Initialization

Needs["MaTeX`"]
SetOptions[MaTeX,"Preamble"->{"\\usepackage{amssymb,amsmath,latexsym,amsfonts,amsthm,xcolor,bm,mhchem}","\\definecolor{darkgreen}{RGB}{0, 180, 0}"}];

Beryllium

Data

Be={
{"(^3)P(1(s^2)2(s^1)2(p^1))",3.210,3.332,3.186,2.874,2.111,2.400,2.363,2.433,2.866,2.864,2.862},
{"(^1)P(1(s^2)2(s^1)2(p^1))",3.210,4.276,4.554,4.922,6.036,6.191,6.263,6.255,6.581,6.579,6.577},
{"(^3)P(1(s^2)2(p^2))",6.691,6.864,7.020,7.112,7.480,7.792,7.824,7.745,7.664,7.659,7.669},
{"(^1)D(1(s^2)2(p^2))",7.598,7.762,7.933,8.188,8.945,9.373,9.424,9.047,8.612,8.618,8.624}
};

Table of excitation energies

TableForm[Be\[Transpose],
TableHeadings->{{"State","SF-TDBLYP","SF-TDB3LYP","SF-TD-CAM-B3LYP","SF-TDBHHLYP","SF-CIS","SF-BSE@(Subscript[G, 0])(Subscript[W, 0])","SF-dBSE@(Subscript[G, 0])(Subscript[W, 0])","SF-ADC(2)-s","SF-ADC(2)-x","SF-ADC(3)","FCI"},None}, TableAlignments->Left]

⟨(S^2)⟩ values

TableForm[
{
{"(^1)S(1(s^2)2(s^2))",0.0023,0.0003,0.0008,0.0037,0.0037,0.0015,,0},
{"(^3)P(1(s^2)2s2p)",1.0000,1.9807,1.8388,1.9985,1.9985,2.0000,,2},
{"(^1)P(1(s^2)2s2p)",1.0000,0.0229,0.1640,0.0234,0.0235,0.0142,,0},
{"(^3)P(1(s^2)2(p^2))",1.0000,1.0000,1.0000,1.0000,1.000,1.0000,,2},
{"(^1)D(1(s^2)2(p^2))",0.0134,0.0019,0.0062,0.0133,0.0133,0.0059,,0}
},
TableHeadings->{None,{"State","SF-TDA-BLYP","SF-TDA-B3LYP","SF-TDA-BHHLYP","SF-TDA-BSE@(Subscript[G, 0])(Subscript[W, 0])","SF-TDA-BSE@evGW","SF-CIS","SF-ADC(2)","FCI"}}, TableAlignments->Center]

Graph

ΔΕ=Table[Be[[;;,k]],{k,2,12}];
state=Be[[;;,1]];
method={"SF-TD-BLYP","SF-TD-B3LYP","SF-TD-CAM-B3LYP","SF-TD-BH\\&HLYP","SF-CIS","SF-BSE@G$_0$W$_0$","SF-dBSE@G$_0$W$_0$","SF-ADC(2)-s","SF-ADC(2)-x","SF-ADC(3)","FCI"};
color={Red,Red,Red,Red,Purple,Blue,Blue,Orange,Orange,Orange,Black};

Show[{
ListPlot[Table[Callout[Table[{2m-3/2,ΔΕ[[m,k]]},{m,Length[ΔΕ]}],state[[k]]],{k,4}],Joined->True,PlotStyle->{{LightGreen,Thickness[0.01]},{LightOrange,Thickness[0.01]},{LightRed,Thickness[0.01]},{LightPurple,Thickness[0.01]}}]
,
Show[
Table[Plot[If[2m-2≤x≤2m-1,ΔΕ[[m]]],{x,0,2Length[ΔΕ]-1},PlotStyle->Directive[Thick,color[[m]]]],{m,Length[ΔΕ]}]
]
},
Frame->True,Axes->False,PlotRange->{{-0.5,21.5},{1.9,9.8}},GridLines->{{5.5,7.5,11.5,17.5},Automatic},FrameTicks->{{Automatic,None},{Table[{2k-3/2,Rotate[MaTeX["\\text{"<>method[[k]]<>"}",FontSize->20],π/2]},{k,Length[method]}],None}},
BaseStyle->16,PlotRangePadding->0,FrameStyle->Directive[Thick,16,Black],AspectRatio->1,FrameLabel->{None,MaTeX["\\text{Excitation energy (eV)}",FontSize->24]},ImageSize->700]

`

Cyclobutadiene

(Subscript[D, 2h])

Data

CBDD2h={
{"1 (^3)(Subscript[B, 1  g])",1.750,1.790,1.583,1.521,1.438,1.403,1.573,1.576,1.456,1.654,1.516,1.475},
{"1 (^1)(Subscript[B, 1  g])",2.260,2.379,2.813,3.836,2.704,2.883,3.208,3.141,3.285,3.416,3.260,3.215},
{"2 (^1)(Subscript[A, 1  g])",4.094,4.238,4.528,5.499,4.540,4.621,4.247,3.796,4.334,4.360,4.205,4.176}
};

Table of excitation energies

TableForm[CBDD2h\[Transpose],
TableHeadings->{{"State","SF-TD-B3LYP","SF-TD-CAM-B3LYP","SF-TD-BHHLYP","SF-CIS","SF-BSE@(Subscript[G, 0])(Subscript[W, 0])","SF-dBSE@(Subscript[G, 0])(Subscript[W, 0])","SF-ADC(2)-s","SF-ADC(2)-x","SF-ADC(3)","EOM-SF-CCSD","EOM-SF-CCSD(fT)","EOM-SF-CCSD(dT)"},None}, TableAlignments->Left]

