A similarity renormalization group approach to many-body perturbation theory

Summary

Authors:
Antoine Marie and Pierre-François Loos
Date:
-February-2023
DOI:

This Mathematica notebook provides the numerical calculations used in the accompanying manuscript: 
“A Similarity Renormalization Group Approach To Many-Body Perturbation

Theory”
Readers are invited to reproduce, and extend, the results presented within this notebook. Each cell must be evaluated sequentially to ensure the correct functionality.

This notebook is organized such as we first define modules for each methods considered in the manuscript and then a main module is used to selectively call them.

Any questions, queries, or reports of errors should be addressed to the corresponding authors Antoine Marie and Pierre-François Loos using the addresses  amarie@irsamc.ups-tlse.fr and loos@irsamc.ups-tlse.fr

Initialisation

HaToEv=27.211396641308;

SetDirectory[NotebookDirectory[]]
Needs["MaTeX`"]
SetOptions[MaTeX,"Preamble"->{"\\usepackage{amssymb,amsmath,latexsym,amsfonts,amsthm,xcolor,bm,mhchem}"}];

Colorblind-friendly color map

Map[RGBColor,{"#EE7733","#0077BB","#33BBEE","#EE3377","#CC3311","#009988","#BBBBBB"}]

Map[RGBColor,{"#4477AA","#66CCEE","#228833","#CCBB44","#EE6677","#AA3377","#BBBBBB"}]

Graphics`PlotMarkers[]

DONE Fig 1: Regularizing surfaces

Fqs[η_,x_,y_]:=(1/2)((x/((x^2)+(η^2)))+(y/((y^2)+(η^2))))
FSRG[s_,x_,y_]:=((x+y)/((x^2)+(y^2)))(1-Exp[-((x^2)+(y^2))s])

fig1=Grid[
{{With[{η=1},Plot3D[Fqs[η,x,y],{x,-5,5},{y,-5,5},Epilog->Text[MaTeX["f_\\text{qs}(x,y;\\eta) = \\frac{1}{2} \\left( \\frac{x}{x^2+\\eta^2} + \\frac{y}{y^2+\\eta^2} \\right)",FontSize->18],Offset[{30,-10},Scaled[{0,1}]],{-1,1.3}],
PlotPoints->100,MaxRecursion->2,ColorFunction->"DarkRainbow",PlotTheme->"Scientific",PerformanceGoal->"Quality",BoxStyle->Directive[Black,16,Thickness[0.005]],AxesStyle->Directive[Black,16,Thick],ImagePadding->{{0, 0}, {0, 0}},PlotRange->{{-5,5},{-5,5},{-0.65,0.65}},AxesLabel->{MaTeX["x",FontSize->20],MaTeX["y",FontSize->20],None},BoxRatios->{1,1,2/3},ImageSize->400,BoxStyle->Thick,BaseStyle->Directive[16],ViewPoint->{0.65,-1.75,1.25},PlotStyle->Opacity[0.75]]],With[{η=1},Plot3D[FSRG[1/2(η^2),x,y],{x,-5,5},{y,-5,5},Epilog->Text[MaTeX["f_\\text{SRG}(x,y;\\eta) = \\frac{x+y}{x^2+y^2} \\left[ 1 - e^{-(x^2+y^2)/(2\\eta^2)} \\right]",FontSize->18],Offset[{30,-10},Scaled[{0,1}]],{-0.9,1.3}],
PlotPoints->100,MaxRecursion->2,ColorFunction->"DarkRainbow",PlotTheme->"Scientific",PerformanceGoal->"Quality",BoxStyle->Directive[Black,16,Thickness[0.005]],AxesStyle->Directive[Black,16,Thick],ImagePadding->{{0, 0}, {0, 0}},PlotRange->{{-5,5},{-5,5},{-0.65,0.65}},AxesLabel->{MaTeX["x",FontSize->20],MaTeX["y",FontSize->20],None},BoxRatios->{1,1,2/3},ImageSize->400,BoxStyle->Thick,BaseStyle->Directive[16],ViewPoint->{0.65,-1.75,1.25},PlotStyle->Opacity[0.75]]]
}},Spacings->0]

Export["/home/amarie/SRGGW/Manuscript/fig1.pdf",fig1]

Reading data

GW20={"He","Ne","H2","Li2","LiH","HF","Ar","H2O","LiF","HCl","BeO","CO","N2","CH4","BH3","NH3","BF","BN","SH2","F2","MgO","O3"};

η={0.1,0.05,0.01,0.005,0.001,0};

s={0.001,0.005,0.01,0.05,0.1,0.5,1,5,10,50,100,500,1000};

CCSD(T) reference values

IPCC=({-2.9008363941999997,-128.84397521,-1.1727563203,-14.954065643,-8.0485792426,-100.37485717999999,-527.0972445499999,-76.36545609999999,-107.32796894,-460.38778630999997,-89.800367408,-113.20946273,-109.42697376000001,-40.470575977,-26.560204646000003,-56.505005495000006,-124.55674452,-79.313452072,-398.98405212,-199.36411599000002,-274.79151816,-225.22418033}-{-1.9990340818999999,-128.05500153,-0.57012504494,-14.761061243,-7.7538843298,-99.78136691,-526.52383844,-75.89928664199999,-106.90633856,-459.92219804,-89.434577606,-112.69518056,-108.85589872999999,-39.941848822,-26.070931874999996,-56.104160905,-124.1470274,-78.870684267,-398.60233826,-198.78316023,-274.49845522,-224.75184375999999})*HaToEv

EACC=({-2.8030488212,-128.65688365,-1.1230533801,-14.966586752,-8.059419844,-100.35058937999999,-527.00363456,-76.343189003,-107.34069356,-460.36679174,-89.879935026,-113.15163825,-109.33986433999999,-40.446810496000005,-26.556781619,-56.482628107,-124.5273945,-79.42449044899999,-398.96484976,-199.37588721999998,-274.8481983,-225.29098123}-{-2.9008363941999997,-128.84397521,-1.1727563203,-14.954065643,-8.0485792426,-100.37485717999999,-527.0972445499999,-76.36545609999999,-107.32796894,-460.38778630999997,-89.800367408,-113.20946273,-109.42697376000001,-40.470575977,-26.560204646000003,-56.505005495000006,-124.55674452,-79.313452072,-398.98405212,-199.36411599000002,-274.79151816,-225.22418033})*HaToEv

Hartree-Fock

HF={{-24.976293,-23.151995,-16.156918,-4.957862,-8.212617,-17.686766,-16.083439,-13.883223,-12.910687,-12.981328,-10.454922,-15.113741,-16.678573,-14.832313,-13.586605,-11.6918,-11.042148,-11.551604,-10.487306,-18.154401,-8.745371,-13.291955},
{2.702384, 5.474937, 1.33009, 0.082251, -0.198592, 0.810196, 2.972673, 0.796117, -0.285769, 0.792256, -1.804701, 1.803864, 2.200212, 0.791416, 0.812077, 0.800025, 1.060882, -2.966944, 0.759471, 1.711542, -1.396083, -1.319369}};

G0W0

G0W0SymRPA={{{},
{},
{-24.58847,-21.46467,-16.48893,-5.377488,-8.216344,-16.25008,-15.715822,-12.895961,-11.404754,-12.78256,-9.740571,-14.798176,-17.097814,-14.764508,-13.684434,-11.215134,-11.339283,-11.758813,-10.505643,-16.347891,-8.401262,-13.562724},
{},
{-24.588416,-21.464612,-16.488853,-5.377145,-8.216023,-16.249995,-15.715755,-12.895859,-11.404613,-12.782475,-9.740359,-14.798084,-17.09775,-14.764425,-13.684346,-11.215023,-11.339173,-11.758683,-10.505548,-16.34781,-8.40087,-13.56266},
{}},
{{},
{},
{},
{},
{2.65895,5.246455,1.280342,-0.16754,-0.269279,0.714515,2.676362,0.67958,-0.330101,0.643785,-2.276537,1.658112,2.100852,0.696179,0.463157,0.679951,0.901451,-3.903774,0.604519,0.531724,-1.643795,-2.185079},
{}}
};

