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     AxesOrigin -> {0, 0}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, DisplayFunction -> Identity, 
     PlotRangePadding -> {{
        Scaled[0.02], 
        Scaled[0.02]}, {
        Scaled[0.05], 
        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
     DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> 
     Identity, Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], 
     Method -> {
      "DefaultBoundaryStyle" -> Automatic, 
       "DefaultGraphicsInteraction" -> {
        "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
         "Effects" -> {
          "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
           "Droplines" -> {
            "freeformCursorMode" -> True, 
             "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
       "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None,
        "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& )}}, 
     PlotRange -> {{-3, 0}, {-2.17569115126694, 0.8402362019897942}}, 
     PlotRangeClipping -> True, PlotRangePadding -> {{
        Scaled[0.02], 
        Scaled[0.02]}, {
        Scaled[0.02], 
        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}], 
   FormBox[
    FormBox[
     TemplateBox[{
      "\"RHF_GS_min\"", "\"RHF_GS_max\"", "\"RHF_ES_min\"", "\"RHF_ES_max\"", 
       "\"sb_RHF\""}, "LineLegend", DisplayFunction -> (FormBox[
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         StyleBox[
          PaneBox[
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               TagBox[
                GridBox[{{
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
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                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
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                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
                    RGBColor[0.880722, 0.611041, 0.142051], 
                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
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                    GrayLevel[0]]], 
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                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
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                    EdgeForm[
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
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                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, {
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                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    Opacity[1.], 
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                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}}, 
                 GridBoxAlignment -> {
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                 AutoDelete -> False, 
                 GridBoxDividers -> {
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                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
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             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
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             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
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           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
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                    FrameStyle -> 
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                    FrontEnd`Private`$ColorSelectorInitialColor = 
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                    FrameStyle -> 
                    RGBColor[
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                    FrontEnd`Private`$ColorSelectorInitialColor = 
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For R>0 the sb-UHF solution is a minimum because the symmetry breaking \
minimize the repulsion and for R<0 this is a maximum because the symmetry \
breaking minimize the attraction.
For R>0 the sb-UHF 1 is the \[OpenCurlyDoubleQuote]bonding\
\[CloseCurlyDoubleQuote] solution and the sb-UHF 2 is the antibonding \
solution. There is a point a which the bonding solution becomes better than \
the ground state of the symmetric solution, and an other point at which the \
anti bonding solution becomes higher than the symetric solution.
We can do the same reasoning for R<0.\
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For R > 0:
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-the sb_UHF solution is a minimum and exist for R>3/2  before it is a \
holomorphic solution
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holomorphic solution
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Those points are the Coulson-Fischer points of the sb-RHF and sb-UHF \
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