(* Kimball model and energy derived from experimental molecule data source, ES Febuary 2013 *) 
Clear[tw,n2,n,nb,bc,bh,u,u1,u2];

ChemicalData["Butane","MoleculePlot"]

t1=0.01889726*ChemicalData["Butane","AtomPositions"];
(*MatrixForm[t]*)

(*ChemicalData["Butane","BondTally"]*)

u=ChemicalData["Butane","VertexTypes"]

n=Length[u]

un=Table[If[u[[i]]=="H","Z",u[[i]]],{i,1,n}]

num=Table[i,{i,1,n}];

um=Table[{un[[i]],num[[i]]},{i,1,n}];

us=Sort[um]

num=Table[us[[i,2]],{i,1,n}]

For[i=1,i<n+1,i++,If[us[[i,1]]=="Z",us[[i,1]]="H"]];

u1=Table[If[us[[i,1]]=="C",0.255,If[us[[i,1]]=="H",0.1,If[us[[i,1]]=="N",0.24,If[us[[i,1]]=="O",0.178]]]],{i,1,n}]
u2=Table[If[us[[i,1]]=="C",0.258,If[us[[i,1]]=="H",0.6,If[us[[i,1]]=="N",0.22522,If[us[[i,1]]=="O",0.178]]]],{i,1,n}]

u=Table[us[[i,1]],{i,1,n}]

cn=Table[If[u[[i]]=="C",6.0,If[u[[i]]=="H",1.0,If[u[[i]]=="N",7.0,If[u[[i]]=="O",8.0]]]],{i,1,n}]

bc=0;
For[i=1, i<n+1,i++,If[u[[i]]≠"H", bc=bc+1]];
bc
bh=n-bc

ChemicalData["Butane","MolecularFormulaString"]

t=Table[t1[[num[[i]]]],{i,1,n}];

Plot1=Table[Graphics3D[{If[u[[i]]=="N",Lighter[Blue],If[u[[i]]=="O",Lighter[Red],Lighter[Brown]]],Sphere[{t[[i,1]],t[[i,2]],t[[i,3]]},u1[[i]]]}],{i,1,n}];

Plot2=Table[Graphics3D[Text[i,{t[[i,1]]-0.3,t[[i,2]],t[[i,3]]} ,{1,0}]],{i,1,n}];

ChemicalData["Butane","CHStructureDiagram"]

x=Table[t[[i,1]],{i,1,n}];
y=Table[t[[i,2]],{i,1,n}];
z=Table[t[[i,3]],{i,1,n}];

(* Distance matrix Bohr *)
Dij=Table[If[i≥j,If[sq=Sqrt[(x[[i]]-x[[j]])^2+(y[[i]]-y[[j]])^2+(z[[i]]-z[[j]])^2]; sq<3.0,sq,0],0],{i,1,n},{j,1,n}];
(*MatrixForm[Dij]*)

For[i=1 ,i<n+1,i++,
For[j=1, j<i,j++,
If[(Dij[[i,j]]≠0 && u[[i]]== "H"),If[u[[j]]=="C",u2[[i]]=0.5693,If[u[[j]]=="F",u2[[i]]=0.5,If[u[[j]]=="N",u2[[i]]=0.5541,If[u[[j]]=="O",u2[[i]]=0.5241]]]]]]]
u2

Fij=Dij-u2;
(*MatrixForm[Fij];*)
Gij=Table[If[i≥j,If[Fij[[i,j]]>0,Fij[[i,j]],0]," "],{i,1,n},{j,1,n}];
(*MatrixForm[Gij];*)

Hij=Transpose[Gij];
(*MatrixForm[Hij];*)

Kij=Hij-u2;
(*MatrixForm[Kij];*)
Lij=Table[If[i≤j,If[Kij[[i,j]]>0,Kij[[i,j]],0]," "],{i,1,n},{j,1,n}];
(*MatrixForm[Lij];*)

