Multiple solutions in GW

ShowPlot[Listofplots_,LabelPlot_,FontSizeLabel_,xLabel_,yLabel_,FontSizexyLabel_]:=Module[{ShowFrame},


ShowFrame=Show[Listofplots,Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,PlotLabel-> MaTeX[LabelPlot,FontSize->FontSizeLabel],
ImageSize->800,FrameLabel-> {
MaTeX[xLabel,FontSize->FontSizexyLabel],
MaTeX[yLabel,FontSize->FontSizexyLabel]
}];

Return[ShowFrame]];

PlotList[plot_,colorline_,rangeplot_,legend_,legendSize_,placement_,styleplot_]:=Module[{plotlist},

plotlist=ListPlot[plot,PlotStyle->{Directive[Thickness[0.006],colorline,styleplot]},PlotRange->rangeplot,InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{colorline,Thickness[0.01]}]},{MaTeX[legend,FontSize->legendSize]}],placement]];

Return[plotlist]];

TwoAxisPlot[{f_,g_},{x_,x1_,x2_}]:=Module[{fgraph,ggraph,frange,grange,fticks,gticks},{fgraph,ggraph}=MapIndexed[Plot[#,{x,x1,x2},Axes->True,PlotStyle->ColorData[1][#2[[1]]]]&,{f,g}];{frange,grange}=(PlotRange/.AbsoluteOptions[#,PlotRange])[[2]]&/@{fgraph,ggraph};fticks=N@FindDivisions[frange,5];
gticks=Quiet@Transpose@{fticks,ToString[NumberForm[#,2],StandardForm]&/@Rescale[fticks,frange,grange]};
Show[fgraph,ggraph/.Graphics[graph_,s___]:>Graphics[GeometricTransformation[graph,RescalingTransform[{{0,1},grange},{{0,1},frange}]],s],Axes->False,Frame->True,FrameStyle->{ColorData[1]/@{1,2},{Automatic,Automatic}},FrameTicks->{{fticks,gticks},{Automatic,Automatic}}]]

OptionsQP={PlotRange->{{0.95,1.35},{20,30}},InterpolationOrder->2,Joined->True};

OptionsZ={PlotRange->{{0.95,1.4},{-0.01,1}},InterpolationOrder->2,Joined->True};

R around 2.2 bohr (around 1.15 A)

unfold G0W0

unfsol=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["FFeG0W0"]*HaToeV,{k,0.95,1.35,0.01}];

unfsolQP=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["FFeG0W0"]*HaToeV,{k,0.95,1.18,0.01}];

unfsol5QP=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["FFeG0W0"]*HaToeV,{k,1.23,1.35,0.01}];

coordQP=Table[k,{k,0.95,1.22,0.01}];
(*unfsol4QP=Table[{coordQP[[l]],unfsolQP[[l,4]]},{l,1,Length[unfsolQP]}];*)
unfsol4QP=Table[{coordQP[[l]],unfsol[[l,4]]},{l,1,Length[coordQP]}];

coord5QP=Table[k,{k,1.23,1.35,0.01}];
(*unfsol5QP=Table[{coord5QP[[l]],unfsol5QP[[l,5]]},{l,1,Length[coord5QP]}];*)
unfsol5QP=Table[{coord5QP[[l]],unfsol5QP[[l,5]]},{l,1,Length[coord5QP]}];

unfZ=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["ZunfG0W0"],{k,0.95,1.35,0.01}];

coord=Table[k,{k,0.95,1.35,0.01}];

unfsol2=Table[{coord[[l]],unfsol[[l,2]]},{l,1,Length[unfsol]}];
unfsol3=Table[{coord[[l]],unfsol[[l,3]]},{l,1,Length[unfsol]}];
unfsol4=Table[{coord[[l]],unfsol[[l,4]]},{l,1,Length[unfsol]}];
unfsol5=Table[{coord[[l]],unfsol[[l,5]]},{l,1,Length[unfsol]}];
unfsol6=Table[{coord[[l]],unfsol[[l,6]]},{l,1,Length[unfsol]}];
unfsol7=Table[{coord[[l]],unfsol[[l,7]]},{l,1,Length[unfsol]}];
unfsol8=Table[{coord[[l]],unfsol[[l,8]]},{l,1,Length[unfsol]}];
unfsol9=Table[{coord[[l]],unfsol[[l,9]]},{l,1,Length[unfsol]}];

unfZ1=Table[{coord[[l]],unfZ[[l,1]]},{l,1,Length[unfZ]}];
unfZ2=Table[{coord[[l]],unfZ[[l,2]]},{l,1,Length[unfZ]}];
unfZ3=Table[{coord[[l]],unfZ[[l,3]]},{l,1,Length[unfZ]}];
unfZ4=Table[{coord[[l]],unfZ[[l,4]]},{l,1,Length[unfZ]}];
unfZ5=Table[{coord[[l]],unfZ[[l,5]]},{l,1,Length[unfZ]}];
unfZ6=Table[{coord[[l]],unfZ[[l,6]]},{l,1,Length[unfZ]}];
unfZ7=Table[{coord[[l]],unfZ[[l,7]]},{l,1,Length[unfZ]}];
unfZ8=Table[{coord[[l]],unfZ[[l,8]]},{l,1,Length[unfZ]}];
unfZ9=Table[{coord[[l]],unfZ[[l,9]]},{l,1,Length[unfZ]}];

unfplotsol3=ListPlot[unfsol3,PlotStyle->{Directive[Thickness[0.006],Yellow]},PlotLegends->Placed[LineLegend[{Directive[{Yellow,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°4}",FontSize->16]}],{After,Center}],OptionsQP];

unfplotsol4=ListPlot[unfsol4,PlotStyle->{Directive[Thickness[0.01],Blue]},PlotLegends->Placed[LineLegend[{Directive[{Blue,Thickness[0.02]}]},{MaTeX["\\textbf{(p=3, s=4)}",FontSize->24]}],{After,Center}],OptionsQP];

unfplotsol4QP=ListPlot[unfsol4QP,PlotStyle->{Directive[Thickness[0.02],Blue,Opacity[0.5]]},PlotRange->{{0.95,1.35},{20,30}},InterpolationOrder->2,Joined->True];

unfplotsol5=ListPlot[unfsol5,PlotStyle->{Directive[Thickness[0.01],Red]},PlotLegends->Placed[LineLegend[{Directive[{Red,Thickness[0.02]}]},{MaTeX["\\textbf{(p=3, s=5)}",FontSize->24]}],{After,Center}],OptionsQP];

unfplotsol5QP=ListPlot[unfsol5QP,PlotStyle->{Directive[Thickness[0.02],Red,Opacity[0.5]]},PlotRange->{{1.25,1.35},{20,30}},InterpolationOrder->2,Joined->True];

unfplotsol6=ListPlot[unfsol6,PlotStyle->{Directive[Thickness[0.006],Red]},PlotLegends->Placed[LineLegend[{Directive[{Red,Thickness[0.01]}]},{MaTeX["\\textbf{(p=3, s=6)}",FontSize->16]}],{After,Center}],OptionsQP];

