(* Kimball model and energy derived from Wolfram source, ES 11 March 2013 *) 
Clear[tw,n2,n,nb,bc,bh,u,u1,u2,Vee,Vne,Vnn];

ChemicalData["VitaminA","MoleculePlot"]

t1=0.01889726*ChemicalData["VitaminA","AtomPositions"];
MatrixForm[t1]

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

n=Length[t1]

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

num1=Table[i,{i,1,n}];

um=Table[{un[[i]],num1[[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,If[us[[i,1]]=="Cl",0.5]]]]],{i,1,n}]
u2=Table[If[us[[i,1]]=="C",0.2557,If[us[[i,1]]=="H",0.6,If[us[[i,1]]=="N",0.22522,If[us[[i,1]]=="O",0.178,If[us[[i,1]]=="Cl",0.5]]]]],{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,If[u[[i]]=="Cl",17.0]]]]],{i,1,n}]

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

ChemicalData["VitaminA","MolecularFormulaString"]

DeleteFile[ "C:\\Kimb_Mathem\\tmp3"];
For[i=1,i<n+1,i++,
{u[[i]],Extract[t1,{i}]}>>> "C:\\Kimb_Mathem\\tmp3"]

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

ChemicalData["VitaminA","CHStructureDiagram"]

(* Distance Matrix Bohr *)
dc=Table[Norm[t[[i]]-t[[j]]],{i,1,n},{j,1,n}];

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

(* connected pairs: distance criteria < 3.0 bohr *)
Dij=Table[If[(dc[[i,j]]<3.0||(u[[i]]=="Cl" && j==10 && i== 17)),dc[[i,j]],0],{i,1,n},{j,1,n}];
MatrixForm[Prepend[Dij,num1]]

nc=0;  (* parse into prim, sec, tert, and quart C cores with different radii *)
For[i=1,i<bc+1,i++,If[u[[i]]=="C",nc=nc+1,nc]]
cnt=Table[0,{i,1,nc}];
pri=cnt; sec=cnt;ter=cnt; qua=cnt;
nc

For[j=1,j<nc+1,j++,
For[i=bc+1,i<n+1,i++,If[ Dij[[i,j]]≠0 ,cnt[[j]]=cnt[[j]]+1,0]]];
cnt

n1=0; n2=0; n3=0; n4=0;
For[i=1,i<nc+1,i++,If[cnt[[i]]==3,n1=n1+1;pri[[n1]]=i,If[cnt[[i]]==2,n2=n2+1;sec[[n2]]=i,If[cnt[[i]]==1,n3=n3+1;ter[[n3]]=i,If[cnt[[i]]=0,n4=n4+1;qua[[n4]]=i]]]]];
For [i=1, i<nc+1,i++,If[pri[[i]]≠0,u2[[pri[[i]]]]=0.2547]]
For [i=1, i<nc+1,i++,If[sec[[i]]≠0,u2[[sec[[i]]]]=0.255]]
For [i=1, i<nc+1,i++,If[ter[[i]]≠0,u2[[ter[[i]]]]=0.2557]]
For [i=1, i<nc+1,i++,If[qua[[i]]≠0,u2[[qua[[i]]]]=0.2577]]
con=Table[{i},{i,1,bc}];
For[i=1,i<bc+1,i++,
For[j=1,j<bc+1,j++,If[ Dij[[i,j]]≠0 ,con[[i]]={con[[i]],j}]]];
conn=Table[Flatten[con[[i]]],{i,1,bc}];

MatrixForm[conn, TableAlignments->Left]

Eij=Table[If[i≥j,Dij[[i,j]],0],{i,1,bc-1},{j,1,bc-1}];
CD=Select[Flatten[Eij],(#≥2.4 &&#≤2.6) &]
Mean[CD] ± StandardDeviation[CD]

CC=Select[Flatten[Eij],(#≥2.6) &]
Mean[CC] ± StandardDeviation[CC]

Eij=Table[If[i≥j,Dij[[i,j]],0],{i,bc+1,n},{j,1,bc-1}];
CH=Select[Flatten[Eij],(#>0 &&#≤2.1) &]
Mean[CH] ± StandardDeviation[CH]

For[i=1 ,i<n+1,i++,
For[j=1, j<bc+1,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

(* subtract core radii from pair distances *)
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];*)

(* determine bond cloud radii *)
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];*)

(* determine kinetic energy *)
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

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

Clear[c,v,p,Q,P]; (*c1=20; c2=21; c3=51;*)

