Merge branch 'master' of github.com:pfloos/EPAWTFT

Conflicts:
	Manuscript/EPAWTFT.tex

Manuscript/EPAWTFT.bbl

@@ -6,7 +6,7 @@
 %Control: page (0) single
 %Control: year (1) truncated
 %Control: production of eprint (0) enabled
-\begin{thebibliography}{148}%
+\begin{thebibliography}{157}%
 \makeatletter
 \providecommand \@ifxundefined [1]{%
  \@ifx{#1\undefined}
@@ -1418,4 +1418,92 @@
   {journal} {\bibinfo  {journal} {Theor. Chem. Acc.}\ }\textbf {\bibinfo
   {volume} {137}},\ \bibinfo {pages} {149} (\bibinfo {year}
   {2018})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Romaniello}\ \emph {et~al.}(2009)\citenamefont
+  {Romaniello}, \citenamefont {Guyot},\ and\ \citenamefont
+  {Reining}}]{Romaniello_2009}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
+  {Romaniello}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Guyot}}, \
+  and\ \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont {Reining}},\ }\href
+  {\doibase 10.1063/1.3249965} {\bibfield  {journal} {\bibinfo  {journal} {J.
+  Chem. Phys.}\ }\textbf {\bibinfo {volume} {131}},\ \bibinfo {pages} {154111}
+  (\bibinfo {year} {2009})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Romaniello}\ \emph {et~al.}(2012)\citenamefont
+  {Romaniello}, \citenamefont {Bechstedt},\ and\ \citenamefont
+  {Reining}}]{Romaniello_2012}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
+  {Romaniello}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
+  {Bechstedt}}, \ and\ \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
+  {Reining}},\ }\href {\doibase 10.1103/PhysRevB.85.155131} {\bibfield
+  {journal} {\bibinfo  {journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume}
+  {85}},\ \bibinfo {pages} {155131} (\bibinfo {year} {2012})}\BibitemShut
+  {NoStop}%
+\bibitem [{\citenamefont {Di~Sabatino}\ \emph {et~al.}(2015)\citenamefont
+  {Di~Sabatino}, \citenamefont {Berger}, \citenamefont {Reining},\ and\
+  \citenamefont {Romaniello}}]{DiSabatino_2015}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
+  {Di~Sabatino}}, \bibinfo {author} {\bibfnamefont {J.~A.}\ \bibnamefont
+  {Berger}}, \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont {Reining}}, \
+  and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Romaniello}},\
+  }\href {\doibase 10.1063/1.4926327} {\bibfield  {journal} {\bibinfo
+  {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {143}},\ \bibinfo
+  {pages} {024108} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Tarantino}\ \emph {et~al.}(2017)\citenamefont
+  {Tarantino}, \citenamefont {Romaniello}, \citenamefont {Berger},\ and\
+  \citenamefont {Reining}}]{Tarantino_2017}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
+  {Tarantino}}, \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
+  {Romaniello}}, \bibinfo {author} {\bibfnamefont {J.~A.}\ \bibnamefont
+  {Berger}}, \ and\ \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
+  {Reining}},\ }\href {\doibase 10.1103/PhysRevB.96.045124} {\bibfield
+  {journal} {\bibinfo  {journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume}
+  {96}},\ \bibinfo {pages} {045124} (\bibinfo {year} {2017})}\BibitemShut
+  {NoStop}%
+\bibitem [{\citenamefont {Deur}\ \emph {et~al.}(2017)\citenamefont {Deur},
+  \citenamefont {Mazouin},\ and\ \citenamefont {Fromager}}]{Deur_2017}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
+  {Deur}}, \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont {Mazouin}}, \
+  and\ \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Fromager}},\ }\href
+  {\doibase 10.1103/PhysRevB.95.035120} {\bibfield  {journal} {\bibinfo
+  {journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume} {95}} (\bibinfo {year}
+  {2017}),\ 10.1103/PhysRevB.95.035120}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Deur}\ \emph {et~al.}(2018)\citenamefont {Deur},
+  \citenamefont {Mazouin}, \citenamefont {Senjean},\ and\ \citenamefont
+  {Fromager}}]{Deur_2018}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
+  {Deur}}, \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont {Mazouin}},
+  \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Senjean}}, \ and\
+  \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Fromager}},\ }\href
+  {\doibase 10.1140/epjb/e2018-90124-7} {\bibfield  {journal} {\bibinfo
+  {journal} {Eur. Phys. J. B}\ }\textbf {\bibinfo {volume} {91}} (\bibinfo
+  {year} {2018}),\ 10.1140/epjb/e2018-90124-7}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Senjean}\ and\ \citenamefont
+  {Fromager}(2018)}]{Senjean_2018}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
+  {Senjean}}\ and\ \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
+  {Fromager}},\ }\href {\doibase 10.1103/PhysRevA.98.022513} {\bibfield
+  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume}
+  {98}} (\bibinfo {year} {2018}),\ 10.1103/PhysRevA.98.022513}\BibitemShut
+  {NoStop}%
+\bibitem [{\citenamefont {Sagredo}\ and\ \citenamefont
+  {Burke}(2018)}]{Sagredo_2018}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
+  {Sagredo}}\ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
+  {Burke}},\ }\href {\doibase 10.1063/1.5043411} {\bibfield  {journal}
+  {\bibinfo  {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {149}},\
+  \bibinfo {pages} {134103} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Fromager}(2020)}]{Fromager_2020}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
+  {Fromager}},\ }\href {\doibase 10.1103/PhysRevLett.124.243001} {\bibfield
+  {journal} {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo
+  {volume} {124}},\ \bibinfo {pages} {243001} (\bibinfo {year}
+  {2020})}\BibitemShut {NoStop}%
 \end{thebibliography}%

