(* Kimball model and energy derived from Fcio PDF ES 09 April 2013 *) 
Clear[tw,n2,n,nb,bc,bh,u,u1,u2,Vee,Vne,Vnn];

t1=1.889726*{{5.814000,7.901000,-30.790000},{3.149000,9.127000,-32.553000},{7.561000,7.561000,-33.767000},{8.734000,7.364000,-29.079000},{4.284000,8.853000,-27.804000},{5.414000,8.329000,-32.810000},{4.176000,8.724000,-33.336000},{4.234000,8.885000,-34.812000},{5.508000,8.110000,-35.193000},{6.231000,7.974000,-33.857000},{5.069000,6.778000,-35.737000},{4.414000,10.364000,-34.998000},{5.765000,10.849000,-34.445000},{5.916000,12.319000,-34.970000},{5.142000,12.710000,-35.755000},{6.849000,13.100000,-34.365000},{7.823000,7.602000,-31.299000},{8.325000,7.402000,-32.599000},{9.709000,6.944000,-32.504000},{10.063000,6.898000,-31.198000},{8.840000,7.323000,-30.421000},{10.619000,6.520000,-33.613000},{11.404000,6.476000,-30.694000},{12.230000,5.860000,-31.424000},{11.980000,6.812000,-29.317000},{6.414000,8.128000,-28.791000},{7.622000,7.715000,-28.293000},{7.607000,7.550000,-26.801000},{6.354000,8.377000,-26.431000},{5.580000,8.411000,-27.700000},{7.295000,6.054000,-26.600000},{6.117000,9.115000,-25.348000},{6.780000,8.846000,-23.951000},{4.151000,8.893000,-30.252000},{3.559000,9.101000,-29.003000},{2.191000,9.503000,-29.146000},{1.987000,9.548000,-30.540000},{3.201000,9.181000,-31.159000},{1.206000,9.693000,-28.061000},{1.006000,9.719000,-31.567000},{-0.232000,9.845000,-31.472000},{1.731000,9.571000,-32.936000},{0.954000,8.467000,-33.637000},{0.490000,8.533000,-34.647000},{0.870000,7.311000,-32.986000},{0.000000,6.330000,-33.596000},{7.224000,14.416000,-34.971000},{8.030000,14.064000,-36.222000},{9.229000,14.456000,-36.548000},{10.000000,15.424000,-35.643000},{9.845000,13.847000,-37.852000},{10.210000,14.811000,-39.006000},{10.445000,13.908000,-40.267000},{11.728000,14.401000,-40.937000},{11.656000,15.933000,-41.054000},{11.893000,13.769000,-42.326000},{13.295000,14.105000,-42.858000},{13.478000,13.468000,-44.244000},{14.922000,13.678000,-44.734000},{15.274000,15.178000,-44.701000},{15.069000,13.129000,-46.168000},{16.549000,13.150000,-46.600000},{16.688000,12.603000,-48.036000},{18.176000,12.549000,-48.442000},{18.306000,12.130000,-49.919000},{18.932000,11.550000,-47.546000},{8.063000,7.337000,-34.708000},{9.632000,7.088000,-28.527000},{3.754000,9.033000,-26.869000},{3.346000,8.469000,-35.288000},{6.100000,8.660000,-35.924000},{5.945000,6.194000,-36.020000},{4.506000,6.241000,-34.974000},{4.437000,6.933000,-36.612000},{3.637000,10.934000,-34.488000},{4.379000,10.647000,-36.050000},{6.503000,10.162000,-34.858000},{5.668000,10.782000,-33.361000},{10.549000,7.234000,-34.434000},{11.646000,6.486000,-33.248000},{10.326000,5.531000,-33.966000},{12.343000,7.840000,-29.315000},{11.203000,6.700000,-28.561000},{12.805000,6.136000,-29.093000},{8.518000,7.936000,-26.344000},{7.262000,5.829000,-25.534000},{6.330000,5.820000,-27.050000},{8.072000,5.454000,-27.073000},{5.046000,9.035000,-25.159000},{6.425000,10.129000,-25.603000},{6.426000,9.584000,-23.232000},{6.512000,7.847000,-23.607000},{7.864000,8.920000,-24.042000},{1.096000,10.757000,-27.852000},{0.244000,9.282000,-28.367000},{1.551000,9.181000,-27.163000},{1.753000,10.514000,-33.483000},{-0.003000,5.422000,-32.993000},{-1.013000,6.729000,-33.656000},{0.359000,6.099000,-34.599000},{7.811000,14.925000,-34.206000},{6.277000,14.909000,-35.190000},{7.425000,14.425000,-37.054000},{8.131000,12.979000,-36.191000},{10.832000,15.857000,-36.199000},{9.333000,16.219000,-35.309000},{10.384000,14.885000,-34.777000},{9.116000,13.146000,-38.259000},{10.770000,13.344000,-37.570000},{11.113000,15.333000,-38.688000},{9.357000,15.480000,-39.121000},{9.577000,14.032000,-40.914000},{10.542000,12.882000,-39.911000},{12.575000,14.104000,-40.318000},{12.563000,16.305000,-41.530000},{10.791000,16.212000,-41.655000},{11.563000,16.370000,-40.060000},{11.131000,14.178000,-42.990000},{11.774000,12.689000,-42.236000},{14.045000,13.711000,-42.172000},{13.401000,15.187000,-42.935000},{12.793000,13.925000,-44.958000},{13.274000,12.398000,-44.193000},{15.615000,13.136000,-44.090000},{16.297000,15.319000,-45.049000},{14.591000,15.726000,-45.350000},{15.183000,15.551000,-43.681000},{14.494000,13.737000,-46.867000},{14.706000,12.102000,-46.219000},{17.143000,12.531000,-45.927000},{16.932000,14.170000,-46.572000},{16.156000,13.247000,-48.736000},{16.271000,11.598000,-48.097000},{18.635000,13.529000,-48.312000},{19.360000,12.095000,-50.196000},{17.861000,11.145000,-50.058000},{17.789000,12.854000,-50.549000},{19.981000,11.519000,-47.840000},{18.856000,11.865000,-46.505000},{18.494000,10.558000,-47.657000}};
MatrixForm[t1]