G0W0SymTDA={{},
{},
{},
{},
{-24.454162,-20.845919,-16.530702,-5.453359,-8.144555,-15.641055,-15.602545,-12.417807,-10.751003,-12.696334,-9.32538,-14.603221,-17.364737,-14.667361,-13.662675,-10.910541,-11.379826,-11.850654,-10.467744,-15.55351,-8.098392,-13.68235},
{}};

G0W0SymRPAx={{},
{},
{-23.871737,-20.56383,-16.175927,-5.137431,-7.556204,-15.393792,-15.295048,-12.163201,-10.492868,-12.405945,-9.026429,-14.318873,-16.80509,-14.370258,-13.323661,-10.638561,-11.074026,None,-10.201372,-15.290438,-7.469754,-13.127764},
{},
{-23.871559,-20.563688,-16.175604,-5.132731,-7.554098,-15.393567,-15.294847,-12.162902,-10.49246,-12.405667,-9.025588,-14.318537,-16.804864,-14.369985,-13.323335,-10.638188,-11.073464,None,-10.201015,-15.290176,-7.464778,-13.127197},
{}};

G0W0SymTDAx={};

evGW

evGWSymRPA={};

evGWSymTDA={};

evGWSymRPAx={{},
{},
{-24.571336,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{},
{-24.571364,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{}};

evGWSymTDAx={};

Sym-qsGW

qsGWSymRPA={
{{-24.934069,-22.200782,-16.722873,-5.200219,-8.601953,-17.010196,-16.013439,-13.515143,-12.438653,-13.091837,-10.675835,-14.90943,-16.618816,-15.039503,-13.958174,-11.646779,-11.417688,-12.147547,-10.753569,-17.009361,-9.151831,-13.789911},{-24.680206,-21.928051,-16.583056,-5.331986,-8.489331,-16.678896,-15.804793,-13.207279,-12.070501,-12.910891,-10.517659,-14.57466,-16.201969,-14.821497,-13.766309,-11.388351,-11.316055,-12.061925,-10.617815,-16.579011,-8.913896,-13.668544},{-24.581903,-21.825235,-16.449688,-5.395586,-8.252719,-16.449407,-15.610426,-12.977273,-11.750972,-12.769609,-10.31523,-14.341903,-15.928778,-14.665674,-13.621641,-11.178003,-11.186397,-11.891533,-10.498492,-16.273019,-8.538768,-13.336473},
{-24.617788,-21.829495,-16.432537,-5.399934,-8.238833,-16.436237,-15.555234,-12.960096,-11.727268,-12.765772,-10.296723,-14.334703,-15.922018,-14.656069,-13.61681,-11.163338,-11.179388,-11.875619,-10.495565,-16.220888,-8.51027,-13.307872},
{-24.65558,-21.842774,-16.407867,-5.395255,-8.267713,-16.430735,-15.625184,-12.94687,-11.730343,-12.74958,-10.285993,-14.336421,-15.923488,-14.641067,-13.593145,-11.147109,-11.16452,-11.935735,-10.515133,-16.147619,-8.484707,-13.317213},
{-24.657592,-21.711059,None,-5.382811,None,None,None,None,None,None,None,None,None,None,-13.578803,None,None,None,None,None,None,None},
{-24.658219,-21.847924,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{-24.658287,-21.843772,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None}},

{{2.656729,5.189106,1.28005,-0.183854,-0.266742,0.699175,2.641355,0.654637,-0.32589,0.62893,-2.101498,1.614192,2.09843,0.683098,0.290819,0.657902,0.865647,-3.414919,0.584045,-0.102015,-1.723766,-2.226803},
{2.656384,5.188789,1.280062,-0.212267,-0.268958,None,2.638956,0.65329,-0.32695,0.628148,-2.103074,1.611631,2.097537,0.682139,0.285279,0.656596,0.862897,-3.427228,0.58238,-0.080136,-1.72735,-2.221904},
{2.656008,5.188121,None,-0.220681,-0.272481,0.699092,2.640488,0.651661,-0.331226,0.630344,-2.099549,1.609593,2.098151,0.681608,0.27866,0.656369,0.863345,-3.493864,0.58149,None,-1.714799,-2.250142},
{2.655987,5.184945,None,-0.211964,None,None,None,None,None,None,None,None,None,None,0.279373,None,None,None,None,None,None,None},
{2.655986,5.188494,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{2.655978,5.188001,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None}}
};

qsGWSymRPA[[1,1]]-qsGWSymRPA[[1,3]]

For Helium MolGW gives -24.9763 for η=0.001 at (10^(-5)) for the convergence criteria, it gives -24.658275 at (10^(-6))

qsGWSymTDA={{-24.43274,-21.226875,-16.49276,-5.493546,-8.184454,-15.802583,-15.439642,-12.425299,-11.066795,-12.646682,-10.214296,-13.830228,None,-14.509981,-13.577517,-10.774188,-11.126459,-12.055776,-10.437816,-15.291429,-7.791857,-12.253501},
{-24.475129,-21.232006,-16.464686,-5.502337,-8.165519,-15.787685,-15.42452,-12.400907,-11.020907,-12.645151,-10.208469,-13.818932,-15.153428,-14.497127,-13.570172,-10.754667,-11.114572,-12.058396,-10.436396,-15.230617,-7.761043,-12.223341},
{-24.529299,-21.255348,None,-5.510069,-8.204163,None,-15.330597,None,-10.958588,None,None,-13.825477,None,None,-13.542585,-10.73955,-11.105096,None,-10.458897,None,None,-12.255622},
{-24.532552,-21.130308,None,None,-8.191942,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{-24.533519,-21.25133,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{-24.533561,-21.251502,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None}};

qsGWSymRPAx={{-23.767641,-20.980657,-16.167673,-5.379706,-7.676587,-15.711335,-15.162147,-12.315843,-10.873766,-12.319889,None,-13.602089,-15.09165,-14.217076,-13.172642,-10.629166,-10.800839,None,None,-10.110578,None},
{-23.856137,-20.988863,-16.140408,-5.170483,-7.268214,-15.67131,None,-12.253995,-10.764452,-12.288851,None,-13.540934,-15.00835,-14.190342,-13.136605,-10.589921,-10.729186,None,None,-10.062781,None,None},
{-23.104906,-21.00482,None,None,-7.051277,-15.17821,None,-12.394835,-10.675338,-12.321998,None,-13.503045,None,None,-13.145002,-10.650999,-10.781868,None,None,None,None,None},
{-23.089448,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{-23.084703,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{-23.089448,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None}};

qsGWSymTDAx={{-23.505302,-19.83864,-16.174882,-5.554805,-7.267156,-14.352378,-14.718261,-11.064005,-9.068543,-11.895957,-9.597878,-12.449395,-13.461068,-13.65804,-12.927049,-9.575141,-10.572681,-11.681542,-9.786105,-13.184232,-6.758224,-10.194518},
{-23.612221,-19.846704,-16.137932,-5.301147,-5.880946,-14.289669,None,-10.955693,-8.7223,-11.862876,-9.541711,-12.320091,None,-13.599217,-12.871157,-9.428752,-10.493484,-11.691423,-9.73893,-13.276253,-6.77014,-9.955881},
{-22.616485,-19.86084,None,None,None,-14.343147,None,None,None,-11.881488,None,None,None,None,None,None,None,None,None,None,None,None},
{-22.598128,-19.861499,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{-22.592448,-19.861731,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None},
{-22.592213,-19.861745,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None}};

