created for Pierre-Francois Loos at 2019-12-13 10:34:29 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
@@ -8534,13 +8534,12 @@
 
 @article{BytLaiRuedenJCP05,
 	Author = {Bytautas,Laimutis and Ruedenberg,Klaus},
+	Date-Modified = {2019-12-13 10:34:29 +0100},
 	Doi = {10.1063/1.1869493},
-	Eprint = {https://doi.org/10.1063/1.1869493},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {15},
 	Pages = {154110},
 	Title = {Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine},
-	Url = {https://doi.org/10.1063/1.1869493},
 	Volume = {122},
 	Year = {2005},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.1869493}}
@@ -11892,13 +11891,12 @@
 
 @article{FerGinTou-JCP-18,
 	Author = {Fert{\'e},Anthony and Giner,Emmanuel and Toulouse,Julien},
+	Date-Modified = {2019-12-13 10:32:50 +0100},
 	Doi = {10.1063/1.5082638},
-	Eprint = {https://doi.org/10.1063/1.5082638},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {8},
 	Pages = {084103},
 	Title = {Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density},
-	Url = {https://doi.org/10.1063/1.5082638},
 	Volume = {150},
 	Year = {2019},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}}
@@ -12627,14 +12625,12 @@
 
 @article{LooPraSceTouGin-JCPL-19,
 	Author = {Loos, Pierre-Fran{\c c}ois and Pradines, Barth{\'e}l{\'e}my and Scemama, Anthony and Toulouse, Julien and Giner, Emmanuel},
+	Date-Modified = {2019-12-13 10:33:25 +0100},
 	Doi = {10.1021/acs.jpclett.9b01176},
-	Eprint = {https://doi.org/10.1021/acs.jpclett.9b01176},
+	Journal = {J. Phys. Chem. Lett.},
-	Journal = {The Journal of Physical Chemistry Letters},
-	Note = {PMID: 31090432},
 	Number = {11},
 	Pages = {2931-2937},
 	Title = {A Density-Based Basis-Set Correction for Wave Function Theory},
-	Url = {https://doi.org/10.1021/acs.jpclett.9b01176},
 	Volume = {10},
 	Year = {2019},
 	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.9b01176}}
@@ -12673,13 +12669,12 @@
 
 @article{GinSceTouLoo-JCP-19,
 	Author = {Giner,Emmanuel and Scemama,Anthony and Toulouse,Julien and Loos,Pierre-Fran{\c c}ois},
+	Date-Modified = {2019-12-13 10:33:54 +0100},
 	Doi = {10.1063/1.5122976},
-	Eprint = {https://doi.org/10.1063/1.5122976},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {14},
 	Pages = {144118},
 	Title = {Chemically accurate excitation energies with small basis sets},
-	Url = {https://doi.org/10.1063/1.5122976},
 	Volume = {151},
 	Year = {2019},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.5122976}}
@@ -12725,13 +12720,12 @@
 
 @article{ShiWer-JCP-10,
 	Author = {Shiozaki,Toru and Werner,Hans-Joachim},
+	Date-Modified = {2019-12-13 10:30:35 +0100},
 	Doi = {10.1063/1.3489000},
-	Eprint = {https://doi.org/10.1063/1.3489000},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {14},
 	Pages = {141103},
 	Title = {Communication: Second-order multireference perturbation theory with explicit correlation: CASPT2-F12},
-	Url = {https://doi.org/10.1063/1.348900},
 	Volume = {133},
 	Year = {2010},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.348900},
@@ -12739,26 +12733,24 @@
 
 @article{GuoSivValNee-JCP-17,
 	Author = {Guo,Yang and Sivalingam,Kantharuban and Valeev,Edward F. and Neese,Frank},
+	Date-Modified = {2019-12-13 10:30:13 +0100},
 	Doi = {10.1063/1.4996560},
-	Eprint = {https://doi.org/10.1063/1.4996560},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {6},
 	Pages = {064110},
 	Title = {Explicitly correlated N-electron valence state perturbation theory (NEVPT2-F12)},
-	Url = {https://doi.org/10.1063/1.4996560},
 	Volume = {147},
 	Year = {2017},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.4996560}}
 
