(* 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[     34167,        924]
NotebookOptionsPosition[     32642,        870]
NotebookOutlinePosition[     33154,        889]
CellTagsIndexPosition[     33111,        886]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"CH4", " ", "molecule", " ", "with", " ", 
     RowBox[{"C", "[", 
      RowBox[{"1", "s2", " ", "4", "sp"}], "]"}]}], ",", " ", "overlap", ",", 
    " ", 
    RowBox[{"parametrized", " ", "ES", " ", "30.12", ".2012"}]}], " ", "*)"}],
   "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"Variables", ":", " ", "P"}], ",", "Q", ",", "R", ",", "S"}], " ",
    "*)"}], "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{"with", " ", 
    StyleBox["exchange",
     FontColor->RGBColor[1, 0, 0]]}], " ", "*)"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Clear", "[", 
    RowBox[{
    "k1", ",", "k2", ",", "s1", ",", "s2", ",", " ", "Z", ",", " ", "P", ",", 
     "Q", ",", "R", ",", "S", ",", "Vne", ",", "Vee", ",", "Vnn", ",", "Veec",
      ",", "Vnec", ",", "Veecb"}], "]"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Clear", "[", 
     RowBox[{
     "Vnecb", ",", "Vnncb", ",", "Veebb", ",", "Vnebb", ",", "Vnebb", ",", 
      "d2", ",", "d1", ",", "d3"}], "]"}], ";"}]}]}]], "Input",
 CellChangeTimes->{{3.565873007236067*^9, 3.5658730119004745`*^9}}],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"Z", "=", "6.0"}], ";", " ", 
    RowBox[{"w3", "=", 
     RowBox[{"Sqrt", "[", "3", "]"}]}], ";", " ", 
    RowBox[{"wd", "=", 
     RowBox[{"Sin", "[", 
      RowBox[{"ArcCos", "[", 
       RowBox[{
        RowBox[{"-", "1"}], "/", "3"}], "]"}], "]"}]}], ";", "   ", 
    RowBox[{"ad", "=", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"8", "/", "3"}], "]"}]}], ";"}], 
   "                                               ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"R", "=", "1.046"}], ";", " ", 
    RowBox[{"S", "=", " ", "1.012"}], ";"}], " ", "\[IndentingNewLine]", 
   RowBox[{"(*", " ", "core", " ", "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Tc", "=", 
     RowBox[{"2.25", "*", 
      RowBox[{"k1", "/", 
       RowBox[{"P", "^", "2"}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vnec", "=", 
     RowBox[{
      RowBox[{"-", "3.0"}], "*", 
      RowBox[{"Z", "/", "P"}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Veec", "=", 
     RowBox[{"3.0", "*", 
      RowBox[{"s1", "/", "P"}]}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", " ", "bond", " ", "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Tb", "=", 
     RowBox[{"9.0", "*", 
      RowBox[{"k2", "/", 
       RowBox[{"Q", "^", "2"}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vneb", "=", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"(", 
        RowBox[{"2", "/", "Q"}], ")"}]}], "*", 
      RowBox[{"(", 
       RowBox[{"1.5", "-", 
        RowBox[{"0.5", "*", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"S", "/", "Q"}], ")"}], "^", "2"}]}]}], ")"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Veeb", "=", 
     RowBox[{"3.0", "*", 
      RowBox[{"s2", "/", "Q"}]}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{"core", "-", "bond"}], " ", "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vnecb", "=", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"(", 
         RowBox[{"2.0", "*", 
          RowBox[{"Z", "/", "Q"}]}], ")"}]}], "*", 
       RowBox[{"(", 
        RowBox[{"1.5", "-", 
         RowBox[{"0.5", "*", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{"R", "/", "Q"}], ")"}], "^", "2"}]}]}], ")"}]}], "-", 
      RowBox[{"2.0", "/", 
       RowBox[{"(", 
