ChemWiki - User contributions [en]

Rep:Jed159827

2017-12-17T22:55:40Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs'''<br>

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
|-
| '''HOMO -0.20104'''
| '''HOMO -0.19197'''
|-
| '''LUMO -0.01511'''
| '''LUMO -0.04242'''
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
|'''-233.321033'''
|'''-267.068132'''
|'''E-500.418691'''
|'''-500.417323'''
|}

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol''<br>
''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93'' kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

''Gibbs free energy of endo transition state = -500.332149'' <br>
''Gibbs free energy of exo transition state = -500.329163''<br>
''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol''<br>
''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

This exercise investigates the reaction between xylyene and sulphur dioxide, which can undergo three different reaction pathways, via an exo or endo transition state, or via a chelotropic reaction. Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations.

Log files: <br>
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

'''Thermochemistry - Sum of electronic and thermal Free Energies:'''

''Xylyene= 0.178186'' <br>
''SO2= -0.112724''<br>
''Diels-Alder endo= 0.056109''<br>
''Diels-Alder exo= 0.021696''<br>
''Diels-Alder TS endo = 0.092078''<br>
''Diels-Alder TS exo = 0.090556''<br>
''Chelotropic adduct = -0.000002''<br>
''Chelotropic TS = 0.099062''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

''Free energy of reactants = 0.065462'' <br />
''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol'' <br />
''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol'' <br />
''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol'''<br />
''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''<br />
''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. This conclusion is supported by the following graph, showing the energy profiles for each reaction.

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring that can undergo a similar reaction. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px|left|frame|Endo Product]]<br>[[File:Jed15_exo_extra.PNG|300px|right|frame|Exo Product]]
<br style="clear:right">

However, the Gibbs free energy value for each product, shown below, indicates that this reaction is highly unfavourable

''Endo product = 0.067302 Hartrees''<br>
''Exo product = 0.065608 Hartrees''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

These exercises demonstrate the power of computational chemistry in studying potential energy surfaces and transition states. From some relatively short and simple procedures on the computer, useful thermochemical and mechanistic information can be extracted and used to obtain useful chemical information, without the need for any complex laboratory work. However, the nature of these electrocyclic reactions that were studied lend themselves very well to this kind of analysis, due to the simplicity of the bond forming and bond breaking. In general only Carbon-Carbon bonds are being broken and formed, and the mechanisms are concerted and relatively simplistic. If a transition state needed to be analysed that was part of a more complex reaction involving different atoms and a large number of molecules, or if multiple transition states were present in a reaction, these methods may need to be developed and expanded upon to give useful results. Further work in this area could involve investigating more pericyclic reactions, such as those involving conrotation or disrotation.

Rep:Jed159827

2017-12-17T22:44:48Z

Jed15: /* Exercise 3: Diels-Alder vs Cheletropic */

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

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'''Cyclohexadiene LUMO'''

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<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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'''Dioxole HOMO'''

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<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
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'''Dioxole LUMO'''

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'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
<jmol>
<jmolApplet>
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<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 4 (a4)
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<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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'''Exo Product MOs'''

HOMO

<jmol>
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<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
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LUMO

<jmol>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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'''Endo Product MOs
'''
HOMO

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LUMO

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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
|-
| '''HOMO -0.20104'''
| '''HOMO -0.19197'''
|-
| '''LUMO -0.01511'''
| '''LUMO -0.04242'''
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
|'''-233.321033'''
|'''-267.068132'''
|'''E-500.418691'''
|'''-500.417323'''
|}

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol''<br>
''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93'' kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

''Gibbs free energy of endo transition state = -500.332149'' <br>
''Gibbs free energy of exo transition state = -500.329163''<br>
''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol''<br>
''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

This exercise investigates the reaction between xylyene and sulphur dioxide, which can undergo three different reaction pathways, via an exo or endo transition state, or via a chelotropic reaction. Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations.

