The Lanthanides in Crystals - LiYF4.nb

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The following loop loads the fitted parameters for the lanthanide ions from \
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eigenvectors for the given parameters describing a trivalent lanthanide. It \
can use precomputed symbolic matrices for the Hamiltonian if they have been \
loaded already and defined as symbols of the form \
symbolicHamiltonians[{symmetry, numE}].\\n\\nThe function returns a list with \
six elements {eigenEnergies, ln, simplerStateLabels, eigensys, basis, \
truncatedStates}. The elements of the list are as follows:\\n\\n1. \
eigenEnergies are the calculated energies (in the case of an odd number of \
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eigensys but with the truncated eigenvectors so that the total probability \
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cases. Default is True.\\n  - \\\"OutputDirectory\\\" -> \\\"calcs\\\". The \
directory where the output files are saved. Default is \\\"calcs\\\", may be \
a folder not yet created.\\n  - \\\"Explorer\\\" -> True or False. If True, \
the energy level diagram is interactive. Default is False.\\n  - \\\"Host\\\" \
-> \\\"crystalHost\\\". The host material. Default is \\\"LaF3\\\".\\n  - \
\\\"SymmetrySimplifier\\\" a list of two elements, the first one being the \
name of the assumed symmetry for the crystal field and the second being a \
list of replacement rules applied to simplify the Hamiltonian used to make \
calculations. Default is {\\\"C2v\\\", {B12 -> 0, ...}}\\n\"\>", 
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    "FastIonSolver[params] calculates energy levels and eigenvectors for the \
given parameters describing a trivalent lanthanide. It can use precomputed \
symbolic matrices for the Hamiltonian if they have been loaded already and \
defined as symbols of the form symbolicHamiltonians[{symmetry, numE}].\n\nThe \
function returns a list with six elements {eigenEnergies, ln, \
simplerStateLabels, eigensys, basis, truncatedStates}. The elements of the \
list are as follows:\n\n1. eigenEnergies are the calculated energies (in the \
case of an odd number of electrons the Kramers degeneracy may have been \
removed from this list according to the option \"Remove Kramers\");\n2. ln is \
simply a string labelling the corresponding lanthanide;\n3. \
simplerStateLabels is a list of strings providing the multiplet assignments \
that this function assumes;\n3. eigensys is a list of tuples where the first \
element is the energy corresponding to the eigenvector given as the second \
element (in the case of an odd number of electrons the Kramers degeneracy may \
have been removed from this list according to the option \"Remove Kramers\");\
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constructed and diagonalized, equal to BasisLSJMJ[numE];\n6. truncatedStates \
is the same as eigensys but with the truncated eigenvectors so that the total \
probability adds up to at least eigenstateTruncationProbability (determined \
by the option \"eigenstateTruncationProbability\").\n\nThis function admits \
the following options:\n  - \"MakeNotebook\" -> True or False. If True, a \
notebook with a summary of the data is created. Default is True.\n  - \
\"NotebookSave\" -> True or False. If True, the results notebook is saved \
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0.9. The probability sum of the truncated eigenvectors. Default is 0.9.\n  - \
\"Max Eigenstates in Table\" -> 100. The maximum number of eigenstates to be \
shown in the table shown in the results notebook. Default is 100.\n  - \
\"Sparse\" -> True or False. If True, the numerical Hamiltonian is kept in \
sparse form. Default is True.\n  - \"PrintFun\" -> Print, PrintTemporary, or \
other to serve as a printer for progress messages. Default is Print.\n  - \
\"SaveData\" -> True or False. If True, the resulting data is saved to disk. \
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Default is False.\n  - \"Host\" -> \"crystalHost\". The host material. \
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first one being the name of the assumed symmetry for the crystal field and \
the second being a list of replacement rules applied to simplify the \
Hamiltonian used to make calculations. Default is {\"C2v\", {B12 -> 0, ...}}\n\
", "Documentation" -> None, "OwnValues" -> None, "UpValues" -> None, 
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          Blank[]], 
         OptionsPattern[]] :> 
       Module[{$CellContext`params = <|$CellContext`params0|>, \
$CellContext`paramKeys, $CellContext`numE, $CellContext`PrintFun, \
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$CellContext`maxStatesInTable, $CellContext`Duplicator, $CellContext`host, \
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$CellContext`numEH, $CellContext`simpleHam, $CellContext`endTime, \
$CellContext`loadTime, $CellContext`numHam, $CellContext`basis, \
$CellContext`eigensys, $CellContext`eigenEnergies, \
$CellContext`titleTemplate, $CellContext`title, $CellContext`parsedStates, \
$CellContext`stateLabels, $CellContext`simplerStateLabels, \
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$CellContext`exportFname, $CellContext`tinyexportFname, \
$CellContext`tinyExport, $CellContext`nbFname, \
$CellContext`uncertaintySentence, $CellContext`sigmaRMS, \
$CellContext`energyUncertaintyTemplate}, $CellContext`paramKeys = 
          Keys[$CellContext`params]; Which[
           
