(* Kimball model and energy derived from RHF/4-21G optimization, ES 05 April 2013 *) 
Clear[tw,n2,n,nb,bc,bh,u,u1,u2,Vee,Vne,Vnn];

t1=1.889726*{{4.3046917509,-3.0703804373,-0.0534968436},{3.9524509586,-1.6270020770,-0.0229967489},{2.6219345129,-1.2226692299,-0.0108919987},{2.3013661514,0.1406897696,0.0098447154},{0.9553275750,0.6534496137,0.0141123946},{-0.0160836500,-0.1170316466,0.0238636163},{-1.3303659155,0.4546316424,0.0125638483},{-2.4314494340,-0.4669148237,0.0148934019},{-3.7458887896,0.0441398988,-0.0228331897},{-3.9654457612,1.4513608383,-0.0460665200},{-2.9193124548,2.3252265054,-0.0366091281},{-1.5815185106,1.8287441851,-0.0107394372},{-0.6276242138,2.7941911390,-0.0133432213},{0.2410961670,2.3734671772,-0.0054237325},{-3.0864731703,3.4090852512,-0.0511024847},{-4.9973196043,1.8220720882,-0.0708761851},{-4.8486083142,-0.8485334191,-0.0376482360},{-4.6445690442,-2.2025943872,-0.0081703095},{-3.3319011612,-2.7174021075,0.0412413922},{-2.2502207251,-1.8751373988,0.0520708825},{-1.2369328368,-2.2926296528,0.0906487311},{-3.1864901721,-3.8025183198,0.0707181890},{-5.4924434656,-2.8950229625,-0.0220865950},{-5.8635407603,-0.4363877745,-0.0742008773},{3.3366855699,1.0999465577,0.0193775656},{3.1438958382,2.4497884954,0.0378765211},{2.2091531179,2.6285578870,0.0338002375},{4.6780352358,0.6831440121,0.0106173166},{4.9732749820,-0.6691365280,-0.0107142256},{6.0188011478,-0.9982311277,-0.0185038087},{5.4831630205,1.4271679121,0.0199743657},{1.8264187927,-1.9805338302,-0.0184539583},{4.8389704522,-3.3207295880,-0.9799975660},{4.9606032459,-3.3325614371,0.7875125314},{3.4190522488,-3.7169834602,0.0027914637}};
MatrixForm[t1]

u={"C","C","C","C","N","N","C","C","C","C","C","C","O","H","H","H","C","C","C","C","H","H","H","H","C","O","H","C","C","H","H","H","H","H","H"};

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",0.12,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",0.4507]]]]],{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

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}];
Plot1o=Table[Graphics3D[{Opacity[0.8],If[u[[i]]=="N",Lighter[Blue],If[u[[i]]=="H",Lighter[White],If[u[[i]]=="O",Lighter[Red],If[u[[i]]=="Cl",Lighter[Green],If[u[[i]]=="B",Lighter[Orange],Darker[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}];
Show[Plot1o,Plot2,{AspectRatio->Automatic,Boxed->True, Axes->Automatic,AxesLabel->{xl,yl,zl},SphericalRegion->True}]

(* Distance Matrix Bohr *)
dc=Table[Norm[t[[i]]-t[[j]]],{i,1,n},{j,1,n}];
MatrixForm[Prepend[dc,num1]]

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" && dc[[i,j]]<3.24)),dc[[i,j]],0],{i,1,n},{j,1,n}];
MatrixForm[Prepend[Dij,num1]]

(* count C atoms *)
nc=0;  
For[i=1,i<bc+1,i++,If[u[[i]]=="C",nc=nc+1,nc]]
cnt=Table[0,{nc}];
pri=cnt; sec=cnt;ter=cnt; qua=cnt;
nc

(* count H atoms bonded to each C atom *)
For[j=1,j≤nc,j++,
For[i=bc+1,i≤n,i++,If[ Dij[[i,j]]≠0 ,cnt[[j]]=cnt[[j]]+1,0]]];
cnt