Log files: <br>
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

'''Thermochemistry - Sum of electronic and thermal Free Energies:'''

''Xylyene= 0.178186'' <br>
''SO2= -0.112724''<br>
''Diels-Alder endo= 0.056109''<br>
''Diels-Alder exo= 0.021696''<br>
''Diels-Alder TS endo = 0.092078''<br>
''Diels-Alder TS exo = 0.090556''<br>
''Chelotropic adduct = -0.000002''<br>
''Chelotropic TS = 0.099062''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

''Free energy of reactants = 0.065462'' <br />
''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol'' <br />
''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol'' <br />
''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol'''<br />
''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''<br />
''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. This conclusion is supported by the following graph, showing the energy profiles for each reaction.

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring that can undergo a similar reaction. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px|left|frame|Endo Product]]<br>[[File:Jed15_exo_extra.PNG|300px|right|frame|Exo Product]]
<br style="clear:right">

However, the Gibbs free energy value for each product, shown below, indicates that this reaction is highly unfavourable

''Endo product = 0.067302 Hartrees''<br>
''Exo product = 0.065608 Hartrees''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T22:37:59Z

Jed15: /* Exercise 3: Diels-Alder vs Cheletropic */

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
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Ethene Bond Lengths
<jmol>
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<script>measure 1 4 </script>
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Transition State Bond Lengths
<jmol>
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<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
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Product Bond Lengths
<jmol>
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Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

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<color>white</color>
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<script>frame 9; vibration 1;rotate x -20; </script>
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</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

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'''Cyclohexadiene LUMO'''

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<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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'''Dioxole HOMO'''

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<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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'''Dioxole LUMO'''

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'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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'''Exo Product MOs'''

HOMO

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<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
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<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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LUMO

<jmol>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
|-
| '''HOMO -0.20104'''
| '''HOMO -0.19197'''
|-
| '''LUMO -0.01511'''
| '''LUMO -0.04242'''
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
|'''-233.321033'''
|'''-267.068132'''
|'''E-500.418691'''
|'''-500.417323'''
|}

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol''<br>
''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93'' kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

''Gibbs free energy of endo transition state = -500.332149'' <br>
''Gibbs free energy of exo transition state = -500.329163''<br>
''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol''<br>
''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

This exercise investigates the reaction between xylyene and sulphur dioxide, which can undergo three different reaction pathways, via an exo or endo transition state, or via a chelotropic reaction. Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations.

Log files: <br>
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

'''Thermochemistry - Sum of electronic and thermal Free Energies:'''

''Xylyene= 0.178186'' <br>
''SO2= -0.112724''<br>
''Diels-Alder endo= 0.056109''<br>
''Diels-Alder exo= 0.021696''<br>
''Diels-Alder TS endo = 0.092078''<br>
''Diels-Alder TS exo = 0.090556''<br>
''Chelotropic adduct = -0.000002''<br>
''Chelotropic TS = 0.099062''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

''Free energy of reactants = 0.065462'' <br />
''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol'' <br />
''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol'' <br />
''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol'''<br />
''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''<br />
''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. This conclusion is supported by the following graph, showing the energy profiles for each reaction.

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring that can undergo a similar reaction. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px|left|frame|Endo Product]]<br>
[[File:Jed15_exo_extra.PNG|300px|right|frame|Exo Product]]
<br style="clear:right">

However, the Gibbs free energy value for each product, shown below, indicates that this reaction is highly unfavourable

''Endo product = 0.067302 Hartrees''<br>
''Exo product = 0.065608 Hartrees''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T22:35:33Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
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Transition State 2 (s4)
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<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s5)
<jmol>
<jmolApplet>
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<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

<jmol>
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<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
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<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
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LUMO

<jmol>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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'''Endo Product MOs
'''
HOMO

<jmol>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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LUMO

<jmol>
<jmolApplet>
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<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
|-
| '''HOMO -0.20104'''
| '''HOMO -0.19197'''
|-
| '''LUMO -0.01511'''
| '''LUMO -0.04242'''
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
|'''-233.321033'''
|'''-267.068132'''
|'''E-500.418691'''
|'''-500.417323'''
|}

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol''<br>
''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93'' kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

''Gibbs free energy of endo transition state = -500.332149'' <br>
''Gibbs free energy of exo transition state = -500.329163''<br>
''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol''<br>
''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

This exercise investigates the reaction between xylyene and sulphur dioxide, which can undergo three different reaction pathways, via an exo or endo transition state, or via a chelotropic reaction. Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations.