unfplotsol7=ListPlot[unfsol7,PlotStyle->{Directive[Thickness[0.006],Purple]},PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°7}",FontSize->16]}],{After,Center}],OptionsQP];

unfplotsol8=ListPlot[unfsol8,PlotStyle->{Directive[Thickness[0.006],Black]},PlotLegends->Placed[LineLegend[{Directive[{Black,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°8}",FontSize->16]}],{After,Center}],OptionsQP];

unfplotsol9=ListPlot[unfsol9,PlotStyle->{Directive[Thickness[0.006],Darker[Green]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°9}",FontSize->16]}],{After,Center}],OptionsQP];

unfPlotZ4=ListPlot[unfZ4,PlotStyle->{Directive[Thickness[0.006],Blue]},PlotLegends->Placed[LineLegend[{Directive[{Blue,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°4}",FontSize->16]}],{After,Center}],OptionsZ];

unfPlotZ5=ListPlot[unfZ5,PlotStyle->{Directive[Thickness[0.006],Orange]},PlotLegends->Placed[LineLegend[{Directive[{Orange,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°5}",FontSize->16]}],{After,Center}],OptionsZ];

unfPlotZ6=ListPlot[unfZ6,PlotStyle->{Directive[Thickness[0.006],Red]},PlotLegends->Placed[LineLegend[{Directive[{Red,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°6}",FontSize->16]}],{After,Center}],OptionsZ];

unfPlotZ7=ListPlot[unfZ7,PlotStyle->{Directive[Thickness[0.006],Purple]},PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°7}",FontSize->16]}],{After,Center}],OptionsZ];

unfPlotZ8=ListPlot[unfZ8,PlotStyle->{Directive[Thickness[0.006],Black]},PlotLegends->Placed[LineLegend[{Directive[{Black,Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°8}",FontSize->16]}],{After,Center}],OptionsZ];

unfPlotZ9=ListPlot[unfZ9,PlotStyle->{Directive[Thickness[0.006],Darker[Green]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.01]}]},{MaTeX["\\textbf{p=3 sol n°9}",FontSize->16]}],{After,Center}],OptionsZ];

Show[{unfplotsol4,unfplotsol5},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,PlotLabel-> MaTeX["\\textbf{\\ce{H2}~/~6-31G}",FontSize->24],
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R} ~\\textbf{(\\AA)}",FontSize->22],
MaTeX["\\bm{\\epsilon}_{\\textbf{p}}  \\textbf{(eV)}",FontSize->22]
}];

Show[{ResourceFunction["MultipleAxesListPlot"][{unfsol4,unfZ4},Joined->True,PlotStyle->{Directive[Blue,Thickness[0.01]],Directive[CapForm["Butt"],Thickness[0.013],Blue,Dashed]},PlotRange-> {22,30},"SecondaryPlotRange"-> {0,1},PlotLegends->{Placed[LineLegend[{Directive[{Blue,Thickness[0.02]}]},{MaTeX["\\textbf{(p=3, s=4)}",FontSize->24]}],{After,Center}](*,Placed[LineLegend[{Directive[{CapForm["Butt"],Blue,Thickness[0.01],Dashed}]},{MaTeX["\\textbf{p=3 sol n°4}",FontSize->16]}],{After,Center}]*)}],

ResourceFunction["MultipleAxesListPlot"][{unfsol4,unfZ5},Joined->True,
PlotStyle->{Blue,Directive[CapForm["Butt"],Thickness[0.013],Red,Dashed]},PlotRange-> {22,30},"SecondaryPlotRange"-> {0,1},PlotLegends->{Placed[LineLegend[{Directive[{Red,Thickness[0.02]}]},{MaTeX["\\textbf{(p=3, s=5)}",FontSize->24]}],{After,Center}](*,Placed[LineLegend[{Directive[{CapForm["Butt"],Red,Thickness[0.01],Dashed}]},{MaTeX["\\textbf{p=3 sol n°5}",FontSize->16]}],{After,Center}]*)}],ListPlot[unfsol5,PlotStyle->{Directive[Thickness[0.01],Red]},Joined->True],
unfplotsol4QP,unfplotsol5QP}

,Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,(*PlotLabel-> MaTeX["\\textbf{\\ce{H2}~/~6-31G}",FontSize->24],*)
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\epsilon}_{\\textbf{p,s}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24],None,MaTeX["\\bm{Z}_{\\textbf{p,s}}",FontSize->24]}]

(*η=0.01*)
soleta0dot01=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"][[3]]*HaToeV},{k,0.95,1.35,0.01}];

(*η=0.1*)
soleta0dot1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"][[1]]*HaToeV},{k,0.95,1.35,0.01}];

(*η=1*)
soleta1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"][[1]]*HaToeV},{k,0.95,1.35,0.01}];

(*η=10*)
soleta10=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"][[1]]*HaToeV},{k,0.95,1.35,0.01}];

Plotsoleta0dot01=ListPlot[soleta0dot01,PlotStyle->{Directive[Thickness[0.007],Brown,Dotted]},PlotRange->{{0.95,1.3},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Brown,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\eta=0.01}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

Plotsoleta0dot1=ListPlot[soleta0dot1,PlotStyle->{Directive[Thickness[0.007],Darker[Green],Dotted]},PlotRange->{{0.95,1.3},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\eta=0.1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

Plotsoleta1=ListPlot[soleta1,PlotStyle->{Directive[Thickness[0.007],Orange,Dotted]},PlotRange->{{0.95,1.3},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Orange,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\eta=1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

Plotsoleta10=ListPlot[soleta10,PlotStyle->{Directive[Thickness[0.007],Purple,Dotted]},PlotRange->{{0.95,1.3},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\eta=10}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

Show[{unfplotsol4,unfplotsol4QP,unfplotsol5QP,unfplotsol5,(*Plotsoleta0dot01,*)Plotsoleta0dot1,Plotsoleta1,Plotsoleta10},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,PlotLabel-> MaTeX["f_{\\eta}(\\Delta)=(\\Delta \\pm i\\eta)^{-1}",FontSize->24],
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\epsilon}_{\\textbf{p,s}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24]
}]

(*η=0.01*)
RegEvangel0dot01=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.95,1.35,0.01}];

(*η=0.1*)
RegEvangel0dot1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.95,1.35,0.01}];

(*η=1*)
RegEvangel1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.95,1.35,0.01}];

(*η=10*)
RegEvangel10=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.95,1.35,0.01}];

PlotRegEvangel0dot01=ListPlot[RegEvangel0dot01,PlotStyle->{Directive[Thickness[0.007],Brown,Dotted]},PlotRange->{{0.95,1.35},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Thickness[0.01],Brown,Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\kappa=0.01}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotRegEvangel0dot1=ListPlot[RegEvangel0dot1,PlotStyle->{Directive[Thickness[0.007],Darker[Green],Dotted]},PlotRange->{{0.95,1.35},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Thickness[0.01],Darker[Green],Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\kappa=0.1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotRegEvangel1=ListPlot[RegEvangel1,PlotStyle->{Directive[Thickness[0.007],Orange,Dotted]},PlotRange->{{0.95,1.35},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Thickness[0.01],Orange,Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\kappa=1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotRegEvangel10=ListPlot[RegEvangel10,PlotStyle->{Directive[Thickness[0.007],Purple,Dotted]},PlotRange->{{0.95,1.35},{20,30}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Thickness[0.01],Purple,Dotted}]},{MaTeX["\\textbf{(p=3},\\bm{\\kappa=10}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

