ChemWiki - User contributions [en]

Rep:Mod:NIK13additionalfiles

2016-03-11T13:12:26Z

Nik13: /* 1,5-hexadiene TS */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{|
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== 1,5-hexadiene TS ===
{|
|- align="center"
! Chair
! Boat
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13 TRANSITION STATES COPE CHAIRTS OPT+FREQ B3LYP631GD LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 13; rotate x -20</script>
<name>hdCH</name>
</jmolApplet>
<jmolbutton>
<script>frame 13; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script> frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script> frame 12; mo 24; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script>frame 13; measure 1 2; measure 2 5; measure 5 13; measure 13 10; measure 10 9; measure 9 1</script>
<text>C-C Distances</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>hdCH</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 13; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i566/cm</text>
<target>hdCH</target>
</item>
<item>
<script>frame 14; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>194/cm</text>
<target>hdCH</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13 TRANSITION STATES COPE BOATTS OPT+FREQ B3LYP631GD LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 35; rotate x -20</script>
<name>hdBT</name>
</jmolApplet>
<jmolbutton>
<script>frame 35; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script> frame 34; mo 23; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script> frame 34; mo 24; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script>frame 35; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1</script>
<text>C-C Distances</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>hdBT</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 35; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i530/cm</text>
<target>hdBT</target>
</item>
<item>
<script>frame 36; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>135/cm</text>
<target>hdBT</target>
</item>
</jmolmenu>

</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 77; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 77; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 77; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 1 14; measure 4 11</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 77; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i806/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 78; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>62/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 89; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 89; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 89; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 15 14; measure 16 11</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 89; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i812/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 90; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>61/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13additionalfiles

2016-03-11T13:10:57Z

Nik13: /* 1,5-hexadiene TS */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{|
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== 1,5-hexadiene TS ===
{|
|- align="center"
! Chair
! Boat
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13 TRANSITION STATES COPE CHAIRTS OPT+FREQ B3LYP631GD LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 13; rotate x -20</script>
<name>hdCH</name>
</jmolApplet>
<jmolbutton>
<script>frame 13; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script> frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script> frame 12; mo 245; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script>frame 13; measure 1 2; measure 2 5; measure 5 13; measure 13 10; measure 10 9; measure 9 1</script>
<text>C-C Distances</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>hdCH</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 13; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i566/cm</text>
<target>hdCH</target>
</item>
<item>
<script>frame 14; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>194/cm</text>
<target>hdCH</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13 TRANSITION STATES COPE BOATTS OPT+FREQ B3LYP631GD LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 35; rotate x -20</script>
<name>hdBT</name>
</jmolApplet>
<jmolbutton>
<script>frame 35; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script> frame 34; mo 23; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script> frame 34; mo 24; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script>frame 35; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1</script>
<text>C-C Distances</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>hdBT</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 35; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i530/cm</text>
<target>hdBT</target>
</item>
<item>
<script>frame 36; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>135/cm</text>
<target>hdBT</target>
</item>
</jmolmenu>

</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 77; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 77; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 77; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 1 14; measure 4 11</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 77; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i806/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 78; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>62/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 89; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 89; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 89; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 15 14; measure 16 11</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 89; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i812/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 90; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>61/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13additionalfiles

2016-03-11T13:09:37Z

Nik13:

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{|
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== 1,5-hexadiene TS ===
{|
|- align="center"
! Chair
! Boat
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13 TRANSITION STATES COPE CHAIRTS OPT+FREQ B3LYP631GD LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 13; rotate x -20</script>
<name>hdCH</name>
</jmolApplet>
<jmolbutton>
<script>frame 13; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script> frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script> frame 12; mo 245; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script>frame 13; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1</script>
<text>C-C Distances</text>
<target>hdCH</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>hdCH</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 13; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i566/cm</text>
<target>hdCH</target>
</item>
<item>
<script>frame 14; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>194/cm</text>
<target>hdCH</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13 TRANSITION STATES COPE BOATTS OPT+FREQ B3LYP631GD LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 35; rotate x -20</script>
<name>hdBT</name>
</jmolApplet>
<jmolbutton>
<script>frame 35; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script> frame 34; mo 23; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script> frame 34; mo 24; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script>frame 35; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1</script>
<text>C-C Distances</text>
<target>hdBT</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>hdBT</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 35; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i530/cm</text>
<target>hdBT</target>
</item>
<item>
<script>frame 36; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>135/cm</text>
<target>hdBT</target>
</item>
</jmolmenu>

