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Cell["\<\
(* H2C=CH2 with spherical bananas: Two fused methanes with CH4 data \
CH4Mt(min).nb  20.06.2012 TEST! *)
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;\
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Cell["\<\
pi=0.0; (* distance of bananas from C-C axis, pi=0 is regular tetrahedric *)
nc=8;   (* number of clouds *)
sig1=0.3; sig2=0.3; sig4=sig2; (* screening const. from e-e interaction in \
doubly occ. clouds *)
k1=1.027; k2=1.23; k4=k2; (* parameters for kinetic energy of clouds; k=1.0 \
Kimball's lowest value *)
bohr=0.529177; rad=57.29578;\
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Cell["\<\
(* 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 edge assumption *)
R4=R2;\
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Cell["\<\
(* bonding pairs *)
Ekin = Ekin + 2.25*(4*k2/R2^2+2*k4/R4^2);
vee=vee+3.0*(4*sig2/R2+2*sig4/R4);
(* cloud occupation *)
oc={-2,-2,-2,-2,-2,-2,-2,-2};
(* nuclear charges for C1,C2,H3,H4,H5,H6, banana7, banana8 *)
ch={6,6,1,1,1,1,0,0};
(* cloud radii in the same order *)
rr={R1,R1,R2,R2,R2,R2,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, xy plane of molecule *)
(* nuclear coordinates in terms of radii; C nucleus assumed in center of \
C(1s) cloud *)
d1=(R1+R2)*cs;  (* R1+R2 is radius of outer sphere for tetrahedron of equal \
clouds *)
d2=d1+(R1+R2+p)*cs; d3=(R1+R2+p)*ss; 
xn={-d1,d1,-d2,-d2,d2,d2,0,0};
yn={0,0,d3,-d3,-d3,d3,0,0};
zn={0,0,0,0,0,0,0,0};
(* cloud coordinates in terms of radii *)        
d4=d1+(R1+R2)*cs;  d5=(R1+R2)*ss;
xc={-d1,d1,-d4,-d4,d4,d4,0,0};
yc={0,0,d5,-d5,-d5,d5,0,0};
zc={0,0,0,0,0,0,pi+a/2,-pi-a/2};
(* potential energy of protons in CH-clouds with eccentricity p *)
vne=vne-4*(3-(p/R2)^2)/R2;\
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Cell["\<\
(* 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]]]\
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Cell["\<\
(* nn: sum of nuclei-nuclei potential energies *)
vnn = 0.0;
For[i = 1, i < nc-2, i++,
  For[j = i+1, j < nc-1, j++,
    vnn = vnn + \
ch[[i]]*ch[[j]]/Sqrt[(xn[[i]]-xn[[j]])^2+(yn[[i]]-yn[[j]])^2]]]\
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Cell["\<\
(* cn: sum of cloud-nuclei potential energies *)
For[i = 1, i < nc+1, i++,
  For[j = 1, j < nc+1, 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]]]]\
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Cell["\<\
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},{R2,1.24},{p,0.54},{Method -> Automatic}, \
{MaxIterations -> 500}]\
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    RowBox[{
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Cell["\<\
vne  /. t[[2]] 
vee  /. t[[2]] 
vnn  /. t[[2]]
-Epot/Ekin  /. t[[2]]
2*d1*bohr  /. t[[2]]
(R1+R2+p)*bohr  /. t[[2]]
(R1+R2)*bohr  /. t[[2]]
2*w*rad  /. t[[2]]
4*(R1*(R1+2*R4))^(3/2)/(R1+R4)^3 /. t[[2]]\
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Cell["\<\
(* Cvnf: sum of C1-nuclei forces *)
Cvnf = 0.0;
  For[j = 2, j < 7, j++,
    Cvnf = Cvnf - \
(xn[[j]]-xn[[1]])*ch[[1]]*ch[[j]]/((xn[[1]]-xn[[j]])^2+(yn[[1]]-yn[[j]])^2+(\
zn[[1]]-zn[[j]])^2)^(3/2)]\
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Cell["\<\
(* Cvef: sum of C1 - clouds forces *)
Cvef = 0.0;
  For[j = 2, j < nc+1, j++,
    Cvef = Cvef - \
(xc[[j]]-xn[[1]])*oc[[j]]*ch[[1]]/((xc[[1]]-xn[[j]])^2+(yc[[1]]-yn[[j]])^2+(\
zc[[1]]-zn[[j]])^2)^(3/2)]
Cforcetot = Cvnf+Cvef /. t[[2]]
Cforcenn=Cvnf /. t[[2]]