Show[{unfplotsol4,unfplotsol4QP,unfplotsol5,unfplotsol5QP,(*PlotRegEvangel0dot01,*)PlotRegEvangel0dot1,PlotRegEvangel1,PlotRegEvangel10},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,PlotLabel-> MaTeX["f_{\\kappa}(\\Delta)=(1-e^{-2\\Delta^2/\\kappa^2})/\\Delta",FontSize->24],
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->22],
MaTeX["\\bm{\\epsilon}_{\\textbf{p,s}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->22]}]

R around 1.0 bohr (around 0.5 A)

sol=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["FFeG0W0"]*HaToeV,{k,0.40,0.65,0.01}];

solQP7=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["FFeG0W0"]*HaToeV,{k,0.40,0.49,0.01}];

solQP6=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["FFeG0W0"]*HaToeV,{k,0.49,0.49,0.01}];

solQP5=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["FFeG0W0"]*HaToeV,{k,0.49,0.65,0.01}];

coordQP5=Table[k,{k,0.49,0.65,0.01}];
sol5QP=Table[{coordQP5[[l]],solQP5[[l,5]]},{l,1,Length[solQP5]}];

coordQP6=Table[k,{k,0.49,0.50,0.01}];
sol6QP=Table[{coordQP6[[l]],solQP6[[l,6]]},{l,1,Length[solQP6]}];

coordQP7=Table[k,{k,0.40,0.49,0.01}];
sol7QP=Table[{coordQP7[[l]],solQP7[[l,7]]},{l,1,Length[solQP7]}];

Z=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","unfG0W0"},True,False]["ZunfG0W0"],{k,0.40,0.65,0.01}];

coord=Table[k,{k,0.40,0.65,0.01}];

sol4=Table[{coord[[l]],sol[[l,4]]},{l,1,Length[sol]}];
sol5=Table[{coord[[l]],sol[[l,5]]},{l,1,Length[sol]}];
sol6=Table[{coord[[l]],sol[[l,6]]},{l,1,Length[sol]}];
sol7=Table[{coord[[l]],sol[[l,7]]},{l,1,Length[sol]}];
sol8=Table[{coord[[l]],sol[[l,8]]},{l,1,Length[sol]}];
sol9=Table[{coord[[l]],sol[[l,9]]},{l,1,Length[sol]}];

coord=Table[k,{k,0.40,0.65,0.01}];

Z1=Table[{coord[[l]],Z[[l,1]]},{l,1,Length[Z]}];
Z2=Table[{coord[[l]],Z[[l,2]]},{l,1,Length[Z]}];
Z3=Table[{coord[[l]],Z[[l,3]]},{l,1,Length[Z]}];
Z4=Table[{coord[[l]],Z[[l,4]]},{l,1,Length[Z]}];
Z5=Table[{coord[[l]],Z[[l,5]]},{l,1,Length[Z]}];
Z6=Table[{coord[[l]],Z[[l,6]]},{l,1,Length[Z]}];
Z7=Table[{coord[[l]],Z[[l,7]]},{l,1,Length[Z]}];
Z8=Table[{coord[[l]],Z[[l,8]]},{l,1,Length[Z]}];
Z9=Table[{coord[[l]],Z[[l,9]]},{l,1,Length[Z]}];

plotsol4=ListPlot[sol4,PlotStyle->{Directive[Thickness[0.01],Blue]},PlotRange->{{0.30,0.65},{40,67}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Blue,Thickness[0.01]}]},{MaTeX["\\textbf{p=4 sol n°5}",FontSize->24]}],{After,Center}]];

plotsol5=ListPlot[sol5,PlotStyle->{Directive[Thickness[0.01],Blue]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Blue,Thickness[0.02]}]},{MaTeX["\\textbf{(p=4, s=5)}",FontSize->24]}],{After,Center}]];

plotsol5QP=ListPlot[sol5QP,PlotStyle->{Directive[Thickness[0.02],Blue,Opacity[0.5]]},PlotRange->{{0.55,0.65},{40,60}},InterpolationOrder->2,Joined->True];

plotZ5=ListPlot[Z5,PlotStyle->{Directive[Thickness[0.006],Blue]},PlotRange->{{0.40,0.65},All},(*InterpolationOrder->3,*)Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Blue,Thickness[0.01]}]},{MaTeX["\\textbf{p=4 sol n°5}",FontSize->16]}],{After,Center}]];

plotsol6=ListPlot[sol6,PlotStyle->{Directive[Thickness[0.01],Red]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Red,Thickness[0.02]}]},{MaTeX["\\textbf{(p=4, s=6)}",FontSize->24]}],{After,Center}]];

plotsol6QP=ListPlot[sol6QP,PlotStyle->{Directive[Thickness[0.02],Red,Opacity[0.5],PlotMarkers-> None]},PlotRange->{{0.50,0.55},{40,60}},InterpolationOrder->2,Joined->True];

plotZ6=ListPlot[Z6,PlotStyle->{Directive[Thickness[0.006],Orange]},PlotRange->{{0.40,0.65},All},(*InterpolationOrder->3,*)Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Orange,Thickness[0.01]}]},{MaTeX["\\textbf{p=4 sol n°6}",FontSize->16]}],{After,Center}]];

plotsol7=ListPlot[sol7,PlotStyle->{Directive[Thickness[0.01],Darker[Green]]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.02]}]},{MaTeX["\\textbf{(p=4, s=7)}",FontSize->24]}],{After,Center}]];

plotsol7QP=ListPlot[sol7QP,PlotStyle->{Directive[Thickness[0.02],Darker[Green],Opacity[0.5]]},PlotRange->{{0.40,0.50},{40,60}},InterpolationOrder->2,Joined->True];

plotZ7=ListPlot[Z7,PlotStyle->{Directive[Thickness[0.006],Darker[Green]]},PlotRange->{{0.30,0.65},All},(*InterpolationOrder->3,*)Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.01]}]},{MaTeX["\\textbf{p=4 sol n°7}",FontSize->16]}],{After,Center}]];

plotsol8=ListPlot[sol8,PlotStyle->{Directive[Thickness[0.006],Red]},PlotRange->{{0.30,0.65},{40,67}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Red,Thickness[0.01]}]},{MaTeX["\\textbf{p=4 sol n°8}",FontSize->16]}],{After,Center}]];

plotZ8=ListPlot[Z8,PlotStyle->{Directive[Thickness[0.006],Red]},PlotRange->{{0.30,0.65},All},(*InterpolationOrder->3,*)Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Red,Thickness[0.01]}]},{MaTeX["\\textbf{p=4 sol n°8}",FontSize->16]}],{After,Center}]];