</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 77; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 77; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 77; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 1 14; measure 4 11</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 77; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i806/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 78; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>62/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 89; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 89; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 89; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 15 14; measure 16 11</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 89; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i812/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 90; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>61/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

User:Nik13

2016-03-11T13:07:27Z

Nik13:

Hello, Adi <3

( ͡° ͜ʖ ͡°)

Article list:

[[Mod:NIK13|Transition States write-up]]

[[Mod:NIK13additionalfiles|Transition States movable molecules]]

File upload list:
Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2
Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol
NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2
Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol
NIK13 TRANSITION STATES COPE CHAIRTS OPT+FREQ B3LYP631GD LOGMOS.LOG
NIK13 TRANSITION STATES COPE BOATTS OPT+FREQ B3LYP631GD LOGMOS.LOG

[[:File:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png]]

File:NIK13 TRANSITION STATES COPE BOATTS OPT+FREQ B3LYP631GD LOGMOS.LOG

2016-03-11T13:07:09Z

Nik13: JSmol (log) 1,5-hexadiene BOAT

JSmol (log) 1,5-hexadiene BOAT

User:Nik13

2016-03-11T12:58:04Z

Nik13:

Hello, Adi <3

( ͡° ͜ʖ ͡°)

Article list:

[[Mod:NIK13|Transition States write-up]]

[[Mod:NIK13additionalfiles|Transition States movable molecules]]

File upload list:
Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2
Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol
NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2
Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol
NIK13 TRANSITION STATES COPE CHAIRTS OPT+FREQ B3LYP631GD LOGMOS.LOG

[[:File:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png]]

File:NIK13 TRANSITION STATES COPE CHAIRTS OPT+FREQ B3LYP631GD LOGMOS.LOG

2016-03-11T12:57:26Z

Nik13: JSmol (log) 1,5-hexadiene CHAIR

JSmol (log) 1,5-hexadiene CHAIR

Rep:Mod:NIK13additionalfiles

2016-03-11T12:43:37Z

Nik13: /* Cyclohexa-1,3-diene + Maleic Anhydride TS */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 77; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 77; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 77; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 1 14; measure 4 11</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 77; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i806/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 78; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>62/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 89; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 89; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 89; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12; measure 15 14; measure 16 11</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 89; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i812/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 90; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>61/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13additionalfiles

2016-03-11T12:41:39Z

Nik13: /* Cyclohexa-1,3-diene + Maleic Anhydride TS */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 77; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 77; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 77; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 77; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i806/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 78; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>62/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 89; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 89; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 89; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 89; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i812/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 90; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>61/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13additionalfiles

2016-03-11T12:41:07Z

Nik13: /* Cyclohexa-1,3-diene + Maleic Anhydride TS */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 77; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 77; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 77; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 77; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i806/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 78; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>62/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 89; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 89; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 89; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 89; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i812/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 90; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>61/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13additionalfiles

2016-03-11T12:39:45Z

Nik13: /* Cyclohexa-1,3-diene + Maleic Anhydride TS */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 77; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 77; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 76; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 77; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 77; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 78; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 89; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 89; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 34; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 88; mo 35; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 89; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 89; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 90; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13

