Initialization

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

HaToeV=27.21138602;

SetDirectory["~/Dropbox/Manuscripts/Ec/data_AS"];

Hilbert spaces

Five-membered ring

(* cyclopentadiene, furan, imidazole, pyrrole, and thiophene *)

{((Binomial[100-5,18-5])^2),((Binomial[90-5,18-5])^2),((Binomial[90-5,18-5])^2),((Binomial[95-5,18-5])^2),((Binomial[94-10,22-10])^2)}//N

(* benzene, pyrazine, pyridazine, pyridine, pyrimidine, tetrazine, and triazine *)

{((Binomial[114-6,21-6])^2),((Binomial[104-6,21-6])^2),((Binomial[104-6,21-6])^2),((Binomial[109-6,21-6])^2),((Binomial[104-6,21-6])^2),((Binomial[94-6,21-6])^2),((Binomial[99-6,21-6])^2)}//N

TableForm[{
{MoleculePlot3D[Molecule["cyclopentadiene"]],MoleculePlot3D[Molecule["furan"]],MoleculePlot3D[Molecule["imidazole"]],MoleculePlot3D[Molecule["pyrrole"]],MoleculePlot3D[Molecule["thiophene"]]}
,{"cyclopentadiene","furan","imidazole","pyrrole","thiophene"}
},TableAlignments->Center]
TableForm[{
{MoleculePlot3D[Molecule["benzene"]],MoleculePlot3D[Molecule["pyrazine"]],MoleculePlot3D[Molecule["pyridazine"]],MoleculePlot3D[Molecule["pyridine"]],MoleculePlot3D[Molecule["pyrimidine"]],MoleculePlot3D[Molecule["1,2,4,5-tetrazine"]],MoleculePlot3D[Molecule["1,3,5-triazine"]]}
,{"benzene","pyrazine","pyridazine","pyridine","pyrimidine","tetrazine","triazine"}
},TableAlignments->Center]

Modules

(Subscript[E, var]) vs (Subscript[N, det])

EvsNdet[Mol_,Range_,ExpFig_]:=Module[
{NO,LO,OO,HF,CC,
SizeTitle=20,SizeLabel=20,SizeLegend=14,PlotOptions,
CCSDTQ,SCINO,SCILO,SCIOO,SCIPT2NO,SCIPT2LO,SCIPT2OO,SCIrPT2NO,SCIrPT2LO,SCIrPT2OO,
start=9,plot},
NO=Import[ToLowerCase[Mol]<>"_no.dat"];
LO=Import[ToLowerCase[Mol]<>"_loc.dat"];
OO=Import[ToLowerCase[Mol]<>"_opt.dat"];
HF=ToExpression[Mol<>"HF"];
CC=ToExpression[Mol<>"CC"];
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->16,ImageSize->350,AspectRatio->1,GridLines->Automatic,PlotMarkers->"OpenMarkers",
PlotStyle->{
{Thick,Black},
{Thick,Red},{Thick,Blue},
{Thick,Red,Dotted},{Thick,Blue,Dotted}
}
};
CCSDTQ={{0.01,CC[[3,2]]},{(10^9),CC[[3,2]]}};
SCINO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCILO=Table[{LO[[k,1]],(10^3)(LO[[k,2]]-HF)},{k,start,Length[LO]}];
SCIOO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
SCIPT2NO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]+NO[[k,3]]-HF)},{k,start,Length[NO]}];
SCIPT2LO=Table[{LO[[k,1]],(10^3)(LO[[k,2]]+LO[[k,3]]-HF)},{k,start,Length[LO]}];
SCIPT2OO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]+OO[[k,3]]-HF)},{k,start,Length[OO]}];
SCIrPT2NO=Table[{NO[[k,1]],(10^3)(NO[[k,2]]+NO[[k,5]]-HF)},{k,start,Length[NO]}];
SCIrPT2LO=Table[{LO[[k,1]],(10^3)(LO[[k,2]]+LO[[k,5]]-HF)},{k,start,Length[LO]}];
SCIrPT2OO=Table[{OO[[k,1]],(10^3)(OO[[k,2]]+OO[[k,5]]-HF)},{k,start,Length[OO]}];
plot=ListLogLinearPlot[{CCSDTQ,SCINO,SCIOO,SCIrPT2NO,SCIrPT2OO},
PlotLabel->MaTeX["\\text{"<>Mol<>"/cc-pVDZ}",FontSize->SizeTitle],
FrameLabel->{
MaTeX["\\text{Number of determinants}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{CCSDTQ}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}+E_\\text{PT2}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}+E_\\text{PT2}^\\text{OO}$}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotRange->{{(10^3),2 (10^8)},Range},PlotOptions];
If[ExpFig,Export[ToString[Mol]<>"_EvsNdet.pdf",plot]];
Return[plot];
];

