partial answers

Response_Letter/Response_Letter.tex

@@ -80,14 +80,14 @@ I do not think that it is clearly mentioned in the article when the notation app
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 {I assume that in Fig.~1 authors plot the lowest solution after the diagonalization for each orbital p.}
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-\alert{
+\alert{In Fig.~1 we plot the quasiparticle solution for each orbital, i.e, the solution with the largest spectral weight which is obtained using the ``normal'' $G_0W_0$ scheme.
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 {In Fig.~2, the thick and thin solid lines are hardly visible. A better way of displaying is necessary. 
 Otherwise it all is a bit incomprehensible.}
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-\alert{
+\alert{Visibility of the different solid lines has been improved. Thank you for this valuable comment.
 }
 
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@@ -105,7 +105,8 @@ However, I cannot understand how the authors can claim that the correction intro
 These qp energies are different by 2-3 eV. How are the smooth curves advantageous if the results are so incorrect? 
 Could authors elaborate?}
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-\alert{
+\alert{Indeed the HOMO and LUMO orbitals do not show discontinuities along the dissociation coordinate so no need for a correction. Thus, it is an important feature that the regularization introduces only a small correction for these orbitals. Moreover, it is also essential to notice that we talk here about the $G_0W_0$ scheme but in case of a partially self-consistent scheme then the use of regularization seems critical.
+%It is also true that the regularization introduces a correction of few eVs for the LUMO+1 (p=3) and LUMO+2 (p=4) orbitals but  
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