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+\bibcite{HolUmrSha-JCP-17}{{57}{2017}{{Holmes\ \emph  {et~al.}}}{{Holmes, Umrigar,\ and\ Sharma}}}
+\bibcite{QP2}{{58}{2019}{{Garniron\ \emph  {et~al.}}}{{Garniron, Gasperich, Applencourt, Benali, Fert{\'e}, Paquier, Pradines, Assaraf, Reinhardt, Toulouse, Barbaresco, Renon, David, Malrieu, V{\'e}ril, Caffarel, Loos, Giner,\ and\ Scemama}}}
+\bibcite{SceGarCafLoo-JCTC-18}{{59}{2018{}}{{Scemama\ \emph  {et~al.}}}{{Scemama, Garniron, Caffarel,\ and\ Loos}}}
+\bibcite{LooSceBloGarCafJac-JCTC-18}{{60}{2018{}}{{Loos\ \emph  {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}}
+\bibcite{SceBenJacCafLoo-JCP-18}{{61}{2018{}}{{Scemama\ \emph  {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}}
+\bibcite{LooBogSceCafJac-JCTC-19}{{62}{2019{}}{{Loos\ \emph  {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}}
+\bibcite{DasHer-JCC-17}{{63}{2017}{{Dasgupta\ and\ Herbert}}{{}}}
+\bibcite{SheLeiVanSch-JCP-98}{{64}{1998}{{Sherrill\ \emph  {et~al.}}}{{Sherrill, Leininger, Huis,\ and\ Schaefer}}}
+\bibcite{Sch-Science-86}{{65}{1986}{{{H. F. Schaeffer III}}}{{}}}
+\bibcite{BauTay-JCP-86}{{66}{1986}{{Bauschlicher\ and\ Taylor}}{{}}}
+\bibcite{JenBun-JCP-88}{{67}{1988}{{Jensen\ and\ Bunker}}{{}}}
+\bibcite{SheVanYamSch-JMS-97}{{68}{1997}{{Sherrill\ \emph  {et~al.}}}{{Sherrill, {Van Huis}, Yamaguchi,\ and\ Schaefer}}}
+\bibcite{AbrShe-JCP-04}{{69}{2004}{{Abrams\ and\ Sherrill}}{{}}}
+\bibcite{AbrShe-CPL-05}{{70}{2005}{{Abrams\ and\ Sherrill}}{{}}}
+\bibcite{ZimTouZhaMusUmr-JCP-09}{{71}{2009}{{Zimmerman\ \emph  {et~al.}}}{{Zimmerman, Toulouse, Zhang, Musgrave,\ and\ Umrigar}}}
+\bibcite{GouPieWlo-MP-10}{{72}{2010}{{Gour\ \emph  {et~al.}}}{{Gour, Piecuch,\ and\ Wloch}}}
+\bibcite{ChiHolAdaOttUmrShaZim-JPCA-18}{{73}{2018}{{Chien\ \emph  {et~al.}}}{{Chien, Holmes, Otten, Umrigar, Sharma,\ and\ Zimmerman}}}
+\bibcite{HelJorOls-BOOK-02}{{74}{2002}{{Helgaker\ \emph  {et~al.}}}{{Helgaker, J{\o }rgensen,\ and\ Olsen}}}
+\bibcite{LooGalJac-JPCL-18}{{75}{2018{}}{{Loos\ \emph  {et~al.}}}{{Loos, Galland,\ and\ Jacquemin}}}
+\bibcite{LooJac-JCTC-19}{{76}{2019}{{Loos\ and\ Jacquemin}}{{}}}
+\bibcite{CaiTozRei-JCP-00}{{77}{2000}{{Cai\ \emph  {et~al.}}}{{Cai, Tozer,\ and\ Reimers}}}
+\bibcite{RubSerMer-JCP-08}{{78}{2008}{{Rubio\ \emph  {et~al.}}}{{Rubio, Serrano-Andr{\'e}s,\ and\ Merch{\'a}n}}}
+\bibcite{LiPal-JCP-11}{{79}{2011}{{Li\ and\ Paldus}}{{}}}
+\bibcite{SchGoe-JCTC-17}{{80}{2017}{{Schwabe\ and\ Goerigk}}{{}}}
+\bibcite{BarDelPerMat-JMS-97}{{81}{1997}{{Bartlett\ \emph  {et~al.}}}{{Bartlett, Bene, Perera,\ and\ Mattie}}}
+\bibcite{Var-JCP-08}{{82}{2008}{{Varandas}}{{}}}
+\bibcite{PurZhaKra-JCP-09}{{83}{2009}{{Purwanto\ \emph  {et~al.}}}{{Purwanto, Zhang,\ and\ Krakauer}}}
+\bibcite{AngCimPas-MP-12}{{84}{2012}{{Angeli\ \emph  {et~al.}}}{{Angeli, Cimiraglia,\ and\ Pastore}}}
+\bibcite{BooCleThoAla-JCP-11}{{85}{2011}{{Booth\ \emph  {et~al.}}}{{Booth, Cleland, Thom,\ and\ Alavi}}}
+\bibcite{Sha-JCP-15}{{86}{2015}{{Sharma}}{{}}}
+\bibcite{SokCha-JCP-16}{{87}{2016}{{Sokolov\ and\ Chan}}{{}}}
+\bibcite{VarRoc-PTRSMPES-18}{{88}{2018}{{Varandas\ and\ Rocha}}{{}}}
+\bibcite{SerMarNebLinRoo-JCP-93}{{89}{1993}{{{Serrano-Andr\'es}\ \emph  {et~al.}}}{{{Serrano-Andr\'es}, Merch\'an, Nebot-Gil, Lindh,\ and\ Roos}}}
+\bibcite{WatGwaBar-JCP-96}{{90}{1996}{{Watts\ \emph  {et~al.}}}{{Watts, Gwaltney,\ and\ Bartlett}}}
+\bibcite{WibOliTru-JPCA-02}{{91}{2002}{{Wiberg\ \emph  {et~al.}}}{{Wiberg, de~Oliveria,\ and\ Trucks}}}
+\bibcite{BarPaiLis-JCP-04}{{92}{0004}{{Barbatti\ \emph  {et~al.}}}{{Barbatti, Paier,\ and\ Lischka}}}
+\bibcite{Ang-JCC-08}{{93}{2008}{{Angeli}}{{}}}
+\bibcite{SchSilSauThi-JCP-08}{{94}{2008}{{Schreiber\ \emph  {et~al.}}}{{Schreiber, Silva-Junior, Sauer,\ and\ Thiel}}}
+\bibcite{SilSchSauThi-JCP-10}{{95}{2010{}}{{Silva-Junior\ \emph  {et~al.}}}{{Silva-Junior, Schreiber, Sauer,\ and\ Thiel}}}
+\bibcite{SilSauSchThi-MP-10}{{96}{2010{}}{{Silva-Junior\ \emph  {et~al.}}}{{Silva-Junior, Sauer, Schreiber,\ and\ Thiel}}}
+\bibcite{Ang-IJQC-10}{{97}{2010}{{Angeli}}{{}}}
+\bibcite{DadSmaBooAlaFil-JCTC-12}{{98}{2012}{{Daday\ \emph  {et~al.}}}{{Daday, Smart, Booth, Alavi,\ and\ Filippi}}}
+\bibcite{FelPetDav-JCP-14}{{99}{2014}{{Feller\ \emph  {et~al.}}}{{Feller, Peterson,\ and\ Davidson}}}
+\bibstyle{apsrev4-1}
+\newlabel{LastBibItem}{{99}{8}{}{section*.15}{}}
+\newlabel{LastPage}{{}{8}{}{}{}}
diff --git a/HAL/Ex-srDFT.bbl b/HAL/Ex-srDFT.bbl
new file mode 100644
index 0000000..5947ab3
--- /dev/null
+++ b/HAL/Ex-srDFT.bbl
@@ -0,0 +1,1031 @@
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+\bibitem [{\citenamefont {Kutzelnigg}(1985)}]{Kut-TCA-85}%
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+  {Seminario}}}\ (\bibinfo  {publisher} {Elsevier},\ \bibinfo {address}
+  {Amsterdam},\ \bibinfo {year} {1996})\ pp.\ \bibinfo {pages}
+  {327--357}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Leininger}\ \emph {et~al.}(1997)\citenamefont
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+\bibitem [{\citenamefont {Parr}\ and\ \citenamefont
+  {Yang}(1989)}]{ParYan-BOOK-89}%
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+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.~G.}\ \bibnamefont
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+\bibitem [{\citenamefont {Szabo}\ and\ \citenamefont
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+\bibitem [{\citenamefont {Kato}(1957)}]{Kat-CPAM-57}%
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+  {\bibinfo  {journal} {Comm. Pure Appl. Math.}\ }\textbf {\bibinfo {volume}
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+  {NoStop}%
+\bibitem [{\citenamefont {Franck}\ \emph {et~al.}(2015)\citenamefont {Franck},
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+  (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {{Morgan III}}\ and\ \citenamefont
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+  {\bibinfo  {journal} {J. Phys. Chem.}\ }\textbf {\bibinfo {volume} {97}},\
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+\bibitem [{\citenamefont {Loos}\ and\ \citenamefont
+  {Gill}(2010)}]{LooGil-MP-10}%
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+\bibitem [{\citenamefont {Toulouse}\ \emph {et~al.}(2005)\citenamefont
+  {Toulouse}, \citenamefont {Gori-Giorgi},\ and\ \citenamefont
+  {Savin}}]{TouGorSav-TCA-05}%
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+\bibitem [{\citenamefont {Hohenberg}\ and\ \citenamefont
+  {Kohn}(1964)}]{HohKoh-PR-64}%
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+  {\bibinfo  {journal} {Phys. Rev.}\ }\textbf {\bibinfo {volume} {{136}}},\
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+\bibitem [{\citenamefont {Kohn}\ and\ \citenamefont
+  {Sham}(1965)}]{KohSha-PR-65}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
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+  Rev.}\ }\textbf {\bibinfo {volume} {140}},\ \bibinfo {pages} {A1133}
+  (\bibinfo {year} {1965})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Loos}\ and\ \citenamefont
+  {Gill}(2016)}]{LooGil-WIRES-16}%
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+\bibitem [{\citenamefont {Perdew}\ \emph {et~al.}(1996)\citenamefont {Perdew},
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+  \BibitemOpen
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+\bibitem [{\citenamefont {Gori-Giorgi}\ and\ \citenamefont
+  {Savin}(2006)}]{GorSav-PRA-06}%
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+  {\doibase 10.1063/1.1679199} {\bibfield  {journal} {\bibinfo  {journal} {J.
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+  (\bibinfo {year} {1973})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Giner}\ \emph {et~al.}(2013)\citenamefont {Giner},
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+\bibitem [{\citenamefont {Dasgupta}\ and\ \citenamefont
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+  {\bibinfo  {journal} {J. Comput. Chem.}\ }\textbf {\bibinfo {volume} {38}},\
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+\bibitem [{\citenamefont {Sherrill}\ \emph {et~al.}(1998)\citenamefont
+  {Sherrill}, \citenamefont {Leininger}, \citenamefont {Huis},\ and\
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+  \BibitemOpen
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+  {Schaefer}},\ }\href {\doibase 10.1063/1.475465} {\bibfield  {journal}
+  {\bibinfo  {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {108}},\
+  \bibinfo {pages} {1040} (\bibinfo {year} {1998})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {{H. F. Schaeffer III}}(1986)}]{Sch-Science-86}%
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+\bibitem [{\citenamefont {Bauschlicher}\ and\ \citenamefont
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+  {\bibinfo  {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {85}},\
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+\bibitem [{\citenamefont {Jensen}\ and\ \citenamefont
+  {Bunker}(1988)}]{JenBun-JCP-88}%
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+  {\bibinfo  {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {89}},\
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+\bibitem [{\citenamefont {Sherrill}\ \emph {et~al.}(1997)\citenamefont
+  {Sherrill}, \citenamefont {{Van Huis}}, \citenamefont {Yamaguchi},\ and\
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+\bibitem [{\citenamefont {Abrams}\ and\ \citenamefont
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+\bibitem [{\citenamefont {Zimmerman}\ \emph {et~al.}(2009)\citenamefont
+  {Zimmerman}, \citenamefont {Toulouse}, \citenamefont {Zhang}, \citenamefont
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+  {\bibfield  {journal} {\bibinfo  {journal} {J. Chem. Phys.}\ }\textbf
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+\bibitem [{\citenamefont {Purwanto}\ \emph {et~al.}(2009)\citenamefont
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+\bibitem [{\citenamefont {Watts}\ \emph {et~al.}(1996)\citenamefont {Watts},
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+  {Thiel}}]{SilSchSauThi-JCP-10}%
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+  {Thiel}}]{SilSauSchThi-MP-10}%
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+  (\bibinfo {year} {2010})}\BibitemShut {NoStop}%
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+  \citenamefont {Smart}, \citenamefont {Booth}, \citenamefont {Alavi},\ and\
+  \citenamefont {Filippi}}]{DadSmaBooAlaFil-JCTC-12}%
+  \BibitemOpen
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+  {\bibfnamefont {C.}~\bibnamefont {Filippi}},\ }\href {\doibase
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+  (\bibinfo {year} {2012})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Feller}\ \emph {et~al.}(2014)\citenamefont {Feller},
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+  {Davidson}},\ }\href {\doibase 10.1063/1.4894482} {\bibfield  {journal}
+  {\bibinfo  {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {141}},\
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diff --git a/HAL/Ex-srDFT.bib b/HAL/Ex-srDFT.bib
new file mode 100644
index 0000000..5f70b82
--- /dev/null
+++ b/HAL/Ex-srDFT.bib
@@ -0,0 +1,12998 @@
+%% This BibTeX bibliography file was created using BibDesk.
+%% http://bibdesk.sourceforge.net/
+
+%% Created for Pierre-Francois Loos at 2019-09-19 14:59:09 +0200 
+
+
+%% Saved with string encoding Unicode (UTF-8) 
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+@article{HofSchKloKoh-JCP-19,
+	Author = {S. Hofener and N. Schieschke and W. Klopper and A. Kohn},
+	Date-Added = {2019-09-19 14:56:02 +0200},
+	Date-Modified = {2019-09-19 14:59:06 +0200},
+	Doi = {10.1063/1.5094434},
+	Journal = {J. Chem. Phys.},
+	Pages = {184110},
+	Title = {The extended explicitly-correlated second- order approximate coupled-cluster singles and doubles ansatz suitable for response theory},
+	Volume = {150},
+	Year = {2019}}
+
+@article{LooGalJac-JPCL-18,
+	Author = {Loos, Pierre-Fran{\c c}ois and Galland, Nicolas and Jacquemin, Denis},
+	Date-Added = {2019-07-01 13:58:30 +0200},
+	Date-Modified = {2019-07-01 13:59:12 +0200},
+	Doi = {10.1021/acs.jpclett.8b02058},
+	Journal = {J. Phys. Chem. Lett.},
+	Number = {16},
+	Pages = {4646--4651},
+	Title = {Theoretical 0--0 Energies with Chemical Accuracy},
+	Volume = {9},
+	Year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.8b02058}}
+
+@article{LooJac-JCTC-19,
+	Author = {P. F. Loos and D. Jacquemin},
+	Date-Added = {2019-07-01 13:57:45 +0200},
+	Date-Modified = {2019-07-01 14:00:29 +0200},
+	Doi = {10.1021/acs.jctc.8b01103},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {2481--2491},
+	Title = {Chemically accurate 0-0 energies with not-so-accurate excited state geometries},
+	Volume = {15},
+	Year = {2019},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}}
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+	Author = {P. F. Loos and P. M. W. Gill},
+	Date-Added = {2019-07-01 09:27:40 +0200},
+	Date-Modified = {2019-08-01 12:07:15 +0200},
+	Doi = {10.1080/00268976.2010.508472},
+	Journal = {Mol. Phys.},
+	Pages = {2527},
+	Title = {Excited states of spherium},
+	Volume = {108},
+	Year = {2010},
+	Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2010.508472}}
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+@article{KutMor-ZPD-96,
+	Author = {W. Kutzelnigg and J. D. {Morgan III}},
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+	Date-Modified = {2019-08-01 12:05:15 +0200},
+	Doi = {10.1007/BF01426405},
+	Journal = {Z. Phys. D},
+	Pages = {197},
+	Title = {Hund's rules},
+	Volume = {36},
+	Year = {1996},
+	Bdsk-Url-1 = {https://doi.org/10.1007/BF01426405}}
+
+@article{MorKut-JPC-93,
+	Author = {J. D. {Morgan III} and W. Kutzelnigg},
+	Date-Added = {2019-07-01 09:25:54 +0200},
+	Date-Modified = {2019-08-01 12:04:37 +0200},
+	Doi = {10.1021/j100112a051},
+	Journal = {J. Phys. Chem.},
+	Pages = {2425},
+	Title = {Hund's rules, the alternating rule, and symmetry holes},
+	Volume = {97},
+	Year = {1993},
+	Bdsk-Url-1 = {https://doi.org/10.1021/j100112a051}}
+
+@article{LooBloGil-JCP-2015,
+	Author = {P. F. Loos and N. J. Bloomfield and P. M. W. Gill},
+	Date-Added = {2019-07-01 09:23:27 +0200},
+	Date-Modified = {2019-08-01 12:06:46 +0200},
+	Doi = {10.1063/1.4935374},
+	Journal = {J. Chem. Phys.},
+	Pages = {181101},
+	Volume = {143},
+	Year = {2015},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4935374}}
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+@article{GouPieWlo-MP-10,
+	Author = {J. R. Gour and P. Piecuch and M. Wloch},
+	Date-Added = {2019-07-01 08:20:25 +0200},
+	Date-Modified = {2019-07-01 08:21:57 +0200},
+	Doi = {10.1080/00268976.2010.518573},
+	Journal = {Mol. Phys.},
+	Pages = {2633--2646},
+	Title = {Comparison of the completely renormalized equation-of-motion coupled-cluster and Quantum Monte Carlo results for the low-lying electronic states of methylene},
+	Volume = {108},
+	Year = {2010},
+	Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2010.518573}}
+
+@article{SceCafBenJacLoo-RC-19,
+	Author = {A. Scemama and M. Caffarel and A. Benali and D. Jacquemin and P. F. Loos},
+	Date-Added = {2019-05-30 21:47:05 +0200},
+	Date-Modified = {2019-08-01 12:12:37 +0200},
+	Doi = {10.1016/j.rechem.2019.100002},
+	Journal = {Res. Chem.},
+	Pages = {100002},
+	Title = {Influence of Pseudopotentials on Excitation Energies From Selected Configuration Interaction and Diffusion Monte Carlo},
+	Volume = {1},
+	Year = {2019},
+	Bdsk-Url-1 = {https://doi.org/10.1016/j.rechem.2019.100002}}
+
+@article{SheLeiVanSch-JCP-98,
+	Author = {C. D. Sherrill and M. L. Leininger and T. J. Van Huis and H. F. Schaefer},
+	Date-Added = {2019-05-28 22:50:09 +0200},
+	Date-Modified = {2019-08-01 12:13:44 +0200},
+	Doi = {10.1063/1.475465},
+	Journal = {J. Chem. Phys.},
+	Pages = {1040},
+	Title = {Structures and vibrational frequencies in the full configuration interaction limit: Predictions for four electronic states of methylene using a triple-zeta plus double polarization (TZ2P) basis.},
+	Volume = {108},
+	Year = {1998},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.475465}}
+
+@article{BauTay-JCP-86,
+	Author = {C. W. Bauschlicher and P. R. Taylor},
+	Date-Added = {2019-05-28 22:46:11 +0200},
+	Date-Modified = {2019-08-01 12:14:48 +0200},
+	Doi = {10.1063/1.451431},
+	Journal = {J. Chem. Phys.},
+	Pages = {6510-6512},
+	Title = {A full CI treatment of the 1A1-3B1 separation in methylene},
+	Volume = {85},
+	Year = {1986},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.451431}}
+
+@article{Sch-Science-86,
+	Author = {{H. F. Schaeffer III}},
+	Date-Added = {2019-05-28 22:42:40 +0200},
+	Date-Modified = {2019-08-01 12:14:24 +0200},
+	Doi = {10.1126/science.231.4742.1100},
+	Journal = {Science},
+	Pages = {1100-1107},
+	Title = {Methylene: A paradigm for computational quantum chemistry},
+	Year = {1986},
+	Bdsk-Url-1 = {https://doi.org/10.1126/science.231.4742.1100}}
+
+@article{BarDelPerMat-JMS-97,
+	Author = {Rodney J. Bartlett and Janet E. Del Bene and S.Ajith Perera and Renee-Peloquin Mattie},
+	Date-Added = {2019-05-28 13:34:13 +0200},
+	Date-Modified = {2019-05-28 13:35:03 +0200},
+	Doi = {https://doi.org/10.1016/S0166-1280(97)90277-3},
+	Issn = {0166-1280},
+	Journal = {J. Mol. Struct. (THEOCHEM)},
+	Keywords = {Ammonia, Spectra, Heat of formation, Properties, Correlation effects},
+	Pages = {157--168},
+	Title = {Ammonia: The Prototypical Lone Pair Molecule},
+	Url = {http://www.sciencedirect.com/science/article/pii/S0166128097902773},
+	Volume = {400},
+	Year = {1997},
+	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0166128097902773},
+	Bdsk-Url-2 = {https://doi.org/10.1016/S0166-1280(97)90277-3}}
+
+@article{SchGoe-JCTC-17,
+	Author = {Schwabe, Tobias and Goerigk, Lars},
+	Date-Added = {2019-05-28 13:33:10 +0200},
+	Date-Modified = {2019-08-01 12:07:31 +0200},
+	Doi = {10.1021/acs.jctc.7b00386},
+	Journal = {J. Chem. Theory Comput.},
+	Number = {9},
+	Pages = {4307--4323},
+	Title = {Time-Dependent Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling},
+	Volume = {13},
+	Year = {2017},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00386}}
+
+@article{RubSerMer-JCP-08,
+	Author = {Mercedes Rubio and Luis Serrano-Andr{\'e}s and Manuela Merch{\'a}n},
+	Date-Added = {2019-05-28 12:21:04 +0200},
+	Date-Modified = {2019-08-01 12:08:44 +0200},
+	Doi = {10.1063/1.2837827},
+	Journal = {J. Chem. Phys.},
+	Number = {10},
+	Pages = {104305},
+	Title = {Excited States of the Water Molecule: Analysis of the Valence and Rydberg Character},
+	Volume = {128},
+	Year = {2008},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.2837827}}
+
+@article{LiPal-JCP-11,
+	Author = {Xiangzhu Li and Josef Paldus},
+	Date-Added = {2019-05-28 12:20:10 +0200},
+	Date-Modified = {2019-08-01 12:09:03 +0200},
+	Doi = {10.1063/1.3595513},
+	Journal = {J. Chem. Phys.},
+	Number = {21},
+	Pages = {214118},
+	Title = {Multi-Reference State-Universal Coupled-Cluster Approaches to Electronically Excited States},
+	Volume = {134},
+	Year = {2011},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3595513}}
+
+@article{CaiTozRei-JCP-00,
+	Author = {Zheng-Li Cai and David J. Tozer and Jeffrey R. Reimers},
+	Date-Added = {2019-05-28 12:19:14 +0200},
+	Date-Modified = {2019-08-01 12:08:23 +0200},
+	Doi = {10.1063/1.1312826},
+	Journal = {J. Chem. Phys.},
+	Number = {17},
+	Pages = {7084--7096},
+	Title = {Time-Dependent Density-Functional Determination of Arbitrary Singlet and Triplet Excited-State Potential Energy Surfaces: Application to the Water Molecule},
+	Volume = {113},
+	Year = {2000},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.1312826}}
+
+@article{PurZhaKra-JCP-09,
+	Author = {Purwanto, Wirawan and Zhang, Shiwei and Krakauer, Henry},
+	Date-Added = {2019-05-28 12:00:39 +0200},
+	Date-Modified = {2019-05-28 12:00:56 +0200},
+	Doi = {10.1063/1.3077920},
+	File = {/Users/loos/Zotero/storage/JDM6C32K/Purwanto et al. - 2009 - Excited state calculations using phaseless auxilia.pdf},
+	Issn = {0021-9606, 1089-7690},
+	Journal = {J. Chem. Phys.},
+	Language = {en},
+	Month = mar,
+	Number = {9},
+	Pages = {094107},
+	Shorttitle = {Excited State Calculations Using Phaseless Auxiliary-Field Quantum {{Monte Carlo}}},
+	Title = {Excited State Calculations Using Phaseless Auxiliary-Field Quantum {{Monte Carlo}}: {{Potential}} Energy Curves of Low-Lying {{C2}} Singlet States},
+	Volume = {130},
+	Year = {2009},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3077920}}
+
+@article{Var-JCP-08,
+	Author = {Varandas, A. J. C.},
+	Date-Added = {2019-05-28 11:58:55 +0200},
+	Date-Modified = {2019-05-28 11:59:09 +0200},
+	Doi = {10.1063/1.3036115},
+	Issn = {0021-9606, 1089-7690},
+	Journal = {J. Chem. Phys.},
+	Language = {en},
+	Month = dec,
+	Number = {23},
+	Pages = {234103},
+	Shorttitle = {Extrapolation to the Complete-Basis-Set Limit and the Implications of Avoided Crossings},
+	Title = {Extrapolation to the Complete-Basis-Set Limit and the Implications of Avoided Crossings: {{The X $\Sigma$1g}}+, {{B $\Delta$1g}}, and {{B}}${'}$ {{$\Sigma$1g}}+ States of {{C2}}},
+	Volume = {129},
+	Year = {2008},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3036115}}
+
+@article{VarRoc-PTRSMPES-18,
+	Author = {Varandas, A. J. C. and Rocha, C. M. R.},
+	Date-Added = {2019-05-28 11:58:55 +0200},
+	Date-Modified = {2019-05-28 11:59:35 +0200},
+	Doi = {10.1098/rsta.2017.0145},
+	File = {/Users/loos/Zotero/storage/VP3T2AAG/Varandas and Rocha - 2018 - iCi sub ini sub ( ini =2−4) c.pdf},
+	Issn = {1364-503X, 1471-2962},
+	Journal = {Philos. Trans. R. Soc. Math. Phys. Eng. Sci.},
+	Language = {en},
+	Month = mar,
+	Number = {2115},
+	Pages = {20170145},
+	Shorttitle = {{\emph{C}} {\textsubscript{ {\emph{n}} }} ( {\emph{n}} =2-4)},
+	Title = {{\emph{C}} {\textsubscript{ {\emph{n}} }} ( {\emph{n}} =2-4): Current Status},
+	Volume = {376},
+	Year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1098/rsta.2017.0145}}
+
+@article{SokCha-JCP-16,
+	Author = {Sokolov, Alexander Yu. and Chan, Garnet Kin-Lic},
+	Date-Added = {2019-05-28 11:57:29 +0200},
+	Date-Modified = {2019-05-28 11:58:02 +0200},
+	Doi = {10.1063/1.4941606},
+	Issn = {0021-9606, 1089-7690},
+	Journal = {J. Chem. Phys.},
+	Language = {en},
+	Month = feb,
+	Number = {6},
+	Pages = {064102},
+	Title = {A Time-Dependent Formulation of Multi-Reference Perturbation Theory},
+	Volume = {144},
+	Year = {2016},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4941606}}
+
+@article{Sha-JCP-15,
+	Author = {Sharma, Sandeep},
+	Date-Added = {2019-05-28 11:56:29 +0200},
+	Date-Modified = {2019-05-28 11:56:44 +0200},
+	Doi = {10.1063/1.4905237},
+	Issn = {0021-9606, 1089-7690},
+	Journal = {J. Chem. Phys.},
+	Language = {en},
+	Month = jan,
+	Number = {2},
+	Pages = {024107},
+	Title = {A General Non-{{Abelian}} Density Matrix Renormalization Group Algorithm with Application to the {{C}} {\textsubscript{2}} Dimer},
+	Volume = {142},
+	Year = {2015},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4905237}}
+
+@article{AbrShe-JCP-04,
+	Author = {Abrams, Micah L. and Sherrill, C. David},
+	Date-Added = {2019-05-28 11:54:44 +0200},
+	Date-Modified = {2019-05-28 11:55:26 +0200},
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+	Issn = {0021-9606, 1089-7690},
+	Journal = {J. Chem. Phys.},
+	Language = {en},
+	Month = nov,
+	Number = {19},
+	Pages = {9211-9219},
+	Shorttitle = {Full Configuration Interaction Potential Energy Curves for the {{X 1$\Sigma$g}}+, {{B 1$\Delta$g}}, and {{B}}${'}$ {{1$\Sigma$g}}+ States of {{C2}}},
+	Title = {Full Configuration Interaction Potential Energy Curves for the {{X 1$\Sigma_g^+$}}, {{B 1$\Delta_g$}}, and {{B}}${'}$ {{1$\Sigma_g^+$}} States of {{C$_2$}}: {{A}} Challenge for Approximate Methods},
+	Volume = {121},
+	Year = {2004},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.1804498}}
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+@article{AbrShe-CPL-05,
+	Author = {Abrams, Micah L. and Sherrill, C. David},
+	Date-Added = {2019-05-28 11:54:44 +0200},
+	Date-Modified = {2019-05-28 11:55:38 +0200},
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+	Month = {Aug},
+	Number = {1-3},
+	Pages = {121--124},
+	Publisher = {Elsevier BV},
+	Title = {Important configurations in configuration interaction and coupled-cluster wave functions},
+	Url = {http://dx.doi.org/10.1016/j.cplett.2005.06.107},
+	Volume = {412},
+	Year = {2005},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2005.06.107}}
+
+@article{AngCimPas-MP-12,
+	Author = {Angeli, Celestino and Cimiraglia, Renzo and Pastore, Mariachiara},
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+	Issn = {0026-8976, 1362-3028},
+	Journal = {Mol. Phys.},
+	Language = {en},
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+	Pages = {2963-2968},
+	Shorttitle = {A Comparison of Various Approaches in Internally Contracted Multireference Configuration Interaction},
+	Title = {A Comparison of Various Approaches in Internally Contracted Multireference Configuration Interaction: The Carbon Dimer as a Test Case},
+	Volume = {110},
+	Year = {2012},
+	Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2012.689872}}
+
+@article{SchSilSauThi-JCP-08,
+	Author = {Schreiber, M. and Silva-Junior, M. R. and Sauer, S. P. A. and Thiel, W.},
+	Date-Added = {2019-05-28 11:41:37 +0200},
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+	Journal = {J. Chem. Phys.},
+	Pages = {134110},