SRG-qsGW

SRG={
{{-25.176906,-23.36228,-16.215128,-4.960221,-8.231864,-17.811892,-16.112036,-13.964657,-13.0057,-13.003532,-10.493372,-15.181113,-16.748939,-14.88923,-13.636844,-11.749634,-11.078597,-11.581006,-10.504464,-18.327593,-8.772861,-13.389272},
{-25.484509,-23.514675,-16.381224,-4.966426,-8.29124,-17.974605,-16.2096,-14.121096,-13.143589,-13.083993,-10.585091,-15.329923,-16.930429,-15.046371,-13.781839,-11.890775,-11.161459,-11.667937,-10.569561,-18.516115,-8.85537,-13.60331},
{-25.583807,-23.490045,-16.507991,-4.973477,-8.343308,-18.007873,-16.286024,-14.189885,-13.190732,-13.156827,-10.651161,-15.416621,-17.067399,-15.160879,-13.893603,-11.98157,-11.224836,-11.747585,-10.634777,-18.519854,-8.929025,-13.73543},
{-25.545264,-22.909858,-16.823434,-5.023824,-8.535998,-17.719966,-16.394738,-14.11325,-13.045163,-13.338397,-10.805859,-15.466766,-17.39625,-15.376877,-14.167216,-12.077971,-11.414123,-12.035331,-10.85516,-18.010485,-9.164844,-13.966918},
{-25.320976,-22.515922,-16.897756,-5.070158,-8.631299,-17.413177,-16.310439,-13.905549,-12.82894,-13.332396,-10.815487,-15.328453,-17.182083,-15.350868,-14.204447,-11.981133,-11.474534,-12.157376,-10.910126,-17.5549,-9.239748,-13.948371},
{-24.705776,-21.790854,-16.706807,-5.255847,-8.663311,-16.662012,-15.874833,-13.257833,-12.166496,-13.011908,-10.65184,-14.711563,-16.299802,-14.921754,-13.902088,-11.481249,-11.442181,-12.189231,-10.734907,-16.528167,-9.065207,-13.711444},
{-24.581741,-21.654345,-16.568235,-5.351782,-8.563194,-16.475179,-15.733978,-13.05711,-11.9094,-12.866151,-10.514909,-14.492464,-16.055542,-14.749811,-13.728311,-11.293004,-11.352139,-12.083869,-10.606725,-16.318858,-8.924434,-13.559213},
{-24.542527,-21.59439,-16.451338,-5.442764,-8.251557,-16.344196,-15.631666,-12.884998,-11.598962,-12.729113,-10.218763,-14.332987,-15.916132,-14.62708,-13.587728,-11.110855,-11.188443,-11.913643,-10.45835,-16.221255,-8.50067,-13.286612},
{-24.542629,-21.5941,-16.450004,-5.410576,-8.177027,-16.343528,-15.629999,-12.881216,-11.582686,-12.723769,-10.182651,-14.329749,-15.914494,-14.625252,-13.585157,-11.101538,-11.174651,-11.903926,-10.448752,-16.220998,-8.392056,-13.272501},
{-24.543343,-21.593163,-16.449793,-5.366619,-8.148174,-16.34352,-15.6311,-12.881045,-11.581244,-12.723553,-10.176187,-14.32968,-15.913865,-14.625549,-13.585376,-11.100918,-11.173675,-11.902442,-10.447952,-16.221495,-8.356267,-13.269795},
{-24.543999,-21.59274,-16.449545,-5.366933,-8.148274,-16.343898,-15.631796,-12.881152,-11.581161,-12.723516,-10.176167,-14.329844,-15.913758,-14.625627,-13.585433,-11.100927,-11.173889,-11.902236,-10.447914,-16.221751,-8.356254,-13.269536},
{-24.545287,-21.591238,-16.448985,-5.367843,-8.148475,-16.344085,-15.632115,-12.881566,-11.580833,-12.72369,-10.175931,-14.330155,-15.913328,-14.625523,-13.585584,-11.100582,-11.174613,-11.901888,-10.447727,-16.222283,-8.356195,-13.268975},{-24.545577,-21.590984,-16.448815,-5.368114,-8.148611,-16.344709,-15.632172,-12.881761,-11.580763,-12.723951,-10.175798,-14.330245,-15.913882,-14.625652,-13.585763,-11.100329,-11.175071,-11.901614,-10.447591,-16.222347,-8.356234,-13.268916}}
,
{{2.696606,5.47314,1.328785,0.08219,-0.199467,0.80681,2.970022,0.794744,-0.287439,0.792166,-1.817504,1.802011,2.199454,0.791129,0.810846,0.799643,1.057117,-2.991766,0.759633,1.614706,-1.411859,-1.413462},
{2.68696,5.45469,1.324936,0.082059,-0.202433,0.7997,2.962207,0.790417,-0.289959,0.790664,-1.84374,1.796154,2.196859,0.789697,0.805725,0.797488,1.050806,-3.053203,0.759161,1.372069,-1.455961,-1.631931},
{2.683056,5.431759,1.321803,0.081879,-0.205079,0.794036,2.953864,0.785938,-0.291409,0.788246,-1.860083,1.79087,2.194443,0.787905,0.798503,0.7947,1.047037,-3.099103,0.757653,1.182104,-1.491856,-1.778506},
{2.673962,5.329912,1.311752,0.080592,-0.214524,0.769661,2.89619,0.76035,-0.297272,0.768012,-1.895222,1.765798,2.18046,0.774894,0.737971,0.774583,1.029163,-3.230923,0.74112,0.603047,-1.591226,-2.086726},
{2.669338,5.276556,1.305992,0.079436,-0.219615,0.753334,2.844203,0.739899,-0.301073,0.747754,-1.907328,1.745069,2.167545,0.761945,0.674012,0.755782,1.012222,-3.281189,0.722722,0.381463,-1.618426,-2.136097},
{2.658792,5.200881,1.289566,0.063896,-0.232878,0.712828,2.700612,0.682316,-0.313574,0.674244,-1.973378,1.678876,2.122918,0.714044,0.436724,0.694649,0.942348,-3.342733,0.646732,0.048721,-1.63469,-2.144589},
{2.657463,5.193767,1.283767,0.038906,-0.241486,0.704009,2.665024,0.666455,-0.319748,0.647152,-2.022653,1.652338,2.107532,0.696554,0.355381,0.674737,0.909518,-3.368499,0.614163,-0.020873,-1.63824,-2.144484},
{2.657301,5.191188,1.279953,-0.096291,-0.263253,0.70007,2.648662,0.657197,-0.327371,0.628886,-2.114906,1.625833,2.098412,0.684917,0.303099,0.660727,0.868879,-3.430943,0.586423,-0.066084,-1.689126,-2.165148},
{2.657291,5.191172,1.279923,-0.162287,-0.267979,0.700052,2.648471,0.657087,-0.327726,0.628571,-2.125609,1.625317,2.098351,0.684787,0.30198,0.660388,0.866589,-3.43664,0.585703,-0.066534,-1.703651,-2.166741},
{2.657248,5.191142,1.279918,-0.211909,-0.269491,0.700048,2.648007,0.657052,-0.327785,0.628424,-2.128343,1.625072,2.098345,0.684765,0.301623,0.660337,0.86588,-3.438329,0.58554,-0.067471,-1.708329,-2.167729},
{2.65721,5.191145,1.279921,-0.212799,-0.269509,0.700063,2.647746,0.657042,-0.327803,0.628389,-2.128476,1.624959,2.098344,0.684761,0.301551,0.66033,0.865636,-3.438303,0.58551,-0.067905,-1.708696,-2.168131},
{2.657146,5.191169,1.279934,-0.213055,-0.269552,0.700061,2.647605,0.657015,-0.327815,0.628346,-2.128551,1.624805,2.098338,0.684755,0.301465,0.660319,0.865057,-3.438263,0.585468,-0.068117,-1.709032,-2.168903},{2.657135,5.191169,1.279941,-0.213092,-0.269577,0.70008,2.647596,0.657003,-0.327817,0.628338,-2.128522,1.624754,2.098344,0.684755,0.301388,0.660314,0.864719,-3.438526,0.585448,-0.068201,-1.709077,-2.169119}}
};

