(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 8581, 266] NotebookOptionsPosition[ 7035, 212] NotebookOutlinePosition[ 8024, 248] CellTagsIndexPosition[ 7981, 245] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["\<\ (* Fe+++ ion + 6 Cl- in Oh 02.02.12/15.07.2013 *) Clear[k1,k2,k3,k4,k5,k6,sig1,sig2,sig3,sig4,sig5,c,z,R1,R2,R3,R4,R5,R6,R7,S5,\ S6,S2,S3,S4]; c = {k1 -> 0.98, k2 -> 0.98, k3 -> 1.15, k4 -> 2.6, k5 -> 0.98, k6 -> 1.05, \ k7-> 6.5 ,sig1 -> 0.3, sig2 -> 0.302, sig3 -> 0.302, sig4 -> 0.302, sig5 -> 0.302, sig6 -> 0.302}; \ z=26.; z1=17.0; (* Fe He+Ne shell *) T = 2.25*k1/R1^2+9.*k2/R2^2 /. c; ad = Sqrt[3./8.]; sq2=Sqrt[2]; 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); (* Fe 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); (* Fe+++ shell octahedron, full with 5/6 charge each*) T = T + (5.*9./8)*k4/R4^2 /. c; Vee = Vee+(90.+12*(5/6)^2/sq2+1.5*(5/6)^2)/(S3+R4) /. c; Vne = Vne - 6.0*z/(S3+R4) /. c; S4 = R4*6^(1/3); (* Cl- He+Ne shell *) Tf = 2.25*k5/R5^2+9.*k6/R6^2 /. c; Veef=3.0*sig5/R5+12*sig2/R6+16/(R5+R6)+24*ad/(R5+R6) /. c; Vnef=-3.0*z1/R5-7.5*z1/(R5+R6) /. c; S5 = R6*1.587401052 /. c; (* Cl- Ar shell *) Tf = Tf + 9.*k7/R7^2 /. c; Veef = Veef+12.*sig6/R7+80/(S5+R7)+24.*ad/(S5+R7) /. c; Vnef = Vnef-8.45*z/(S5+R7) /. c; S6 = R7*1.587401052 /. c; T=T+6*Tf; Vee=Vee+6*Veef; Vne=Vne+6*Vnef; (* Fe+++/6 Cl- *) Vnn = (6*z*z1 + 12*z1*z1/sq2+1.5*z1*z1)/(S6+S4); Vee = Vee+(6*23*18 + 12*18*18/sq2 + 1.5*18*18)/(S6+S4); Vne = Vne -(6*z*18+6*z1*23+24*z1*18/sq2+3*z1*18)/(S6+S4); func = T + Vnn + Vne + Vee; \ \>", "Input", PageWidth->WindowWidth, InitializationCell->True, CellChangeTimes->{{3.58288040795399*^9, 3.582880450276864*^9}, { 3.582880697833699*^9, 3.5828807039957104`*^9}}, ShowSpecialCharacters->False], Cell[CellGroupData[{ Cell["\<\ t = FindMinimum[func, {R1,0.05052}, {R2,0.16}, {R3,0.4178}, {R4,1.171}, {R5,0.0812},{R6,0.30885},{R7,1.65},{Method -> \"Newton\"}, {MaxIterations \ -> 500}]\ \>", "Input", PageWidth->WindowWidth, InitializationCell->True, CellChangeTimes->{{3.58288040795399*^9, 3.582880450276864*^9}, { 3.582880581317095*^9, 3.5828805879003067`*^9}, {3.5828806217835655`*^9, 3.582880625324772*^9}}, ShowSpecialCharacters->False], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "4006.147176392835`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"R1", "\[Rule]", "0.050519726125930385`"}], ",", RowBox[{"R2", "\[Rule]", "0.160185774924115`"}], ",", RowBox[{"R3", "\[Rule]", "0.41779711379268575`"}], ",", RowBox[{"R4", "\[Rule]", "1.1714901206866224`"}], ",", RowBox[{"R5", "\[Rule]", "0.08122814611177`"}], ",", RowBox[{"R6", "\[Rule]", "0.3088524920666065`"}], ",", RowBox[{"R7", "\[Rule]", "1.6497427514924456`"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.5828805370130167`*^9, {3.582880604795136*^9, 3.5828806319391837`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ N[Vne /. c /. t[[2]],10] N[Vnn /. c /. t[[2]],10] N[Vee /. c /. t[[2]],10] N[-(Vee+Vne+Vnn)/T /. c /. t[[2]],10] N[(S2+R3) /. c /. t[[2]],10] N[(S3+R4) /. c /. t[[2]],10] N[(S4) /. c /. t[[2]],10] d = S4+S6 /. c /. t[[2]] N[0.529177*(S4+S6) /. c /. t[[2]],10] (* xy plane *) plot2=Graphics[{Circle[{0,0},R1], Circle[{0,0},S2],Circle[{0,0},S3], Circle[{0,0},S4],Circle[{d,0},R5], Circle[{d,0},S5],Circle[{d,0},S6], Circle[{-d,0},R5], Circle[{-d,0},S5],Circle[{-d,0},S6], Circle[{0,d},R5], Circle[{0,d},S5],Circle[{0,d},S6],Circle[{0,-d},R5], Circle[{0,-d},S5],Circle[{0,-d},S6] (* Disk[{x[[3]],y[[3]]},0.08], Disk[{x[[8]],y[[8]]},0.08], Disk[{x[[13]],y[[13]]},0.08], Disk[{x[[18]],y[[18]]},0.08], Disk[{0,0},0.08], {Thickness[0.006], Line[{{0,0},{S4+S6,0}}], Line[{{0,0},{-S4-S6,0}}] }*)} ] /. t[[2]] /. c; 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