+	Title = {Benchmarks for Electronically Excited States: CASPT2, CC2, CCSD and CC3},
+	Volume = 128,
+	Year = 2008,
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.2889385}}
+
+@article{SilSauSchThi-MP-10,
+	Author = {Silva-Junior, M. R. and Sauer, S. P. A. and Schreiber, M. and Thiel, W.},
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+	Journal = {Mol. Phys.},
+	Pages = {453--465},
+	Title = {Basis Set Effects on Coupled Cluster Benchmarks of Electronically Excited States: CC3, CCSDR(3) and CC2},
+	Volume = 108,
+	Year = 2010,
+	Bdsk-Url-1 = {https://doi.org/10.1080/00268970903549047}}
+
+@article{SilSchSauThi-JCP-10,
+	Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
+	Date-Added = {2019-05-28 11:41:37 +0200},
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+	Journal = {J. Chem. Phys.},
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+	Title = {Benchmarks of Electronically Excited States: Basis Set Effecs Benchmarks of Electronically Excited States: Basis Set Effects on CASPT2 Results},
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+	Year = 2010,
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3499598}}
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+@article{Ang-JCC-08,
+	Author = {C. Angeli},
+	Date-Added = {2019-05-28 11:37:39 +0200},
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+	Journal = {J. Comput. Chem.},
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+	Volume = {30},
+	Year = {2008},
+	Bdsk-Url-1 = {https://doi.org/10.1002/jcc.21155}}
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+	Author = {Angeli, Celestino},
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+	Year = {2010},
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+@article{DadSmaBooAlaFil-JCTC-12,
+	Author = {Daday, Csaba and Smart, Simon and Booth, George H. and Alavi, Ali and Filippi, Claudia},
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+	Date-Modified = {2019-05-28 11:39:00 +0200},
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+	Volume = {8},
+	Year = {2012},
+	Bdsk-Url-1 = {https://doi.org/10.1021/ct300486d}}
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+@article{SerMarNebLinRoo-JCP-93,
+	Author = {{Serrano-Andr\'es}, Luis and Merch\'an, Manuela and Nebot-Gil, Ignacio and Lindh, Roland and Roos, Bj\"orn O.},
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+	Pages = {3151-3162},
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+	Year = 2002,
+	Bdsk-Url-1 = {https://doi.org/10.1021/jp014123x}}
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+@article{BarPaiLis-JCP-04,
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+	Volume = {130},
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+	Author = {T. Shiozaki and H.-J. Werner},
+	Date-Added = {2019-05-25 17:44:44 +0200},
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+	Journal = {J. Chem. Phys.},
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+	Volume = {134},
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+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3587632}}
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+@article{ShiWer-JCP-10,
+	Author = {T. Shiozaki and H.-J. Werner},
+	Date-Added = {2019-05-25 17:43:35 +0200},
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+	Title = {Communication: Second-order multireference perturbation theory with explicit correlation: CASPT2-F12},
+	Volume = {133},
+	Year = {2010},
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+	Author = {T. Shiozaki and G. Knizia and H.-J. Werner},
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+	Journal = {J. Chem. Phys.},
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+	Volume = {134},
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+	Author = {T. Shiozaki and H.-J. Werner},
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+	Author = {C. Neiss and C. Hattig and W. Klopper},
+	Date-Added = {2019-05-25 17:37:42 +0200},
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+	Volume = {125},
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+	Author = {M. Hanauer and A. Kohn},
+	Date-Added = {2019-05-25 17:36:39 +0200},
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+	Author = {H. Fliegl and C. Hattig and W. Klopper},
+	Date-Added = {2019-05-25 17:35:21 +0200},
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+	Author = {Q. Ma and H.-J. Werner},
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+	Volume = {8},
+	Year = {2018},
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+	Author = {J. L. Whitten},
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+@article{BouBenMayCaf-JCP-09,
+	Author = {T. Bouab\c{c}a and N. Ben Amor and D. Maynau and M. Caffarel},
+	Journal = {J. Chem. Phys.},
+	Pages = {114107},
+	Volume = {130},
+	Year = {2009}}
+
+@article{BouBraCaf-JCP-10,
+	Author = {T. Bouab\c{c}a and B. Bra\"ida and M. Caffarel},
+	Journal = {J. Chem. Phys.},
+	Pages = {044111},
+	Title = {Multi-Jastrow trial wavefunctions for electronic structure calculations with quantum Monte Carlo},
+	Volume = {133},
+	Year = {2010}}
+
+@article{BouChiLegDucBlaJac-JCTC-14,
+	Author = {{P. Boulanger, S. Chibani, B. Le Guennic, I. Duchemin, X. Blase, and D. Jacquemin}},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {4548},
+	Volume = {10},
+	Year = {2014}}
+
+@article{BouJacDucBla-JCTC-14,
+	Author = {P. Boulanger and D. Jacquemin and I. Duchemin and X. Blase},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {1212},
+	Volume = {10},
+	Year = {2014}}
+
+@article{BowSugAld-PRB-94,
+	Author = {C. Bowen and G. Sugiyama and B. J. Alder},
+	Journal = {Phys. Rev. B},
+	Pages = {14838},
+	Volume = {{50}},
+	Year = {1996}}
+
+@article{BoyCou-JPB-73,
+	Author = {R. J. Boyd and C. A. Coulson},
+	Journal = {J. Phys. B},
+	Pages = {782},
+	Volume = {6},
+	Year = {1973}}
+
+@article{BoySarUga-JPB-88,
+	Author = {R. J. Boyd and C. Sarasola and J. M. Ugalde},
+	Journal = {J. Phys. B},
+	Pages = {2555},
+	Volume = {21},
+	Year = {1988}}
+
+@article{BraHib-02,
+	Author = {B. Braida and L. Thogersen and W. Wu and P. C. Hiberty},
+	Journal = {J. Am. Chem. Soc.},
+	Pages = {11781},
+	Volume = {124},
+	Year = {2002}}
+
+@article{BraHib-04,
+	Author = {B. Braida and P. C. Hiberty},
+	Journal = {J. Am. Chem. Soc.},
+	Pages = {14890},
+	Volume = {126},
+	Year = {2004}}
+
+@article{BraHib-08,
+	Author = {B. Braida and P. C. Hiberty},
+	Journal = {J. Phys. Chem. A},
+	Pages = {13045},
+	Volume = {112},
+	Year = {2008}}
+
+@article{BraTouCafUmr-JCP-11,
+	Author = {B. Bra\"ida and J. Toulouse and M. Caffarel and C. J. Umrigar},
+	Journal = {J. Chem. Phys.},
+	Pages = {084108},
+	Title = {Quantum Monte Carlo with Jastrow-valence-bond wave functions},
+	Volume = {134},
+	Year = {2011}}
+
+@misc{BraTouCafUmr-JJJ-XX-note2,
+	Note = {In our BOVB wave functions, we use different sets of orbital coefficients, but a single set of basis exponents shared by all orbital sets.}}
+
+@misc{BraTouCafUmr-JJJ-XX-note3,
+	Note = {Bouab\c{c}a {\it et al.}~\cite{BouBraCaf-JCP-10} have introduced a wave function with several Jastrow factors attached to individual molecular orbitals. With such a wave function, the correlation effects can be treated differently in atomic and binding regions. In the case of the FH molecule, no atomic core Jastrow was used and two different valence Jastrow factors (one for the lone pairs paying a role in the bond and the other one for the $\sigma$-bond) were introduced. The resulting binding energy was essentially exact within error bars. Combining the various VB wave functions discussed in this work with this multi-Jastrow approach is presently under investigation.}}
+
+@misc{BraTouCafUmr-JJJ-XX-note,
+	Note = {In the condensed-matter community, ``stricly localized orbitals'' often refers to orbitals that vanish exactly at some finite distance. In the present work, ``stricly localized orbitals'' is employed in the sense usually used in the quantum chemistry community, i.e. orbitals expanded on Gaussian or Slater basis functions centered on a single atom. Thus, these orbitals vanish exactly only at infinite distance.}}
+
+@article{BreAda-JCP-11,
+	Author = {E. Br\'emond and C. Adamo},
+	Journal = {J. Chem. Phys.},
+	Pages = {024106},
+	Volume = {135},
+	Year = {2011}}
+
+@article{BreBou-PRB-96,
+	Author = {J. L. Bretonnet and M. Boulahbak},
+	Journal = {Phys. Rev. B},
+	Pages = {6859},
+	Volume = {{53}},
+	Year = {1996}}
+
+@incollection{BreCepRey-INC-01,
+	Author = {D. Bressanini and D. M. Ceperley and P. Reynolds},
+	Booktitle = {Recent Advances in Quantum Monte Carlo Methods, II},
+	Editor = {S. Rothstein},
+	Publisher = {World Scientific},
+	Title = {What do we know about wave function nodes?},
+	Year = {2001}}
+
+@article{BreMelMor-PRA-98,
+	Author = {D. Bressanini and M. Mella and G. Morosi},
+	Journal = {Phys. Rev. A},
+	Pages = {1678},
+	Volume = {57},
+	Year = {1998}}
+
+@article{BreMorTar-JCP-05,
+	Author = {D. Bressanini and G. Morosi and S. Tarasco},
+	Journal = {J. Chem. Phys.},
+	Pages = {204109},
+	Volume = {123},
+	Year = {2005}}
+
+@article{BroDevLem-PRB-80,
+	Author = {F. Brosens and J. T. Devreese and L. F. Lemmens},
+	Journal = {Phys. Rev. B},
+	Pages = {1363},
+	Volume = {{21}},
+	Year = {1980}}
+
+@article{BroPanSto-PRL-09,
+	Author = {Christian Brouder and Gianluca Panati and Gabriel Stoltz},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {230401},
+	Volume = {103},
+	Year = {2009}}
+
+@article{BroTraLopNee-JCP-07,
+	Author = {M. D. Brown and J. R. Trail and P. L\'opez R\'ios and R. J. Needs},
+	Journal = {J. Chem. Phys.},
+	Pages = {224110},
+	Title = {Energies of the first row atoms from quantum Monte Carlo},
+	Volume = {126},
+	Year = {2007}}
+
+@article{BroYinLor-SR-13,
+	Author = {V. Brosco and Z.-J. Ying and J. Lorenzana},
+	Journal = {Sci. Rep.},
+	Pages = {2172},
+	Volume = {3},
+	Year = {2013}}
+
+@article{BruHamNea-JCP-15,
+	Author = {F. Bruneval and S. M. Hamed and J. B. Neaton},
+	Journal = {J. Chem. Phys.},
+	Pages = {244101},
+	Volume = {142},
+	Year = {2015}}
+
+@article{BruProKroBre-JCP-17,
+	Author = {Iulia Emilia Brumboiu and Georgia Prokopiou and Leeor Kronik and Barbara Brena},
+	Journal = {J. Chem. Phys.},
+	Pages = {044301},
+	Volume = {147},
+	Year = {2017}}
+
+@phdthesis{Bru-THESIS-05,
+	Author = {F. Bruneval},
+	School = {Ecole Polytechnique},
+	Year = {2005}}
+
+@article{BuiBae-MP-02,
+	Author = {M. A. Buijse and E. J. Baerends},
+	Journal = {Mol. Phys.},
+	Pages = {401},
+	Volume = {100},
+	Year = {2002}}
+
+@article{BurCruLam-JCP-98,
+	Author = {K. Burke and F. G. Cruz and K.-C. Lam},
+	Journal = {J. Chem. Phys},
+	Pages = {8161},
+	Volume = {109},
+	Year = {1998}}
+
+@article{BurErnPer-CPL-97,
+	Author = {K. Burke and M. Ernzerhof and J. P. Perdew},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {115},
+	Volume = {265},
+	Year = {1997}}
+
+@article{BurFilDol-JCP-07,
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+	Journal = {J. Chem. Phys.},
+	Pages = {234105},
+	Volume = {126},
+	Year = {2007}}
+
+@article{Bur-JCP-12,
+	Author = {K. Burke},
+	Journal = {J. Chem. Phys.},
+	Pages = {150901},
+	Title = {{Perspective on density functional theory}},
+	Volume = {136},
+	Year = {2012}}
+
+@article{BurPerErn-JCP-98,
+	Author = {K. Burke and J. P. Perdew and M. Ernzerhof},
+	Journal = {J. Chem. Phys},
+	Pages = {3760},
+	Volume = {109},
+	Year = {1998}}
+
+@article{BurPer-IJQC-95,
+	Author = {K. Burke and J. P. Perdew},
+	Journal = {Int. J. Quantum. Chem.},
+	Pages = {199},
+	Volume = {{56}},
+	Year = {1995}}
+
+@article{BurPerLan-PRL-94,
+	Author = {K. Burke and J. P. Perdew and D. C. Langreth},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {1283},
+	Volume = {73},
+	Year = {1994}}
+
+@article{BurPerLev-PRA-96,
+	Author = {K. Burke and J. P. Perdew and M. Levy},
+	Journal = {Phys. Rev. A},
+	Pages = {R2915},
+	Volume = {53},
+	Year = {1996}}
+
+@inbook{BurPerWan-INC-98,
+	Address = {NY},
+	Author = {Kieron Burke and John P. Perdew and Y. Wang},
+	Booktitle = {Electronic Density Functional Theory: Recent Progress and New Directions},
+	Date-Modified = {2013-02-12 00:16:04 +0000},
+	Editor = {J. F. Dobson and G. Vignale and M. P. Das},
+	Organization = {Plenum},
+	Pages = {81},
+	Pub-Num = {34},
+	Publisher = {Plenum},
+	Title = {Derivation of a generalized gradient approximation: The PW91 density functional},
+	Url = {http://link.springer.com/chapter/10.1007%2F978-1-4899-0316-7_7},
+	Year = {1997},
+	Bdsk-Url-1 = {http://link.springer.com/chapter/10.1007%2F978-1-4899-0316-7_7}}
+
+@article{BygAllMan-JCP-12,
+	Author = {P. J. Bygrave and N. L. Allan and F. R. Manby},
+	Journal = {J. Chem. Phys.},
+	Pages = {164102},
+	Volume = {137},
+	Year = {2012}}
+
+@article{BylKle-PRB-90,
+	Author = {D. M. Bylander and L. Kleinman},
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+	Pages = {7868},
+	Volume = {41},
+	Year = {1990}}
+
+@article{ByrCotMon-JCP-11,
+	Author = {{J. N. Byrd, R. C\^ot\'e, and J. A. Montgomery, Jr}},
+	Journal = {J. Chem. Phys.},
+	Pages = {244307},
+	Volume = {135},
+	Year = {2011}}
+
+@article{BytRue-JCP-05,
+	Author = {L. Bytautas and K. Ruedenberg},
+	Journal = {J. Chem. Phys.},
+	Pages = {154110},
+	Volume = {122},
+	Year = {2005}}
+
+@misc{BytRue-JCP-05-note,
+	Note = {Note that this estimate of the exact well depth differs from the one used in Ref.~\onlinecite{UmrTouFilSorHeg-JJJ-XX} where we used instead the scalar-relativistic, valence-corrected estimate of Ref.~\onlinecite{BytRue-JCP-05} since calculations were performed with a relativistic pseudopotential.}}
+
+@article{CadWah-ADNDT-74,
+	Author = {P. E. Cade and A. C. Wahl},
+	Journal = {At. Data Nucl. Data Tables},
+	Pages = {340},
+	Volume = {13},
+	Year = {1974}}
+
+@article{Caf-ActNum-98,
+	Author = {R. E. Caflisch},
+	Journal = {Acta Numerica},
+	Pages = {1},
+	Title = {{Monte Carlo and quasi-Monte Carlo methods}},
+	Volume = {1998},
+	Year = {1998}}
+
+@article{CafCla-JCP-88,
+	Author = {M. Caffarel and P. Claverie},
+	Doi = {10.1063/1.454228},
+	Journal = {J. Chem. Phys.},
+	Keywords = {QUANTUM STATISTICAL MECHANICS; MONTE CARLO METHOD; FERMIONS; FEYNMAN PATH INTEGRAL; SCHROEDINGER EQUATION},
+	Number = {2},
+	Pages = {1100-1109},
+	Publisher = {AIP},
+	Title = {{Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman--Kac formula. II. Applications to simple systems}},
+	Volume = {88},
+	Year = {1988},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.454228}}
+
+@article{CaiRei-JCP-00,
+	Author = {Z.-L. Cai and J. R. Reimers},
+	Journal = {J. Chem. Phys.},
+	Pages = {527},
+	Volume = {112},
+	Year = {2000}}
+
+@article{CaiZanKitKocKreScr-PRA-05,
+	Author = {J. Caillat and J. Zanghellini and M. Kitzler and O. Koch and W. Kreuzer and A. Scrinzi},
+	Journal = {Phys. Rev. A},
+	Pages = {012712},
+	Volume = {71},
+	Year = {2005}}
+
+@article{CalSor-PRB-98,
+	Author = {{M. Calandra Buonaura and S. Sorella}},
+	Journal = {Phys. Rev. B},
+	Pages = {11446},
+	Title = {{Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers}},
+	Volume = {57},
+	Year = {1998}}
+
+@article{CanBoyTha-JCP-93,
+	Author = {N. M. Cann and R. J. Boyd and A. J. Thakkar},
+	Journal = {J. Chem. Phys.},
+	Pages = {7132},
+	Volume = {98},
+	Year = {1993}}
+
+@article{CanMou-NL-14,
+	Author = {Eric Canc\`es and Nahia Mourad},
+	Journal = {Nonlinearity},
+	Number = {9},
+	Pages = {1999},
+	Title = {A mathematical perspective on density functional perturbation theory},
+	Volume = {27},
+	Year = {2014}}
+
+@article{CanPer-JCP-08,
+	Author = {E. Canc\`es and K. Pernal},
+	Journal = {J. Chem. Phys.},
+	Pages = {134108},
+	Title = {{Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations}},
+	Volume = {128},
+	Year = {2008}}
+
+@article{CapNalPar-JCP-82,
+	Author = {Joseph F. Capitani and Roman F. Nalewajski and Robert G. Parr},
+	Journal = {The Journal of Chemical Physics},
+	Keywords = {MOLECULES; MOLECULAR STRAUCTURE; FUNCTIONALS; BORN&#150;OPPENHEIMER APPROXIMATION; GROUND STATES; HAMILTONIANS; ELECTRON DENSITY; NUCLEI; ELECTRIC FIELDS; EXCITED STATES; BOUND STATE; USES},
+	Number = {1},
+	Pages = {568-573},
+	Publisher = {AIP},
+	Title = {Non-Born--Oppenheimer density functional theory of molecular systems},
+	Url = {http://link.aip.org/link/?JCP/76/568/1},
+	Volume = {76},
+	Year = {1982},
+	Bdsk-Url-1 = {http://link.aip.org/link/?JCP/76/568/1}}
+
+@article{CarGod-JCP-88,
+	Author = {{E. A. Carter and W. A. Goddard III}},
+	Journal = {J. Chem. Phys.},
+	Pages = {3132},
+	Volume = {88},
+	Year = {1988}}
+
+@article{CarSilMet-JCP-79,
+	Author = {D. P. Carroll and H. J. Silverstone and R. M. Metzger},
+	Journal = {J. Chem. Phys.},
+	Pages = {4142},
+	Volume = {71},
+	Year = {1979}}
+
+@article{CarTruGag-JCTC-15,
+	Author = {R. K. Carlson and D. G. Truhlar and L. Gagliardi},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {4077},
+	Volume = {11},
+	Year = {2015}}
+
+@article{CarTruGag-JPCA-17,
+	Author = {R. K. Carlson and D. G. Truhlar and L. Gagliardi},
+	Journal = {J. Phys. Chem. A},
+	Pages = {5540},
+	Volume = {121},
+	Year = {2017}}
+
+@article{CasAttSor-JCP-04,
+	Author = {Michele Casula and Claudio Attaccalite and Sandro Sorella},
+	Journal = {J. Chem. Phys.},
+	Pages = {7110},
+	Title = {Correlated geminal wave function for molecules: An efficient resonating valence bond approach},
+	Volume = {121},
+	Year = {2004}}
+
+@article{CasGutGuaGadSalDau-JCP-00,
+	Author = {M. E. Casida and F. Gutierrez and J. Guan and F.-X. Gadea and D. Salahub and J.-P. Daudey},
+	Journal = {J. Chem. Phys.},
+	Pages = {7062},
+	Volume = {113},
+	Year = {2000}}
+
+@article{CasHui-ARPC-12,
+	Author = {M. E. Casida and M. Huix-Rotllant},
+	Journal = {Annu. Rev. Phys. Chem.},
+	Pages = {287},
+	Title = {Progress in Time-Dependent Density-Functional Theory},
+	Volume = {63},
+	Year = {2012}}
+
+@incollection{CasHui-TCC-15,
+	Author = {M. E. Casida and M. Huix-Rotllant},
+	Booktitle = {Density-Functional Methods for Excited States},
+	Doi = {10.1007/128_2015_632},
+	Editor = {N. Ferr\'e and M. Filatov and M. Huix-Rotllant},
+	Publisher = {Springer},
+	Series = {Topics in Current Chemistry},
+	Year = {2015},
+	Bdsk-Url-1 = {https://doi.org/10.1007/128_2015_632}}
+
+@incollection{Cas-INC-95,
+	Address = {Singapore},
+	Author = {M. E. Casida},
+	Booktitle = {Recent Advances in Density Functional Methods, Part I},
+	Editor = {D. P. Chong},
+	Pages = {155},
+	Publisher = {World Scientific},
+	Year = {1995}}
+
+@article{CasJamCasSal-JCP-98,
+	Author = {M. E. Casida and C. Jamorski and K. C. Casida and D. R. Salahub},
+	Journal = {J. Chem. Phys.},
+	Pages = {4439},
+	Volume = {108},
+	Year = {1998}}
+
+@article{Cas-JCP-05,
+	Author = {M. E. Casida},
+	Journal = {J. Chem. Phys.},
+	Pages = {054111},
+	Volume = {122},
+	Year = {2005}}
+
+@article{Cas-JCP-18,
+	Author = {D. Casanova},
+	Journal = {J. Chem. Phys.},
+	Pages = {124118},
+	Volume = {148},
+	Year = {2018}}
+
+@article{Cas-JMS-09,
+	Author = {M. E. Casida},
+	Journal = {J. Mol. Struct.: THEOCHEM},
+	Pages = {3},
+	Volume = {914},
+	Year = {2009}}
+
+@article{CasMelRap-JCP-03,
+	Author = {M. Casalegno and M. Mella and A. M. Rappe},
+	Journal = {J. Chem. Phys.},
+	Pages = {7193},
+	Volume = {118},
+	Year = {2003}}
+
+@article{CasPol-PR-48,
+	Author = {H. B. G. Casimir and D. Polder},
+	Journal = {Phys. Rev.},
+	Pages = {360},
+	Volume = {73},
+	Year = {1948}}
+
+@article{Cas-PRA-95,
+	Author = {M. E. Casida},
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+	Pages = {2005},
+	Volume = {51},
+	Year = {1995}}
+
+@article{Cas-PRB-99,
+	Author = {M. E. Casida},
+	Journal = {Phys. Rev. B},
+	Pages = {4694},
+	Volume = {59},
+	Year = {1999}}
+
+@article{CasSal-JCP-00,
+	Author = {M. E. Casida and D. R. Salahub},
+	Journal = {J. Chem. Phys.},
+	Pages = {8918},
+	Volume = {113},
+	Year = {2000}}
+
+@article{CasSor-JCP-03,
+	Author = {M. Casula and S. Sorella},
+	Journal = {J. Chem. Phys.},
+	Pages = {6500},
+	Volume = {119},
+	Year = {2003}}
+
+@article{CatPicSamVan-PRB-96,
+	Author = {{F. Catara, G. Piccitto, M. Sambataro, and N. Van Giai}},
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+
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+	Volume = {5},
+	Year = {2009}}
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+	Volume = {45},
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+
+@article{CepBer-JCP-88,
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+	Journal = {J. Chem. Phys.},
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+	Volume = {89},
+	Year = {1988}}
+
+@article{CepCheKal-PRB-77,
+	Author = {D. Ceperley and G. V. Chester and M. H. Kalos},
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+	Title = {{Fermion nodes}},
+	Volume = {63},
+	Year = {1991}}
+
+@incollection{CepKal-INC-79,
+	Address = {Berlin},
+	Author = {D. M. Ceperley and M. H. Kalos},
+	Booktitle = {Monte Carlo Methods in Statistical Physics},
+	Editor = {K. Binder},
+	Pages = {145-194},
+	Publisher = {Springer},
+	Title = {Quantum Many-Body Problem},
+	Year = {1979}}
+
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+
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+	Volume = {100},
+	Year = {1994}}
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+	Volume = {131},
+	Year = {2009}}
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+	Volume = {{47}},
+	Year = {1993}}
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+	Pages = {1571},
+	Volume = {17},
+	Year = {1996}}
+
+@article{Fel-JCP-13,
+	Author = {D. Feller},
+	Journal = {J. Chem. Phys.},
+	Pages = {074103},
+	Volume = {138},
+	Year = {2013}}
+
+@article{Fel-JCP-92,
+	Author = {D. Feller},
+	Journal = {J. Chem. Phys.},
+	Pages = {6104},
+	Volume = {96},
+	Year = {1992}}
+
+@article{Fel-JCP-93,
+	Author = {D. Feller},
+	Journal = {J. Chem. Phys.},
+	Pages = {7059},
+	Volume = {98},
+	Year = {1993}}
+
+@article{FelPetHil-JCP-10,
+	Author = {D. Feller and K. A. Peterson and J. G. Hill},
+	Journal = {J. Chem. Phys.},
+	Pages = {184102},
+	Volume = {133},
+	Year = {2010}}
+
+@article{FerAss-JCP-02,
+	Author = {N. Ferr\'e and X. Assfeld},
+	Journal = {J. Chem. Phys.},
+	Pages = {4119},
+	Volume = {117},
+	Year = {2002}}
+
+@article{FerBalLop-JCTC-15,
+	Author = {R. G. Fernando and M. C. Balhoff and K. Lopata},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {646},
+	Volume = {11},
+	Year = {2015}}
+
+@article{FerLopAguEmaRam-IJQC-01,
+	Author = {{J. Fern\'andez Rico, R. L\'opez, A. Aguado, I. Ema, and G. Ram\'irez}},
+	Journal = {Int. J. Quantum Chem.},
+	Pages = {148},
+	Volume = {81},
+	Year = {2001}}
+
+@article{Fer-PR-57,
+	Author = {R. A. Ferrell},
+	Journal = {Phys. Rev.},
+	Pages = {450},
+	Volume = {{107}},
+	Year = {1957}}
+
+@article{FerRamLopFer-CCCC-88,
+	Author = {{J. Fern\'andez Rico, G. Ram\'irez, R. L\'opez and J. I. Fern\'andez-Alonso}},
+	Journal = {Collection Czechoslovak Chem. Commun.},
+	Pages = {2250},
+	Volume = {{53}},
+	Year = {1988}}
+
+@book{FetWal-BOOK-03,
+	Author = {A. L. Fetter and J. D. Walecka},
+	Publisher = {Dover},
+	Title = {Quantum Theory of Many-Particle Systems},
+	Year = {2003}}
+
+@article{FilAssMor-JCP-16,
+	Author = {C. Filippi, R. Assaraf and S. Moroni},
+	Journal = {J. Chem. Phys.},
+	Pages = {194105},
+	Title = {{Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo}},
+	Volume = {144},
+	Year = {2016}}
+
+@article{FilFah-JCP-00,
+	Author = {Claudia Filippi and Stephen Fahy},
+	Journal = {J. Chem. Phys.},
+	Pages = {3523},
+	Volume = {112},
+	Year = {2000}}
+
+@incollection{FilGonUmr-INC-96,
+	Address = {Amsterdam},
+	Author = {Claudia Filippi and Xavier Gonze and C. J. Umrigar},
+	Booktitle = {Recent Developments of Modern Density Functional Theory},
+	Editor = {J. M. Seminario},
+	Pages = {295-326},
+	Publisher = {Elsevier},
+	Title = {Generalized gradient approximations to density functional theory: comparison with exact results},
+	Year = {1996}}
+
+@misc{Fil-PRIV-XX,
+	Author = {C. Filippi},
+	Note = {private communication}}
+
+@article{FilSha-CPL-00,
+	Author = {Michael Filatov and Sason Shaik},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {409},
+	Volume = {332},
+	Year = {1999}}
+
+@article{FilSha-CPL-99,
+	Author = {M. Filatov and S. Shaik},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {429},
+	Title = {{A spin-restricted ensemble-referenced Kohn-Sham method and its application to diradicaloid situations}},
+	Volume = {304},
+	Year = {1999}}
+
+@article{FilSha-JPCA-00,
+	Author = {Michael Filatov and Sason Shaik},
+	Journal = {J. Phys. Chem. A},
+	Pages = {6628},
+	Volume = {104},
+	Year = {2000}}
+
+@article{FilSha-JPCA-99,
+	Author = {Michael Filatov and Sason Shaik},
+	Journal = {J. Phys. Chem. A},
+	Pages = {8885},
+	Volume = {103},
+	Year = {1999}}
+
+@article{FilShaWoeGriPey-CPL-00,
+	Author = {Michael Filatov and Sason Shaik and M. Woeller and S. Grimme and S.D. Peyerimhoff},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {135},
+	Volume = {316},
+	Year = {2000}}
+
+@misc{FilTouUmr-JJJ-XX,
+	Author = {Claudia Filippi and Julien Toulouse and C. J. Umrigar},
+	Title = {in preparation}}
+
+@article{FilUmrGon-JCP-97,
+	Author = {C. Filippi and C. J. Umrigar and X. Gonze},
+	Journal = {J. Chem. Phys.},
+	Pages = {9994},
+	Title = {{Excitation energies from density functional perturbation theory}},
+	Volume = {107},
+	Year = {1997}}
+
+@article{FilUmrGon-PRA-96,
+	Author = {C. Filippi and C. J. Umrigar and X. Gonze},
+	Journal = {Phys. Rev. A},
+	Pages = {4810},
+	Volume = {54},
+	Year = {1996}}
+
+@article{FilUmr-JCP-96,
+	Author = {C. Filippi and C. J. Umrigar},
+	Journal = {J. Chem. Phys.},