           MemberQ[$CellContext`paramKeys, 
            qlanth`nE], $CellContext`numE = $CellContext`params[qlanth`nE], 
           
           MemberQ[$CellContext`paramKeys, 
            "nE"], $CellContext`numE = $CellContext`params["nE"], 
           
           MemberQ[$CellContext`paramKeys, 
            "numE"], $CellContext`numE = $CellContext`params["numE"], True, 
           Print["The number of electrons was not specified in params, \
exiting ..."]; Return[Null]; Null]; $CellContext`energyUncertaintyTemplate = 
          StringTemplate[
           "\nWhen the Hamiltonian was fitted to experimental data, the root \
mean square deviation between the data and the model energies was \
`energySigma` K."]; $CellContext`sigmaRMS = 
          OptionValue[
           "Energy Uncertainty in K"]; $CellContext`uncertaintySentence = 
          If[$CellContext`sigmaRMS === 0., "", 
            $CellContext`energyUncertaintyTemplate[<|
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$CellContext`PrintFun = OptionValue["PrintFun"]; $CellContext`makeNotebook = 
          OptionValue["MakeNotebook"]; $CellContext`onlyEnergies = 
          OptionValue[
           "EnergiesOnly"]; $CellContext`eigenstateTruncationProbability = 
          OptionValue[
           "eigenstateTruncationProbability"]; $CellContext`maxStatesInTable = 
          OptionValue["Max Eigenstates in Table"]; $CellContext`Duplicator[
            Pattern[$CellContext`aList, 
             Blank[]]] := Flatten[
            Map[{#, #}& , $CellContext`aList]]; $CellContext`host = 
          OptionValue["Host"]; $CellContext`ln = 
          Part[qonstants`theLanthanides, $CellContext`numE]; \
$CellContext`terms = qlanth`AllowedNKSLJTerms[
            
            Min[$CellContext`numE, 
             14 - $CellContext`numE]]; $CellContext`termNames = 
          Map[First, $CellContext`terms]; $CellContext`PrintFun[
          "> Calculating simpler term labels ..."]; \
$CellContext`termSimplifier = 
          Table[$CellContext`termN -> 
            If[StringLength[$CellContext`termN] == 3, 
              
              StringTake[$CellContext`termN, {1, 
               2}], $CellContext`termN], {$CellContext`termN, \
$CellContext`termNames}]; 
         If[$CellContext`numE > 
           7, $CellContext`PrintFun[
            "> Conjugating the parameters accounting for the hole-particle \
equivalence ..."]; $CellContext`params = 
            qlanth`HoleElectronConjugation[$CellContext`params]; \
$CellContext`params[qlanth`t2Switch] = 0; 
           Null, $CellContext`params[qlanth`t2Switch] = 1; 
           Null]; $CellContext`PrintFun[
          "> Loading the symbolic Hamiltonian for this configuration ..."]; \
$CellContext`startTime = Now; $CellContext`numH = 
          14 - $CellContext`numE; $CellContext`numEH = 
          Min[$CellContext`numE, $CellContext`numH]; {$CellContext`symGroup, \
$CellContext`symmetrySimplifier} = 
          OptionValue["SymmetrySimplifier"]; $CellContext`simpleHam = If[
            ValueQ[
             
             qlanth`symbolicHamiltonians[{$CellContext`symGroup, \
$CellContext`numEH}]], 
            
            qlanth`symbolicHamiltonians[{$CellContext`symGroup, \
$CellContext`numEH}], 
            
            qlanth`SimplerSymbolicHamMatrix[$CellContext`numE, \
$CellContext`symmetrySimplifier, 
             "PrependToFilename" -> $CellContext`symGroup <> "-", "Overwrite" -> 
             False]]; $CellContext`endTime = Now; $CellContext`loadTime = 
          QuantityMagnitude[$CellContext`endTime - $CellContext`startTime, 
            "Seconds"]; $CellContext`PrintFun[
          ">> Loading the symbolic Hamiltonian took ", $CellContext`loadTime, 
           " seconds."]; If[
           Not[
            