P=Length[conn[[12]]]
c=Table[conn[[12,i]],{i,1,P}]

v=Table[Join[t[[c[[i]]]],{1}],{i,1,P}]
x2=t[[c[[2]],1]]; y2=t[[c[[2]],2]]; z2=t[[c[[2]],3]]; (* to be set to (0,0,0) *)
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{-x2,-y2,-z2,1}};

p=v.Q;
t1=Table[Join[t[[i]],{1}],{i,1,n}];
t=t1.Q;
For[i=1,i<P+1,i++,p[[i]]=Take[p[[i]],3]];
p
For[i=1,i<n+1,i++,t[[i]]=Take[t[[i]],3]];

(* Rotation of general triangle into xy plane with one point, O atom, at 0rigin by translation, one leg on x-axis O - C atoms; example: COH in Vitamine A    ES 8.3.2013 *)

(* rotate p1 around x-axis until the z-comp = 0 *)

T1=ArcTan[p[[1,3]]/p[[1,2]]]

U=p; t1=t;
T=RotationMatrix[T1,{1,0,0}];
p=U.T;
t=t1.T;

(* Rotate p1 around z-axis to make y-comp to 0 *)

T1=ArcTan[p[[1,2]]/p[[1,1]]]

U=p; t1=t;
T=RotationMatrix[T1,{0,0,1}];
p=U.T;
t=t1.T;

(* rotate p2 around x-axis to make z-comp = 0 *)

T1=ArcTan[p[[3,3]]/p[[3,2]]]

U=p; t1=t;
T=RotationMatrix[T1,{1,0,0}];
p=U.T
t=t1.T;

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

Plot1=Table[Graphics3D[{If[u[[i]]=="N",Lighter[Blue],If[u[[i]]=="O",Lighter[Red],If[u[[i]]=="Cl",Lighter[Green],If[u[[i]]=="B",Lighter[Orange],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]]-0.6,t[[i,2]],t[[i,3]]} ,{1,0}]],{i,1,n}];

Plota = Table[Graphics3D[{Opacity[0.5],Sphere[p[[i]],u2[[c[[i]]]]]}],{i,1,P}];
Plotc = Table[Graphics3D[{Tube[{p[[i]],p[[j]]},0.02]}],{i,1,P-1},{j,i+1,P}];
Plotb0=Table[Graphics3D[Text[c[[i]],p[[i]],{1,0}]],{i,1,P}];
Show[Plota,Plotb0,(*Plotb1,Plotb2,*)Plotc,{Axes->Automatic,AxesLabel->{xl,yl,zl},AspectRatio->Automatic,Boxed->False,PlotRange->Automatic, SphericalRegion->True}]
(* now add O lone pairs perpendicular to COH plane and retransform into molecular skeleton *)

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[(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]]]],{i,1,cw}];
wyc=Table[(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]]]],{i,1,cw}];   
wzc=Table[(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]]]],{i,1,cw}];

Plot7=Table[Graphics3D[{Darker[Brown,0.4],Opacity[0.5],If[wxc[[i]]≠0,Sphere[{wxc[[i]],wyc[[i]],wzc[[i]]},a[[i,3]]]]}],{i,1,cw}];

wxh=Table[(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]]]],{i,cw+1,nb}];
wyh=Table[(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]]]],{i,cw+1,nb}];
wzh=Table[(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]]]],{i,cw+1,nb}];

Plot8=Table[Graphics3D[{Opacity[0.5],Sphere[{wxh[[i]],wyh[[i]],wzh[[i]]},a[[i+cw,3]]]}],{i,1,bh}];

conj={9,11,12,14,15,16,17,19}; nj=Length[conj];
rpo=1.4;
px=Table[x[[conj[[i]]]],{i,1,nj}];
py=Table[y[[conj[[i]]]],{i,1,nj}];
pz=Table[z[[conj[[i]]]]+rpo,{i,1,nj}];
Plot8a=Table[Graphics3D[{Opacity[0.3],Lighter[Cyan],Sphere[{px[[i]],py[[i]],pz[[i]]},rpo]}],{i,1,nj}];
rpi=1.4;
qx=Table[x[[conj[[i]]]],{i,1,nj}];
qy=Table[y[[conj[[i]]]],{i,1,nj}];
qz=Table[z[[conj[[i]]]]-rpi,{i,1,nj}];
Plot8b=Table[Graphics3D[{Opacity[0.3],Lighter[Yellow],Sphere[{qx[[i]],qy[[i]],qz[[i]]},rpi]}],{i,1,nj}];