(Subscript[E, var]) vs (Subscript[E, PT2])

EvsPT2[Mol_,Range_,ExpFig_]:=Module[
{NO,LO,OO,HF,CC,
SizeTitle=20,SizeLabel=20,SizeLegend=14,PlotOptions,
CCSDTQ,SCIPT2NO,SCIrPT2NO,SCIPT2LO,SCIrPT2LO,SCIPT2OO,SCIrPT2OO,fitPT2NO,fitrPT2NO,fitPT2OO,fitrPT2OO,
start=9,nfit=4,wPT2OO,wrPT2OO,TabPT2,TabrPT2,plot},
NO=Import[ToLowerCase[Mol]<>"_no.dat"];
LO=Import[ToLowerCase[Mol]<>"_loc.dat"];
OO=Import[ToLowerCase[Mol]<>"_opt.dat"];
HF=ToExpression[Mol<>"HF"];
CC=ToExpression[Mol<>"CC"];
PlotOptions={Joined->True,PlotTheme->"Detailed",BaseStyle->16,ImageSize->350,AspectRatio->1,GridLines->Automatic,PlotMarkers->"OpenMarkers",
PlotStyle->{
{Thick,Black},{Thick,Red},{Thick,Blue}
}
};
CCSDTQ={{-1000,CC[[3,2]]},{0,CC[[3,2]]}};
SCIPT2NO=Table[{(10^3)(NO[[k,3]]),(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCIrPT2NO=Table[{(10^3)(NO[[k,5]]),(10^3)(NO[[k,2]]-HF)},{k,start,Length[NO]}];
SCIPT2LO=Table[{(10^3)(LO[[k,3]]),(10^3)(LO[[k,2]]-HF)},{k,start,Length[LO]}];
SCIrPT2LO=Table[{(10^3)(LO[[k,5]]),(10^3)(LO[[k,2]]-HF)},{k,start,Length[LO]}];
SCIPT2OO=Table[{(10^3)(OO[[k,3]]),(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
SCIrPT2OO=Table[{(10^3)(OO[[k,5]]),(10^3)(OO[[k,2]]-HF)},{k,start,Length[OO]}];
wPT2OO=Table[(10^3)OO[[k,4]],{k,start,Length[OO]}];
wrPT2OO=Table[(10^3)OO[[k,6]],{k,start,Length[OO]}];
fitPT2NO=Fit[Take[SCIPT2NO,-nfit],{1,x},x];
fitrPT2NO=Fit[Take[SCIrPT2NO,-nfit],{1,x},x];
fitPT2OO=Fit[Take[SCIPT2OO,-nfit],{1,x},x];
fitrPT2OO=Fit[Take[SCIrPT2OO,-nfit],{1,x},x];
plot=Show[{
ListPlot[{CCSDTQ,SCIrPT2NO,SCIrPT2OO},
PlotLabel->MaTeX["\\text{"<>Mol<>"/cc-pVDZ}",FontSize->SizeTitle],
FrameLabel->{
MaTeX["\\text{$E_\\text{PT2}$ ($mE_h$)}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{CCSDTQ}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{NO}$ vs $E_\\text{PT2}^\\text{NO}$}",FontSize->SizeLegend],
MaTeX["\\text{$E_\\text{var}^\\text{OO}$ vs $E_\\text{PT2}^\\text{OO}$}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotOptions,PlotRange->{{-200,0},Range}]
,
Plot[{fitrPT2NO,fitrPT2OO},{x,-200,0},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{"<>ToString[nfit]<>"-point linear fit}",FontSize->SizeLegend]
},LegendMargins->0,LegendMarkerSize->{{40,10}}],{Right,Top}],
PlotStyle->{{Thick,Dashed,Black},{Thick,Dashed,Black}}]
}];
TabPT2=TableForm[Table[{k,LinearModelFit[Take[SCIPT2OO,-k],{1,x},x,Weights->1/((Take[wPT2OO,-k])^2)]["ParameterTable"]},{k,3,8}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}];
TabrPT2=TableForm[Table[{k,LinearModelFit[Take[SCIrPT2OO,-k],{1,x},x,Weights->1/((Take[wrPT2OO,-k])^2)]["ParameterTable"]},{k,3,8}],TableAlignments->Center,TableHeadings->{None,{"Nb points","Fit parameters"}}];
If[ExpFig,Export[ToString[Mol]<>"_EvsPT2.pdf",plot]];
Return[Row[{plot,TabrPT2}]];
];