+	Pages = {213},
+	Title = {Multiconfiguration wave functions for quantum Monte Carlo calculations of first-row diatomic molecules},
+	Volume = {{105}},
+	Year = {1996}}
+
+@article{Fil-WIR-14,
+	Author = {M. Filatov},
+	Journal = {WIREs Comput. Mol. Sci.},
+	Pages = {146},
+	Title = {{Spin-restricted ensemble-referenced Kohn-Sham method: basic principles and application to strongly correlated ground and excited states of molecules}},
+	Volume = {5},
+	Year = {2015}}
+
+@article{FilZacBud-JCTC-09,
+	Author = {C. Filippi and M. Zaccheddu and F. Buda},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {2074},
+	Title = {Absorption Spectrum of the Green Fluorescent Protein Chromophore: A Difficult Case for ab Initio Methods?},
+	Volume = {5},
+	Year = {2009}}
+
+@article{FilZacBud-JJJ-XX,
+	Author = {Claudia Filippi and Maurizio Zaccheddu and Francesco Buda},
+	Note = {unpublished}}
+
+@incollection{FlaCafSav-INC-97,
+	Address = {Singapore},
+	Author = {H.-J. Flad and M. Caffarel and A. Savin},
+	Booktitle = {Recent advances in quantum Monte Carlo methods},
+	Editor = {W. A. Lester},
+	Pages = {73},
+	Publisher = {World Scientific},
+	Title = {Quantum Monte Carlo calculations with multi-reference trial wave functions},
+	Year = {1997}}
+
+@misc{Fla-PRIV-XX,
+	Author = {H. J. Flad},
+	Title = {private communication}}
+
+@article{FlaSav-JCP-95,
+	Author = {H.-J. Flad and A. Savin},
+	Journal = {J. Chem. Phys.},
+	Pages = {691},
+	Volume = {103},
+	Year = {1995}}
+
+@article{FlaSavPre-JCP-92,
+	Author = {H.-J. Flad and A. Savin and H. Preuss},
+	Journal = {J. Chem. Phys.},
+	Pages = {459},
+	Volume = {97},
+	Year = {1992}}
+
+@article{FlaSavScuNicPre-CPL-94,
+	Author = {H.-J. Flad and A. Savin and M. Schultheiss and A. Nicklass and H. Preuss},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {274},
+	Volume = {222},
+	Year = {1994}}
+
+@article{FloGda-JCP-05,
+	Author = {J. R. Flores and R. J. Gdanitz},
+	Journal = {J. Chem. Phys.},
+	Pages = {144316},
+	Volume = {123},
+	Year = {2005}}
+
+@article{Foc-ZP-30,
+	Author = {V. Fock},
+	Journal = {Z. Phys.},
+	Pages = {855},
+	Volume = {63},
+	Year = {1930}}
+
+@article{FouMitNeeRaj-RMP-01,
+	Author = {W. M. C. Foulkes and L. Mitas and R. J. Needs and G. Rajagopal},
+	Journal = {Rev. Mod. Phys.},
+	Pages = {33},
+	Title = {{Quantum Monte Carlo simulations of solids}},
+	Volume = {{73}},
+	Year = {2001}}
+
+@article{FraDurMes-JCP-97,
+	Author = {X. Fradera and M. Duran and J. Mestres},
+	Journal = {J. Chem. Phys.},
+	Pages = {3576},
+	Volume = {107},
+	Year = {1997}}
+
+@article{FraFilAmo-JCTC-12,
+	Author = {F. Fracchia and C. Filippi and C. Amovilli},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {1943},
+	Title = {Size-extensive wave functions for quantum Monte Carlo: A linear scaling generalized valence bond approach},
+	Volume = {8},
+	Year = {2012}}
+
+@misc{FraLupTou-JJJ-XX,
+	Author = {O. Franck and E. Luppi and J. Toulouse},
+	Note = {unpublished}}
+
+@article{FraMusLupTou-JCP-15,
+	Author = {O. Franck and B. Mussard and E. Luppi and J. Toulouse},
+	Date-Modified = {2019-08-01 12:03:43 +0200},
+	Doi = {10.1063/1.4907920},
+	Journal = {J. Chem. Phys.},
+	Pages = {074107},
+	Title = {Basis Convergence Of Range-Separated Density-Functional Theory},
+	Volume = {142},
+	Year = {2015},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4907920}}
+
+@misc{FraMusLupTou-JJJ-XX,
+	Author = {O. Franck and B. Mussard and E. Luppi and J. Toulouse},
+	Note = {Basis convergence of range-separated density-functional theory, arXiv:1412.2613, to appear in J. Chem. Phys.}}
+
+@misc{FraMusLupTou-JJJ-XX-note1,
+	Note = {Note that the partial-wave expansion of any {\it odd} power of $r_{12}$ contains an infinite number of terms. In contrast, the partial-wave expansion of any {\it even} power of $r_{12}$ terminates at a finite $\ell$.}}
+
+@misc{FraMusLupTou-JJJ-XX-note2,
+	Note = {For a discussion of angular and radial correlation and the shape of the correlation hole in the He atom with the long-range interaction, see Ref.~\onlinecite{PolColLeiStoWerSav-IJQC-03}.}}
+
+@misc{FraMusLupTou-JJJ-XX-note3,
+	Note = {For $\mu=1$ the difference between the long-range MP2 correlation energies for $X=5$ and $X=6$ is still as small as about 0.2 mhartree.}}
+
+@misc{FraMusLupTou-JJJ-XX-note4,
+	Note = {For $r_1=r_2$, $f\lr_\ell >0$ for $\ell=0$ and $f\lr_\ell <0$ for $\ell \geq 1$.}}
+
+@article{FreHuxMor-PRA-84,
+	Author = {{D. E. Freund, B. D. Huxtable, and J. D. Morgan III}},
+	Journal = {Phys. Rev. A},
+	Pages = {980},
+	Volume = {29},
+	Year = {1984}}
+
+@article{FreLev-JCP-82,
+	Author = {Karl F. Freed and Mel Levy},
+	Journal = {The Journal of Chemical Physics},
+	Keywords = {ALGORITHMS; ELECTRON DENSITY; FUNCTIONALS; SERIES EXPANSION; WAVE FUNCTIONS; GROUND STATES},
+	Number = {1},
+	Pages = {396-398},
+	Publisher = {AIP},
+	Title = {Direct first principles algorithm for the universal electron density functional},
+	Url = {http://link.aip.org/link/?JCP/77/396/1},
+	Volume = {77},
+	Year = {1982},
+	Bdsk-Url-1 = {http://link.aip.org/link/?JCP/77/396/1}}
+
+@article{Fre-PRB-77,
+	Author = {D. L. Freeman},
+	Journal = {Phys. Rev. B},
+	Pages = {5512},
+	Volume = {{15}},
+	Year = {1977}}
+
+@article{FroCimJen-PRA-10,
+	Author = {Fromager, Emmanuel and Cimiraglia, Renzo and Jensen, Hans J\o{}rgen Aa.},
+	Date-Modified = {2019-05-13 20:54:11 +0200},
+	Doi = {10.1103/PhysRevA.81.024502},
+	Issue = {2},
+	Journal = {Phys. Rev. A},
+	Month = {Feb},
+	Numpages = {4},
+	Pages = {024502},
+	Publisher = {American Physical Society},
+	Title = {Merging Multireference Perturbation And Density-Functional Theories By Means Of Range Separation: Potential Curves For ${\mathrm{Be}}_{2}$, ${\mathrm{Mg}}_{2}$, And ${\mathrm{Ca}}_{2}$},
+	Url = {https://link.aps.org/doi/10.1103/PhysRevA.81.024502},
+	Volume = {81},
+	Year = {2010},
+	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.81.024502},
+	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.81.024502}}
+
+@article{Fro-JCP-11,
+	Author = {E. Fromager},
+	Journal = {J. Chem. Phys.},
+	Pages = {244106},
+	Volume = {135},
+	Year = {2011}}
+
+@article{FroJen-JCP-11,
+	Author = {E. Fromager and H. J. Aa. Jensen},
+	Journal = {J. Chem. Phys.},
+	Pages = {034116},
+	Volume = {135},
+	Year = {2011}}
+
+@article{FroJen-PRA-08,
+	Author = {E. Fromager and H. J. Aa. Jensen},
+	Journal = {Phys. Rev. A},
+	Pages = {022504},
+	Volume = {78},
+	Year = {2008}}
+
+@misc{FroKneJen-ARX-12,
+	Author = {Emmanuel Fromager and Stefan Knecht and H. J. Aa. Jensen},
+	Note = {\url{http://fr.arxiv.org/abs/1211.4829v1}}}
+
+@article{FroKneJen-JCP-13,
+	Author = {E. Fromager and S. Knecht and H. J. Aa. Jensen},
+	Journal = {J. Chem. Phys.},
+	Pages = {084101},
+	Title = {{Multi-configuration time-dependent density-functional theory based on range separation}},
+	Volume = {138},
+	Year = {2013}}
+
+@article{FroReaWahWahJen-JCP-09,
+	Author = {E. Fromager and F. R\'eal and P. W{\aa}hlin and U. Wahlgren and H. J. Aa. Jensen},
+	Journal = {J. Chem. Phys.},
+	Pages = {054107},
+	Volume = {131},
+	Year = {2009}}
+
+@article{FroTouJen-JCP-07,
+	Author = {E. Fromager and J. Toulouse and H. J. Aa. Jensen},
+	Date-Modified = {2019-08-01 11:59:44 +0200},
+	Doi = {10.1063/1.3187032},
+	Journal = {J. Chem. Phys.},
+	Pages = {074111},
+	Title = {On The Universality Of The Long-/Short-Range Separation In Multiconfigurational Density-Functional Theory},
+	Volume = {126},
+	Year = {2007},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3187032}}
+
+@article{FucGon-PRB-02,
+	Author = {M. Fuchs and X. Gonze},
+	Journal = {Phys. Rev. B},
+	Pages = {235109},
+	Volume = {65},
+	Year = {2002}}
+
+@article{FucNiqGonBur-JCP-05,
+	Abstract = {We show that density functional theory within the RPA (random phase
+        approximation for the exchange-correlation energy) provides a correct
+        description of bond dissociation in H2 in a spin-restricted Kohn-<96>Sham
+        formalism, i.e., without artificial symmetry breaking. We present
+        accurate adiabatic connection curves both at equilibrium and beyond
+        the Coulson-Fisher point. The strong curvature at large bond length
+        implies important static (left-<96>right) correlation, justifying modern
+        hybrid functional constructions but also demonstrating their limitations.
+        Although exact at infinite separation and accurate near the equilibrium
+        bond length, the RPA dissociation curve displays unphysical repulsion
+        at larger but finite bond lengths. Going beyond the RPA by including
+        the exact exchange kernel (RPA + X), we find a similar repulsion.
+        We argue that this deficiency is due to the absence of double excitations
+        in adiabatic linear response theory. Further analyzing the H2 dissociation
+        limit we show that the RPA + X is not size consistent, in contrast
+        to the RPA.},
+	Author = {Fuchs, M. and Niquet, Y. M. and Gonze, X. and Burke, K.},
+	Doi = {10.1063/1.1858371},
+	Journal = {J. Chem. Phys.},
+	Pages = {094116},
+	Title = {Describing static correlation in bond dissociation by Kohn-Sham density functional theory},
+	Volume = {122},
+	Year = {2005},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.1858371}}
+
+@article{FukIwaSaw-PR-64,
+	Author = {N. Fukuda and F. Iwamoto and K. Sawada},
+	Journal = {Phys. Rev.},
+	Pages = {A932},
+	Volume = {135},
+	Year = {1964}}
+
+@book{Ful-BOOK-93,
+	Address = {Berlin},
+	Author = {P. Fulde},
+	Publisher = {Springer},
+	Title = {Electron Correlations in Molecules and Solids},
+	Year = {1993}}
+
+@article{Fur-JCP-01,
+	Author = {F. Furche},
+	Journal = {J. Chem. Phys.},
+	Pages = {5982},
+	Volume = {114},
+	Year = {2001}}
+
+@article{Fur-JCP-08,
+	Author = {F. Furche},
+	Journal = {J. Chem. Phys.},
+	Pages = {114105},
+	Volume = {129},
+	Year = {2008}}
+
+@article{FurPer-JCP-06,
+	Author = {F. Furche and J. P. Perdew},
+	Journal = {J. Chem. Phys.},
+	Pages = {044103},
+	Volume = {124},
+	Year = {2006}}
+
+@article{Fur-PRA-04,
+	Author = {Filipp Furche},
+	Eid = {022514},
+	Journal = {Physical Review A (Atomic, Molecular, and Optical Physics)},
+	Keywords = {density functional theory; HF calculations; boson systems; electron pairs; ground states; Schrodinger equation},
+	Number = {2},
+	Numpages = {10},
+	Pages = {022514},
+	Publisher = {APS},
+	Title = {Towards a practical pair density-functional theory for many-electron systems},
+	Url = {http://link.aps.org/abstract/PRA/v70/e022514},
+	Volume = {70},
+	Year = {2004},
+	Bdsk-Url-1 = {http://link.aps.org/abstract/PRA/v70/e022514}}
+
+@article{Fur-PRB-01,
+	Author = {F. Furche},
+	Journal = {Phys. Rev. B},
+	Pages = {195120},
+	Volume = {64},
+	Year = {2001}}
+
+@incollection{FurRap-INC-05,
+	Address = {Amsterdam},
+	Author = {F. Furche and D. Rappoport},
+	Booktitle = {Computational Photochemistry},
+	Editor = {M. Olivucci},
+	Pages = {93-128},
+	Publisher = {Elsevier},
+	Series = {Theoretical and Computational Chemistry, Vol. 16},
+	Title = {Density functional methods for excited states: equilibrium structure and electronic spectra},
+	Year = {2005}}
+
+@article{FurVoo-JCP-05,
+	Author = {F. Furche and T. Van Voorhis},
+	Journal = {J. Chem. Phys.},
+	Pages = {164106},
+	Title = {Fluctuation-dissipation theorem density-functional theory},
+	Volume = {122},
+	Year = {2005}}
+
+@article{GagTruLiCarHoyBa-ACR-17,
+	Author = {{L. Gagliardi, D. G. Truhlar, G. Li Manni, R. K. Carlson, C. E. Hoyer, and J. Lucas Bao}},
+	Journal = {Acc. Chem. Res.},
+	Pages = {66},
+	Volume = {50},
+	Year = {2017}}
+
+@book{Gal-BOOK-02,
+	Author = {G. A. Gallup},
+	Publisher = {Cambridge University Press},
+	Title = {Valence Bond Methods: Theory and applications},
+	Year = {2002}}
+
+@article{GalBueSar-CPL-03a,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {330},
+	Volume = {378},
+	Year = {2003}}
+
+@article{GalBueSar-CPL-03,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {327},
+	Volume = {370},
+	Year = {2003}}
+
+@article{GalBueSar-JCP-01,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {J. Chem. Phys.},
+	Pages = {1166},
+	Volume = {115},
+	Year = {2001}}
+
+@article{GalBueSar-JCP-02,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {J. Chem. Phys.},
+	Pages = {6071},
+	Volume = {117},
+	Year = {2002}}
+
+@article{GalBueSar-JCP-03,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {J. Chem. Phys.},
+	Pages = {6858},
+	Volume = {118},
+	Year = {2003}}
+
+@article{GalBueSar-JCP-05a,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {J. Chem. Phys.},
+	Pages = {034302},
+	Volume = {123},
+	Year = {2005}}
+
+@article{GalBueSar-JCP-05,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {J. Chem. Phys.},
+	Pages = {154307},
+	Volume = {122},
+	Year = {2005}}
+
+@article{GalBueSar-JCP-99,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {J. Chem. Phys.},
+	Pages = {10903},
+	Volume = {111},
+	Year = {1999}}
+
+@article{GalBueSar-PRA-00,
+	Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa},
+	Journal = {Phys. Rev. A},
+	Pages = {052505},
+	Volume = {61},
+	Year = {2000}}
+
+@article{GalHanCohCha-CPL-05,
+	Author = {P. T. A. Galek and N. C. Handy and A. J. Cohen and G. K.-L. Chan},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {156},
+	Volume = {404},
+	Year = {2005}}
+
+@article{GalHanLes-MP-06,
+	Author = {{P. T. A. Galek, N. C. Handy, and W. A. Lester Jr}},
+	Journal = {Mol. Phys.},
+	Pages = {3069},
+	Volume = {104},
+	Year = {2006}}
+
+@article{GamCatGra-PRC-09,
+	Author = {D. Gambacurta and F. Catara and M. Grasso},
+	Journal = {Phys. Rev. C},
+	Pages = {014303},
+	Title = {{Self-consistent extension of random-phase approximation enlarged beyond particle-hole configurations}},
+	Volume = {80},
+	Year = {2009}}
+
+@article{GarBulHenScu-JCP-15,
+	Author = {Alejandro J. Garza and Ireneusz W. Bulik and Thomas M. Henderson and Gustavo E. Scuseria},
+	Journal = {J. Chem. Phys.},
+	Pages = {044109},
+	Volume = {142},
+	Year = {2015}}
+
+@article{GarBulHenScu-PCCP-15,
+	Author = {A. J. Garza and I. W. Bulik and T. M. Henderson and G. E. Scuseria},
+	Journal = {Phys. Chem. Chem. Phys.},
+	Pages = {22412},
+	Volume = {17},
+	Year = {2015}}
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+
+@article{JanLiuAng-JCP-10,
+	Author = {G. Jansen and R.-F. Liu and J. G. \'Angyan},
+	Journal = {J. Chem. Phys.},
+	Pages = {154106},
+	Volume = {133},
+	Year = {2010}}
+
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+	Pages = {428},
+	Volume = {XXV},
+	Year = {1962}}
+
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+	Journal = {Phys. Rev. B},
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+
+@article{JanScu-JCP-09,
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+	Journal = {J. Chem. Phys.},
+	Pages = {154106},
+	Volume = {131},
+	Year = {2009}}
+
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+	Author = {B. G. Janesko and G. E. Scuseria},
+	Journal = {Phys. Chem. Chem. Phys.},
+	Pages = {9677},
+	Volume = {11},
+	Year = {2009}}
+
+@article{JarDav-PRA-98,
+	Author = {A. A. Jarzecki and E. R. Davidson},
+	Journal = {Phys. Rev. A},
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+	Volume = {{58}},
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+	Volume = {110},
+	Year = {1984}}
+
+@article{JenBun-JCP-88,
+	Author = {P. Jensen and P. R. Bunker},
+	Date-Modified = {2019-08-01 12:16:57 +0200},
+	Doi = {10.1063/1.455184},
+	Journal = {J. Chem. Phys.},
+	Pages = {1327},
+	Title = {The potential surface and stretching frequencies of X3B1 methylene (CH2) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian.},
+	Volume = {89},
+	Year = {1988},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.455184}}
+
+@article{JenDyaSauFae-JCP-96,
+	Author = {H. J. Aa. Jensen and K. G. Dyall and T. Saue and K. F{\ae}gri},
+	Journal = {J. Chem. Phys.},
+	Pages = {4083},
+	Volume = {104},
+	Year = {1996}}
+
+@incollection{Jen-INC-94,
+	Address = {New York},
+	Author = {H. J. Aa. Jensen},
+	Booktitle = {Relativistic and Electron Correlation Effects in Molecules and Solids},
+	Editor = {G. L. Malli},
+	Pages = {179},
+	Publisher = {Plenum},
+	Year = {1994}}
+
+@article{JenJorAgr-JCP-87,
+	Author = {H. J. Aa. Jensen and P. Jorgensen and H. Agren},
+	Journal = {J. Chem. Phys.},
+	Pages = {451},
+	Volume = {{87}},
+	Year = {1987}}
+
+@article{JenJorAgrOls-JCP-88,
+	Author = {H. J. Aa. Jensen and P. J{\o}rgensen and H. Agren and J. Olsen},
+	Journal = {J. Chem. Phys.},
+	Pages = {3834},
+	Volume = {{88}},
+	Year = {1988}}
+
+@article{JenJor-JCP-84,
+	Author = {H. J. Aa. Jensen and P. J{\o}rgensen},
+	Journal = {J. Chem. Phys.},
+	Pages = {1204},
+	Volume = {{80}},
+	Year = {1984}}
+
+@article{JiaEng-JCP-07,
+	Author = {Hong Jiang and Eberhard Engel},
+	Doi = {10.1063/1.2795707},
+	Journal = {J. Chem. Phys.},
+	Keywords = {density functional theory; eigenvalues and eigenfunctions; ground states; ionisation potential; orbital calculations; perturbation theory; potential energy functions},
+	Pages = {184108},
+	Title = {Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms},
+	Volume = {127},
+	Year = {2007},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.2795707}}
+
+@article{JieNorSer-JCP-05,
+	Author = {A. Jiemchooroj and P. Norman and Bo E. Sernelius},
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+
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+	Year = {2006}}
+
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+
+@article{JohMorCohYan-JCP-08,
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+	Journal = {J. Chem. Phys.},
+	Pages = {204112},
+	Volume = {129},
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+
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+	Year = {1989}}
+
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+	Keywords = {OZONE; SULFUR DIOXIDE; GROUND STATES; EXCITED STATES; ELECTRONIC STRUCTURE; CONFIGURATION INTERACTION; DISSOCIATION ENERGY; ATMOSPHERIC CHEMISTRY},
+	Number = {1},
+	Pages = {325-332},
+	Publisher = {AIP},
+	Title = {Energy surfaces of low-lying states of O[sub 3] and SO[sub 2]},
+	Url = {http://link.aip.org/link/?JCP/82/325/1},
+	Volume = {82},
+	Year = {1985},
+	Bdsk-Url-1 = {http://link.aip.org/link/?JCP/82/325/1}}
+
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+	Pages = {334},
+	Volume = {79},
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+
+@article{JouSri-JCP-98,
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+	Pages = {5212},
+	Volume = {109},
+	Year = {1998}}
+
+@article{JurSpoCerHob-PCCP-06,
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+	Journal = {Phys. Chem. Chem. Phys.},
+	Pages = {1985},
+	Volume = {8},
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+
+@article{KadVoo-JCP-10,
+	Author = {{B. Kaduk and T. Van Voorhis}},
+	Journal = {J. Chem. Phys.},
+	Pages = {061102},
+	Volume = {133},
+	Year = {2010}}
+
+@article{KalTou-JCP-18,
+	Author = {C. Kalai and J. Toulouse},
+	Doi = {10.1063/1.5025561},
+	Journal = {J. Chem. Phys.},
+	Pages = {164105},
+	Title = {A general range-separated double-hybrid density-functional theory},
+	Volume = {148},
+	Year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.5025561}}
+
+@misc{KalTou-JJJ-XX-note1,
+	Note = {The geometries are available in the Minnesota Database at http://comp.chem.umn.edu/db/.}}
+
+@misc{KalTou-JJJ-XX-note2,
+	Note = {The term ``range-separated double hybrid (RSDH)'' has already been used in Ref.~\onlinecite{SanCivUsvTouShaMas-JCP-15} to designate the RSH+MP2 method and in Refs.~\onlinecite{CorStoJenFro-PRA-13,CorFro-IJQC-14} to generically designate several kinds of range-separated MP2/DFT hybrids. In the present work, we use RSDH to designate the specific scheme corresponding to Eq.~(\ref{EmulRSDH}).}}
+
+@misc{KalTou-JJJ-XX-note3,
+	Note = {We use the AE49 set of Fast {\it et al.}~\cite{FasCorSanTru-JPCA-99} to facilitate comparisons with previous related works~\cite{ShaTouSav-JCP-11,SouShaTou-JCP-14,MusReiAngTou-JCP-15} where this set was used. We do not expect any special difficulties with the six molecules that have been dropped from the G2-1 set.}}
+
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+
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+	Pages = {12868},
+	Volume = {112},
+	Year = {2008}}
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+	Date-Modified = {2019-08-01 12:03:13 +0200},
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+	Volume = {120},
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+
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+
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+
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+
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+
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+
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+
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+	Volume = {110},
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+
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+	Volume = {107},
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+
+@misc{KohHan-JJJ-XXa,
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+	Note = {unpublished}}
+
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+	Author = {W. Kohn and W. Hanke},
+	Note = {unpublished}}
+
+@article{Koh-JCP-72,
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+	Volume = {140},
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+	Author = {A. Kollias and P. Reinhardt and R. Assaraf},
+	Note = {unpublished.}}
+
+@article{KolTho-NL-12,
+	Author = {Kolb, Brian and Thonhauser, T.},
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+
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+
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+
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+	Volume = {134},
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+
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+	Volume = {34},
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+	Author = {E. Kraka},
+	Journal = {Chem. Phys.},
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+@misc{lifetimes-note1,
+	Note = {For $\ell=0$, $R_2(r)$ only diverges as $1/r$ at $r=0$ which is normalizable, i.e. $\int_0^\infty \text{d}r r^2 |R_2(r)|^2 < \infty$. However, even in this case, the expectation value of the Hamiltonian operator is infinite. For $\ell \geq 1$, $R_2(r)$ is not even normalizable.}}
+
+@misc{lifetimes-note2,
+	Note = {The general solution of the Schr\"odinger equation given in Eqs.~(\ref{solR})-(\ref{solR2}) is valid for $Z\not=0$. For $Z=0$, $R_1(r)$ in Eq.~(\ref{solR1}) becomes identically zero, and should be replaced by a function which has the same expression as $R_2(r)$ with the substitution $\sqrt{-2E} \to -\sqrt{-2E}$. The continuum scattering states are then obtained as a linear combination of these two functions. However, our analysis of complex-energy states remains unchanged. Thus, our procedure for determining the lifetimes is still valid for $Z=0$.}}
+
+@misc{lifetimes-note3,
+	Note = {Because we do not impose spherical symmetry in our calculations, we do not have exactly degenerate s, p, and d states.}}
+
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+	Volume = {52},
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+
+@article{LivBae-PCCP-07,
+	Author = {E. Livshits and R. Baer},
+	Journal = {Phys. Chem. Chem. Phys.},
+	Pages = {2932},
+	Volume = {9},
+	Year = {2007}}
+
+@article{LjuKovFerFoeSan-PRB-15,
+	Author = {M. P. Ljungberg and P. Koval and F. Ferrari and D. Foerster and D. S\'anchez-Portal},
+	Journal = {Phys. Rev. B},
+	Pages = {075422},
+	Volume = {92},
+	Year = {2015}}
+
+@article{LocHea-JCP-07,
+	Author = {Rohini C. Lochan and Martin Head-Gordon},
+	Journal = {J. Chem. Phys.},
+	Pages = {164101},
+	Volume = {126},
+	Year = {2007}}
+
+@article{Lon-DFS-65,
+	Author = {H. C. Longuet-Higgins},
+	Journal = {Discuss. Faraday Soc.},
+	Pages = {7},
+	Volume = {40},
+	Year = {1965}}
+
+@article{Lon-ZP-30,
+	Author = {F. London},
+	Journal = {Z. Physik},
+	Pages = {245},
+	Volume = {63},
+	Year = {1930}}
+
+@article{LooGil-WIRES-16,
+	Author = {Pierre-Francois Loos and Peter M. W. Gill},
+	Date-Modified = {2019-05-13 20:56:19 +0200},
+	Doi = {doi: 10.1002/wcms.1257},
+	Journal = {WIREs Comput. Mol. Sci.},
+	Pages = {410},
+	Title = {The Uniform Electron Gas},
+	Volume = {6},
+	Year = {2016},
+	Bdsk-Url-1 = {https://doi.org/10.1002/wcms.1257}}
+
+@article{LopGov-JCTC-11,
+	Author = {K. Lopata and N. Govind},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {1344},
+	Title = {Modeling Fast Electron Dynamics with Real-Time Time-Dependent Density Functional Theory: Application to Small Molecules and Chromophores},
+	Volume = {7},
+	Year = {2011}}
+
+@article{LopGov-JCTC-13,
+	Author = {K. Lopata and N. Govind},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {4939},
+	Volume = {9},
+	Year = {2013}}
+
+@article{LopMaDruTowNee-PRE-06,
+	Author = {{P. L\'opez Rios, A. Ma, N. D. Drummond, M. D. Towler, and R. J. Needs}},
+	Journal = {Phys. Rev. E},
+	Pages = {066701},
+	Title = {{Inhomogeneous backflow transformations in quantum Monte Carlo calculations}},
+	Volume = {74},
+	Year = {2006}}
+
+@article{LopRamGarFer-JCP-87,
+	Author = {{R. L\'opez, G. Ram\'irez, J. M. Garc\'ia de la Vega and J. Fern\'andez Rico}},
+	Journal = {J. chim. phys.},
+	Pages = {695},
+	Volume = {{84}},
+	Year = {1987}}
+
+@article{LosFdeAguMar-JPC-07,
+	Author = {{A. M. Losa, I. Fdez.-Galv\'an, M. A. Aguilar, and M. E. Mart\'in}},
