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)2s2p)",3.210,3.332,2.874,2.400,2.407,2.376,2.363,2.370,2.335,2.111,2.433,2.866,2.864,2.862},
{"(^1)P(1(s^2)2s2p)",3.210,4.276,4.922,6.191,6.199,6.241,6.263,6.273,6.317,6.036,6.255,6.581,6.579,6.577},
{"(^3)P(1(s^2)2(p^2))",6.691,6.864,7.112,7.792,7.788,7.668,7.824,7.820,7.689,7.480,7.745,7.664,7.659,7.669},
{"(^1)D(1(s^2)2(p^2))",7.598,7.762,8.188,9.373,9.388,9.417,9.424,9.4410,9.470,8.945,9.047,8.612,8.618,8.624}
};

Table of excitation energies

TableForm[Be,
TableHeadings->{None,{"State","SF-TDBLYP","SF-TDB3LYP","SF-TDBHHLYP","SF-BSE@(Subscript[G, 0])(Subscript[W, 0])","SF-BSE@evGW","SF-dBSE@(Subscript[G, 0])(Subscript[W, 0])","SF-dBSE@evGW","SF-CIS","SF-ADC(2)","SF-ADC(2)-x","SF-ADC(3)","FCI"}}, TableAlignments->Center]

⟨(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,2,15}];
state=Be[[;;,1]];
method={"SF-TD-BLYP","SF-TD-B3LYP","SF-TD-BH\\&HLYP","SF-BSE@G$_0$W$_0$","SF-BSE@evGW","SF-BSE@qsGW","SF-dBSE@G$_0$W$_0$","SF-dBSE@evGW","SF-dBSE@qsGW","SF-CIS","SF-ADC(2)-s","SF-ADC(2)-x","SF-ADC(3)","FCI"};
color={Red,Red,Red,Blue,Blue,Blue,Blue,Blue,Blue,Orange,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]}]
]
},
(*PlotLabel->MaTeX["\\text{Be/6-31G}",FontSize->30],*)
Frame->True,Axes->False,PlotRange->{{-0.5,27.5},{0,10}},GridLines->{{5.5,17.5,25.5},None},FrameTicks->{{Automatic,None},{Table[{2k-1,Rotate[MaTeX["\\text{"<>method[[k]]<>"}",FontSize->20],π/2]},{k,Length[method]}],None}},
BaseStyle->20,PlotRangePadding->0,FrameStyle->Directive[Thick,20,Black],AspectRatio->1,FrameLabel->{None,MaTeX["\\text{Excitation energy (eV)}",FontSize->20]},ImageSize->700]

`

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"}