Cyclopentadiene

MP & CC calculations

CyclopentadieneHF=-192.808319784581;
CyclopentadieneMP={{5,-663.374798421},{6,-701.038770308868},{7,-734.485164342225},{8,-733.4333154}};
CyclopentadieneCCn={{5,-669.867722683},{7,-736.574222273275},{9,-738.366684546823}};
CyclopentadieneCC={{6,-707.237579224683},{8,-736.246708418799},{10,-738.202355812839}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{CyclopentadieneMP,CyclopentadieneCCn,CyclopentadieneCC},Joined->True,PlotOptions,
PlotLabel->MaTeX["\\text{Cyclopentadiene/cc-pVDZ}",FontSize->SizeLabel],
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=CyclopentadieneMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=CyclopentadieneCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=CyclopentadieneCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Cyclopentadiene",{-760,-300},True]
EvsPT2["Cyclopentadiene",{-760,-400},True]

Furan

Shanks for the 6-31G basis

FuranHF=-228.523990058384;
FuranCCn={{5,-229.001730644282},{7,-229.040591463170},{9,-229.041751058791},{11,-229.041751139916}};
FuranCC={{6,-229.022381696587},{8,-229.039971317883},{10,-229.041597770327}};

s=(FuranCCn[[;;,2]]-FuranHF)(10^3)
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=(FuranCC[[;;,2]]-FuranHF)(10^3)
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations for the 6-31G basis

Furan=Import["furan_6-31g.dat"];

SizeTitle=30;SizeLabel=24;SizeLegend=24;
PlotOptions={Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1,GridLines->Automatic,PlotMarkers->"OpenMarkers",
PlotStyle->{
{Thick,Gray},{Thick,Black},{Thick,Blue},{Thick,Red},{Thick,Dashed,Green}
}
};
start=9;
nfit=3;
CCSDT={{-1000,(FuranCC[[2,2]]-FuranHF)(10^3)},{0,(FuranCC[[2,2]]-FuranHF)(10^3)}};
CCSDTQ={{-1000,(FuranCC[[3,2]]-FuranHF)(10^3)},{0,(FuranCC[[3,2]]-FuranHF)(10^3)}};
SCIPT2=Table[{(10^3)(Furan[[k,3]]-Furan[[k,2]]),(10^3)(Furan[[k,2]]-FuranHF)},{k,start,Length[Furan]}];
fitPT2=Fit[Take[SCIPT2,-nfit],{1,x},x]
SCIrPT2=Table[{(10^3)(Furan[[k,5]]-Furan[[k,2]]),(10^3)(Furan[[k,2]]-FuranHF)},{k,start,Length[Furan]}];
fitrPT2=Fit[Take[SCIrPT2,-nfit],{1,x},x]
Show[{
ListPlot[{
CCSDT,CCSDTQ,SCIPT2,SCIrPT2
},
PlotLabel->MaTeX["\\text{Furan/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{$E_\\text{PT2}$ or $E_\\text{rPT2}$ ($mE_h$)}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{CCSDT}",FontSize->SizeLegend],
MaTeX["\\text{CCSDTQ}",FontSize->SizeLegend],
MaTeX["\\text{$\\Delta E_\\text{var.}$ vs $E_\\text{PT2}$}",FontSize->SizeLegend],
MaTeX["\\text{$\\Delta E_\\text{var.}$ vs $E_\\text{rPT2}$}",FontSize->SizeLegend]
}],{Right,Top}],
PlotOptions,
PlotRange->{{-200,0},Automatic},
Joined->False
]
,
Plot[{fitPT2,fitrPT2},{x,-200,0},PlotStyle->{{Thick,Dashed,Blue},{Thick,Dashed,Red}}]
}]
(*Export["furanEcvsPT2.pdf",%];*)

