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(* [NaCl6/6]infG Kimball, Ne/Ar-centers,  17.2.2012 *)
Clear[k1,k2,k3,k4,k5,sig1,sig2,sig3,sig4,sig5,c,z,R1,R2,R3,R4,R5,S2,S3,S4];
c = {k1 -> 0.99, k2 -> 2.65, k3 -> 0.99, k4 -> 1.22, k5 -> 3.42, sig1 -> 0.3, \
sig2 -> 0.3, sig3 -> 0.3, sig4 -> 0.3, sig5 -> 0.3}; z=11.0; z1=17.0;
ad = Sqrt[3./8.]; M = 1.7476; (* Madelung constant for rocksalt structure *)

(* He and Neon shell of Na+ *)
T = 2.25*k1/R1^2+9.0*k2/R2^2 /. c;
Vee = 3.0*sig1/R1+12.0*sig2/R2+16/(R1+R2)+24*ad/(R1+R2) /. c;
Vne = -3.0*z/R1-8.0*z/(R1+R2);
S2 = R2*4^(1/3);

(* He and Neon shell of Cl- *)
T = T + 2.25*k3/R3^2+9.0*k4/R4^2 /. c;
Vee = Vee + 3.0*sig3/R3+12.0*sig4/R4+16/(R3+R4)+24*ad/(R3+R4) /. c;
Vne = Vne -3.0*z1/R3-8.0*z1/(R3+R4);
S3 = R4*4^(1/3);

(* Argon shell, full for Cl- *)
T = T + 9.0*k5/R5^2 /. c;
Vee = Vee+12.0*sig5/R5+80.0/(S3+R5)+24.0*ad/(S3+R5) /. c;
Vne = Vne-8.35*z1/(S3+R5);
S4 = R5*4^(1/3);

(* Na+Cl- ionpair; these terms sum up to -1/d *)
d=S2+S4 /. c;
(* Vnn=z*z1/d;
Vee=Vee+(z-1)*(z1+1)/d;
Vne=Vne-(z*(z1+1)+(z-1)*z1)/d; *)

func = T + Vee + Vne - M/d;

t = FindMinimum[func, {R1,0.136}, {R2,1.131},{R3,0.082228}, {R4,0.33557}, \
{R5,2.2276785}, {Method -> Automatic},
{MaxIterations -> 500}]

N[-(Vee+Vne-M/d)/T /. c /. t[[2]],10]
N[d*0.529177 /. c /. t[[2]],10]
N[S2*0.529177 /. c /. t[[2]],10]
N[S4*0.529177 /. c /. t[[2]],10]\
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