 @article{TorVal-JCP-09,
 	Author = {Torheyden,Martin and Valeev,Edward F.},
+	Date-Modified = {2019-12-13 10:31:19 +0100},
 	Doi = {10.1063/1.3254836},
-	Eprint = {https://doi.org/10.1063/1.3254836},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {17},
 	Pages = {171103},
 	Title = {Universal perturbative explicitly correlated basis set incompleteness correction},
-	Url = {https://doi.org/10.1063/1.3254836},
 	Volume = {131},
 	Year = {2009},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.3254836}}
@@ -12766,9 +12758,10 @@
 @article{Ten-CPL-07,
 	Abstract = {We propose a simple F12 geminal correction in multi-reference perturbation theory. An explicitly correlated term is introduced in the external excitations of the first order wave function in an internally contracted manner. By the use of the s- and p-wave cusp conditions, the F12 correction is expressed as the expectation value of a two-body effective operator, which reduces to the MP2-F12/A∗(SP) energy in the single reference limit. The performance of the F12 multi-reference perturbation method is demonstrated for C, CH2, O2, and SiC3.},
 	Author = {Seiichiro Ten-no},
+	Date-Modified = {2019-12-13 10:29:25 +0100},
 	Doi = {https://doi.org/10.1016/j.cplett.2007.09.006},
 	Issn = {0009-2614},
-	Journal = {Chemical Physics Letters},
+	Journal = {Chem. Phys. Lett.},
 	Number = {1},
 	Pages = {175 - 179},
 	Title = {A simple F12 geminal correction in multi-reference perturbation theory},
@@ -12795,13 +12788,12 @@
 
 @article{TorKniWer-JCP-11,
 	Author = {Shiozaki,Toru and Knizia,Gerald and Werner,Hans-Joachim},
+	Date-Modified = {2019-12-13 10:30:31 +0100},
 	Doi = {10.1063/1.3528720},
-	Eprint = {https://doi.org/10.1063/1.3528720},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {3},
 	Pages = {034113},
 	Title = {Explicitly correlated multireference configuration interaction: MRCI-F12},
-	Url = {https://doi.org/10.1063/1.3528720},
 	Volume = {134},
 	Year = {2011},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.3528720}}
@@ -12823,12 +12815,10 @@
 @article{HauMaoMukKlo-CPL-12,
 	Abstract = {We present a universally applicable explicit electron correlation (F12) correction and apply it to Mukherjee's multi-reference perturbation theory (Mk-MRPT2). Two different F12 corrections are proposed: one is a universal F12 correction which is added to the conventional orbital correction, which is referred to as Mk-MRPT2+F12. In the second type of F12 correction the individual F12 contributions are added to each matrix element of the effective Hamiltonian. Subsequent diagonalization yields the Mk-MRPT2-F12 correction. Thereby, we achieve for both F12 corrections the accuracy of a quadruple-ζ basis set calculation when a triple-ζ basis set is employed and the F12 correction is added. Both F12 corrections reduce to MP2-F12/1A (fixed) in the single-reference limit.},
 	Author = {Robin Haunschild and Shuneng Mao and Debashis Mukherjee and Wim Klopper},
-	Doi = {https://doi.org/10.1016/j.cplett.2012.02.020},
+	Date-Modified = {2019-12-13 10:32:04 +0100},
-	Issn = {0009-2614},
+	Journal = {Chem. Phys. Lett.},
-	Journal = {Chemical Physics Letters},
 	Pages = {247 - 251},
 	Title = {A universal explicit electron correlation correction applied to Mukherjee's multi-reference perturbation theory},
-	Url = {http://www.sciencedirect.com/science/article/pii/S0009261412002072},
 	Volume = {531},
 	Year = {2012},
 	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261412002072},
@@ -12836,26 +12826,24 @@
 