SRGTDA={{-25.190867,-23.378114,-16.220013,-4.960492,-8.23349,-17.819574,-16.115949,-13.969083,-13.013877,-13.006391,-10.49908,-15.186008,-16.765188,-14.894135,-13.641373,-11.753011,-11.08243,-11.588403,-10.506455,-18.338594,-8.780716,-13.406391},
{-25.521948,-23.520946,-16.40232,-4.967452,-8.298473,-17.97826,-16.227069,-14.126711,-13.157475,-13.097601,-10.606321,-15.341851,-17.001269,-15.06635,-13.800885,-11.899777,-11.173556,-11.702114,-10.579701,-18.516911,-8.888936,-13.670064},
{-25.628013,-23.457291,-16.544113,-4.975401,-8.356322,-17.986833,-16.314209,-14.182966,-13.193161,-13.180459,-10.683222,-15.424704,-17.191011,-15.193139,-13.925881,-11.989039,-11.242048,-11.810532,-10.653524,-18.478199,-8.984229,-13.842484},
{-25.562662,-22.6419,-16.908591,-5.032761,-8.574291,-17.507958,-16.427936,-13.975174,-12.910411,-13.382307,-10.843182,-15.376456,-17.280138,-15.424261,-14.237855,-12.017229,-11.440436,-12.234544,-10.901891,-17.66064,-9.262436,-14.201621},
{-25.296546,-22.117866,-16.996799,-5.086615,-8.680732,-17.072311,-16.313396,-13.660433,-12.585135,-13.363217,-10.831478,-15.141508,-16.848766,-15.374294,-14.27729,-11.845541,-11.499472,-12.419943,-10.957816,-16.997249,-9.100216,-14.234273},
{-24.579918,-21.191243,-16.782189,-5.309404,-8.696551,-16.086154,-15.76116,-12.800456,-11.67349,-12.947992,-10.59309,-14.309615,-15.680317,-14.824062,-13.910077,-11.166355,-11.439707,-12.392123,-10.723678,-15.614783,-8.595479,-12.924894},
{-24.435789,-21.009445,-16.626775,-5.426334,-8.568241,-15.846297,-15.587142,-12.550295,-11.328327,-12.767422,-10.428246,-14.043164,-15.387658,-14.616107,-13.704966,-10.933817,-11.329775,-12.231847,-10.566642,-15.355557,-8.314263,-12.552377},
{-24.389588,-20.925193,-16.497669,-5.538946,-8.182914,-15.665527,-15.461755,-12.32138,-10.884731,-12.601222,-10.097546,-13.844805,-15.214901,-14.469251,-13.541053,-10.699138,-11.136967,-12.044538,-10.389181,-15.223688,-7.705746,-12.23687},
{-24.389716,-20.924732,-16.496301,-5.505276,-8.090112,-15.664268,-15.459824,-12.315068,-10.855421,-12.594493,-10.056923,-13.839537,-15.212263,-14.466981,-13.5381,-10.684875,-11.120797,-12.036505,-10.377441,-15.223114,-7.610314,-12.223984},
{-24.390779,-20.922873,-16.495979,-5.461264,-8.053149,-15.663689,-15.46133,-12.314584,-10.852075,-12.594142,-10.049105,-13.839237,-15.211548,-14.467453,-13.538441,-10.683634,-11.11971,-12.035927,-10.37634,-15.223645,-7.58316,-12.221331},
{-24.391619,-20.92187,-16.495597,-5.461974,-8.053279,-15.664584,-15.461837,-12.314818,-10.851789,-12.594108,-10.049052,-13.839527,-15.211318,-14.467575,-13.53849,-10.683625,-11.120134,-12.035914,-10.376293,-15.223735,-7.583493,-12.22108},
{-24.393137,-20.919254,-16.494583,-5.463172,-8.053476,-15.664556,-15.461654,-12.315553,-10.850594,-12.594205,-10.049556,-13.840119,None,-14.467388,-13.538562,-10.683252,-11.12131,-12.035623,-10.376138,-15.223535,-7.583626,-12.220464}};

We are missing (Subscript[N, 2]) for s=500 in TDA

SRGTDHF={{-25.173435,-23.369757,-16.21108,-4.959969,-8.230463,-17.814002,-16.110063,-13.964416,-13.00622,-13.001714,-10.491588,-15.17958,-16.743486,-14.886171,-13.633564,-11.748081,-11.076827,None,-10.502822,-18.331568,-8.769807,-13.384457},
{-25.517689,-23.581367,-16.372379,-4.965188,-8.286985,-18.012267,-16.206887,-14.138961,-13.166712,-13.078766,-10.582854,-15.337598,-16.915535,-15.042403,-13.775465,-11.895054,-11.1584,None,-10.563334,-18.573458,-8.844293,-13.599866},
{-25.656117,-23.61259,-16.503932,-4.970558,-8.338252,-18.086003,-16.291719,-14.237011,-13.242555,-13.1544,-10.653981,-15.443831,-17.053618,-15.166475,-13.892268,-12.00251,-11.223841,None,-10.627739,-18.632702,-8.914086,-13.744736},
{-25.759911,-23.11349,-16.889785,-5.013438,-8.547731,-17.943452,-16.491231,-14.304051,-13.226976,-13.402113,-10.867267,-15.625369,-17.446277,-15.48216,-14.240497,-12.21842,-11.44289,None,-10.889635,-18.302961,-9.179422,-14.071786},
{-25.565353,-22.642041,-17.036139,-5.056211,-8.67812,-17.634716,-16.465021,-14.148371,-13.036818,-13.459444,-10.921327,-15.564205,-17.503289,-15.540627,-14.354843,-12.198946,-11.53132,None,-11.001253,-17.840918,-9.286026,-14.104236},
{-24.526233,-21.285737,-16.953789,-5.24096,-8.869552,-16.481814,-15.890951,-13.281297,-12.190975,-13.137459,-10.829636,-14.893003,-16.41394,-15.130573,-14.14608,-11.636018,-11.573609,None,-10.916709,None,None,None},
{-24.057573,-20.886318,-16.706398,-5.360712,-8.815193,-15.984683,-15.566507,-12.815093,-11.736477,-12.855273,-10.688084,-14.467491,-15.87048,-14.772111,-13.837356,-11.248201,-11.470975,None,-10.704102,None,None,None},
{-23.644397,-20.470423,-16.163289,-5.614804,-8.297315,-15.299831,-15.075203,-12.070655,-10.701322,-12.306314,None,-13.671859,-15.00574,-14.148816,-13.185217,-10.528778,-11.025592,None,-10.190835,None,None,None},
{-23.639789,-20.465323,-16.099659,-5.628153,-7.963139,-15.241066,-15.009126,-11.936023,-10.375762,-12.207123,None,-13.517489,-14.879784,-14.071165,-13.085167,-10.370691,-10.842302,None,-10.069692,None,None,None},
{-23.640539,-20.466126,-16.092517,-5.340616,-7.178208,-15.231669,-14.984384,-11.89436,-10.119309,-12.152931,None,-13.452635,-14.829399,-14.050256,-13.059124,-10.267834,-10.713933,None,-9.989651,None,None,None},
{-23.643303,-20.466241,-16.092246,-5.134165,-6.854129,-15.231291,-14.984528,-11.894927,-10.116395,-12.145635,None,-13.447749,-14.822748,-14.049218,-13.0582,-10.265792,-10.711808,None,-9.982445,None,None,None},
{-23.646877,-20.466252,-16.091273,-4.886631,-5.983724,-15.239237,None,-11.907457,-10.114793,-12.13956,None,-13.442974,-14.829677,-14.048513,-13.057606,-10.263223,-10.709216,None,-9.976844,None,None,None}};

-0.66934915*HaToEv

-0.85901*HaToEv

BN never converge, at 0.5 we lose MgO, O3 and F2 and at 5 we lose BeO as well. Finally at s=500 we lose Ar