Log files: <br>
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

'''Thermochemistry'''

Sum of electronic and thermal Free Energies:

''Xylyene= 0.178186'' <br>
''SO2= -0.112724''<br>
''Diels-Alder endo= 0.056109''<br>
''Diels-Alder exo= 0.021696''<br>
''Diels-Alder TS endo = 0.092078''<br>
''Diels-Alder TS exo = 0.090556''<br>
''Chelotropic adduct = -0.000002''<br>
''Chelotropic TS = 0.099062''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

''Free energy of reactants = 0.065462'' <br />
''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol'' <br />
''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol'' <br />
''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol'''<br />
''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''<br />
''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. This conclusion is supported by the following graph, showing the energy profiles for each reaction.

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring that can undergo a similar reaction. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px|left|Endo Product]]<br>
[[File:Jed15_exo_extra.PNG|300px|right|Exo Product]]

However, the Gibbs free energy value for each product, shown below, indicates that this reaction is highly unfavourable

''Endo product = 0.067302 Hartrees''<br>
''Exo product = 0.065608 Hartrees''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T22:32:42Z

Jed15: /* Exercise 3: Diels-Alder vs Cheletropic */

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
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Ethene Bond Lengths
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Transition State Bond Lengths
<jmol>
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Product Bond Lengths
<jmol>
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Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
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<script>frame 9; vibration 1;rotate x -20; </script>
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</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

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'''Cyclohexadiene LUMO'''

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'''Dioxole HOMO'''

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'''Dioxole LUMO'''

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'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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'''Exo Product MOs'''

HOMO

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LUMO

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'''Endo Product MOs
'''
HOMO

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LUMO

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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
|-
| '''HOMO -0.20104'''
| '''HOMO -0.19197'''
|-
| '''LUMO -0.01511'''
| '''LUMO -0.04242'''
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
|'''-233.321033'''
|'''-267.068132'''
|'''E-500.418691'''
|'''-500.417323'''
|}

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol''<br>
''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93'' kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

''Gibbs free energy of endo transition state = -500.332149'' <br>
''Gibbs free energy of exo transition state = -500.329163''<br>
''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol''<br>
''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

This exercise investigates the reaction between xylyene and sulphur dioxide, which can undergo three different reaction pathways, via an exo or endo transition state, or via a chelotropic reaction. Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations.

Log files: <br>
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

'''Thermochemistry'''

Sum of electronic and thermal Free Energies:

''Xylyene= 0.178186'' <br>
''SO2= -0.112724''<br>
''Diels-Alder endo= 0.056109''<br>
''Diels-Alder exo= 0.021696''<br>
''Diels-Alder TS endo = 0.092078''<br>
''Diels-Alder TS exo = 0.090556''<br>
''Chelotropic adduct = -0.000002''<br>
''Chelotropic TS = 0.099062''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

''Free energy of reactants = 0.065462'' <br />
''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol'' <br />
''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol'' <br />
''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol'''<br />
''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''<br />
''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. This conclusion is supported by the following graph, showing the energy profiles for each reaction.

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring that can undergo a similar reaction. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

''Endo product = 0.067302''<br>
''Exo product = 0.065608''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T22:25:11Z

Jed15: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
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'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
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<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
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LUMO

<jmol>
<jmolApplet>
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<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
|-
| '''HOMO -0.20104'''
| '''HOMO -0.19197'''
|-
| '''LUMO -0.01511'''
| '''LUMO -0.04242'''
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
|'''-233.321033'''
|'''-267.068132'''
|'''E-500.418691'''
|'''-500.417323'''
|}

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol''<br>
''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93'' kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

''Gibbs free energy of endo transition state = -500.332149'' <br>
''Gibbs free energy of exo transition state = -500.329163''<br>
''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol''<br>
''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations

Log files:
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''<br>
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T22:20:13Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
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Transition State 2 (s4)
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<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s5)
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<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