 @article{KonVal-JCP-11,
 	Author = {Kong,Liguo and Valeev,Edward F.},
+	Date-Modified = {2019-12-13 10:31:43 +0100},
 	Doi = {10.1063/1.3664729},
-	Eprint = {https://doi.org/10.1063/1.3664729},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {21},
 	Pages = {214105},
 	Title = {SF-[2]R12: A spin-adapted explicitly correlated method applicable to arbitrary electronic states},
-	Url = {https://doi.org/10.1063/1.3664729},
 	Volume = {135},
 	Year = {2011},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.3664729}}
 
 @article{BooCleAlaTew-JCP-12,
 	Author = {Booth,George H. and Cleland,Deidre and Alavi,Ali and Tew,David P.},
+	Date-Modified = {2019-12-13 10:32:27 +0100},
 	Doi = {10.1063/1.4762445},
-	Eprint = {https://doi.org/10.1063/1.4762445},
+	Journal = {J. Chem. Phys.},
-	Journal = {The Journal of Chemical Physics},
 	Number = {16},
 	Pages = {164112},
 	Title = {An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo},
-	Url = {https://doi.org/10.1063/1.4762445},
 	Volume = {137},
 	Year = {2012},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.4762445}}

Manuscript/srDFT_SC.tex

@@ -341,7 +341,7 @@ Then, in Sec.~\ref{sec:results}, we apply the method to the calculation of the p
 \section{Theory}
 \label{sec:theory}
 %%%%%%%%%%%%%%%%%%%%%%%%
-As the theory behind the present basis-set correction has been exposed in details in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, we only briefly recall the main equations and concepts needed for this study in Secs.~\ref{sec:basic}, \ref{sec:wee}, and \ref{sec:mur}. More specifically, in Sec.~\ref{sec:basic} we recall the basic mathematical framework of the present theory by introducing the \titou{density functional complementary to a basis set $\Bas$}. Section \ref{sec:wee} introduces the effective non-divergent interaction in the basis set $\Bas$, which leads us to the definition of the effective \textit{local} range-separation parameter in Sec.~\ref{sec:mur}. Then, Sec.~\ref{sec:functional} exposes the new approximate RSDFT-based complementary correlation functionals. The generic form of such functionals is exposed in Sec.~\ref{sec:functional_form}, their properties in the context of the basis-set correction are discussed in Sec.~\ref{sec:functional_prop}, and the specific requirements for strong correlation are discussed in Sec.~\ref{sec:requirements}. Finally, the actual form of the functionals used in this work are introduced in Sec.~\ref{sec:final_def_func}. 
+As the theory behind the present basis-set correction has been exposed in details in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, we only briefly recall the main equations and concepts needed for this study in Secs.~\ref{sec:basic}, \ref{sec:wee}, and \ref{sec:mur}. More specifically, in Sec.~\ref{sec:basic} we recall the basic mathematical framework of the present theory by introducing the \titou{density functional complementary to a basis set $\Bas$}. Section \ref{sec:wee} introduces the effective non-divergent interaction in the basis set $\Bas$, which leads us to the definition of the effective \textit{local} range-separation parameter in Sec.~\ref{sec:mur}. Then, Sec.~\ref{sec:functional} exposes the new approximate RSDFT-based complementary correlation functionals. The generic form of such functionals is exposed in Sec.~\ref{sec:functional_form}, their properties in the context of the basis-set correction are discussed in Sec.~\ref{sec:functional_prop}, and the specific requirements for strong correlation are discussed in Sec.~\ref{sec:requirements}. Finally, the actual form of the functionals used in this work are introduced in Sec.~\ref{sec:def_func}. 
 
 \subsection{Basic equations}
 \label{sec:basic}