diff --git a/Notebooks/eDFT_FUEG.nb b/Notebooks/eDFT_FUEG.nb
index 93a4b97..7709eeb 100644
--- a/Notebooks/eDFT_FUEG.nb
+++ b/Notebooks/eDFT_FUEG.nb
@@ -10,10 +10,10 @@
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 NotebookFileLineBreakTest
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-NotebookOptionsPosition[  12185160,     259415]
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-CellTagsIndexPosition[  12185564,     259430]
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+CellTagsIndexPosition[  12185664,     259435]
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@@ -68549,9 +68557,9 @@ BgTPNB14mLTbxY6mOOgqyn/J+aYK58P8C+NHq0bInJORdIiw3HKibBtUf5qA
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@@ -68622,8 +68630,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     AbsoluteThickness[1.6], 
-                    GrayLevel[0], 
-                    Dashing[0.18], 
+                    RGBColor[1, 0, 0], 
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@@ -68633,8 +68640,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     AbsoluteThickness[1.6], 
-                    GrayLevel[0], 
-                    Dashing[0.18], 
+                    RGBColor[1, 0, 0], 
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@@ -68670,8 +68676,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     AbsoluteThickness[1.6], 
-                    GrayLevel[0], 
-                    Dashing[0.18], 
+                    RGBColor[1, 0, 0], 
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@@ -68691,7 +68696,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
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@@ -68701,7 +68706,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
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-                    RGBColor[1, 0, 0], 
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@@ -68727,7 +68732,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
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-                    RGBColor[1, 0, 0], 
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@@ -68747,7 +68752,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
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                     AbsoluteThickness[1.6], 
-                    RGBColor[1, 0, 0], 
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@@ -68758,7 +68763,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
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@@ -68787,7 +68792,7 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
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                     PointSize[0.5], 
                     AbsoluteThickness[1.6], 
-                    RGBColor[1, 0, 0], 
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@@ -68808,7 +68813,8 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
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                     AbsoluteThickness[1.6], 
-                    RGBColor[0, 0, 1], 
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@@ -68818,7 +68824,8 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     AbsoluteThickness[1.6], 
-                    RGBColor[0, 0, 1], 
+                    RGBColor[1, 0, 0], 
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@@ -68854,7 +68861,8 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0]]], 
                     PointSize[0.5], 
                     AbsoluteThickness[1.6], 
-                    RGBColor[0, 0, 1], 
+                    RGBColor[1, 0, 0], 
+                    Dashing[0.18], 
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@@ -68985,6 +68993,96 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
                     GrayLevel[0], Editable -> False, Selectable -> False], 
                     ",", 
                     RowBox[{"Thickness", "[", "0.01`", "]"}]}], "]"}], ",", 
+                   RowBox[{"Directive", "[", 
+                    RowBox[{
+                    RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
+                    ",", 
+                    RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                    InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[1, 0, 0], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
+                    False]], Appearance -> None, BaseStyle -> {}, 
+                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
+                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[1, 0, 0]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
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+                    RowBox[{"Thickness", "[", "0.01`", "]"}]}], "]"}], ",", 
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+                    RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                    InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0, 0, 1], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
+                    False]], Appearance -> None, BaseStyle -> {}, 
+                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
+                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0, 0, 1]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0, 0, 1], Editable -> False, Selectable -> 
+                    False], ",", 
+                    RowBox[{"Thickness", "[", "0.01`", "]"}]}], "]"}], ",", 
                    RowBox[{"Directive", "[", 
                     RowBox[{
                     RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
@@ -69030,51 +69128,6 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
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-                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
-                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
-                    Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
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-                    StyleBox[
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-                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
-                    False]], Appearance -> None, BaseStyle -> {}, 
-                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
-                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
-                    If[
-                    Not[
-                    AbsoluteCurrentValue["Deployed"]], 
-                    SelectionMove[Typeset`box$, All, Expression]; 
-                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
-                    FrontEnd`Private`$ColorSelectorInitialColor = 
-                    RGBColor[1, 0, 0]; 
-                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
-                    MathLink`CallFrontEnd[
-                    FrontEnd`AttachCell[Typeset`box$, 
-                    FrontEndResource["RGBColorValueSelector"], {
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-                    "ClosingActions" -> {
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                     RowBox[{
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@@ -69121,51 +69174,6 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
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                     RowBox[{"Dashing", "[", "0.02`", "]"}], ",", 
                     RowBox[{"Thickness", "[", "0.01`", "]"}]}], "]"}], ",", 
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-                    RectangleBox[{0, 0}]}, {
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-                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
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-                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
-                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
-                    Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
-                    AbsoluteCurrentValue[Magnification]}]], 
-                    StyleBox[
-                    RowBox[{"RGBColor", "[", 
-                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
-                    False]], Appearance -> None, BaseStyle -> {}, 
-                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
-                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
-                    If[
-                    Not[
-                    AbsoluteCurrentValue["Deployed"]], 
-                    SelectionMove[Typeset`box$, All, Expression]; 
-                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
-                    FrontEnd`Private`$ColorSelectorInitialColor = 
-                    RGBColor[0, 0, 1]; 
-                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
-                    MathLink`CallFrontEnd[
-                    FrontEnd`AttachCell[Typeset`box$, 
-                    FrontEndResource["RGBColorValueSelector"], {
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-                    "ClosingActions" -> {
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                    RowBox[{"Directive", "[", 
                     RowBox[{
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@@ -69364,9 +69372,10 @@ AeRhYPycAYE34vD4q7n/45ZxtqwDevwCAObl4Mw=
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+   3.792839520926496*^9, 3.792839572797037*^9}, 3.797870490842554*^9, 
+   3.797870662524585*^9},
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+  "Out[180]=",ExpressionUUID->"a872635c-12ae-45fc-9152-697c64904906"]
 }, Open  ]],
 
