diff --git a/Manuscript/BSE_JPCL.tex b/Manuscript/BSE_JPCL.tex
index 906784e..e95e01d 100644
--- a/Manuscript/BSE_JPCL.tex
+++ b/Manuscript/BSE_JPCL.tex
@@ -301,7 +301,9 @@ Taking then $( \Sigma^{\GW}-V^{\XC} )$ as a correction to the KS xc potential $V
     \varepsilon_p^{\GW} = \varepsilon_p^{\KS} +
     \mel{\phi_p^{\KS}}{\Sigma^{\GW}(\varepsilon_p^{\GW}) - V^{\XC}}{\phi_p^{\KS}}.
 \end{equation}
-Such an approach, where input KS energies are corrected to yield better electronic energy levels, is labeled as the single-shot, or perturbative, $G_0W_0$ technique. This simple scheme was used in the early $GW$ studies of extended semiconductors and insulators, \cite{Strinati_1980,Hybertsen_1986,Godby_1988,Linden_1988} 
+Such an approach, where input KS energies are corrected to yield better electronic energy levels, is labeled as the single-shot, or perturbative, $G_0W_0$ technique. 
+\titou{T2: Shall we introduce the renormalization factor?}
+This simple scheme was used in the early $GW$ studies of extended semiconductors and insulators, \cite{Strinati_1980,Hybertsen_1986,Godby_1988,Linden_1988} 
 surfaces, \cite{Northrup_1991,Blase_1994,Rohlfing_1995} and 2D systems, \cite{Blase_1995} allowing to dramatically reduced the errors associated with KS eigenvalues in conjunction with common local or gradient-corrected approximations to the xc potential.
 In particular, the well-known ``band gap" problem, \cite{Perdew_1983,Sham_1983} namely the underestimation of the occupied to unoccupied bands energy gap at the LDA KS level, was dramatically reduced, bringing the agreement with experiment to within a few tenths of an eV  [REFS] with an $\mathcal{O}(N^4)$ computational scaling (see below). 
 Another important feature compared to other perturbative techniques, the $GW$ formalism can tackle finite size and periodic systems, and does not present any divergence in the limit of zero gap (metallic) systems. \cite{Campillo_1999} 
@@ -418,6 +420,27 @@ Then, these are used as input variables for the $GW$ calculation, whose main pur
 Depending on the level of self-consistency, only the eigenvalues or both the eigenvalues and the orbitals are updated.
 In the case of a $G_0W_0$ calculation, a single, perturbative correction is applied to the orbital energies only.
 The partially self-consistent ev$GW$ scheme update
+
+The simplest and most popular variant is perturbative GW, or $G_0W_0$, \cite{Hybertsen_1985, Hybertsen_1986} which has been widely used in the literature to study solids, atoms and molecules. \cite{Bruneval_2012, Bruneval_2013, vanSetten_2015, vanSetten_2018}
+Although $G_0W_0$ provides accurate results (at least for weakly/moderately correlated systems), it is strongly starting-point dependent due to its perturbative nature, and violates some important conservation laws, such as the conservation of energy, momentum and particle number. \cite{Martin_1959, Baym_1961, Baym_1962}
+Improvements may be obtained via partial self-consistency while the conservation laws are satisfied at full self-consistency.
+However, things are not that simple, as self-consistency and vertex corrections are known to cancel to some extent. \cite{ReiningBook}
+Indeed, there is a long-standing debate about the importance of partial and full self-consistency in GW. \cite{Stan_2006, Stan_2009, Rostgaard_2010, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b, Koval_2014, Wilhelm_2018}
+In some situations, it has been found that self-consistency can worsen spectral properties compared to the simpler $G_0W_0$ method.