        RowBox[{"R", "+", "S"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Veecb", "=", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"2", "/", "Q"}], ")"}], "*", 
      RowBox[{"(", 
       RowBox[{"3.0", "-", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"R", "/", "Q"}], ")"}], "^", "2"}], "-", 
        RowBox[{"0.6", "*", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"P", "/", "Q"}], ")"}], "^", "2"}]}]}], ")"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vex", "  ", "=", " ", 
     RowBox[{
      RowBox[{"-", 
       StyleBox["1.2",
        FontColor->RGBColor[1, 0, 0]]}], 
      StyleBox["*",
       FontColor->RGBColor[1, 0, 0]], 
      StyleBox[
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{"P", "/", "Q"}], ")"}], "^", "3"}], "/", "Q"}],
       FontColor->RGBColor[1, 0, 0]]}]}], 
    StyleBox[";",
     FontColor->RGBColor[1, 0, 0]]}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Veecb", " ", "=", " ", 
     RowBox[{"Veecb", " ", "+", " ", "Vex"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vnncb", "=", 
     RowBox[{"Z", "/", 
      RowBox[{"(", 
       RowBox[{"R", "+", "S"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{"bond", "-", "bond"}], " ", "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d1", "=", " ", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"R", "+", "S"}], ")"}], "*", "ad"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d2", "=", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"R", "^", "2"}], "+", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"R", "+", "S"}], ")"}], "^", "2"}], "+", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"2", "/", "3"}], ")"}], "*", "R", "*", 
        RowBox[{"(", 
         RowBox[{"R", "+", "S"}], ")"}]}]}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d3", "=", " ", 
     RowBox[{"R", "*", "ad"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vnebb", " ", "=", " ", 
     RowBox[{
      RowBox[{"-", "4"}], "/", "d2"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Veebb", " ", "=", " ", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"4", "/", "Q"}], ")"}], "*", 
      RowBox[{"(", 
       RowBox[{"1.2", "-", 
        RowBox[{"0.5", "*", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"d3", "/", "Q"}], ")"}], "^", "2"}]}], "+", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"3", "/", "16"}], ")"}], "*", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"d3", "/", "Q"}], ")"}], "^", "3"}]}], "-", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"1", "/", "160"}], ")"}], "*", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"d3", "/", "Q"}], ")"}], "^", "5"}]}]}], ")"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vnnbb", " ", "=", "  ", 
     RowBox[{"1", "/", "d1"}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{"sum", " ", "terms"}], " ", "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"T", " ", "=", " ", 
     RowBox[{"Tc", "+", 
      RowBox[{"4", "*", "Tb"}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vne", " ", "=", " ", 
     RowBox[{"Vnec", "+", 
      RowBox[{"4", "*", "Vneb"}], "+", 
      RowBox[{"4", "*", "Vnecb"}], "+", 
      RowBox[{"6", "*", "Vnebb"}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vee", " ", "=", " ", 
     RowBox[{"Veec", "+", 
      RowBox[{"4", "*", "Veeb"}], "+", 
      RowBox[{"4", "*", "Veecb"}], "+", 
      RowBox[{"6", "*", "Veebb"}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Vnn", " ", "=", " ", 
     RowBox[{
      RowBox[{"4", "*", "Vnncb"}], "+", 
      RowBox[{"6", "*", "Vnnbb"}]}]}], ";"}], 
   "\[IndentingNewLine]"}]}]], "Input",
