Manu: saving work

Response_Letter/Response_Letter.tex

@@ -2,6 +2,7 @@
 \usepackage{UPS_letterhead,xcolor,mhchem,mathpazo,ragged2e,hyperref,physics,amsmath}
 \newcommand{\alert}[1]{\textcolor{red}{#1}}
 \definecolor{darkgreen}{HTML}{009900}
+\newcommand{\manu}[1]{\textcolor{blue}{Manu: #1}}
 
 
 \begin{document}
@@ -158,12 +159,33 @@ usefulness of the Taylor expansions.}
 	{Fig. 1: It would be nice to see plots of these exact quantities for comparison, since there are layers of approximation and assumptions here. 
 	Either that, or some similar demonstrations for the models used to build GIC-eLDA. }
 	\\
-	\alert{bla bla bla}
+	\alert{For clarity, the discussion of Fig. 1 (Fig. 3 in the
+revised manuscript) has been extended. We now refer explicitly to the
+expression of the GIC-eLDA ensemble energy where it can be readily seen
+that its curvature can only originate from the weight-dependence of the
+individual KS-eLDA energies. We then refer to the next paragraph where
+we (now) explain where the linear and quadratic variations of the
+individual energies come from (see our response to the previous comment).
+The additional ghost-interaction errors that might be
+introduced into the orbitals is then mentioned, as a second layer of
+approximation. We also point out in the revised discussion that, in the exact theory,
+individual energies would not exhibit any weight dependence, which means
+that the deviation from linearity of the ensemble energy would be zero.}
 
 	\item 
 	{Fig. 2: Why does the crossover point for the 1st excitation curves disappear for $L=8\pi$? }
 	\\
-	\alert{We do not know.}
+	\alert{It is clear from our derivations that the individual
+correlation energies should vary with both the density {\it
+and} the ensemble weights. There is in principle no reason to expect the
+same variations for different ensembles and density regimes. The fact
+that, for $L=8\pi$, electron correlation is strong and therefore the
+density is more localized, is probably the reason for the disappearance
+of the crossover point. We were not able to rationalize this observation
+further but we still mention in the revised manuscript that it is an
+illustration of the importance of both the density and the weights in
+the evaluation of individual energies within an ensemble.}\manu{Do
+you agree?}
 
 	\item 
 	{Page 8: If the authors have evidence of behavior between $w=(0,0)$ and the equiensemble, instead of just these endpoints, that would be interesting to mention for the eDFT crowd. }