(* parse into prim, sec, tert, and quart C cores with different radii *)
n1=0; n2=0; n3=0; n4=0;
For[i=1,i≤nc,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,i++,If[pri[[i]]≠0,u2[[pri[[i]]]]=0.2572]]
For [i=1, i≤nc,i++,If[sec[[i]]≠0,u2[[sec[[i]]]]=0.2556]]
For [i=1, i≤nc,i++,If[ter[[i]]≠0,u2[[ter[[i]]]]=0.2578]]
For [i=1, i≤nc,i++,If[qua[[i]]≠0,u2[[qua[[i]]]]=0.258]]

Eij=Table[If[i≥j,Dij[[i,j]],0],{i,1,nc},{j,1,nc}];
CD=Select[Flatten[Eij],(#≥2.4 &&#≤2.73) &]
Mean[CD] ± StandardDeviation[CD]

CC=Select[Flatten[Eij],(#≥2.73) &]
Mean[CC] ± StandardDeviation[CC]

Eij=Table[If[i≥j,Dij[[i,j]],0],{i,bc+1,n},{j,1,nc}];
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," "]];

con=Table[{i},{i,1,n}]; conj=Table[0,{nc}];
For[i=1,i≤n,i++,
For[j=1,j≤n,j++,If[ Dij[[i,j]]≠0 ,con[[i]]={con[[i]],j}]]];
conn=Table[Flatten[con[[i]]],{i,1,n}];
(* identify C atoms at double bonds *)
j=0;
For[i=1,i≤nc,i++,If[Length[conn[[i]]]==4,j=j+1;conj[[j]]=i]];
conj=Take[conj,{1,j}]
nj=Length[conj];
MatrixForm[conn, TableAlignments->Left]

Clear[c,v,p,Q,P,v1,v2,nk,nl]; (*c1=20; c2=21; c3=51;*) 
rpo=1.4;
rpi=1.4;
tpo=Table[{0,0,0},{nj+2}];
tpu=Table[{0,0,0},{nj+2}];
P=3; c={0,0,0,0,0}; 
(*--------------------------------------------------------------------------*)
(* construct the π clouds for C atoms *)

Do[(c=conn[[conj[[k]]]];
c=Take[c,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]];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{-x2,-y2,-z2,1}};
p=v.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
T1=ArcTan[p[[1,3]]/p[[1,2]]];
U=p;
T=RotationMatrix[T1,{1,0,0}];
p=U.T;
T2=ArcTan[p[[1,2]]/p[[1,1]]];
U=p;
T=RotationMatrix[T2,{0,0,1}];
p=U.T;
T3=ArcTan[p[[3,3]]/p[[3,2]]];
U=p;
T=RotationMatrix[T3,{1,0,0}];
p=Chop[U.T];
mk=p;
ml=p;
mk[[1,3]]=rpo;
ml[[1,3]]=-rpi;
U=p;
U1=mk;
U2=ml;
T=RotationMatrix[-T3,{1,0,0}];
p=U.T;
mk=U1.T;
ml=U2.T;
U=p;
U1=mk;
U2=ml;
T=RotationMatrix[-T2,{0,0,1}];
p=U.T;
mk=U1.T;
ml=U2.T;
U=p;
U1=mk;
U2=ml;
T=RotationMatrix[-T1,{1,0,0}];
p=U.T;
mk=U1.T;
ml=U2.T;
Clear[v,v1,v2];
v  =Table[Join[p[[i]],{1}],{i,1,P}];
v1=Table[Join[mk[[i]],{1}],{i,1,P}];
v2=Table[Join[ml[[i]],{1}],{i,1,P}];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{x2,y2,z2,1}};
p=v.Q;
mk=v1.Q;
ml=v2.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
mk=Table[Take[mk[[i]],3],{i,1,P}];
ml=Table[Take[ml[[i]],3],{i,1,P}];
tpo[[k]]=mk[[1]];
tpu[[k]]=ml[[1]]),{k,nj}];

(*-------------------------------------------------------------------------*)
(* construct the π clouds for the azo N atoms *)

k=1;
Clear[conn];
conn={{18,2,5},{19,4,3}};