 CellChangeTimes->{{3.5657937844427853`*^9, 3.565793859915718*^9}, {
  3.5657939244998317`*^9, 3.5657939397722583`*^9}, {3.565793996977559*^9, 
  3.5657939986155615`*^9}, {3.5657940383800316`*^9, 3.5657940478960485`*^9}, {
  3.56579427071124*^9, 3.5657942777000523`*^9}, {3.565794526754489*^9, 
  3.565794534008502*^9}, {3.5657947993649683`*^9, 3.5657948132177925`*^9}, {
  3.565850116187584*^9, 3.565850119993991*^9}, {3.5658501746564865`*^9, 
  3.565850180116496*^9}, {3.5658502827958765`*^9, 3.565850289051488*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"c", "=", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"k1", " ", "->", " ", "1.0"}], ",", " ", 
       RowBox[{"k2", "->", " ", "0.625"}], ",", " ", 
       RowBox[{"s1", " ", "->", " ", "0.3"}], ",", " ", 
       RowBox[{"s2", " ", "->", " ", "0.3"}]}], "}"}]}], ";"}], "  ", "*)"}], 
  RowBox[{
   RowBox[{"c", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"k1", " ", "->", " ", "1.0525"}], ",", " ", 
      RowBox[{"k2", " ", "->", " ", "0.6"}], ",", " ", 
      RowBox[{"s1", " ", "->", " ", "0.25742249"}], ",", 
      RowBox[{"s2", " ", "->", " ", "0.22958899"}]}], "}"}]}], 
   ";"}]}]], "Input",
 CellChangeTimes->{{3.5658502327197886`*^9, 3.565850234045791*^9}, {
  3.5658504150841093`*^9, 3.5658504185941153`*^9}, {3.5658504575317836`*^9, 
  3.5658504740366125`*^9}, {3.5658505065626698`*^9, 3.565850557512359*^9}, {
  3.5658724931527634`*^9, 3.5658726217281895`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"func", "=", 
   RowBox[{
    RowBox[{"T", "+", "Vne", "+", "Vee", "+", "Vnn"}], " ", "/.", " ", 
    "c"}]}], ";"}]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"t", "=", 
  RowBox[{"FindMinimum", "[", 
   RowBox[{"func", ",", 
    RowBox[{"{", 
     RowBox[{"P", ",", "0.27"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"Q", ",", "1.2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"Method", " ", "\[Rule]", " ", "\"\<Newton\>\""}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"MaxIterations", " ", "\[Rule]", " ", "500"}], "}"}]}], "]"}], 
  " "}]], "Input",
 CellChangeTimes->{{3.5657940640420766`*^9, 3.5657940686128845`*^9}, {
   3.5657941840686874`*^9, 3.565794228700366*^9}, {3.5657943375885572`*^9, 
   3.565794373016219*^9}, {3.5657945833981886`*^9, 3.565794635861081*^9}, 
   3.5658503504375954`*^9, {3.5658504852686324`*^9, 3.565850486064234*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "40.478944011343515`"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"P", "\[Rule]", "0.27573957394771975`"}], ",", 
     RowBox[{"Q", "\[Rule]", "1.6972279061598257`"}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{
  3.5657938697437353`*^9, 3.565793956620288*^9, 3.565794077785701*^9, {
   3.565794257170416*^9, 3.565794283924463*^9}, 3.5657943450765705`*^9, 
   3.56579437914703*^9, 3.565794540186113*^9, {3.565794589076599*^9, 
   3.565794642896693*^9}, 3.565794819707404*^9, 3.565850072398307*^9, 
   3.5658501252824*^9, 3.5658501872301087`*^9, 3.5658502411750035`*^9, 
   3.5658502950886984`*^9, 3.5658503612796144`*^9, 3.5658504234457235`*^9, {
   3.5658504644425955`*^9, 3.5658505629879684`*^9}, 3.565850752731102*^9, 
   3.5658509457502413`*^9, 3.565851037712403*^9, 3.565851114776538*^9, 
   3.5658511497829995`*^9, 3.56585144630832*^9, {3.5658515405168858`*^9, 
   3.565851553121708*^9}, 3.565851598018587*^9, 3.565855760667498*^9, 
   3.565856024151961*^9, 3.565856155628992*^9, 3.565856195237461*^9, 
   3.565856309991263*^9, 3.565856341144518*^9, 3.5658563893174024`*^9, 
   3.56585851193513*^9, 3.565858624426928*^9, {3.565872500749977*^9, 