            MemberQ[$CellContext`paramKeys, 
             qlanth`\[Sigma]SS]], $CellContext`PrintFun[
            "> params does not implicitly specify if the spin-spin \
contribution should be included. Including it by default ..."]; \
$CellContext`params[qlanth`\[Sigma]SS] = 1; Null]; $CellContext`params = 
          qlanth`ParamPad[$CellContext`params, 
            "PrintFun" -> $CellContext`PrintFun]; \
$CellContext`PrintFun[$CellContext`params]; $CellContext`numHam = 
          
          qlanth`ReplaceInSparseArray[$CellContext`simpleHam, \
$CellContext`params]; If[
           Not[
            OptionValue["Sparse"]], $CellContext`numHam = 
           Normal[$CellContext`numHam]]; $CellContext`PrintFun[
          "> Calculating the SLJ basis ..."]; $CellContext`basis = 
          qlanth`BasisLSJMJ[$CellContext`numE]; 
         If[$CellContext`onlyEnergies, $CellContext`PrintFun[
            "> Diagonalizing the numerical Hamiltonian to get just the \
energies ..."]; $CellContext`startTime = Now; $CellContext`eigenEnergies = 
            Eigenvalues[$CellContext`numHam]; $CellContext`endTime = 
            Now; $CellContext`diagonalTime = 
            QuantityMagnitude[$CellContext`endTime - $CellContext`startTime, 
              "Seconds"]; $CellContext`PrintFun[
            ">> Diagonalization took ", $CellContext`diagonalTime, 
             " seconds."]; $CellContext`eigenEnergies = 
            Sort[$CellContext`eigenEnergies]; $CellContext`eigenEnergies = \
$CellContext`eigenEnergies - Part[$CellContext`eigenEnergies, 1]; If[
             MemberQ[
              Keys[$CellContext`params], qlanth`\[Epsilon]], 
             AddTo[$CellContext`eigenEnergies, 
              $CellContext`params[qlanth`\[Epsilon]]]]; If[
             And[
              OddQ[$CellContext`numE], 
              OptionValue["Remove Kramers"]], $CellContext`PrintFun[
              "> Since there's an odd number of electrons energies come in \
pairs, taking just one for each pair ..."]; $CellContext`eigenEnergies = 
              Part[$CellContext`eigenEnergies, 
                Span[1, All, 2]]; Null]; Return[$CellContext`eigenEnergies]; 
           Null, $CellContext`PrintFun[
            "> Diagonalizing the numerical Hamiltonian ..."]; \
$CellContext`startTime = Now; $CellContext`eigensys = 
            Eigensystem[$CellContext`numHam]; $CellContext`endTime = 
            Now; $CellContext`diagonalTime = 
            QuantityMagnitude[$CellContext`endTime - $CellContext`startTime, 
              "Seconds"]; $CellContext`PrintFun[
            ">> Diagonalization took ", $CellContext`diagonalTime, 
             " seconds."]; $CellContext`eigensys = 
            Chop[$CellContext`eigensys]; $CellContext`eigensys = 
            Transpose[$CellContext`eigensys]; Null]; $CellContext`eigensys = 
          qlanth`ShiftedLevels[$CellContext`eigensys]; $CellContext`eigensys = 
          SortBy[$CellContext`eigensys, First]; $CellContext`energyShift = 
          0; $CellContext`energyShift = If[
            MemberQ[
             Keys[$CellContext`params], qlanth`\[Epsilon]], 
            Chop[
             Round[
              $CellContext`params[qlanth`\[Epsilon]], 0.1]], 0.]; 
         If[qlanth`\[Epsilon] =!= 0., $CellContext`eigensys = 
           Map[{Part[#, 1] + $CellContext`energyShift, 
              
              Part[#, 2]}& , $CellContext`eigensys]]; \
$CellContext`eigenEnergies = Chop[
            Map[First, $CellContext`eigensys]]; If[
           And[
            OddQ[$CellContext`numE], 
            OptionValue["Remove Kramers"]], $CellContext`PrintFun[
            "> Since there's an odd number of electrons energies come in \
pairs, taking just one for each pair ..."]; $CellContext`eigenEnergies = 
            Part[$CellContext`eigenEnergies, 
              Span[1, All, 2]]; Null]; $CellContext`titleTemplate = 
          StringTemplate[
           "Energy Level Diagram of \!\(\*SuperscriptBox[\(`ion`\), \
\(\(3\)\(+\)\)]\)"]; $CellContext`title = $CellContext`titleTemplate[<|
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          qlanth`ParseStates[$CellContext`eigensys, $CellContext`basis]; If[
           And[
            OddQ[$CellContext`numE], 
            OptionValue["Remove Kramers"]], $CellContext`parsedStates = 
           Part[$CellContext`parsedStates, 
             Span[1, All, 2]]]; $CellContext`stateLabels = 
          Map[Part[#, -1]& , $CellContext`parsedStates]; \
$CellContext`simplerStateLabels = Map[ReplaceAll[
              Part[#, 2], $CellContext`termSimplifier] <> ToString[
              Part[#, 3], 
              InputForm]& , $CellContext`parsedStates]; $CellContext`PrintFun[
          ">> Truncating eigenvectors to given probability ..."]; \
$CellContext`startTime = Now; $CellContext`truncatedStates = 
          qlanth`ParseStatesByProbabilitySum[$CellContext`eigensys, \
$CellContext`basis, $CellContext`eigenstateTruncationProbability, 
            0.01]; $CellContext`endTime = Now; $CellContext`truncationTime = 
          QuantityMagnitude[$CellContext`endTime - $CellContext`startTime, 
            "Seconds"]; $CellContext`PrintFun[
          ">>> Truncation took ", $CellContext`truncationTime, " seconds."]; 
         If[$CellContext`makeNotebook, $CellContext`hamImage = 
            misc`HamTeX[$CellContext`numE, 
              "T2" -> $CellContext`params[qlanth`T2] === 
               0.]; $CellContext`PrintFun[
            "> Putting together results in a notebook ..."]; \
$CellContext`energyDiagram = Framed[
              