+	Journal = {J. Phys. Chem. B},
+	Pages = {9864},
+	Volume = {111},
+	Year = {2007}}
+
+@article{LotBar-JCP-11,
+	Author = {V. Lotrich and R. J. Bartlett},
+	Journal = {J. Chem. Phys.},
+	Pages = {184108},
+	Volume = {134},
+	Year = {2011}}
+
+@article{Low-AP-56,
+	Author = {P.-O. L\"owdin},
+	Journal = {Adv. Phys.},
+	Pages = {1},
+	Volume = {5},
+	Year = {1956}}
+
+@article{Low-JCP-50,
+	Author = {P.-O. L\"owdin},
+	Journal = {J. Chem. Phys.},
+	Pages = {365},
+	Volume = {18},
+	Year = {1950}}
+
+@article{Low-RMP-63,
+	Author = {P.-O. L\"owdin},
+	Journal = {Rev. Mod. Phys.},
+	Pages = {496},
+	Volume = {35},
+	Year = {1963}}
+
+@article{LowShu-PR-56,
+	Author = {P.-O. L\"owdin and H. Shull},
+	Journal = {Phys. Rev.},
+	Pages = {1730},
+	Volume = {101},
+	Year = {1956}}
+
+@article{LufRefPacResRamKroPus-PRB-14,
+	Author = {D. L\"uftner and Sivan Refaely-Abramson and Michael Pachler and Roland Resel and Michael G. Ramsey and Leeor Kronik and Peter Puschnig},
+	Journal = {Phys. Rev. B},
+	Pages = {075204},
+	Volume = {90},
+	Year = {2014}}
+
+@article{LuLiRocGal-PRL-09,
+	Author = {Deyu Lu and Yan Li and Dario Rocca and Giulia Galli},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {206411},
+	Volume = {102},
+	Year = {2009}}
+
+@article{LuNguGal-JCP-10,
+	Author = {Deyu Lu and Huy-Viet Nguyen and Giulia Galli},
+	Journal = {J. Chem. Phys.},
+	Pages = {154110},
+	Volume = {133},
+	Year = {2010}}
+
+@article{LupHea-JCP-13,
+	Author = {E. Luppi and M. Head-Gordon},
+	Journal = {J. Chem. Phys.},
+	Pages = {164121},
+	Title = {{The role of Rydberg and continuum levels in computing high harmonic generation spectra of the hydrogen atom using time-dependent configuration interaction}},
+	Volume = {139},
+	Year = {2013}}
+
+@article{Lut-ZPC-23,
+	Author = {A. Luthy},
+	Journal = {Z. Phys. Chem., Stoechiom. Verwandtschaftsl.},
+	Pages = {284},
+	Volume = {107},
+	Year = {1923}}
+
+@article{LynTru-JPCA-03,
+	Author = {B. J. Lynch and D. G. Truhlar},
+	Journal = {J. Phys. Chem. A},
+	Pages = {8996},
+	Title = {Small Representative Benchmarks for Thermochemical Calculations},
+	Volume = {107},
+	Year = {2003}}
+
+@misc{LynZhaTru-JJJ-XX,
+	Note = {The geometries are available in the Minnesota Databases for Chemistry and Solid-State Physics at http://comp.chem.umn.edu/db/.}}
+
+@article{MaBru-PR-68,
+	Author = {S.-K. Ma and K. A. Brueckner},
+	Journal = {Phys. Rev.},
+	Pages = {165},
+	Volume = {{165}},
+	Year = {1968}}
+
+@article{MacVos-JPC-79,
+	Author = {A. H. MacDonald and S. H. Vosko},
+	Journal = {J. Phys. C},
+	Pages = {2977},
+	Volume = {12},
+	Year = {1978}}
+
+@article{MaDruTowNee-PRE-05,
+	Author = {A. Ma and N. D. Drummond and M. D. Towler and R. J. Needs},
+	Journal = {Phys. Rev. E},
+	Pages = {066704},
+	Volume = {71},
+	Year = {2005}}
+
+@book{Mah-BOOK-09,
+	Address = {Princeton},
+	Author = {Gerald D. Mahan},
+	Publisher = {Princeton University Press},
+	Title = {Quantum Mechanics in a Nutshell},
+	Year = {2009}}
+
+@article{MaiZhaCavBur-JCP-04,
+	Author = {N. T. Maitra and F. Zhang and R. J. Cave and K. Burke},
+	Journal = {J. Chem. Phys.},
+	Pages = {5932},
+	Volume = {120},
+	Year = {2004}}
+
+@article{MalMcd-CPL-98,
+	Author = {N. O. J. Malcolm and J. J. W. McDouall},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {121},
+	Volume = {282},
+	Year = {1998}}
+
+@article{MalMcd-JPC-96,
+	Author = {N. O. J. Malcolm and J. J. W. McDouall},
+	Journal = {J. Phys. Chem.},
+	Pages = {10131},
+	Volume = {100},
+	Year = {1996}}
+
+@article{MalPenYanBalHol-TCA-14,
+	Author = {A. Malek and D. Peng and W. Yang and R. Balawender and A. Holas},
+	Journal = {Theor. Chem. Acc.},
+	Pages = {1559},
+	Volume = {133},
+	Year = {2014}}
+
+@article{ManLuc-JCP-01,
+	Author = {S. Manten and A. L\"uchow},
+	Journal = {J. Chem. Phys.},
+	Pages = {5362},
+	Volume = {115},
+	Year = {2001}}
+
+@article{MarAzaCasSor-JCP-09,
+	Author = {M. Marchi and S. Azadi and M. Casula and S. Sorella},
+	Journal = {J. Chem. Phys.},
+	Pages = {154116},
+	Title = {Correlated geminal wave function for molecules: An efficient resonating valence bond approach},
+	Volume = {131},
+	Year = {2009}}
+
+@article{MarCasMalMulBot-JCP-07,
+	Author = {M. A. L. Marques and A. Castro and G. Malloci and G. Mulas and S. Botti},
+	Journal = {J. Chem. Phys.},
+	Pages = {014107},
+	Volume = {127},
+	Year = {2007}}
+
+@article{Mar-CPL-96,
+	Author = {J. M. L. Martin},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {669},
+	Volume = {259},
+	Year = {1996}}
+
+@article{MarGarRub-PRL-06,
+	Abstract = {We present a first-principles description of anisotropic materials
+        characterized by having both weak (dispersionlike) and strong covalent
+        bonds, based on the adiabatic-connection fluctuation-dissipation
+        theorem with density functional theory. For hexagonal boron nitride
+        the in-plane and out-of-plane bonding as well as vibrational dynamics
+        are well described both at equilibrium and when the layers are pulled
+        apart. Bonding in covalent and ionic solids is also described. The
+        formalism allows us to ping down the deficiencies of common exchange-correlation
+        functionals and provides insight toward the inclusion of dispersion
+        interactions into the correlation functional.},
+	Author = {Marini, A. and Garc\'ia-Gonz\'alez, P. and Rubio, A.},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {136404},
+	Title = {First-Principles Description of Correlation Effects in Layered Materials},
+	Volume = {96},
+	Year = {2006}}
+
+@article{MarHeiKle-WIRES-18,
+	Author = {Christel M. Marian and Adrian Heil and Martin Kleinschmidt},
+	Journal = {WIREs Comput. Mol. Sci.},
+	Note = {doi: 10.1002/wcms.1394},
+	Pages = {e1394},
+	Title = {The DFT/MRCI method},
+	Year = {2018}}
+
+@article{MarLosFdeAgu-JCP-04,
+	Author = {{M. E. Mart\'in, A. M. Losa, I. Fdez.-Galv\'an, and M. A. Aguilar}},
+	Journal = {J. Chem. Phys.},
+	Pages = {3710},
+	Volume = {121},
+	Year = {2004}}
+
+@article{MarMea-JCP-78,
+	Author = {D. J. Margoliash and W. J. Meath},
+	Journal = {J. Chem. Phys.},
+	Pages = {1426},
+	Volume = {68},
+	Year = {1978}}
+
+@article{MaRohMol-JCTC-10,
+	Author = {Y. Ma and M. Rohlfing and C. Molteni},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {257},
+	Volume = {6},
+	Year = {2010}}
+
+@article{MaRohMol-PRB-09,
+	Author = {Y. Ma and M. Rohlfing and C. Molteni},
+	Journal = {Phys. Rev. B},
+	Pages = {241405},
+	Volume = {80},
+	Year = {2009}}
+
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+	Pages = {604},
+	Volume = {{110}},
+	Year = {1958}}
+
+@article{MarWer-JPCA-09,
+	Author = {O. Marchetti and H.-J. Werner},
+	Journal = {J. Phys. Chem. A},
+	Pages = {11580},
+	Volume = {113},
+	Year = {2009}}
+
+@article{Math10-PROG-15,
+	Note = {{Wolfram Research, Inc., Mathematica, Version 10.3, Champaign, IL (2015)}}}
+
+@article{Math9-PROG-12,
+	Note = {{Wolfram Research, Inc., Mathematica, Version 9.0, Champaign, IL (2012)}}}
+
+@article{MatKogRomDeh-PRA-98,
+	Author = {H. Matsuyama and T. Koga and E. Romera and J. S. Dehesa},
+	Journal = {Phys. Rev. A},
+	Pages = {1759},
+	Volume = {57},
+	Year = {1998}}
+
+@article{MatKoh-JCP-01,
+	Author = {Ann E. Mattsson and Walter Kohn},
+	Journal = {The Journal of Chemical Physics},
+	Keywords = {surface energy; density functional theory; errors; surface potential; jellium},
+	Number = {8},
+	Pages = {3441-3443},
+	Publisher = {AIP},
+	Title = {An energy functional for surfaces},
+	Url = {http://link.aip.org/link/?JCP/115/3441/1},
+	Volume = {115},
+	Year = {2001},
+	Bdsk-Url-1 = {http://link.aip.org/link/?JCP/115/3441/1}}
+
+@article{Mat-S-02,
+	Author = {A. E. Mattson},
+	Journal = {Science},
+	Pages = {759},
+	Volume = {298},
+	Year = {2002}}
+
+@article{MccStrWis-PRA-91,
+	Author = {C. W. McCurdy and C. K. Stroud and M. K. Wisinski},
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+	Pages = {5980},
+	Volume = {43},
+	Year = {1991}}
+
+@article{Mcd-MP-03,
+	Author = {J. J. W. McDouall},
+	Journal = {Mol. Phys.},
+	Pages = {361},
+	Title = {Combining two-body density functionals with multiconfigurational wavefunctions: diatomic molecules},
+	Volume = {101},
+	Year = {2003}}
+
+@article{MclBal-RMP-64,
+	Author = {McLachlan, A. D. and Ball, M. A.},
+	Doi = {10.1103/RevModPhys.36.844},
+	Journal = {Rev. Mod. Phys.},
+	Pages = {844-855},
+	Title = {Time-dependent Hartree-Fock Theory for Molecules},
+	Volume = {36},
+	Year = {1964},
+	Bdsk-Url-1 = {https://doi.org/10.1103/RevModPhys.36.844}}
+
+@book{McW-BOOK-92,
+	Address = {London},
+	Author = {R. McWeeny},
+	Publisher = {Academic Press},
+	Title = {Methods of Molecular Quantum Mechanics. Second Edition},
+	Year = {1992}}
+
+@article{Mcw-CCA-84,
+	Author = {R. McWeeny},
+	Journal = {Croat. Chem. Acta},
+	Pages = {865},
+	Volume = {57},
+	Year = {1984}}
+
+@article{MelSan-PRE-05,
+	Author = {Melko, R. G. and Sandvik, A. W.},
+	Doi = {10.1103/PhysRevE.72.026702},
+	Issue = {2},
+	Journal = {Phys. Rev. E},
+	Numpages = {22},
+	Pages = {026702},
+	Publisher = {American Physical Society},
+	Title = {{Stochastic series expansion algorithm for the $S=1∕2$ $XY$ model with four-site ring exchange}},
+	Url = {http://link.aps.org/doi/10.1103/PhysRevE.72.026702},
+	Volume = {72},
+	Year = {2005},
+	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.72.026702},
+	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevE.72.026702}}
+
+@article{MenAnd-JCP-81,
+	Author = {F. Mentch and J. B. Anderson},
+	Journal = {J. Chem. Phys.},
+	Pages = {6307},
+	Volume = {74},
+	Year = {1981}}
+
+@incollection{MerValUga-INC-03,
+	Address = {Dordrecht},
+	Author = {J. M. Mercero and E. Valderrama and J. M. Ugalde},
+	Booktitle = {NATO-ASI Series in Metal-Ligand Interaction in Molecular-, Nano-, Micro, and Macro-systems in Complex Environments},
+	Editor = {N. Russo, D. R. Salahub and M. Witko},
+	Publisher = {Kluwer Academic Publishers},
+	Year = {2003}}
+
+@article{MetRosRosTelTel-JCP-53,
+	Author = {N. Metropolis and A. W. Rosenbluth and M. N. Rosenbluth and A. H. Teller and E. Teller},
+	Journal = {J. Chem. Phys.},
+	Pages = {1087},
+	Title = {{Equations of state calculations by fast computing machines}},
+	Volume = {21},
+	Year = {1953}}
+
+@article{MeyMulSch-JMS-96,
+	Author = {H. Meyer and T. M\"uller and A. Schweig},
+	Journal = {J. Mol. Struct. (Theochem)},
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+	Volume = {306},
+	Year = {1996}}
+
+@article{MieSavStoPre-CPL-89,
+	Author = {B. Miehlich and A. Savin and H. Stoll and H. Preuss},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {200},
+	Volume = {157},
+	Year = {1989}}
+
+@article{MieStoSav-MP-97,
+	Author = {B. Miehlich and H. Stoll and A. Savin},
+	Journal = {Mol. Phys.},
+	Pages = {527},
+	Title = {A correlation-energy density functional for multideterminantal wavefunctions},
+	Volume = {{91}},
+	Year = {1997}}
+
+@article{Mil-PR-65,
+	Author = {{W. L. McMillan}},
+	Journal = {Phys. Rev.},
+	Pages = {A442},
+	Title = {{Ground state of liquid He$^4$}},
+	Volume = {138},
+	Year = {1965}}
+
+@article{MisJezSza-PRL-03,
+	Author = {A. J. Misquitta and B. Jeziorski and K. Szalewicz},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {033201},
+	Volume = {91},
+	Year = {2003}}
+
+@article{Mit-PRA-81,
+	Author = {M. H. Mittleman},
+	Journal = {Phys. Rev. A},
+	Pages = {1167},
+	Volume = {24},
+	Year = {1981}}
+
+@article{MiyAryKotSchUsuTer-PRB-02,
+	Author = {Miyake, T. and Aryasetiawan, F. and Kotani, T. and Schilfgaarde, M. v. and Usuda, M. and Terakura, K.},
+	Journal = {Phys. Rev. B.},
+	Pages = {245103},
+	Title = {Total energy of solids: An exchange and random-phase approximation correlation study},
+	Volume = {66},
+	Year = {2002}}
+
+@book{Moi-BOOK-11,
+	Address = {Cambridge},
+	Author = {Nimrod Moiseyev},
+	Publisher = {Cambridge University Press},
+	Title = {Non-Hermitian Quantum Mechanics},
+	Year = {2011}}
+
+@article{MolPle-PR-34,
+	Author = {C. M{\o}ller and M. S. Plesset},
+	Journal = {Phys. Rev.},
+	Pages = {618},
+	Volume = {46},
+	Year = {1934}}
+
+@misc{Molpro-PROG-02,
+	Address = {Birmingham, UK},
+	Author = {R. D. Amos and A. Bernhardsson and A. Berning and P. Celani and D. L. Cooper and M. J. O. Deegan and A. J. Dobbyn and F. Eckert and C. Hampel and G. Hetzer and P. J. Knowles and T. Korona and R. Lindh and A. W. Lloyd and S. J. {McNicholas} and F. R. Manby and W. Meyer and M. E. Mura and A. Nicklass and P. Palmieri and R. Pitzer and G. Rauhut and M. {Sch\"{u}tz} and U. Schumann and H. Stoll and A. J. Stone and R. Tarroni and T. Thorsteinsson and H.-J. Werner},
+	Title = {MOLPRO, a package of ab initio programs designed by {H.-J.~Werner} and {P.~J. Knowles}, version 2002.2},
+	Year = {2002}}
+
+@misc{Molpro-PROG-10,
+	Address = {Cardiff, UK},
+	Author = {H.-J. Werner and P. J. Knowles and G. Knizia and F. R. Manby and M. {Sch\"{u}tz} and P. Celani and T. Korona and R. Lindh and A. Mitrushenkov and G. Rauhut and K. R. Shamasundar and T. B. Adler and R. D. Amos and A. Bernhardsson and A. Berning and D. L. Cooper and M. J. O. Deegan and A. J. Dobbyn and F. Eckert and E. Goll and C. Hampel and A. Hesselmann and G. Hetzer and T. Hrenar and G. Jansen and C. K\"oppl and Y. Liu and A. W. Lloyd and R. A. Mata and A. J. May and S. J. McNicholas and W. Meyer and M. E. Mura and A. Nicklass and D. P. O'Neill and P. Palmieri and K. Pfl\"uger and R. Pitzer and M. Reiher and T. Shiozaki and H. Stoll and A. J. Stone and R. Tarroni and T. Thorsteinsson and M. Wang and A. Wolf},
+	Note = {see http://www.molpro.net},
+	Title = {MOLPRO, version 2010.1, a package of ab initio programs},
+	Year = 2010}
+
+@misc{Molproshort-PROG-02,
+	Address = {Birmingham, UK},
+	Title = {MOLPRO, a package of ab initio programs designed by {H.-J.~Werner} and {P.~J. Knowles}, version 2002.2},
+	Year = {2002}}
+
+@misc{Molproshort-PROG-08,
+	Address = {Cardiff, UK},
+	Author = {H.-J. Werner and P. J. Knowles and R. Lindh and F. R. Manby and M. {Sch\"{u}tz} and others},
+	Note = {see www.molpro.net},
+	Title = {MOLPRO, version 2008.2, a package of ab initio programs},
+	Year = {2008}}
+
+@misc{Molproshort-PROG-10,
+	Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}},
+	Note = {Cardiff, UK, 2010, see \url{http://www.molpro.net}},
+	Title = {MOLPRO, version 2010.1, a package of ab initio programs}}
+
+@misc{Molproshort-PROG-12,
+	Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}},
+	Note = {Cardiff, UK, 2012, see \url{http://www.molpro.net}},
+	Title = {MOLPRO, version 2012.1, a package of ab initio programs}}
+
+@misc{Molproshort-PROG-15,
+	Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}},
+	Note = {{Cardiff, UK, 2015, see \url{http://www.molpro.net}}},
+	Title = {{MOLPRO, version 2015.1, a package of ab initio programs}}}
+
+@misc{Molproweb-PROG-XX,
+	Note = {\url{http://www.molpro.net}},
+	Title = {MOLPRO, a package of ab initio programs}}
+
+@article{MomShi-JCP-87,
+	Author = {T. Momose and T. Shida},
+	Journal = {J. Chem. Phys.},
+	Pages = {2832},
+	Volume = {87},
+	Year = {1987}}
+
+@article{MorCepSen-PRL-95,
+	Author = {S. Moroni and D. M. Ceperley and G. Senatore},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {689},
+	Volume = {75},
+	Year = {1995}}
+
+@article{MorCohYan-JCP-06a,
+	Author = {Paula Mori-S\'anchez and Aron J. Cohen and Weitao Yang},
+	Journal = {J. Chem. Phys.},
+	Pages = {091102},
+	Volume = {124},
+	Year = {2006}}
+
+@article{MorCohYan-JCP-06,
+	Author = {P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang},
+	Journal = {J. Chem. Phys.},
+	Pages = {201102},
+	Volume = {125},
+	Year = {2006}}
+
+@article{MorCohYan-PRA-12,
+	Author = {P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang},
+	Journal = {Phys. Rev. A},
+	Pages = {042507},
+	Volume = {85},
+	Year = {2012}}
+
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+	Number = {9},
+	Pages = {7145-7151},
+	Publisher = {AIP},
+	Title = {A study of O[sub 3], S[sub 3], CH[sub 2], and Be[sub 2] using Kohn--Sham theory with accurate quadrature and large basis sets},
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+@article{MusAng-CTC-15,
+	Abstract = {Abstract The charge density response function and the exchange hole are closely related to each other via the fundamental fluctuation--dissipation theorem of physics. A simple approximate model of the static response function is visually compared on several examples in order to demonstrate this relationship. This study is completed by illustrating the well-known isomorphism between the exchange hole and the square of the dominant localized orbital lying in the space region of the reference point of the exchange hole function. The implications of these relationships for the interpretation of common chemical concepts, such as delocalization, are discussed. },
+	Author = {Bastien Mussard and J\'anos G. \'Angy\'an},
+	Doi = {http://dx.doi.org/10.1016/j.comptc.2014.10.039},
+	Issn = {2210-271X},
+	Journal = {Computational and Theoretical Chemistry},
+	Keywords = {Topological analysis},
+	Note = {Special Issue: Understanding structure and reactivity from topology and beyond},
+	Number = {0},
+	Pages = {44 - 52},
+	Title = {Relationships between charge density response functions, exchange holes and localized orbitals},
+	Url = {http://www.sciencedirect.com/science/article/pii/S2210271X14004952},
+	Volume = {1053},
+	Year = {2015},
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+@incollection{MusCocAssOttUmrTou-AQC-18,
+	Author = {B. Mussard and E. Coccia and R. Assaraf and M. Otten and C. J. Umrigar and J. Toulouse},
+	Booktitle = {Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems},
+	Doi = {10.1016/bs.aiq.2017.05.005},
+	Editor = {P. E. Hoggan},
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+	Publisher = {Academic Press},
+	Series = {Advances in Quantum Chemistry Vol. 76},
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+	Date-Modified = {2019-08-01 12:02:10 +0200},
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+	Note = {See the supplementary material for the detailed results of the calculations on the AE49 and DBH24/08 datasets.}}
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+	Note = {unpublished}}
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+	Author = {J. Paldus and J. {\v C}i{\v z}ek},
+	Journal = {J. Chem. Phys.},
+	Pages = {2293},
+	Volume = {54},
+	Year = {1971}}
+
+@article{PalCiz-PRA-70,
+	Author = {J. Paldus and J. {\v C}i{\v z}ek},
+	Journal = {Phys. Rev. A},
+	Pages = {2268},
+	Volume = {2},
+	Year = {1970}}
+
+@article{Pal-JCP-77,
+	Author = {J. Paldus},
+	Journal = {J. Chem. Phys.},
+	Pages = {303},
+	Volume = {67},
+	Year = {1977}}
+
+@article{PalOniDelCorRei-PRB-99,
+	Author = {Maurizia Palummo and Giovanni Onida and Rodolfo Del Sole and Massimiliano Corradini and Lucia Reining},
+	Journal = {Phys. Rev. B},
+	Pages = {11329},
+	Volume = {{60}},
+	Year = {1999}}
+
+@article{PalPavHubSch-EPJB-11,
+	Author = {G. Pal and Y. Pavlyukh and W. H\"ubner and H. C. Schneider},
+	Journal = {Eur. Phys. J. B.},
+	Pages = {327},
+	Volume = {79},
+	Year = {2011}}
+
+@article{Pan-CPL-93,
+	Author = {I. Panas},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {255},
+	Volume = {201},
+	Year = {1993}}
+
+@article{pan:5642,
+	Author = {Xiao-Yin Pan and Viraht Sahni},
+	Issue = {12},
+	Journal = {The Journal of Chemical Physics},
+	Keywords = {ground states; molecular configurations; density functional theory; Schrodinger equation; ionisation potential; wave functions; eigenvalues and eigenfunctions; electron correlations; hydrogen},
+	Page = {5642-5649},
+	Publisher = {AIP},
+	Title = {Quantal density functional theory of the hydrogen molecule},
+	Url = {http://link.aip.org/link/?JCP/120/5642/1},
+	Volume = {120},
+	Year = {2004},
+	Bdsk-Url-1 = {http://link.aip.org/link/?JCP/120/5642/1}}
+
+@article{PaqTou-JCP-18,
+	Author = {Julien Paquier and Julien Toulouse},
+	Doi = {10.1063/1.5049773},
+	Journal = {J. Chem. Phys.},
+	Pages = {174110},
+	Title = {Four-component relativistic range-separated density-functional theory: Short-range exchange local-density approximation},
+	Volume = {149},
+	Year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.5049773}}
+
+@misc{PaqTou-JJJ-XX-note,
+	Note = {See Supplementary Information for details on the calculation of the sums over spins in Eqs.~(\ref{epsxC}) and (\ref{epsxB}), details on the calculation of the large-$\ct$ expansions in Eqs.~(\ref{epsCsrasymp}) and~(\ref{epsBsrasymp}), and for a Mathematica notebook containing the complete expressions of the large-$\ct$ expansions in Eqs.~(\ref{epsCsrasymp}) and~(\ref{epsBsrasymp}) and of the Pad\'e approximants in Eqs.~(\ref{PadeC}) and~(\ref{PadeB}).}}
+
+@article{parr:3801,
+	Author = {Robert G. Parr and Robert A. Donnelly and Mel Levy and William E. Palke},
+	Journal = {The Journal of Chemical Physics},
+	Number = {8},
+	Pages = {3801-3807},
+	Publisher = {AIP},
+	Title = {Electronegativity: The density functional viewpoint},
+	Url = {http://link.aip.org/link/?JCP/68/3801/1},
+	Volume = {68},
+	Year = {1978},
+	Bdsk-Url-1 = {http://link.aip.org/link/?JCP/68/3801/1}}
+
+@book{ParYan-BOOK-89,
+	Address = {New York},
+	Author = {R. G. Parr and W. Yang},
+	Publisher = {Oxford University Press},
+	Title = {Density-Functional Theory of Atoms and Molecules},
+	Year = {1989}}
+
+@article{PasGidPer-PRA-13,
+	Author = {E. Pastorczak and N. I. Gidopoulos and K. Pernal},
+	Journal = {Phys. Rev. A},
+	Pages = {062501},
+	Volume = {87},
+	Year = {2013}}
+
+@article{PatCenJezJezSza-JPCA-07,
+	Author = {Konrad Patkowski and Wojciech Cencek and M. Jeziorska and B. Jeziorski and Krzysztof Szalewicz},
+	Journal = {J. Phys. Chem. A},
+	Pages = {7611},
+	Volume = {111},
+	Year = {2007}}
+
+@article{PatVas-PRB-72,
+	Author = {K. N. Pathak and P. Vashishta},
+	Journal = {Phys. Rev. B.},
+	Pages = {3649},
+	Volume = {{7}},
+	Year = {1972}}
+
+@book{Pauncz-BOOK-79,
+	Address = {New York},
+	Author = {R. Pauncz},
+	Publisher = {Plenum Press},
+	Title = {Spin Eigenfunctions},
+	Year = {1979}}
+
+@article{PauPilTouEll-JCP-10,
+	Author = {Fran\c{c}oise Pauzat and Julien Pilm\'e and Julien Toulouse and Yves Ellinger},
+	Journal = {J. Chem. Phys.},
+	Pages = {054301},
+	Title = {About the collapse of the 3.3 µm CH stretching band with ionization in polycyclic aromatic hydrocarbons: Configuration interaction and quantum Monte Carlo studies of the CH fragment},
+	Volume = {133},
+	Year = {2010}}
+
+@article{PeaBenHelToz-JCP-08,
+	Author = {M. J. Peach and P. Benfield and T. Helgaker and D. J. Tozer},
+	Journal = {J. Chem. Phys.},
+	Pages = {044118},
+	Volume = {128},
+	Year = {2008}}
+
+@article{PeaCohToz-PCCP-06,
+	Author = {M. J. G. Peach and A. J. Cohen and D. J. Tozer},
+	Journal = {Phys. Chem. Chem. Phys.},
+	Pages = {4543},
+	Volume = {8},
+	Year = {2006}}
+
+@article{PeaHelSalKeaLutTozHan-PCCP-06,
+	Author = {M. J. G. Peach and T. Helgaker and P. Salek and T. W. Keal and O. B. Lutn{\ae}s and D. J. Tozer and N. C. Handy},
+	Journal = {Phys. Chem. Chem. Phys.},
+	Pages = {558},
+	Volume = {8},
+	Year = {2006}}
+
+@article{PeaTeaHelToz-JCTC-15,
+	Author = {M. J. G. Peach and A. M. Teale and T. Helgaker and D. J. Tozer},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {5262},
+	Volume = {11},
+	Year = {2015}}
+
+@article{PeaToz-JPCA-12,
+	Author = {M. J. G. Peach and D. J. Tozer},
+	Journal = {J. Phys. Chem. A},
+	Pages = {9783},
+	Volume = {116},
+	Year = {2012}}
+
+@misc{PedJen-JJJ-XX,
+	Author = {J. K. Pedersen and H. J. A. Jensen},
+	Note = {(unpublished)},
+	Title = {{A second order MCSCF-DFT hybrid algorithm}}}
+
+@misc{PedJen-JJJ-XX_fr,
+	Author = {J. K. Pedersen and H. J. A. Jensen},
+	Note = {non publi{\'e}}}
+
+@phdthesis{Ped-THESIS-04,
+	Address = {Odense},
+	Author = {J. K. Pedersen},
+	School = {University of Southern Denmark},
+	Title = {Description of correlation and relativistic effects in calculations of molecular properties},
+	Type = {{PhD thesis}},
+	Year = {2004}}
+
+@article{PeiNecWar-PRA-03,
+	Author = {K. Peirs and D. Van Neck and M. Waroquier},
+	Eid = {012505},
+	Issue = {1},
+	Journal = {Physical Review A (Atomic, Molecular, and Optical Physics)},
+	Keywords = {density functional theory; atomic structure; Green's function methods; ab initio calculations},
+	Numpages = {12},
+	Page = {012505},
+	Publisher = {APS},
+	Title = {Algorithm to derive exact exchange-correlation potentials from correlated densities in atoms},
+	Url = {http://link.aps.org/abstract/PRA/v67/e012505},
+	Volume = {67},
+	Year = {2003},
+	Bdsk-Url-1 = {http://link.aps.org/abstract/PRA/v67/e012505}}
+
+@article{PerBurErn-PRL-96,
+	Author = {J. P. Perdew and K. Burke and M. Ernzerhof},
+	Date-Modified = {2019-08-01 12:11:11 +0200},
+	Doi = {10.1103/PhysRevLett.77.3865},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {3865},
+	Title = {Generalized Gradient Approximation Made Simple},
+	Volume = {77},
+	Year = {1996},
+	Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.77.3865}}
+
+@article{PerCheVosJacPedSinFio-PRB-92,
+	Author = {J. P. Perdew and J. A. Chevary and S. H. Vosko and K. A. Jackson and M. R. Pederson and D. J. Singh and C. Fiolhais},
+	Journal = {Phys. Rev. B},
+	Pages = {6671},
+	Volume = {{46}},
+	Year = {1992}}
+
+@book{PerEngDreGroGodNogCasMar-BOOK-03,
+	Address = {Berlin},
+	Editor = {C. Fiolhais and F. Nogueira and M. A. L. Marques},
+	Publisher = {Springer},
+	Series = {Vol. 620 of Lecture Notes in Physics},
+	Title = {A Primer in Density Functional Theory},
+	Year = {2003}}
+
