(* Mg atom nach Kimball, Aussen-sp-Kugeln 13.09.2012 *)
Clear[k1,k2,k3, sig1,sig2,c,z,R1,R2,R3,a];
c = {k1 -> 1.0, k2 -> 1.0, k3 -> 1.0, sig1 -> 0.28, sig2 -> 0.3, sig3 -> 0.3};
z=12.0;
T = 2.25*k1/R1^2+9.0*k2/R2^2+2.25*k3/R3^2 /. c;
ad = 8./3.;  
b=(R1+R2)*Sqrt[2/3];
a = (R1+R2)/Sqrt[3]+Sqrt[(R2+R3)^2-b^2];
g=Sqrt[b^2+(a+(R1+R2)/Sqrt[3])^2];
Vee=3.0*sig1/R1+4.0*3.0*sig2/R2+16/(R1+R2)+24/((R1+R2)*Sqrt[ad])+8/(R2+R3)+4.5/a+8/g /. c;
Vne=-3.0*z/R1-8*z/(R1+R2)-2*z/a;

func = T + Vee + Vne /. c;

t = FindMinimum[func, {R1,0.119}, {R2,0.47}, {R3,2.25},{MaxIterations -> 500}]

-(Vne+Vee)/T /. t[[2]]

plot1=Graphics[{{GrayLevel[0.6],Disk[{a1,b},R2],Disk[{a1,-b},R2],Disk[{-a1,0},R2]},
Circle[{0,0},R1],Disk[{0,0},0.06],Circle[{a1,b},R2],
Circle[{a1,-b},R2],Circle[{-a1,0},R2], 
Circle[{a,0},R3],Circle[{-a,0},R3]}] /. t[[2]]

Show[plot1,{AspectRatio -> Automatic, Axes -> True, GridLines -> Automatic, 
PlotRange -> {{-6,6},{-3,3}}, Frame -> True}]

plot2=Graphics[{{GrayLevel[0.6],Disk[{-a1,b},R2],Disk[{-a1,-b},R2],Disk[{a1,0},R2]},Circle[{0,0},R1],Disk[{0,0},0.06],Circle[{-a1,b},R2],
Circle[{-a1,-b},R2],Circle[{a1,0},R2], 
Circle[{a,0},R3],Circle[{-a,0},R3]}] /. t[[2]]

Show[plot2,{AspectRatio -> Automatic,Axes -> True,GridLines -> Automatic, 
PlotRange -> {{-6,6},{-3,3}}, Frame -> True}]