2016-03-11T12:36:05Z

Nik13: /* g) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| class="wikitable" align="centre"
|- align="centre"
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_gauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT+FREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt+Freq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
|
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>frame 76; mo 34; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>frame 88; mo 34; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T12:35:12Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| class="wikitable" align="centre"
|- align="centre"
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_gauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT+FREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt+Freq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>frame 76; mo 34; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>frame 88; mo 34; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T12:33:06Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| class="wikitable" align="centre"
|- align="centre"
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_gauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT+FREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt+Freq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T12:32:38Z

Nik13: /* g) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| class="wikitable" align="centre"
|- align="centre"
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_gauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT+FREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt+Freq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13additionalfiles

2016-03-11T12:32:01Z

Nik13: /* Cyclohexa-1,3-diene + Maleic Anhydride TS */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

File:NIK13 TRANSITION STATES BII CH13DENE-MALANH OPT+FREQ TSBERNY FC SEMIAM1 NOEIGEN EXO LOGMOS.LOG

2016-03-11T12:30:42Z

Nik13: Nik13 uploaded a new version of File:NIK13 TRANSITION STATES BII CH13DENE-MALANH OPT+FREQ TSBERNY FC SEMIAM1 NOEIGEN EXO LOGMOS.LOG

JSmol file for cyclohexa-1,3-diene + maleic anhydride EXO

Rep:Mod:NIK13additionalfiles

2016-03-11T12:29:24Z

Nik13: /* 1,5-Hexadiene anti2 */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; measure 6 1; measure 1 2; measure 2 3; measure 3 4; measure 4 5</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13

2016-03-11T12:19:07Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| class="wikitable" align="centre"
|- align="centre"
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_gauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13additionalfiles

2016-03-11T12:14:04Z

Nik13:

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>HFhd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>HFhd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>HFhd</target>
</jmolbutton>
</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 61; rotate x -20</script>
<name>B3hd</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>B3hd</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>B3hd</target>
</jmolbutton>
</jmol>
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

Rep:Mod:NIK13additionalfiles

2016-03-11T12:09:53Z

Nik13: /* 1,5-Hexadiene anti2 */

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| class="wikitable"
! HF/3-21G
! B3LYP/6-31G*
|-
|
jmol
|
jmol
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

User:Nik13

2016-03-11T12:09:03Z

Nik13:

Hello, Adi <3

( ͡° ͜ʖ ͡°)

Article list:

[[Mod:NIK13|Transition States write-up]]

[[Mod:NIK13additionalfiles|Transition States movable molecules]]

File upload list:
Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2
Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol
NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2
Nik13_Transition_States_A_15hdene_Opt_HF321G_anti2.mol

[[:File:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png]]

File:Nik13 Transition States A 15hdene Opt HF321G anti2.mol

2016-03-11T12:08:46Z

Nik13: anti2 HF321G

anti2 HF321G

Rep:Mod:NIK13additionalfiles

2016-03-11T12:07:05Z

Nik13:

Welcome to the page containing Nathaniel Keymer's additional files from his [[Mod:NIK13|Transition States Wiki write up]].

=== 1,5-Hexadiene anti2 ===
{| style="text-align:centre"
! HF/3-21G
! B3LYP/6-31G*
|-
|
jmol
|
jmol
|}

=== Butadiene + Ethylene TS ===
<jmol> //Group all the HTML within "jmol"
<jmolApplet> //Initialise the applet
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script> //Set the variables (vibrating and spinning) as the applet initialises.
<name>EthBut</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EthBut</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i956/cm</text>
<target>EthBut</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>EthBut</target>
</item>
</jmolmenu>

</jmol>

=== Cyclohexa-1,3-diene + Maleic Anhydride TS ===
{|
|- align="center"
! Endo
! Exo
|- align="center"
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMEndo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>EthBut</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMEndo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMEndo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMEndo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMEndo</target>
</item>
</jmolmenu>