              qlanth`EnergyLevelDiagram[$CellContext`eigensys, 
               "Title" -> $CellContext`title, "Explorer" -> 
               OptionValue["Explorer"], "Background" -> White], Background -> 
              White, FrameMargins -> 50]; $CellContext`appToFname = 
            OptionValue["Append to Filename"]; $CellContext`statesTable = Map[{
               Round[
                Part[#, 1]], 
               Part[#, 2]}& , 
              Part[$CellContext`truncatedStates, 
               Span[1, 
                Min[
                 
                 Length[$CellContext`eigensys], \
$CellContext`maxStatesInTable]]]]; $CellContext`statesTableHeader = {
             "Energy/\!\(\*SuperscriptBox[\(cm\), \(-1\)]\)", 
              "\[Psi]"}; $CellContext`statesTable = 
            Prepend[$CellContext`statesTable, $CellContext`statesTableHeader]; \
$CellContext`statesTable = 
            Grid[$CellContext`statesTable, Frame -> All, Spacings -> {2, 2}, 
              FrameStyle -> Blue, 
              Dividers -> {{False, True, False}, {
                True, True}}]; $CellContext`DefaultIfMissing[
              Pattern[$CellContext`expr, 
               Blank[]]] := If[
              FreeQ[$CellContext`expr, 
               Missing[]], $CellContext`expr, 
              "NA"]; $CellContext`diffTableData = 
            Transpose[{$CellContext`simplerStateLabels, 
               Map[
               Round[#, 
                 1]& , $CellContext`eigenEnergies]}]; $CellContext`diffTable = 
            TableForm[$CellContext`diffTableData, 
              TableHeadings -> {
               None, {"coarse label", 
                 "E/\!\(\*SuperscriptBox[\(cm\), \(-1\)]\)"}}]; \
$CellContext`nb = CreateDocument[{
               TextCell[
                Style[
                 DisplayForm[
                  RowBox[{
                    
                    SuperscriptBox[$CellContext`host <> 
                    ":" <> $CellContext`ln, "3+"], "(", 
                    SuperscriptBox["f", $CellContext`numE], ")"}]]], "Title", 
                TextAlignment -> Center], 
               TextCell[
                Show[$CellContext`hamImage, ImageSize -> 600], "Output", 
                TextAlignment -> Center], 
               TextCell[
                Select[$CellContext`params, And[# =!= 0, # =!= 0.]& ], 
                "Output", TextAlignment -> Center], 
               TextCell["Energy Diagram", "Section", TextAlignment -> Center], 
               TextCell[$CellContext`energyDiagram, TextAlignment -> Center], 
               
               TextCell[
               "Multiplet Assignments & Energy Levels", "Section", 
                TextAlignment -> Center], 
               TextCell[
               "The following table shows the multiplet assignments and \
energies of the eigenstates.\nThe energies are rounded to the nearest K .\n\
The coarse label for each state corresponds to the LSJ term with the largest \
contribution to the corresponding eigenvector." <> \
$CellContext`uncertaintySentence, "Text", TextAlignment -> Center], 
               
               TextCell[$CellContext`diffTable, "Output", TextAlignment -> 
                Center], 
               TextCell[
               "Truncated Eigenstates", "Section", TextAlignment -> Center], 
               TextCell[
               "These are some of the resultant eigenstates which add up to \
at least a total probability of " <> 
                ToString[$CellContext`eigenstateTruncationProbability] <> ".",
                 "Text", TextAlignment -> Center], 
               
