Initialization

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

Cyclobutadiene

(Subscript[D, 2h])

Geometry

(Subscript[D, 2h]) geometry (in angstrom) obtained at the CC3(full)/aug-cc-pVTZ

C          -0.78248546      -0.67208001       0.00000000
  C           0.78248546      -0.67208001       0.00000000
  C          -0.78248546       0.67208001       0.00000000
  C           0.78248546       0.67208001       0.00000000
  H          -1.54227765      -1.43404123      -0.00000000
  H           1.54227765      -1.43404123       0.00000000
  H          -1.54227765       1.43404123       0.00000000
  H           1.54227765       1.43404123      -0.00000000

Data

Standard methods

(* %T1 (CC3/aug-cc-pVTZ)  98.7%, 95.0%, 0.84% *)

CBDD2h={
(* CC3 *)
{"CC3","6-31+G(d)",1.420,3.341,4.658},
{"","aug-cc-pVDZ",1.396,3.158,4.711},
{"","aug-cc-pVTZ",1.402,3.119,4.777},
{"","aug-cc-pVQZ",1.409,3.113,4.774},
(* CCSDT *)
{"CCSDT","6-31+G(d)",1.442,3.357,4.311},
{"","aug-cc-pVDZ",1.411,3.175,4.327},
{"","aug-cc-pVTZ",1.411,3.139,4.429},
(* CCSDT *)
 {"CCSDTQ","6-31+G(d)","",3.340,4.073},
(* CASSCF(4,4) *)
 {"SA2-CASSCF(4,4)","6-31+G(d)",1.662,4.657,4.439},
{"","aug-cc-pVDZ",1.672,4.563,4.448},
{"","aug-cc-pVTZ",1.670,4.546,4.441},
{"","aug-cc-pVQZ",1.671,4.549,4.440},
(* CASPT2(4,4) *)
 {"CASPT2(4,4)","6-31+G(d)",1.440,3.162,4.115},
{"","aug-cc-pVDZ",1.414,2.971,4.068},
{"","aug-cc-pVTZ",1.412,2.923,4.072},
{"","aug-cc-pVQZ",1.417,2.911,4.081},
(* XMS-CASPT2(4,4) *)
 {"XMS-CASPT2(4,4)","6-31+G(d)","","",4.151},
{"","aug-cc-pVDZ","","",4.105},
{"","aug-cc-pVTZ","","",4.114},
{"","aug-cc-pVQZ","","",4.125},
(* SC-NEVPT2(4,4) *)
 {"SC-NEVPT2(4,4)","6-31+G(d)",1.407,2.707,4.145},
{"","aug-cc-pVDZ",1.381,2.479,4.109},
{"","aug-cc-pVTZ",1.379,2.422,4.108},
{"","aug-cc-pVQZ",1.384,2.408,4.125},
(* PC-NEVPT2(4,4) *)
 {"PC-NEVPT2(4,4)","6-31+G(d)",1.409,2.652,4.120},
{"","aug-cc-pVDZ",1.384,2.424,4.084},
{"","aug-cc-pVTZ",1.382,2.368,4.083},
{"","aug-cc-pVQZ",1.387,2.353,4.091},
(* MRCI(4,4) *)
 {"MRCI(4,4)","6-31+G(d)",1.564,3.802,4.265},
{"","aug-cc-pVDZ",1.558,3.670,4.254},
{"","aug-cc-pVTZ",1.568,3.678,4.270},
{"","aug-cc-pVQZ",1.574,3.681,4.280},
(* CASSCF(12,12) *)
 {"SA2-CASSCF(12,12)","6-31+G(d)",1.675,3.924,4.220},
{"","aug-cc-pVDZ",1.685,3.856,4.221},
{"","aug-cc-pVTZ",1.686,3.844,4.217},
{"","aug-cc-pVQZ",1.687,3.846,4.216},
(* CASPT2(12,12) *)
 {"CASPT2(12,12)","6-31+G(d)",1.508,3.407,4.099},
{"","aug-cc-pVDZ",1.489,3.256,4.044},
{"","aug-cc-pVTZ",1.480,3.183,4.043},
{"","aug-cc-pVQZ",1.482,3.163,4.047},
(* XMS-CASPT2(12,12) *)
 {"XMS-CASPT2(12,12)","6-31+G(d)","","",4.111},
{"","aug-cc-pVDZ","","",4.056},
{"","aug-cc-pVTZ","","",4.059},
{"","aug-cc-pVQZ","","",4.065},
(* SC-NEVPT2(12,12) *)
 {"SC-NEVPT2(12,12)","6-31+G(d)",1.522,3.409,4.130},
{"","aug-cc-pVDZ",1.511,3.266,4.093},
{"","aug-cc-pVTZ",1.501,3.188,4.086},
{"","aug-cc-pVQZ",1.503,3.167,4.088},
(* PC-NEVPT2(12,12) *)
 {"PC-NEVPT2(12,12)","6-31+G(d)",1.487,3.296,4.103},
{"","aug-cc-pVDZ",1.472,3.141,4.064},
{"","aug-cc-pVTZ",1.462,3.063,4.056},
{"","aug-cc-pVQZ",1.464,3.043,4.059},
(* MRCI(12,12) *)
 {"MRCI(12,12)","6-31+G(d)","","",4.125},
(* CIPSI *)
 {"CIPSI","6-31+G(d)",Around[1.486 , 0.005],Around[3.348,0.024],Around[4.084,0.012]},
{"","aug-cc-pVDZ",Around[1.458,0.009],Around[3.187,0.035],Around[4.041,0.036]},
{"","aug-cc-pVTZ",Around[1.461,0.030],Around[3.142,0.035],Around[4.065,0.055]}
};