MP & CC calculations

FuranHF=-228.643312572484575;
FuranMP={{5,-707.450373824},{6,-727.820193088592},{7,-766.627890777360},{8,-759.8932275}};
FuranCCn={{5,-717.183336927},{7,-765.730048755297},{9,-766.866256888079}};
FuranCC={{6,-734.972685409664},{8,-764.332120385917},{10,-766.65420877679}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{FuranMP,FuranCCn,FuranCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Furan/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=FuranMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=FuranCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=FuranCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Furan",{-780,-300},True]
EvsPT2["Furan",{-780,-450},True]

Imidazole

MP & CC calculations

ImidazoleHF=-224.835356714467;
ImidazoleMP={{5,-720.429915262},{6,-737.828542914060},{7,-777.223689935675},{8,-770.7756855}};
ImidazoleCCn={{5,-729.015795304},{7,-776.111512572204},{9,-777.204281879068}};
ImidazoleCC={{6,-744.198886306645},{8,-774.551173949665},{10,-776.949476371663}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{ImidazoleMP,ImidazoleCCn,ImidazoleCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Imidazole/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=ImidazoleMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ImidazoleCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ImidazoleCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Imidazole",{-810,-300},True]
EvsPT2["Imidazole",{-810,-450},True]

Pyrrole

MP & CC calculations

PyrroleHF=-208.828614693633;
PyrroleMP={{5,-695.721950709},{6,-720.603108743368},{7,-756.459033548742},{8,-752.2589064}};
PyrroleCCn={{5,-702.531904930},{7,-756.270764152895},{9,-757.576382167585}};
PyrroleCC={{6,-725.712852643528},{8,-755.183721462796},{10,-757.360899120397}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{PyrroleMP,PyrroleCCn,PyrroleCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Pyrrole/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=PyrroleMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrroleCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrroleCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Pyrrole",{-790,-300},True]
EvsPT2["Pyrrole",{-790,-450},True]

Thiophene

MP & CC calculations

ThiopheneHF=-551.321002444800;
ThiopheneMP={{5,-661.487676839},{6,-689.433481554693},{7,-726.576354093504},{8,-721.5988552}};
ThiopheneCCn={{5,-669.535846587},{7,-726.268305928940},{9,-727.662544525096}};
ThiopheneCC={{6,-694.455334004781},{8,-725.135024376793},{10,-727.450489687365}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{ThiopheneMP,ThiopheneCCn,ThiopheneCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Thiophene/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=ThiopheneMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ThiopheneCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=ThiopheneCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Thiophene",{-760,-300},True]
EvsPT2["Thiophene",{-760,-400},True]

Benzene

MP & CC calculations

BenzeneHF=-230.722244985640;
BenzeneMP={{5,-782.332077228},{6,-816.387142630248},{7,-858.539911321773},{8,-853.7830144}};
BenzeneCCn={{5,-789.412298096},{7,-859.142698599615},{9,-860.586074871286}};
BenzeneCC={{6,-821.788776613854},{8,-857.926313401076},{10,-860.365191225800}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{BenzeneMP,BenzeneCCn,BenzeneCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=BenzeneMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=BenzeneCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=BenzeneCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Benzene",{-890,-300},True]
EvsPT2["Benzene",{-890,-550},True]

Pyrazine

MP & CC calculations

PyrazineHF=-262.703010944756;
PyrazineMP={{5,-834.617733280},{6,-853.655354014131},{7,-902.907089183363},{8,-893.8350552}};
PyrazineCCn={{5,-844.463447870},{7,-901.497912273981},{9,-902.636842327822}};
PyrazineCC={{6,-861.028517352127},{8,-899.350733684886},{10,-902.330775312939}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{PyrazineMP,PyrazineCCn,PyrazineCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Pyrazine/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=PyrazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Pyrazine",{-930,-300},True]
EvsPT2["Pyrazine",{-930,-600},True]

Pyridazine

MP & CC calculations

PyridazineHF=-262.669873445804;
PyridazineMP={{5,-838.740583969},{6,-857.275882097803},{7,-907.925790862876},{8,-898.2587542}};
PyridazineCCn={{5,-848.908853611},{7,-906.214393900430},{9,-907.453759605642}};
PyridazineCC={{6,-864.874528282081},{8,-903.988565095408},{10,-907.116636262810}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{PyridazineMP,PyridazineCCn,PyridazineCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Pyridazine/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=PyridazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Pyridazine",{-930,-300},True]
EvsPT2["Pyridazine",{-930,-600},True]