               TextCell[$CellContext`statesTable, "Output", TextAlignment -> 
                Center]}, WindowSelected -> True, 
              WindowTitle -> $CellContext`ln <> 
               " in " <> $CellContext`host <> $CellContext`appToFname, 
              WindowSize -> {1600, 800}]; If[
             OptionValue[
             "SaveData"], $CellContext`exportFname = 
              FileNameJoin[{$CellContext`workDir, 
                 OptionValue["OutputDirectory"], $CellContext`ln <> 
                 " in " <> $CellContext`host <> $CellContext`appToFname <> 
                 ".mx"}]; SelectionMove[$CellContext`nb, After, Notebook]; 
             NotebookWrite[$CellContext`nb, 
               Cell["Reload Data", "Section", TextAlignment -> Center]]; 
             NotebookWrite[$CellContext`nb, 
               Cell[
               "{eigenEnergies, ln, simplerStateLabels, eigensys, basis, \
truncatedStates} = Import[FileNameJoin[{NotebookDirectory[],\"" <> Part[
                  StringSplit[$CellContext`exportFname, "/"], -1] <> "\"}]];",
                 "Input"]]; NotebookWrite[$CellContext`nb, 
               Cell[
               "Manipulate[First[MinimalBy[truncatedStates, Abs[First[#] - \
energy] &]], {energy,0}]", "Input"]]; 
             SelectionMove[$CellContext`nb, Before, Notebook]; 
             Export[$CellContext`exportFname, {$CellContext`eigenEnergies, \
$CellContext`ln, $CellContext`simplerStateLabels, $CellContext`eigensys, \
$CellContext`basis, $CellContext`truncatedStates}]; \
$CellContext`tinyexportFname = FileNameJoin[{$CellContext`workDir, 
                 OptionValue["OutputDirectory"], $CellContext`ln <> 
                 " in " <> $CellContext`host <> $CellContext`appToFname <> 
                 " - tiny.m"}]; $CellContext`tinyExport = <|
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                "eigenEnergies" -> $CellContext`eigenEnergies, 
                "simplerStateLabels" -> $CellContext`simplerStateLabels|>; 
             Export[$CellContext`tinyexportFname, $CellContext`tinyExport]; 
             Null]; If[
             OptionValue[
             "NotebookSave"], $CellContext`nbFname = 
              FileNameJoin[{$CellContext`workDir, 
                 OptionValue["OutputDirectory"], $CellContext`ln <> 
                 " in " <> $CellContext`host <> $CellContext`appToFname <> 
                 ".nb"}]; $CellContext`PrintFun[
              ">> Saving notebook to ", $CellContext`nbFname, " ..."]; 
             NotebookSave[$CellContext`nb, $CellContext`nbFname]; Null]; 
           Null]; Return[{$CellContext`eigenEnergies, $CellContext`ln, \
$CellContext`simplerStateLabels, $CellContext`eigensys, $CellContext`basis, \
$CellContext`truncatedStates}]; Null]}], "SubValues" -> None, "DefaultValues" -> 
    None, "NValues" -> None, "FormatValues" -> None, 
    "Options" -> {
     "Sparse" -> True, "Host" -> "LaF3", "SaveData" -> True, "PrintFun" -> 
      Print, "Explorer" -> False, "MakeNotebook" -> True, "NotebookSave" -> 
      True, "EnergiesOnly" -> False, "Remove Kramers" -> True, 
      "Append to Filename" -> "", "Energy Uncertainty in K" -> 1, 
      "OutputDirectory" -> "calcs", "Max Eigenstates in Table" -> 100, 
      "eigenstateTruncationProbability" -> 0.9, 
      "SymmetrySimplifier" -> {
       "C2v", {qlanth`B12 -> 0, qlanth`B14 -> 0, qlanth`B16 -> 0, qlanth`B34 -> 
         0, qlanth`B36 -> 0, qlanth`B56 -> 0, qlanth`S12 -> 0, qlanth`S14 -> 
         0, qlanth`S16 -> 0, qlanth`S22 -> 0, qlanth`S24 -> 0, qlanth`S26 -> 
         0, qlanth`S34 -> 0, qlanth`S36 -> 0, qlanth`S44 -> 0, qlanth`S46 -> 
         0, qlanth`S56 -> 0, qlanth`S66 -> 0, qlanth`T11p -> 0, qlanth`T11 -> 
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lanthanide ion describe by params. This is done using the data saved in fname \
which corresponds to output files from FastIonSolverLaF3. This function saves \
a tabular file, a raw data file, and a CSV file. The tabular file contains \
the following columns: \\n    \[Psi]i:simple, (* main contribution to the \
wavefuction |i>*)\\n    \[Psi]f:simple, (* main contribution to the \
wavefuction |j>*)\\n    \[Psi]i:idx,    (* index of the wavefuction |i>*)\\n  \
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energy of the initial state in K *)\\n    Ef/K,           (* energy of the \