Lij=Table[If[i≤j,If[Lij[[i,j]]>0,If[u[[j]]≠"H",0.5*Lij[[i,j]],Lij[[i,j]]],0]," "],{i,1,n},{j,1,n}];  
Qij=Lij;
(*MatrixForm[Lij];*)

Nij=Table[If[i≤j,If[Lij[[i,j]]>0,2.25/Lij[[i,j]]^2,0]," "],{i,1,n},{j,1,n}];
(*MatrixForm[Nij]*)

Tval=Sum[If[i≤j,Nij[[i,j]],0],{i,1,n},{j,1,n}]

Tcor=Sum[If[u[[i]]≠"H",2.25/u2[[i]]^2,0],{i,1,n}]

Ttot=Tval+Tcor  (* plus π and lone pairs: + 8.7616 *)

TvalH=Sum[If[(i≤j && u[[j]]== "H"),Nij[[i,j]],0],{i,1,n},{j,1,n}]

TvalC=Tval-TvalH

Vnn=0.0;
For[ i=1,i<n,i++,
For[j=i+1,j<n+1,j++,
Vnn=Vnn+cn[[i]]*cn[[j]]/Sqrt[(x[[i]]-x[[j]])^2+(y[[i]]-y[[j]])^2+(z[[i]]-z[[j]])^2]]];
Vnn

Mij=Prepend[Qij,u];
Oij=Transpose[Mij];
Pij=Prepend[Oij,Prepend[u," "]];

(*MatrixForm[Pij];*)

(* sigma bond cloud radii *)

(*For[i=2,i<n+2,i++,
For[j=2,j≤i,j++,
If[Pij[[i,j]]>0,Print[u[[i-1]],i-1," ",u[[j-1]],j-1,"  ",Extract[Pij,{i,j}]]]]]*)

DeleteFile[ "C:\\Kimb_Mathem\\tmp4"];
For[i=2,i<n+2,i++,
For[j=2,j≤i,j++,
If[Pij[[i,j]]>0,{i-1,j-1,Extract[Pij,{i,j}]}>>> "C:\\Kimb_Mathem\\tmp4"]]]

a=ReadList["C:\\Kimb_Mathem\\tmp4"]
nb=Length[a]
cw=nb-bh

wxc=Table[If[u[[a[[i,1]]]]≠"H",(a[[i,3]]+u2[[a[[i,1]]]])/(u2[[a[[i,1]]]]+2*a[[i,3]]+u2[[a[[i,2]]]])*(x[[a[[i,2]]]]-x[[a[[i,1]]]])+x[[a[[i,1]]]],0],{i,1,nb}];

wyc=Table[If[u[[a[[i,1]]]]≠"H",(a[[i,3]]+u2[[a[[i,1]]]])/(u2[[a[[i,1]]]]+2*a[[i,3]]+u2[[a[[i,2]]]])*(y[[a[[i,2]]]]-y[[a[[i,1]]]])+y[[a[[i,1]]]],0],{i,1,nb}];

wzc=Table[If[u[[a[[i,1]]]]≠"H",(a[[i,3]]+u2[[a[[i,1]]]])/(u2[[a[[i,1]]]]+2*a[[i,3]]+u2[[a[[i,2]]]])*(z[[a[[i,2]]]]-z[[a[[i,1]]]])+z[[a[[i,1]]]],0],{i,1,nb}];

Plot7=Table[Graphics3D[{Darker[Gray],{Opacity[0.5],If[wxc[[i]]≠0,Sphere[{wxc[[i]],wyc[[i]],wzc[[i]]},a[[i,3]]]]}}],{i,1,nb}];

wxh=Table[If[u[[a[[i,1]]]]=="H",(a[[i,3]]+u2[[a[[i,2]]]])/(u2[[a[[i,1]]]]+a[[i,3]]+u2[[a[[i,2]]]])*(x[[a[[i,1]]]]-x[[a[[i,2]]]])+x[[a[[i,2]]]],0],{i,1,nb}];

wyh=Table[If[u[[a[[i,1]]]]=="H",(a[[i,3]]+u2[[a[[i,2]]]])/(u2[[a[[i,1]]]]+a[[i,3]]+u2[[a[[i,2]]]])*(y[[a[[i,1]]]]-y[[a[[i,2]]]])+y[[a[[i,2]]]],0],{i,1,nb}];

wzh=Table[If[u[[a[[i,1]]]]=="H",(a[[i,3]]+u2[[a[[i,2]]]])/(u2[[a[[i,1]]]]+a[[i,3]]+u2[[a[[i,2]]]])*(z[[a[[i,1]]]]-z[[a[[i,2]]]])+z[[a[[i,2]]]],0],{i,1,nb}];

