<description/> <author>Andrei Tokmakoff</author> <company/> <keywords/> <revisedBy>Andrei Tokmakoff</revisedBy> </userData> <identityInfo> <revision>9</revision> <documentID>3AB81A94-E75D-4747-9553-79589730C015</documentID> <versionID>2A0961C2-722F-4930-AC0E-1F6285578926</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> 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<currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="611" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="601" left="18" top="12.75" width="382.5" height="28.5" align-x="18" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">Absorption Lineshape for the Displaced Harmonic Oscillator Model </inlineAttr> </f> </text> </region> <region region-id="602" left="18" top="32.25" width="478.5" height="24" align-x="18" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11">Investigate the low temperature lineshape for electronic transition coupled to a single harmonic mode.</f> </text> </region> <region region-id="603" left="18" top="50.25" width="351.75" height="12" align-x="18" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11">We will perform calculations for t</f> <f family="Arial" charset="0" size="11"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">hree couplings: weak medium, and strong:</inlineAttr> </f> </text> </region> <region region-id="504" left="390" top="51" width="44.25" height="12.75" align-x="400.5" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="D1B9BA29-FF8C-4765-9391-28CBAEA23201" version-id="B87CFA29-400F-4290-A6DA-165F4767DEF2" branch-id="00000000-0000-0000-0000-000000000000" revision-num="1" is-modified="false" region-id="0" href="D:\Documents\5.74\2009\MathCad\7.3._Gaussian-Stochastic_model_for_lineshape.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>0da188e30e1802fc9ebc735e2644b593</hash> </originRef> <parentRef doc-id="D1B9BA29-FF8C-4765-9391-28CBAEA23201" version-id="B87CFA29-400F-4290-A6DA-165F4767DEF2" branch-id="00000000-0000-0000-0000-000000000000" 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show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Lets work in units of </text> </region> <region region-id="394" left="144" top="69" width="38.25" height="12.75" align-x="169.5" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">hbar</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="395" left="210" top="69" width="32.25" height="15" align-x="229.5" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="eg">μ</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="396" left="258" top="69" width="26.25" height="12.75" align-x="271.5" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="605" left="18" top="98.25" width="207" height="36" align-x="18" align-y="108" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Define the frequency of the electronic transition: <tab/> <tab/> <sp count="3"/>and the vibrational frequency: </text> </region> <region region-id="178" 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Set up displacement grid </text> </region> <region region-id="379" left="162" top="147" width="42.75" height="12.75" align-x="171" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>200</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="380" left="240" top="147" width="65.25" height="18" align-x="254.25" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">q</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:real>-5</ml:real> <ml:apply> <ml:mult/> <ml:real>0.05</ml:real> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="607" left="18" top="164.25" width="72" height="12" align-x="24" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Set up time grid<tab/> </text> </region> <region region-id="372" left="240" top="165" width="36.75" height="18" align-x="252" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id 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<ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">q</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:id xml:space="preserve">hbar</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="559" left="348" top="300" width="179.25" height="159" align-x="348" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="15"/> <rendering item-idref="16"/> </region> <region region-id="611" left="18" top="356.25" width="282.75" height="24" align-x="38.25" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11">Lineshape function, Dephasing function and dipole correlation function </f> </text> </region> <region region-id="565" left="60" top="384.75" width="117.75" height="21" align-x="93.75" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="567" left="60" top="438.75" width="147.75" height="23.25" align-x="94.5" align-y="456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">C</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="eg">μ</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">-1</ml:imag> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="326" left="24" top="494.25" width="364.5" height="12" align-x="31.5" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="11">Plot the correlation function and dephasing function for low and high coupling</f> </text> </region> <region region-id="541" left="156" top="519" width="41.25" height="18" align-x="172.5" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.2</ml:real> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="542" left="378" top="519" width="34.5" height="18" align-x="394.5" align-y="528" 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disable-calc="false" item-idref="24"/> <rendering item-idref="25"/> </region> <region region-id="348" left="24" top="734.25" width="102.75" height="12" align-x="24" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="11">Absorption lineshape:</f> </text> </region> <region region-id="349" left="54" top="759" width="86.25" height="12.75" align-x="78" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">g</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:equal/> <ml:id 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<ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0.25</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="eg">μ</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">exp</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="345" left="24" top="926.25" width="218.25" height="12" align-x="24" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="11">Plot lineshapes for low, mid and high coupling.