 Cell[CellGroupData[{
@@ -108191,7 +108200,7 @@ BgRkAhzetOV2G1ULObzYvp75OUeAw33XeMdZhgJw90Pig90BPX4AQ+WyZQ==
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 }, Open  ]]
 }, Closed]]
-}, Closed]],
+}, Open  ]],
 
 Cell[CellGroupData[{
 
@@ -108249,7 +108258,7 @@ Cell[BoxData[
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    3.792730679959948*^9}},
  CellLabel->
-  "In[160]:=",ExpressionUUID->"50f17805-7200-4b3c-b22f-93fe413f41d1"],
+  "In[155]:=",ExpressionUUID->"50f17805-7200-4b3c-b22f-93fe413f41d1"],
 
 Cell[BoxData[{
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@@ -129987,7 +129996,7 @@ Cell[BoxData[{
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  CellLabel->
-  "In[161]:=",ExpressionUUID->"c1653e8d-0575-4801-bc8f-798d7044242f"],
+  "In[156]:=",ExpressionUUID->"c1653e8d-0575-4801-bc8f-798d7044242f"],
 
 Cell[BoxData[
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    3.791022741662944*^9}},
  CellLabel->
-  "In[164]:=",ExpressionUUID->"9a7e4774-dffc-448a-afaa-994d57f46dce"]
+  "In[159]:=",ExpressionUUID->"9a7e4774-dffc-448a-afaa-994d57f46dce"]
 }, Closed]],
 
 Cell[CellGroupData[{
@@ -155803,7 +155812,7 @@ Cell[BoxData[{
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  CellLabel->
-  "In[165]:=",ExpressionUUID->"ff395d89-6534-42e4-9d67-65463ac7c5cb"],
+  "In[160]:=",ExpressionUUID->"ff395d89-6534-42e4-9d67-65463ac7c5cb"],
 
 Cell[BoxData[
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  CellLabel->
-  "In[168]:=",ExpressionUUID->"cf0e8cee-80b4-479d-a37e-48ee03d75c07"],
+  "In[163]:=",ExpressionUUID->"cf0e8cee-80b4-479d-a37e-48ee03d75c07"],
 
 Cell[BoxData[
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    3.791021432818749*^9, 3.791021433209086*^9}},
  CellLabel->
-  "In[169]:=",ExpressionUUID->"200b6655-02a0-4b98-91e6-d144e70af0d1"]
+  "In[164]:=",ExpressionUUID->"200b6655-02a0-4b98-91e6-d144e70af0d1"]
 }, Closed]],
 
 Cell[CellGroupData[{
@@ -200385,7 +200394,7 @@ Cell[BoxData[
 d012096d22b7"]
 }, Open  ]]
 }, Closed]]
-}, Open  ]],
+}, Closed]],
 
 Cell[CellGroupData[{
 
@@ -221673,7 +221682,7 @@ Cell[BoxData[
   "Out[243]//TableForm=",ExpressionUUID->"5ba94eff-f26d-4169-8793-\
 b1426af42038"]
 }, Open  ]]
-}, Open  ]],
+}, Closed]],
 