   3.5658726257217965`*^9}, 3.5658727212251644`*^9, 3.565872945849959*^9, 
   3.5658763291000814`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"u", "=", 
   RowBox[{"t", "[", 
    RowBox[{"[", "2", "]"}], "]"}]}], ";"}]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Vne", " ", "/.", "u"}]], "Input"],

Cell[BoxData[
 RowBox[{"-", "121.6774575830695`"}]], "Output",
 CellChangeTimes->{
  3.565793869852936*^9, 3.565793956713888*^9, 3.565794077894901*^9, {
   3.5657942572796164`*^9, 3.565794284033663*^9}, 3.5657943451857705`*^9, 
   3.5657943792562304`*^9, 3.5657945402017126`*^9, {3.565794589092199*^9, 
   3.5657946429122934`*^9}, 3.565794819707404*^9, 3.565850072413907*^9, 
   3.5658501252980003`*^9, 3.5658501872301087`*^9, 3.5658502411906033`*^9, 
   3.5658502950886984`*^9, 3.5658503612952147`*^9, 3.5658504234613237`*^9, {
   3.5658504644581957`*^9, 3.5658505630035686`*^9}, 3.565850752731102*^9, 
   3.5658509457658415`*^9, 3.5658510377280025`*^9, 3.565851114792138*^9, 
   3.5658511497985992`*^9, 3.5658514463239202`*^9, {3.565851540532486*^9, 
   3.565851553137308*^9}, 3.565851598034187*^9, 3.565855760683098*^9, 
   3.565856024151961*^9, 3.565856155644592*^9, 3.5658561952530613`*^9, 
   3.565856310006863*^9, 3.5658563411601176`*^9, 3.565856389333002*^9, 
   3.5658585119507303`*^9, 3.565858624442528*^9, {3.5658725007655773`*^9, 
   3.5658726257373962`*^9}, 3.5658727212407646`*^9, 3.5658729458655586`*^9, 
   3.565876329115681*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Vee", " ", "/.", "u"}], "  ", "/.", " ", "c"}]], "Input"],

Cell[BoxData["29.10658328720129`"], "Output",
 CellChangeTimes->{
  3.5657938698997355`*^9, 3.565793956776288*^9, 3.565794077941701*^9, {
   3.565794257326416*^9, 3.5657942840804634`*^9}, 3.5657943452325706`*^9, 
   3.56579437931863*^9, 3.5657945402017126`*^9, {3.5657945891077986`*^9, 
   3.5657946429278936`*^9}, 3.5657948197230043`*^9, 3.5658500724295073`*^9, 
   3.5658501253136*^9, 3.5658501872457085`*^9, 3.5658502412062035`*^9, 
   3.5658502951042986`*^9, 3.565850361310815*^9, 3.5658504234613237`*^9, {
   3.565850464473796*^9, 3.5658505630035686`*^9}, 3.565850752746702*^9, 
   3.5658509457658415`*^9, 3.5658510377280025`*^9, 3.565851114792138*^9, 
   3.5658511497985992`*^9, 3.5658514463239202`*^9, {3.565851540532486*^9, 
   3.565851553137308*^9}, 3.565851598034187*^9, 3.565855760698698*^9, 
   3.5658560241675606`*^9, 3.565856155644592*^9, 3.5658561952686615`*^9, 
   3.565856310006863*^9, 3.5658563411601176`*^9, 3.5658563893486023`*^9, 
   3.5658585119663305`*^9, 3.565858624458128*^9, {3.5658725007811775`*^9, 
   3.5658726257529964`*^9}, 3.5658727212407646`*^9, 3.565872945881159*^9, 
   3.565876329115681*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"4", "*", "Vex"}], " ", "/.", " ", "u"}]], "Input"],

Cell[BoxData[
 RowBox[{"-", "0.012127684278115993`"}]], "Output",
 CellChangeTimes->{
  3.565793869930936*^9, 3.5657939568074884`*^9, 3.5657940779885015`*^9, {
   3.5657942573576164`*^9, 3.565794284111663*^9}, 3.5657943452793703`*^9, 
   3.5657943793654304`*^9, 3.565794540217313*^9, {3.5657945891077986`*^9, 
   3.5657946429434934`*^9}, 3.565794819738604*^9, 3.5658500724295073`*^9, 
   3.5658501253136*^9, 3.5658501872457085`*^9, 3.5658502412062035`*^9, 
   3.5658502951042986`*^9, 3.565850361326415*^9, 3.565850423476924*^9, {
   3.565850464489396*^9, 3.565850563019169*^9}, 3.565850752746702*^9, 
   3.565850945781441*^9, 3.5658510377436028`*^9, 3.5658511148077383`*^9, 
   3.5658511498141994`*^9, 3.5658514463395205`*^9, {3.565851540548086*^9, 
   3.5658515531529083`*^9}, 3.5658515980497866`*^9, 3.565855760698698*^9, 
   3.565856024183161*^9, 3.565856155660192*^9, 3.5658561952686615`*^9, 