+A famous example has been provided by the calculations performed on the uniform electron gas, \cite{Holm_1998, Holm_1999,Holm_2000, Garcia-Gonzalez_2001} 
+a paradigm central to many areas of physics and chemistry. \cite{Loos_2016}
+This was further evidenced in real extended systems by several authors. \cite{Schone_1998, Ku_2002, Kutepov_2016, Kutepov_2017}
+However, other approximations may have caused such deterioration, \eg, pseudo-potentials \cite{deGroot_1995} or finite-basis set effects. \cite{Friedrich_2006}
+These studies have cast doubt on the importance of self-consistent schemes within $GW$, at least for solid-state calculations.
+For finite systems such as atoms and molecules, the situation is less controversial, and partially or fully self-consistent GW methods have shown great promise. \cite{Ke_2011, Blase_2011, Faber_2011, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b, Koval_2014, Hung_2016, Blase_2018, Jacquemin_2017}
+
+
+There exist two main types of partially self-consistent GW methods: 
+i) \textit{``eigenvalue-only quasiparticle''} GW (ev$GW$), \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011} 
+where the quasiparticle (QP) energies are updated at each iteration, and 
+ii) \textit{``quasiparticle self-consistent''} GW (qs$GW$), \cite{Faleev_2004, vanSchilfgaarde_2006, Kotani_2007, Ke_2011, Kaplan_2016} 
+where one updates both the QP energies and the corresponding orbitals.
+Note that a starting point dependence remains in ev$GW$ as the orbitals are not self-consistently optimized in this case.
 \\
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -626,6 +649,8 @@ Here goes the conclusion.
 %%%%%%%%%%%%%%%%%%%%%%%%
 \section*{Acknowledgments}
 %%%%%%%%%%%%%%%%%%%%%%%%
+Funding from the \textit{``Centre National de la Recherche Scientifique''} is acknowledged. 
+This work has also been supported through the EUR Grant NanoX ANR-17-EURE-0009 in the framework of the \textit{``Programme des Investissements d'Avenir''}.
 DJ acknowledges the \textit{R\'egion des Pays de la Loire} for financial support. 
 
 %%%%%%%%%%%%%%%%%%%%
@@ -664,6 +689,6 @@ and theoretical groups. He is the author of more than 500 scientific papers. He
 \begin{center}
 	\includegraphics[width=3cm]{PFLoos}
 \end{center}
-\noindent{\bfseries Pierre-Fran\c{c}ois Loos} was born in Nancy, France in 1982. He received his M.S.~in Computational and Theoretical Chemistry from the Universit\'e Henri Poincar\'e (Nancy, France) in 2005 and his Ph.D.~from the same university in 2008. From 2009 to 2013, He was undertaking postdoctoral research with Peter M.W.~Gill at the Australian National University (ANU). From 2013 to 2017, he was a \textit{``Discovery Early Career Researcher Award''} recipient at the ANU. Since 2017, he holds a researcher position from the \textit{``Centre National de la Recherche Scientifique (CNRS)} at the \textit{Laboratoire de Chimie et Physique Quantiques} in Toulouse (France), and was awarded, in 2019, an ERC consolidator grant for the development of new excited-state methodologies.
+\noindent{\bfseries Pierre-Fran\c{c}ois Loos} was born in Nancy, France in 1982. He received his M.S.~in Computational and Theoretical Chemistry from the Universit\'e Henri Poincar\'e (Nancy, France) in 2005 and his Ph.D.~from the same university in 2008. From 2009 to 2013, He was undertaking postdoctoral research with Peter M.W.~Gill at the Australian National University (ANU). From 2013 to 2017, he was a \textit{``Discovery Early Career Researcher Award''} recipient and, then, a senior lecturer at the ANU. Since 2017, he holds a researcher position from the \textit{``Centre National de la Recherche Scientifique (CNRS)} at the \textit{Laboratoire de Chimie et Physique Quantiques} in Toulouse (France), and was awarded, in 2019, an ERC consolidator grant for the development of new excited-state methodologies.