Show[{plotsol5,plotsol6,plotsol7},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,PlotLabel-> MaTeX["\\textbf{\\ce{H2}~/~6-31G}",FontSize->24],
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R} ~\\textbf{(\\AA)}",FontSize->22],
MaTeX["\\bm{\\epsilon}_{\\textbf{p}}  \\textbf{(eV)}",FontSize->22]
},PlotRange->{{0.40,0.65},{40,67}}];

Show[{ResourceFunction["MultipleAxesListPlot"][{sol5,Z5},Joined->True,PlotStyle->{Directive[Blue,Thickness[0.01]],Directive[CapForm["Butt"],Thickness[0.013],Blue,Dashed]},PlotRange-> {40,60},"SecondaryPlotRange"-> {0,1},PlotLegends->{Placed[LineLegend[{Directive[{Blue,Thickness[0.02]}]},{MaTeX["\\textbf{(p=4, s=5)}",FontSize->24]}],{After,Center}]}],

ResourceFunction["MultipleAxesListPlot"][{sol6,Z6},Joined->True,
PlotStyle->{Directive[Red,Thickness[0.01]],Directive[CapForm["Butt"],Thickness[0.013],Red,Dashed]},PlotRange-> {40,60},"SecondaryPlotRange"-> {0,1},PlotLegends->{Placed[LineLegend[{Directive[{Red,Thickness[0.02]}]},{MaTeX["\\textbf{(p=4, s=6)}",FontSize->24]}],{After,Center}]}],

ResourceFunction["MultipleAxesListPlot"][{sol7,Z7},Joined->True,
PlotStyle->{Directive[Darker[Green],Thickness[0.01]],Directive[CapForm["Butt"],Thickness[0.013],Darker[Green],Dashed]},PlotRange-> {40,60},"SecondaryPlotRange"-> {0,1},PlotLegends->{Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.02]}]},{MaTeX["\\textbf{(p=4, s=7)}",FontSize->24]}],{After,Center}]}],
plotsol7QP,plotsol6QP,plotsol5QP}

,Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\epsilon}_{\\textbf{p,s}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24],None,MaTeX["\\bm{Z}_{\\textbf{p,s}}",FontSize->24]}]

(*η=0.01*)
Regsoleta0dot01=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

(*η=0.1*)
Regsoleta0dot1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

(*η=1*)
Regsoleta1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

(*η=10*)
Regsoleta10=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

PlotRegsoleta0dot01=ListPlot[Regsoleta0dot01,PlotStyle->{Directive[Thickness[0.007],Brown,Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Brown,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\eta=0.01}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotRegsoleta0dot1=ListPlot[Regsoleta0dot1,PlotStyle->{Directive[Thickness[0.007],Darker[Green],Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\eta=0.1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotRegsoleta1=ListPlot[Regsoleta1,PlotStyle->{Directive[Thickness[0.007],Orange,Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Orange,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\eta=1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotRegsoleta10=ListPlot[Regsoleta10,PlotStyle->{Directive[Thickness[0.007],Purple,Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\eta=10}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

Show[{plotsol5,plotsol6,plotsol7,plotsol7QP,plotsol5QP,plotsol6QP(*,PlotRegsoleta0dot01*),PlotRegsoleta0dot1,PlotRegsoleta1,PlotRegsoleta10},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,PlotLabel-> MaTeX["f_{\\eta}(\\Delta)=(\\Delta \\pm i\\eta)^{-1}",FontSize->24],
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->22],
MaTeX["\\bm{\\epsilon}_{\\textbf{p,s}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->22]}]

(*η=0.01*)
Evangel0dot01=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

(*η=0.1*)
Evangel0dot1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

(*η=1*)
Evangel1=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

(*η=10*)
Evangel10=Table[{k,MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0w"]*HaToeV},{k,0.40,0.65,0.01}];

PlotEvangel0dot01=ListPlot[Evangel0dot01,PlotStyle->{Directive[Thickness[0.007],Brown,Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Brown,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\kappa=0.01}\\textbf{)}",FontSize->24]}],{After,Center}]];

PlotEvangel0dot1=ListPlot[Evangel0dot1,PlotStyle->{Directive[Thickness[0.007],Darker[Green],Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Darker[Green],Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\kappa=0.1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotEvangel1=ListPlot[Evangel1,PlotStyle->{Directive[Thickness[0.007],Orange,Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Orange,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\kappa=1}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

PlotEvangel10=ListPlot[Evangel10,PlotStyle->{Directive[Thickness[0.007],Purple,Dotted]},PlotRange->{{0.40,0.65},{40,60}},InterpolationOrder->2,Joined->True,
PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01],Dotted}]},{MaTeX["\\textbf{(p=4},\\bm{\\kappa=10}~\\textbf{au)}",FontSize->24]}],{After,Center}]];

Show[{plotsol5,plotsol7QP,plotsol6,plotsol6QP,plotsol7,plotsol5QP(*,PlotEvangel0dot01,*),PlotEvangel0dot1,PlotEvangel1,PlotEvangel10},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,PlotLabel-> MaTeX["f_{\\kappa}(\\Delta)=(1-e^{-2\\Delta^2/\\kappa^2})/\\Delta",FontSize->24],
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\epsilon}_{\\textbf{p,s}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24]}]

eG0W0

eG0W0=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

eG0W0w=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","dynGOWO"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

coord=Table[k,{k,0.25,1.28,0.01}];

eG0W01=Table[{coord[[l]],eG0W0[[l,1]]},{l,Length[eG0W0]}];
eG0W02=Table[{coord[[l]],eG0W0[[l,2]]},{l,Length[eG0W0]}];
eG0W03=Table[{coord[[l]],eG0W0[[l,3]]},{l,Length[eG0W0]}];
eG0W04=Table[{coord[[l]],eG0W0[[l,4]]},{l,Length[eG0W0]}];