SRGTDAHF={{-25.182407,-23.385349,-16.214237,-4.960184,-8.231599,-17.821622,-16.113749,-13.968723,-13.014226,-13.004273,-10.49681,-15.183842,-16.757352,-14.889706,-13.636647,-11.75095,-11.080113,-11.584296,-10.504506,-18.342535,-8.77676,-13.399616},
{-25.545112,-23.600505,-16.386591,-4.966057,-8.292217,-18.023906,-16.224287,-14.148561,-13.186525,-13.091397,-10.604153,-15.349847,-16.97857,-15.057619,-13.789235,-11.904136,-11.169333,-11.68615,-10.572116,-18.586751,-8.875626,-13.661803},
{-25.692038,-23.606185,-16.529307,-4.972166,-8.347966,-18.083347,-16.321902,-14.240992,-13.260207,-13.177475,-10.68871,-15.455831,-17.168159,-15.1925,-13.916667,-12.013036,-11.239886,-11.787533,-10.644631,-18.619475,-8.968947,-13.848853},
{-25.79173,-22.853815,-16.961695,-5.021012,-8.581506,-17.759816,-16.548677,-14.196506,-13.12892,-13.460299,-10.931142,-15.552411,-17.550611,-15.534403,-14.306529,-12.17963,-11.46772,-12.231923,-10.941903,-18.002969,-9.303792,-14.339968},
{-25.568061,-22.182158,-17.131013,-5.070664,-8.728291,-17.270362,-16.502025,-13.908292,-12.800021,-13.51727,-10.972671,-15.374482,-17.17321,-15.580048,-14.43483,-12.079796,-11.552501,-12.490627,-11.06514,-17.272614,-9.223117,-14.458965},
{-24.387338,-20.306069,-17.052213,-5.296798,-8.935941,-15.55448,-15.730793,-12.563425,-11.455099,-13.059348,-10.743895,-14.293043,-15.489259,-14.985608,-14.168821,-11.152257,-11.548597,-12.667344,-10.911452,-14.972356,-8.62054,-12.640413},
{-23.846685,-19.746144,-16.780155,-5.450874,-8.863025,-14.851792,-15.283684,-11.902303,-10.771291,-12.670394,-10.497529,-13.708564,-14.739093,-14.499058,-13.790267,-10.591893,-11.408893,-12.402588,-10.62166,-14.064598,-8.187553,-11.719633},
{-23.352329,-19.070501,-16.178131,-5.792904,-8.213601,-13.793363,-14.569293,-10.836419,-9.12619,-11.878682,-9.581251,-12.618365,-13.52198,-13.624147,-12.963658,-9.586194,-10.857692,-11.700156,-9.90208,-12.648099,-6.916056,-10.321964},
{-23.346283,-19.057871,-16.106968,-5.829966,-7.77412,-13.656071,-14.464219,-10.579115,-8.448941,-11.721101,-9.248022,-12.353479,-13.271125,-13.494218,-12.823714,-9.323599,-10.625762,-11.561939,-9.717443,-12.4136,-6.523757,-9.952478},
{-23.348562,-19.060231,-16.099363,-5.564817,-6.469521,-13.621829,-14.43403,-10.439393,-6.843591,-11.632985,-8.96345,-12.170362,-13.069004,-13.448887,-12.781965,-9.044546,-10.439394,-11.478668,-9.579503,-12.314771,-6.260857,-9.590335},
{-23.35274,-19.06059,-16.099114,-5.338265,-5.618011,-13.618258,-14.434225,-10.436893,-5.444378,-11.626534,-8.86922,-12.156055,-13.02703,-13.446915,-12.780448,-9.034561,-10.43608,-11.470044,-9.57163,-12.280386,-6.299126,-9.541887},
{-23.357046,-19.060682,-16.097378,None,None,-13.615286,-14.435322,-10.418801,None,-11.622208,-8.718976,-12.175761,-13.004067,-13.445588,-12.778869,-9.025801,-10.432158,-11.293881,-9.566311,None,-6.552631,-9.523386}};

For s=500 we are missing LiH Li2 LiF and F2

SRGBSE={{},
{},
{},
{},
{},
{},
{},
{},
{},
{},
{},
{}};

-10.77191217*HaToEv

-10.79324284*HaToEv

GW20 convergence

We are using a black box script and look at the number of converged calculation. The parameters are a DIIS space of size 5 and convergence to (10^(-5)) in less than 65 iterations.

TableForm[{{"η","Method",0.1,0.05,0.01,0.005,0.001,0},{"Nb of cv/20","non-TDA",22,21,20,4,2,2},{"Nb of cv/20","TDA",21,22,12,3,2,2},{"Nb of cv/20","TDHF",17,16,11,1,1,1}}]

NON-TDA CASE: 0.05 need HF / 0.01 need H2 and F2 / 0.005 only He Ne Li2 BH3 / 0.001 and 0 only He Ne. 

TDA CASE: 0.1 need N2 / 0.01 has only He,Ne,Li2,LiH,Ar,LiF,CO,BH3,NH3,BF,SH2,O3 / 0.005 He,Ne and LiH /  0.001 and 0 only He Ne. 

TDHF CASE: 0.1 need BeO,BN,SH2,MgO,O3 / 0.05 need Ar,BeO,BN,SH2,MgO,O3 / 0.01 / 0.005, 0.001 and 0 only He

For any value of s up to 500 in the SRG scheme we reached convergence using these parameters !!!

SRG[[-1]]-SRG[[-2]]

The previous list shows that we reached convergence to (10^(-3)) eV for every SRG calculation.

SRG100={0.02324,0.00331,0.00100,0.00036,0.00022, 0.00002,0.0000001};
SRG10000={0.02324,0.00330,0.00088,0.00021,0.00012,0.00009,0.00003,0.00005,0.00004,0.00002,0.00003,0.00002,0.00005,0.00005,0.00006,0.00015,0.00015,0.00032,0.00024,0.00011,0.00009,0.00008,0.00006,0.00007,0.00004,0.00003,0.00002,0.00007,0.00006,0.00006,0.00015,0.00019,0.00023,0.00026,0.00014,0.00022,0.00014,0.00012,0.00010,0.00008,0.00007,0.00004,0.00007,0.00003,0.00009,0.00007,0.00006,0.00004,0.00006,0.00006,0.00006,0.00004,0.00003,0.00004,0.00010,0.00011,0.00016,0.00006,0.00007,0.00003,0.00004,0.00004,0.00009,0.00006,0.00004,0.00003}  ;

SRG100=Transpose[{Range[Length@SRG100],SRG100}];
SRG10000=Transpose[{Range[Length@SRG10000],SRG10000}];

ListLogPlot[{SRG100,SRG10000},ImageSize->500,PlotTheme->"Scientific",FrameStyle->Directive[Black,18,Thick],FrameLabel->{{MaTeX["\\text{Conv}",FontSize->18],None},{MaTeX["\\text{Nb Iter}",FontSize->18],None}},Joined->True,PlotRange->{{1,64},{(10^(-5)),(10^(-1))}},PlotMarkers->{"●",12},AspectRatio->1/2]

eta01={0.03545,0.00968, 0.00314, 0.00225, 0.00018,0.00005,0.00001};
eta005={0.03510,0.01914,0.00630,0.00236,0.00066, 0.00017,0.00004,0.00001,0.00000};
eta001={0.03728, 0.04729, 0.02772, 0.01982, 0.01804,0.01436,0.01780,0.00758,0.00552,0.00531,0.00503,0.00461,0.00570,0.00328,0.00163,0.00130,0.00187,0.00173,0.00095,0.00042,0.00065,0.00013, 0.00010,0.00004,0.00003,0.00003,0.00001, 0.00001, 0.00000};
eta0005={0.03792,0.05848,0.05434,0.03952,0.03695,0.02678,0.04053,0.03553,0.03980,0.02909,0.02992,0.03301,0.02603,0.01902,0.01528,0.02873,0.03217,0.04906,0.03944,0.02596,0.02804,0.01435,0.01344,0.01514,0.00927,0.02388,0.01307,0.00667,0.03077,0.01369,0.00933,0.02341,0.00651,0.00559,0.04587,0.01534,0.01381,0.01420,0.01268,0.00789, 0.01373, 0.01451,0.04511,0.02112,0.01066,0.01250,0.01822,0.00947,0.01053, 0.00806, 0.00421, 0.00743,0.00443,0.01041,0.00766, 0.00947,0.01873,0.01552,0.00685, 0.00731, 0.00738,0.00503,0.00421,0.01054, 0.00262,0.01719};
eta01=Transpose[{Range[Length@eta01],eta01}];
eta005=Transpose[{Range[Length@eta005],eta005}];
eta001=Transpose[{Range[Length@eta001],eta001}];
eta0005=Transpose[{Range[Length@eta0005],eta0005}];

ListLogPlot[{eta01,eta005,eta001,eta0005},ImageSize->500,PlotTheme->"Scientific",FrameStyle->Directive[Black,18,Thick],FrameLabel->{{MaTeX["\\text{Conv}",FontSize->18],None},{MaTeX["\\text{Nb Iter}",FontSize->18],None}},Joined->True,PlotRange->{{1,64},{(10^(-5)),(10^(-1))}},PlotMarkers->{"●",12},AspectRatio->1/2]