   3.565856310022463*^9, 3.5658563411757174`*^9, 3.5658563893486023`*^9, 
   3.5658585119663305`*^9, 3.565858624458128*^9, {3.5658725007811775`*^9, 
   3.5658726257529964`*^9}, 3.5658727212563643`*^9, 3.565872945896759*^9, 
   3.565876329131281*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Vnn", " ", "/.", " ", "u"}]], "Input"],

Cell[BoxData["13.447149958296778`"], "Output",
 CellChangeTimes->{
  3.5657938699621353`*^9, 3.5657939568386884`*^9, 3.565794078019701*^9, {
   3.565794257388816*^9, 3.5657942841428633`*^9}, 3.5657943453105707`*^9, 
   3.5657943793966303`*^9, 3.565794540217313*^9, {3.565794589123399*^9, 
   3.565794642959093*^9}, 3.565794819754204*^9, 3.5658500724451075`*^9, 
   3.5658501253292003`*^9, 3.5658501872613087`*^9, 3.5658502412218037`*^9, 
   3.5658502951198983`*^9, 3.565850361342015*^9, 3.565850423492524*^9, {
   3.565850464489396*^9, 3.565850563034769*^9}, 3.5658507527623024`*^9, 
   3.565850945781441*^9, 3.5658510377436028`*^9, 3.5658511148077383`*^9, 
   3.5658511498141994`*^9, 3.5658514463395205`*^9, {3.565851540548086*^9, 
   3.5658515531529083`*^9}, 3.565851598065387*^9, 3.5658557607142982`*^9, 
   3.565856024183161*^9, 3.565856155660192*^9, 3.5658561952842617`*^9, 
   3.565856310022463*^9, 3.5658563411757174`*^9, 3.5658563893642025`*^9, 
   3.5658585119819307`*^9, 3.565858624473728*^9, {3.5658725007967772`*^9, 
   3.5658726257685966`*^9}, 3.5658727212563643`*^9, 3.5658729459123588`*^9, 
   3.565876329131281*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     RowBox[{"(", 
      RowBox[{"Vne", "+", "Vee", "+", "Vnn"}], ")"}]}], "/", "T"}], " ", "/.",
    "u"}], "/.", "c"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"(", 
    RowBox[{"R", "+", "S"}], ")"}], "*", "0.529177"}], " ", "/.", 
  "u"}]}], "Input"],

Cell[BoxData["2.0474621325217033`"], "Output",
 CellChangeTimes->{
  3.565793870008936*^9, 3.5657939568854885`*^9, 3.565794078082101*^9, {
   3.5657942574356165`*^9, 3.565794284189663*^9}, 3.5657943453729706`*^9, 
   3.5657943794590306`*^9, 3.565794540217313*^9, {3.565794589138999*^9, 
   3.565794642959093*^9}, 3.565794819754204*^9, 3.565850072460707*^9, 
   3.5658501253292003`*^9, 3.565850187276909*^9, 3.565850241237404*^9, 
   3.5658502951198983`*^9, 3.565850361342015*^9, 3.565850423492524*^9, {
   3.5658504645049963`*^9, 3.5658505630503693`*^9}, 3.565850752777902*^9, 
   3.565850945797041*^9, 3.565851037759203*^9, 3.565851114823338*^9, 
   3.5658511498297997`*^9, 3.5658514463551207`*^9, {3.565851540563686*^9, 
   3.565851553168508*^9}, 3.565851598065387*^9, 3.5658557607142982`*^9, 
   3.565856024198761*^9, 3.5658561556757917`*^9, 3.5658561952842617`*^9, 
   3.565856310038063*^9, 3.5658563411913176`*^9, 3.5658563893642025`*^9, 
   3.565858511997531*^9, 3.565858624489328*^9, {3.565872500812377*^9, 
   3.565872625784197*^9}, 3.565872721271964*^9, 3.5658729459123588`*^9, 
   3.565876329146881*^9}],

Cell[BoxData["1.089046266`"], "Output",
 CellChangeTimes->{
  3.565793870008936*^9, 3.5657939568854885`*^9, 3.565794078082101*^9, {
   3.5657942574356165`*^9, 3.565794284189663*^9}, 3.5657943453729706`*^9, 
   3.5657943794590306`*^9, 3.565794540217313*^9, {3.565794589138999*^9, 
   3.565794642959093*^9}, 3.565794819754204*^9, 3.565850072460707*^9, 
   3.5658501253292003`*^9, 3.565850187276909*^9, 3.565850241237404*^9, 
   3.5658502951198983`*^9, 3.565850361342015*^9, 3.565850423492524*^9, {
   3.5658504645049963`*^9, 3.5658505630503693`*^9}, 3.565850752777902*^9, 
   3.565850945797041*^9, 3.565851037759203*^9, 3.565851114823338*^9, 
   3.5658511498297997`*^9, 3.5658514463551207`*^9, {3.565851540563686*^9, 