</jmol>
|
<jmol>
<jmolApplet>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; mo OFF; frame 61; rotate x -20</script>
<name>CMExo</name>
</jmolApplet>
<jmolbutton>
<script>frame 61; if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>HOMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script> frame 60; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
<text>LUMO</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>frame 61; measure 2 12; measure 3 9; measure 1 4; measure 1 2; measure 3 4; measure 9 12</script>
<text>C-C Distances</text>
<target>CMExo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>CMExo</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 61; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i956/cm</text>
<target>CMExo</target>
</item>
<item>
<script>frame 62; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>147/cm</text>
<target>CMExo</target>
</item>
</jmolmenu>

</jmol>
|}

User:Nik13

2016-03-11T12:00:02Z

Nik13:

Hello, Adi <3

( ͡° ͜ʖ ͡°)

Article list:

[[Mod:NIK13|Transition States write-up]]

[[Mod:NIK13additionalfiles|Transition States movable molecules]]

File upload list:
Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2
Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol
NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2

[[:File:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png]]

Rep:Mod:NIK13

2016-03-11T11:59:38Z

Nik13: /* c) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| class="wikitable" align="centre"
|- align="centre"
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_anti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_HF321G_gauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

File:Nik13 Transition States A 15hdene Opt HF321G gauche3.mol

2016-03-11T11:58:53Z

Nik13: gauche3

gauche3

File:Nik13 Transition States A 15hdene Opt HF321G anti1.mol

2016-03-11T11:57:48Z

Nik13: anti1

anti1

Rep:Mod:NIK13

2016-03-11T11:56:18Z

Nik13: /* c) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| class="wikitable" align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:54:08Z

Nik13: /* g) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_15hdene_Opt_B3LYP631Gd_anti2.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_A_COPE_CHAIRTS_OPT%2BFREQ_B3LYP631GD.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Nik13_Transition_States_A_Cope_boatTS_Opt%2BFreq_B3LYP631Gd.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

File:NIK13 TRANSITION STATES A COPE CHAIRTS OPT+FREQ B3LYP631GD.mol2

2016-03-11T11:51:12Z

Nik13: chairTS

chairTS

File:Nik13 Transition States A Cope boatTS Opt+Freq B3LYP631Gd.mol

2016-03-11T11:50:48Z

Nik13: boatTS

boatTS

File:Nik13 Transition States A 15hdene Opt B3LYP631Gd anti2.mol2

2016-03-11T11:50:12Z

Nik13: anti2

anti2

Rep:Mod:NIK13

2016-03-11T11:45:41Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of anti2}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of chair}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of boat}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:45:23Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of anti2}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of chair}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of boat}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:41:08Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of anti2}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of chair}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of boat}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:37:55Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of anti2}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of chair}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of boat}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG</uploadedFileContents>
<script>mo 1; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

User:Nik13

2016-03-11T11:36:46Z

Nik13:

Hello, Adi <3

( ͡° ͜ʖ ͡°)

Article list:

[[Mod:NIK13|Transition States write-up]]

[[Mod:NIK13additionalfiles|Transition States movable molecules]]

File upload list:

[[:File:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_EXO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png]]

File:NIK13 TRANSITION STATES BII CH13DENE-MALANH OPT+FREQ TSBERNY FC SEMIAM1 NOEIGEN EXO LOGMOS.LOG

2016-03-11T11:35:54Z

Nik13: JSmol file for cyclohexa-1,3-diene + maleic anhydride EXO

JSmol file for cyclohexa-1,3-diene + maleic anhydride EXO

Rep:Mod:NIK13

2016-03-11T11:34:21Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of anti2}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of chair}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of boat}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

User:Nik13

2016-03-11T11:32:16Z

Nik13:

Hello, Adi <3

( ͡° ͜ʖ ͡°)

Article list:

[[Mod:NIK13|Transition States write-up]]

[[Mod:NIK13additionalfiles|Transition States movable molecules]]

File upload list:

[[:File:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png]]

[[:File:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN.LOG]]

[[:File:NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_BDENE-EENE_OPT+FREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen.mol]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png]]

[[:File:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png]]

[[:File:NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG|NIK13_TRANSITION_STATES_BII_CH13DENE-MALANH_OPT%2BFREQ_TSBERNY_FC_SEMIAM1_NOEIGEN_ENDO_LOGMOS.LOG]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Endo_HOMO_top.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_side.png]]