final state in K *)\\n    \[Lambda]/nm,   (* transition wavelength in nm \
*)\\n    \[CapitalDelta]\[Lambda]/nm, (* uncertainty in the transition \
wavelength in nm *)\\n    \[Tau]/s,       (* radiative lifetime in s *)\\n    \
AMD/s^-1        (* magnetic dipole transition rate in s^-1 *)\\n\\nThe raw \
data file contains the following keys: \\n    - Line Strength, (* Line \
strength array *)\\n    - AMD, (* Magnetic dipole transition rates in 1/s \
*)\\n    - fMD, (* Oscillator strengths from ground to excited states *)\\n   \
 - Radiative lifetimes, (* Radiative lifetimes in s *)\\n    - Transition \
Energies / K, (* Transition energies in K *)\\n    - Transition Wavelengths \
in nm. (* Transition wavelengths in nm *)\\n\\nThe CSV file contains the same \
information as the tabular file. \\n\\nThe function also creates a notebook \
with a Manipulate that allows the user to select a wavelength interval and a \
lifetime power of ten. The results notebook is saved in the examples \
directory.\\n\\nThe function takes the following options: \\n    - \\\"Make \
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material. Default is LaF3.\\n    - \\\"Wavelength Range\\\" -> {50,2000}. The \
range of wavelengths in nm for the Manipulate object in the created notebook. \
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    "MagneticDipoleTransitions[params, fname] calculates the magnetic dipole \
transition rates and oscillator strengths for the lanthanide ion describe by \
params. This is done using the data saved in fname which corresponds to \
output files from FastIonSolverLaF3. This function saves a tabular file, a \
raw data file, and a CSV file. The tabular file contains the following \
columns: \n    \[Psi]i:simple, (* main contribution to the wavefuction |i>*)\n\
    \[Psi]f:simple, (* main contribution to the wavefuction |j>*)\n    \
\[Psi]i:idx,    (* index of the wavefuction |i>*)\n    \[Psi]f:idx,    (* \
index of the wavefuction |j>*)\n    Ei/K,           (* energy of the initial \
state in K *)\n    Ef/K,           (* energy of the final state in K *)\n    \
\[Lambda]/nm,   (* transition wavelength in nm *)\n    \[CapitalDelta]\
\[Lambda]/nm, (* uncertainty in the transition wavelength in nm *)\n    \
\[Tau]/s,       (* radiative lifetime in s *)\n    AMD/s^-1        (* \
magnetic dipole transition rate in s^-1 *)\n\nThe raw data file contains the \
following keys: \n    - Line Strength, (* Line strength array *)\n    - AMD, \
(* Magnetic dipole transition rates in 1/s *)\n    - fMD, (* Oscillator \
strengths from ground to excited states *)\n    - Radiative lifetimes, (* \
Radiative lifetimes in s *)\n    - Transition Energies / K, (* Transition \
energies in K *)\n    - Transition Wavelengths in nm. (* Transition \
wavelengths in nm *)\n\nThe CSV file contains the same information as the \
tabular file. \n\nThe function also creates a notebook with a Manipulate that \
allows the user to select a wavelength interval and a lifetime power of ten. \
The results notebook is saved in the examples directory.\n\nThe function \
takes the following options: \n    - \"Make Notebook\" -> True or False. If \
True, the results notebook is created. Default is True.\n    - \"Print \
Function\" -> PrintTemporary or Print. The function used to print the \
progress of the calculation. Default is PrintTemporary.\n    - \"Host\" -> \
\"CrystalHost\". The host material. Default is LaF3.\n    - \"Wavelength \
Range\" -> {50,2000}. The range of wavelengths in nm for the Manipulate \
object in the created notebook. Default is {50,2000}.\n\nThe function returns \
an association containing the following keys: Line Strength, AMD, fMD, \
Radiative lifetimes, Transition Energies / K, Transition Wavelengths in nm.", 
    "Documentation" -> None, "OwnValues" -> None, "UpValues" -> None, 
    "DownValues" -> 
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{$CellContext`MagneticDipoleTransitions[
         Pattern[$CellContext`params, 
          Blank[Association]], 
         Pattern[$CellContext`fname, 
          Blank[String]], 
         OptionsPattern[]] :> 
       Module[{$CellContext`numE, $CellContext`host, $CellContext`PrintFun, \
$CellContext`\[Lambda]Range, $CellContext`header, $CellContext`ln, \
$CellContext`energy\[CapitalDelta]}, $CellContext`paramKeys = 
          Keys[$CellContext`params]; Which[
           