1/(Sqrt[2000])//N

s dependence

Fig 2: Water

nbSol=2;
datanonTDA=Transpose[{s,-SRG[[;;,nbSol]]+IPCC[[nbSol]]}];
dataTDA=Transpose[{s,-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}];

interpnonTDA[x_]=Interpolation[Transpose[{Log10[s],-SRG[[;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];
interpTDA[x_]=Interpolation[Transpose[{Log10[s],-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];

Show[ListLogLinearPlot[datanonTDA,PlotTheme->"Scientific",PlotStyle->,ImageSize->600,FrameStyle->Directive[Black,18,Thick],FrameLabel->{{MaTeX["\\Delta\\text{IP(eV)}~\\text{w.r.t.}~\\text{CCSD(T)}",FontSize->18],None},{MaTeX["s",FontSize->18],MaTeX["\\ce{Ne}",FontSize->18]}},PlotRange->{{0.001,500},{-0.8,2.2}},ImagePadding->{{70, 10}, {50, 35}},PlotMarkers->{"●",12}],
ListLogLinearPlot[dataTDA,PlotStyle->,PlotMarkers->{"●",12}],

LogLinearPlot[Evaluate@interpnonTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],
LogLinearPlot[Evaluate@interpTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],

LogLinearPlot[{-SRG[[1,nbSol]]+IPCC[[nbSol]],-qsGWSymRPA[[-1,nbSol]]+IPCC[[nbSol]],-qsGWSymTDA[[-1,2]]+IPCC[[nbSol]]},{x,0.0001,500},PlotStyle->{{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]}}],
Epilog->{Inset[LineLegend[{Directive[,Thickness[0.01],Dashed],Directive[,Thickness[0.01],Dashed],Directive[,Dashed,Thickness[0.01]]},
{MaTeX["\\text{qs$GW$ TDA}~\\eta=0",FontSize->18],
MaTeX["\\text{qs$GW$}~\\eta=0",FontSize->18],
MaTeX["\\text{HF}",FontSize->18]
},LegendLayout->"ReversedColumn"],Scaled[{0.8,0.525}]],Inset[LineLegend[{Directive[,Thickness[0.01]],Directive[,Thickness[0.01]]},
{MaTeX["\\text{SRG-qs$GW$ TDA}",FontSize->18],
MaTeX["\\text{SRG-qs$GW$}",FontSize->18]},LegendLayout->"ReversedColumn"],Scaled[{0.17,0.525}]]}
]

nbSol=8;
datanonTDA=Transpose[{s,-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}];
dataTDA=Transpose[{s,-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}];

interpnonTDA[x_]=Interpolation[Transpose[{Log10[s],-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];
interpTDA[x_]=Interpolation[Transpose[{Log10[s],-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];

fig2=Show[ListLogLinearPlot[datanonTDA,PlotTheme->"Scientific",PlotStyle->,ImageSize->600,FrameStyle->Directive[Black,18,Thick],FrameLabel->{{MaTeX["\\Delta\\text{IP(eV)}~\\text{wrt}~\\text{CCSD(T)}",FontSize->22],None},{MaTeX["s",FontSize->22],None}},PlotRange->{{0.001,500},{-0.6,1.8}},ImagePadding->{{75, 5}, {55, 5}},PlotMarkers->{"●",12}],
ListLogLinearPlot[dataTDA,PlotStyle->,PlotMarkers->{"●",12}],

LogLinearPlot[Evaluate@interpnonTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],
LogLinearPlot[Evaluate@interpTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],

LogLinearPlot[{-HF[[1,nbSol]]+IPCC[[nbSol]],-qsGWSymRPA[[1,2,nbSol]]+IPCC[[nbSol]],-qsGWSymTDA[[2,nbSol]]+IPCC[[nbSol]]},{x,0.0001,500},PlotStyle->{{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]}}],

Epilog->{Inset[LineLegend[{Directive[,Thickness[0.01],Dashed],Directive[,Thickness[0.01],Dashed],Directive[,Dashed,Thickness[0.01]]},
{MaTeX["\\text{qs}GW_{\\text{TDA}}~\\eta=0.05",FontSize->22],
MaTeX["\\text{qs$GW$}~\\eta=0.05",FontSize->22],
MaTeX["\\text{HF}",FontSize->22]
},LegendLayout->"ReversedColumn"],Scaled[{0.77,0.575}]],Inset[LineLegend[{Directive[,Thickness[0.01]],Directive[,Thickness[0.01]]},
{MaTeX["\\text{SRG-qs}GW_{\\text{TDA}}",FontSize->22],
MaTeX["\\text{SRG-qs$GW$}",FontSize->22]},LegendLayout->"ReversedColumn"],Scaled[{0.18,0.575}]]}
]

Export["/home/amarie/SRGGW/Manuscript/fig2.pdf",fig2]

Fig 3: LiH, Li2 and BeO

nbSol=4;
datanonTDA=Transpose[{s,-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}];
dataTDA=Transpose[{s,-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}];

interpnonTDA[x_]=Interpolation[Transpose[{Log10[s],-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];
interpTDA[x_]=Interpolation[Transpose[{Log10[s],-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];

fig3a=Show[ListLogLinearPlot[datanonTDA,PlotTheme->"Scientific",PlotStyle->,ImageSize->600,FrameStyle->Directive[Black,20,Thick],FrameLabel->{{MaTeX["\\Delta\\text{IP(eV)}~\\text{w.r.t.}~\\text{CCSD(T)}",FontSize->20],None},{MaTeX["s",FontSize->24],MaTeX["\\ce{Li2}",FontSize->24]}},PlotRange->{{0.001,500},{-0.35,0.4}},ImagePadding->{{75, 10}, {55, 40}},PlotMarkers->{"●",12}],
ListLogLinearPlot[dataTDA,PlotStyle->,PlotMarkers->{"●",12}],

LogLinearPlot[Evaluate@interpnonTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],
LogLinearPlot[Evaluate@interpTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],

LogLinearPlot[{-HF[[1,nbSol]]+IPCC[[nbSol]],-qsGWSymRPA[[1,2,nbSol]]+IPCC[[nbSol]],-qsGWSymTDA[[2,nbSol]]+IPCC[[nbSol]]},{x,0.0001,500},PlotStyle->{{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]}}]
]

nbSol=5;
datanonTDA=Transpose[{s,-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}];
dataTDA=Transpose[{s,-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}];

interpnonTDA[x_]=Interpolation[Transpose[{Log10[s],-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];
interpTDA[x_]=Interpolation[Transpose[{Log10[s],-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];

fig3b=Show[ListLogLinearPlot[datanonTDA,PlotTheme->"Scientific",PlotStyle->,ImageSize->600,FrameStyle->Directive[Black,20,Thick],FrameLabel->{{None,None},{MaTeX["s",FontSize->24],MaTeX["\\ce{LiH}",FontSize->24]}},PlotRange->{{0.001,500},{-0.15,0.8}},ImagePadding->{{75, 10}, {55, 40}},PlotMarkers->{"●",12}],
ListLogLinearPlot[dataTDA,PlotStyle->,PlotMarkers->{"●",12}],

LogLinearPlot[Evaluate@interpnonTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],
LogLinearPlot[Evaluate@interpTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],

LogLinearPlot[{-HF[[1,nbSol]]+IPCC[[nbSol]],-qsGWSymRPA[[1,2,nbSol]]+IPCC[[nbSol]],-qsGWSymTDA[[2,nbSol]]+IPCC[[nbSol]]},{x,0.0001,500},PlotStyle->{{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]}}],