[[:File:Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png|Nik13_Transition_States_Bii_ch13dene-malanh_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_Exo_HOMO_top.png]]

File:NIK13 TRANSITION STATES BII CH13DENE-MALANH OPT+FREQ TSBERNY FC SEMIAM1 NOEIGEN ENDO LOGMOS.LOG

2016-03-11T11:31:18Z

Nik13: JSmol file cyclohexa-1,3-diene + maleic anhydride ENDO

JSmol file cyclohexa-1,3-diene + maleic anhydride ENDO

Rep:Mod:NIK13

2016-03-11T11:14:09Z

Nik13: /* g) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

{| border="2" cellpadding="5"
|-align="center"
!
! anti2
! chair form
! boat form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of anti2}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of chair}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of boat}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -234.61171062
| -234.54309263
| -234.55698303
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
|
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:07:40Z

Nik13: /* f) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

'''Predictions of which conformers lead from which transition state'''
{| class="wikitable"
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:06:56Z

Nik13: /* f) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

{| class="wikitable"
|- align="center"
! rowspan="2" | Predictions of which conformers lead from which transition state
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:06:22Z

Nik13: /* f) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

{| class="wikitable"
! rowspan="2" | Predictions of which conformers lead from which transition state
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:05:31Z

Nik13: /* f) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

{| class="wikitable"
! rowspan="2" | Predictions of which conformers lead from which transition state
!
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:04:59Z

Nik13: /* f) */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

{| class="wikitable"
! rowspan="2" | Predictions of which conformers lead from which transition state
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T11:04:28Z

Nik13: /* Optimizing the "Chair" and "Boat" Transition Structures */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

{| class:"wikitable"
! rowspan="2" | Predictions of which conformers lead from which transition state
|- align="center"
! Chair TS
! Boat TS
|- align="center"
| gauche2
| gauche1
|- align="center"
| gauche5
| gauche3
|- align="center"
| anti1
| gauche 4
|- align="center"
|
| gauche6
|- align="center"
|
| anti2
|- align="center"
|
| anti3
|- align="center"
|
| anti4
|}

An IRC optimisation was performed on the chair transition structure. It was chosen that the optimisation should proceed only in the forwards direction (as it would be symmetrical), that the force constant should be calculated at every step and that there should be 60 steps. When the calculation ran out of steps, it was observed that the structure looked similar to '''gauche2'''. Therefore, a normal optimisation to minimum at the HF/3-21G level was run, giving '''gauche2'''. After the IRC, the energy was -231.69157889 hartrees and the point group was C1. After the second optimisation, the energy was -231.69166702 and the point group was C2.

=== g) ===

Both chair and boat structures were optimised to a transition state using the Berny method at the B3LYP/6-31G* level.

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />

Rep:Mod:NIK13

2016-03-11T10:43:43Z

Nik13: /* The reaction of cyclohexa-1,3-diene and maleic anhydride */

To view the molecules mentioned in this Wiki dynamically, please click [[Mod:NIK13additionalfiles|here]].

= Module 3: Transition Structures =
The computational study of transition structures is useful both as a method of studying a reaction and as a predictive tool for determining the likely structure of the products or the reactants. It can be used to assess the energy barrier a reaction faces and give an understanding of the mechanism through an assessment of the associated molecular orbitals. It is a powerful tool in the chemical toolbox, both for investigating the reactions we don't understand and for clarifying the reactions we do.

This Wiki will discuss the exercises and calculations set out in the [[Mod:phys3|Transition Sates script]].

= The Cope Rearrangement Tutorial =

== Optimizing the Reactants and Products ==

Throughout this section, reference is made to the conformations of 1,5-hexadiene, the structures of which may be found [[Mod:phys3_appendix1|here]].

