(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 884440, 15724] NotebookOptionsPosition[ 879273, 15559] NotebookOutlinePosition[ 879737, 15577] CellTagsIndexPosition[ 879694, 15574] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["This ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" file is used to construct arrays of Franck-Condon factors and \ wavelength matrices. The user must input molecular constants for the upper \ and lower electronic states. From this information, a Morse potential is \ created and used to numerically integrate Schrodinger's equation in order to \ get eigenfunctions. A two-step symplectic integrator is used for the \ numerical integration.\n\nExpand the sections below and read the comments to \ see how it works.\n\nAll of the numbers given in this file are for the A->B \ transition in SrO.\n\nReferences:\nR. W. Nicholls, ", FontSize->14], StyleBox["J. Quant. Spectrosc. Radiat. Transfer,", FontSize->14, FontSlant->"Italic"], StyleBox[" vol. 5, pp. 647-667 (1965).\nR. W. Nicholls, ", FontSize->14], StyleBox["The Astrophysical Journal Supplement Series", FontSize->14, FontSlant->"Italic"], StyleBox[", vol. 47, pp. 279-290 (1981).\nXue-Shen Liu et. al., ", FontSize->14], StyleBox["Int. J. Quant. Chem.", FontSize->14, FontSlant->"Italic"], StyleBox[", vol. 79, pp. 343-349 (2000).\n\nAuthor: Dan Farkas, Yale \ University Physics Dept.\nDate: November 2007\nemail: daniel.farkas@yale.edu", FontSize->14] }], "Text", CellChangeTimes->{{3.403000654367875*^9, 3.403000966711625*^9}}], Cell[CellGroupData[{ Cell["Constructing Morse Potential", "Section", CellChangeTimes->{{3.402659048320875*^9, 3.40265908311775*^9}}], Cell[CellGroupData[{ Cell["Universal", "Subsection", CellChangeTimes->{{3.40266998218025*^9, 3.402669989024*^9}}], Cell["Universal constants given in CGS units.", "Text", CellChangeTimes->{{3.402998273055375*^9, 3.40299829197725*^9}}, FontSize->14], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Planck", "=", RowBox[{"6.626", "*", SuperscriptBox["10", RowBox[{"-", "27"}]]}]}], ";"}], " ", RowBox[{"(*", " ", RowBox[{"CGS", " ", "units"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"hbar", "=", RowBox[{"Planck", "/", RowBox[{"(", RowBox[{"2", "\[Pi]"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Mu]", "=", "13.5325856"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{"Reduced", " ", "mass", " ", "in", " ", "AMU"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Mu]A", "=", RowBox[{"1.66054", "*", SuperscriptBox["10", RowBox[{"-", "24"}]]}]}], ";", " ", RowBox[{"(*", " ", RowBox[{ "value", " ", "of", " ", "1", " ", "AMU", " ", "in", " ", "grams"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"SpeedLight", "=", RowBox[{"2.99792458", "*", SuperscriptBox["10", "10"]}]}], ";", " ", RowBox[{"(*", " ", RowBox[{"cm", "/", "sec"}], " ", "*)"}], "\[IndentingNewLine]"}]}], "Input",\ CellChangeTimes->{{3.40266998961775*^9, 3.402670019070875*^9}, { 3.402850747992875*^9, 3.4028507492585*^9}, {3.40285457897725*^9, 3.402854586242875*^9}, {3.40285544422725*^9, 3.402855446867875*^9}, 3.4029195675085*^9, {3.402944371274125*^9, 3.402944372524125*^9}, { 3.40294503491475*^9, 3.40294503528975*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Lower state 1", "Subsection", CellChangeTimes->{{3.402669966727125*^9, 3.402669971524*^9}, { 3.402850751821*^9, 3.40285075285225*^9}, {3.402857616336625*^9, 3.402857616696*^9}, 3.4029442980085*^9, {3.402999480071*^9, 3.402999481805375*^9}}], Cell[TextData[{ "Enter here the properties of the lower vibrational state. For the Morse \ potential, three pieces of data are needed: the vibrational frequency ", Cell[BoxData[ FormBox[ SubscriptBox["\[Omega]", "e"], TraditionalForm]]], ", the first anharmonic term ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["\[Omega]", "e"], SubscriptBox["x", "e"]}], TraditionalForm]]], ", and the internuclear separation ", Cell[BoxData[ FormBox[ SubscriptBox["r", "e"], TraditionalForm]]], " (obtained from the rotational frequency ", Cell[BoxData[ FormBox[ SubscriptBox["B", "e"], TraditionalForm]]], ").\nFrom this, we calculate the dissociation energy ", Cell[BoxData[ FormBox[ SubscriptBox["D", "e"], TraditionalForm]]], " assuming an anharmonic potential (not entirely correct for the Morse \ potential, but close enough). The formula for ", Cell[BoxData[ FormBox[ SubscriptBox["D", "e"], TraditionalForm]]], " is from Herzberg (III.97). The relationship for \[Beta] is from Herzberg \ (III,100) and the mathematical form of the Morse potential is given by \ Herzberg (III,98).\n\nAll energy values should be entered in ", Cell[BoxData[ FormBox[ SuperscriptBox["cm", RowBox[{"-", "1"}]], TraditionalForm]]], ". 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