Initialization

HaToeV=27.21138602;

(*Titou's path*)
(*SetDirectory["~/Dropbox/Manuscripts/ufGW/Data"];*)

(*Enzo's path*)
SetDirectory["~/Work/ufGW/Data"];

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

Numerical data

ϵ4={{1.0,23.284472},{1.025,23.540448},{1.05,23.781121},{1.075,24.002084},{1.1,24.196931},{1.125,24.355758},{1.15,24.463104},{1.175,24.497569},{1.2,24.439877},{1.225,24.289859},{1.25,24.069414},{1.275,23.805244},{1.3,23.516919},{1.325,23.216331},{1.35,22.910393}};

ϵ5={{1.1,27.103397},{1.125,26.784466},{1.15,26.509573},{1.175,26.299399},{1.2,26.172614},{1.225,26.128902},{1.25,26.146006},{1.275,26.197002},{1.3,26.262232},{1.325,26.329847},{1.35,26.393103}};

ListPlot[{ϵ4,ϵ5},PlotTheme->"Web",Joined->True]

Z4={{1.0,0.964721},{1.025,0.961772},{1.05,0.956999},{1.075,0.948699},{1.1,0.933404},{1.125,0.904167},{1.15,0.848555},{1.175,0.751875},{1.2,0.616552},{1.225,0.476710},{1.25,0.365270},{1.275,0.287739},{1.3,0.235707},{1.325,0.200378},{1.35,0.175725}};

Z5={{1.1,0.021813},{1.125,0.048282},{1.15,0.100987},{1.175,0.194635},{1.2,0.326815},{1.225,0.463419},{1.25,0.571546},{1.275,0.645708},{1.3,0.694337},{1.325,0.726254},{1.35,0.747506}};

ListPlot[{Z4,Z5},PlotTheme->"Web",Joined->True]

ZZ4={{1.0,0.000259},{1.025,0.001499},{1.05,0.004661},{1.075,0.011599},{1.1,0.026034},{1.125,0.055329},{1.15,0.112492},{1.175,0.212615},{1.2,0.352622},{1.225,0.496698},{1.25,0.610946},{1.275,0.690069},{1.3,0.742975},{1.325,0.778807},{1.35,0.803778}};

ZZ5={{1.1,0.947557},{1.125,0.917757},{1.15,0.860133},{1.175,0.759591},{1.2,0.619206},{1.225,0.474792},{1.25,0.360243},{1.275,0.280855},{1.3,0.227717},{1.325,0.191686},{1.35,0.166547}};

(* (1) -> (2,2) *)

ListPlot[{ZZ4,ZZ5},PlotTheme->"Web",Joined->True]

eps=Import["~/Dropbox/quack/H2_6-31g_e_3.dat"];
epsZ=Import["~/Dropbox/quack/H2_6-31g_Z_3.dat"];

ListPlot[Table[{eps[[k,1]],eps[[k,n]]},{n,2,10},{k,Length[eps]}],PlotTheme->"Web",Joined->True]

ListPlot[Table[{epsZ[[k,1]],epsZ[[k,n]]},{n,3,6},{k,Length[eps]}],PlotTheme->"Web",Joined->True]

Downfolding BSE

(H^((p)))=(({{(Subscript[ϵ, p]^HF), (Subscript[V, p]^(2h1p)), (Subscript[V, p]^(2p1h))}, {((Subscript[V, p]^(2h1p)))\[Transpose], (C^(2h1p)), 0}, {((Subscript[V, p]^(2p1h)))\[Transpose], 0, (C^(2p1h))}}))

Det[(H^((p)))-ω 1]==0

Det[(({{(Subscript[ϵ, p]^HF)-ω, (Subscript[V, p]^(2h1p)), (Subscript[V, p]^(2p1h))}, {((Subscript[V, p]^(2h1p)))\[Transpose], (C^(2h1p))-ω 1, 0}, {((Subscript[V, p]^(2p1h)))\[Transpose], 0, (C^(2p1h))-ω 1}}))]==0

