(* Cs atom Kimball, Ne,Ar,Ni,Kr,Pd-centers, 4 5sp-spheres tetrahedral 28.12.2011
   vne contribution of each shell roughly parametrized to fda *)
Clear[k1,k2,k3,k4,k5,k6,k7,k8sig1,sig2,sig3,sig4,sig5,sig6,sig7,c,z,R1,R2,R3,R4,R5,R6,R7,R8S2,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, k8 -> 1.0, sig1 -> 0.3, sig2 -> 0.3, sig3 -> 0.3, sig4 -> 0.3, sig5 -> 0.3, sig6 -> 0.3, sig7 -> 0.3}; z=55.;

(* 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/R1-8.0*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-8.35*z/(S2+R3);
S3 = R3*4^(1/3);

(* Ni shell trigbipyr, d10 with 5*2 charges; *)
T = T + (10.*9./8.)*k4/R4^2 /. c;
Vee = Vee+5.*3.*sig4/R4+(180.+25.898766)/(S3+R4) /. c; (* 2+24/Sqrt[2]+12/Sqrt[3] *)
Vne = Vne - 10.5*z/(S3+R4);
S4 = R4*5^(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-9.7*z/(S4+R5);
S5 = R5*4^(1/3);

(* Pd shell trigbipyr, d10 with 5*2 charges *)
T = T + (10.*9./8)*k6/R6^2 /. c;
Vee = Vee+5.*3.*sig6/R6+(360.+25.898766)/(S5+R6) /. c;
Vne = Vne - 10.95*z/(S5+R6);
S6 = R6*5^(1/3);

(* Xe shell *)
T = T + (8.*9./8.)*k7/R7^2 /. c;
Vee = Vee+12.*sig7/R7+(368+24.*ad)/(S6+R7) /. c;
Vne = Vne-8.3*z/(S6+R7);
S7 = R7*4^(1/3);

(* Cs outer sphere *)
T = T + 1.125*k8/R8^2 /. c;
Vee = Vee+54/(S7+R8);
Vne = Vne - z/(S7+R8);
S8 = R8;


func = T + Vee + Vne;

t = FindMinimum[func, {R1,0.0234209}, {R2,0.0660675}, {R3,0.1135267}, {R4,0.1653891},{R5,0.2159044},
{R6,0.3677186},{R7,0.8571924},{R8,4.0272848},{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) /. c /. t[[2]],10]
N[(S3) /. c /. t[[2]],10]
N[(S4) /. c /. t[[2]],10]
N[(S5) /. c /. t[[2]],10]
N[(S6) /. c /. t[[2]],10]
N[S7 /. c /. t[[2]],10]
N[S8 /. c /. t[[2]],10]

plot1=Graphics[{Circle[{0,0},R1],Circle[{0,0},S2],Circle[{0,0},S3],
     Circle[{0,0},S4],Circle[{0,0},S5],Circle[{0,0},S6],Circle[{0,0},S7],
     Circle[{0,0},S8]}] /. c /. t[[2]];
     
Show[plot1,{AspectRatio → Automatic,Axes -> True,GridLines -> Automatic,
PlotRange → {{-4.2,4.2},{-4.2,4.2}}, Frame -> True}]

Cs_Xe_vne_1.png

Cs_Xe_vne_2.png

Cs_Xe_vne_3.png

Cs_Xe_vne_4.png

Cs_Xe_vne_5.png

Cs_Xe_vne_6.png

Cs_Xe_vne_7.png

Cs_Xe_vne_8.png

Cs_Xe_vne_9.png

Cs_Xe_vne_10.png

Cs_Xe_vne_11.png

Cs_Xe_vne_12.gif

Created with the Wolfram Language