Manuscript/EPAWTFT.bib

@@ -1,13 +1,121 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2020-12-01 21:24:39 +0100 
+%% Created for Pierre-Francois Loos at 2020-12-02 16:02:26 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
+@article{DiSabatino_2015,
+	author = {Di Sabatino,S. and Berger,J. A. and Reining,L. and Romaniello,P.},
+	date-added = {2020-12-02 16:02:21 +0100},
+	date-modified = {2020-12-02 16:02:21 +0100},
+	doi = {10.1063/1.4926327},
+	journal = {J. Chem. Phys.},
+	number = {2},
+	pages = {024108},
+	title = {Reduced density-matrix functional theory: Correlation and spectroscopy},
+	volume = {143},
+	year = {2015},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4926327}}
+
+@article{Romaniello_2009,
+	author = {Romaniello, P. and Guyot, S. and Reining, L.},
+	date-added = {2020-12-02 16:01:08 +0100},
+	date-modified = {2020-12-02 16:01:18 +0100},
+	doi = {10.1063/1.3249965},
+	journal = {J. Chem. Phys.},
+	pages = {154111},
+	title = {The Self-Energy beyond {{GW}}: {{Local}} and Nonlocal Vertex Corrections},
+	volume = {131},
+	year = {2009},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3249965}}
+
+@article{Tarantino_2017,
+	author = {Tarantino, Walter and Romaniello, Pina and Berger, J. A. and Reining, Lucia},
+	date-added = {2020-12-02 16:00:19 +0100},
+	date-modified = {2020-12-02 16:00:29 +0100},
+	doi = {10.1103/PhysRevB.96.045124},
+	journal = {Phys. Rev. B},
+	pages = {045124},
+	title = {Self-Consistent {{Dyson}} Equation and Self-Energy Functionals: {{An}} Analysis and Illustration on the Example of the {{Hubbard}} Atom},
+	volume = {96},
+	year = {2017},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.96.045124}}
+
+@article{Romaniello_2012,
+	author = {Romaniello, Pina and Bechstedt, Friedhelm and Reining, Lucia},
+	date-added = {2020-12-02 15:59:28 +0100},
+	date-modified = {2020-12-02 15:59:40 +0100},
+	doi = {10.1103/PhysRevB.85.155131},
+	journal = {Phys. Rev. B},
+	pages = {155131},
+	title = {Beyond the {{GW}} Approximation: {{Combining}} Correlation Channels},
+	volume = {85},
+	year = {2012},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.155131}}
+
+@article{Fromager_2020,
+	author = {Fromager, Emmanuel},
+	date-added = {2020-12-02 15:58:21 +0100},
+	date-modified = {2020-12-02 15:58:33 +0100},
+	doi = {10.1103/PhysRevLett.124.243001},
+	journal = {Phys. Rev. Lett.},
+	pages = {243001},
+	title = {Individual Correlations in Ensemble Density Functional Theory: State- and Density-Driven Decompositions without Additional Kohn-Sham Systems},
+	volume = {124},
+	year = {2020},
+	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.124.243001},
+	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.124.243001}}
+
+@article{Deur_2018,
+	abstract = {Gross\textendash{}Oliveira\textendash{}Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excitedstate densities. The ensemble energy (i.e. the weighted sum of ground- and excited-state energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOK-DFT is the exchange-correlation functional. Developing density-functional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a Legendre\textendash{}Fenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exact-exchange-only functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.},