((Subscript[ϵ, p]^HF)-ω)Det[(({{(C^(2h1p))-ω 1, 0}, {0, (C^(2p1h))-ω 1}}))]-((Subscript[V, p]^(2h1p)))\[Transpose](({{(Subscript[V, p]^(2h1p)), (Subscript[V, p]^(2p1h))}, {0, (C^(2p1h))-ω 1}}))+((Subscript[V, p]^(2p1h)))\[Transpose](({{(Subscript[V, p]^(2h1p)), (Subscript[V, p]^(2p1h))}, {(C^(2h1p))-ω 1, 0}}))=0

((Subscript[ϵ, p]^HF)-ω)((C^(2h1p))-ω 1)((C^(2p1h))-ω 1)-((Subscript[V, p]^(2h1p)))\[Transpose]((C^(2p1h))-ω 1)(Subscript[V, p]^(2h1p))-((Subscript[V, p]^(2p1h)))\[Transpose]((C^(2h1p))-ω 1)(Subscript[V, p]^(2p1h))=0

(Subscript[ϵ, p]^HF)-ω=((((Subscript[V, p]^(2h1p)))\[Transpose]((C^(2p1h))-ω 1)(Subscript[V, p]^(2h1p))+((Subscript[V, p]^(2p1h)))\[Transpose]((C^(2h1p))-ω 1)(Subscript[V, p]^(2p1h)))/(((C^(2h1p))-ω 1)((C^(2p1h))-ω 1)))=0

Two-determinant reference

Let’s consider that additionally to the 1h or 1p reference determinant, we now have an additional 2h1p or 2p1h configuration in the reference space.
Let’s denote the reference determinant as P (where P can be a particle or a hole) and the 2h1p or 2p1h configuration as QIA (where Q can be a particle or a hole).

(H^((P)))=(({{(Subscript[ϵ, P]^HF), (Subscript[V, Q[IA],P]), (Subscript[V, p]^(2h1p)), (Subscript[V, p]^(2p1h))}, {(Subscript[V, P,Q[IA]]), (Subscript[C, Q[IA],Q[IA]]), (Subscript[C, Q[IA]]^(2h1p)), (Subscript[C, Q[IA]]^(2h1p))}, {((Subscript[V, P]^(2h1p)))\[Transpose], ((Subscript[C, Q[IA]]^(2h1p)))\[Transpose], (C^(2h1p)), 0}, {((Subscript[V, P]^(2p1h)))\[Transpose], ((Subscript[C, Q[IA]]^(2h1p)))\[Transpose], 0, (C^(2p1h))}}))

The matrix elements are

(Subscript[V, P,k[lc]]^(2h1p))=(Sqrt[2])(BraKet[Pc, kl])	(Subscript[V, P,[kc]d]^(2p1h))=(Sqrt[2])(BraKet[Pk, dc])

(Subscript[V, P,Q[IA]])=(Sqrt[2])(BraKet[PA, QI])

(Subscript[C, i[ja],k[lc]]^(2h1p))=(((Subscript[ϵ, i])+(Subscript[ϵ, j])-(Subscript[ϵ, a]))(Subscript[δ, jl])(Subscript[δ, ac])-2(BraKet[jc, al]))(Subscript[δ, ik])	(Subscript[C, [ia]b,[kc]d]^(2p1h))=(((Subscript[ϵ, a])+(Subscript[ϵ, b])-(Subscript[ϵ, i]))(Subscript[δ, ik])(Subscript[δ, ac])+2(BraKet[ak, ic]))(Subscript[δ, bd])

(Subscript[C, Q[IA],Q[IA]])=Sign[(Subscript[ϵ, Q])-μ](((Subscript[ϵ, Q])+(Subscript[ϵ, A])-(Subscript[ϵ, I]))+2(BraKet[IA, AI]))

(Subscript[C, Q[IA],k[lc]]^(2h1p))=-2(BraKet[Ic, Al])(Subscript[δ, Qk])	(Subscript[C, [IA]Q,[kc]d]^(2p1h))=+2(BraKet[Ak, Ic])(Subscript[δ, Qd])