eG0W03first={{0.25`,15.648495823987071`},{0.26`,15.729434188026525`},{0.27`,15.810724212940952`},{0.28`,15.892309505544603`},{0.29`,15.974142257634208`},{0.3`,16.056184702078344`},{0.31`,16.138410270475056`},{0.32`,16.220804329435616`},{0.33`,16.303364433591202`},{0.33999999999999997`,16.386100088234592`},{0.35`,16.469032062296588`},{0.36`,16.55219131981705`},{0.37`,16.635617662926904`},{0.38`,16.71935849358009`},{0.39`,16.803465919726445`},{0.4`,16.887996990952203`},{0.41000000000000003`,16.973010849923828`},{0.42000000000000004`,17.058567590317956`},{0.43`,17.144726959551754`},{0.44`,17.231547247969473`},{0.45`,17.31908437305157`},{0.45999999999999996`,17.407391154650277`},{0.47`,17.496516769529403`},{0.48`,17.5865063656053`},{0.49`,17.677400814678638`},{0.5`,17.769236578111176`},{0.51`,17.862045663890658`},{0.52`,17.955855650986592`},{0.53`,18.050689762899886`},{0.54`,18.146566972916048`},{0.55`,18.24350212800931`},{0.56`,18.341506079985933`},{0.5700000000000001`,18.440585815896718`},{0.5800000000000001`,18.54074458312526`},{0.5900000000000001`,18.641982004321616`},{0.6000000000000001`,18.744294180689185`},{0.61`,18.84767378314477`},{0.62`,18.952110130968336`},{0.63`,19.057589258674763`},{0.64`,19.164093973093397`},{0.65`,19.271603900208422`},{0.66`,19.38009552576521`},{0.6699999999999999`,19.489542227835933`},{0.6799999999999999`,19.599914305349895`},{0.69`,19.711179001679305`},{0.7`,19.823300525714057`},{0.71`,19.936240069511747`},{0.72`,20.04995582500877`},{0.73`,20.164402998243364`},{0.74`,20.279533822315322`},{0.75`,20.395297569615288`},{0.76`,20.511640561609887`},{0.77`,20.628506177525136`},{0.78`,20.7458348599292`},{0.79`,20.86356411855063`},{0.8`,20.98162852899529`},{0.81`,21.09995972780673`},{0.8200000000000001`,21.21848640050265`},{0.83`,21.337134262223213`},{0.84`,21.455826028438064`},{0.85`,21.574481373429844`},{0.86`,21.693016873118246`},{0.87`,21.81134592892614`},{0.88`,21.929378667275422`},{0.89`,22.047021809513524`},{0.9`,22.164178504391124`},{0.91`,22.28074811386431`},{0.92`,22.396625940777398`},{0.93`,22.511702883330766`},{0.9400000000000001`,22.625864998722093`},{0.9500000000000001`,22.738992950395776`},{0.96`,22.850961311096846`},{0.97`,22.961637680858736`},{0.98`,23.070881571583683`},{0.99`,23.178542994023655`},{1.`,23.28446066315377`},{1.01`,23.38845971618522`},{1.02`,23.49034880195755`},{1.03`,23.589916362334495`},{1.04`,23.686925872180534`},{1.05`,23.78110974013353`},{1.06`,23.8721614973261`},{1.07`,23.959725822071835`},{1.08`,24.043385882109728`},{1.0899999999999999`,24.122647478244303`},{1.1`,24.196919623110617`},{1.1099999999999999`,24.265491691253306`},{1.12`,24.32750844455821`},{1.13`,24.38194658243859`},{1.1400000000000001`,24.427600588100905`}};

eG0W03second={{1.15`,26.50956495038344`},{1.1600000000000001`,26.416468719042314`},{1.17`,26.335188484302883`},{1.1800000000000002`,26.266997110930383`},{1.19`,26.21273772074084`},{1.2000000000000002`,26.172606539212133`},{1.21`,26.146055175747247`},{1.22`,26.131865443649932`},{1.23`,26.12836451975798`},{1.24`,26.133687381409008`},{1.25`,26.14599849068642`},{1.26`,26.163632147006126`},{1.27`,26.185155246674334`},{1.28`,26.209376355477318`}};

eG0W04first={{0.25`,73.1658781429719`},{0.26`,71.81760743991371`},{0.27`,70.51462959958658`},{0.28`,69.25620241982433`},{0.29`,68.04135008623385`},{0.3`,66.86896061557889`},{0.31`,65.73787812213749`},{0.32`,64.64699091243413`},{0.33`,63.59531707724171`},{0.33999999999999997`,62.582090042132165`},{0.35`,61.606847348380334`},{0.36`,60.66952657003674`},{0.37`,59.770572199406836`},{0.38`,58.91105625836908`},{0.39`,58.09280272271226`},{0.4`,57.31851046082652`},{0.41000000000000003`,56.591807303239825`},{0.42000000000000004`,55.91715379403642`},{0.43`,55.29944563087232`},{0.44`,54.743178903658944`},{0.45`,54.25121291078142`},{0.45999999999999996`,53.82352457916883`},{0.47`,53.456623674648384`},{0.48`,53.14405587593118`}};

eG0W04second ={{0.49`,48.98628833730924`},{0.5`,48.75287362874032`},{0.51`,48.56093318441592`},{0.52`,48.40771611357907`},{0.53`,48.2870082290667`},{0.54`,48.192090369614796`}};

eG0W04third={{0.55`,43.86976118129043`},{0.56`,43.376001253157455`},{0.5700000000000001`,42.880311749180166`},{0.5800000000000001`,42.38616248655124`},{0.5900000000000001`,41.896068529642186`},{0.6000000000000001`,41.41185177932022`},{0.61`,40.93483068925511`},{0.62`,40.46595554837813`},{0.63`,40.00590478969797`},{0.64`,39.55515397079247`},{0.65`,39.11402566319189`},{0.66`,38.68272595443338`},{0.6699999999999999`,38.26137148047547`},{0.6799999999999999`,37.850009682052075`},{0.69`,37.4486341652224`},{0.7`,37.05719646938071`},{0.71`,36.675615180730425`},{0.72`,36.303783050474124`},{0.73`,35.94157260492807`},{0.74`,35.58884059793676`},{0.75`,35.24543157261558`},{0.76`,34.91118072378243`},{0.77`,34.58591621586789`},{0.78`,34.269461064700295`},{0.79`,33.96163467590905`},{0.8`,33.662254105080066`},{0.81`,33.37113509503917`},{0.8200000000000001`,33.08809293168844`},{0.83`,32.81294315263223`},{0.84`,32.54550213510008`},{0.85`,32.28558758531695`},{0.86`,32.03301894533019`},{0.87`,31.78761773288441`},{0.88`,31.549207824447837`},{0.89`,31.317615691434657`},{0.9`,31.092670596454674`},{0.91`,30.874204756163888`},{0.92`,30.662053475134968`},{0.93`,30.4560552548401`},{0.9400000000000001`,30.256051882897662`},{0.9500000000000001`,30.061888500970497`},{0.96`,29.87341365872898`},{0.97`,29.690479351757944`},{0.98`,29.51294104661136`},{0.99`,29.340657694676285`},{1.`,29.17349173430112`},{1.01`,29.011309084338347`},{1.02`,28.85397912745622`},{1.03`,28.701374686165373`},{1.04`,28.553371990865767`},{1.05`,28.409850641016412`},{1.06`,28.27069355947179`},{1.07`,28.135786942121868`},{1.08`,28.005020200304482`},{1.0899999999999999`,27.878285900373772`},{1.1`,27.755479697021418`},{1.1099999999999999`,27.63650026409261`},{1.12`,27.5212492215772`},{1.13`,27.409631058329673`},{1.1400000000000001`,27.30155305434841`},{1.15`,27.196925198950996`},{1.1600000000000001`,27.095660108586166`},{1.17`,26.997672941775033`},{1.1800000000000002`,26.90288131451287`},{1.19`,26.811205213704078`},{1.2000000000000002`,26.722566911815072`},{1.21`,26.636890879393622`},{1.22`,26.554103700060875`},{1.23`,26.474133984096028`},{1.24`,26.3969122851722`},{1.25`,26.322371015126016`},{1.26`,26.250444363318827`},{1.27`,26.181068215091845`},{1.28`,26.1141800726269`}};