=== a) ===
A structure of 1,5-hexadiene with an "anti" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''anti1''' conformation, with energy -231.69260235 hartrees and point group C2

=== b) ===
A structure of 1,5-hexadiene with an "gauche" linkage was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It turned out to be the '''gauche6''' conformation, with energy -231.68916020 hartrees and point group C1

As expected, the conformation generated for '''b)''' was of higher energy than that generated for '''a)''' due to the steric clashes a gauche linkage requires.

=== c) ===
'''anti2''' looks as though it might be the lowest energy conformer, as it seems to have the fewest steric interactions. It was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69253523 hartrees and point group C<sub>i</sub>.

'''gauche3''' was created from the cyclohexane fragment and optimised to a minimum at the HF/3-21G level of theory. It has energy -231.69266122 hartrees and point group C1.

The π* orbitals in '''anti1''', '''anti2''' and '''gauche3''' all conjugate with σ* orbitals on the corresponding 3 or 4 atom. This creates a shortening and a strengthening on the C<sub>2</sub>-C<sub>3</sub> and C<sub>4</sub>-C<sub>5</sub> bonds. In '''anti1''' and '''anti2''', this conjugation is with C-C antibonds; in '''gauche3''', it is with C-H antibonds. '''gauche3''' is therefore less destabilised by this interaction.

{| align="centre"
|- align="centre"
| {{fontcolor1|white|red|anti1}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|anti2}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
| {{fontcolor1|white|red|gauche3}}
<nowiki>
<jmol> <jmolApplet> <title></title><color>white</color><size>200</size> <uploadedFileContents>Phys3_gauche.log</uploadedFileContents> <script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script> </jmolApplet> </jmol>
</nowiki>
|- align="centre"
| '''anti1'''
| '''anti2'''
| '''gauche3'''
|}

=== d) ===
The structures created in '''a)''' were '''anti1''' and '''gauche6'''.

=== e) ===
'''anti2''' was created in '''c)'''. The energy is in good agreement with [[Mod:phys3_appendix1|that provided]].

=== f) ===
'''anti2''' was optimised to a further minimum at the B3LYP/6-31G* level. It was returned with energy -234.61171062 hartrees and point group C<sub>i</sub>. [[Mod:NIK13additionalfiles#1,5-Hexadiene anti2|The geometry barely changed]].

=== g) ===
A frequency calculation was run on '''anti2''' at the B3LYP/6-31G* level. There were no imaginary frequencies in the resulting Vibrations output.

[[Image:Nik13_Transition_States_A_15hdene_Freq_B3LYP631Gd_anti2_predicted_IR_spectrum.png|frame|center|anti2 predicted IR spectrum]]

{| class="wikitable"
|- align="center"
! Sum of electronic and<br>zero-point Energies<br>/ hartrees
! Sum of electronic and<br>thermal Energies<br>/ hartrees
! Sum of electronic and<br>thermal Enthalpies<br>/ hartrees
! Sum of electronic and<br>thermal free Energies<br>/hartrees
|- align="center"
| -234.469219
| -234.461869
| -234.460925
| -234.500809
|}

== Optimizing the "Chair" and "Boat" Transition Structures ==

=== a) ===

A first guess at the 1,5-cyclohexadiene chair transition structure was constructed out of two (CH<sub>2</sub>-CH-CH<sub>2</sub>) units, which in turn were created from the propane fragment.

=== b) ===

The 1,5-hexadiene chair was optimised to a transition state using the Berny method at the HF/3-21G level. At the same time, a frequency calculation was run on it. There was one imaginary frequency at -187.91 cm<sup>-1</sup>, in line with expectation. Imaginary frequencies are the compuational manifestation of the restoring force of the quantum harmonic oscilator, acting against bond formation. If there were a bond there, it would resonate at the same magnitude of frequency. As there is no bond, we can only imagine - and calculate - what it would be like if there were one.

=== c) ===

An optimisation of the 1,5-hexadiene chair was set up using frozen coordinates. The atoms that would be forming bonds were frozen and the rest of the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

=== d) ===

An optimisation of the 1,5-hexadiene chair was set up using unfrozen coordinates. The atoms that would be forming bonds were set to derivative and the molecule was optimised to a transition state using the Berny method at the HF/3-21G level.