Spin-flip methods

CBDD2hSF=
{(* SF-CIS *)
 {"SF-CIS","6-31+G(d)",{0,0.0812},{0.1678+1.3467,2.0446},{2.5077+1.3467,0.0449},{4.0323+1.3467,0.0915}},
{"","aug-cc-pVDZ",{0,0.0829},{0.1842+1.3031,2.0497},{2.4177+1.3031,0.0549},{4.0452+1.3031,0.0946}},
{"","aug-cc-pVTZ",{0,0.0852},{0.2021+1.2700,2.0537},{2.4312+1.2700,0.0575},{4.0721+1.2700,0.0985}},
{"","aug-cc-pVTZ",{0,0.0855},{0.2039+1.2673,2.0541},{2.4342+1.2673,0.0579},{4.0750+1.2673,0.1001}},
(* SF-TD-B3LYP *)
 {"SF-TD-B3LYP","6-31+G(d)",{0,0.0103},{0.9898+0.7163,1.9901},{1.4945+0.7163,0.0272},{3.2768+0.7163,0.0166}},
{"","aug-cc-pVDZ",{0,0.0102},{0.9673+0.7383,1.9896},{1.4655+0.7383,0.0281},{3.2542+0.7383,0.0162}},
{"","aug-cc-pVTZ",{0,0.0108},{0.9826+0.7201,1.9890},{1.4788+0.7201,0.0299},{3.2679+0.7201,0.0168}},
(* SF-TD-PBE0 *)
 {"SF-TD-PBE0","6-31+G(d)",{0,0.0115},{1.0782+0.6087,2.0018},{1.7051+0.6087,0.0173},{3.4805+0.6087,0.0179}},
{"","aug-cc-pVDZ",{0,0.0118},{1.0593+0.6251,2.0014},{1.6761+0.6251,0.0191},{3.4598+0.6251,0.0181}},
{"","aug-cc-pVTZ",{0,0.0126},{1.0852+0.5966,2.0013},{1.6994+0.5966,0.0209},{3.4848+0.5966,0.0191}},
(* SF-TD-BHHLYP *)
 {"SF-TD-BHHLYP","6-31+G(d)",{0,0.0276},{0.5312+1.0209,2.0150},{1.7582+1.0209,0.0225},{3.4074+1.0209,0.0401}},
{"","aug-cc-pVDZ",{0,0.0278},{0.5216+1.0249,2.0161},{1.7186+1.0249,0.0245},{3.3968+1.0249,0.0401}},
{"","aug-cc-pVTZ",{0,0.0285},{0.5353+1.0049,2.0172},{1.7268+1.0049,0.0256},{3.4097+1.0049,0.0410}},
(* SF-TD-M06-2X *)
 {"SF-TD-M06-2X","6-31+G(d)",{0,0.0281},{-0.4566+1.9337,2.0115},{0.9015+1.9337,0.0135},{2.4444+1.9337,0.0388}},
{"","aug-cc-pVDZ",{0,0.0282},{-0.4555+1.9224,2.0129},{0.8623+1.9224,0.0156},{2.4372+1.9224,0.0387}},
{"","aug-cc-pVTZ",{0,0.0288},{+1.8515,2.0140},{-0.3898+1.8515,0.0174},{2.5055+1.8515,0.0396}},
(* SF-TD-CAM-B3LYP *)
 {"SF-TD-CAM-B3LYP","6-31+G(d)",{0,0.0138},{0.9020+0.8479,1.9895},{1.4886+0.8479,0.0292},{3.2920+0.0228,0.0166}},
{"","aug-cc-pVDZ",{0,0.0140},{0.8835+0.8612,1.9901},{1.4615+0.8612,0.0310},{3.2791+0.8612,0.0230}},
{"","aug-cc-pVTZ",{0,0.0145},{0.8956+0.8469,1.9899},{1.4713+0.8469,0.0326},{3.2910+0.8469,0.0235}},