+@article{PerErnBur-JCP-96,
+	Author = {J. P. Perdew and M. Ernzerhof and K. Burke},
+	Journal = {J. Chem. Phys},
+	Pages = {9982},
+	Volume = {105},
+	Year = {1996}}
+
+@article{PerErnBurSav-IJQC-97,
+	Author = {J. P. Perdew and M. Ernzerhof and K. Burke and A. Savin},
+	Journal = {Int. J. Quantum Chem.},
+	Pages = {197},
+	Volume = {{61}},
+	Year = {1997}}
+
+@article{PerGieGriBae-JCP-07,
+	Author = {K. Pernal and K. Giesbertz and O. Gritsenko and E. J. Baerends},
+	Journal = {J. Chem. Phys.},
+	Pages = {214101},
+	Volume = {127},
+	Year = {2007}}
+
+@article{PerGriBae-PRA-07,
+	Author = {K. Pernal and O. Gritsenko and E. J. Baerends},
+	Journal = {Phys. Rev. A},
+	Pages = {012506},
+	Volume = {75},
+	Year = {2007}}
+
+@article{Per-IJQC-93,
+	Author = {J. P. Perdew},
+	Journal = {Int. J. Quantum. Chem.: Quantum Chem. Symp.},
+	Pages = {93},
+	Volume = {27},
+	Year = {1993}}
+
+@incollection{Per-INC-91,
+	Address = {berlin},
+	Author = {J. P. Perdew},
+	Booktitle = {Electronic Structure of Solids '91},
+	Editor = {P. Ziesche and H. Eschrig},
+	Publisher = {Akademie Verlag},
+	Year = {1991}}
+
+@article{Per-JCP-12,
+	Author = {K. Pernal},
+	Journal = {J. Chem. Phys.},
+	Pages = {184105},
+	Title = {{Excitation energies from range-separated time-dependent density and density matrix functional theory}},
+	Volume = {136},
+	Year = {2012}}
+
+@article{PerLanSah-PRL-77,
+	Author = {J. P. Perdew and D. C. Langreth and V. Sahni},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {1030},
+	Volume = {{38}},
+	Year = {1977}}
+
+@article{PerLev-PRL-83,
+	Author = {J. P. Perdew and M. Levy},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {1884},
+	Volume = {51},
+	Year = {1983}}
+
+@article{PerMcMZun-PRA-81,
+	Author = {J. P. Perdew and E. R. McMullen and A. Zunger},
+	Journal = {Phys. Rev. A},
+	Pages = {2785},
+	Volume = {{23}},
+	Year = {1981}}
+
+@article{PerParLevBal-PRL-82,
+	Author = {J. P. Perdew and R. G. Parr and M. Levy and J. L. Balduz},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {1691},
+	Title = {Density-functional theory for fractional particle number: Derivative discontinuity of the energy},
+	Volume = {49},
+	Year = {1982}}
+
+@article{PerPerMorIll-JCC-07,
+	Author = {A. J. P\'erez-Jim\'enez and J. M. P\'erez-Jord\'a and I. De P. R. Moreira and F. Illas},
+	Journal = {J. Comput. Chem.},
+	Pages = {2559},
+	Volume = {28},
+	Year = {2007}}
+
+@article{PerPerSan-JCP-07,
+	Author = {A. J. P\'erez-Jim\'enez and J. M. P\'erez-Jord\'a and J. C. Sancho-Garc\'ia},
+	Journal = {J. Chem. Phys.},
+	Pages = {104102},
+	Title = {Combining two-body density correlation functionals with multiconfigurational wave functions using natural orbitals and occupation numbers},
+	Volume = {127},
+	Year = {2007}}
+
+@article{Per-PRA-10,
+	Author = {Katarzyna Pernal},
+	Journal = {Phys. Rev. A},
+	Pages = {052511},
+	Volume = {81},
+	Year = {2010}}
+
+@article{Per-PRB-86,
+	Author = {J. P. Perdew},
+	Journal = {Phys. Rev. B},
+	Pages = {8822},
+	Volume = {{33}},
+	Year = {1986}}
+
+@article{Per-PRL-85,
+	Author = {J. P. Perdew},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {1665},
+	Volume = {{55}},
+	Year = {1985}}
+
+@article{PerSavBur-PRA-95,
+	Author = {J. P. Perdew and A. Savin and K. Burke},
+	Journal = {Phys. Rev. A},
+	Pages = {4531},
+	Title = {{Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory}},
+	Volume = {51},
+	Year = {1995}}
+
+@article{PerWan2-PRB-92,
+	Author = {J. P. Perdew and Y. Wang},
+	Journal = {Phys. Rev. B},
+	Pages = {12947},
+	Volume = {{46}},
+	Year = {1992}}
+
+@article{PerWan-PRB-86,
+	Author = {J. P. Perdew and Y. Wang},
+	Journal = {Phys. Rev. B},
+	Pages = {8800},
+	Volume = {{33}},
+	Year = {1986}}
+
+@article{PerWan-PRB-92,
+	Author = {J. P. Perdew and Y. Wang},
+	Journal = {Phys. Rev. B},
+	Pages = {13244},
+	Volume = {45},
+	Year = {1992}}
+
+@article{PerZun-PRB-81,
+	Author = {J. P. Perdew and A. Zunger},
+	Journal = {Phys. Rev. B},
+	Pages = {5048},
+	Volume = {23},
+	Year = {1981}}
+
+@article{PetDun-JCP-02,
+	Author = {{K. A. Peterson and T. H. Dunning, Jr}},
+	Journal = {J. Chem. Phys.},
+	Pages = {10548},
+	Volume = {117},
+	Year = {2002}}
+
+@article{PetDun-JPC-95,
+	Author = {{K. A. Peterson and T. H. Dunning Jr.}},
+	Journal = {J. Phys. Chem.},
+	Pages = {3898},
+	Volume = {99},
+	Year = {1995}}
+
+@article{PetGosGro-PRL-96,
+	Author = {M. Petersilka and U. J. Gossmann and E. K. U. Gross},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {1212},
+	Volume = {76},
+	Year = {1996}}
+
+@article{PetGro-IJQC-96,
+	Author = {M. Petersilka and E. K. U. Gross},
+	Journal = {Int. J. Quantum Chem. Symp.},
+	Pages = {1393},
+	Volume = {30},
+	Year = {1996}}
+
+@article{PetHolChaNigUmr-PRL-12,
+	Author = {F. R. Petruzielo and A. A. Holmes and H. J. Changlani and M. P. Nightingale and C. J. Umrigar},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {230201},
+	Title = {Semistochastic Projector Monte Carlo Method},
+	Volume = {109},
+	Year = {2012}}
+
+@article{PetKenDun-JCP-93b,
+	Author = {{K. A. Peterson, R. A. Kendall and T. H. Dunning Jr.}},
+	Journal = {J. Chem. Phys.},
+	Pages = {9790},
+	Volume = {99},
+	Year = {1993}}
+
+@article{PetTouUmr-JCP-11,
+	Author = {F. R. Petruzielo and J. Toulouse and C. J. Umrigar},
+	Journal = {J. Chem. Phys.},
+	Pages = {064104},
+	Title = {Basis set construction for molecular electronic structure theory: Natural orbital and Gauss--Slater basis for smooth pseudopotentials},
+	Volume = {134},
+	Year = {2011}}
+
+@article{PetTouUmr-JCP-12,
+	Author = {F. R. Petruzielo and J. Toulouse and C. J. Umrigar},
+	Date-Modified = {2019-05-13 20:57:32 +0200},
+	Journal = {J. Chem. Phys.},
+	Pages = {124116},
+	Title = {{Approaching Chemical Accuracy With Quantum Monte Carlo}},
+	Volume = {136},
+	Year = {2012}}
+
+@article{PevHea-JCP-13,
+	Author = {Roberto Peverati and Martin Head-Gordon},
+	Journal = {J. Chem. Phys.},
+	Pages = {024110},
+	Title = {Orbital optimized double-hybrid density functionals},
+	Volume = {139},
+	Year = {2013}}
+
+@article{PevTru-JPCL-11,
+	Author = {Roberto Peverati and Donald G. Truhlar},
+	Journal = {J. Phys. Chem. Lett.},
+	Pages = {2810},
+	Volume = {2},
+	Year = {2011}}
+
+@article{PevTru-JPCL-12,
+	Author = {Roberto Peverati and Donald G. Truhlar},
+	Journal = {J. Phys. Chem. Lett.},
+	Pages = {117},
+	Volume = {3},
+	Year = {2012}}
+
+@article{PevTru-PTRSA-14,
+	Abstract = {Kohn{\textendash}Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange{\textendash}correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading{\textemdash}as a long-range goal{\textemdash}to a functional with good accuracy for all problems, i.e. a universal functional. To guide our path towards that goal and to measure our progress, we have developed{\textemdash}building on earlier work of our group{\textemdash}a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes, such as atomization, complexation, proton addition and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For this paper, we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test two wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore, the results provide a status report on the quest for a universal functional.},
+	Author = {Peverati, Roberto and Truhlar, Donald G.},
+	Doi = {10.1098/rsta.2012.0476},
+	Isbn = {1471-2962},
+	Issn = {1364-503X},
+	Journal = {Phil. Trans. R. Soc. A},
+	Note = {preprint at http://arxiv.org/abs/1212.0944},
+	Number = {2011},
+	Pages = {20120476},
+	Publisher = {The Royal Society},
+	Title = {Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics},
+	Volume = {372},
+	Year = {2014},
+	Bdsk-Url-1 = {https://doi.org/10.1098/rsta.2012.0476}}
+
+@article{PhiKanZgi-JCP-15,
+	Author = {J. J. Phillips and A. A. Kananenka and D. Zgid},
+	Journal = {J. Chem. Phys.},
+	Pages = {194108},
+	Volume = {142},
+	Year = {2015}}
+
+@article{PicGos-MP-73,
+	Author = {B. T. Pickup and O. Goscinski},
+	Journal = {Mol. Phys.},
+	Pages = {1013},
+	Volume = {26},
+	Year = {1973}}
+
+@book{PinNoz-BOOK-89,
+	Author = {D. Pines and P. Nozi\`eres},
+	Publisher = {Addison-Wesley Publishing Company},
+	Title = {The Theory of Quantum Liquids},
+	Year = {1989}}
+
+@article{PisDov-IJQC-80,
+	Author = {C. Pisani and R. Dovesi},
+	Journal = {Int. J. Quantum Chem.},
+	Pages = {501},
+	Volume = {17},
+	Year = {1980}}
+
+@article{PisMasCasHalSchUsv-JCC-08,
+	Author = {C. Pisani and L. Maschio and S. Casassa and M. Halo and M. Sch\"utz and D. Usvyat},
+	Journal = {J. Comput. Chem.},
+	Pages = {2113},
+	Volume = {29},
+	Year = {2008}}
+
+@article{BytLaiRuedenJCP05,
+	Author = {Bytautas,Laimutis and Ruedenberg,Klaus},
+	Doi = {10.1063/1.1869493},
+	Eprint = {https://doi.org/10.1063/1.1869493},
+	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}}
+
+@article{pittner:10275,
+	Author = {Jiri Pittner and Petr Nachtigall and Petr Carsky and Jozef Masik and Ivan Hubac},
+	Journal = {The Journal of Chemical Physics},
+	Keywords = {organic compounds; silicon compounds; coupled cluster calculations; configuration interactions},
+	Number = {21},
+	Pages = {10275-10282},
+	Publisher = {AIP},
+	Title = {Assessment of the single-root multireference Brillouin--Wigner coupled- cluster method: Test calculations on CH[sub 2], SiH[sub 2], and twisted ethylene},
+	Url = {http://link.aip.org/link/?JCP/110/10275/1},
+	Volume = {110},
+	Year = {1999},
+	Bdsk-Url-1 = {http://link.aip.org/link/?JCP/110/10275/1}}
+
+@article{PolColLeiStoWerSav-IJQC-03,
+	Author = {R. Pollet and F. Colonna and T. Leininger and H. Stoll and H.-J. Werner and A. Savin},
+	Journal = {Int. J. Quantum. Chem.},
+	Pages = {84},
+	Title = {Exchange-Correlation Energies and Correlation Holes for Some Two- and Four-Electron Atoms along a Nonlinear Adiabatic Connection in Density Functional Theory},
+	Volume = {{91}},
+	Year = {2003}}
+
+@article{PolSavLeiSto-JCP-02,
+	Author = {R. Pollet and A. Savin and T. Leininger and H. Stoll},
+	Journal = {J. Chem. Phys.},
+	Pages = {1250},
+	Title = {Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules},
+	Volume = {{116}},
+	Year = {2002}}
+
+@phdthesis{Pol-THESIS-01,
+	Author = {R. Pollet},
+	School = {Universit\'e Paris 6},
+	Title = {D\'eveloppement et applications d'une m\'ethode g\'en\'eralisant la th\'eorie de la fonctionnelle de la densit\'e \`a plusieurs d\'eterminants de Slater},
+	Type = {Th\`ese de doctorat},
+	Year = {2001}}
+
+@article{Pop-RMP-99,
+	Author = {J. A. Pople},
+	Date-Modified = {2019-05-13 20:11:17 +0200},
+	Journal = {Rev. Mod. Phys.},
+	Pages = {1267},
+	Title = {{Nobel Lecture: Quantum Chemical Models}},
+	Volume = {{71}},
+	Year = {1999}}
+
+@article{PorDer-PRA-02,
+	Author = {S. G. Porsev and A. Derevianko},
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+	Note = {unpublished}}
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+
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+	Author = {E. Rebolini},
+	School = {Universit\'e Pierre et Marie Curie},
+	Title = {Range-separated density-functional theory for molecular excitation energies},
+	Type = {{Th\`ese de doctorat}},
+	Url = {https://tel.archives-ouvertes.fr/tel-01027522},
+	Year = {2014},
+	Bdsk-Url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}}
+
+@phdthesis{Reb-THESIS-14_eng,
+	Author = {E. Rebolini},
+	School = {Universit\'e Pierre et Marie Curie},
+	Title = {Range-separated density-functional theory for molecular excitation energies},
+	Type = {{PhD thesis}},
+	Url = {https://tel.archives-ouvertes.fr/tel-01027522},
+	Year = {2014},
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+
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+	Doi = {http://dx.doi.org/10.1063/1.4943003},
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+	Pages = {094107},
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+
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+	Note = {The last two terms of the kernel in Eq. (31) of Ref.~\onlinecite{ZhaSteYan-JCP-13} contain non-antisymmetrized two-electron integrals. However, these terms can also be written with a factor of $1/2$ and antisymmetrized two-electron integrals, leading to our Eq.~(\ref{eq:eff kernel iajb}).}}
+
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+	Author = {E. Rebolini and J. Toulouse and A. Savin},
+	Booktitle = {Electronic Structure and Reactivity},
+	Editor = {S. K. Ghosh and P. K. Chattaraj},
+	Note = {preprint at http://arxiv.org/abs/1304.1314},
+	Pages = {367-390},
+	Publisher = {CRC Press},
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+	Year = {2013}}
+
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+
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+	Volume = {141},
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+	Author = {Julien Toulouse and Francois Colonna and Andreas Savin},
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+	Author = {J. Toulouse and F. Colonna and A. Savin},
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+	Volume = {70},
+	Year = {2004},
+	Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.70.062505}}
+
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+	Note = {For Ne$_{2}$ at equilibrium distance with aug-cc-pVQZ basis, the counterpoise correction on the interaction energy is 16 $\mu$H for RSH+RPAx and 62 $\mu$H for standard MP2.}}
+
+@article{TouGerJanSavAng-PRL-09,
+	Author = {J. Toulouse and I. C. Gerber and G. Jansen and A. Savin and J. G. \'Angy\'an},
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+
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+	Author = {J. Toulouse and P. Gori-Giorgi and A. Savin},
+	Journal = {Int. J. Quantum Chem.},
+	Pages = {2026},
+	Title = {Scaling relations, virial theorem and energy densities for long-range and short-range density functionals},
+	Volume = {106},
+	Year = {2006}}
+
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+	Author = {J. Toulouse and P. Gori-Giorgi and A. Savin},
+	Date-Modified = {2019-08-01 12:10:05 +0200},
+	Doi = {10.1007/s00214-005-0688-2},
+	Journal = {Theor. Chem. Acc.},
+	Pages = {305},
+	Title = {A Short-Range Correlation Energy Density Functional With Multi-Determinantal Reference},
+	Volume = {114},
+	Year = {2005},
+	Bdsk-Url-1 = {https://doi.org/10.1007/s00214-005-0688-2}}
+
+@misc{Tou-JJJ-XX,
+	Author = {S. Dubillard and E. Eliav and L. Visscher and R. Bast and T. Saue},
+	Note = {unpublished}}
+
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+	Author = {Julien Toulouse},
+	Journal = {Phys. Rev. B},
+	Pages = {035117},
+	Title = {Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction},
+	Volume = {72},
+	Year = {2005}}
+
+@article{TouRebGouDobSeaAng-JCP-13,
+	Author = {Julien Toulouse and Elisa Rebolini and Tim Gould and John F. Dobson and Prasenjit Seal and J\'anos G. \'Angy\'an},
+	Journal = {J. Chem. Phys.},
+	Pages = {194106},
+	Title = {Assessment of range-separated time-dependent density-functional theory for calculating $C_6$ dispersion coefficients},
+	Volume = {138},
+	Year = {2013}}
+
+@article{TouSavFla-IJQC-04,
+	Author = {J. Toulouse and A. Savin and H.-J. Flad},
+	Date-Modified = {2019-08-01 11:58:08 +0200},
+	Doi = {10.1002/qua.20259},
+	Journal = {Int. J. Quantum Chem.},
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+	Volume = {100},
+	Year = {2004},
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+
+@misc{TouSav-JJJ-XX,
+	Author = {J. Toulouse and A. Savin},
+	Title = {in preparation}}
+
+@article{TouSav-JMS-06,
+	Author = {Julien Toulouse and Andreas Savin},
+	Journal = {J. Mol. Struct. (Theochem)},
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+	Title = {Local density approximation for long-range or for short-range energy functionals?},
+	Volume = {762},
+	Year = {2006}}
+
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+	Author = {J. Toulouse and K. Sharkas and E. Br\'emond and C. Adamo},
+	Journal = {J. Chem. Phys.},
+	Pages = {101102},
+	Title = {Rationale for a new class of double-hybrid approximations in density-functional theory},
+	Volume = {135},
+	Year = {2011}}
+
+@phdthesis{Tou-THESIS-05,
+	Author = {J. Toulouse},
+	Note = {tel.archives-ouvertes.fr/tel-00550772},
+	School = {Universit\'e Pierre et Marie Curie (Paris 6)},
+	Year = {2005}}
+
+@article{TouUmr-JCP-07,
+	Author = {J. Toulouse and C. J. Umrigar},
+	Journal = {J. Chem. Phys.},
+	Pages = {084102},
+	Title = {{Optimization of quantum Monte Carlo wave functions by energy minimization}},
+	Volume = {126},
+	Year = {2007}}
+
+@article{TouUmr-JCP-08,
+	Author = {J. Toulouse and C. J. Umrigar},
+	Journal = {J. Chem. Phys.},
+	Pages = {174101},
+	Title = {{Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules}},
+	Volume = {128},
+	Year = {2008}}
+
+@misc{TouUmr-JJJ-XX,
+	Author = {J. Toulouse and C. J. Umrigar},
+	Note = {unpublished}}
+
+@misc{TouZhuAngSav-JJJ-XX-note2,
+	Note = {In the context of density-functional theory RPA is usually derived from the Kohn-Sham reference, while in the context of many-body perturbation theory (see appendices) RPA is usually derived from the HF reference. Therefore, both PBE+RPA and HF+RPA are theoretically justified.}}
+
+@misc{TouZhuAngSav-JJJ-XX-note3,
+	Note = {The inverse of a 4-point function $\chi (1,2;1',2')$ is defined according to $\int d1'd2' \chi (1,2;1',2') \chi^{-1} (2',1';4,3) = \delta(1,3) \delta (2,4)$.}}
+
+@misc{TouZhuAngSav-JJJ-XX-note,
+	Note = {The short-range self-energy correction $\Delta \Sigma^\sr_\l$ is wrongly missing in Eq.~(11) of Ref.~\onlinecite{TouGerJanSavAng-PRL-09}. However, in practice, this term vanishes in the RPA or RPAx approximation so that the results of Ref.~\onlinecite{TouGerJanSavAng-PRL-09} are correct.}}
+
+@article{TouZhuAngSav-PRA-10,
+	Author = {Julien Toulouse and Wuming Zhu and J\'anos G. \'Angy\'an and Andreas Savin},
+	Date-Modified = {2019-05-13 20:49:02 +0200},
+	Journal = {Phys. Rev. A},
+	Pages = {032502},
+	Title = {Range-Separated Density-Functional Theory With The Random-Phase Approximation: Detailed Formalism And Illustrative Applications},
+	Volume = {82},
+	Year = {2010}}
+
+@article{TouZhuSavJanAng-JCP-11,
+	Author = {J. Toulouse and W. Zhu and A. Savin and G. Jansen and J. G. \'Angy\'an},
+	Date-Modified = {2019-08-01 12:01:35 +0200},
+	Doi = {10.1063/1.3626551},
+	Journal = {J. Chem. Phys.},
+	Pages = {084119},
+	Title = {Closed-Shell Ring Coupled Cluster Doubles Theory With Range Separation Applied On Weak Intermolecular Interactions},
+	Volume = {135},
+	Year = {2011},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3626551}}
+
+@misc{TouZhuSavJanAng-JJJ-XX,
+	Author = {J. Toulouse and W. Zhu and A. Savin and G. Jansen and J. G. \'Angyan},
+	Note = {unpublished}}
+
+@misc{TouZhuSavJanAng-JJJ-XX-note,
+	Note = {In Ref.~\onlinecite{Hes-JCP-11}, AC-RPA, NRPA1, NRPA3, and NRPA4 refer to what we call here RPAx-I, RPAx-II, RPA-SO2, and RPA-SO1, respectively. In addition, NRPA2 corresponds to the variant of Fukuda {\it et al.}, i.e. $2E_{c,\RPAxII}-E_{c,\text{MP2}}$.}}
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+	Journal = {J. Chem. Phys.},
+	Pages = {174101},
+	Volume = {133},
+	Year = {2010}}
+
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+	Journal = {J. Chem. Phys.},
+	Pages = {5656},
+	Volume = {111},
+	Year = {1999}}
+
+@article{UgaBoy-IJQC-85,
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+	Journal = {Int. J. Quantum. Chem.},
+	Pages = {439},
+	Volume = {27},
+	Year = {1985}}
+
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+	Author = {Carsten A. Ullrich},
+	Publisher = {OUP Oxford},
+	Title = {Time-Dependent Density-Functional Theory: Concepts and Applications},
+	Year = {2011}}
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+	Note = {The convergence in 2 iterations, mentioned near the end of Ref.~\onlinecite{UmrFil-PRL-05} was obtained using the correlated sampling adjustment of $a_\diag$ and the TU Hessian.}}
+
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+	Address = {Singapore},
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+	Booktitle = {High Performance Computing and its Application to the Physical Sciences, Proceedings of the Mardi Gras '93 Conference},
+	Editor = {D. A. Browne {\it et al.}},
+	Publisher = {World Scientific},
+	Year = {1993}}
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+	Year = {1989}}
+
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+	Address = {Dordrecht},
+	Author = {C. J. Umrigar},
+	Booktitle = {Quantum Monte Carlo Methods in Physics and Chemistry},
+	Editor = {M. P. Nightingale and C. J. Umrigar},
+	Pages = {129},
+	Publisher = {Kluwer},
+	Series = {NATO ASI Ser. C 525},
+	Year = {1999}}
+
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+	Author = {C. J. Umrigar and M. P. Nightingale and K. J. Runge},
+	Journal = {J. Chem. Phys.},
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+	Year = {1993}}
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+	Booktitle = {Electronic Density Functional Theory},
+	Doi = {10.1007/978-1-4899-0316-7_12},
+	Editor = {Dobson, John F. and Vignale, Giovanni and Das, Mukunda P.},
+	Pages = {167-176},
+	Publisher = {Springer US},
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+	Author = {C. J. Umrigar},
+	Note = {unpublished}}
+
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+	Author = {C. J. Umrigar},
+	Note = {unpublished}}
+
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+	Author = {C. J. Umrigar},
+	Note = {non publi{\'e}}}
+
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+	Address = {Berlin},
+	Author = {C. J. Umrigar and K. G. Wilson and J. W. Wilkins},
+	Booktitle = {Computer Simulation Studies in Condensed Matter Physics: Recent Developments},
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+	Publisher = {Springer},
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+	Volume = {122},
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+	School = {University of Cambridge},
+	Title = {Spectral Moments in the Homogeneous Electron Gas},
+	Year = {2003}}
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+	Author = {W. Yang and P. Mori-S{\'a}nchez and A. J. Cohen},
+	Journal = {J. Chem. Phys.},
+	Pages = {104114},
+	Volume = {139},
+	Year = {2013}}
+
+@article{YanPerKur-PRB-00,
+	Author = {Yan, Z. and Perdew, J. P. and Kurth, S.},
+	Journal = {Phys. Rev. B.},
+	Pages = {16430-16439},
+	Title = {Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes},
+	Volume = {61},
+	Year = {2000}}
+
+@article{YanTewHan-CPL-04,
+	Author = {Takeshi Yanai and David P. Tew and Nicholas C. Handy},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {51},
+	Volume = {393},
+	Year = {2004}}
+
+@article{YanWu-PRL-02,
+	Author = {Weitao Yang and Qin Wu},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {143002},
+	Title = {Direct Method for Optimized Effective Potentials in Density-Functional Theory},
+	Volume = {89},
+	Year = {2002}}
+
+@article{YanZhaAye-PRL-00,
+	Author = {Weitao Yang and Yingkai Zhang and Paul W. Ayers},
+	Journal = {Phys. Rev. Lett.},
+	Pages = {5172},
+	Volume = {84},
+	Year = {2000}}
+
+@article{Yar-CPL-81,
+	Author = {D. R. Yarkony},
+	Journal = {Chem. Phys. Lett.},
+	Pages = {634},
+	Volume = {77},
+	Year = {1981}}
+
+@article{Yas-PRL-02,
+	Author = {Koji Yasuda},
+	Eid = {053001},
+	Journal = {Physical Review Letters},
+	Keywords = {density functional theory; electron density; electron correlations; Schrodinger equation; scaling phenomena; electron gas},
+	Number = {5},
+	Numpages = {4},
+	Pages = {053001},
+	Publisher = {APS},
+	Title = {Local Approximation of the Correlation Energy Functional in the Density Matrix Functional Theory},
+	Url = {http://link.aps.org/abstract/PRL/v88/e053001},
+	Volume = {88},
+	Year = {2002},
+	Bdsk-Url-1 = {http://link.aps.org/abstract/PRL/v88/e053001}}
+
+@article{YeaJor-JCP-79,
+	Author = {D. L. Yeager and P. J{\o}rgensen},
+	Journal = {J. Chem. Phys.},
+	Pages = {755},
+	Volume = {{71}},
+	Year = {1979}}
+
+@article{YinSuCheShaWu-JCTC-12,
+	Author = {F. Ying and P. Su and Z. Chen and S. Shaik and W. Wu},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {1608},
+	Volume = {8},
+	Year = {2012}}
+
+@article{Yu-IJQC-13,
+	Author = {F. Yu},
+	Journal = {Int. J. Quantum Chem.},
+	Pages = {2355},
+	Volume = {113},
+	Year = {2013}}
+
+@article{ZahLeaGor-JCP-13,
+	Author = {F. Zahariev and S. S. Leang and M. S. Gordon},
+	Journal = {J. Chem. Phys.},
+	Pages = {244108},
+	Volume = {138},
+	Year = {2013}}
+
+@book{ZalPapMezLes-BOOK-11,
+	Address = {Netherlands},
+	Editor = {R. Zalesny and M. G. Papadopoulos and P. G. Mezey and J. Leszczynski},
+	Publisher = {Springer},
+	Series = {Challenges and Advances in Computational Chemistry and Physics Vol. 13},
+	Title = {Linear-Scaling Techniques in Computational Chemistry and Physics},
+	Year = {2011}}
+
+@article{ZanSov-PRA-80,
+	Author = {A. Zangwill and P. Soven},
+	Journal = {Phys. Rev. A},
+	Pages = {1561},
+	Volume = {21},
+	Year = {1980}}
+
+@article{ZarKoh-PRB-76,
+	Author = {E. Zaremba and W. Kohn},
+	Journal = {Phys. Rev. B},
+	Pages = {2270},
+	Volume = {13},
+	Year = {1976}}
+
+@article{ZecGorMorBac-PRB-04,
+	Author = {Lorenzo Zecca and Paola Gori-Giorgi and Saverio Moroni and Giovanni B. Bachelet},
+	Journal = {Phys. Rev. B},
+	Keywords = {density functional theory; Monte Carlo methods; ground states; electron gas; electron density; electron correlations},
+	Number = {20},
+	Pages = {205127},
+	Publisher = {APS},
+	Title = {Local density functional for the short-range part of the electron-electron interaction},
+	Volume = {70},
+	Year = {2004}}
+
+@article{ZeiMea-MP-77,