PloteG0W01=ListPlot[eG0W01,PlotStyle->{Directive[Thickness[0.006],Black]},PlotLegends->Placed[LineLegend[{Directive[{Black,Thickness[0.01]}]},{MaTeX["\\textbf{HOMO (p=1)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W02=ListPlot[eG0W02,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Cyan],Thickness[0.01]}]},{MaTeX["\\textbf{LUMO (p=2)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W03=ListPlot[eG0W03,PlotStyle->{Directive[Thickness[0.006],Gray]},PlotLegends->Placed[LineLegend[{Directive[{Gray,Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+1 (p=3)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W03first=ListPlot[eG0W03first,PlotStyle->{Directive[Thickness[0.006],Gray]},PlotLegends->Placed[LineLegend[{Directive[{Gray,Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+1 (p=3)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W03second=ListPlot[eG0W03second,PlotStyle->{Directive[Thickness[0.004],Gray]},InterpolationOrder->2,Joined->True];

PloteG0W04=ListPlot[eG0W04,PlotStyle->{Directive[Thickness[0.006],Purple]},PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.005]}]},{MaTeX["\\textbf{LUMO+2 (p=4)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W04first=ListPlot[eG0W04first,PlotStyle->{Directive[Thickness[0.006],Purple]},PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+2 (p=4)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W04second=ListPlot[eG0W04second,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True];

PloteG0W04third=ListPlot[eG0W04third,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True];

Show[{PloteG0W01,PloteG0W02,PloteG0W03first,PloteG0W03second,PloteG0W04first,PloteG0W04second,PloteG0W04third},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,(*PlotLabel-> MaTeX["\\textbf{\\ce{H2}~/~6-31G}",FontSize->24],*)
ImageSize->800,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\epsilon}_{\\textbf{p}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24]
},PlotRange->{{0.27,1.25},{-20,75}},Axes->False]

(*κ=1*)
eG0W0Reg1=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

coord=Table[k,{k,0.25,1.28,0.01}];

eG0W01Reg1=Table[{coord[[l]],eG0W0Reg1[[l,1]]},{l,Length[eG0W0Reg1]}];
eG0W02Reg1=Table[{coord[[l]],eG0W0Reg1[[l,2]]},{l,Length[eG0W0Reg1]}];
eG0W03Reg1=Table[{coord[[l]],eG0W0Reg1[[l,3]]},{l,Length[eG0W0Reg1]}];
eG0W04Reg1=Table[{coord[[l]],eG0W0Reg1[[l,4]]},{l,Length[eG0W0Reg1]}];

PloteG0W01Reg1=ListPlot[eG0W01Reg1,PlotStyle->{Directive[Thickness[0.006],Black]},PlotLegends->Placed[LineLegend[{Directive[{Black,Thickness[0.01]}]},{MaTeX["\\textbf{HOMO~(p=1},\\bm{\\kappa=1}~\\textbf{au)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W02Reg1=ListPlot[eG0W02Reg1,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Cyan],Thickness[0.01]}]},{MaTeX["\\textbf{LUMO~(p=2},\\bm{\\kappa=1}~\\textbf{au)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W03Reg1=ListPlot[eG0W03Reg1,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Gray],Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+1~(p=3},\\bm{\\kappa=1}~\\textbf{au)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W04Reg1=ListPlot[eG0W04Reg1,PlotStyle->{Directive[Thickness[0.006],Purple]},PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+2~(p=4},\\bm{\\kappa=1}~\\textbf{au)} ",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

Show[{PloteG0W01Reg1,PloteG0W02Reg1,PloteG0W03Reg1,PloteG0W04Reg1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,
ImageSize->900,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\tilde{\\epsilon}}_{\\textbf{p}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24]
},PlotRange->{{0.27,1.25},{-20,75}},Axes->False]

(*η=1*)
eG0W0Regeta1=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

coord=Table[k,{k,0.25,1.28,0.01}];

eG0W01Regeta1=Table[{coord[[l]],eG0W0Regeta1[[l,1]]},{l,Length[eG0W0Regeta1]}];
eG0W02Regeta1=Table[{coord[[l]],eG0W0Regeta1[[l,2]]},{l,Length[eG0W0Regeta1]}];
eG0W03Regeta1=Table[{coord[[l]],eG0W0Regeta1[[l,3]]},{l,Length[eG0W0Regeta1]}];
eG0W04Regeta1=Table[{coord[[l]],eG0W0Regeta1[[l,4]]},{l,Length[eG0W0Regeta1]}];

PloteG0W01Regeta1=ListPlot[eG0W01Regeta1,PlotStyle->{Directive[Thickness[0.006],Black]},PlotLegends->Placed[LineLegend[{Directive[{Black,Thickness[0.01]}]},{MaTeX["\\textbf{HOMO~(p=1},\\bm{\\eta=1}~\\textbf{au)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W02Regeta1=ListPlot[eG0W02Regeta1,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Cyan],Thickness[0.01]}]},{MaTeX["\\textbf{LUMO~(p=2},\\bm{\\eta=1}~\\textbf{au)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W03Regeta1=ListPlot[eG0W03Regeta1,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Gray],Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+1~(p=3},\\bm{\\eta=1}~\\textbf{au)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W04Regeta1=ListPlot[eG0W04Regeta1,PlotStyle->{Directive[Thickness[0.006],Purple]},PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+2~(p=4},\\bm{\\eta=1}~\\textbf{au)} ",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

Show[{PloteG0W01Regeta1,PloteG0W02Regeta1,PloteG0W03Regeta1,PloteG0W04Regeta1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,
ImageSize->900,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\tilde{\\epsilon}}_{\\textbf{p}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24]
},PlotRange->{{0.27,1.25},{-20,75}},Axes->False]

(*η = 100 meV*)
eG0W0Regeta100meV=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

coord=Table[k,{k,0.25,1.28,0.01}];

eG0W01Regeta100meV=Table[{coord[[l]],eG0W0Regeta100meV[[l,1]]},{l,Length[eG0W0Regeta100meV]}];
eG0W02Regeta100meV=Table[{coord[[l]],eG0W0Regeta100meV[[l,2]]},{l,Length[eG0W0Regeta100meV]}];
eG0W03Regeta100meV=Table[{coord[[l]],eG0W0Regeta100meV[[l,3]]},{l,Length[eG0W0Regeta100meV]}];
eG0W04Regeta100meV=Table[{coord[[l]],eG0W0Regeta100meV[[l,4]]},{l,Length[eG0W0Regeta100meV]}];

PloteG0W01Regeta100meV=ListPlot[eG0W01Regeta100meV,PlotStyle->{Directive[Thickness[0.006],Black]},PlotLegends->Placed[LineLegend[{Directive[{Black,Thickness[0.01]}]},{MaTeX["\\textbf{HOMO~(p=1},\\bm{\\eta=100}~\\textbf{meV)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W02Regeta100meV=ListPlot[eG0W02Regeta100meV,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Cyan],Thickness[0.01]}]},{MaTeX["\\textbf{LUMO~(p=2},\\bm{\\eta=100}~\\textbf{meV)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W03Regeta100meV=ListPlot[eG0W03Regeta100meV,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},PlotLegends->Placed[LineLegend[{Directive[{Darker[Gray],Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+1~(p=3},\\bm{\\eta=100}~\\textbf{meV)}",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