</f> </text> </region> <region region-id="235" left="150" top="954" width="317.25" height="150" align-x="150" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="29"/> <rendering item-idref="30"/> </region> <region region-id="31" left="60" top="957" width="12.75" height="12.75" align-x="65.25" align-y="966" show-border="false" 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<ml:apply> <ml:indexer/> <ml:id xml:space="preserve">q</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:real>-5</ml:real> <ml:apply> <ml:mult/> <ml:real>0.05</ml:real> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="607" left="18" top="164.25" width="72" height="12" align-x="24" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Set up time grid<tab/> </text> </region> <region region-id="372" left="240" top="165" width="36.75" height="18" align-x="252" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">i</ml:id> <ml:real>0.1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="608" left="18" top="182.25" width="95.25" height="12" align-x="18" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Set up frequency grid: </text> </region> <region region-id="374" left="240" top="183" width="92.25" height="18" align-x="255.75" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>-4</ml:real> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0.05</ml:real> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="508" left="372" top="192" width="24" height="71.25" align-x="377.25" align-y="210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:sequence> <ml:real>0.2</ml:real> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:sequence> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="609" left="18" top="212.25" width="257.25" height="12" align-x="18" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11">The unitless displacement of the two harmonic wells is:</f> </text> </region> <region region-id="610" left="18" top="260.25" width="242.25" height="12" align-x="32.25" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11">Ground and excited state potential energy surfaces</f> </text> </region> <region region-id="551" left="36" top="284.25" width="93" height="27.75" align-x="69" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="g">V</ml:id> <ml:boundVars> <ml:id xml:space="preserve">qx</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">qx</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="552" left="162" top="276.75" width="186.75" height="37.5" align-x="201.75" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="e">V</ml:id> <ml:boundVars> <ml:id xml:space="preserve">q</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">q</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:id xml:space="preserve">hbar</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="559" left="348" top="300" width="179.25" height="159" align-x="348" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="15"/> <rendering item-idref="16"/> </region> <region region-id="611" left="18" top="356.25" width="282.75" height="24" align-x="38.25" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11">Lineshape function, Dephasing function and dipole correlation function </f> </text> </region> <region region-id="565" left="60" top="384.75" width="117.75" height="21" align-x="93.75" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">g</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">-1</ml:imag> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="566" left="60" top="417" width="79.5" height="18.75" align-x="93.75" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="567" left="60" top="438.75" width="147.75" height="23.25" align-x="94.5" align-y="456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">C</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="eg">μ</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">-1</ml:imag> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="326" left="24" top="494.25" width="364.5" height="12" align-x="31.5" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="11">Plot the correlation function and dephasing function for low and high coupling</f> </text> </region> <region region-id="541" left="156" top="519" width="41.25" height="18" align-x="172.5" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.2</ml:real> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="542" left="378" top="519" width="34.5" height="18" align-x="394.5" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:real>2</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="543" left="6" top="534" width="288.75" height="183" align-x="6" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="22"/> <rendering item-idref="23"/> </region> <region region-id="544" left="288" top="534" width="244.5" height="159.75" align-x="288" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="24"/> <rendering item-idref="25"/> </region> <region region-id="348" left="24" top="734.25" width="102.75" height="12" align-x="24" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="11">Absorption lineshape:</f> </text> </region> <region region-id="349" left="54" top="759" width="86.25" height="12.75" align-x="78" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">g</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">g</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="350" left="54" top="775.5" width="233.25" height="43.5" align-x="92.25" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">σ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="eg">μ</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">J</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:factorial/> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:id xml:space="preserve">δ</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">J</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:real>10</ml:real> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="346" left="24" top="830.25" width="158.25" height="12" align-x="24" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="11">Envelope of vibronic progression:</f> </text> </region> <region region-id="342" left="54" top="858" width="255.75" height="44.25" align-x="102.75" align-y="882" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Env</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0.25</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="eg">μ</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">exp</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve" subscript="eg">ω</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve" subscript="0">ω</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="345" left="24" top="926.25" width="218.25" height="12" align-x="24" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="11">Plot lineshapes for low, mid and high coupling.</f> </text> </region> <region region-id="235" left="150" top="954" width="317.25" height="150" align-x="150" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="29"/> <rendering item-idref="30"/> </region> <region region-id="31" left="60" top="957" width="12.75" height="12.75" align-x="65.25" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> </ml:parens> </math> <rendering item-idref="31"/> </region> <region region-id="139" left="90" top="957" width="41.25" height="18" align-x="106.5" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">D</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.2</ml:real> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="256" left="150" top="1110" width="317.25" height="150" align-x="150" align-y="1110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="33"/> <rendering item-idref="34"/> </region> <region region-id="257" left="66" top="1113" width="14.25" height="12.75" align-x="72" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> </ml:parens> </math> <rendering item-idref="35"/> </region> <region region-id="258" left="96" top="1113" width="34.5" height="18" align-x="112.5" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id 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