 (*SF-TD-ωB97X-V *)
 {"SF-TD-ωB97X-V","6-31+G(d)",{0,0.0134},{0.7600+1.0505,1.9871},{1.3263+1.0505,0.0281},{3.1694+1.0505,0.0224}},
{"","aug-cc-pVDZ",{0,0.0142},{0.7418+1.0580,1.9868},{1.2979+1.0580,0.0328},{3.1586+1.0580,0.0234}},
{"","aug-cc-pVTZ",{0,0.0146},{0.7578+1.0390,1.9864},{1.3121+1.0390,0.0346},{3.1738+1.0390,0.0239}},
(* SF-ADC(2)-s *)
 {"SF-ADC(2)-s","6-31+G(d)",{0,""},{0.208053+1.369355,""},{1.934013+1.369355,""},{2.826881+1.369355,""}},
{"","aug-cc-pVDZ",{0,""},{0.221852+1.290924,""},{1.825240+1.290924,""},{2.822946+1.290924,""}},
{"","aug-cc-pVTZ",{0,""},{0.229434+1.301218,""},{1.797447+1.301218,""},{2.829496+1.301218,""}},
{"","aug-cc-pVQZ",{0,""},{0.228423+1.315407,""},{1.785153+1.315407,""},{2.824823+1.315407,""}},
(* SF-ADC(2)-x *)
 {"SF-ADC(2)-x","6-31+G(d)",{0,""},{-0.503748+2.061201,""},{1.170812+2.061201,""},{1.666343+2.061201,""}},
{"","aug-cc-pVDZ",{0,""},{-0.501005+2.024877,""},{1.014360+2.024877,""},{1.655718+2.024877,""}},
{"","aug-cc-pVTZ",{0,""},{-0.486246+2.025630,""},{1.005678+2.025630,""},{1.677724+2.025630,""}},
(* SF-ADC(3) *)
 {"SF-ADC(3)","6-31+G(d)",{0,""},{-0.177101+1.612001,""},{1.739502+1.612001,""},{2.630312+1.612001,""}},
{"","aug-cc-pVDZ",{0,""},{-0.169470+1.591304,""},{1.588302+1.591304,""},{2.616757+1.591304,""}},
{"","aug-cc-pVTZ",{0,""},{-0.168414+1.587260,""},{1.574672+1.587260,""},{2.636246+1.587260,""}},
(* SF-EOM-CCSD *)
 {"SF-EOM-CCSD","6-31+G(d)",{0,""},{0.0185+1.6443,""},{1.8709+1.6443,""},{2.6311+1.6443,""}},
 {"","aug-cc-pVDZ",{0,""},{0.0201+1.5905,""},{1.7242+1.5905,""},{2.2655+1.5905,""}},
 {"","aug-cc-pVTZ",{0,""},{0.0246+1.5845,""},{1.7085+1.5845,""},{2.6605+1.5845,""}},
(* SF-EOM-CCSD *)
 {"SF-EOM-CC(2,3)","6-31+G(d)",{0,""},{-0.2682+1.7587,""},{1.5740+1.7587,""},{2.3020+1.7587,""}},
 {"","aug-cc-pVDZ",{0,""},{-0.2976+1.7616,""},{1.3945+1.7616,""},{2.2655+1.7616,""}}
(* SF-XX *)
 (*{"SF-XX","6-31+G(d)",{,},{,},{,},{,}},
{"","aug-cc-pVDZ",{,},{,},{,},{,}},
{"","aug-cc-pVTZ",{,},{,},{,},{,}},
{"","aug-cc-pVQZ",{,},{,},{,},{,}}*)
};