 
 \end{document}
diff --git a/Manuscript/xbbib.bib b/Manuscript/xbbib.bib
index 6781c2f..5c46609 100644
--- a/Manuscript/xbbib.bib
+++ b/Manuscript/xbbib.bib
@@ -1,13 +1,524 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2020-05-15 09:00:18 +0200 
+%% Created for Pierre-Francois Loos at 2020-05-15 15:13:22 +0200 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
+@article{Martin_1959,
+	Author = {Martin, Paul C. and Schwinger, Julian},
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+	Title = {Excitation Spectra of Aromatic Molecules within a Real-Space {{G W}} -{{BSE}} Formalism: {{Role}} of Self-Consistency and Vertex Corrections},
+	Volume = {94},
+	Year = {2016},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.94.085125}}
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+	Author = {Kutepov, Andrey L.},
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+	Pages = {155101},
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+	Author = {Kutepov, A. L. and Kotliar, G.},
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+	Issn = {2469-9950, 2469-9969},
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+	Language = {en},
+	Month = jul,
+	Number = {3},
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+	Volume = {96},
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+
+@article{Caruso_2016,
+	Author = {F. Caruso and M. Dauth and M. J. {van Setten} and P. Rinke},
+	Date-Added = {2020-05-15 15:07:54 +0200},
+	Date-Modified = {2020-05-15 15:07:54 +0200},
+	Doi = {10.1021/acs.jctc.6b00774},
+	Journal = {J. Chem. Theory Comput.},
+	Pages = {5076},
+	Title = {Benchmark of GW Approaches for the GW100 Test Set},
+	Volume = {12},
+	Year = {2016},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00774}}
+
+@article{Ren_2015,
+	Author = {Ren, Xinguo and Marom, Noa and Caruso, Fabio and Scheffler, Matthias and Rinke, Patrick},
+	Date-Added = {2020-05-15 15:07:54 +0200},
+	Date-Modified = {2020-05-15 15:07:54 +0200},
+	Doi = {10.1103/PhysRevB.92.081104},
+	File = {/Users/loos/Zotero/storage/DK4SKK42/Ren_2015.pdf},
+	Issn = {1098-0121, 1550-235X},
+	Journal = {Phys. Rev. B},
+	Language = {en},
+	Month = aug,
+	Number = {8},
+	Pages = {081104},
+	Shorttitle = {Beyond the {{G W}} Approximation},
+	Title = {Beyond the {{G W}} Approximation: {{A}} Second-Order Screened Exchange Correction},
+	Volume = {92},
+	Year = {2015},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.92.081104}}
+
+@article{Caruso_2013,
+	Author = {Caruso, Fabio and Rohr, Daniel R. and Hellgren, Maria and Ren, Xinguo and Rinke, Patrick and Rubio, Angel and Scheffler, Matthias},
+	Date-Added = {2020-05-15 15:07:54 +0200},
+	Date-Modified = {2020-05-15 15:07:54 +0200},
+	Doi = {10.1103/PhysRevLett.110.146403},
+	File = {/Users/loos/Zotero/storage/UF9F4UWC/Caruso_2013a.pdf;/Users/loos/Zotero/storage/Y3IZUCIX/Caruso_2013b.pdf},
+	Issn = {0031-9007, 1079-7114},
+	Journal = {Phys. Rev. Lett.},
+	Language = {en},
+	Month = apr,
+	Number = {14},
+	Pages = {146403},
+	Shorttitle = {Bond {{Breaking}} and {{Bond Formation}}},
+	Title = {Bond {{Breaking}} and {{Bond Formation}}: {{How Electron Correlation}} Is {{Captured}} in {{Many}}-{{Body Perturbation Theory}} and {{Density}}-{{Functional Theory}}},