{| class="wikitable" align="center"
|- align="center"
!
! b) Standard Optimisation
! c,d) Frozen Optimisation
|- align="center"
| C<sub>1</sub>-C<sub>6</sub> new bond length / Å
| 2.02049
| 2.02069
|- align="center"
| C<sub>3</sub>-C<sub>4</sub> new bond length / Å
| 2.02036
| 2.02059
|}

The geometries of the two structures are very similar. The standard optimisation produced slightly shorter bond lengths, but the two methods give very similar results.

=== e) ===

1,5-hexadiene boat was optimised to a transition state using the QST2 method at the HF/3-21G level. It produced a viable transition structure with an imaginary frequency of -839.62 cm<sup>-1</sup>

=== f) ===

=== g) ===

= The Diels-Alder Cycloaddition =

== The reaction of butadiene and ethylene ==
C''is-''butadiene and ethylene were created from the ''n''-butane and ethane pre-loaded fragments respectively and were optimised to a minimum at the semi-empirical AM1 level. Their addition transition state was created from the bicyclo[2.2.2]octane pre-loaded fragment with an inter-fragment distance was set to 2.2 Å and (after a few attempts without the opt=NoEigen keyword) was optimised to a transition state using the Berny method at the semi-empirical AM1 level. There was a single imaginary vibrational frequency at -955.99 cm<sup>-1</sup>, indicating that this was a transition state.

The [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|two new bonds]] are being formed synchronously. The four carbon atoms are extending directly towards each other at the same time. In contrast, the lowest real (positive) frequency is given by a transverse vibration: the two fragments rotate with respect to each other, in turn drawing each pair of carbon atoms closer together and temporarily increasing the bond order of each bond. This is asynchronous bond formation.

The HOMO-LUMO pairs in butadiene and ethylene must be of the right symmetry in order to be able to react. As can be seen from their calculated molecular orbitals (below), they are indeed. Not only are they of just the right symmetries, but they align in space well and have good orbital overlap. The two orbitals forming the transition state HOMO are antisymmetric relative to the plane of symmetry of the transition state, making the HOMO antisymmetric, and those forming the LUMO are symmetric, which makes the LUMO symmetric. The reaction is favoured by there being multiple MOs interacting. For this reason, Diels-Alder is a fairly facile reaction, and it can be favoured further, as will be seen below.

[[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|The partly formed bonds are calculated to be 2.12 Å long]]. To put this in context, the [[w:Nominative_determinism|appropriately named]] A Bondi puts the mean van der Waals radius of carbon at 1.70 Å.<ref name="j100785a001">A Bondi, "van der Waals Volumes and Radii", ''J. Phys. Chem.'', '''1964''', ''68 (3)'', 441-451.{{DOI|10.1021/j100785a001}}</ref> Experimental data shows C-C bond lengths in cyclohexene to be around 1.5 Å, with the C3-C4 bond (i.e. the one that is being formed here) measured at 1.515 ± 0.020 Å.<ref name="ja01036a004">Joseph F Chiang, Simon Harvey Bauer, "Molecular structure of cyclohexene", ''J. Am. Chem. Soc.'', '''1969''', ''91 (8)'' 1898-1901.{{DOI|10.1021/ja01036a004}}</ref> The two atoms are much closer to the 1.5 Å of a bond than to the 3.4 Å separation they would have with no bonding interaction. This suggests the two molecules are well on their way to becoming one at the transition state.

Ciang and Bauer give the cyclohexene C<sub>1</sub>=C<sub>2</sub> bond length as 1.335 ± 0.003 Å. This happenes to be [[Mod:NIK13additionalfiles#Butadiene .2B Ethylene TS|closer to the calculated lengths of the other bonds]] in the molecule than the value for single bonded C-C. Not only that, but the three bonds that were double bonds in the separate molecules ''remain the shortest in the transition structure''. This suggests that the molecule is, in fact, not as far along the reaction coordinate as it seemed and the π bonds retain a lot of their character (although some π density is moving away from the old bonds and into the new ones).