   3.565851553168508*^9}, 3.565851598065387*^9, 3.5658557607142982`*^9, 
   3.565856024198761*^9, 3.5658561556757917`*^9, 3.5658561952842617`*^9, 
   3.565856310038063*^9, 3.5658563411913176`*^9, 3.5658563893642025`*^9, 
   3.565858511997531*^9, 3.565858624489328*^9, {3.565872500812377*^9, 
   3.565872625784197*^9}, 3.565872721271964*^9, 3.5658729459123588`*^9, 
   3.565876329146881*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"plot1", "=", 
   RowBox[{
    RowBox[{"Graphics", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}], ",", "P"}], "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}], ",", "0.1"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}], ",", "Q"}], "]"}], ",", "\n", "\t", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{"R", "/", "2"}]}], ",", 
           RowBox[{"wd", "*", "w3", "*", 
            RowBox[{"R", "/", "2"}]}]}], "}"}], ",", "Q"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{"R", "/", "2"}]}], ",", 
           RowBox[{
            RowBox[{"-", "wd"}], "*", "w3", "*", 
            RowBox[{"R", "/", "2"}]}]}], "}"}], ",", "Q"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"wd", "*", "R"}], ",", "0"}], "}"}], ",", "Q"}], "]"}], 
       ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
           RowBox[{"wd", "*", "w3", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}]}], "}"}], ",", 
         "0.1"}], "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
           RowBox[{
            RowBox[{"-", "wd"}], "*", "w3", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}]}], "}"}], ",", 
         "0.1"}], "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"wd", "*", 
            RowBox[{"(", 
             RowBox[{"R", "+", "S"}], ")"}]}], ",", "0"}], "}"}], ",", 
         "0.1"}], "]"}], ",", "\n", "\t", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Thickness", "[", "0.012", "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"wd", "*", 
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}]}], ",", "0"}], "}"}]}], "}"}], 
          "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"-", "wd"}], "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
              RowBox[{"wd", "*", "w3", "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}]}], "}"}]}], 
           "}"}], "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"-", "wd"}], "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
              RowBox[{
               RowBox[{"-", "wd"}], "*", "w3", "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}]}], "}"}]}], 
           "}"}], "]"}]}], "}"}]}], "}"}], "]"}], "/.", " ", "u"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  StyleBox[
   RowBox[{"Show", "[", 
    RowBox[{"plot1", ",", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"AspectRatio", "->", "Automatic"}], ",", " ", 
       RowBox[{"PlotRange", "->", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"-", "3"}], ",", "3"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "}"}]}], ",", 
       RowBox[{"Axes", "->", "True"}], ",", 
       RowBox[{"GridLines", "->", "Automatic"}], ",", 
       RowBox[{"Frame", "->", "True"}]}], "}"}]}], "]"}],
   FontSize->12], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"plot1", "=", 
   RowBox[{
    RowBox[{"Graphics3D", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Opacity", "[", "0.3", "]"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"0", ",", "0", ",", "R"}], "}"}], ",", "Q"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{"R", "/", "2"}]}], ",", 
             RowBox[{"wd", "*", "w3", "*", 
              RowBox[{"R", "/", "2"}]}], ",", 
