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@xndc
Created January 22, 2016 21:26
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Mathematica implementation of a primitive (and wrong) algorithm for computing the first ionization energy of a given atom
eclist[z_] := ElementData[z, "ElectronConfigurationString"][[1]] /.
Superscript[a_, b_] -> {a, b}
orbitals[z_] := Partition[Flatten[If[StringQ[eclist[z][[1]]],
Join[
orbitals[StringReplace[eclist[z][[1]], ("[" ~~ base__ ~~ "]") -> base]],
Drop[eclist[z], 1]],
eclist[z]]], 3]
lastOrbital[z_] := Last[orbitals[z]]
doesShellExist[z_, n_] := Count[orbitals[z], {n, _, _}] > 0
countShellElectrons[z_, n_] :=
Total[#[[3]] & /@ Cases[orbitals[z], {n, _, _}]]
countOrbitalElectrons[z_, n_, l_] :=
Total[#[[3]] & /@ Cases[orbitals[z], {n, l, _}]]
countShellSPElectrons[z_, n_] :=
countOrbitalElectrons[z, n, "s"] + countOrbitalElectrons[z, n, "p"]
countShellSPDElectrons[z_, n_] :=
countShellSPElectrons[z, n] + countOrbitalElectrons[z, n, "d"]
calculateInnerContribs[z_, n_, use085_] := If[doesShellExist[z, n],
If[use085, 0.85, 1]*countShellElectrons[z, n] +
calculateInnerContribs[z, n - 1, False],
0]
shieldConst[z_] := With[{l = lastOrbital[z]}, If[l[[1]] == 1, (l[[3]] - 1)*0.3,
If[l[[2]] == "d" \[Or] l[[2]] == "f",
If[l[[2]] == "d",
((l[[3]] - 1)*0.35) + calculateInnerContribs[z, l[[1]] - 1, False] +
countShellSPElectrons[z, l[[1]]],
((l[[3]] - 1)*0.35) + calculateInnerContribs[z, l[[1]] - 1, False] +
countShellSPDElectrons[z, l[[1]]]],
((l[[3]] - 1)*0.35) + calculateInnerContribs[z, l[[1]] - 1, True]]]]
zeff[z_] := ElementData[z, "AtomicNumber"] - shieldConst[z]
neff[z_] := With[{n = lastOrbital[z][[1]]}, Piecewise[{
{1, n == 1}, {2, n == 2}, {3, n == 3},
{3.7, n == 4}, {4, n == 5}, {4.2, n == 6}}]]
ei[z_] := (zeff[z]^2/neff[z]^2)*13.6*Quantity["eV"]
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