+	author = {Deur, Killian and Mazouin, Laurent and Senjean, Bruno and Fromager, Emmanuel},
+	date-added = {2020-12-02 15:57:26 +0100},
+	date-modified = {2020-12-02 15:57:38 +0100},
+	doi = {10.1140/epjb/e2018-90124-7},
+	journal = {Eur. Phys. J. B},
+	title = {Exploring Weight-Dependent Density-Functional Approximations for Ensembles in the {{Hubbard}} Dimer},
+	volume = {91},
+	year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1140/epjb/e2018-90124-7}}
+
+@article{Sagredo_2018,
+	author = {Sagredo, Francisca and Burke, Kieron},
+	date-added = {2020-12-02 15:56:44 +0100},
+	date-modified = {2020-12-02 15:56:56 +0100},
+	doi = {10.1063/1.5043411},
+	journal = {J. Chem. Phys.},
+	pages = {134103},
+	title = {Accurate double excitations from ensemble density functional calculations},
+	volume = {149},
+	year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.5043411}}
+
+@article{Deur_2017,
+	author = {Deur, Killian and Mazouin, Laurent and Fromager, Emmanuel},
+	date-added = {2020-12-02 15:56:14 +0100},
+	date-modified = {2020-12-02 15:56:22 +0100},
+	doi = {10.1103/PhysRevB.95.035120},
+	journal = {Phys. Rev. B},
+	title = {Exact Ensemble Density Functional Theory for Excited States in a Model System: {{Investigating}} the Weight Dependence of the Correlation Energy},
+	volume = {95},
+	year = {2017},
+	Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.95.035120}}
+
+@article{Senjean_2018,
+	author = {Senjean, Bruno and Fromager, Emmanuel},
+	date-added = {2020-12-02 15:55:29 +0100},
+	date-modified = {2020-12-02 15:55:41 +0100},
+	doi = {10.1103/PhysRevA.98.022513},
+	journal = {Phys. Rev. A},
+	title = {Unified Formulation of Fundamental and Optical Gap Problems in Density-Functional Theory for Ensembles},
+	volume = {98},
+	year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.98.022513}}
+
 @article{Blase_2018,
 	author = {Blase, Xavier and Duchemin, Ivan and Jacquemin, Denis},
 	date-added = {2020-12-01 21:12:31 +0100},
@@ -54,7 +162,8 @@
 	pages = {845--856},
 	title = {The Calculations of Excited-State Properties with Time-Dependent Density Functional Theory},
 	volume = {42},
-	year = {2013}}
+	year = {2013},
+	Bdsk-Url-1 = {https://doi.org/10.1039/C2CS35394F}}
 
 @article{Laurent_2013,
 	author = {Laurent, Ad{\`e}le D. and Jacquemin, Denis},
@@ -65,7 +174,8 @@
 	pages = {2019--2039},
 	title = {TD-DFT Benchmarks: A Review},
 	volume = {113},
-	year = {2013}}
+	year = {2013},
+	Bdsk-Url-1 = {https://doi.org/10.1002/qua.24438}}
 
 @article{Gonzales_2012,
 	author = {Gonz{\'a}lez, Leticia and Escudero, D. and Serrano-Andr\`es, L.},

RapportStage/Rapport.tex

@@ -38,7 +38,6 @@
 \usepackage{siunitx}
 \usepackage[version=4]{mhchem}
 
-
 \usepackage{xcolor} % gestion de différentes couleurs
 
 \definecolor{linkcolor}{rgb}{0,0,0.6} % définition de la couleur des liens pdf