(* Xe atom Kimball, Ne,Ar,Zn,Kr,Cd-centers, 4 5sp-spheres tetrahedral 21.12.2011 *)
Clear[k1,k2,k3,k4,k5,k6,k7,sig1,sig2,sig3,sig4,sig5,sig6,sig7,c,z,R1,R2,R3,R4,R5,R6,R7,S2,S3,S4,S5,S6,S7];
c = {k1 -> 1.0, k2 -> 1.0, k3 -> 1.0, k4 -> 1.0, k5 -> 1.0, k6 -> 1.0, k7 -> 1.0, sig1 -> 0.3, sig2 -> 0.302, sig3 -> 0.302, sig4 -> 0.302, sig5 -> 0.302, sig6 -> 0.302, sig7 -> 0.302}; z=54.;

(* He+Ne shell *)
T = (2.*9./8.)*k1/R1^2+(8.*9./8.)*k2/R2^2 /. c;
ad = Sqrt[3./8.]; 
Vee=3.0*sig1/R1+12.*sig2/R2+16/(R1+R2)+24*ad/(R1+R2) /. c;
Vne=-3.0*z/R1-8.*z/(R1+R2);
S2 = R2*4^(1/3);

(* Ar shell *)
T = T + (8.*9./8)*k3/R3^2 /. c;
Vee = Vee+12.*sig3/R3+80./(S2+R3)+24.*ad/(S2+R3) /. c;
Vne = Vne-8.45*z/(S2+R3);
S3 = R3*4^(1/3);

(* Zn shell octahedron, d10 with 2 charges; *)
T = T + (12.*9./8)*k4/R4^2 /. c;
Vee = Vee+6.*3.*sig4/R4+(216.+60./Sqrt[2])/(S3+R4) /. c;
Vne = Vne - 12.6*z/(S3+R4);
S4 = R4*6^(1/3);

(* Kr shell *)
T = T + (8.*9./8.)*k5/R5^2 /. c;
Vee = Vee+12.*sig5/R5+224./(S4+R5)+24.*ad/(S4+R5) /. c;
Vne = Vne-8.45*z/(S4+R5);
S5 = R5*4^(1/3);

(* Cd shell octahedron, d10 s2 full*)
T = T + (12.*9./8)*k6/R6^2 /. c;
Vee = Vee+6.*3.*sig6/R6+(432.+60./Sqrt[2])/(S5+R6) /. c;
Vne = Vne - 12.6*z/(S5+R6);
S6 = R6*6^(1/3);

(* Xe shell *)
T = T + (8*9./8)*k7/R7^2 /. c;
Vee = Vee+12.*sig7/R7+432./(S6+R7)+24.*ad/(S6+R7) /. c;
Vne = Vne-8.45*z/(S6+R7);
S7 = R7*4^(1/3);

func = T + Vee + Vne;

t = FindMinimum[func, {R1,0.02384}, {R2,0.0667}, {R3,0.1142}, {R4,0.19},{R5,0.27},{R6,0.5},{R7,5.3},{Method -> "Newton"}, {MaxIterations -> 500}]

N[Vne /. c /. t[[2]],10]
N[Vee /. c /. t[[2]],10]
N[-(Vee+Vne)/T /. c /. t[[2]],10]
N[(S2+R3) /. c /. t[[2]],10]
N[(S3+R4) /. c /. t[[2]],10]
N[(S4+R5) /. c /. t[[2]],10]
N[(S5+R6) /. c /. t[[2]],10]
N[(S6+R7) /. c /. t[[2]],10]

SphericalPlot3D[{0.1,0.22,0.37,0.62,0.93,6.2},{θ,0,π},{ϕ,0,3π/2},Mesh->None, PlotRange->{{-6,6},{-6,6},{-6,6}},Boxed->False ] /.c /. t[[2]]