Plot8=Table[Graphics3D[{Opacity[0.5],If[wxh[[i]]≠0,Sphere[{wxh[[i]],wyh[[i]],wzh[[i]]},a[[i,3]]]]}],{i,1,nb}];

Plot9= Table[Graphics3D[{Darker[Red,0.8],Cylinder[{{x[[a[[i,1]]]],y[[a[[i,1]]]],z[[a[[i,1]]]]},{x[[a[[i,2]]]],y[[a[[i,2]]]],z[[a[[i,2]]]]}},0.05]}],{i,1,nb}];
Show[Plot1,Plot7,Plot8,Plot9,{AspectRatio->Automatic,Boxed->False}]
Show[Plot1,Plot2,Plot9,{AspectRatio->Automatic}]

twc=Table[If[wxc[[i]]≠0,{wxc[[i]],wyc[[i]],wzc[[i]]}],{i,1,cw}];
twh=Table[If[wxh[[i+cw]]≠0,{wxh[[i+cw]],wyh[[i+cw]],wzh[[i+cw]]}],{i,1,bh}];
tw=Join[twc,twh];
(*MatrixForm[tw]*)

Vee=0.0; Vne=0.0;
bw=Length[tw]

For[i=1,i<bw,i++,
For[j=i+1,j<bw+1,j++,
Vee=Vee+4/Sqrt[(tw[[i,1]]-tw[[j,1]])^2+(tw[[i,2]]-tw[[j,2]])^2+(tw[[i,3]]-tw[[j,3]])^2]]]
Vee

For[i=1,i<bc,i++,
For[j=i+1,j<bc+1,j++,
Vee=Vee+4/Sqrt[(t[[i,1]]-t[[j,1]])^2+(t[[i,2]]-t[[j,2]])^2+(t[[i,3]]-t[[j,3]])^2]]]
Vee

For[i=1,i<bw+1,i++,
For[j=1,j<bc+1,j++,
Vee=Vee+4/Sqrt[(tw[[i,1]]-t[[j,1]])^2+(tw[[i,2]]-t[[j,2]])^2+(tw[[i,3]]-t[[j,3]])^2]]]
Vee

sc=0.15;
For[i=1 ,i<bc+1,i++,Vee=Vee+3*sc/u2[[i]]]
sw=0.2;
For[i=1 ,i<nb+1,i++,Vee=Vee+3*sw/a[[i,3]]]
Vee

For[i=1,i<bw+1,i++,
For[j=1,j<n+1,j++,
Vne=Vne-2*cn[[j]]/Sqrt[(tw[[i,1]]-t[[j,1]])^2+(tw[[i,2]]-t[[j,2]])^2+(tw[[i,3]]-t[[j,3]])^2]]]
Vne

For[i=1,i<n+1,i++,
For[j=i,j<n+1,j++,If[i≠j,
Vne=Vne-2*cn[[j]]/Sqrt[(t[[i,1]]-t[[j,1]])^2+(t[[i,2]]-t[[j,2]])^2+(t[[i,3]]-t[[j,3]])^2],0]]]
Vne

For[i=1,i<bc+1,i++,Vne=Vne-3*cn[[i]]/u2[[i]]]
Vne

For[i=bc+1,i<bh+1,i++,Vne=Vne-(3-(u2[[i]]/a[[i,3]])^2)/a[[i,3]]]

Vee
Vnn
Vne
Vtot=Vne+Vee+Vnn
Ttot
-Vtot/Ttot
Etot=Ttot+Vtot