some more refs

Manuscript/SRGGW.bib

@@ -4965,6 +4965,39 @@
 	year = {2010},
 	bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115105},
 	bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.81.115105}}
+	
+@article{Godby_1986,
+  title = {Accurate {{Exchange-Correlation Potential}} for {{Silicon}} and {{Its Discontinuity}} on {{Addition}} of an {{Electron}}},
+  author = {Godby, R. W. and Schl{\"u}ter, M. and Sham, L. J.},
+  year = {1986},
+  journal = {Phys. Rev. Lett.},
+  volume = {56},
+  number = {22},
+  pages = {2415--2418},
+  doi = {10.1103/PhysRevLett.56.2415}
+}
+
+@article{Godby_1987,
+  title = {Trends in Self-Energy Operators and Their Corresponding Exchange-Correlation Potentials},
+  author = {Godby, R. W. and Schl{\"u}ter, M. and Sham, L. J.},
+  year = {1987},
+  journal = {Phys. Rev. B},
+  volume = {36},
+  number = {12},
+  pages = {6497--6500},
+  doi = {10.1103/PhysRevB.36.6497}
+}
+
+@article{Godby_1987a,
+  title = {Quasiparticle Energies in {{GaAs}} and {{AlAs}}},
+  author = {Godby, R. W. and Schl{\"u}ter, M. and Sham, L. J.},
+  year = {1987},
+  journal = {Phys. Rev. B},
+  volume = {35},
+  number = {8},
+  pages = {4170--4171},
+  doi = {10.1103/PhysRevB.35.4170}
+}
 
 @article{Godby_1988,
 	author = {Godby, R. W. and Schl\"uter, M. and Sham, L. J.},
@@ -6146,6 +6179,17 @@
 	bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.45.290},
 	bdsk-url-2 = {http://dx.doi.org/10.1103/PhysRevLett.45.290}}
 
+@article{Strinati_1982,
+  title = {Dynamical Aspects of Correlation Corrections in a Covalent Crystal},
+  author = {Strinati, G. and Mattausch, H. J. and Hanke, W.},
+  year = {1982},
+  journal = {Physical Review B},
+  volume = {25},
+  number = {4},
+  pages = {2867--2888},
+  doi = {10.1103/PhysRevB.25.2867}
+}
+
 @article{Strinati_1988,
 	author = {Strinati, G.},
 	date-added = {2020-05-18 21:40:28 +0200},
@@ -15981,6 +16025,41 @@
   doi = {10.1021/acs.jctc.6b00774}
 }
 
+@article{Blase_2011,
+  title = {First-Principles \$\textbackslash mathit\{\vphantom\}{{GW}}\vphantom\{\}\$ Calculations for Fullerenes, Porphyrins, Phtalocyanine, and Other Molecules of Interest for Organic Photovoltaic Applications},
+  author = {Blase, X. and Attaccalite, C. and Olevano, V.},
+  year = {2011},
+  journal = {Physical Review B},
+  volume = {83},
+  number = {11},
+  pages = {115103},
+  doi = {10.1103/PhysRevB.83.115103}
+}
+
+@article{Shishkin_2007,
+  title = {Self-Consistent \${{GW}}\$ Calculations for Semiconductors and Insulators},
+  author = {Shishkin, M. and Kresse, G.},
+  year = {2007},
+  journal = {Physical Review B},
+  volume = {75},
+  number = {23},
+  pages = {235102},
+  doi = {10.1103/PhysRevB.75.235102}
+}
+
+@article{Wilhelm_2016,
+  title = {{{GW}} in the {{Gaussian}} and {{Plane Waves Scheme}} with {{Application}} to {{Linear Acenes}}},
+  author = {Wilhelm, Jan and Del Ben, Mauro and Hutter, J{\"u}rg},
+  year = {2016},
+  journal = {Journal of Chemical Theory and Computation},
+  volume = {12},
+  number = {8},
+  pages = {3623--3635},
+  issn = {1549-9618},
+  doi = {10.1021/acs.jctc.6b00380}
+}
+
+
 @article{Gallandi_2015,
   title = {Long-{{Range Corrected DFT Meets GW}}: {{Vibrationally Resolved Photoelectron Spectra}} from {{First Principles}}},
   author = {Gallandi, Lukas and K{\"o}rzd{\"o}rfer, Thomas},