           MemberQ[$CellContext`paramKeys, 
            qlanth`nE], $CellContext`numE = $CellContext`params[qlanth`nE], 
           
           MemberQ[$CellContext`paramKeys, 
            "nE"], $CellContext`numE = $CellContext`params["nE"], 
           
           MemberQ[$CellContext`paramKeys, 
            "numE"], $CellContext`numE = $CellContext`params["numE"], True, 
           Print["The number of electrons was not specified in params, \
exiting ..."]; Return[Null]; Null]; $CellContext`host = 
          OptionValue["Host"]; $CellContext`\[Lambda]Range = 
          OptionValue["Wavelength Range"]; $CellContext`PrintFun = 
          OptionValue[
           "Print Function"]; {$CellContext`\[Lambda]min, $CellContext`\
\[Lambda]max} = 
          OptionValue["Wavelength Range"]; $CellContext`header = {
           "\[Psi]i:simple", "\[Psi]f:simple", "\[Psi]i:idx", "\[Psi]f:idx", 
            "Ei/K", "Ef/K", "\[Lambda]/nm", "\[CapitalDelta]\[Lambda]/nm", 
            "\[Tau]/s", "AMD/s^-1"}; $CellContext`ln = 
          Part[{"Ce", "Pr", "Nd", "Pm", "Sm", "Eu", "Gd", "Tb", "Dy", "Ho", 
             "Er", "Tm", 
             "Yb"}, $CellContext`numE]; {$CellContext`eigenEnergies, \
$CellContext`ln, $CellContext`simplerStateLabels, $CellContext`eigensys, \
$CellContext`basis, $CellContext`truncatedStates} = 
          Import[$CellContext`fname]; Clear[$CellContext`truncatedStates]; 
         Clear[$CellContext`basis]; If[
           
           OddQ[$CellContext`numE], $CellContext`eigenEnergies = 
            Part[$CellContext`eigenEnergies, 
              Span[1, All, 2]]; $CellContext`simplerStateLabels = 
            Part[$CellContext`simplerStateLabels, 
              Span[1, All, 2]]; $CellContext`eigensys = 
            Part[$CellContext`eigensys, 
              Span[1, All, 2]]; 
           Null]; $CellContext`eigenEnergies = $CellContext`eigenEnergies - 
           Part[$CellContext`eigenEnergies, 
            1]; $CellContext`magIon = <||>; $CellContext`PrintFun[
          "Calculating the M1 spontaneous transition rates ..."]; \
$CellContext`magIon["AMD"] = 
          qlanth`MagDipoleRates[$CellContext`eigensys, $CellContext`numE, 
            "Units" -> "SI", "Lifetime" -> False]; $CellContext`magIon["AMD"] = 
          ReplaceAll[
            $CellContext`magIon["AMD"], {
            0. -> Indeterminate}]; $CellContext`PrintFun[
          "Calculating the oscillator strength for transitions from the \
ground state ..."]; $CellContext`magIon["fMD"] = 
          qlanth`GroundMagDipoleOscillatorStrength[$CellContext`eigensys, \
$CellContext`numE]; $CellContext`PrintFun[
          "Calculating the natural radiative lifetimes ..."]; \
$CellContext`magIon["Radiative lifetimes"] = 
          1./$CellContext`magIon["AMD"]; $CellContext`PrintFun[
          "Calculating the transition energies in K ..."]; \
$CellContext`transitionEnergies = Outer[Subtract, 
            Map[First, $CellContext`eigensys], 
            Map[First, $CellContext`eigensys]]; $CellContext`magIon[
           "Transition Energies / K"] = 
          misc`ReplaceDiagonal[$CellContext`transitionEnergies, 
            Indeterminate]; $CellContext`PrintFun[
          "Calculating the transition wavelengths in nm ..."]; \
$CellContext`magIon["Transition Wavelengths in nm"] = 
          10^7/$CellContext`magIon[
           "Transition Energies / K"]; $CellContext`energy\[CapitalDelta] = 
          OptionValue["Energy Uncertainty in K"]; $CellContext`PrintFun[
          "Estimating the uncertainties in \[Lambda]/nm assuming a " <> 
           ToString[$CellContext`energy\[CapitalDelta]] <> 
           " K uncertainty in energies."]; $CellContext`\[Lambda]uncertainty = \
$CellContext`energy\[CapitalDelta] Sqrt[2.] 
           10^(-7) $CellContext`magIon[
             "Transition Wavelengths in nm"]^2; $CellContext`PrintFun[
          "Formatting a tabular output file ..."]; $CellContext`startTime = 
          Now; $CellContext`numEigenvecs = 
          Length[$CellContext`eigensys]; $CellContext`roundedEnergies = 
          Round[$CellContext`eigenEnergies, 1.]; $CellContext`simpleFromTo = 
          Outer[{#, #2}& , $CellContext`simplerStateLabels, \
$CellContext`simplerStateLabels]; $CellContext`fromTo = Outer[{#, #2}& , 
            Range[$CellContext`numEigenvecs], 
            Range[$CellContext`numEigenvecs]]; $CellContext`energyPairs = 
          Outer[{#, #2}& , $CellContext`roundedEnergies, \
$CellContext`roundedEnergies]; $CellContext`allTransitions = \
{$CellContext`simpleFromTo, $CellContext`fromTo, $CellContext`energyPairs, 
            $CellContext`magIon[
            "Transition Wavelengths in nm"], \
$CellContext`\[Lambda]uncertainty, 
            $CellContext`magIon["AMD"], 
            $CellContext`magIon[
            "Radiative lifetimes"]}; $CellContext`allTransitions = 
          Map[Flatten, 
            Transpose[
             Map[
             Flatten[#, 
               1]& , $CellContext`allTransitions]]]; \
$CellContext`allTransitions = 
          Select[$CellContext`allTransitions, Part[#, 3] != 
            Part[#, 4]& ]; $CellContext`allTransitions = 
          Select[$CellContext`allTransitions, Part[#, 10] > 
            0& ]; $CellContext`allTransitions = 
          Transpose[$CellContext`allTransitions]; $CellContext`endTime = 
          Now; $CellContext`PrintFun[">> Formatting the tabular output took ", 
           