Let us now solve the secular equations

(({{(Subscript[ϵ, P]^HF)-ω, (Subscript[V, Q[IA]]), (Subscript[V, P]^(2h1p)), (Subscript[V, P]^(2p1h))}, {(Subscript[V, Q[IA]]), (Subscript[C, Q[IA],Q[IA]])-ω, (Subscript[C, Q[IA]]^(2h1p)), (Subscript[C, Q[IA]]^(2p1h))}, {((Subscript[V, P]^(2h1p)))\[Transpose], ((Subscript[C, Q[IA]]^(2h1p)))\[Transpose], (C^(2h1p))-ω I, 0}, {((Subscript[V, P]^(2p1h)))\[Transpose], ((Subscript[C, Q[IA]]^(2p1h)))\[Transpose], 0, (C^(2p1h))-ω I}}))(({{(Subscript[c, P])}, {(Subscript[c, Q[IA]])}, {(c^(2h1p))}, {(c^(2p1h))}}))==(({{0}, {0}, {0}, {0}}))

The fourth line yields

((Subscript[V, P]^(2p1h)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2p1h)))\[Transpose](Subscript[c, Q[IA]])+((C^(2p1h))-ω I)(c^(2p1h))==0	⟹	(c^(2p1h))==-((((C^(2p1h))-ω I))^(-1))(((Subscript[V, P]^(2p1h)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2p1h)))\[Transpose](Subscript[c, Q[IA]]))

The third line yields

((Subscript[V, P]^(2h1p)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2h1p)))\[Transpose](Subscript[c, Q[IA]])+((C^(2h1p))-ω I)(c^(2h1p))==0	⟹	(c^(2h1p))==-((((C^(2h1p))-ω I))^(-1))(((Subscript[V, P]^(2h1p)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2h1p)))\[Transpose](Subscript[c, Q[IA]]))

The second line yields

(Subscript[V, Q[IA]])(Subscript[c, P])+((Subscript[C, Q[IA],Q[IA]])-ω)(Subscript[c, Q[IA]])+(Subscript[C, Q[IA]]^(2h1p))(c^(2h1p))+(Subscript[C, Q[IA]]^(2p1h))(c^(2p1h))==0	
⟹	(Subscript[V, Q[IA]])(Subscript[c, P])+((Subscript[C, Q[IA],Q[IA]])-ω)(Subscript[c, Q[IA]])-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))(((Subscript[V, P]^(2h1p)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2h1p)))\[Transpose](Subscript[c, Q[IA]]))-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))(((Subscript[V, P]^(2p1h)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2p1h)))\[Transpose](Subscript[c, Q[IA]]))==0

⟹	(Subscript[V, Q[IA]])(Subscript[c, P])+((Subscript[C, Q[IA],Q[IA]])-ω)(Subscript[c, Q[IA]])-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[V, P]^(2h1p)))\[Transpose](Subscript[c, P])-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[C, Q[IA]]^(2h1p)))\[Transpose](Subscript[c, Q[IA]])-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[V, P]^(2p1h)))\[Transpose](Subscript[c, P])-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[C, Q[IA]]^(2p1h)))\[Transpose](Subscript[c, Q[IA]])==0

⟹	((Subscript[V, Q[IA]])-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[V, P]^(2h1p)))\[Transpose]-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[V, P]^(2p1h)))\[Transpose])(Subscript[c, P])+(((Subscript[C, Q[IA],Q[IA]])-ω)-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[C, Q[IA]]^(2h1p)))\[Transpose]-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[C, Q[IA]]^(2p1h)))\[Transpose])(Subscript[c, Q[IA]])==0

The first line yields

((Subscript[ϵ, P]^HF)-ω)(Subscript[c, P])+(Subscript[V, Q[IA]])(Subscript[c, Q[IA]])+(Subscript[V, P]^(2h1p))(c^(2h1p))+(Subscript[V, P]^(2p1h))(c^(2p1h))==0

⟹	((Subscript[ϵ, P]^HF)-ω)(Subscript[c, P])+(Subscript[V, Q[IA]])(Subscript[c, Q[IA]])-(Subscript[V, p]^(2h1p))((((C^(2h1p))-ω I))^(-1))(((Subscript[V, P]^(2h1p)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2h1p)))\[Transpose](Subscript[c, Q[IA]]))-(Subscript[V, P]^(2p1h))((((C^(2p1h))-ω I))^(-1))(((Subscript[V, P]^(2p1h)))\[Transpose](Subscript[c, P])+((Subscript[C, Q[IA]]^(2p1h)))\[Transpose](Subscript[c, Q[IA]]))==0