Epilog->{Inset[LineLegend[{Directive[,Thickness[0.01],Dashed],Directive[,Thickness[0.01],Dashed],Directive[,Dashed,Thickness[0.01]]},
{MaTeX["\\text{qs$GW$}~\\eta=0.05",FontSize->24],
MaTeX["\\text{qs}GW_{\\text{TDA}}~\\eta=0.05",FontSize->24],
MaTeX["\\text{HF}",FontSize->24]
},LegendLayout->"ReversedColumn"],Scaled[{0.77,0.815}]],Inset[LineLegend[{Directive[,Thickness[0.01]],Directive[,Thickness[0.01]]},
{MaTeX["\\text{SRG-qs}GW_{\\text{TDA}}",FontSize->24],
MaTeX["\\text{SRG-qs$GW$}",FontSize->24]}],Scaled[{0.19,0.85}]]}
]

nbSol=11;
datanonTDA=Transpose[{s,-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}];
dataTDA=Transpose[{s,-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}];

interpnonTDA[x_]=Interpolation[Transpose[{Log10[s],-SRG[[1,;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];
interpTDA[x_]=Interpolation[Transpose[{Log10[s],-SRGTDA[[;;,nbSol]]+IPCC[[nbSol]]}],InterpolationOrder->2][Log10[x]];

fig3c=Show[ListLogLinearPlot[datanonTDA,PlotTheme->"Scientific",PlotStyle->,ImageSize->600,FrameStyle->Directive[Black,20,Thick],FrameLabel->{{None,None},{MaTeX["s",FontSize->24],MaTeX["\\ce{BeO}",FontSize->24]}},PlotRange->{{0.001,500},{-0.05,1}},ImagePadding->{{75, 10}, {55, 40}},PlotMarkers->{"●",12}],
ListLogLinearPlot[dataTDA,PlotStyle->,PlotMarkers->{"●",12}],

LogLinearPlot[Evaluate@interpnonTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],
LogLinearPlot[Evaluate@interpTDA[x],{x,0.001,500},PlotStyle->{,Thickness[0.007]}],

LogLinearPlot[{-HF[[1,nbSol]]+IPCC[[nbSol]],-qsGWSymRPA[[1,2,nbSol]]+IPCC[[nbSol]],-qsGWSymTDA[[2,nbSol]]+IPCC[[nbSol]]},{x,0.0001,500},PlotStyle->{{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]},{,Dashed,Thickness[0.007]}}]
]

fig3=GraphicsRow[{fig3a,fig3b,fig3c},ImageSize->1800,Spacings->-72.5]

Export["/home/amarie/SRGGW/Manuscript/fig3.pdf",fig3]

η dependence

ListLogLinearPlot[Transpose[{η,Sym[[;;,1]]}],PlotTheme->"Scientific",ImageSize->Large,FrameStyle->Directive[Black,16,Thick],FrameLabel->{{MaTeX["\\epsilon_{\\text{HOMO}}",FontSize->16],None},{MaTeX["s",FontSize->16],MaTeX["\\ce{He}",FontSize->16]}},PlotRange->{{0.0009,0.1},{-24.8,-24.4}},Joined->True,ImagePadding->{{Automatic, 15}, {Automatic, Automatic}}]

ListLogLinearPlot[Transpose[{η,Sym[[;;,2]]}],PlotTheme->"Scientific",ImageSize->Large,FrameStyle->Directive[Black,16,Thick],FrameLabel->{{MaTeX["\\epsilon_{\\text{HOMO}}",FontSize->16],None},{MaTeX["s",FontSize->16],MaTeX["\\ce{He}",FontSize->16]}},PlotRange->{{0.0009,0.1},{-22,-21.4}},Joined->True,ImagePadding->{{Automatic, 15}, {Automatic, Automatic}}]

GW20+2 statistics on IP

{Mean[IPCC-HF[[1]]],Mean[Abs[IPCC-HF[[1]]]],StandardDeviation[IPCC-HF[[1]]],Min[IPCC-HF[[1]]],Max[IPCC-HF[[1]]]}

{Mean[IPCC-G0W0SymRPA[[1,5]]],Mean[Abs[IPCC-G0W0SymRPA[[1,5]]]],StandardDeviation[IPCC-G0W0SymRPA[[1,5]]],Min[IPCC-G0W0SymRPA[[1,5]]],Max[IPCC-G0W0SymRPA[[1,5]]]}

{Mean[IPCC-qsGWSymRPA[[1,1]]],Mean[Abs[IPCC-qsGWSymRPA[[1,1]]]],StandardDeviation[IPCC-qsGWSymRPA[[1,1]]],Min[IPCC-qsGWSymRPA[[1,1]]],Max[IPCC-qsGWSymRPA[[1,1]]]}

DiffSRG=Table[IPCC,{i,Length[SRG[[1]]]}]-SRG[[1]];
MSE=Map[Mean,DiffSRG];
AbsDiffSRG=Abs[DiffSRG];
MAE=Map[Mean,AbsDiffSRG];
SDE=Map[StandardDeviation,DiffSRG];
MMax=Map[Max,DiffSRG];
MMin=Map[Min,DiffSRG];
tmp=Transpose[{s[[;;]],MSE,MAE,SDE,MMax,MMin}];
TableForm@PrependTo[tmp,{"s","MSE","MAE","SDE","Max","Min"}]

ListColor=ColorData[112,"ColorList"]

fig4a=Show[{Histogram[IPCC-HF[[1]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[1]],Thick}],PlotRange->{{-1,+3},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{HF}",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[1]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[IPCC-HF[[1]],Automatic,"PDF",PlotRange->{{-1,+3},All},PlotStyle->Directive[ListColor[[1]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig4b=Show[{Histogram[IPCC-G0W0SymRPA[[1,5]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[2]],Thick}],PlotRange->{{-1,+3},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["G_0W_0\\text{@HF}~\\eta=0.001",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[2]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[IPCC-G0W0SymRPA[[1,5]],Automatic,"PDF",PlotRange->{{-1,+3},All},PlotStyle->Directive[ListColor[[2]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig4c=Show[{Histogram[IPCC-qsGWSymRPA[[1,1]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[3]],Thick}],PlotRange->{{-1,+3},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{qs}GW~\\eta=0.1",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[3]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[IPCC-qsGWSymRPA[[1,1]],Automatic,"PDF",PlotRange->{{-1,+3},All},PlotStyle->Directive[ListColor[[3]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig4d=Show[{Histogram[DiffSRG[[-2]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[4]],Thick}],PlotRange->{{-1,+3},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{SRG-qs}GW~s=100",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[4]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[DiffSRG[[-2]],Automatic,"PDF",PlotRange->{{-1,+3},All},PlotStyle->Directive[ListColor[[4]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig4=Grid[{{fig4a,fig4b,fig4c,fig4d}}]

Export["/home/amarie/SRGGW/Manuscript/fig4.pdf",fig4]

data=Transpose[{(1/(Sqrt[2s])),MAE}]//N
fig5=ListLogLinearPlot[{data,{{1,0.653445},{0.5,0.433521},{0.1,0.253505},{0.05,0.245843},{0.01,0.236092}}},PlotTheme->"Scientific",PlotStyle->{,},ImageSize->600,FrameStyle->Directive[Black,18,Thick],FrameLabel->{{MaTeX["\\text{MAE}",FontSize->18],None},{MaTeX["\\eta",FontSize->18],None}},PlotRange->{{0.009,30},{-0.01,1.05}},ImagePadding->{{70, 10}, {50, 35}},PlotMarkers->{"●",12},Joined->True]

Export["/home/amarie/SRGGW/Manuscript/fig5.pdf",fig5]

1/(2*(0.1^2))

DiffSRG=Table[IPCC,{i,5}]-qsGWSymRPA[[1,;;5]];
MSE=Map[Mean,DiffSRG];
AbsDiffSRG=Abs[DiffSRG];
MAE=Map[Mean,AbsDiffSRG];
SDE=Map[StandardDeviation,DiffSRG];
MMax=Map[Max,DiffSRG];
MMin=Map[Min,DiffSRG];
tmp=Transpose[{{1,0.5,0.1,0.05,0.01},MSE,MAE,SDE,MMax,MMin}];
TableForm@PrependTo[tmp,{"s","MSE","MAE","SDE","Max","Min"}]

{{}}

{Mean[IPCC-G0W0SymTDA[[5]]],Mean[Abs[IPCC-G0W0SymTDA[[5]]]],StandardDeviation[IPCC-G0W0SymTDA[[5]]],Min[IPCC-G0W0SymTDA[[5]]],Max[IPCC-G0W0SymTDA[[5]]]}