Pyridine

MP & CC calculations

PyridineHF=-246.715184707013;
PyridineMP={{5,-807.471827567},{6,-834.035340573813},{7,-879.923597854822},{8,-872.875093}};
PyridineCCn={{5,-816.328319360},{7,-879.599675234389},{9,-880.821972634781}};
PyridineCC={{6,-840.701382579433},{8,-877.874903251700},{10,-880.821972634781}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{PyridineMP,PyridineCCn,PyridineCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Pyridine/cc-pVDZ}",FontSize->SizeLabel],,
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=PyridineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyridineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Pyridine",{-930,-300},True]
EvsPT2["Pyridine",{-930,-550},True]

Pyrimidine

MP & CC calculations

PyrimidineHF=-262.713652796899;
PyrimidineMP={{5,-830.057493278},{6,-849.612212994749},{7,-899.266633591386},{8,-889.9912031}};
PyrimidineCCn={{5,-841.308837134},{7,-898.365293520950},{9,-899.263868742531}};
PyrimidineCC={{6,-857.976308572695},{8,-896.080430191809},{10,-898.976078520330}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{PyrimidineMP,PyrimidineCCn,PyrimidineCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Pyrimidine/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=PyrimidineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrimidineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=PyrimidineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Pyrimidine",{-930,-300},True]
EvsPT2["Pyrimidine",{-930,-600},True]

Tetrazine

MP & CC calculations

TetrazineHF=-294.615743073901;
TetrazineMP={{5,-895.922989130},{6,-899.456957539510},{7,-958.570330486010},{8,-944.2694261}};
TetrazineCCn={{5,-908.969490669},{7,-954.853218744419},{9,-955.880388848436}};
TetrazineCC={{6,-909.100948888639},{8,-951.585113405389},{10,-955.428165912650}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{TetrazineMP,TetrazineCCn,TetrazineCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Tetrazine/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=TetrazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TetrazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TetrazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Tetrazine",{-990,-300},True]
EvsPT2["Tetrazine",{-990,-650},True]

Triazine

MP & CC calculations

TriazineHF=-278.717319389695;
TriazineMP={{5,-850.519282476},{6,-863.593139716035},{7,-916.717801063422},{8,-905.4360103}};
TriazineCCn={{5,-864.406418639},{7,-915.583810723581},{9,-916.075626870853}};
TriazineCC={{6,-873.819918012385},{8,-912.716493155011},{10,-915.770573661020}};

SizeTitle=30;SizeLabel=20;SizeLegend=20;
PlotOptions={
Joined->True,PlotTheme->"Detailed",BaseStyle->18,ImageSize->Large,AspectRatio->1/2,GridLines->Automatic,PlotMarkers->{"OpenMarkers",Large},
PlotStyle->{
{Thickness[0.01],Black},{Thickness[0.01],Darker[Green]},{Thickness[0.01],Red},{Thickness[0.01],Blue}
}
};
ListPlot[{TriazineMP,TriazineCCn,TriazineCC},Joined->True,PlotOptions,
FrameTicks->{{Automatic,None},{{5,6,7,8,9,10},None}},
PlotLabel->MaTeX["\\text{Triazine/cc-pVDZ}",FontSize->SizeLabel],
FrameLabel->{
MaTeX["\\text{Computational cost $\\mathcal{O}(N^\\alpha)$}",FontSize->SizeLabel],
MaTeX["\\text{Correlation energy (m$E_h$)}",FontSize->SizeLabel]},
PlotLegends->Placed[LineLegend[{
MaTeX["\\text{MP$n$}",FontSize->SizeLegend],MaTeX["\\text{CC$n$}",FontSize->SizeLegend],
MaTeX["\\text{CC}",FontSize->SizeLegend]
}],{Right,Top}]]

Shanks

s=TriazineMP[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TriazineCCn[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

s=TriazineCC[[;;,2]]
s=Table[((s[[n+1]]s[[n-1]]-((s[[n]])^2))/(s[[n+1]]-2s[[n]]+s[[n-1]])),{n,2,Length[s]-1}]

CIPSI  calculations

EvsNdet["Triazine",{-940,-300},True]
EvsPT2["Triazine",{-940,-600},True]