(* Zn atom Kimball, Ne,Ar-centers, 6 4sd-spheres octahedral 21.12.2011 *)
Clear[k1,k2,k3,k4,sig1,sig2,sig3,sig4,c,z,R1,R2,R3,R4,S2,S3];
c = {k1 -> 1.0, k2 -> 0.98, k3 -> 0.97, k4 -> 0.95, sig1 -> 0.3, sig2 -> 0.302, sig3 -> 0.302, sig4 -> 0.302}; z=48.;

(* Ne shell *)
T = 2.25*k1/R1^2+9.*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 + 9.*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);

(* valence shell octahedron, full*)
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);
func = T + Vee + Vne;

t = FindMinimum[func, {R1,0.044}, {R2,0.133}, {R3,0.286}, {R4,0.683},{Method -> Automatic}, {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]