Do[(c=conn[[k]];
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]];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{-x2,-y2,-z2,1}};
p=v.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
T1=ArcTan[p[[1,3]]/p[[1,2]]];
U=p;
T=RotationMatrix[T1,{1,0,0}];
p=U.T;
T2=ArcTan[p[[1,2]]/p[[1,1]]];
U=p;
T=RotationMatrix[T2,{0,0,1}];
p=U.T;
T3=ArcTan[p[[3,3]]/p[[3,2]]];
U=p;
T=RotationMatrix[T3,{1,0,0}];
p=Chop[U.T];
nk=p;
nl=p;
nk[[1,3]]=rpo;
nl[[1,3]]=-rpi;
U=p;
U1=nk;
U2=nl;
T=RotationMatrix[-T3,{1,0,0}];
p=U.T;
nk=U1.T;
nl=U2.T;
U=p;
U1=nk;
U2=nl;
T=RotationMatrix[-T2,{0,0,1}];
p=U.T;
nk=U1.T;
nl=U2.T;
U=p;
U1=nk;
U2=nl;
T=RotationMatrix[-T1,{1,0,0}];
p=U.T;
nk=U1.T;
nl=U2.T;
Clear[v,v1,v2];
v  =Table[Join[p[[i]],{1}],{i,1,P}];
v1=Table[Join[nk[[i]],{1}],{i,1,P}];
v2=Table[Join[nl[[i]],{1}],{i,1,P}];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{x2,y2,z2,1}};
p=v.Q;
nk=v1.Q;
nl=v2.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
nk=Table[Take[nk[[i]],3],{i,1,P}];
nl=Table[Take[nl[[i]],3],{i,1,P}];
tpo[[nj+k]]=nk[[1]];
tpu[[nj+k]]=nl[[1]]),{k,2}];

(*-----------------------------------------------------------------*)
(* construct the LP's for the O atoms *)

k=1;
Clear[conn];
conn={{10,20,22},{29,21,15}};
rlo=1.125;
tlo={{0.0,0.0,0.0},{0.0,0.0,0.0}};
tlu={{0.0,0.0,0.0},{0.0,0.0,0.0}};
Do[(c=conn[[k]];
a1=dc[[c[[2]],c[[1]]]]; a2=dc[[c[[2]],c[[3]]]]; d1=dc[[c[[1]],c[[3]]]];
α=ArcCos[(a1^2+a2^2-d1^2)/(2*a1*a2)];
L=(u2[[c[[2]]]]+rlo);
β=ArcSin[rln/L];
If[k==1,γ=-α/4,γ=3*π/2+α/2];
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]];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{-x2,-y2,-z2,1}};
p=v.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
T1=ArcTan[p[[1,3]]/p[[1,2]]];
U=p;
T=RotationMatrix[T1,{1,0,0}];
p=U.T;
T2=ArcTan[p[[1,2]]/p[[1,1]]];
U=p;
T=RotationMatrix[T2,{0,0,1}];
p=U.T;
T3=ArcTan[p[[3,3]]/p[[3,2]]];
U=p;
T=RotationMatrix[T3,{1,0,0}];
p=Chop[U.T];
nk=p;
nl=p;
nk[[2,2]]=L*Cos[γ]; nk[[2,1]]=-L*Sin[γ];  nk[[2,3]]=rlo; 
nl[[2,2]]=nk[[2,2]]; nl[[2,1]]=nk[[2,1]];  nl[[2,3]]=-rlo;
(*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}];
Plotd=Graphics3D[{Opacity[0.5],Lighter[Red],Sphere[nk[[2]],rlo]}];
Plote=Graphics3D[{Opacity[0.5],Lighter[Red],Sphere[nl[[2]],rlo]}];
Plotb0=Table[Graphics3D[Text[c[[i]],p[[i]],{1,0}]],{i,1,P}];
Show[Plotd,Plote,Plota,Plotb0,(*Plotb1,Plotb2,*)Plotc,{Axes->Automatic,AxesLabel->{xl,yl,zl},AspectRatio->Automatic,Boxed->False,PlotRange->Automatic, SphericalRegion->True}]*)
U=p;
U1=nk;
U2=nl;
T=RotationMatrix[-T3,{1,0,0}];
p=U.T;
nk=U1.T;
nl=U2.T;
U=p;
U1=nk;
U2=nl;
T=RotationMatrix[-T2,{0,0,1}];
p=U.T;
nk=U1.T;
nl=U2.T;
U=p;
U1=nk;
U2=nl;
T=RotationMatrix[-T1,{1,0,0}];
p=U.T;
nk=U1.T;
nl=U2.T;
Clear[v,v1,v2];
v  =Table[Join[p[[i]],{1}],{i,1,P}];
v1=Table[Join[nk[[i]],{1}],{i,1,P}];
v2=Table[Join[nl[[i]],{1}],{i,1,P}];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{x2,y2,z2,1}};
p=v.Q;
nk=v1.Q;
nl=v2.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
nk=Table[Take[nk[[i]],3],{i,1,P}];
nl=Table[Take[nl[[i]],3],{i,1,P}];
tlo[[k]]=nk[[2]];
tlu[[k]]=nl[[2]]),{k,2}];