PloteG0W04Regeta100meV=ListPlot[eG0W04Regeta100meV,PlotStyle->{Directive[Thickness[0.006],Purple]},PlotLegends->Placed[LineLegend[{Directive[{Purple,Thickness[0.01]}]},{MaTeX["\\textbf{LUMO+2~(p=4},\\bm{\\eta=100}~\\textbf{meV)} ",FontSize->24]}],{After,Center}],InterpolationOrder->2,Joined->True];

Show[{PloteG0W01Regeta100meV,PloteG0W02Regeta100meV,PloteG0W03Regeta100meV,PloteG0W04Regeta100meV},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->20,
ImageSize->900,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->24],
MaTeX["\\bm{\\tilde{\\epsilon}}_{\\textbf{p}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->24]
},PlotRange->{{0.27,1.25},{-20,75}},Axes->False]

Difference for κ = 1

Diff1=Table[{coord[[l]],eG0W0[[l,1]]-eG0W0Reg1[[l,1]]},{l,Length[eG0W0Reg1]}];
Diff2=Table[{coord[[l]],eG0W0[[l,2]]-eG0W0Reg1[[l,2]]},{l,Length[eG0W0Reg1]}];
Diff3=Table[{coord[[l]],eG0W0[[l,3]]-eG0W0Reg1[[l,3]]},{l,Length[eG0W0Reg1]}];
Diff4=Table[{coord[[l]],eG0W0[[l,4]]-eG0W0Reg1[[l,4]]},{l,Length[eG0W0Reg1]}];

PlotDiff1=ListPlot[Diff1,PlotStyle->{Directive[Thickness[0.006],Black]},InterpolationOrder->2,Joined->True,PlotRange->All];

PlotDiff2=ListPlot[Diff2,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},InterpolationOrder->2,Joined->True,PlotRange->All];

PlotDiff3=ListPlot[Diff3,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},InterpolationOrder->2,Joined->True,PlotRange->All];

PlotDiff4=ListPlot[Diff4,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True,PlotRange->All];

GraphicsGrid[{{Show[{PlotDiff1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{1}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{1}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-(10^(-2)),(10^(-2))}},Axes->False,AspectRatio->1/3]},{Show[{PlotDiff2},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{2}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{2}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-(10^(-2)),(10^(-2))}},Axes->False,AspectRatio->1/3]},{Show[{PlotDiff3},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{3}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{3}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{PlotDiff4},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{4}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{4}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]}},Frame->None]

Difference for κ = 0.1

(*κ=0.1*)
eG0W0Reg0dot1=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

Reg0dot1Diff1=Table[{coord[[l]],eG0W0[[l,1]]-eG0W0Reg0dot1[[l,1]]},{l,Length[eG0W0Reg0dot1]}];
Reg0dot1Diff2=Table[{coord[[l]],eG0W0[[l,2]]-eG0W0Reg0dot1[[l,2]]},{l,Length[eG0W0Reg0dot1]}];
Reg0dot1Diff3=Table[{coord[[l]],eG0W0[[l,3]]-eG0W0Reg0dot1[[l,3]]},{l,Length[eG0W0Reg0dot1]}];
Reg0dot1Diff4=Table[{coord[[l]],eG0W0[[l,4]]-eG0W0Reg0dot1[[l,4]]},{l,Length[eG0W0Reg0dot1]}];

PlotDiff1=ListPlot[Reg0dot1Diff1,PlotStyle->{Directive[Thickness[0.006],Black]},InterpolationOrder->2,Joined->True,PlotRange->All];

PlotDiff2=ListPlot[Reg0dot1Diff2,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},InterpolationOrder->2,Joined->True,PlotRange->All];

PlotDiff3=ListPlot[Reg0dot1Diff3,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},InterpolationOrder->2,Joined->True,PlotRange->All];

PlotDiff4=ListPlot[Reg0dot1Diff4,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True,PlotRange->All];

GraphicsGrid[{{Show[{PlotDiff1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{1}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{1}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-(10^(-2)),(10^(-2))}},Axes->False,AspectRatio->1/3]},{Show[{PlotDiff2},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{2}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{2}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-(10^(-2)),(10^(-2))}},Axes->False,AspectRatio->1/3]},{Show[{PlotDiff3},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{3}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{3}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{PlotDiff4},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{4}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{4}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]}},Frame->None]

Difference for κ = 10

(*κ=10*)
eG0W0Reg10=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

Reg10Diff1=Table[{coord[[l]],eG0W0[[l,1]]-eG0W0Reg10[[l,1]]},{l,Length[eG0W0Reg10]}];
Reg10Diff2=Table[{coord[[l]],eG0W0[[l,2]]-eG0W0Reg10[[l,2]]},{l,Length[eG0W0Reg10]}];
Reg10Diff3=Table[{coord[[l]],eG0W0[[l,3]]-eG0W0Reg10[[l,3]]},{l,Length[eG0W0Reg10]}];
Reg10Diff4=Table[{coord[[l]],eG0W0[[l,4]]-eG0W0Reg10[[l,4]]},{l,Length[eG0W0Reg10]}];

Reg10PlotDiff1=ListPlot[Reg10Diff1,PlotStyle->{Directive[Thickness[0.006],Black]},InterpolationOrder->2,Joined->True];

Reg10PlotDiff2=ListPlot[Reg10Diff2,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},InterpolationOrder->2,Joined->True];

Reg10PlotDiff3=ListPlot[Reg10Diff3,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},InterpolationOrder->2,Joined->True,PlotRange->All];

Reg10PlotDiff4=ListPlot[Reg10Diff4,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True,PlotRange->All];

GraphicsGrid[{{Show[{Reg10PlotDiff1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{1}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{1}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-1.1,1.1}},Axes->False,AspectRatio->1/3]},{Show[{Reg10PlotDiff2},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{2}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{2}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-0.3,0.3}},Axes->False,AspectRatio->1/3]},{Show[{Reg10PlotDiff3},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{3}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{3}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{Reg10PlotDiff4},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{4}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{4}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]}},Frame->None]

Difference for κ = 10

(*κ=10*)
eG0W0Reg10=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

Reg10Diff1=Table[{coord[[l]],eG0W0[[l,1]]-eG0W0Reg10[[l,1]]},{l,Length[eG0W0Reg10]}];
Reg10Diff2=Table[{coord[[l]],eG0W0[[l,2]]-eG0W0Reg10[[l,2]]},{l,Length[eG0W0Reg10]}];
Reg10Diff3=Table[{coord[[l]],eG0W0[[l,3]]-eG0W0Reg10[[l,3]]},{l,Length[eG0W0Reg10]}];
Reg10Diff4=Table[{coord[[l]],eG0W0[[l,4]]-eG0W0Reg10[[l,4]]},{l,Length[eG0W0Reg10]}];