Table of excitation energies

TableForm[CBDD2h,
TableHeadings->{None,{"Method","Basis","1 (^3)(Subscript[B, 1  g])","1 (^1)(Subscript[B, 1  g])","2 (^1)(Subscript[A, g])"}}, TableAlignments->Left]

TableForm[SetAccuracy[CBDD2hSF,4],
TableHeadings->{None,{"Method","Basis","1 (^1)(Subscript[A, g])","1 (^3)(Subscript[B, 1  g])","1 (^1)(Subscript[B, 1  g])","2 (^1)(Subscript[A, g])"}}, TableAlignments->Left]
Export["tabSF.png",%];

Graph

ΔΕ=Table[CBDD2h[[;;,k]],{k,2,12}];
state=CBDD2h[[;;,1]];
method={"SF-TDB3LYP","SF-TDBH\\&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->{{-0.5,21.5},{1,5.6}},GridLines->{{5.5,7.5,11.5,17.5,23.5},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]

`

(Subscript[D, 4h])

Geometry

(Subscript[D, 4h]) geometry (in angstrom) obtained at the RO-CCSD(T)(full)/aug-cc-pVTZ

C     0.000000    1.017702    0.000000
C     1.017702   -0.000000    0.000000
C    -1.017702    0.000000    0.000000
C    -0.000000   -1.017702    0.000000
H     0.000000    2.092429    0.000000
H     2.092429   -0.000000    0.000000
H    -0.000000   -2.092429    0.000000
H    -2.092429    0.000000    0.000000