⟹	(((Subscript[ϵ, P]^HF)-ω)-(Subscript[V, p]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[V, P]^(2h1p)))\[Transpose]-(Subscript[V, p]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[V, P]^(2p1h)))\[Transpose])(Subscript[c, P])+((Subscript[V, Q[IA]])-(Subscript[V, P]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[C, Q[IA]]^(2h1p)))\[Transpose]-(Subscript[V, P]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[C, Q[IA]]^(2p1h)))\[Transpose])(Subscript[c, Q[IA]])==0

Finally, we end up wit the new dynamical system

(({{((Subscript[ϵ, P]^HF)-ω)-(Subscript[V, P]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[V, P]^(2h1p)))\[Transpose]-(Subscript[V, P]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[V, P]^(2p1h)))\[Transpose], (Subscript[V, Q[IA]])-(Subscript[V, P]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[C, Q[IA]]^(2h1p)))\[Transpose]-(Subscript[V, P]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[C, Q[IA]]^(2p1h)))\[Transpose]}, {(Subscript[V, Q[IA]])-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[V, P]^(2h1p)))\[Transpose]-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[V, P]^(2p1h)))\[Transpose], ((Subscript[C, Q[IA],Q[IA]])-ω)-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[C, Q[IA]]^(2h1p)))\[Transpose]-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[C, Q[IA]]^(2p1h)))\[Transpose]}}))(({{(Subscript[c, P])}, {(Subscript[c, Q[IA]])}}))==(({{0}, {0}}))

with elements

(Subscript[Σ, P])[ω]=-(Subscript[V, P]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[V, P]^(2h1p)))\[Transpose]-(Subscript[V, P]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[V, P]^(2p1h)))\[Transpose]
(Subscript[Σ, Q[IA]])[ω]=-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[C, Q[IA]]^(2h1p)))\[Transpose]-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[C, Q[IA]]^(2p1h)))\[Transpose]
(Subscript[Σ, Q[IA],P])[ω]=-(Subscript[C, Q[IA]]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[V, P]^(2h1p)))\[Transpose]-(Subscript[C, Q[IA]]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[V, P]^(2p1h)))\[Transpose]
(Subscript[Σ, P,Q[IA]])[ω]=-(Subscript[V, P]^(2h1p))((((C^(2h1p))-ω I))^(-1))((Subscript[C, Q[IA]]^(2h1p)))\[Transpose]-(Subscript[V, P]^(2p1h))((((C^(2p1h))-ω I))^(-1))((Subscript[C, Q[IA]]^(2p1h)))\[Transpose]

The final result is

∴(({{(Subscript[ϵ, P]^HF)+(Subscript[Σ, P])[ω]-ω, (Subscript[V, Q[IA]])+(Subscript[Σ, P,Q[IA]])[ω]}, {(Subscript[V, Q[IA]])+(Subscript[Σ, Q[IA],P])[ω], (Underscript[(Subscript[C, Q[IA],Q[IA]]), (Underscript[⏟, (Subscript[ϵ, Q[IA]])])])+(Subscript[Σ, Q[IA]])[ω]-ω}}))(({{(Subscript[c, P])}, {(Subscript[c, Q[IA]])}}))==(({{0}, {0}}))

Let us now linearize the various quantities

(Subscript[(Subscript[Σ, P])[ω]≈(Subscript[Σ, P])[(Subscript[ϵ, P])]+(ω-(Subscript[ϵ, P]))((∂(Subscript[Σ, P])[ω])/(∂ω))\[RightBracketingBar], ω=(Subscript[ϵ, P])])

(Subscript[(Subscript[Σ, Q[IA]])[ω]≈(Subscript[Σ, Q[IA]])[(Subscript[ϵ, Q[IA]])]+(ω-(Subscript[ϵ, Q[IA]]))((∂(Subscript[Σ, Q[IA]])[ω])/(∂ω))\[RightBracketingBar], ω=(Subscript[ϵ, Q[IA]])])