+	Author = {G. D. Zeiss and W. J. Meath},
+	Journal = {Mol. Phys.},
+	Pages = {1155},
+	Volume = {33},
+	Year = {1977}}
+
+@article{ZhaBur-PRA-04,
+	Author = {F. Zhang and K. Burke},
+	Journal = {Phys. Rev. A},
+	Pages = {052510},
+	Volume = {69},
+	Year = {2004}}
+
+@article{ZhaLuoXu-JCP-10b,
+	Author = {I. Y. Zhang and Y. Luo and X. Xu},
+	Journal = {J. Chem. Phys.},
+	Pages = {104105},
+	Volume = {133},
+	Year = {2010}}
+
+@article{ZhaLuoXu-JCP-10,
+	Author = {I. Y. Zhang and Y. Luo and X. Xu},
+	Journal = {J. Chem. Phys.},
+	Pages = {194105},
+	Volume = {132},
+	Year = {2010}}
+
+@article{ZhaLynTru-JPCA-04,
+	Author = {Y. Zhao and B. J. Lynch and D. G. Truhlar},
+	Journal = {J. Phys. Chem. A},
+	Pages = {4786},
+	Volume = {108},
+	Year = {2004}}
+
+@article{ZhaLynTru-PCCP-05,
+	Author = {Y. Zhao and B. J. Lynch and D. G. Truhlar},
+	Journal = {Phys. Chem. Chem. Phys.},
+	Pages = {43},
+	Volume = {7},
+	Year = {2005}}
+
+@article{ZhaPar-PRA-92,
+	Author = {Q. Zhao and R. G. Parr},
+	Journal = {Phys. Rev. A.},
+	Pages = {2337},
+	Volume = {{46}},
+	Year = {1992}}
+
+@article{ZhaSchTru-JCTC-06,
+	Author = {Y. Zhao and N. E. Schultz and D. G. Truhlar},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {364},
+	Volume = {2},
+	Year = {2006}}
+
+@article{ZhaSteYan-JCP-13,
+	Abstract = {We present a dynamical second-order kernel for the Bethe-Salpeter equation to calculate electronic excitation energies. The derivation takes explicitly the functional derivative of the exact second-order self energy with respect to the one-particle Green's function. It includes naturally a frequency dependence, going beyond the adiabatic approximation. Perturbative calculations under the Tamm-Dancoff approximation, using the configuration interaction singles (CIS) eigenvectors, reveal an appreciable improvement over CIS, time-dependent Hartree-Fock, and adiabatic time-dependent density functional theory results. The perturbative results also compare well with equation-of-motion coupled-cluster and experimental results.},
+	Author = {Zhang, Du and Steinmann, Stephan N and Yang, Weitao},
+	Journal = {J. Chem. Phys.},
+	Month = oct,
+	Number = {15},
+	Pages = {154109},
+	Pmid = {24160502},
+	Publisher = {American Institute of Physics},
+	Title = {{Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation.}},
+	Volume = {139},
+	Year = {2013}}
+
+@article{ZhaSuBreAdaXu-JCP-12,
+	Author = {I. Y. Zhang and N. Q. Su and E. A. G. Br\'emond and C. Adamo},
+	Journal = {J. Chem. Phys.},
+	Pages = {174103},
+	Volume = {136},
+	Year = {2012}}
+
+@article{ZhaTru-JCTC-07,
+	Author = {Y. Zhao and D. G. Truhlar},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {289},
+	Title = {Density Functionals for Noncovalent Interaction Energies of Biological Importance},
+	Volume = {3},
+	Year = {2007}}
+
+@article{ZhaTru-TCA-08,
+	Author = {Y. Zhao and D. G. Truhlar},
+	Journal = {Theor. Chem. Acc.},
+	Pages = {215},
+	Volume = {120},
+	Year = {2008}}
+
+@article{ZhaWuXu-CC-10,
+	Author = {I. Y. Zhang and J. Wu and X. Xu},
+	Journal = {Chem. Commun.},
+	Pages = {3057},
+	Volume = {46},
+	Year = {2010}}
+
+@article{ZhaXuGod-PNAS-09,
+	Author = {{Y. Zhang, X. Xu and W. A. Goddard III}},
+	Journal = {Proc. Natl. Acad. Sci. U.S.A.},
+	Pages = {4963},
+	Volume = {106},
+	Year = {2009}}
+
+@article{ZhaXuGod-PNAS-09_fr,
+	Author = {{Y. Zhang, X. Xu et W. A. Goddard III}},
+	Journal = {Proc. Natl. Acad. Sci. U.S.A.},
+	Pages = {4963},
+	Volume = {106},
+	Year = {2009}}
+
+@article{ZhaXu-IRPC-11,
+	Author = {I. Y. Zhang and X. Xu},
+	Journal = {Int. Rev. Phys. Chem.},
+	Pages = {115},
+	Volume = {30},
+	Year = {2011}}
+
+@article{ZhaXu-JPCL-13,
+	Author = {I. Y. Zhang and X. Xu},
+	Journal = {J. Phys. Chem. Lett.},
+	Pages = {1669},
+	Volume = {4},
+	Year = {2013}}
+
+@article{ZhaXuJunGod-PNAS-11,
+	Author = {{I. Y. Zhang, X. Xu, Y. Jung, and W. A. Goddard III}},
+	Journal = {Proc. Natl. Acad. Sci. U.S.A.},
+	Pages = {19896},
+	Volume = {108},
+	Year = {2011}}
+
+@article{ZhaYan-JCP-98,
+	Author = {Y. Zhang and W. Yang},
+	Journal = {J. Chem. Phys.},
+	Pages = {2604},
+	Volume = {109},
+	Year = {1998}}
+
+@article{ZheZhaTru-JCTC-07,
+	Author = {J. Zheng and Y. Zhao and D. G. Truhlar},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {569},
+	Volume = {3},
+	Year = {2007}}
+
+@article{ZheZhaTru-JCTC-09,
+	Author = {J. Zheng and Y. Zhao and D. G. Truhlar},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {808},
+	Volume = {5},
+	Year = {2009}}
+
+@article{ZhoChu-PRA-09,
+	Author = {Z. Zhou and S.-I. Chu},
+	Journal = {Phys. Rev. A},
+	Pages = {053412},
+	Volume = {79},
+	Year = {2009}}
+
+@article{ZhuTouSavAng-JCP-10,
+	Author = {Wuming Zhu and Julien Toulouse and Andreas Savin and J\'anos G. \'Angy\'an},
+	Journal = {J. Chem. Phys.},
+	Pages = {244108},
+	Title = {Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions},
+	Volume = {132},
+	Year = {2010}}
+
+@misc{ZhuTouSavAng-JJJ-XX,
+	Author = {W. Zhu and J. Toulouse and A. Savin and J. G. \'Angy\'an},
+	Note = {unpublished}}
+
+@article{ZieCio-PA-05,
+	Author = {P. Ziesche and J. Cioslowski},
+	Journal = {Physica A},
+	Year = {to appear}}
+
+@article{Zie-JPC-80,
+	Author = {P. Ziesche},
+	Journal = {J. Phys. C},
+	Pages = {3625},
+	Volume = {13},
+	Year = {1980}}
+
+@article{ZieSetKryAutWan-JCP-09,
+	Author = {T. Ziegler and M. Seth and M. Krykunov and J. Autschbach and F. Wang},
+	Journal = {J. Chem. Phys.},
+	Pages = {154102},
+	Volume = {130},
+	Year = {2009}}
+
+@article{ZimParKou-JCP-04,
+	Author = {U. Zimmerli and M. Parrinello and P. Koumoutsakos},
+	Journal = {J. Chem. Phys.},
+	Pages = {2693},
+	Volume = {120},
+	Year = {2004}}
+
+@article{ZimTouZhaMusUmr-JCP-09,
+	Author = {P. M. Zimmerman and J. Toulouse and Z. Zhang and C. B. Musgrave and C. J. Umrigar},
+	Date-Modified = {2019-08-01 12:18:05 +0200},
+	Doi = {10.1063/1.3220671},
+	Journal = {J. Chem. Phys.},
+	Pages = {124103},
+	Title = {Excited states of methylene from quantum Monte Carlo},
+	Volume = {131},
+	Year = {2009},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.3220671}}
+
+@article{ZucPodMosJezSza-JCP-08,
+	Author = {P. S. Zuchowski and R. Podeszwa and R. Moszynski and B. Jeziorski and K. Szalewicz},
+	Journal = {J. Chem. Phys.},
+	Pages = {084101},
+	Title = {{Symmetry-adapted perturbation theory utilizing density functional description of monomers for high-spin open-shell complexes}},
+	Volume = {129},
+	Year = {2008}}
+
+@article{FerGinTou-JCP-19,
+	Author = {Fert{\'e},Anthony and Giner,Emmanuel and Toulouse,Julien},
+	Date-Modified = {2019-05-13 20:52:59 +0200},
+	Doi = {10.1063/1.5082638},
+	Journal = {J. Chem. Phys.},
+	Number = {8},
+	Pages = {084103},
+	Title = {Range-Separated Multideterminant Density-Functional Theory With A Short-Range Correlation Functional Of The On-Top Pair Density},
+	Volume = {150},
+	Year = {2019},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}}
+
+@article{PazMorGorBac-PRB-06,
+	Author = {Paziani, Simone and Moroni, Saverio and Gori-Giorgi, Paola and Bachelet, Giovanni B.},
+	Date-Modified = {2019-05-13 20:56:02 +0200},
+	Doi = {10.1103/PhysRevB.73.155111},
+	Issue = {15},
+	Journal = {Phys. Rev. B},
+	Month = {Apr},
+	Numpages = {9},
+	Pages = {155111},
+	Publisher = {American Physical Society},
+	Title = {Local-Spin-Density Functional For Multideterminant Density Functional Theory},
+	Url = {https://link.aps.org/doi/10.1103/PhysRevB.73.155111},
+	Volume = {73},
+	Year = {2006},
+	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.73.155111},
+	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.73.155111}}
+
+@article{GinTewGarAla-JCTC-18,
+	Author = {Giner, Emmanuel and Tew, David P. and Garniron, Yann and Alavi, Ali},
+	Doi = {10.1021/acs.jctc.8b00591},
+	Eprint = {https://doi.org/10.1021/acs.jctc.8b00591},
+	Journal = {Journal of Chemical Theory and Computation},
+	Note = {PMID: 30347156},
+	Number = {12},
+	Pages = {6240-6252},
+	Title = {Interplay between Electronic Correlation and Metal--Ligand Delocalization in the Spectroscopy of Transition Metal Compounds: Case Study on a Series of Planar Cu2+ Complexes},
+	Url = {https://doi.org/10.1021/acs.jctc.8b00591},
+	Volume = {14},
+	Year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00591}}
+
+@article{LooBogSceCafJac-JCTC-19,
+	Author = {Loos, Pierre-Fran{\c c}ois and Boggio-Pasqua, Martial and Scemama, Anthony and Caffarel, Michel and Jacquemin, Denis},
+	Date-Modified = {2019-05-30 11:26:43 +0200},
+	Doi = {10.1021/acs.jctc.8b01205},
+	Journal = {J. Chem. Theory Comput.},
+	Number = {3},
+	Pages = {1939-1956},
+	Title = {Reference Energies for Double Excitations},
+	Volume = {15},
+	Year = {2019},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01205}}
+
+@article{LooSceBloGarCafJac-JCTC-18,
+	Author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Blondel, Aymeric and Garniron, Yann and Caffarel, Michel and Jacquemin, Denis},
+	Date-Modified = {2019-04-07 14:03:07 +0200},
+	Doi = {10.1021/acs.jctc.8b00406},
+	Journal = {J. Chem. Theory Comput.},
+	Number = {8},
+	Pages = {4360-4379},
+	Title = {A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks},
+	Volume = {14},
+	Year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}}
+
+@article{HolUmrSha-JCP-17,
+	Author = {Holmes,Adam A. and Umrigar,C. J. and Sharma,Sandeep},
+	Date-Modified = {2019-08-01 12:07:52 +0200},
+	Doi = {10.1063/1.4998614},
+	Journal = {J. Chem. Phys.},
+	Number = {16},
+	Pages = {164111},
+	Title = {Excited States Using Semistochastic Heat-Bath Configuration Interaction},
+	Volume = {147},
+	Year = {2017},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4998614}}
+
+@article{stochastic_pt_yan,
+	Author = {Yann Garniron and Anthony Scemama and Pierre-Fran{\c c}ois Loos and Michel Caffarel},
+	Doi = {10.1063/1.4992127},
+	Journal = {J. Chem. Phys.},
+	Number = {3},
+	Pages = {034101},
+	Title = {Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory},
+	Url = {https://doi.org/10.1063/1.4992127},
+	Volume = {147},
+	Year = {2017},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4992127}}
+
+@article{GorSav-PRA-06,
+	Author = {Gori-Giorgi, Paola and Savin, Andreas},
+	Date-Modified = {2019-05-13 20:55:31 +0200},
+	Doi = {10.1103/PhysRevA.73.032506},
+	Issue = {3},
+	Journal = {Phys. Rev. A},
+	Month = {Mar},
+	Numpages = {9},
+	Pages = {032506},
+	Publisher = {American Physical Society},
+	Title = {Properties Of Short-Range And Long-Range Correlation Energy Density Functionals From Electron-Electron Coalescence},
+	Url = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506},
+	Volume = {73},
+	Year = {2006},
+	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506},
+	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.73.032506}}
+
+@article{HalHelJorKloKocOlsWil-CPL-98,
+	Abstract = {Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by rij-dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations.},
+	Author = {Asger Halkier and Trygve Helgaker and Poul J{\o}rgensen and Wim Klopper and Henrik Koch and Jeppe Olsen and Angela K. Wilson},
+	Date-Modified = {2019-05-13 21:01:16 +0200},
+	Doi = {https://doi.org/10.1016/S0009-2614(98)00111-0},
+	Issn = {0009-2614},
+	Journal = {Chem. Phys. Lett.},
+	Number = {3},
+	Pages = {243 - 252},
+	Title = {Basis-Set Convergence In Correlated Calculations On Ne, N2, And H2O},
+	Url = {http://www.sciencedirect.com/science/article/pii/S0009261498001110},
+	Volume = {286},
+	Year = {1998},
+	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261498001110},
+	Bdsk-Url-2 = {https://doi.org/10.1016/S0009-2614(98)00111-0}}
+
+@article{DasHer-JCC-17,
+	Author = {Dasgupta, Saswata and Herbert, John M.},
+	Date-Modified = {2019-08-01 12:08:12 +0200},
+	Doi = {10.1002/jcc.24761},
+	Journal = {J. Comput. Chem.},
+	Number = {12},
+	Pages = {869-882},
+	Title = {Standard grids for high-precision integration of modern density functionals: SG-2 and SG-3},
+	Volume = {38},
+	Year = {2017},
+	Bdsk-Url-1 = {https://doi.org/10.1002/jcc.24761}}
+
+@article{Tenno-CPL-04,
+	Abstract = {We employ the Slater-type function as a geminal basis function to incorporate the inter-electron distance in explicitly correlated theory. It is shown that the use of the Slater-type geminals confers numerical and computational advantages over the previous explicitly correlated methods. The performance of the resulting method is examined in some benchmark calculations at the second order M{\o}ller--Plesset perturbation theory. The results reveal that the Slater-type function is promising compared to the ordinary Gaussian-type geminals and linear r12 function.},
+	Author = {Seiichiro Ten-no},
+	Date-Modified = {2019-05-13 20:12:36 +0200},
+	Doi = {https://doi.org/10.1016/j.cplett.2004.09.041},
+	Issn = {0009-2614},
+	Journal = {Chem. Phys. Lett.},
+	Number = {1},
+	Pages = {56 - 61},
+	Title = {Initiation Of Explicitly Correlated Slater-Type Geminal Theory},
+	Url = {http://www.sciencedirect.com/science/article/pii/S000926140401379X},
+	Volume = {398},
+	Year = {2004},
+	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S000926140401379X},
+	Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2004.09.041}}
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+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \matrixdeterminant with sig. 'm' on line 102.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \mdet with sig. '' on line 103.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \spmqty with sig. 'm' on line 105.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \sPmqty with sig. 'm' on line 106.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \sbmqty with sig. 'm' on line 107.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \svmqty with sig. 'm' on line 108.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \smallmatrixquantity with sig. ' s g o d() d|| ' on line
+. 133.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \smqty with sig. '' on line 134.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \smallmatrixdeterminant with sig. 'm' on line 135.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \smdet with sig. '' on line 136.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \argopen with sig. 's' on line 138.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \argclose with sig. 's' on line 139.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \braces with sig. '' on line 141.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \@braces with sig. ' s t\big t\Big t\bigg t\Bigg m m m ' on
+. line 156.
+.................................................
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\big ' for the command '\@braces' should be a single
+* character.
+*************************************************
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\Big ' for the command '\@braces' should be a single
+* character.
+*************************************************
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\bigg ' for the command '\@braces' should be a single
+* character.
+*************************************************
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\Bigg ' for the command '\@braces' should be a single
+* character.
+*************************************************
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \fbraces with sig. ' s t\big t\Big t\bigg t\Bigg m m m m '
+. on line 174.
+.................................................
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\big ' for the command '\fbraces' should be a single
+* character.
+*************************************************
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\Big ' for the command '\fbraces' should be a single
+* character.
+*************************************************
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\bigg ' for the command '\fbraces' should be a single
+* character.
+*************************************************
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\Bigg ' for the command '\fbraces' should be a single
+* character.
+*************************************************
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \absolutevalue with sig. ' l m ' on line 176.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \abs with sig. '' on line 177.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \norm with sig. ' l m ' on line 178.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \order with sig. ' l m ' on line 179.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \evaluated with sig. ' s g d[| d(| ' on line 194.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \eval with sig. '' on line 195.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \poissonbracket with sig. ' l m m ' on line 197.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \pb with sig. '' on line 198.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \commutator with sig. ' l m m ' on line 201.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \comm with sig. '' on line 202.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \anticommutator with sig. ' l m m ' on line 203.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \acommutator with sig. '' on line 204.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \acomm with sig. '' on line 205.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \vectorbold with sig. ' s m ' on line 208.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \vb with sig. '' on line 209.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \vectorarrow with sig. ' s m ' on line 211.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \va with sig. '' on line 212.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \vectorunit with sig. ' s m ' on line 214.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \vu with sig. '' on line 215.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \dotproduct with sig. '' on line 217.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \vdot with sig. '' on line 218.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \crossproduct with sig. '' on line 220.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \cross with sig. '' on line 221.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \cp with sig. '' on line 222.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \gradient with sig. ' g o d() ' on line 232.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \grad with sig. '' on line 233.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \divergence with sig. ' g o d() ' on line 243.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \div with sig. '' on line 246.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \curl with sig. ' g o d() ' on line 256.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \laplacian with sig. ' g o d() ' on line 266.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \principalvalue with sig. 'g' on line 274.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \pv with sig. '' on line 275.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \PV with sig. 'g' on line 276.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \Re with sig. 'g' on line 277.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \Im with sig. 'g' on line 278.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \opbraces with sig. ' m g o d() ' on line 299.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \trigbraces with sig. ' m o d() ' on line 305.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \sin with sig. '' on line 309.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \cos with sig. '' on line 310.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \tan with sig. '' on line 311.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \csc with sig. '' on line 312.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \sec with sig. '' on line 313.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \cot with sig. '' on line 314.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \arcsin with sig. '' on line 316.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \arccos with sig. '' on line 317.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \arctan with sig. '' on line 318.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \arccsc with sig. '' on line 320.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \arcsec with sig. '' on line 322.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \arccot with sig. '' on line 324.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \asin with sig. '' on line 327.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \acos with sig. '' on line 329.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \atan with sig. '' on line 331.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \acsc with sig. '' on line 333.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \asec with sig. '' on line 335.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \acot with sig. '' on line 337.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \sinh with sig. '' on line 339.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \cosh with sig. '' on line 340.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \tanh with sig. '' on line 341.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \csch with sig. '' on line 343.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \sech with sig. '' on line 345.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \coth with sig. '' on line 346.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \exp with sig. '' on line 348.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \log with sig. '' on line 349.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \ln with sig. '' on line 350.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \det with sig. '' on line 351.
+.................................................
+.................................................
+. LaTeX info: "xparse/redefine-command"
+. 
+. Redefining command \Pr with sig. '' on line 352.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \tr with sig. '' on line 353.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \Tr with sig. '' on line 354.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \Res with sig. '' on line 355.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qqtext with sig. ' s m ' on line 377.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qq with sig. '' on line 378.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qcomma with sig. '' on line 380.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qc with sig. '' on line 381.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qif with sig. 's' on line 383.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qthen with sig. 's' on line 384.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qelse with sig. 's' on line 385.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qotherwise with sig. 's' on line 386.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qunless with sig. 's' on line 387.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qgiven with sig. 's' on line 388.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qusing with sig. 's' on line 389.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qassume with sig. 's' on line 390.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qsince with sig. 's' on line 391.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qlet with sig. 's' on line 392.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qfor with sig. 's' on line 393.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qall with sig. 's' on line 394.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qeven with sig. 's' on line 395.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qodd with sig. 's' on line 396.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qinteger with sig. 's' on line 397.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qand with sig. 's' on line 398.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qor with sig. 's' on line 399.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qas with sig. 's' on line 400.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qin with sig. 's' on line 401.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \qcc with sig. 's' on line 402.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \differential with sig. ' o g d() ' on line 415.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \dd with sig. '' on line 416.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \derivative with sig. ' s o m g d() ' on line 435.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \dv with sig. '' on line 436.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \partialderivative with sig. ' s o m g g d() ' on line 460.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \pderivative with sig. '' on line 461.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \pdv with sig. '' on line 462.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \variation with sig. ' o g d() ' on line 474.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \var with sig. '' on line 475.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \functionalderivative with sig. ' s o m g d() ' on line
+. 494.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \fderivative with sig. '' on line 495.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \fdv with sig. '' on line 496.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \bra with sig. ' s m t\ket s g ' on line 526.