+	Volume = {110},
+	Year = {2013},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.110.146403}}
+
+@article{Caruso_2013a,
+	Author = {Caruso, Fabio and Rinke, Patrick and Ren, Xinguo and Rubio, Angel and Scheffler, Matthias},
+	Date-Added = {2020-05-15 15:07:54 +0200},
+	Date-Modified = {2020-05-15 15:07:54 +0200},
+	Doi = {10.1103/PhysRevB.88.075105},
+	File = {/Users/loos/Zotero/storage/SACFAD2T/Caruso_2013.pdf},
+	Issn = {1098-0121, 1550-235X},
+	Journal = {Phys. Rev. B},
+	Language = {en},
+	Month = aug,
+	Number = {7},
+	Pages = {075105},
+	Shorttitle = {Self-Consistent {{G W}}},
+	Title = {Self-Consistent {{G W}} : {{All}}-Electron Implementation with Localized Basis Functions},
+	Volume = {88},
+	Year = {2013},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.88.075105}}
+
+@phdthesis{Caruso_2013b,
+	Author = {Caruso, Fabio},
+	Date-Added = {2020-05-15 15:07:54 +0200},
+	Date-Modified = {2020-05-15 15:07:54 +0200},
+	File = {/Users/loos/Zotero/storage/I5Q6ZQCS/Caruso_PhD.pdf},
+	School = {Freie Universit{\"a}t Berlin},
+	Title = {Self-Consistent {{GW}} Approach for the Unified Description of Ground and Excited States of Finite Systems},
+	Type = {{{PhD Thesis}}},
+	Year = {2013}}
+
+@article{Hellgren_2015,
+	Author = {Hellgren, Maria and Caruso, Fabio and Rohr, Daniel R. and Ren, Xinguo and Rubio, Angel and Scheffler, Matthias and Rinke, Patrick},
+	Date-Added = {2020-05-15 15:07:54 +0200},
+	Date-Modified = {2020-05-15 15:07:54 +0200},
+	Doi = {10.1103/PhysRevB.91.165110},
+	File = {/Users/loos/Zotero/storage/CXHEK6Z6/Hellgren_2015.pdf},
+	Issn = {1098-0121, 1550-235X},
+	Journal = {Phys. Rev. B},
+	Language = {en},
+	Month = apr,
+	Number = {16},
+	Pages = {165110},
+	Title = {Static Correlation and Electron Localization in Molecular Dimers from the Self-Consistent {{RPA}} and {{G W}} Approximation},
+	Volume = {91},
+	Year = {2015},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.91.165110}}
+
+@article{Caruso_2012,
+	Author = {Caruso, F. and Rinke, P. and Ren, X. and Scheffler, M. and Rubio, A.},
+	Date-Added = {2020-05-15 15:07:54 +0200},
+	Date-Modified = {2020-05-15 15:07:54 +0200},
+	Doi = {10.1103/PhysRevB.86.081102},
+	File = {/Users/loos/Zotero/storage/2ZGZT4DZ/Caruso_2012.pdf},
+	Issn = {1098-0121, 1550-235X},
+	Journal = {Phys. Rev. B},
+	Language = {en},
+	Month = aug,
+	Number = {8},
+	Pages = {081102(R)},
+	Shorttitle = {Unified Description of Ground and Excited States of Finite Systems},
+	Title = {Unified Description of Ground and Excited States of Finite Systems: {{The}} Self-Consistent {{G W}} Approach},
+	Volume = {86},
+	Year = {2012},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.86.081102}}
+
+@article{Holm_1998,
+	Author = {Holm, Bengt and {von Barth}, Ulf},
+	Date-Added = {2020-05-15 15:07:36 +0200},
+	Date-Modified = {2020-05-15 15:07:36 +0200},
+	File = {/Users/loos/Zotero/storage/F8I9X5AH/Holm_1998.pdf},
+	Journal = {Phys. Rev. B},
+	Number = {4},
+	Pages = {2108},
+	Title = {Fully Self-Consistent {{GW}} Self-Energy of the Electron Gas},
+	Volume = {57},
+	Year = {1998}}
+
+@article{vonBarth_1996,
+	Author = {{von Barth}, Ulf and Holm, Bengt},
+	Date-Added = {2020-05-15 15:07:36 +0200},
+	Date-Modified = {2020-05-15 15:07:36 +0200},