Manuscript/SRGGW.tex

@@ -52,7 +52,7 @@ Here comes the abstract.
 One-body Green's functions provide a natural and elegant way to access charged excitations energies of a physical system. \cite{Martin_2016}
 The one-body non-linear Hedin's equations give a recipe to obtain the exact interacting one-body Green's function and therefore the exact ionization potentials and electron affinities. \cite{Hedin_1965}
 Unfortunately, fully solving the Hedin's equations is out of reach and one must resort to approximations.
-In particular, the GW approximation, \cite{Hedin_1965} which has first been mainly used in the context of solids \ant{ref?} and is now widely used for molecules as well \ant{ref?}, provides fairly accurate results for weakly correlated systems\cite{Hung_2017,vanSetten_2015,vanSetten_2018,Caruso_2016,Korbel_2014,Bruneval_2021} at a low computational cost. \cite{Foerster_2011,Liu_2016,Wilhelm_2018,Forster_2021,Duchemin_2021}
+In particular, the GW approximation, \cite{Hedin_1965} which has first been mainly used in the context of solids \cite{Strinati_1980,Strinati_1982,Hybertsen_1985,Hybertsen_1986,Godby_1986,Godby_1987,Godby_1987a,Godby_1988,Blase_1995} and is now widely used for molecules as well \ant{ref?}, provides fairly accurate results for weakly correlated systems\cite{Hung_2017,vanSetten_2015,vanSetten_2018,Caruso_2016,Korbel_2014,Bruneval_2021} at a low computational cost. \cite{Foerster_2011,Liu_2016,Wilhelm_2018,Forster_2021,Duchemin_2021}
 
 The $GW$ approximation is an approximation for the self-energy $\Sigma$ which role is to relate the exact interacting Green's function $G$ to a non-interacting reference one $G_0$ through the Dyson equation
 \begin{equation}
@@ -131,10 +131,10 @@ In fact, these cases are related to the discontinuities and convergence problems
 One obvious flaw of the one-shot scheme mentioned above is its starting point dependence.
 Indeed, in Eq.~(\ref{eq:G0W0}) we chose to use the HF orbital energies but this is arbitrary and one could have chosen Kohn-Sham orbitals for example.
 Therefore, one could try to optimise the starting point to obtain the best one-shot energies possible. \cite{Korzdorfer_2012,Marom_2012,Bruneval_2013,Gallandi_2015,Caruso_2016, Gallandi_2016}
-Alternatively, one could solve this equation self-consistently leading to the eigenvalue only self-consistent scheme. \cite{Kaplan_2016}
+Alternatively, one could solve this equation self-consistently leading to the eigenvalue only self-consistent scheme. \cite{Shishkin_2006,Blase_2011,Marom_2012,Kaplan_2016,Wilhelm_2016}
 To do so one use the energy of the quasi-particle solution of the previous iteration to build Eq.~(\ref{eq:G0W0}) and then solves for $\omega$ again until convergence is reached.
 However, if the quasi-particle solution is not well-defined, self-consistency can be quite difficult, if not impossible, to reach. 
-Even if self-consistency has been reached, the starting point dependence has not been totally removed because the results still depend on the starting molecular orbitals.
+Even if self-consistency has been reached, the starting point dependence has not been totally removed because the results still depend on the starting molecular orbitals. \cite{Marom_2012}
 
 To update both the energies and the molecular orbitals, one needs to take into account the off-diagonal elements in Eq.~(\ref{eq:quasipart_eq}).
 To take into account the effect of off-diagonal elements without fully solving the quasi-particle equation, one can resort to the quasi-particle self-consistent (qs) scheme in which $\bSig(\omega)$ is replaced by a static approximation $\bSig^{\qs}$.