Reg10PlotDiff1=ListPlot[Reg10Diff1,PlotStyle->{Directive[Thickness[0.006],Black]},InterpolationOrder->2,Joined->True];

Reg10PlotDiff2=ListPlot[Reg10Diff2,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},InterpolationOrder->2,Joined->True];

Reg10PlotDiff3=ListPlot[Reg10Diff3,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},InterpolationOrder->2,Joined->True,PlotRange->All];

Reg10PlotDiff4=ListPlot[Reg10Diff4,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True,PlotRange->All];

GraphicsGrid[{{Show[{Reg10PlotDiff1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{1}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{1}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{Reg10PlotDiff2},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{2}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{2}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{Reg10PlotDiff3},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{3}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{3}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{Reg10PlotDiff4},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{4}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{4}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]}},Frame->None]

Difference for η = 0.1

(*η=0.1*)
eG0W0eta0dot1=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

eta0dot1Diff1=Table[{coord[[l]],eG0W0[[l,1]]-eG0W0eta0dot1[[l,1]]},{l,Length[eG0W0eta0dot1]}];
eta0dot1Diff2=Table[{coord[[l]],eG0W0[[l,2]]-eG0W0eta0dot1[[l,2]]},{l,Length[eG0W0eta0dot1]}];
eta0dot1Diff3=Table[{coord[[l]],eG0W0[[l,3]]-eG0W0eta0dot1[[l,3]]},{l,Length[eG0W0eta0dot1]}];
eta0dot1Diff4=Table[{coord[[l]],eG0W0[[l,4]]-eG0W0eta0dot1[[l,4]]},{l,Length[eG0W0eta0dot1]}];

eta0dot1PlotDiff1=ListPlot[eta0dot1Diff1,PlotStyle->{Directive[Thickness[0.006],Black]},InterpolationOrder->2,Joined->True];

eta0dot1PlotDiff2=ListPlot[eta0dot1Diff2,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},InterpolationOrder->2,Joined->True];

eta0dot1PlotDiff3=ListPlot[eta0dot1Diff3,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},InterpolationOrder->2,Joined->True,PlotRange->All];

eta0dot1PlotDiff4=ListPlot[eta0dot1Diff4,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True,PlotRange->All];

GraphicsGrid[{{Show[{eta0dot1PlotDiff1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{1}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{1}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-(10^(-2)),(10^(-2))}},Axes->False,AspectRatio->1/3]},{Show[{eta0dot1PlotDiff2},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{2}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{2}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-(10^(-2)),(10^(-2))}},Axes->False,AspectRatio->1/3]},{Show[{eta0dot1PlotDiff3},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{3}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{3}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{eta0dot1PlotDiff4},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{4}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{4}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]}},Frame->None]

Difference for η = 1

(*η=1*)
eG0W0eta1=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

eta1Diff1=Table[{coord[[l]],eG0W0[[l,1]]-eG0W0eta1[[l,1]]},{l,Length[eG0W0eta1]}];
eta1Diff2=Table[{coord[[l]],eG0W0[[l,2]]-eG0W0eta1[[l,2]]},{l,Length[eG0W0eta1]}];
eta1Diff3=Table[{coord[[l]],eG0W0[[l,3]]-eG0W0eta1[[l,3]]},{l,Length[eG0W0eta1]}];
eta1Diff4=Table[{coord[[l]],eG0W0[[l,4]]-eG0W0eta1[[l,4]]},{l,Length[eG0W0eta1]}];

eta1PlotDiff1=ListPlot[eta1Diff1,PlotStyle->{Directive[Thickness[0.006],Black]},InterpolationOrder->2,Joined->True,PlotRange->All];

eta1PlotDiff2=ListPlot[eta1Diff2,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},InterpolationOrder->2,Joined->True,PlotRange->All];

eta1PlotDiff3=ListPlot[eta1Diff3,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},InterpolationOrder->2,Joined->True,PlotRange->All];

eta1PlotDiff4=ListPlot[eta1Diff4,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True,PlotRange->All];

GraphicsGrid[{{Show[{eta1PlotDiff1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{1}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{1}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-0.5,0.5}},Axes->False,AspectRatio->1/3]},{Show[{eta1PlotDiff2},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{2}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{2}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-0.2,0.2}},Axes->False,AspectRatio->1/3]},{Show[{eta1PlotDiff3},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{3}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{3}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{eta1PlotDiff4},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{4}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{4}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]}},Frame->None]

Difference for η = 10

(*η=10*)
eG0W0eta10=Table[MainModule[2,4,2,{1,1},{{0.0,0.0,0.0},{0.0,0.0,k}},"6-31g",{"HF","G0W0"},True,False]["eG0W0"]*HaToeV,{k,0.25,1.28,0.01}];

eta10Diff1=Table[{coord[[l]],eG0W0[[l,1]]-eG0W0eta10[[l,1]]},{l,Length[eG0W0eta10]}];
eta10Diff2=Table[{coord[[l]],eG0W0[[l,2]]-eG0W0eta10[[l,2]]},{l,Length[eG0W0eta10]}];
eta10Diff3=Table[{coord[[l]],eG0W0[[l,3]]-eG0W0eta10[[l,3]]},{l,Length[eG0W0eta10]}];
eta10Diff4=Table[{coord[[l]],eG0W0[[l,4]]-eG0W0eta10[[l,4]]},{l,Length[eG0W0eta10]}];

eta10PlotDiff1=ListPlot[eta10Diff1,PlotStyle->{Directive[Thickness[0.006],Black]},InterpolationOrder->2,Joined->True];

eta10PlotDiff2=ListPlot[eta10Diff2,PlotStyle->{Directive[Thickness[0.006],Darker[Cyan]]},InterpolationOrder->2,Joined->True];

eta10PlotDiff3=ListPlot[eta10Diff3,PlotStyle->{Directive[Thickness[0.006],Darker[Gray]]},InterpolationOrder->2,Joined->True,PlotRange->All];

eta10PlotDiff4=ListPlot[eta10Diff4,PlotStyle->{Directive[Thickness[0.006],Purple]},InterpolationOrder->2,Joined->True,PlotRange->All];

GraphicsGrid[{{Show[{eta10PlotDiff1},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{1}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{1}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-1.1,1.1}},Axes->False,AspectRatio->1/3]},{Show[{eta10PlotDiff2},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{2}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{2}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->{All,{-1.1,1.1}},Axes->False,AspectRatio->1/3]},{Show[{eta10PlotDiff3},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{3}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{3}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]},{Show[{eta10PlotDiff4},Frame->True,FrameStyle->Directive[Black,Thick],
BaseStyle->16,
ImageSize->1000,FrameLabel-> {
MaTeX["\\bm{R}_{\\text{H-H}} ~\\textbf{(\\AA)}",FontSize->16],
MaTeX["\\bm{\\epsilon}_{\\textbf{4}}^{\\text{GW}}-~\\bm{\\tilde{\\epsilon}}_{\\textbf{4}}^{\\text{GW}}  \\textbf{(eV)}",FontSize->16]
},PlotRange->All,Axes->False,AspectRatio->1/3]}},Frame->None]