Graph

ΔΕ=Table[CBDD2h[[;;,k]],{k,2,13}];
state=CBDD2h[[;;,1]];
method={"SF-TD-B3LYP","SF-TD-CAM-B3LYP","SF-TD-BH\\&HLYP","SF-CIS","SF-BSE@G$_0$W$_0$","SF-dBSE@G$_0$W$_0$","SF-ADC(2)-s","SF-ADC(2)-x","SF-ADC(3)","EOM-SF-CCSD","EOM-SF-CCSD(fT)","EOM-SF-CCSD(dT)"};
color={Red,Red,Red,Purple,Blue,Blue,Orange,Orange,Orange,Black,Black,Black};

Show[{
ListPlot[Table[Callout[Table[{2m-3/2,ΔΕ[[m,k]]},{m,Length[ΔΕ]}],state[[k]]],{k,3}],Joined->True,PlotStyle->{{LightGreen,Thickness[0.01]},{LightOrange,Thickness[0.01]},{LightRed,Thickness[0.01]},{LightPurple,Thickness[0.01]}}]
,
Show[
Table[Plot[If[2m-2≤x≤2m-1,ΔΕ[[m]]],{x,0,2Length[ΔΕ]-1},PlotStyle->Directive[Thick,color[[m]]]],{m,Length[ΔΕ]}]
]
},
PlotLabel->MaTeX["\\text{CBD (D$_{2h}$)}",FontSize->30],
Frame->True,Axes->False,PlotRange->{{-0.5,23.5},{1,5.6}},GridLines->{{3.5,5.5,9.5,15.5},Automatic},FrameTicks->{{Automatic,None},{Table[{2k-3/2,Rotate[MaTeX["\\text{"<>method[[k]]<>"}",FontSize->20],π/2]},{k,Length[method]}],None}},
BaseStyle->16,PlotRangePadding->0,FrameStyle->Directive[Thick,16,Black],AspectRatio->1,FrameLabel->{None,MaTeX["\\text{Excitation energy (eV)}",FontSize->24]},ImageSize->600]

`

(Subscript[D, 4h])

Data

CBDD4h={
{"1 (^3)(Subscript[A, 2  g])",-0.020,0.012,0.048,0.317,-0.049,0.012,0.265,0.217,0.083,0.369,0.163,0.098},
{"2 (^1)(Subscript[A, 1  g])",0.547,0.677,1.465,3.125,1.189,1.507,1.658,1.123,1.621,1.824,1.530,1.456},
{"1 (^1)(Subscript[B, 2  g])",0.486,0.595,1.282,2.650,1.480,1.841,1.904,1.799,1.930,2.143,1.921,1.853}
};

Table of excitation energies

TableForm[CBDD4h\[Transpose],
TableHeadings->{{"State","SF-TDB3LYP","SF-TD-CAM-B3LYP","SF-TD-BHHLYP","SF-CIS","SF-BSE@(Subscript[G, 0])(Subscript[W, 0])","SF-dBSE@(Subscript[G, 0])(Subscript[W, 0])","SF-ADC(2)-s","SF-ADC(2)-x","SF-ADC(3)","EOM-SF-CCSD","EOM-SF-CCSD(fT)","EOM-SF-CCSD(dT)"},None}, TableAlignments->Left]

Graph

ΔΕ=Table[CBDD4h[[;;,k]],{k,2,13}];
state=CBDD4h[[;;,1]];
method={"SF-TD-B3LYP","SF-TD-CAM-B3LYP","SF-TD-BH\\&HLYP","SF-CIS","SF-BSE@G$_0$W$_0$","SF-dBSE@G$_0$W$_0$","SF-ADC(2)-s","SF-ADC(2)-x","SF-ADC(3)","EOM-SF-CCSD","EOM-SF-CCSD(fT)","EOM-SF-CCSD(dT)"};
color={Red,Red,Red,Purple,Blue,Blue,Orange,Orange,Orange,Black,Black,Black};

Show[{
ListPlot[Table[Callout[Table[{2m-3/2,ΔΕ[[m,k]]},{m,Length[ΔΕ]}],state[[k]]],{k,3}],Joined->True,PlotStyle->{{LightGreen,Thickness[0.01]},{LightOrange,Thickness[0.01]},{LightRed,Thickness[0.01]},{LightPurple,Thickness[0.01]}}]
,
Show[
Table[Plot[If[2m-2≤x≤2m-1,ΔΕ[[m]]],{x,0,2Length[ΔΕ]-1},PlotStyle->Directive[Thick,color[[m]]]],{m,Length[ΔΕ]}]
]
},
PlotLabel->MaTeX["\\text{CBD (D$_{4h}$)}",FontSize->30],
Frame->True,Axes->False,PlotRange->{{-0.5,23.5},{-0.2,3.2}},GridLines->{{3.5,5.5,9.5,15.5},Automatic},FrameTicks->{{Automatic,None},{Table[{2k-3/2,Rotate[MaTeX["\\text{"<>method[[k]]<>"}",FontSize->20],π/2]},{k,Length[method]}],None}},
BaseStyle->16,PlotRangePadding->0,FrameStyle->Directive[Thick,16,Black],AspectRatio->1,FrameLabel->{None,MaTeX["\\text{Excitation energy (eV)}",FontSize->24]},ImageSize->600]

`

Spin-conserved transition: radicals

{"BeF","BeH","BH2","CH","CH3","C2H3","CN","CNO","CON","CO+","HCO","HOC","NCO","NH2","NO","OH"}

Spin-flip transition: double excitations

{"beryllium","carbon dimer","ethylene","formaldehyde","glyoxal","nitrosomethane","nitroxyl"}