+.................................................
+*************************************************
+* LaTeX warning: "xparse/not-single-char"
+* 
+* Argument delimiter '\ket ' for the command '\bra' should be a single
+* character.
+*************************************************
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \ket with sig. ' s m ' on line 533.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \innerproduct with sig. ' s m g ' on line 548.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \braket with sig. '' on line 549.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \ip with sig. '' on line 550.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \outerproduct with sig. ' s m g ' on line 565.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \dyad with sig. '' on line 566.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \op with sig. '' on line 567.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \ketbra with sig. '' on line 568.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \expectationvalue with sig. ' s s m g ' on line 587.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \expval with sig. '' on line 588.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \ev with sig. '' on line 589.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \vev with sig. ' m ' on line 590.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \matrixelement with sig. ' s s m m m ' on line 601.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \matrixel with sig. '' on line 602.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \mel with sig. '' on line 603.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \identitymatrix with sig. 'm' on line 633.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \imat with sig. '' on line 634.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \xmatrix with sig. ' s m m m ' on line 659.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \xmat with sig. '' on line 660.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \zeromatrix with sig. ' m g ' on line 662.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \zmat with sig. '' on line 663.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \paulixmatrix with sig. '' on line 665.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \pauliymatrix with sig. '' on line 666.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \paulizmatrix with sig. '' on line 667.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \paulimatrix with sig. 'm' on line 678.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \pmat with sig. '' on line 679.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
+. 
+. Defining command \diagonalmatrix with sig. 'O{} >{\SplitList {,}}m ' on line
+. 681.
+.................................................
+.................................................
+. LaTeX info: "xparse/define-command"
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diff --git a/HAL/Ex-srDFT.out b/HAL/Ex-srDFT.out
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--- /dev/null
+++ b/HAL/Ex-srDFT.out
@@ -0,0 +1,15 @@
+\BOOKMARK [0][-]{section*.2}{Chemically accurate excitation energies with small basis sets}{}% 2
+\BOOKMARK [1][-]{section*.1}{Abstract}{section*.2}% 1
+\BOOKMARK [1][-]{section*.3}{Introduction}{section*.2}% 3
+\BOOKMARK [1][-]{section*.4}{Theory}{section*.2}% 4
+\BOOKMARK [2][-]{section*.5}{Range-separation function}{section*.4}% 5
+\BOOKMARK [2][-]{section*.6}{Short-range correlation functionals}{section*.4}% 6
+\BOOKMARK [1][-]{section*.7}{Computational details}{section*.2}% 7
+\BOOKMARK [1][-]{section*.8}{Results and Discussion}{section*.2}% 8
+\BOOKMARK [2][-]{section*.9}{Methylene}{section*.8}% 9
+\BOOKMARK [2][-]{section*.10}{Rydberg States of Water and Ammonia}{section*.8}% 10
+\BOOKMARK [2][-]{section*.11}{Doubly-Excited States of the Carbon Dimer}{section*.8}% 11
+\BOOKMARK [2][-]{section*.12}{Ethylene}{section*.8}% 12
+\BOOKMARK [1][-]{section*.13}{Conclusion}{section*.2}% 13
+\BOOKMARK [1][-]{section*.14}{Supplementary material}{section*.2}% 14
+\BOOKMARK [1][-]{section*.15}{Acknowledgments}{section*.2}% 15
diff --git a/HAL/Ex-srDFT.pdf b/HAL/Ex-srDFT.pdf
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+
+\newcommand{\pbeotint}[0]{\be{\text{c,md}}{\sr,\PBEot}(\br{})\,\n{}{}(\br{})}
+\newcommand{\pbeint}[0]{\be{\text{c,md}}{\sr,\PBE}(\br{})\,\n{}{}(\br{})}
+
+% basis sets 
+\newcommand{\Bas}{\mathcal{B}}
+\newcommand{\BasFC}{\mathcal{A}}
+\newcommand{\FC}{\text{FC}}
+\newcommand{\occ}{\text{occ}}
+\newcommand{\virt}{\text{virt}}
+\newcommand{\val}{\text{val}}
+\newcommand{\Cor}{\mathcal{C}}
+
+% operators
+\newcommand{\hT}{\Hat{T}}
+\newcommand{\hWee}[1]{\Hat{W}_\text{ee}^{#1}}
+\newcommand{\updw}{\uparrow\downarrow}
+\newcommand{\f}[2]{f_{#1}^{#2}}
+\newcommand{\Gam}[2]{\Gamma_{#1}^{#2}}
+
+% coordinates
+\newcommand{\br}[1]{\mathbf{r}_{#1}}
+\newcommand{\dbr}[1]{d\br{#1}}
+
+\newcommand{\ra}{\rightarrow}
+
+% frozen core
+\newcommand{\WFC}[2]{\widetilde{W}_{#1}^{#2}}
+\newcommand{\fFC}[2]{\widetilde{f}_{#1}^{#2}}
+\newcommand{\rsmuFC}[2]{\widetilde{\mu}_{#1}^{#2}}
+\newcommand{\tn}[2]{\tilde{n}_{#1}^{#2}}
+\newcommand{\ttn}[2]{\mathring{n}_{#1}^{#2}}
+
+
+% energies
+\newcommand{\EHF}{E_\text{HF}}
+\newcommand{\EPT}{E_\text{PT2}}
+\newcommand{\EFCI}{E_\text{FCI}}
+\newcommand{\EsCI}{E_\text{sCI}}
+\newcommand{\EDMC}{E_\text{DMC}}
+\newcommand{\EexFCI}{E_\text{exFCI}}
+\newcommand{\EexDMC}{E_\text{exDMC}}
+\newcommand{\Ead}{\Delta E_\text{ad}}
+\newcommand{\Eabs}{\Delta E_\text{abs}}
+\newcommand{\Evert}{\Delta E_\text{vert}}
+
+\newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$}
+
+\newcommand{\pis}{\pi^\star}
+\newcommand{\si}{\sigma}
+\newcommand{\sis}{\sigma^\star}
+
+\newcommand{\extrfunc}[0]{\epsilon}
+
+
+\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
+\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}
+
+\begin{document}	
+
+\title{\textcolor{blue}{Chemically accurate excitation energies with small basis sets}}
+
+\author{Emmanuel Giner}
+\email[Corresponding author: ]{emmanuel.giner@lct.jussieu.fr}
+\affiliation{\LCT}
+\author{Anthony Scemama}
+\affiliation{\LCPQ}
+\author{Julien Toulouse}
+\affiliation{\LCT}
+\author{Pierre-Fran\c{c}ois Loos}
+\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
+\affiliation{\LCPQ}
+
+\begin{abstract}
+%\begin{wrapfigure}[13]{o}[-1.25cm]{0.5\linewidth}
+%	\centering
+%  \includegraphics[width=\linewidth]{TOC}
+%\end{wrapfigure}
+By combining extrapolated selected configuration interaction (sCI) energies obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner \textit{et al.}, \textit{J.~Chem.~Phys.}~ \textbf{2018}, \textit{149}, 194301}], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-$\zeta$ basis sets.
+We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer and ethylene).
+The present study clearly evidences that special care has to be taken with very diffuse excited states where the present correction does not catch the radial incompleteness of the one-electron basis set.
+\end{abstract}
+
+\maketitle
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Introduction}
+\label{sec:intro}
+%%%%%%%%%%%%%%%%%%%%%%%%
+One of the most fundamental problems of conventional wave function electronic structure methods is their slow energy convergence with respect to the size of the one-electron basis set.
+The overall basis-set incompleteness error can be, qualitatively at least, split in two contributions stemming from the radial and angular incompleteness.
+Although for ground-state properties angular incompleteness is by far the main source of error, it is definitely not unusual to have a significant radial incompleteness in the case of excited states (especially for Rydberg states), which can be alleviated by using additional sets of diffuse basis functions (i.e.~augmented basis sets).
+
+Explicitly-correlated F12 methods \cite{Kut-TCA-85, KutKlo-JCP-91, NogKut-JCP-94} have been specifically designed to efficiently catch angular incompleteness. \cite{Ten-TCA-12, TenNog-WIREs-12, HatKloKohTew-CR-12, KonBisVal-CR-12, GruHirOhnTen-JCP-17, MaWer-WIREs-18}
+Although they have been extremely successful to speed up convergence of ground-state energies and properties, such as correlation and atomization energies, \cite{TewKloNeiHat-PCCP-07} their performance for excited states \cite{FliHatKlo-JCP-06, NeiHatKlo-JCP-06, HanKoh-JCP-09, Koh-JCP-09, ShiWer-JCP-10, ShiKniWer-JCP-11, ShiWer-JCP-11, ShiWer-MP-13} has been much more conflicting. \cite{FliHatKlo-JCP-06, NeiHatKlo-JCP-06}
+However, very encouraging results have been reported recently using the extended explicitly-correlated second-order approximate coupled-cluster singles and doubles ansatz suitable for response theory on systems such as methylene, formaldehyde and imidazole. \cite{HofSchKloKoh-JCP-19}
+
+Instead of F12 methods, here we propose to follow a different route and investigate the performance of the recently proposed density-based basis set
+incompleteness correction. \cite{GinPraFerAssSavTou-JCP-18}
+Contrary to our recent study on atomization and correlation energies, \cite{LooPraSceTouGin-JPCL-19} the present contribution focuses on vertical and adiabatic excitation energies in molecular systems which is a much tougher test for the reasons mentioned above.
+This density-based correction relies on short-range correlation density functionals (with multideterminant reference) from range-separated density-functional theory \cite{Sav-INC-96, LeiStoWerSav-CPL-97, TouColSav-PRA-04, TouSavFla-IJQC-04, AngGerSavTou-PRA-05, GolWerSto-PCCP-05, PazMorGorBac-PRB-06, FroTouJen-JCP-07, TouGerJanSavAng-PRL-09, JanHenScu-JCP-09, FroCimJen-PRA-10, TouZhuSavJanAng-JCP-11, MusReiAngTou-JCP-15, HedKneKieJenRei-JCP-15, HedTouJen-JCP-18, FerGinTou-JCP-19} (RS-DFT) to capture the missing part of the short-range correlation effects, a consequence of the incompleteness of the one-electron basis set.
+Because RS-DFT combines rigorously density-functional theory (DFT) \cite{ParYan-BOOK-89} and wave function theory (WFT) \cite{SzaOst-BOOK-96} via a decomposition of the electron-electron interaction into a non-divergent long-range part and a (complementary) short-range part (treated with WFT and DFT, respectively), the WFT method is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points (the so-called electron-electron cusp). \cite{Kat-CPAM-57}
+Consequently, the energy convergence with respect to the size of the basis set is significantly improved, \cite{FraMusLupTou-JCP-15} and chemical accuracy can be obtained even with small basis sets.
+For example, in Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, we have shown that one can recover quintuple-$\zeta$ quality atomization and correlation energies with triple-$\zeta$ basis sets for a much lower computational cost than F12 methods.
+
+This work is organized as follows. 
+In Sec.~\ref{sec:theory}, the main working equations of the density-based correction are reported and discussed. 
+Computational details are given in Sec.~\ref{sec:compdetails}.
+In Sec.~\ref{sec:res}, we discuss our results for each system and draw our conclusions in Sec.~\ref{sec:ccl}.
+Unless otherwise stated, atomic units are used.
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Theory}
+\label{sec:theory}
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+The present basis-set correction assumes that we have, in a given (finite) basis set $\Bas$, the ground-state and the $k$th excited-state energies, $\E{0}{\Bas}$ and $\E{k}{\Bas}$, their one-electron densities, $\n{k}{\Bas}(\br{})$ and $\n{0}{\Bas}(\br{})$, as well as their opposite-spin on-top pair densities, $\n{2,0}{\Bas}(\br{})$ and $\n{2,k}{\Bas}(\br{})$,
+Therefore, the complete-basis-set (CBS) energy of the ground and excited states may be approximated as \cite{GinPraFerAssSavTou-JCP-18}
+\begin{subequations}
+\begin{align}
+	\label{eq:E0CBS}
+	\E{0}{\CBS} & \approx \E{0}{\Bas} + \bE{}{\Bas}[\n{0}{\Bas}],
+	\\
+	\label{eq:EkCBS}
+	\E{k}{\CBS} & \approx \E{k}{\Bas} + \bE{}{\Bas}[\n{k}{\Bas}],
+\end{align}
+\end{subequations}
+where 
+\begin{equation}
+	\label{eq:E_funcbasis}
+	 \bE{}{\Bas}[\n{}{}]
+	= \min_{\wf{}{} \rightsquigarrow \n{}{}}  \mel*{\wf{}{}}{\hT + \hWee{}}{\wf{}{}} 
+	- \min_{\wf{}{\Bas} \rightsquigarrow \n{}{}}  \mel*{\wf{}{\Bas}}{\hT + \hWee{}}{\wf{}{\Bas}}
+\end{equation}
+is the basis-dependent complementary density functional, 
+\begin{align}
+	\hT & = - \frac{1}{2} \sum_{i}^{\Ne} \nabla_i^2,
+	&
+	\hWee{} & = \sum_{i<j}^{\Ne} r_{ij}^{-1},
+\end{align}
+are the kinetic and electron-electron repulsion operators, respectively, and $\wf{}{\Bas}$ and $\wf{}{}$ are two general $\Ne$-electron normalized wave functions belonging to the Hilbert spaces spanned by $\Bas$ and the complete basis, respectively.
+The notation $\wf{}{} \rightsquigarrow \n{}{}$ in Eq.~\eqref{eq:E_funcbasis} states that $\wf{}{}$ yields the one-electron density $\n{}{}$. 
+
+Hence, the CBS excitation energy associated with the $k$th excited state reads
+\begin{equation}
+\begin{split}
+	\DE{k}{\CBS} 
+	& = \E{k}{\CBS} - \E{0}{\CBS} 
+	\\
+	& \approx \DE{k}{\Bas} + \DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}],
+\end{split}
+\end{equation}
+where
+\begin{equation}
+	\label{eq:DEB}
+	\DE{k}{\Bas} = \E{k}{\Bas} - \E{0}{\Bas}
+\end{equation}
+is the excitation energy in $\Bas$ and
+\begin{equation}
+	\label{eq:DbE}
+	\DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}] = \bE{}{\Bas}[\n{k}{\Bas}] - \bE{}{\Bas}[\n{0}{\Bas}]
+\end{equation}
+its basis-set correction.
+An important property of the present correction is
+\begin{equation}
+  \label{eq:limitfunc}
+        \lim_{\Bas \to \CBS} \DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}] = 0.
+\end{equation}
+In other words, the correction vanishes in the CBS limit, hence guaranteeing an unaltered limit. \cite{LooPraSceTouGin-JPCL-19}
+Note that in Eqs.~\eqref{eq:E0CBS} and \eqref{eq:EkCBS} we have assumed that the same density functional $\bE{}{\Bas}$ can be used for correcting all excited-state energies, which seems a reasonable approximation since the electron-electron cusp effects are largely universal. \cite{Kut-TCA-85, MorKut-JPC-93, KutMor-ZPD-96, Tew-JCP-08, LooGil-MP-10, LooBloGil-JCP-2015}
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Range-separation function}
+\label{sec:rs}
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+As initially proposed in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18} and further developed in Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, we have shown that one can efficiently approximate $\bE{}{\Bas}[\n{}{}]$ by short-range correlation functionals with multi-determinantal (ECMD) reference borrowed from RS-DFT. \cite{TouGorSav-TCA-05}
+The ECMD functional, $\bE{\text{c,md}}{\sr}[\n{}{},\rsmu{}{}]$, is a function of the range-separation parameter $\mu$ and admits, for any $\n{}{}$, the following two limits
+\begin{subequations}
+\begin{align}
+	\label{eq:large_mu_ecmd}
+	\lim_{\mu \to \infty}  \bE{\text{c,md}}{\sr}[\n{}{},\rsmu{}{}] & = 0,
+	\\
+	\label{eq:small_mu_ecmd}
+	\lim_{\mu \to 0}  \bE{\text{c,md}}{\sr}[\n{}{},\rsmu{}{}] & = \Ec[\n{}{}],
+\end{align}
+\end{subequations}
+which correspond to the WFT limit ($\mu \to \infty$) and the Kohn-Sham DFT (KS-DFT) limit ($\mu = 0$).
+In Eq.~\eqref{eq:small_mu_ecmd}, $\Ec[\n{}{}]$ is the usual universal correlation density functional defined in KS-DFT. \cite{HohKoh-PR-64, KohSha-PR-65}
+
+The key ingredient that allows us to exploit ECMD functionals for correcting the basis-set incompleteness error is the range-separated function
+\begin{equation}
+	\label{eq:def_mu}
+	\rsmu{}{\Bas}(\br{}) =  \frac{\sqrt{\pi}}{2} \W{}{\Bas}(\br{},\br{}),
+\end{equation}
+which automatically adapts to the spatial non-homogeneity of the basis-set incompleteness error.
+It is defined such that the long-range interaction of RS-DFT, $\w{}{\lr,\mu}(r_{12}) = \erf( \mu r_{12})/r_{12}$, coincides, at coalescence, with an effective two-electron interaction $\W{}{\Bas}(\br{1},\br{2})$ ``mimicking'' the Coulomb operator in an incomplete basis $\Bas$, i.e.~$\w{}{\lr,\rsmu{}{\Bas}(\br{})}(0) = \W{}{\Bas}(\br{},\br{})$ at any $\br{}$. \cite{GinPraFerAssSavTou-JCP-18}
+The explicit expression of $\W{}{\Bas}(\br{1},\br{2})$ is given by 
+\begin{equation}
+	\label{eq:def_weebasis}
+	\W{}{\Bas}(\br{1},\br{2})   = 
+ 	\begin{cases}
+       \f{}{\Bas}(\br{1},\br{2})/\n{2}{\Bas}(\br{1},\br{2}), 	& \text{if $\n{2}{\Bas}(\br{1},\br{2}) \ne 0$,}
+       \\
+       \infty, 												& \text{otherwise,}
+    \end{cases}
+\end{equation}
+where
+\begin{equation}
+	\label{eq:n2basis}
+	\n{2}{\Bas}(\br{1},\br{2})
+	= \sum_{pqrs \in \Bas}  \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
+\end{equation}
+and $\Gam{pq}{rs} = 2 \mel*{\wf{}{\Bas}}{ \aic{r_\downarrow}\aic{s_\uparrow}\ai{q_\uparrow}\ai{p_\downarrow}}{\wf{}{\Bas}}$ are the opposite-spin pair density associated with $\wf{}{\Bas}$ and its corresponding tensor, respectively, $\SO{p}{}$ is a (real-valued) molecular orbital (MO),
+\begin{equation}
+	\label{eq:fbasis}
+	\f{}{\Bas}(\br{1},\br{2}) 
+	= \sum_{pqrstu \in \Bas}  \SO{p}{1} \SO{q}{2} \V{pq}{rs} \Gam{rs}{tu} \SO{t}{1} \SO{u}{2},
+\end{equation}
+and $\V{pq}{rs}= \braket{pq}{rs}$ are two-electron Coulomb integrals. 
+An important feature of $\W{}{\Bas}(\br{1},\br{2})$ is that it tends to the regular Coulomb operator $r_{12}^{-1}$ as $\Bas \to \CBS${, which implies that 
+\begin{equation}
+	\lim_{\Bas \rightarrow \CBS} \rsmu{}{\Bas}(\br{}) = \infty,
+\end{equation} 
+ensuring that $\bE{}{\Bas}[\n{}{}]$ vanishes when $\Bas$ is complete.
+We refer the interested readers to Refs.~\onlinecite{GinPraFerAssSavTou-JCP-18,LooPraSceTouGin-JPCL-19} for additional details.
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Short-range correlation functionals}
+\label{sec:func}
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+The local-density approximation ($\LDA$) of the ECMD complementary functional is defined as 
+\begin{equation}
+	\label{eq:def_lda_tot}
+	\bE{\LDA}{\Bas}[\n{}{},\rsmu{}{\Bas}] = \int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\LDA}\qty(\n{}{}(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
+\end{equation}
+where $\zeta = (\n{\uparrow}{} - \n{\downarrow}{})/\n{}{}$ is the spin polarization and $\be{\text{c,md}}{\sr,\LDA}(\n{}{},\zeta,\rsmu{}{})$ is the ECMD short-range correlation energy per electron of the uniform electron gas (UEG) \cite{LooGil-WIRES-16} parameterized in Ref.~\onlinecite{PazMorGorBac-PRB-06}.
+
+The functional $\be{\text{c,md}}{\sr,\LDA}$ from Eq.~\eqref{eq:def_lda_tot} presents two main defects: i) at small $\mu$, it overestimates the correlation energy, and ii) UEG-based quantities are hardly transferable when the system becomes strongly correlated. 
+An attempt to solve these problems was suggested by some of the authors in the context of RS-DFT. \cite{FerGinTou-JCP-19}  
+They proposed to interpolate between the usual Perdew-Burke-Ernzerhof ($\PBE$) correlation functional \cite{PerBurErn-PRL-96} $\e{\text{c}}{\PBE}(\n{}{},s,\zeta)$ (where $s=\nabla n/n^{4/3}$ is the reduced density gradient) at $\mu = 0$ and the exact large-$\mu$ behavior. \cite{TouColSav-PRA-04, GorSav-PRA-06, PazMorGorBac-PRB-06}
+In the context of RS-DFT, the large-$\mu$ behavior corresponds to an extremely short-range interaction in the short-range functional.
+In this regime, the ECMD energy
+\begin{align}
+  \label{eq:exact_large_mu}
+  \bE{\text{c,md}}{\sr} = \frac{2\sqrt{\pi} (1 - \sqrt{2})}{3\mu^3} \int \dbr{} \n{2}{}(\br{}) + \order*{\mu^{-4}}
+\end{align}
+only depends on the \textit{exact} on-top pair density $\n{2}{}(\br{}) \equiv \n{2}{}(\br{},\br{})$ which is obtained from the \textit{exact} ground-state wave function $\Psi$ belonging to the many-electron Hilbert space in the CBS limit.
+
+Obviously, an exact quantity such as $\n{2}{}(\br{})$ is out of reach in practical calculations and must be approximated by a function referred here as $\tn{2}{}(\br{})$. 
+For a given $\tn{2}{}(\br{})$, some of the authors proposed the following functional form in order to interpolate between $\e{\text{c}}{\PBE}(\n{}{},s,\zeta)$ at $\mu = 0$ and Eq.~\eqref{eq:exact_large_mu} as $\mu \to \infty$: \cite{FerGinTou-JCP-19} 
+\begin{subequations}
+\begin{gather}
+	\label{eq:epsilon_cmdpbe}
+	\be{\text{c,md}}{\sr,\PBE}(\n{}{},\tn{2}{},s,\zeta,\rsmu{}{}) = \frac{\e{\text{c}}{\PBE}(\n{}{},s,\zeta)}{1 + \beta^\PBE(\n{}{},\tn{2}{},s,\zeta) \rsmu{}{3} },
+	\\
+	\label{eq:beta_cmdpbe}
+	\beta^\PBE(\n{}{},\tn{2}{},s,\zeta) = \frac{3}{2\sqrt{\pi} (1 - \sqrt{2})} \frac{\e{\text{c}}{\PBE}(\n{}{},s,\zeta)}{\tn{2}{}/\n{}{}}.
+\end{gather}
+\end{subequations}
+As illustrated in the context of RS-DFT, \cite{FerGinTou-JCP-19} such a functional form is able to treat both weakly and strongly correlated systems thanks to the explicit inclusion of $\e{\text{c}}{\PBE}$ and $\tn{2}{}$, respectively.
+Therefore, in the present context, we introduce the general form of the $\PBE$-based complementary functional within a given basis set $\Bas$ 
+\begin{multline}
+	\bE{\PBE}{\Bas}[\n{}{},\tn{2}{},\rsmu{}{\Bas}] =
+	\int \n{}{}(\br{}) 
+	\\
+	\times \be{\text{c,md}}{\sr,\PBE}\qty(\n{}{}(\br{}),\tn{2}{}(\br{}),s(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
+\end{multline}
+which has an explicit dependency on both the range-separation function $\rsmu{}{\Bas}(\br{})$ (instead of the range-separation parameter in RS-DFT) and the approximation level of $\tn{2}{}$.
+
+In Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, some of the authors introduced a version of the $\PBE$-based functional, here-referred as $\PBEUEG$
+\begin{equation}
+	\bE{\PBEUEG}{\Bas} 
+	\equiv
+	\bE{\PBE}{\Bas}[\n{}{},\n{2}{\UEG},\rsmu{}{\Bas}],
+\end{equation}
+in which the on-top pair density was approximated by its UEG version, i.e., $\tn{2}{}(\br{}) = \n{2}{\UEG}(\br{})$, with
+\begin{equation}
+	\label{eq:n2UEG}
+ \n{2}{\UEG}(\br{}) \approx n(\br{})^2 [1-\zeta(\br{})^2] g_0(n(\br{})), 
+\end{equation}
+and where $g_0(n)$ is the UEG on-top pair distribution function [see Eq.~(46) of Ref.~\onlinecite{GorSav-PRA-06}]. 
+Note that in Eq.~\eqref{eq:n2UEG} the dependence on the spin polarization $\zeta$ is only approximate.
+As illustrated in Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, the $\PBEUEG$ functional has clearly shown, for weakly correlated systems, to improve energetics over the pure UEG-based functional $\bE{\LDA}{\Bas}$ [see Eq.~\eqref{eq:def_lda_tot}] thanks to the leverage brought by the $\PBE$ functional in the small-$\mu$ regime.
+
+However, the underlying UEG on-top pair density might not be suited for the treatment of excited states and/or strongly correlated systems. 
+Besides, in the context of the present basis-set correction, $\n{2}{\Bas}(\br{})$, the on-top pair density in $\Bas$, must be computed anyway to obtain $\rsmu{}{\Bas}(\br{})$ [see Eqs.~\eqref{eq:def_mu} and \eqref{eq:def_weebasis}].
+Therefore, as in Ref.~\onlinecite{FerGinTou-JCP-19}, we define a better approximation of the exact on-top pair density as
+\begin{equation}
+	\label{eq:ot-extrap}
+  \ttn{2}{\Bas}(\br{}) = \n{2}{\Bas}(\br{}) \qty( 1 + \frac{2}{\sqrt{\pi}\rsmu{}{\Bas}(\br{})})^{-1}
+\end{equation}
+which directly follows from the large-$\mu$ extrapolation of the exact on-top pair density proposed by Gori-Giorgi and Savin \cite{GorSav-PRA-06} in the context of RS-DFT. 
+Using this new ingredient, we propose here the ``$\PBE$-ontop'' (\PBEot) functional
+\begin{equation}
+	\bE{\PBEot}{\Bas}
+	\equiv
+	\bE{\PBE}{\Bas}[\n{}{},\ttn{2}{\Bas},\rsmu{}{\Bas}].
+\end{equation}
+The sole distinction between $\PBEUEG$ and $\PBEot$ is the level of approximation of the exact on-top pair density.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Computational details}
+\label{sec:compdetails}
+%%%%%%%%%%%%%%%%%%%%%%%%
+In the present study, we compute the ground- and excited-state energies, one-electron densities and on-top pair densities with a selected configuration interaction (sCI) method known as CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively). \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15} 
+Both the implementation of the CIPSI algorithm and the computational protocol for excited states is reported in Ref.~\onlinecite{SceCafBenJacLoo-RC-19}.
+The total energy of each state is obtained via an efficient extrapolation procedure of the sCI energies designed to reach near-FCI accuracy. \cite{HolUmrSha-JCP-17, QP2}
+These energies will be labeled exFCI in the following.
+Using near-FCI excitation energies (within a given basis set) has the indisputable advantage to remove the error inherent to the WFT method.
+Indeed, in the present case, the only source of error on the excitation energies is due to basis-set incompleteness.
+We refer the interested reader to Refs.~\onlinecite{HolUmrSha-JCP-17, SceGarCafLoo-JCTC-18, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, LooBogSceCafJac-JCTC-19, QP2} for more details.
+The one-electron densities and on-top pair densities are computed from a very large CIPSI expansion containing up to several million of Slater determinants.
+All the RS-DFT and exFCI calculations have been performed with {\QP}. \cite{QP2}
+For the numerical quadratures, we employ the SG-2 grid. \cite{DasHer-JCC-17}
+Except for methylene for which FCI/TZVP geometries have been taken from Ref.~\onlinecite{SheLeiVanSch-JCP-98}, the other molecular geometries have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJac-JCTC-19} and have been obtained at the CC3/aug-cc-pVTZ level of theory.