+	Doi = {10.1103/PhysRevB.54.8411},
+	File = {/Users/loos/Zotero/storage/QZN2CFQX/vonBarth_1996.pdf},
+	Journal = {Phys. Rev. B},
+	Number = {12},
+	Pages = {8411},
+	Shorttitle = {Self-Consistent {{GW}} 0 Results for the Electron Gas},
+	Title = {Self-Consistent {{GW}} 0 Results for the Electron Gas: {{Fixed}} Screened Potential {{W}} 0 within the Random-Phase Approximation},
+	Volume = {54},
+	Year = {1996},
+	Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.54.8411}}
+
+@article{Holm_1999,
+	Author = {Holm, Bengt},
+	Date-Added = {2020-05-15 15:07:36 +0200},
+	Date-Modified = {2020-05-15 15:07:36 +0200},
+	Doi = {10.1103/PhysRevLett.83.788},
+	Issn = {0031-9007, 1079-7114},
+	Journal = {Phys. Rev. Lett.},
+	Language = {en},
+	Month = jul,
+	Number = {4},
+	Pages = {788--791},
+	Title = {Total {{Energies}} from {{GW Calculations}}},
+	Volume = {83},
+	Year = {1999},
+	Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.83.788}}
+
+@article{Holm_2000,
+	Author = {Holm, B. and Aryasetiawan, F.},
+	Date-Added = {2020-05-15 15:07:36 +0200},
+	Date-Modified = {2020-05-15 15:07:36 +0200},
+	File = {/Users/loos/Zotero/storage/EX4CWKJL/Holm_2000.pdf},
+	Journal = {Phys. Rev. B},
+	Number = {8},
+	Pages = {4858},
+	Title = {Total Energy from the {{Galitskii}}-{{Migdal}} Formula Using Realistic Spectral Functions},
+	Volume = {62},
+	Year = {2000}}
+
 @book{ParrBook,
 	Address = {Clarendon Press},
 	Author = {R. G. Parr and W. Yang},
@@ -773,22 +1284,6 @@
 	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1888},
 	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.51.1888}}
 
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-	Author = {Hybertsen, Mark S. and Louie, Steven G.},
-	Doi = {10.1103/PhysRevB.34.5390},
-	Issue = {8},
-	Journal = {Phys. Rev. B},
-	Month = {Oct},
-	Numpages = {0},
-	Pages = {5390--5413},
-	Publisher = {American Physical Society},
-	Title = {Electron Correlation in Semiconductors and Insulators: Band Gaps and Quasiparticle Energies},
-	Url = {http://link.aps.org/doi/10.1103/PhysRevB.34.5390},
-	Volume = {34},
-	Year = {1986},
-	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.34.5390},
-	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.34.5390}}
-
 @article{Godby_1988,
 	Author = {Godby, R. W. and Schl\"uter, M. and Sham, L. J.},
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@@ -1858,20 +2353,6 @@
 	Year = {2016},
 	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01238}}
 
-@article{Caruso_2016,
-	Author = {Caruso, Fabio and Dauth, Matthias and van Setten, Michiel J. and Rinke, Patrick},
-	Doi = {10.1021/acs.jctc.6b00774},
-	Eprint = {https://doi.org/10.1021/acs.jctc.6b00774},
-	Journal = {Journal of Chemical Theory and Computation},
-	Note = {PMID: 27631585},
-	Number = {10},
-	Pages = {5076-5087},
-	Title = {Benchmark of GW Approaches for the GW100 Test Set},
-	Url = {https://doi.org/10.1021/acs.jctc.6b00774},
-	Volume = {12},
-	Year = {2016},
-	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00774}}
-
 @article{Korbel_2014,
 	Author = {K{\"{o}}rbel, Sabine and Boulanger, Paul and Duchemin, Ivan and Blase, Xavier and Marques, Miguel A. L. and Botti, Silvana},
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