(Subscript[Σ, P,Q[IA]])[ω]

({{(Subscript[ϵ, P]^HF)+(Subscript[Σ, P])[ω]-ω, (Subscript[V, Q[IA]])+(Subscript[Σ, P,Q[IA]])[ω]}, {(Subscript[V, Q[IA]])+(Subscript[Σ, Q[IA],P])[ω], (Subscript[C, Q[IA],Q[IA]])+(Subscript[Σ, Q[IA]])[ω]-ω}})

Solve[((Subscript[Σ, P])+(ω-(Subscript[ϵ, P]))(Subscript[dΣ, P])-ω)((Subscript[Σ, S])+(ω-(Subscript[ϵ, S]))(Subscript[dΣ, S])-ω)-(Subscript[Σ, PS])(Subscript[Σ, SP])==0,ω]//FullSimplify

Eigenvalues[(({{a, λ}, {λ, b}}))]

(a^2)-2 a b+(b^2)//Factor

(((a-b))^2)+4 (λ^2)>0

PES

AspectRatio

SizeTitle=20;
SizeLabel=20;
SizeLegend=20;
PlotOptions={
Joined->True,
InterpolationOrder->1,
PlotTheme->"Scientific",
BaseStyle->18,
ImageSize->500,
AspectRatio->1,
GridLines->Automatic,
PlotStyle->{
{Thickness[0.01],Orange},{Thickness[0.01],Red},{Thickness[0.01],Blue},{Thickness[0.01],Black},{Thickness[0.01],Gray}
},
PlotMarkers->None
};

cc-pVDZ

Loading data

cc3=Import["scan_f2_cc-pvdz_cc3.dat","Data"];
ccsd=Import["scan_f2_cc-pvdz_ccsd.dat","Data"];
g0w0=Import["scan_f2_cc-pvdz_g0w0.dat","Data"];
rg0w0=Import["scan_f2_cc-pvdz_rg0w0.dat","Data"];
revgw=Import["scan_f2_cc-pvdz_revgw.dat","Data"];
rqsgw=Import["scan_f2_cc-pvdz_rqsgw.dat","Data"];

eta0dot1g0w0=Import["scan_f2_cc-pvdz_eta0dot1g0w0.dat","Data"];
eta0dot1evgw=Import["scan_f2_cc-pvdz_eta0dot1evgw.dat","Data"];

eta1g0w0=Import["scan_f2_cc-pvdz_eta1g0w0.dat","Data"];
eta1evgw=Import["scan_f2_cc-pvdz_eta1evgw.dat","Data"];

eta10g0w0=Import["scan_f2_cc-pvdz_eta10g0w0.dat","Data"];
eta10evgw=Import["scan_f2_cc-pvdz_eta10evgw.dat","Data"];

kappa0dot1g0w0=Import["scan_f2_cc-pvdz_kappa0dot1g0w0.dat","Data"];
kappa0dot1evgw=Import["scan_f2_cc-pvdz_kappa0dot1evgw.dat","Data"];

kappa1g0w0=Import["scan_f2_cc-pvdz_kappa1g0w0.dat","Data"];
kappa1evgw=Import["scan_f2_cc-pvdz_kappa1evgw.dat","Data"];

kappa10g0w0=Import["scan_f2_cc-pvdz_kappa10g0w0.dat","Data"];
kappa10evgw=Import["scan_f2_cc-pvdz_kappa10evgw.dat","Data"];

Ground state

ListPlot[{
cc3,ccsd,g0w0,rg0w0,revgw
},
FrameLabel->{
Style["(Subscript[R, F - F]) (Å)",FontSize->SizeLabel],
Style["E(F-F) (hartree)",FontSize->SizeLabel]},
PlotLegends->Placed[{
Style["CC3",FontSize->SizeLegend],
Style["CCSD",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 0 au)",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 1 au)",FontSize->SizeLegend],
Style["BSE@evGW@HF (κ = 1 au)",FontSize->SizeLegend]
},{Right,Top}],
PlotRange->{{1.1,1.65},{-199,-199.125}},
PlotOptions
]