Plot9= Table[Graphics3D[{If[(a[[i,3]]>0.98 && a[[i,3]]<1.05),({Lighter[Orange,0.5],Tube[{{x[[a[[i,1]]]],y[[a[[i,1]]]]+0.12,z[[a[[i,1]]]]},{x[[a[[i,2]]]],y[[a[[i,2]]]]+0.12,z[[a[[i,2]]]]}},0.06],Tube[{{x[[a[[i,1]]]],y[[a[[i,1]]]]-0.12,z[[a[[i,1]]]]},{x[[a[[i,2]]]],y[[a[[i,2]]]]-0.12,z[[a[[i,2]]]]}},0.06]}),Tube[{{x[[a[[i,1]]]],y[[a[[i,1]]]],z[[a[[i,1]]]]},{x[[a[[i,2]]]],y[[a[[i,2]]]],z[[a[[i,2]]]]}},0.06]]}],{i,1,nb}];

Show[Plot1,Plot2,Plot7,Plot8,Plot8a,Plot8b,Plot9,{AspectRatio->Automatic,Boxed->False, SphericalRegion->True}]
Show[Plot1,Plot2,Plot9,{Axes->Automatic,AxesLabel->{xl,yl,zl},AspectRatio->Automatic,Boxed->True, SphericalRegion->True}]

tc=Table[{x[[i]],y[[i]],z[[i]]},{i,1,bc}];   (* core clouds *)
twc=Table[{wxc[[i]],wyc[[i]],wzc[[i]]},{i,1,cw}];  (* Bond cöouds between cores *)
twh=Table[{wxh[[i]],wyh[[i]],wzh[[i]]},{i,1,bh}]; (* H-bonding clouds *) 
tpo=Table[{px[[i]],py[[i]],pz[[i]]},{i,1,nj}]; (* pi clouds above *)
tpu=Table[{qx[[i]],qy[[i]],qz[[i]]},{i,1,nj}]; (* pi clouds below *) 
tw=Join[tc,twc,twh,tpo,tpu];
bt=Length[tw]
MatrixForm[tw]
(* coordinates of clouds *)

(* cloud-cloud distances *)
dw=Table[Norm[tw[[i]]-tw[[j]]],{i,1,bt},{j,1,bt}];
(*MatrixForm[dw]*)

(* nucleus-nucleus distances *)
(*MatrixForm[dc] *)

tv1=Table[{x[[i]],y[[i]],z[[i]]},{i,1,bc}];
tv2=Table[{0,0,0},{i,1,cw}];
tv3= Table[{x[[i]],y[[i]],z[[i]]},{i,bc+1,n}];
tv4 =Table[{0,0,0},{i,1,nj}]; 
tv5 =Table[{0,0,0},{i,1,nj}]; 
tv  = Join[tv1,tv2,tv3,tv4,tv5];
MatrixForm[tv]

ow=Join[Table[-2.0,{i,1,bc+nb}],Table[-0.5,{i,1,2*nj}]]
cnv=Join[Table[cn[[i]],{i,1,bc}],Table[0.0,{i,1,cw}],Table[cn[[i]],{i,bc+1,n}],Table[0.0,{i,1,2*nj}]]

(* nucleus-cloud distances *)
dcw=Table[sq=Norm[tw[[i]]-tv[[j]]];If[(sq> 0.1 && i≠j),1/sq,0],{i,1,bt},{j,1,bt}];
(*MatrixForm[dcw]*)

Vee=0.0; Vnn=0.0;

(* all clouds repulsion *)
For[i=1,i<bt,i++,
For[j=i+1,j<bt+1,j++,
Vee=Vee+ow[[i]]*ow[[j]]/dw[[i,j]]]]
Vee

(* half cloud with other common halfcloud: subtract WW *)
For [i=nb+bc+1,i<nb+bc+nj+1,i++,Vee=Vee-ow[[i]]*ow[[i+nj]]/dw[[i,i+nj]]];
Vee

sc=0.43;   (* core clouds *)
For[i=1 ,i<bc+1,i++,Vee=Vee+3*sc/u2[[i]]]
sw=0.43;  (* bonding clouds *)
For[i=1 ,i<nb+1,i++,Vee=Vee+3*sw/a[[i,3]]]
Vee

(* all nuclei with all clouds, except i = j *)
Vne=cnv.(ow.dcw)

(* core nuclei in their cloud centers *)

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

(* protons in their bonding cloud, distance u2[[a[[i,1]]]] to cloud center *)
For[i=cw+1,i<nb+1,i++,Vne=Vne-(3-(u2[[a[[i,1]]]]/a[[i,3]])^2)/a[[i,3]]]
Vne

(* nucleus-nucleus *)
For[i=1,i<n,i++,
For[j=i+1,j<n+1,j++,Vnn=Vnn+cn[[i]]*cn[[j]]/dc[[i,j]]]]
Vnn

Vee
Vnn
Vne
Tpi = 2.296*nj*0.5*1.125*(1/rpo^2+1/rpi^2) (* pi kin e added *)
Vtot=Vne+Vee+Vnn
Ttot =Ttot+Tpi
Vir   =-Vtot/Ttot
Etot=Ttot+Vtot