+For the sake of completeness, all these geometries are reported in the {\SI}.
+Frozen-core calculations are systematically performed and defined as such: a \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}.
+The frozen-core density-based correction is used consistently with the frozen-core approximation in WFT methods.
+We refer the reader to Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} for an explicit derivation of the equations associated with the frozen-core version of the present density-based basis-set correction.
+Compared to the exFCI calculations performed to compute energies and densities, the basis-set correction represents, in any case, a marginal computational cost.
+In the following, we employ the AVXZ shorthand notations for Dunning's aug-cc-pVXZ basis sets.
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Results and Discussion}
+\label{sec:res}
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+%=======================
+\subsection{Methylene}
+\label{sec:CH2}
+%=======================
+
+Methylene is a paradigmatic system in electronic structure theory. \cite{Sch-Science-86} 
+Due to its relative small size, its ground and excited states have been thoroughly studied with high-level ab initio methods. \cite{Sch-Science-86, BauTay-JCP-86, JenBun-JCP-88, SheVanYamSch-JMS-97, SheLeiVanSch-JCP-98, AbrShe-JCP-04, AbrShe-CPL-05, ZimTouZhaMusUmr-JCP-09, GouPieWlo-MP-10, ChiHolAdaOttUmrShaZim-JPCA-18}
+
+As a first test of the present density-based basis-set correction, we consider the four lowest-lying states of methylene ($1\,^{3}B_1$, $1\,^{1}A_1$, $1\,^{1}B_1$ and $2\,^{1}A_1$) at their respective equilibrium geometry and compute the corresponding adiabatic transition energies for basis sets ranging from AVDZ to AVQZ.
+We have also computed total energies at the exFCI/AV5Z level and used these alongside the quadruple-$\zeta$ ones to extrapolate the total energies to the CBS limit with the usual extrapolation formula \cite{HelJorOls-BOOK-02}
+\begin{equation}
+	\E{}{\text{AVXZ}}(\tX) = \E{}{\CBS} + \alpha \, \tX^{-3}.
+\end{equation}
+These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{tab:CH2} alongside reference values from the literature obtained with various deterministic and stochastic approaches. \cite{ChiHolAdaOttUmrShaZim-JPCA-18, SheLeiVanSch-JCP-98, JenBun-JCP-88, SheLeiVanSch-JCP-98, ZimTouZhaMusUmr-JCP-09}
+Total energies for each state can be found in the {\SI}.
+The exFCI/CBS values are still off by a few tenths of a {\kcal} compared to the DMC results of Zimmerman \textit{et al.} \cite{ZimTouZhaMusUmr-JCP-09} which are extremely close from the experimentally-derived adiabatic energies.
+The reason of this discrepancy is probably due to the frozen-core approximation which has been applied in our case and has shown to significantly affect adiabatic energies. \cite{LooGalJac-JPCL-18, LooJac-JCTC-19}
+However, the exFCI/CBS energies are in perfect agreement with the semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}, as expected.
+
+Figure \ref{fig:CH2} clearly shows that, for the double-$\zeta$ basis, the exFCI adiabatic energies are far from being chemically accurate with errors as high as 0.15 eV.
+From the triple-$\zeta$ basis onward, the exFCI excitation energies are chemically accurate though (i.e. error below 1 {\kcal} or 0.043 eV), and converge steadily to the CBS limit when one increases the size of the basis set.
+Concerning the basis-set correction, already at the double-$\zeta$ level, the $\PBEot$ correction returns chemically accurate excitation energies.
+The performance of the $\PBEUEG$ and $\LDA$ functionals is less impressive. 
+Yet, they still yield significant reductions of the basis-set incompleteness error, hence representing a good compromise between computational cost and accuracy.
+Note that the results for the $\PBEUEG$ functional are not represented in Fig.~\ref{fig:CH2} as they are very similar to the $\LDA$ ones (similar considerations apply to the other systems studied below).
+It is also quite evident that, the basis-set correction has the tendency of over-correcting the excitation energies via an over-stabilization of the excited states compared to the ground state.
+This trend is quite systematic as we shall see below.
+
+%%% TABLE 1 %%%
+	\begin{squeezetable}
+	\begin{table}
+	\caption{
+	Adiabatic transition energies (in eV) of excited states of methylene for various methods and basis sets.
+	The relative difference with respect to the exFCI/CBS result is reported in square brackets.
+	See {\SI} for total energies.}
+	\label{tab:CH2}
+	\begin{ruledtabular}
+	\begin{tabular}{lllll}
+				&				&	\mc{3}{c}{Transitions}	\\
+	\cline{3-5}
+	Method		&	Basis set	&	\tabc{$1\,^{3}B_1 \ra 1\,^{1}A_1$}		
+								&	\tabc{$1\,^{3}B_1 \ra 1\,^{1}B_1$}	
+								&	\tabc{$1\,^{3}B_1 \ra 2\,^{1}A_1$}		\\
+	\hline
+	exFCI		&	AVDZ					
+								&	$0.441$ [$+0.057$]	
+								&	$1.536$ [$+0.152$]
+								&	$2.659$ [$+0.162$]	\\	
+				&	AVTZ					
+								&	$0.408$ [$+0.024$]	
+								&	$1.423$ [$+0.040$]	
+								&	$2.546$ [$+0.049$]	\\	
+				&	AVQZ					
+								&	$0.395$ [$+0.011$]	
+								&	$1.399$ [$+0.016$]	
+								&	$2.516$ [$+0.020$]	\\	
+				&	AV5Z					
+								&	$0.390$ [$+0.006$]	
+								&	$1.392$ [$+0.008$]	
+								&	$2.507$ [$+0.010$]	\\	
+				&	CBS					
+								&	$0.384$	
+								&	$1.384$	
+								&	$2.497$	\\	
+								\\
+	exFCI+$\PBEot$	&	AVDZ					
+								&	$0.347$ [$-0.037$]	
+								&	$1.401$ [$+0.017$]	
+								&	$2.511$ [$+0.014$]	\\	
+				&	AVTZ					
+								&	$0.374$ [$-0.010$]	
+								&	$1.378$ [$-0.006$]	
+								&	$2.491$ [$-0.006$]	\\	
+				&	AVQZ					
+								&	$0.379$ [$-0.005$]	
+								&	$1.378$ [$-0.006$]	
+								&	$2.489$ [$-0.008$]	\\	
+								\\
+	exFCI+$\PBEUEG$	&	AVDZ					
+								&	$0.308$ [$-0.076$]	
+								&	$1.388$ [$+0.004$]	
+								&	$2.560$ [$+0.064$]	\\	
+				&	AVTZ					
+								&	$0.356$ [$-0.028$]	
+								&	$1.371$ [$-0.013$]	
+								&	$2.510$ [$+0.013$]	\\	
+				&	AVQZ					
+								&	$0.371$ [$-0.013$]
+								&	$1.375$ [$-0.009$]	
+								&	$2.498$ [$+0.002$]	\\	
+								\\
+	exFCI+$\LDA$	&	AVDZ					
+								&	$0.337$ [$-0.047$]	
+								&	$1.420$ [$+0.036$]	
+								&	$2.586$ [$+0.089$]	\\	
+				&	AVTZ					
+								&	$0.359$ [$-0.025$]	
+								&	$1.374$ [$-0.010$]	
+								&	$2.514$ [$+0.017$]	\\	
+				&	AVQZ					
+								&	$0.370$ [$-0.014$]	
+								&	$1.375$ [$-0.009$]	
+								&	$2.499$ [$-0.002$]	\\	
+								\\
+	SHCI\fnm[1]	&	AVQZ					
+								&	$0.393$	
+								&	$1.398$	
+								&	$2.516$	\\
+	CR-EOMCC (2,3)D\fnm[2]&	AV5Z					
+								&	$0.430$	
+								&	$1.464$	
+								&	$2.633$	\\
+	FCI\fnm[3]	&	TZ2P					
+								&	$0.483$	
+								&	$1.542$	
+								&	$2.674$	\\
+	DMC\fnm[4]	&							
+								&	$0.406$	
+								&	$1.416$	
+								&	$2.524$	\\
+	Exp.\fnm[5]	&							
+								&	$0.406$	
+								&	$1.415$	
+	\end{tabular}
+	\end{ruledtabular}
+	\fnt[1]{Semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}.}
+	\fnt[2]{Completely-renormalized equation-of-motion coupled cluster (CR-EOMCC) calculations from Refs.~\onlinecite{GouPieWlo-MP-10}.}
+	\fnt[3]{Reference \onlinecite{SheLeiVanSch-JCP-98}.}
+	\fnt[4]{Diffusion Monte Carlo (DMC) calculations from Ref.~\onlinecite{ZimTouZhaMusUmr-JCP-09} obtained with a CAS(6,6) trial wave function.}
+	\fnt[5]{Experimentally-derived values. See footnotes of Table II from Ref.~\onlinecite{GouPieWlo-MP-10} for additional details.}
+	\end{table}
+	\end{squeezetable}
+%%% %%% %%%
+
+%%% FIG 1 %%%
+\begin{figure}
+	\includegraphics[width=\linewidth]{fig1.pdf}
+	\caption{Error in adiabatic excitation energies (in eV) of methylene for various basis sets and methods.
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
+	See Table \ref{tab:CH2} for raw data.}
+	\label{fig:CH2}
+\end{figure}
+%%% %%% %%%
+
+%=======================
+\subsection{Rydberg States of Water and Ammonia}
+\label{sec:H2O-NH3}
+%=======================
+
+For the second test, we consider the water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, SceCafBenJacLoo-RC-19} and ammonia \cite{SchGoe-JCTC-17, BarDelPerMat-JMS-97, LooSceBloGarCafJac-JCTC-18} molecules.
+They are both well studied and possess Rydberg excited states which are highly sensitive to the radial completeness of the one-electron basis set, as evidenced in Ref.~\onlinecite{LooSceBloGarCafJac-JCTC-18}.
+Table \ref{tab:Mol} reports vertical excitation energies for various singlet and triplet excited states of water and ammonia at various levels of theory (see the {\SI} for total energies).
+The basis-set corrected theoretical best estimates (TBEs) have been extracted from Ref.~\onlinecite{LooSceBloGarCafJac-JCTC-18} and have been obtained on the same geometries.
+These results are also depicted in Figs.~\ref{fig:H2O} and \ref{fig:NH3} for \ce{H2O} and \ce{NH3}, respectively.
+One would have noticed that the basis-set effects are particularly strong for the third singlet excited state of water and the third and fourth singlet excited states of ammonia where this effect is even magnified.
+In other words, substantial error remains in these cases even with the largest AVQZ basis set.
+In these cases, one really needs doubly augmented basis sets to reach radial completeness.
+The first observation worth reporting is that all three RS-DFT correlation functionals have very similar behaviors and they significantly reduce the error on the excitation energies for most of the states.
+However, these results also clearly evidence that special care has to be taken for very diffuse excited states where the present correction cannot catch the radial incompleteness of the one-electron basis set, a feature which is far from being a cusp-related effect.
+In other words, the DFT-based correction recovers dynamic correlation effects only and one must ensure that the basis set includes enough diffuse functions in order to describe Rydberg states.
+
+%%% TABLE 2 %%%
+	\begin{squeezetable}
+	\begin{table*}
+	\caption{
+	Vertical excitation energies (in eV) of excited states of water, ammonia, carbon dimer and ethylene for various methods and basis sets.
+	The TBEs have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJac-JCTC-19} on the same geometries.
+	See the {\SI} for total energies.}
+	\label{tab:Mol}
+	\begin{ruledtabular}
+	\begin{tabular}{lllddddddddddddd}
+				&				&					&				&	\mc{12}{c}{Deviation with respect to TBE}		
+	\\
+	\cline{5-16}
+				&				&					&				&	\mc{3}{c}{exFCI}	
+																	&	\mc{3}{c}{exFCI+$\PBEot$}	
+																	&	\mc{3}{c}{exFCI+$\PBEUEG$}	
+																	&	\mc{3}{c}{exFCI+$\LDA$}
+	\\
+	\cline{5-7}	\cline{8-10}	\cline{11-13}	\cline{14-16}
+	Molecule	&	Transition		&	Nature		&	\tabc{TBE}	&	\tabc{AVDZ}	&	\tabc{AVTZ}	&	\tabc{AVQZ}	
+																	&	\tabc{AVDZ}	&	\tabc{AVTZ}	&	\tabc{AVQZ}	
+																	&	\tabc{AVDZ}	&	\tabc{AVTZ}	&	\tabc{AVQZ}	
+																	&	\tabc{AVDZ}	&	\tabc{AVTZ}	&	\tabc{AVQZ}	
+	\\
+	\hline
+	Water		&	$1\,^{1}A_1 \ra 1\,^{1}B_1$		&	Ryd.	&	7.70\fnm[1]		&	-0.17	&	-0.07	&	-0.02	
+																	&	0.01	&	0.00	&	0.02	
+																	&	-0.02	&	-0.01	&	0.00	
+																	&	-0.04	&	-0.01	&	0.01
+	\\
+				&	$1\,^{1}A_1 \ra 1\,^{1}A_2$		&	Ryd.	&	9.47\fnm[1]		&	-0.15	&	-0.06	&	-0.01	
+																	&	0.03	&	0.01	&	0.03	
+																	&	0.00	&	0.00	&	0.02	
+																	&	-0.03	&	0.00	&	0.00
+	\\
+				&	$1\,^{1}A_1 \ra 2\,^{1}A_1$		&	Ryd.	&	9.97\fnm[1]		&	-0.03	&	0.02	&	0.06	
+																	&	0.13	&	0.08	&	0.09	
+																	&	0.10	&	0.07	&	0.08		
+																	&	0.09	&	0.07	&	0.03
+	\\
+				&	$1\,^{1}A_1 \ra 1\,^{3}B_1$		&	Ryd.	&	7.33\fnm[1]		&	-0.19	&	-0.08	&	-0.03	
+																	&	0.02	&	0.00	&	0.02	
+																	&	0.05	&	0.01	&	0.02	
+																	&	0.00	&	0.00	&	0.04
+	\\
+				&	$1\,^{1}A_1 \ra 1\,^{3}A_2$		&	Ryd.	&	9.30\fnm[1]		&	-0.16	&	-0.06	&	-0.01	
+																	&	0.04	&	0.02	&	0.04	
+																	&	0.07	&	0.03	&	0.04	
+																	&	0.03	&	0.03	&	0.04
+	\\
+				&	$1\,^{1}A_1 \ra 1\,^{3}A_1$		&	Ryd.	&	9.59\fnm[1]		&	-0.11	&	-0.05	&	-0.01	
+																	&	0.07	&	0.02	&	0.03	
+																	&	0.09	&	0.03	&	0.03	
+																	&	0.06	&	0.03	&	0.04
+	\\
+	\\
+	Ammonia		&	$1\,^{1}A_{1} \ra 1\,^{1}A_{2}$		&	Ryd.	&	6.66\fnm[1]	&	-0.18	&	-0.07	&	-0.04	
+																				&	-0.04	&	-0.02	&	-0.01	
+																				&	-0.07	&	-0.03	&	-0.02	
+																				&	-0.07	&	-0.03	&	-0.02	
+	\\
+				&	$1\,^{1}A_{1} \ra 1\,^{1}E$		&	Ryd.		&	8.21\fnm[1]	&	-0.13	&	-0.05	&	-0.02	
+																				&	0.01	&	0.00	&	0.01	
+																				&	-0.03	&	-0.01	&	0.00	
+																				&	-0.03	&	0.00	&	0.00	
+	\\
+				&	$1\,^{1}A_{1} \ra 2\,^{1}A_{1}$		&	Ryd.	&	8.65\fnm[1]	&	1.03	&	0.68	&	0.47	
+																				&	1.17	&	0.73	&	0.50	
+																				&	1.12	&	0.72	&	0.49	
+																				&	1.11	&	0.71	&	0.49	
+	\\
+				&	$1\,^{1}A_{1} \ra 2\,^{1}A_{2}$		&	Ryd.	&	8.65\fnm[2]	&	1.22	&	0.77	&	0.59	
+																				&	1.36	&	0.83	&	0.62	
+																				&	1.33	&	0.81	&	0.61	
+																				&	1.32	&	0.81	&	0.61	
+	\\
+				&	$1\,^{1}A_{1} \ra 1\,^{3}A_{2}$		&	Ryd.	&	9.19\fnm[1]	&	-0.18	&	-0.06	&	-0.03	
+																				&	-0.03	&	0.00	&	-0.02	
+																				&	-0.07	&	-0.02	&	-0.03	
+																				&	-0.07	&	-0.01	&	-0.03	
+	\\
+	\\
+	Carbon dimer	&	$1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$		&	Val.	&	2.04\fnm[3]	&	0.17	&	0.05	&	0.02
+																								&	0.04	&	0.00	&	0.00
+																								&	0.15	&	0.04	&	0.02
+																								&	0.17	&	0.05	&	0.02
+	\\
+						&	$1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$	&	Val.	&	2.38\fnm[3]	&	0.12	&	0.04	&	0.02
+																								&	0.00	&	0.00	&	0.00
+																								&	0.11	&	0.03	&	0.02
+																								&	0.13	&	0.04	&	0.02
+	\\
+	\\
+	Ethylene	&	$1\,^{1}A_{1g} \ra 1\,^{1}B_{3u}$		&	Ryd.	&	7.43\fnm[3]	&	-0.12	&	-0.04	&	
+																					&	-0.05	&	-0.01	&	
+																					&	-0.04	&	-0.01	&	
+																					&	-0.02	&	0.00	&	
+	\\
+				&	$1\,^{1}A_{1g} \ra 1\,^{1}B_{1u}$		&	Val.	&	7.92\fnm[3]	&	0.01	&	0.01	&	
+																					&	0.00	&	0.00	&	
+																					&	0.06	&	0.03	&	
+																					&	0.06	&	0.03	&	
+	\\
+				&	$1\,^{1}A_{1g} \ra 1\,^{1}B_{1g}$		&	Ryd.	&	8.10\fnm[3]	&	-0.1	&	-0.02	&	
+																					&	-0.03	&	0.00	&	
+																					&	-0.02	&	0.00	&		
+																					&	0.00	&	0.01	&	
+	\\
+				&	$1\,^{1}A_{1g} \ra 1\,^{3}B_{1u}$		&	Val.	&	4.54\fnm[3]	&	0.01	&	0.00	&	
+																					&	0.05	&	0.03	&	
+																					&	0.08	&	0.04	&	
+																					&	0.07	&	0.04	&	
+	\\
+				&	$1\,^{1}A_{1g} \ra 1\,^{3}B_{3u}$		&	Val.	&	7.28\fnm[4]	&	-0.12	&	-0.04	&	
+																					&	-0.04	&	0.00	&	
+																					&	0.00	&	0.00	&	
+																					&	0.00	&	0.02	&	
+	\\
+				&	$1\,^{1}A_{1g} \ra 1\,^{3}B_{1g}$		&	Val.	&	8.00\fnm[4]	&	-0.07	&	-0.01	&	
+																					&	0.00	&	0.03	&	
+																					&	0.04	&	0.03	&	
+																					&	0.05	&	0.04	&	
+	\end{tabular}
+	\end{ruledtabular}
+	\fnt[1]{exFCI/AVQZ data corrected with the difference between CC3/d-AV5Z and exFCI/AVQZ values. \cite{LooSceBloGarCafJac-JCTC-18} 
+	d-AV5Z is the doubly augmented V5Z basis set.}
+	\fnt[2]{exFCI/AVTZ data corrected with the difference between CC3/d-AV5Z and exFCI/AVTZ values. \cite{LooSceBloGarCafJac-JCTC-18}}
+	\fnt[3]{exFCI/CBS obtained from the exFCI/AVTZ and exFCI/AVQZ data of Ref.~\onlinecite{LooBogSceCafJac-JCTC-19}.}
+	\fnt[4]{exFCI/AVDZ data corrected with the difference between CC3/d-AV5Z and exFCI/AVDZ values. \cite{LooSceBloGarCafJac-JCTC-18}}
+	\end{table*}
+	\end{squeezetable}
+%%% %%% %%%
+
+%%% FIG 2 %%%
+\begin{figure}
+	\includegraphics[width=\linewidth]{fig2.pdf}
+	\caption{Error in vertical excitation energies (in eV) of water for various basis sets and methods.
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
+	See Table \ref{tab:Mol} for raw data.}
+	\label{fig:H2O}
+\end{figure}
+%%% %%% %%%
+
+%%% FIG 3 %%%
+\begin{figure}
+	\includegraphics[width=\linewidth]{fig3.pdf}
+	\caption{Error in vertical excitation energies (in eV) of ammonia for various basis sets and methods.
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
+	See Table \ref{tab:Mol} for raw data.}
+	\label{fig:NH3}
+\end{figure}
+%%% %%% %%%
+
+%=======================
+\subsection{Doubly-Excited States of the Carbon Dimer}
+\label{sec:C2}
+%=======================
+In order to have a miscellaneous test set of excitations, in a third time, we propose to study some doubly-excited states of the carbon dimer \ce{C2}, a prototype system for strongly correlated and multireference systems. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, HolUmrSha-JCP-17, VarRoc-PTRSMPES-18}
+These two valence excitations --- $1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$ and $1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$ --- are both of $(\pi,\pi) \ra (\si,\si)$ character.
+They have been recently studied with state-of-the-art methods, and have been shown to be ``pure'' doubly-excited states as they involve an insignificant amount of single excitations. \cite{LooBogSceCafJac-JCTC-19} 
+The vertical excitation energies associated with these transitions are reported in Table \ref{tab:Mol} and represented in Fig.~\ref{fig:C2}.
+An interesting point here is that one really needs to consider the $\PBEot$ functional to get chemically accurate excitation energies with the AVDZ atomic basis set.
+We believe that the present result is a direct consequence of the multireference character of the \ce{C2} molecule.
+In other words, the UEG on-top pair density used in the $\LDA$ and $\PBEUEG$ functionals (see Sec.~\ref{sec:func}) is a particularly bad approximation of the true on-top pair density for the present system.
+
+%%% FIG 5 %%%
+\begin{figure}
+	\includegraphics[width=\linewidth]{fig4.pdf}
+	\caption{Error in vertical excitation energies (in eV) for two doubly-excited states of the carbon dimer for various basis sets and methods.
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
+	See Table \ref{tab:Mol} for raw data.}
+	\label{fig:C2}
+\end{figure}
+%%% %%% %%%
+
+It is interesting to study the behavior of the key quantities involved in the basis-set correction for different states as the basis-set incompleteness error is obviously state specific. 
+In Fig.~\ref{fig:C2_mu}, we report $\rsmu{}{\Bas}(z)$, $\n{}{\Bas}(z) \be{\text{c,md}}{\sr,\PBEot}(z)$, and $\n{2}{\Bas}(z)$ 
+along the nuclear axis ($z$) for the two $^1 \Sigma_g^+$ electronic states of \ce{C2} computed with the AVDZ, AVTZ, and AVQZ basis sets. 
+The graphs gathered in Fig.~\ref{fig:C2_mu} illustrate several general features regarding the present basis-set correction: 
+\begin{itemize}
+	\item the maximal values of $\rsmu{}{\Bas}(z)$ are systematically close to the nuclei, a signature of the atom-centered basis set;
+	\item the overall magnitude of $\rsmu{}{\Bas}(z)$ increases with the basis set, which reflects the improvement of the description of the correlation effects when enlarging the basis set;
+	\item the absolute value of the energetic correction decreases when the size of the basis set increases;
+	\item there is a clear correspondence between the values of the energetic correction and the on-top pair density. 
+\end{itemize}
+Regarding now the differential effect of the basis-set correction in the special case of the two $^1 \Sigma_g^+$ states studied here, we observe that: 
+\begin{itemize}
+	\item $\rsmu{}{\Bas}(z)$ has the same overall behavior for the two states, with slightly more fine structure in the case of the ground state. 
+	Such feature is consistent with the fact that the two states considered are both of $\Sigma_g^+$ symmetry and of valence character. 
+	\item $\n{2}{}(z)$ is overall larger in the excited state, specially in the bonding and outer regions. 
+	This is can be explained by the nature of the electronic transition which qualitatively corresponds to a double excitation from $\pi$ to $\sigma$ orbitals, therefore increasing the overall electronic population on the bond axis. 
+	\item The energetic correction clearly stabilizes preferentially the excited state rather than the ground state, illustrating that short-range correlation effects are more pronounced in the former than in the latter. 
+	This is linked to the larger values of the excited-state on-top pair density. 
+\end{itemize}
+
+%%% FIG 4 %%%
+\begin{figure*}
+	\includegraphics[height=0.35\linewidth]{fig5a.pdf}
+	\includegraphics[height=0.35\linewidth]{fig5b.pdf}
+	\includegraphics[height=0.35\linewidth]{fig5c.pdf}
+	\caption{$\rsmu{}{\Bas}$ (left), $\n{}{\Bas} \be{\text{c,md}}{\sr,\PBEot}$ (center) and $\n{2}{\Bas}$ (right) along the molecular axis ($z$) for the ground state (black curve) and second doubly-excited state (red curve) of \ce{C2} for various basis sets $\Bas$.
+	The two electronic states are both of $\Sigma_g^+$ symmetry. 
+	The carbon nuclei are located at $z= \pm 1.180$ bohr and are represented by the thin black lines.}
+	\label{fig:C2_mu}
+\end{figure*}
+%%% %%% %%%
+
+%=======================
+\subsection{Ethylene}
+\label{sec:C2H4}
+%=======================
+
+As a final example, we consider the ethylene molecule, yet another system which has been particularly scrutinized theoretically using high-level ab initio methods. \cite{SerMarNebLinRoo-JCP-93, WatGwaBar-JCP-96, WibOliTru-JPCA-02, BarPaiLis-JCP-04, Ang-JCC-08, SchSilSauThi-JCP-08, SilSchSauThi-JCP-10, SilSauSchThi-MP-10, Ang-IJQC-10, DadSmaBooAlaFil-JCTC-12, FelPetDav-JCP-14, ChiHolAdaOttUmrShaZim-JPCA-18}
+We refer the interested reader to the work of Feller \textit{et al.}\cite{FelPetDav-JCP-14} for an exhaustive investigation dedicated to the excited states of ethylene using state-of-the-art CI calculations.
+In the present context, ethylene is a particularly interesting system as it contains a mixture of valence and Rydberg excited states. 
+Our basis-set corrected vertical excitation energies are gathered in Table \ref{tab:Mol} and depicted in Fig.~\ref{fig:C2H4}.
+Note that exFCI/AVQZ calculations are inaccessible for ethylene. 
+The exFCI+$\PBEot$/AVDZ excitation energies are at near chemical accuracy and the errors drop further when one goes to the triple-$\zeta$ basis.
+Consistently with the previous examples, the $\LDA$ and $\PBEUEG$ functionals are slightly less accurate, although they still correct the excitation energies in the right direction.
+
+%%% FIG 6 %%%
+\begin{figure}
+	\includegraphics[width=\linewidth]{fig6.pdf}
+	\caption{Error in vertical excitation energies (in eV) of ethylene for various basis sets and methods.
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
+	See Table \ref{tab:Mol} for raw data.}
+	\label{fig:C2H4}
+\end{figure}
+%%% %%% %%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Conclusion}
+\label{sec:ccl}
+%%%%%%%%%%%%%%%%%%%%%%%%
+We have shown that, by employing the recently proposed density-based basis-set correction developed by some of the authors, \cite{GinPraFerAssSavTou-JCP-18} one can obtain, using sCI methods, chemically accurate excitation energies with typically augmented double-$\zeta$ basis sets.4
+This nicely complements our recent investigation on ground-state properties, \cite{LooPraSceTouGin-JPCL-19} which has evidenced that one recovers quintuple-$\zeta$ quality atomization and correlation energies with triple-$\zeta$ basis sets.
+The present study clearly shows that, for very diffuse excited states, the present correction relying on short-range correlation functionals from RS-DFT might not be enough to catch the radial incompleteness of the one-electron basis set.
+Also, in the case of multireference systems, we have evidenced that the $\PBEot$ functional, which uses an accurate on-top pair density, is more appropriate than the $\LDA$ and $\PBEUEG$ functionals relying on the UEG on-top pair density.
+We are currently investigating the performance of the present basis-set correction for strongly correlated systems and we hope to report on this in the near future.
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\section*{Supplementary material}
+%%%%%%%%%%%%%%%%%%%%%%%%
+See {\SI} for geometries and additional information (including total energies and energetic correction of the various functionals).
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{acknowledgements}
+PFL would like to thank Denis Jacquemin for numerous discussions on excited states.
+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}.
+\end{acknowledgements}
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+\bibliography{Ex-srDFT}
+
+\end{document}
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