η = 0.1

ListPlot[{
cc3,ccsd,g0w0,eta0dot1g0w0,eta0dot1evgw
},
FrameLabel->{
Style["(Subscript[R, F - F]) (Å)",FontSize->SizeLabel],
Style["E(F-F) (hartree)",FontSize->SizeLabel]},
PlotLegends->Placed[{
Style["CC3",FontSize->SizeLegend],
Style["CCSD",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (η = 0 au)",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (η = 0.1 au)",FontSize->SizeLegend],
Style["BSE@evGW@HF (η = 0.1 au)",FontSize->SizeLegend]
},{Right,Top}],
PlotRange->{{1.1,1.65},{-199,-199.125}},
PlotOptions
]

η = 1

ListPlot[{
cc3,ccsd,g0w0,eta1g0w0,eta1evgw
},
FrameLabel->{
Style["(Subscript[R, F - F]) (Å)",FontSize->SizeLabel],
Style["E(F-F) (hartree)",FontSize->SizeLabel]},
PlotLegends->Placed[{
Style["CC3",FontSize->SizeLegend],
Style["CCSD",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (η = 0 au)",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (η = 1 au)",FontSize->SizeLegend],
Style["BSE@evGW@HF (η = 1 au)",FontSize->SizeLegend]
},{Right,Top}],
PlotRange->{{1.1,1.65},{-199,-199.125}},
PlotOptions
]

η = 10

ListPlot[{
cc3,ccsd,g0w0,eta10g0w0,eta10evgw
},
FrameLabel->{
Style["(Subscript[R, F - F]) (Å)",FontSize->SizeLabel],
Style["E(F-F) (hartree)",FontSize->SizeLabel]},
PlotLegends->Placed[{
Style["CC3",FontSize->SizeLegend],
Style["CCSD",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (η = 0 au)",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (η = 10 au)",FontSize->SizeLegend],
Style["BSE@evGW@HF (η = 10 au)",FontSize->SizeLegend]
},{Right,Top}],
PlotRange->{{1.1,1.65},{-199,-199.125}},
PlotOptions
]

κ = 0.1

ListPlot[{
cc3,ccsd,g0w0,kappa0dot1g0w0(*,kappa0dot1evgw*)
},
FrameLabel->{
Style["(Subscript[R, F - F]) (Å)",FontSize->SizeLabel],
Style["E(F-F) (hartree)",FontSize->SizeLabel]},
PlotLegends->Placed[{
Style["CC3",FontSize->SizeLegend],
Style["CCSD",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 0 au)",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 0.1 au)",FontSize->SizeLegend],
Style["BSE@evGW@HF (κ = 0.1 au)",FontSize->SizeLegend]
},{Right,Top}],
PlotRange->{{1.1,1.65},{-199,-199.125}},
PlotOptions
]

κ = 1

ListPlot[{
cc3,ccsd,g0w0,kappa1g0w0,kappa1evgw
},
FrameLabel->{
Style["(Subscript[R, F - F]) (Å)",FontSize->SizeLabel],
Style["E(F-F) (hartree)",FontSize->SizeLabel]},
PlotLegends->Placed[{
Style["CC3",FontSize->SizeLegend],
Style["CCSD",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 0 au)",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 1 au)",FontSize->SizeLegend],
Style["BSE@evGW@HF (κ = 1 au)",FontSize->SizeLegend]
},{Right,Top}],
PlotRange->{{1.1,1.65},{-199,-199.125}},
PlotOptions
]

κ = 10

ListPlot[{
cc3,ccsd,g0w0,kappa10g0w0,kappa10evgw
},
FrameLabel->{
Style["(Subscript[R, F - F]) (Å)",FontSize->SizeLabel],
Style["E(F-F) (hartree)",FontSize->SizeLabel]},
PlotLegends->Placed[{
Style["CC3",FontSize->SizeLegend],
Style["CCSD",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 0 au)",FontSize->SizeLegend],
Style["BSE@(Subscript[G, 0])(Subscript[W, 0])@HF (κ = 10 au)",FontSize->SizeLegend],
Style["BSE@evGW@HF (κ = 10 au)",FontSize->SizeLegend]
},{Right,Top}],
PlotRange->{{1.1,1.65},{-199,-199.125}},
PlotOptions
]