           QuantityMagnitude[$CellContext`endTime - $CellContext`startTime, 
            "Seconds"], " seconds."]; $CellContext`PrintFun[
          "Rounding wavelengths according to estimated uncertainties ..."]; \
$CellContext`starTime = 
          Now; {$CellContext`roundedWaves, $CellContext`roundedDeltas} = 
          Transpose[
            MapThread[misc`RoundValueWithUncertainty, {
              Part[$CellContext`allTransitions, 7], 
              Part[$CellContext`allTransitions, 8]}]]; 
         Part[$CellContext`allTransitions, 7] = $CellContext`roundedWaves; 
         Part[$CellContext`allTransitions, 
            8] = $CellContext`roundedDeltas; $CellContext`endTime = 
          Now; $CellContext`PrintFun[">> Rounding the wavelengths took ", 
           
           QuantityMagnitude[$CellContext`endTime - $CellContext`startTime, 
            "Seconds"], " seconds."]; $CellContext`PrintFun[
          "Rounding lifetimes and transition rates to three significant \
figures ..."]; $CellContext`startTime = Now; 
         Part[$CellContext`allTransitions, 9] = 
          Map[misc`RoundToSignificantFigures[#, 3]& , 
            Part[$CellContext`allTransitions, 9]]; 
         Part[$CellContext`allTransitions, 10] = 
          Map[misc`RoundToSignificantFigures[#, 3]& , 
            Part[$CellContext`allTransitions, 10]]; $CellContext`finalTable = 
          Transpose[$CellContext`allTransitions]; $CellContext`finalTable = 
          Prepend[$CellContext`finalTable, $CellContext`header]; \
$CellContext`endTime = Now; $CellContext`PrintFun[
          ">> Rounding the lifetimes and transition rates took ", 
           
           QuantityMagnitude[$CellContext`endTime - $CellContext`startTime, 
            "Seconds"], " seconds."]; $CellContext`basename = $CellContext`ln <> 
           " in " <> $CellContext`host <> " - ql - " <> 
           "M1 - tabular.zip"; $CellContext`exportFname = FileNameJoin[{
             
             DirectoryName[$CellContext`fname], $CellContext`basename}]; \
$CellContext`PrintFun[
          "Exporting tabular data to " <> $CellContext`exportFname <> 
           " ..."]; $CellContext`starTime = Now; $CellContext`exportKey = 
          StringReplace[$CellContext`basename, ".zip" -> ".m"]; 
         Export[$CellContext`exportFname, <|$CellContext`exportKey -> \
$CellContext`finalTable|>]; $CellContext`endTime = Now; $CellContext`PrintFun[
          ">> Exporting the tabular data took ", 
           
           QuantityMagnitude[$CellContext`endTime - $CellContext`starTime, 
            "Seconds"], " seconds."]; $CellContext`basename = $CellContext`ln <> 
           " in " <> $CellContext`host <> " - ql - " <> 
           "M1 - raw.zip"; $CellContext`rawexportFname = FileNameJoin[{
             
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*)