 Cell[CellGroupData[{
 
@@ -222215,7 +222224,7 @@ Cell[BoxData[
   "Out[238]//TableForm=",ExpressionUUID->"040db6b8-34e7-4660-bad1-\
 9cd4dbfb23b6"]
 }, Open  ]]
-}, Closed]],
+}, Open  ]],
 
 Cell[CellGroupData[{
 
@@ -222293,7 +222302,7 @@ Cell[BoxData[{
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   3.777634818487727*^9}, {3.777636029288138*^9, 3.7776360359034348`*^9}},
  CellLabel->
-  "In[239]:=",ExpressionUUID->"9b1b0edf-c4cf-43e3-9e3e-88d64f745542"],
+  "In[169]:=",ExpressionUUID->"9b1b0edf-c4cf-43e3-9e3e-88d64f745542"],
 
 Cell[BoxData[
  TagBox[
@@ -222318,65 +222327,63 @@ Cell[BoxData[
      {
       TagBox["\<\"\\!\\(\\*SubscriptBox[\\(E\\), \\(0\\)]\\)\"\>",
        HoldForm], 
-      RowBox[{"-", "0.0586553483508396312`3.768307618384302"}], 
-      RowBox[{"-", "0.0586335549276668644`3.7681462260740313"}], 
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-      "RowsIndexed" -> {}},
+    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}},
     GridBoxDividers->{
-     "Columns" -> {False, True, {False}, False}, "ColumnsIndexed" -> {}, 
-      "Rows" -> {False, True, {False}, False}, "RowsIndexed" -> {}},
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    {OutputFormsDump`HeadedRows, OutputFormsDump`HeadedColumns}],
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    TableForm[
@@ -222491,13 +222496,13 @@ Cell[BoxData[
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-   3.777636471058148*^9, 3.777718177365465*^9},
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 }, Open  ]]
-}, Closed]]
-}, Closed]],
+}, Open  ]]
+}, Open  ]],
 
 Cell[CellGroupData[{
 
@@ -256393,7 +256398,7 @@ Cell[BoxData[
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 }, Closed]],
 
 Cell[CellGroupData[{
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 }, Closed]],
 
 Cell[CellGroupData[{
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 }, Closed]]
 }, Open  ]],
 
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diff --git a/Response_Letter/Response_Letter.tex b/Response_Letter/Response_Letter.tex
index 74fe864..a2bdee4 100644
--- a/Response_Letter/Response_Letter.tex
+++ b/Response_Letter/Response_Letter.tex
@@ -184,16 +184,20 @@ 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{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.}
+	\alert{The legend of Fig.~2 was incorrect (the curves were mislabeled), but this has now been corrected.
+	In the new Fig.~2 (which is now Fig.~4 in the revised manuscript), this crossover has disappeared and the discussion is much more fluid:
+	when the weight of a state increases, this state is stabilized while the two others increases in energy (as it should).
+	The discussion regarding this figure has been modified accordingly.}
+%	\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.}
 
 	\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. }
diff --git a/Revised_Manuscript/EIvsW_n5.pdf b/Revised_Manuscript/EIvsW_n5.pdf
deleted file mode 100644
index 73ebd43..0000000
Binary files a/Revised_Manuscript/EIvsW_n5.pdf and /dev/null differ
diff --git a/Revised_Manuscript/EvsL_5.pdf b/Revised_Manuscript/EvsL_5.pdf
deleted file mode 100644
index 834cd0f..0000000
Binary files a/Revised_Manuscript/EvsL_5.pdf and /dev/null differ
diff --git a/Revised_Manuscript/EvsL_DD.pdf b/Revised_Manuscript/EvsL_DD.pdf
deleted file mode 100644
index c604936..0000000
Binary files a/Revised_Manuscript/EvsL_DD.pdf and /dev/null differ
diff --git a/Revised_Manuscript/EvsN.pdf b/Revised_Manuscript/EvsN.pdf
deleted file mode 100644
index 1510b7b..0000000
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diff --git a/Revised_Manuscript/EvsN_DD.pdf b/Revised_Manuscript/EvsN_DD.pdf
deleted file mode 100644
index 3b0ec1c..0000000
Binary files a/Revised_Manuscript/EvsN_DD.pdf and /dev/null differ
diff --git a/Revised_Manuscript/EvsW_n5.pdf b/Revised_Manuscript/EvsW_n5.pdf
deleted file mode 100644
index 7b12a9d..0000000
Binary files a/Revised_Manuscript/EvsW_n5.pdf and /dev/null differ
diff --git a/Revised_Manuscript/eDFT.tex b/Revised_Manuscript/eDFT.tex
index aebab09..cc3a8ca 100644
--- a/Revised_Manuscript/eDFT.tex
+++ b/Revised_Manuscript/eDFT.tex
@@ -867,7 +867,7 @@ Combining these, one can build the following three-state weight-dependent correl
 