CForcene=Cvef /. t[[2]]\
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Cell["\<\
(* Hvnfx: sum of H3-nuclei forces *)
Hvnfx = 0.0;
  For[j = 1, j < 7, j++,
    If[j != 3,
    Hvnfx = Hvnfx - \
(xn[[j]]-xn[[3]])*ch[[3]]*ch[[j]]/((xn[[3]]-xn[[j]])^2+(yn[[3]]-yn[[j]])^2+(\
zn[[3]]-zn[[j]])^2)^(3/2)]]\
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Cell["\<\
(* Hvefx: sum of H3 - clouds forces *)
Hvefx = 0.0;
  For[j = 1, j < nc+1, j++,
    If[j != 3,
    Hvefx = Hvefx- \
(xc[[j]]-xn[[3]])*oc[[j]]*ch[[3]]/((xc[[j]]-xn[[3]])^2+(yc[[j]]-yn[[3]])^2+(\
zc[[j]]-zn[[3]])^2)^(3/2)]]
Hforcetotx = Hvnfx+Hvefx/. t[[2]]
Hforcennx=Hvnfx /. t[[2]]
HForcenex=Hvefx /. t[[2]]\
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(* Hvnfy: sum of H3-nuclei forces *)
Hvnfy = 0.0;
  For[j = 1, j < 7, j++,
    If[j != 3,
    Hvnfy = Hvnfy - \
(yn[[j]]-yn[[3]])*ch[[3]]*ch[[j]]/((xn[[3]]-xn[[j]])^2+(yn[[3]]-yn[[j]])^2+(\
zn[[3]]-zn[[j]])^2)^(3/2)]]\
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Cell["\<\
(* Hvefy: sum of H3 - clouds forces *)
Hvefy = 0.0;
  For[j = 1, j < nc+1, j++,
    If[j != 3,
    Hvefy = Hvefy - \
(yc[[j]]-yn[[3]])*oc[[j]]*ch[[3]]/((xc[[j]]-xn[[3]])^2+(yc[[j]]-yn[[3]])^2+(\
zc[[j]]-zn[[3]])^2)^(3/2)]]
Hforcetoty = Hvnfy+Hvefy /. t[[2]]
Hforcenny=Hvnfy /. t[[2]]
HForceney=Hvefy /. t[[2]]\
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Cell["\<\
(* Hvnfz: sum of H3-nuclei forces *)
Hvnfz = 0.0;
  For[j = 7, j < 9, j++,
    If[j != 3,
    Hvnfz = Hvnfz - \
(zn[[j]]-zn[[3]])*ch[[3]]*ch[[j]]/((xn[[3]]-xn[[j]])^2+(yn[[3]]-yn[[j]])^2+(\
zn[[3]]-zn[[j]])^2)^(3/2)]]\
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Cell["\<\
(* Hvefz: sum of H3 - clouds forces *)
Hvefz = 0.0;
  For[j = 7, j < nc+1, j++,
    If[j != 3,
    Hvefz = Hvefz - \
(zc[[j]]-zn[[3]])*oc[[j]]*ch[[3]]/((xc[[j]]-xn[[3]])^2+(yc[[j]]-yn[[3]])^2+(\
zc[[j]]-zn[[3]])^2)^(3/2)]]
Hforcetotz = Hvnfz+Hvefz /. t[[2]]
Hforcennz=Hvnfz /. t[[2]]
HForcenez=Hvefz /. t[[2]]        \
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Cell["\<\
(* Wvnfy: sum of w7-nuclei forces *)
Wvnfy = 0.0;
  For[j = 1, j < 7, j++,
    Wvnfy = Wvnfy - \
(yn[[j]]-zc[[7]])*oc[[7]]*ch[[j]]/((xc[[7]]-xn[[j]])^2+(yc[[7]]-yn[[j]])^2+(\
zc[[7]]-zn[[j]])^2)^(3/2)]\
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Cell["\<\
(* Wvefy: sum of W7 - clouds forces *)
Wvefy = 0.0;
  For[j = 1, j < nc+1, j++,
    If[j != 7,
    Wvefy = Wvefy - \
(yc[[j]]-zc[[7]])*oc[[j]]*oc[[7]]/((xc[[j]]-xc[[7]])^2+(yc[[j]]-yc[[7]])^2+(\
zc[[j]]-zc[[7]])^2)^(3/2)]]
Wforcetoty = Wvnfy+Wvefy /. t[[2]]
Wforcenny=Wvnfy /. t[[2]]
WForceney=Wvefy /. t[[2]]\
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Cell["\<\
(* 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]]},R2],Circle[{xc[[6]],yc[[6]]},R2],Circle[{xc[\
[7]],yc[[7]]},R4],Circle[{xc[[8]],yc[[8]]},R4],
Disk[{xn[[1]],yn[[1]]},0.08], 
Disk[{xn[[2]],yn[[2]]},0.08],
Disk[{xn[[3]],yn[[3]]},0.08],
Disk[{xn[[4]],yn[[4]]},0.08],
Disk[{xn[[5]],yn[[5]]},0.08],
Disk[{xn[[6]],yn[[6]]},0.08],
{Thickness[0.008],
Line[{{xn[[2]],yn[[2]]},{xn[[1]],yn[[1]]}}],
Line[{{xn[[1]],yn[[1]]},{xn[[3]],yn[[3]]}}],
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Line[{{xn[[2]],yn[[2]]},{xn[[5]],yn[[5]]}}],
Line[{{xn[[2]],yn[[2]]},{xn[[6]],yn[[6]]}}]}} ] /. t[[2]];

Show[plot1,{AspectRatio \[Rule] Automatic,Axes -> True,GridLines -> \
Automatic, PlotRange \[Rule] {{-4,4},{-3,3}}, Frame -> True}]\
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