             RowBox[{
              RowBox[{"-", "R"}], "/", "3"}]}], "}"}], ",", "Q"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{"R", "/", "2"}]}], ",", 
             RowBox[{
              RowBox[{"-", "wd"}], "*", "w3", "*", 
              RowBox[{"R", "/", "2"}]}], ",", 
             RowBox[{
              RowBox[{"-", "R"}], "/", "3"}]}], "}"}], ",", "Q"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"wd", "*", "R"}], ",", "0", ",", 
             RowBox[{
              RowBox[{"-", "R"}], "/", "3"}]}], "}"}], ",", "Q"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
             RowBox[{"wd", "*", "w3", "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}]}], "/", "3"}]}], "}"}], ",", 
           "0.1"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
             RowBox[{
              RowBox[{"-", "wd"}], "*", "w3", "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}], "/", "2"}]}], ",", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}]}], "/", "3"}]}], "}"}], ",", 
           "0.1"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"wd", "*", 
              RowBox[{"(", 
               RowBox[{"R", "+", "S"}], ")"}]}], ",", "0", ",", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"R", "+", "S"}], ")"}]}], "/", "3"}]}], "}"}], ",", 
           "0.1"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"0", ",", "0", ",", 
             RowBox[{"R", "+", "S"}]}], "}"}], ",", "0.1"}], "]"}]}], "}"}], 
       ",", "\[IndentingNewLine]", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Darker", "[", "Red", "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "P"}], "]"}]}], 
        "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Darker", "[", 
          RowBox[{"Red", ",", "1"}], "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "0.05"}], "]"}]}], 
        "}"}]}], "}"}], "]"}], "/.", " ", "u"}]}], ";"}]}], "Input",
 CellChangeTimes->{
  3.5658500648478937`*^9, {3.5658507234030504`*^9, 3.5658507397986794`*^9}, {
   3.56585083133964*^9, 3.565850903505367*^9}, {3.565851026339983*^9, 
   3.5658510277127852`*^9}, {3.5658510923592987`*^9, 
   3.5658511087393274`*^9}, {3.5658511422793865`*^9, 3.565851180905054*^9}, {
   3.56585133782573*^9, 3.5658514347487*^9}, {3.565851511890836*^9, 
   3.5658515841189623`*^9}, 3.5658555468847227`*^9, 3.565855652403308*^9, {
   3.5658556951941833`*^9, 3.565855704523*^9}, {3.565855743507468*^9, 
   3.565855755051488*^9}, {3.565855995572711*^9, 3.5658560137779427`*^9}, {
   3.565856097347289*^9, 3.565856187546648*^9}, {3.5658562794152093`*^9, 
   3.5658562949528365`*^9}, {3.5658563311605*^9, 3.565856331753301*^9}, {
   3.5658563621889544`*^9, 3.5658563764629793`*^9}, {3.565856964225212*^9, 
   3.565856978280837*^9}, {3.5658570180765066`*^9, 3.565857049728962*^9}, {
   3.565858360817665*^9, 3.5658583719404845`*^9}, {3.5658584208777704`*^9, 
   3.5658584376633997`*^9}, {3.5658584740270643`*^9, 
   3.5658585066155214`*^9}, {3.565858619122919*^9, 3.56585861990292*^9}, {
   3.565872904291486*^9, 3.565872933307537*^9}, {3.5658729732436066`*^9, 
   3.5658729911992383`*^9}}],

Cell[BoxData[
 GraphicsBox[{CircleBox[{0, 0}, 0.27573957394771975`], DiskBox[{0, 0}, 0.1], 
   CircleBox[{0, 0}, 1.6972279061598257`], 
   CircleBox[{-0.49308912874741917`, 0.8540554236504014}, 
    1.6972279061598257`], 
   CircleBox[{-0.49308912874741917`, -0.8540554236504014}, 
    1.6972279061598257`], 
   CircleBox[{0.9861782574948383, 0}, 1.6972279061598257`], 
   DiskBox[{-0.9701505037879432, 1.68034996354926}, 0.1], 
   DiskBox[{-0.9701505037879432, -1.68034996354926}, 0.1], 
   DiskBox[{1.9403010075758864`, 0}, 0.1], 