 %%% FIG 1 %%%
 \begin{figure}
-	\includegraphics[width=0.7\linewidth]{embedding}
+	\includegraphics[width=0.7\linewidth]{fig1}
 	\caption{
 	\label{fig:embedding}
 	\titou{Schematic view of the ``embedding'' scheme: the two-electron finite uniform electron gas (the impurity) is embedded in the infinite uniform electron gas (the bath).
@@ -952,7 +952,7 @@ For small $L$, the system is weakly correlated, while strong correlation effects
 
 %%% FIG 1 %%%
 \begin{figure}
-	\includegraphics[width=\linewidth]{rho}
+	\includegraphics[width=\linewidth]{fig2}
 	\caption{
 	\titou{Ground-state one-electron density $\n{}{}(x)$ of 4-boxium (\ie, $N = 4$) for $L = \pi/32$ (left) and $L = 32\pi$ (right).
 	In the weak correlation regime (small box length), the one-electron density is much more delocalized and uniform than in the strong correlation regime (large box length), where a Wigner crystal starts to appear. \cite{Rogers_2017,Rogers_2016}}
@@ -996,7 +996,7 @@ equi-triensemble (or equal-weight state-averaged) limit where $\bw = (1/3,1/3)$.
 
 %%% FIG 1 %%%
 \begin{figure*}
-	\includegraphics[width=\linewidth]{EvsW_n5}
+	\includegraphics[width=\linewidth]{fig3}
 	\caption{
 	\label{fig:EvsW}
 	Deviation from linearity of the weight-dependent KS-eLDA ensemble energy $\E{eLDA}{(\ew{1},\ew{2})}$ with (dashed lines) and without (solid lines) ghost-interaction correction (GIC) for 5-boxium (\ie, $\nEl = 5$) with a box of length $L = \pi/8$ (left), $L = \pi$ (center), and $L = 8\pi$ (right).
@@ -1044,7 +1044,7 @@ Eqs.~\eqref{eq:min_with_HF_ener_fun} and \eqref{eq:WHF}].
 