Data

CBDD4h={
(* CC3 *)
{"CC3","6-31+G(d)","","",""},
{"","aug-cc-pVDZ","","",""},
{"","aug-cc-pVTZ","","",""},
{"","aug-cc-pVQZ","","",""},
(* SA2-CASSCF(4,4) *)
{"SA2-CASSCF(4,4)","6-31+G(d)",0.447,2.257,3.549},
{"","aug-cc-pVDZ",0.438,2.240,3.443},
{"","aug-cc-pVTZ",0.434,2.234,3.424},
{"","aug-cc-pVQZ",0.435,2.235,3.427},
(* CASPT2(4,4) *)
{"CASPT2(4,4)","6-31+G(d)",0.176,1.588,1.899},
{"","aug-cc-pVDZ",0.137,1.540,1.708},
{"","aug-cc-pVTZ",0.128,1.506,1.635},
{"","aug-cc-pVQZ",0.128,1.498,1.612},
(* SC-NEVPT2(4,4) *)
{"SC-NEVPT2(4,4)","6-31+G(d)",0.083,1.520,1.380},
{"","aug-cc-pVDZ",0.037,1.465,1.140},
{"","aug-cc-pVTZ",0.024,1.428,1.055},
{"","aug-cc-pVQZ",0.024,1.420,1.030},
(* PC-NEVPT2(4,4) *)
{"PC-NEVPT2(4,4)","6-31+G(d)",0.085,1.496,1.329},
{"","aug-cc-pVDZ",0.039,1.440,1.088},
{"","aug-cc-pVTZ",0.026,1.403,1.003},
{"","aug-cc-pVQZ",0.026,1.395,0.977},
(* MRCI(4,4) *)
{"MRCI(4,4)","6-31+G(d)",0.297,1.861,2.571},
{"","aug-cc-pVDZ",0.273,1.823,2.419},
{"","aug-cc-pVTZ",0.271,1.824,2.415},
{"","aug-cc-pVQZ",0.273,1.825,2.413},
(* SA2-CASSCF(12,12) *)
{"SA2-CASSCF(12,12)","6-31+G(d)",0.386,1.974,2.736},
{"","aug-cc-pVDZ",0.374,1.947,2.649},
{"","aug-cc-pVTZ",0.370,1.943,2.634},
{"","aug-cc-pVQZ",0.371,1.945,2.637},
(* CASPT2(12,12) *)
{"CASPT2(12,12)","6-31+G(d)",0.235,1.635,2.170},
{"","aug-cc-pVDZ",0.203,1.588,2.015},
{"","aug-cc-pVTZ",0.183,1.538,1.926},
{"","aug-cc-pVQZ",0.179,1.522,1.898},
(* SC-NEVPT2(12,12) *)
{"SC-NEVPT2(12,12)","6-31+G(d)",0.218,1.644,2.143},
{"","aug-cc-pVDZ",0.189,1.600,1.991},
{"","aug-cc-pVTZ",0.165,1.546,1.892},
{"","aug-cc-pVQZ",0.160,1.529,1.862},
(* PC-NEVPT2(12,12) *)
{"PC-NEVPT2(12,12)","6-31+G(d)",0.189,1.579,2.020},
{"","aug-cc-pVDZ",0.156,1.530,1.854},
{"","aug-cc-pVTZ",0.131,1.476,1.756},
{"","aug-cc-pVQZ",0.126,1.460,1.727},
(* CIPSI *)
 {"CIPSI","6-31+G(d)",Around[0.218,0.028],Around[1.602,0.007],Around[2.126,0.041]},
{"","aug-cc-pVDZ","",Around[1.587,0.005],Around[2.102,0.027]}
};

Table of excitation energies

TableForm[CBDD4h,
TableHeadings->{None,{"Method","Basis","1 (^3)(Subscript[A, 2  g])","1 (^1)(Subscript[A, 1  g])","1 (^1)(Subscript[B, 2  g])"}}, TableAlignments->Left]

Autoisomerisation

Data

Auto={
 {"CASSCF(4,4)","","",7.44,7.52},
 {"CASPT2(4,4)","","",3.88,3.70},
 {"NEVPT2(4,4)","","",9.34,9.28},
 {"CASSCF(12,12)","","",11.42,11.54},
 {"CASPT2(12,12)","","",5.11,5.24},
 {"NEVPT2(12,12)","","",8.28,8.28},
 {"CC3","","","",""},
 {"MR-AQCC,","","","",8.3},
 {"CIPSI",Around[7.86 , 0.28],"","",""}
};

TableForm[Auto,
TableHeadings->{None,{"Method","6-31+G(d)","aug-cc-pVDZ","cc-pVTZ","aug-cc-pVTZ"}}, TableAlignments->Left]