   {Thickness[0.012], LineBox[{{0, 0}, {1.9403010075758864`, 0}}], 
    LineBox[{{0, 0}, {-0.9701505037879432, 1.68034996354926}}], 
    LineBox[{{0, 0}, {-0.9701505037879432, -1.68034996354926}}]}},
  AspectRatio->Automatic,
  Axes->True,
  Frame->True,
  GridLines->Automatic,
  ImageSize->{284., Automatic},
  PlotRange->{{-3, 3}, {-3, 3}}]], "Output",
 CellChangeTimes->{3.5658729459435587`*^9, 3.5658763291624813`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox["Show",
   FontSize->12], 
  StyleBox["[",
   FontSize->12], 
  RowBox[{
   StyleBox["plot1",
    FontSize->12], 
   StyleBox[",",
    FontSize->12], 
   StyleBox[" ",
    FontSize->12], 
   RowBox[{
    StyleBox["{",
     FontSize->12], 
    RowBox[{
     StyleBox[
      RowBox[{"AspectRatio", "->", "Automatic"}],
      FontSize->12], 
     StyleBox[",",
      FontSize->12], 
     RowBox[{
      StyleBox["Boxed",
       FontSize->12], 
      StyleBox[" ",
       FontSize->12], 
      StyleBox["\[Rule]",
       FontSize->12], " ", "False"}]}], 
    StyleBox["}",
     FontSize->12]}]}], 
  StyleBox["]",
   FontSize->12]}]], "Input",
 CellChangeTimes->{
  3.5657936204396973`*^9, {3.5658762991324286`*^9, 3.565876306963642*^9}}],

Cell[BoxData[
 Graphics3DBox[
  {Opacity[
   0.3], {SphereBox[{0, 0, 1.046}, 1.6972279061598257`], 
    SphereBox[{-0.49308912874741917`, 
     0.8540554236504014, -0.3486666666666667}, 1.6972279061598257`], 
    SphereBox[{-0.49308912874741917`, -0.8540554236504014, \
-0.3486666666666667}, 1.6972279061598257`], 
    SphereBox[{0.9861782574948383, 0, -0.3486666666666667}, 
     1.6972279061598257`], 
    SphereBox[{-0.9701505037879432, 1.68034996354926, -0.6859999999999999}, 
     0.1], SphereBox[{-0.9701505037879432, -1.68034996354926, \
-0.6859999999999999}, 0.1], 
    SphereBox[{1.9403010075758864`, 0, -0.6859999999999999}, 0.1], 
    SphereBox[{0, 0, 2.058}, 0.1]}, 
   {RGBColor[
     NCache[
      Rational[2, 3], 0.6666666666666666], 0, 0], 
    SphereBox[{0, 0, 0}, 0.27573957394771975`]}, 
   {RGBColor[0, 0, 0], SphereBox[{0, 0, 0}, 0.05]}},
  AspectRatio->Automatic,
  Boxed->False]], "Output",
 CellChangeTimes->{3.5658763291780815`*^9}]
}, Open  ]]
},
WindowSize->{723, 889},
WindowMargins->{{177, Automatic}, {Automatic, 5}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
CellLabelAutoDelete->True,
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (November 20, 2012)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 1188, 30, 132, "Input"],
Cell[1748, 52, 6971, 205, 732, "Input"],
Cell[8722, 259, 960, 23, 52, "Input"],
Cell[9685, 284, 161, 5, 31, "Input"],
Cell[CellGroupData[{
Cell[9871, 293, 723, 16, 52, "Input"],
Cell[10597, 311, 1325, 24, 31, "Output"]
}, Open  ]],
Cell[11937, 338, 121, 4, 31, "Input"],
Cell[CellGroupData[{
Cell[12083, 346, 57, 1, 31, "Input"],
Cell[12143, 349, 1145, 17, 31, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[13325, 371, 92, 2, 31, "Input"],
Cell[13420, 375, 1127, 16, 31, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[14584, 396, 85, 2, 31, "Input"],
Cell[14672, 400, 1146, 17, 31, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15855, 422, 62, 1, 31, "Input"],
Cell[15920, 425, 1131, 16, 31, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[17088, 446, 336, 12, 52, "Input"],
Cell[17427, 460, 1113, 16, 31, "Output"],
Cell[18543, 478, 1106, 16, 31, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[19686, 499, 10215, 283, 452, "Input"],
Cell[29904, 784, 956, 20, 303, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[30897, 809, 769, 34, 31, "Input"],
Cell[31669, 845, 957, 22, 404, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)