(*-------------------------------------------------------------------------*)
(* next: N18,N19 in C-N=N, N=N-C; one doubly occ LP as sp2 ligand *)
k=1;
Clear[conn];
tpln={{0.0,0.0,0.0},{0.0,0.0,0.0}};
conn={{18,19,5},{19,18,4}};
rln=1.246;
Do[(c=conn[[k]];
a1=dc[[c[[2]],c[[1]]]]; a2=dc[[c[[2]],c[[3]]]]; d1=dc[[c[[1]],c[[3]]]];
α=ArcCos[(a1^2+a2^2-d1^2)/(2*a1*a2)];
β=ArcSin[rln/(u2[[c[[2]]]]+rln)];
If[k==1,γ=π-α/4,γ=3*π/2+α/2];
L=(u2[[c[[2]]]]+rln);
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]];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{-x2,-y2,-z2,1}};
p=v.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
T1=ArcTan[p[[1,3]]/p[[1,2]]];
U=p;
T=RotationMatrix[T1,{1,0,0}];
p=U.T;
T2=ArcTan[p[[1,2]]/p[[1,1]]];
U=p;
T=RotationMatrix[T2,{0,0,1}];
p=U.T;
T3=ArcTan[p[[3,3]]/p[[3,2]]];
U=p;
T=RotationMatrix[T3,{1,0,0}];
p=Chop[U.T];
nk=p;
nk[[2,2]]=L*Cos[γ]; nk[[2,1]]=-L*Sin[γ];  nk[[2,3]]=0; 
(*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}];
Plotd=Graphics3D[{Opacity[0.5],Lighter[Blue],Sphere[nk[[2]],rln]}];
Plotb0=Table[Graphics3D[Text[c[[i]],p[[i]],{1,0}]],{i,1,P}];
Show[Plotd,(*Plote,*)Plota,Plotb0,(*Plotb1,Plotb2,*)Plotc,{Axes->Automatic,AxesLabel->{xl,yl,zl},AspectRatio->Automatic,Boxed->False,PlotRange->All, SphericalRegion->True}]*)
U=p;
U1=nk;
T=RotationMatrix[-T3,{1,0,0}];
p=U.T;
nk=U1.T;
U=p;
U1=nk;
T=RotationMatrix[-T2,{0,0,1}];
p=U.T;
nk=U1.T;
U=p;
U1=nk;
T=RotationMatrix[-T1,{1,0,0}];
p=U.T;
nk=U1.T;
Clear[v,v1,v2];
v  =Table[Join[p[[i]],{1}],{i,1,P}];
v1=Table[Join[nk[[i]],{1}],{i,1,P}];
Q={{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{x2,y2,z2,1}};
p=v.Q;
nk=v1.Q;
p=Table[Take[p[[i]],3],{i,1,P}];
nk=Table[Take[nk[[i]],3],{i,1,P}];
tpln[[k]]=nk[[2]]),{k,2}];