{Mean[IPCC-qsGWSymTDA[[2]]],Mean[Abs[IPCC-qsGWSymTDA[[2]]]],StandardDeviation[IPCC-qsGWSymTDA[[2]]],Min[IPCC-qsGWSymTDA[[2]]],Max[IPCC-qsGWSymTDA[[2]]]}

DiffTDA=Table[IPCC,{i,Length[SRGTDA]-1}]-SRGTDA[[;;-2]];
MSE=Map[Mean,DiffTDA];
AbsDiffTDA=Abs[DiffTDA];
MAE=Map[Mean,AbsDiffTDA];
SDE =Map[StandardDeviation,DiffTDA];
AbsMax=Map[Max,DiffTDA];
AbsMin=Map[Min,DiffTDA];

tmp=Transpose[{s[[;;-2]],MSE,MAE,SDE,AbsMax,AbsMin}];
TableForm@PrependTo[tmp,{"s","MSE","MAE","SDE","Max","Min"}]

Show[{Histogram[-DiffTDA[[-1]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[5]],Thick}],PlotRange->{{-1,+3},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{SRG-qs}GW_{\\text{TDA}}~s=100",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[5]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[-DiffTDA[[-1]],Automatic,"PDF",PlotRange->{{-1,+3},All},PlotStyle->Directive[ListColor[[5]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}]
Show[{Histogram[-qsGWSymTDA[[2]]+IPCC,10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[6]],Thick}],PlotRange->{{-1,+3},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{qs}GW~\\eta=0.1",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[6]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[-qsGWSymTDA[[2]]+IPCC,Automatic,"PDF",PlotRange->{{-1,+3},All},PlotStyle->Directive[ListColor[[6]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}]
Show[{Histogram[-G0W0SymTDA[[5]]+IPCC,10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[7]],Thick}],PlotRange->{{-1,+3},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["G_0W_{\\text{TDA},0}~\\eta=0.001",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[7]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[-G0W0SymTDA[[5]]+IPCC,Automatic,"PDF",PlotRange->{{-1,+3},All},PlotStyle->Directive[ListColor[[7]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}]

{Mean[qsGWSymRPA[[1,1]]-IPCC],Mean[Abs[qsGWSymRPA[[1,1]]-IPCC]],Max[qsGWSymRPA[[1,1]]-IPCC],Min[qsGWSymRPA[[1,1]]-IPCC]}

{Mean[qsGWSymTDA[[2]]-IPCC],Mean[Abs[qsGWSymTDA[[2]]-IPCC]],Max[Abs[qsGWSymTDA[[2]]-IPCC]],Min[Abs[qsGWSymTDA[[2]]-IPCC]]}

{Mean[Select[qsGWSymTDA[[1]]-IPCC,NumericQ]],Mean[Abs[Select[qsGWSymTDA[[1]]-IPCC,NumericQ]]],Max[Abs[Select[qsGWSymTDA[[1]]-IPCC,NumericQ]]],Min[Abs[Select[qsGWSymTDA[[1]]-IPCC,NumericQ]]]}

{Mean[Delete[qsGWSymTDA[[2]]-IPCC,13]],Mean[Abs[Delete[qsGWSymTDA[[2]]-IPCC,13]]],Max[Abs[Delete[qsGWSymTDA[[2]]-IPCC,13]]],Min[Abs[Delete[qsGWSymTDA[[2]]-IPCC,13]]]}

DiffTDA=SRGTDAHF[[;;-2]]-Table[IPCC,{i,Length[SRGTDAHF]-1}];
MSE=Map[Mean,DiffTDA];
AbsDiffTDA=Abs[DiffTDA];
MAE=Map[Mean,AbsDiffTDA];
SDE =Map[StandardDeviation,DiffTDA];
AbsMax=Map[Max,DiffTDA];
AbsMin=Map[Min,DiffTDA];
tmp=Transpose[{s[[;;-2]],MSE,MAE,SDE,AbsMax,AbsMin}];
TableForm@PrependTo[tmp,{"s","MSE","MAE","SDE","Max","Min"}]

Vertex corrections in the polarizability

Mean[Abs[G0W0SymRPA[[5]]-IPCC]]

Mean[Abs[G0W0SymRPA[[5]]-IPCC]]
Mean[G0W0SymRPA[[5]]-IPCC]

Mean[Abs[Select[G0W0SymRPAx[[3]]-IPCC,NumericQ]]]
Mean[Select[G0W0SymRPAx[[3]]-IPCC,NumericQ]]

GW20+2 statistics on EA

{Mean[EACC-HF[[2]]],Mean[Abs[EACC-HF[[2]]]],StandardDeviation[EACC-HF[[2]]],Max[EACC-HF[[2]]],Min[EACC-HF[[2]]]}

{Mean[EACC-G0W0SymRPA[[2,5]]],Mean[Abs[EACC-G0W0SymRPA[[2,5]]]],StandardDeviation[EACC-G0W0SymRPA[[2,5]]],Min[EACC-G0W0SymRPA[[2,5]]],Max[EACC-G0W0SymRPA[[2,5]]]}

{Mean[EACC-qsGWSymRPA[[2,1]]],Mean[Abs[EACC-qsGWSymRPA[[2,1]]]],StandardDeviation[EACC-qsGWSymRPA[[2,1]]],Min[EACC-qsGWSymRPA[[2,1]]],Max[EACC-qsGWSymRPA[[2,1]]]}

DiffSRG=Table[EACC,{i,Length[SRG[[2]]]}]-SRG[[2]];
MSE=Map[Mean,DiffSRG];
AbsDiffSRG=Abs[DiffSRG];
MAE=Map[Mean,AbsDiffSRG];
SDE=Map[StandardDeviation,DiffSRG];
AbsMax=Map[Max,DiffSRG];
AbsMin=Map[Min,DiffSRG];
tmp=Transpose[{s[[;;]],MSE,MAE,SDE,AbsMax,AbsMin}];
TableForm@PrependTo[tmp,{"s","MSE","MAE","SDE","Max","Min"}]

fig6a=Show[{Histogram[EACC-HF[[2]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[1]],Thick}],PlotRange->{{-3,+1},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{HF}",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[1]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[EACC-HF[[2]],Automatic,"PDF",PlotRange->{{-3,+1},All},PlotStyle->Directive[ListColor[[1]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig6b=Show[{Histogram[EACC-G0W0SymRPA[[2,5]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[2]],Thick}],PlotRange->{{-3,+1},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["G_0W_0\\text{@HF}~\\eta=0.001",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[2]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[EACC-G0W0SymRPA[[2,5]],Automatic,"PDF",PlotRange->{{-3,+1},All},PlotStyle->Directive[ListColor[[2]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig6c=Show[{Histogram[EACC-qsGWSymRPA[[2,1]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[3]],Thick}],PlotRange->{{-3,+1},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{qs}GW~\\eta=0.1",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[3]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[EACC-qsGWSymRPA[[2,1]],Automatic,"PDF",PlotRange->{{-3,+1},All},PlotStyle->Directive[ListColor[[3]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig6d=Show[{Histogram[DiffSRG[[-2]],10,"PDF",PlotTheme->"Scientific",ChartBaseStyle->EdgeForm[{ListColor[[4]],Thick}],PlotRange->{{-3,+1},All},FrameLabel->{{None,None},{MaTeX["\\text{Error (eV)}",FontSize->20],MaTeX["\\text{SRG-qs}GW~s=100",FontSize->20]}},ChartStyle->{Directive[Opacity[0.5],ListColor[[4]]]},FrameTicks->{Automatic,None},FrameStyle->Directive[Thick,20,Black],ImageSize->300],
SmoothHistogram[DiffSRG[[-2]],Automatic,"PDF",PlotRange->{{-3,+1},All},PlotStyle->Directive[ListColor[[4]],Thickness[0.01]],Filling->Bottom,PlotTheme->"Web"]}];
fig6=Grid[{{fig6a,fig6b,fig6c,fig6d}}]

Export["/home/amarie/SRGGW/Manuscript/fig6.pdf",fig6]