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Cell["\<\
(*H2O with \"orthogonal\" \[Sigma],\[Pi] LPs, 12.01.2013, not final \
optimization: slight overlaps *)
Clear[z,sig1,sig2,sig3,k1,k2,k3,k4,nc,R1,R2,R3,R4,w,p,vee,vne,vnn,
xn,yn,zn,xc,yc,zc,c1,c2,c3,cs,ss,d1,d2,d3,d4,d5,d6,pi,i,j,d,t];
z=8.0; sig1=0.43; sig2=0.318; sig3=0.36; nc=6; pi=0.0;
k1=0.96; k2=1.355; k3=1.1; k4=1.9; bohr=0.529177; rad=57.29578;\
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Cell["\<\
(* C He shell, i=j each *)
Ekin = 2.25*k1/R1^2;
vee=3.0*sig1/R1;
vne=-3.0*z/R1;\
\>", "Input",
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Cell["\<\
(* bonding and lone pairs *)
Ekin = Ekin + 2.25*(2*k2/R2^2+k3/R3^2+k4/R4^2);
vee=vee+3.0*(2*sig2/R2+sig3/R3);
oc={-2,-2,-2,-2,-1,-1};
ch={z,1,1,0,0,0};
rr={R1,R2,R2,R3,R4,R4};
cs=Cos[w/2];  ss=Sin[w/2];
d1=(R1+R2+p)*cs; d2=(R1+R2+p)*ss; d3=(R1+R2)*cs; d4=(R1+R2)*ss; d5=R1+R3; \
d6=R4;
xn={0,-d1,-d1,0,0,0};
yn={0,d2,-d2,0,0,0};
zn={0,0,0,0,0,0};        
xc={0,-d3,-d3,d5,0,0};
yc={0,d4,-d4,0,0,0};
zc={0,0,0,0,d6,-d6};
vne=vne-2*(3-(p/R2)^2)/R2;
vnn = 0.0;\
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Cell["\<\
(*ww*)
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*)
For[i = 1, i < 3, i++,
  For[j = i+1, j < 4, j++,
    vnn = vnn + \
ch[[i]]*ch[[j]]/Sqrt[(xn[[i]]-xn[[j]])^2+(yn[[i]]-yn[[j]])^2+(zn[[i]]-zn[[j]])\
^2]]]\
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Cell["\<\
(*nw*)
For[i = 1, i < nc+1, i++,
  For[j = 1, j < 4, j++,
    If[i \[NotEqual] 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;
t = FindMinimum[func,{R1,0.19},{R2,1.1},{R3,1.0},{R4,0.9},{w,1.9},{p,0.58},{\
Method -> \"Newton\"}, {MaxIterations -> 500}]\
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Cell["\<\
(* N[func, 14] *)
vne /. t[[2]]
vee /. t[[2]]
vnn /. t[[2]]
-Epot/Ekin /. t[[2]]
(R1+R2+p)*bohr /. t[[2]]
w*rad /. t[[2]]\
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Cell["\<\
(* Hvnfx: sum of forces between H2 - nuclei, x-direction *)
Hvnfx = 0.0;
  For[j = 1, j < 4, j++,
    If[j \[NotEqual] 2,
    Hvnfx = Hvnfx + \
(xn[[j]]-xn[[2]])*ch[[2]]*ch[[j]]/((xn[[2]]-xn[[j]])^2+(yn[[2]]-yn[[j]])^2+(\
zn[[2]]-zn[[j]])^2)^(3/2)]]

(* Hvefx: sum of forces between H2 - clouds, x-direction *)
Hvefx = 0.0;
  For[j = 1, j < nc+1, j++,
    If[j \[NotEqual] 2,
    Hvefx = Hvefx + \
(xc[[j]]-xn[[2]])*oc[[j]]*ch[[2]]/((xc[[j]]-xn[[2]])^2+(yc[[j]]-yn[[2]])^2+(\
zc[[j]]-zn[[2]])^2)^(3/2)]]
Hvefx = Hvefx - 2*p/R2^3*cs /. t[[2]];
Hforcetotx = Hvnfx+Hvefx/. t[[2]]
Hforcennx=Hvnfx /. t[[2]]
HForcenex=Hvefx /. t[[2]]\
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Cell["\<\
(* Hvnfy: sum of forces between H2-nuclei, y-direction *)
Hvnfy = 0.0;
  For[j = 1, j < 4, j++,
    If[j \[NotEqual] 2,
    Hvnfy = Hvnfy - \
(yn[[j]]-yn[[2]])*ch[[j]]*ch[[2]]/((xn[[2]]-xn[[j]])^2+(yn[[2]]-yn[[j]])^2+(\
zn[[2]]-zn[[j]])^2)^(3/2)]]

(* Hvefy: sum of forces between H2 - clouds, y-direction *)
Hvefy = 0.0;
  For[j = 1, j < nc+1, j++,
    If[j \[NotEqual] 2,
    Hvefy = Hvefy - \
(yc[[j]]-yn[[2]])*oc[[j]]*ch[[2]]/((xc[[j]]-xn[[2]])^2+(yc[[j]]-yn[[2]])^2+(\
zc[[j]]-zn[[2]])^2)^(3/2)]]
Hvefy = Hvefy - 2*p/R2^3*ss /. t[[2]];
Hforcetoty = Hvnfy+Hvefy /. t[[2]]
Hforcenny=Hvnfy /. t[[2]]
HForceney=Hvefy /. t[[2]]\
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Cell["\<\
plot1=Graphics[{Circle[{xc[[1]],yc[[1]]},R1],      \
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Show[plot1,{AspectRatio \[Rule] Automatic,Axes -> True,GridLines -> \
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Cell["\<\
plot2=Graphics[{Circle[{xc[[1]],zc[[1]]},R1],      \
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Show[plot2,{AspectRatio \[Rule] Automatic,Axes -> True,GridLines -> \
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