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}];

Plot8a=Table[Graphics3D[{Opacity[0.3],Lighter[Cyan],Sphere[tpo[[i]],rpo]}],{i,1,nj+2}];
Plot8b=Table[Graphics3D[{Opacity[0.3],Lighter[Yellow],Sphere[tpu[[i]],rpi]}],{i,1,nj+2}];
Plot8c=Table[Graphics3D[{Opacity[0.4],Lighter[Red],Sphere[tlo[[i]],rlo]}],{i,1,2}];
Plot8d=Table[Graphics3D[{Opacity[0.4],Lighter[Red],Sphere[tlu[[i]],rlo]}],{i,1,2}];
Plot8e=Table[Graphics3D[{Opacity[0.4],Lighter[Blue],Sphere[tpln[[i]],rln]}],{i,1,2}];

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}];
(*Plot9a= Graphics3D[Tube[{{x[[21]],y[[21]],z[[21]]},{nk[[2,1]],nk[[2,2]],nk[[2,3]]}},0.06]];
Plot9b= Graphics3D[Tube[{{x[[21]],y[[21]],z[[21]]},{nl[[2,1]],nl[[2,2]],nl[[2,3]]}},0.06]];*)
Show[Plot1o,(*Plot2,*)Plot7,Plot8,Plot8a,Plot8b,Plot8c,Plot8d,Plot8e,Plot9,{AspectRatio->Automatic,Boxed->False,(* Axes->Automatic,AxesLabel->{xl,yl,zl},*)SphericalRegion->True}]
Show[Plot1o,Plot2,Plot9,(*Plot9a,Plot9b,*){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 *) 
tw=Join[tc,twc,twh,tpo,tpu,tlo,tlu,tpln];
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]*)
Length[dw]

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

tv1=Table[t[[i]],{i,1,bc}];
tv2=Table[{0,0,0},{i,1,cw}];
tv3= Table[t[[i]],{i,bc+1,n}];
tv4 =Table[{0,0,0},{i,1,nj+2}]; 
tv5 =Table[{0,0,0},{i,1,nj+2}]; 
tv6 =Table[{0,0,0},{i,1,6}]; 
tv  = Join[tv1,tv2,tv3,tv4,tv5,tv6];
MatrixForm[tv]
Length[tv]

ow=Join[Table[-2.0,{i,1,bc+nb}],Table[-0.5,{i,1,2*nj}],Table[-0.5,{i,1,4}],Table[-2.0,{i,1,2}],Table[-2.0,{i,1,4}]];
lw=Length[ow]
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}],Table[0.0,{i,1,10}]];
lc=Length[cnv]

echarg=Sum[ow[[i]],{i,1,lw}]
pcharg=Sum[cnv[[i]],{i,1,lc}]

(* 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}];
Length[dcw]
(*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+3,i++,Vee=Vee-ow[[i]]*ow[[i+nj]]/(rpo+rpi)];
Vee

sc=0.351;   (* core clouds *)
For[i=1 ,i<bc+1,i++,Vee=Vee+3*sc/u2[[i]]]
sw=0.35;  (* bonding clouds *)
For[i=1 ,i<nb+1,i++,Vee=Vee+3*sw/a[[i,3]]]
For[i=1 ,i<5,i++,Vee=Vee+3*sw/rlo]
For[i=1 ,i<3,i++,Vee=Vee+3*sw/rln]
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+2)*0.5*1.125*(1/rpo^2+1/rpi^2) (* pi kin e added *)
Tlo   = 4*2*1.125*(1/rlo^2) (* lp kin e of 2 O added *)
Tln   = 2*2*1.125*(1/rln^2) (* lp kin e of 2 N added *)
Vtot=Vne+Vee+Vnn
Ttot=Ttot+Tpi+Tlo+Tln
Vir   =-Vtot/Ttot
Etot =Ttot+Vtot