[[Image:Mb_da2.jpg|right|thumb|''cis-''Butadiene + Ethylene TS plane of symmetry]]
{| border="2" cellpadding="5"
|-align="center"
| '''Ethylene HOMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_HOMO.png|150px|test]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_LUMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
|- align="center"
| '''Butadiene LUMO:'''
symmetric ('''s''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_LUMO.png|150px]]
|- align="center"
| '''Ethylene LUMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_eene_OptMin_semiAM1_LUMO.png|150px]]
| rowspan="2" | [[Image:Nik13_Transition_States_Bii_bdene-eene_Opt%2BFreq_TSBerny_FC_semiAM1_NoEigen_HOMO.png|150px]]
| rowspan="2" | '''Cyclohexene TS HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
|-align="center"
| '''Butadiene HOMO:'''
antisymmetric ('''a''') relative to<br>
TS plane of symmetry
| [[Image:Nik13_Transition_States_Bi_bdene_OptMin_semiAM1_HOMO.png|150px]]
|}

== The reaction of cyclohexa-1,3-diene and maleic anhydride ==

The transition structures were created by adding to and modifying the atoms in the Butadiene + Ethylene transition structure. They were optimised to a transition state using the Berny method at the semi-empirical AM1 level. Imaginary vibrational frequencies are given below. The exo transition state is 0.68 kcal mol<sup>-1</sup> higher in energy than the endo state.

There is surprisingly little difference in the molecular orbitals between the two forms of the Diels-Alder aduct. The π cloud between the two fragments is a little fuller for the endo form (along the new bonds), but this is only a slight change. Something else must account for the difference in energy. Steric clashes seem the likely answer, a hypothesis supported by Fox, Cardona and Kiwiet.<ref name="jo00384a016">Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet, "Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies", ''J. Org. Chem.'', '''1987''', ''52 (8)'', 1469–1474.{{DOI|10.1021/jo00384a016}}</ref> One end of cyclohexa-1,3-diene is planar, the other is not. The cyclohexa-1,3-diene C<sub>sp<sup>3</sup></sub>-H groups would clash much more with the anhydride group on the maleic anhydride than with the maleic hydrogens. While the maleic anhydride C=C π cloud is of the right phase to interact with its counterpart on the cyclohexa-1,3-diene, lowering the energy of the transition state, the orbitals on the anhydride part of the molecule are antibonding with respect to this. The exo form reduces the interactions here and potentially allows an orbital interaction between the anhydride orbitals and the small p-like orbitals on the C<sub>sp<sup>3</sup></sub>.

[[Image:Bearpark_pic_edit_by_jm906.JPG|right|thumb|Stereochemical considerations of the reaction between cyclohexa-1,3-diene and maleic anhydride]]
{| border="2" cellpadding="5"
|-align="center"
!
! Endo form
! Exo form
|- align="centre"
! [[Mod:NIK13additionalfiles#Cyclohexa-1,3-diene + Maleic Anhydride TS|Click here for a dynamic<br>
version of these molecules]]
| {{fontcolor1|white|red|jsmol of Endo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
| {{fontcolor1|white|red|jsmol of Exo}}
<nowiki>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>200</size>
<uploadedFileContents>Phys3_gauche.log</uploadedFileContents>
<script>mo NO; mo nodots nomesh fill transluchent; mo titleformat; frank off; frame title;</script>
</jmolApplet>
</jmol>
</nowiki>
|- align="centre"
! Energy / hartrees
| -0.05150477
| 0.05041985
|- align="centre"
! Energy / kcal mol<sup>-1</sup>
| -32.32
| -31.64
|- align="centre"
! Imaginary IR frequency / cm<sup>-1</sup>
| -806.45
| -812.20
|}

= References =
<references />