 %%% FIG 2 %%%
 \begin{figure*}
-	\includegraphics[width=\linewidth]{EIvsW_n5}
+	\includegraphics[width=\linewidth]{fig4}
 	\caption{
 	\label{fig:EIvsW}
 	KS-eLDA individual energies, $\E{eLDA}{(0)}$ (black), $\E{eLDA}{(1)}$ (red), and $\E{eLDA}{(2)}$ (blue), as functions of the weights $\ew{1}$ (solid) and $\ew{2}$ (dashed) for 5-boxium (\ie, $\nEl = 5$) with a box of length $L = \pi/8$ (left), $L = \pi$ (center), and $L = 8\pi$ (right).}
@@ -1058,14 +1058,18 @@ energies, which is in agreement with
 the curvature of the GIC-eLDA ensemble energy discussed previously. Interestingly, the
 individual energies do not vary in the same way depending on the state
 considered and the value of the weights. 
-We see for example that, within the biensemble (\ie, $\ew{2}=0$), the energies of
-the ground and first excited-state increase with respect to the
+\titou{On one hand,} we see for example that, within the biensemble (\ie, $\ew{2}=0$), the energies of
+the ground and \titou{second} excited-state increase with respect to the
 first-excited-state weight $\ew{1}$, thus showing that, in this
 case, we
 ``deteriorate'' these states by optimizing the orbitals for the
-ensemble, rather than for each state separately. The reverse actually occurs for the ground state in the triensemble
-as $\ew{2}$ increases. The variations in the ensemble
-weights are essentially linear or quadratic. 
+ensemble, rather than for each state separately. 
+\titou{The singly excited state is, on the other hand, stabilize in the biensemble, which is reasonable as the weight associated with this state increases.
+For the triensemble, as $\ew{2}$ increases, the energy of the ground state increases, while the energy of the first excited state remains stable with a slight increase at large $L$. 
+The second excited state is obviously stabilized by the increase of its weight in the ensemble.
+These are all very sensible observations.}
+
+The variations in the ensemble weights are essentially linear or quadratic. 
 \manurev{This can be rationalized as follows. As readily seen from
 Eqs.~\eqref{eq:EI-eLDA} and \eqref{eq:ind_HF-like_ener}, the individual
 HF-like energies do not depend explicitly on the weights, which means
@@ -1081,23 +1085,25 @@ weights $\bw$ [see Eqs.~\eqref{eq:ens1RDM},
 \eqref{eq:ens_dens_from_ens_1RDM}, and
 \eqref{eq:decomp_ens_correner_per_part}], the latter contributions will contain both linear and quadratic terms in
 $\bw$, as evidenced by Eq.~\eqref{eq:Taylor_exp_DDisc_term} [see the second term on the right-hand
-side].} In the biensemble, the weight dependence of the first
-excitation energy is reduced as the correlation increases. On the other hand, switching from a bi- to a triensemble
+side].} 
+!!! In the biensemble, the weight dependence of the first
+excitation energy is \titou{increased?} as the correlation increases, \titou{while the weight dependence of the second excitation energy is reduced}. 
+On the other hand, switching from a bi- to a triensemble
 systematically enhances the weight dependence, due to the lowering of the
-ground-state energy, as $\ew{2}$ increases.         
-The reverse is observed for the second excited state. 
-\manurev{Finally, we notice that the crossover point of the 
+ground-state energy, as $\ew{2}$ increases.
+The reverse is observed for the second excited state.  !!! \titou{THIS PARAGRAPH MIGHT NEED MODIFICATIONS.}    
+\trashPFL{Finally, we notice that the crossover point of the 
 first-excited-state energies based on
 bi- and triensemble calculations, respectively, disappears in the strong correlation
 regime [see the right panel of Fig.~\ref{fig:EIvsW}], thus illustrating
 the importance of (individual and ensemble) densities, in
 addition to the  
 weights, in the evaluation of individual energies within
-an ensemble. 
+an ensemble.
 }
 %%% FIG 3 %%%
 \begin{figure}
-	\includegraphics[width=\linewidth]{EvsL_5}
+	\includegraphics[width=\linewidth]{fig5}
 	\caption{
 	\label{fig:EvsL}
 	Excitation energies (multiplied by $L^2$) associated with the single excitation $\Ex{}{(1)}$ (bottom) and double excitation $\Ex{}{(2)}$ (top) of 5-boxium for various methods and box lengths $L$.
@@ -1132,7 +1138,7 @@ This conclusion is verified for smaller and larger numbers of electrons
 
 %%% FIG 4 %%%
 \begin{figure*}
-	\includegraphics[width=\linewidth]{EvsN}
+	\includegraphics[width=\linewidth]{fig6}
 	\caption{
 	\label{fig:EvsN}
 	Error with respect to FCI in single and double excitation energies for $\nEl$-boxium for various methods and electron numbers $\nEl$ at $L=\pi/8$ (left), $L=\pi$ (center), and $L=8\pi$ (right).
@@ -1170,7 +1176,7 @@ electrons.
 
 %%% FIG 5 %%%
 \begin{figure*}
-	\includegraphics[width=\linewidth]{EvsL_DD}
+	\includegraphics[width=\linewidth]{fig7}
 	\caption{
 	\label{fig:EvsL_DD}
 	Error with respect to FCI (in \%) associated with the single excitation $\Ex{}{(1)}$ (bottom) and double excitation $\Ex{}{(2)}$ (top) as a function of the box length $L$ for 3-boxium (left), 5-boxium (center), and 7-boxium (right) at the KS-eLDA level with and without the contribution of the ensemble correlation derivative $\DD{c}{(I)}$.
@@ -1227,7 +1233,7 @@ shown).
 
 %%% FIG 6 %%%
 \begin{figure}
-	\includegraphics[width=\linewidth]{EvsN_DD}
+	\includegraphics[width=\linewidth]{fig8}
 	\caption{
 	\label{fig:EvsN_DD}
 	Error with respect to FCI in single and double excitation energies for $\nEl$-boxium (with a box length of $L=8\pi$) as a function of the number of electrons $\nEl$ at the KS-eLDA level with and without the contribution of the ensemble correlation derivative $\DD{c}{(I)}$. 
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