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(* HC-CH with  two fused methanes at face with CH4 data CH4Mt(min).nb  \
04.07.2012 *)
Clear[z,sig1,sig2,sig4,k1,k2,k4,nc,R1,R2,R3,R4,w,p,vee,vne,vnn,
xc,yc,zc,xn,yn,zn,oc,ch,rr,cs,ss,d1,d2,d3,d4,d5,pi,i,j,d,t];
z=6.0;
nc=7;   (* number of clouds *)
sig1=0.3; sig2=0.3; sig4=0.3; (* screening const. from e-e interaction in \
doubly occ. clouds *)
k1=1.0; k2=1.0; k4=1.0; (* parameters for kinetic energy of clouds; k=1.0 \
Kimball's lowest value *)
bohr=0.529177; rad=57.29578;

(* C He-shells *)
Ekin = 2*(2.25*k1/R1^2);
vee=2*(3.0*sig1/R1);
vne=-2*(3.0*z/R1);
(* this is the common face assumption *)
(* R4=R2; k4=k2; sig4=sig2; *)

(* bonding pairs *)
Ekin = Ekin + 2.25*(2*k2/R2^2+3*k4/R4^2);
vee=vee+3.0*(2*sig2/R2+3*sig4/R4);
vne=vne-2*(3-(p/R2)^2)/R2;
(* cloud occupation *)
oc={-2,-2,-2,-2,-2,-2,-2};
(* nuclear charges for C1,C2,H3,H4,face1,face2,face3 *)
ch={6,6,1,1,0,0,0};
(* cloud radii in the same order *)
rr={R1,R1,R2,R2,R4,R4,R4};
(* w is half angle between two C-H of CH4, i.e. 109.47\[Degree]/2 *)
w=ArcCos[-1/3]/2;
cs=Cos[w];  ss=Sin[w];
(* edge length of tetrahedron of 4 equal clouds *)
a=4*(R1+R2)/Sqrt[6]; (* 4/Sqrt[6] is also Sqrt[8/3] *)
(* x is C-C bond axis, xz one mirrorplane of D3h molecule *)
(* R1+R2 is radius of outer sphere for each tetrahedron of equal clouds *)
d1=R1+R4; d2=R1+R2;  
(* cloud coordinates in terms of radii *)        
d3=d2+d1/3; d4=d1*Sqrt[2/3];  d5=d1*Sqrt[8]/3;
xc={-d1/3,d1/3,-d3,d3,0,0,0};
yc={0,0,0,0,0,-d4,d4};
zc={0,0,0,0,d5,-d5/2,-d5/2}; (* 'eclipsed' conformation *)
(* nuclear coordinates in terms of radii; C nuclei assumed in center of C(1s) \
cloud *)
(* CH3 units span tetrahedron of circumsphere radius R1+R2+p, if tetrahedral! \
*)
d6=R1+R2+p; d7=d1/3+d6;
xn={-d1/3,d1/3,-d7,d7,0,0,0};
yn={0,0,0,0,0,0,0};
zn={0,0,0,0,0,0,0};
(* potential energy of protons in CH-clouds with eccentricity p *)

(* cc: sum of cloud-cloud potential energies *)
For[i = 1, i < nc, i++,
  For[j = i+1, j < nc+1, j++,
    vee = vee + \
oc[[i]]*oc[[j]]/Sqrt[(xc[[i]]-xc[[j]])^2+(yc[[i]]-yc[[j]])^2+(zc[[i]]-zc[[j]])\
^2]]]

(* nn: sum of nuclei-nuclei potential energies *)
vnn = 0.0;
For[i = 1, i < nc-3, i++,
  For[j = i+1, j < nc-2, j++,
    vnn = vnn + \
ch[[i]]*ch[[j]]/Sqrt[(xn[[i]]-xn[[j]])^2+(yn[[i]]-yn[[j]])^2+(zn[[i]]-zn[[j]])\
^2]]]

(* cn: sum of cloud-nuclei potential energies *)
For[i = 1, i < nc+1, i++,
  For[j = 1, j < nc-2, j++,
    If[i != j,
      vne = vne + \
oc[[i]]*ch[[j]]/Sqrt[(xc[[i]]-xn[[j]])^2+(yc[[i]]-yn[[j]])^2+(zc[[i]]-zn[[j]])\
^2]]]]

Epot=vne+vee+vnn;
func=Ekin+Epot;
(* results of CH4 computation; if this is not available, decomment the \
minimize function *)
(* R1=0.2623610; R2=1.2461360;  p=0.53986226; *)
(* minimization function for R1, R2, p *)
t = FindMinimum[func,{R1,0.26},{R2,1.29},{R4,1.29},{p,0.54},{Method -> \
Automatic}, {MaxIterations -> 500}]

(* func *)
vne  /. t[[2]]
vee  /. t[[2]]
vnn  /. t[[2]]
-Epot/Ekin  /. t[[2]]
2*d1/3*bohr  /. t[[2]]
(R1+R2+p)*bohr  /. t[[2]]
(R1+R2)*bohr  /. t[[2]]
2*w*rad  /. t[[2]]\
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(* projection on xy-plane of molecule *)
plot1=Graphics[{Circle[{xc[[1]],yc[[1]]},R1],      \
Circle[{xc[[2]],yc[[2]]},R1],Circle[{xc[[3]],yc[[3]]},R2],Circle[{xc[[4]],yc[[\
4]]},R2],Circle[{xc[[5]],yc[[5]]},R4],Circle[{xc[[6]],yc[[6]]},R4],Circle[{xc[\
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1]]},0.08], Disk[{xn[[2]],yn[[2]]},0.08], Disk[{xn[[3]],yn[[3]]},0.08], \
Disk[{xn[[4]],yn[[4]]},0.08] }}]  /. t[[2]]

Show[plot1,{AspectRatio \[Rule] Automatic,Axes -> True,GridLines -> \
Automatic, PlotRange \[Rule] {{-5,5},{-4,4}}, Frame -> True}]

(* projection on xz-plane, perpendicular to molecular plane *)
plot2=Graphics[{Circle[{xc[[1]],zc[[1]]},R1],      \
Circle[{xc[[2]],zc[[2]]},R1],Circle[{xc[[3]],zc[[3]]},R2],Circle[{xc[[4]],zc[[\
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}],Line[{{xc[[3]],zc[[3]]},{xc[[6]],zc[[6]]},{xc[[4]],zc[[4]]}}] }}]  /. t[[2]]

Show[plot2,{AspectRatio \[Rule] Automatic,Axes -> True,GridLines -> \
Automatic, PlotRange \[Rule] {{-5,5},{-4,4}}, Frame -> True}]

(* projection on yz-plane, perpendicular to molecular plane *)
plot3=Graphics[{Circle[{yc[[1]],zc[[1]]},R1],      \
Circle[{yc[[2]],zc[[2]]},R1],Circle[{yc[[3]],zc[[3]]},R2],Circle[{yc[[4]],zc[[\
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{Thickness[0.01], \
GrayLevel[0.75],Line[{{yc[[5]],zc[[5]]},{yc[[6]],zc[[6]]},{yc[[7]],zc[[7]]},{\
yc[[5]],zc[[5]]}}]} }]  /. t[[2]]

Show[plot3,{AspectRatio \[Rule] Automatic,Axes -> True,GridLines -> \
Automatic, PlotRange \[Rule] {{-5,5},{-4,4}}, Frame -> True}]
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