u={"Mg","C","C","C","C","N","C","C","C","C","C","C","C","C","O","O","N","C","C","C","C","C","C","O","C","N","C","C","C","C","C","C","C","N","C","C","C","C","C","C","O","C","C","O","O","C","C","C","C","C","C","C","C","C","C","C","C","C","C","C","C","C","C","C","C","C","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","H","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]]=="Mg",0.5]]]]],{i,1,n}]
u2=Table[If[us[[i,1]]=="C",0.255,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]]=="Mg",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]]=="Mg",2.0]]]]],{i,1,n}]

{6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,6.`,2.,7.`,7.`,7.`,7.`,8.`,8.`,8.`,8.`,8.`,8.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`,1.`}

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]]]]=0.257]]
For [i=1, i≤nc,i++,If[qua[[i]]≠0,u2[[qua[[i]]]]=0.257]]

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+8}];
tpu=Table[{0,0,0},{nj+8}];
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 4 N atoms *)

k=1;
Clear[conn];
conn={{57,5,8},{58,13,16},{59,20,23},{60,27,30}};

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,4}];

(*-------------------------------------------------------------------------*)
(* construct the π clouds for the 4 O atoms in C=O *)
k=1;
Clear[conn];
conn={{61,12,11},{63,18,15},{64,32,33},{66,34,35}};

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+4+k]]=nk[[1]];
tpu[[nj+4+k]]=nl[[1]]),{k,4}];

(* ---------------------------------------------------------------------------------------------
O atoms 62,66 LP *)

k=1;
Clear[conn];
conn={{12,62,36},{34,66,35}};
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[rlo/L];
If[(k==1),γ=π/2-α/2,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]*Cos[β]; nk[[2,1]]=-L*Sin[γ]*Cos[β];  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: N57, N58, N59, N60 one doubly occ LP as sp2 ligand *)
k=1;
Clear[conn];
tpln={{0.0,0.0,0.0},{0.0,0.0,0.0},{0.0,0.0,0.0},{0.0,0.0,0.0}};
conn={{5,57,8},{13,58,16},{20,59,23},{27,60,30}};
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 || k==3),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,4}];

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+8}];
Plot8b=Table[Graphics3D[{Opacity[0.3],Lighter[Yellow],Sphere[tpu[[i]],rpi]}],{i,1,nj+8}];
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,1,4}];

Plot9= Table[Graphics3D[{Lighter[Orange,0.5],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]]]]}},0.1]}],{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,*)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+4}]; 
tv5 =Table[{0,0,0},{i,1,nj+4}]; 
tv6 =Table[{0,0,0},{i,1,16}]; 
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,1,6}],Table[-1.0,{i,1,4}],Table[-2.0,{i,1,16}]];
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+5)}],Table[0.0,{i,1,16}]];
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 *)
Vee=Vee-2/(rpo+rpi)]; (* 5*1/4 C + 3*1/4 N *)
Vee

sc=0.372;   (* core clouds *)
For[i=1 ,i<bc+1,i++,Vee=Vee+3*sc/u2[[i]]]
sw=0.378;  (* bonding clouds *)
For[i=1 ,i<nb+1,i++,Vee=Vee+3*sw/a[[i,3]]]
For[i=1 ,i<9,i++,Vee=Vee+3*sw/rlo]
For[i=1 ,i<4,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+3)*0.5*1.125*(1/rpo^2+1/rpi^2) (* pi kin e added *)
Tpi   = Tpi+ 2.296*4*1.0*1.125*(1/rpo^2+1/rpi^2) (* pi kin e added *)
Tlo   = 8*2*1.125*(1/rlo^2) (* lp kin e of 4 O added *)
Tln   = 3*2*1.125*(1/rln^2) (* lp kin e of 3 N added *)
Vtot=Vne+Vee+Vnn
Ttot=Ttot+Tpi+Tlo+Tln
Vir   =-Vtot/Ttot
Etot =Ttot+Vtot