Examples from Li to Cs: in preparation


You have to download Wolfram CDF Player or install Mathematica™ to view the following atoms:
Arthree concentric shells
Ksingle sphere on top of Ar (figure)
Fe3+5 electrons in 3d-tbp
Zn  complete 3d10
Kr  complete shell
Ru3+  5 electrons in 4d10
Cd  complete 4d10
Xe  see commented routine below (figure)
Cs  single s-cloud on top of Xe (figure)
Explanation of how we have rendered Kimballs atoms spherical, using the Xenon atom. Note, this is the method best studied up to now, but there are other possibilities to explore, e.g. full construction of core pseudopotentials or modelling the inner shells s-p-d- with spherical clouds, using n,l,m quantum numbers, e.g. Ne atom and isoelectronic ions up to Ar8+.
Below, Xe is coded in Mathematica. You can see that from every inner shell a spherical transform S2...7 is inserted into the next shell optimization, all the way up to the topmost Xe-shell. This cascade produces an all spherical atom.- The examples on this page, with the exception of Xe, are not yet energy-optimized with the help of FDA.
(* Xe atom Kimball, Ne,Ar,Ni,Kr,Pd-centers, 4 5sp-spheres tetrahedral 28.12.2011, graphics 02.01.2012, 
vne contribution of each shell roughly parametrized to fda *)
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 -> 0.3, sig3 -> 0.3, sig4 -> 0.3, sig5 -> 0.3, sig6 -> 0.3, sig7 -> 0.3}; 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/R1-8.0*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);

func = T + Vee + Vne;

t = FindMinimum[func, {R1,0.0238707}, {R2,0.0674572}, {R3,0.1164449},
{R4,0.1706207},{R5,0.2248597},{R6,0.3888714},{R7,0.9469972},{Method ->
"Newton"}, {MaxIterations -> 500}]

Vne  /. t[[2]]
Vee  /. t[[2]]
-(Vee+Vne)/T  /. t[[2]]
S2  /. t[[2]]
S3  /. t[[2]]
S4  /. t[[2]]
S5  /. t[[2]]
S6  /. t[[2]]
S7  /. t[[2]]

Result of minimization of energy: First number Etot
{-7239.111108, {R1 -> 0.02387071862, R2 -> 0.06745724961, R3 -> 0.116444851, R4 -> 0.1706207495, R5 -> 0.2248597472, R6 -> 0.3888714432, R7 -> 0.9469972035}}
Vne:   -17213.83955
Vee:  2735.617331
Virial ratio:[Graphics:Images/Xe_S6tbp_rein_gr_4.gif]
Radii S2 to S7 of equivalent spheres:

  0.107081709
  0.1848446789
  0.3569425992
  0.2917573776
  0.6649608143
  1.503264357

Converted by Mathematica      September 16, 2012