<jmol>
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<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
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'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
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<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
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'''Dioxole HOMO'''

<jmol>
<jmolApplet>
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<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
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'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
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<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
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LUMO

<jmol>
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<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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'''Endo Product MOs
'''
HOMO

<jmol>
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<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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LUMO

<jmol>
<jmolApplet>
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<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! Cyclohexadiene HOMO, -0.20104
! Cyclohexadiene LUMO, -0.01511
! Dioxole HOMO, -0.19197,
| Dioxole LUMO, -0.04242
|}

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | Dioxole
|-
| HOMO -0.20104
| HOMO -0.19197
|-
| LUMO -0.01511
| LUMO -0.04242
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations

Log files:
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''<br>
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T22:16:41Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In a potential energy surface, a minimum is a point at which the gradient is zero, and usually corresponds to the reaction coordinate of the reactants and the products, although a minimum can also be found when stable intermediates are formed during a reaction. The gradient of the potential energy surface is also zero at a maximum, such as the transition state of the reaction. This is the highest energy reaction coordinate in a potential energy surface. A vibrational frequency calculation can be completed at this point, which will give a single imaginary frequency, suggesting a negative force constant. This frequency corresponds to the change in geometry that takes place during the reaction. The following exercises investigate transition states for a series of cycloaddition reactions.

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
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Transition State 2 (s4)
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<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s5)
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<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
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</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

This section investigates a Diels Alder reaction, including the construction of MO diagrams, investigating whether the reaction is 'Normal' or 'Inverse Demand', and analysing the thermochemistry of the reaction. Below are all the important molecular orbitals for this reaction, and the MO diagrams for the endo and exo transition states.

'''Cyclohexadiene HOMO'''

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<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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Transition State 2 (s3)
<jmol>
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<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
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<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
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LUMO

<jmol>
<jmolApplet>
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<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

{| class="wikitable"
! Cyclohexadiene HOMO, -0.20104
! Cyclohexadiene LUMO, -0.01511
! Dioxole HOMO, -0.19197,
| Dioxole LUMO, -0.04242
|}

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations

Log files:
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''<br>
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T14:04:05Z

Jed15: /* Exercise 3: Diels-Alder vs Cheletropic */

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
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<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations

Log files:
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''<br>
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T14:02:45Z

Jed15: /* Exercise 3: Diels-Alder vs Cheletropic */

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations

Log files:
[[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T14:01:56Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] <br> [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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Transition State 2 (s3)
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<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
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<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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LUMO

<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the Transition State calculations

Log files: [[File:EXERCISE3_-_JED15_-_XYLYLENE_-_PM6_TS2.LOG
]] <br> [[File:EXERCISE3_-_JED15_-_XYLYLENE_ENDO_-_PM6_TS.LOG]] <br> [[File:EXERCISE3_-_JED15_-_CHELOTROPIC_-_PM6_TS.LOG]]

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

File:EXERCISE3 - JED15 - CHELOTROPIC - PM6 TS.LOG

2017-12-17T13:57:53Z

Jed15:

File:EXERCISE3 - JED15 - XYLYLENE ENDO - PM6 TS.LOG

2017-12-17T13:57:15Z

Jed15:

File:EXERCISE3 - JED15 - XYLYLENE - PM6 TS2.LOG

2017-12-17T13:56:32Z

Jed15:

Rep:Jed159827

2017-12-17T02:12:27Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
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Transition State 2 (s4)
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<jmolApplet>
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<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s5)
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<jmolApplet>
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<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
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</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
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LUMO

<jmol>
<jmolApplet>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
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'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
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<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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LUMO

<jmol>
<jmolApplet>
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<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image. The .log files are also found below for the IRC and Transition State calculations

[[File:Jed15_dielsalder_endo_irc.log]]<br>
[[File:Jed15_dielsalder_exo_irc.log]]<br>
[[File:Jed15_chelotropic_irc.log]]<br>

[[File:Jed15_dielsalder_endo_TS.log]]<br>
[[File:Jed15_dielsalder_exo_TS.log]]<br>
[[File:Jed15_chelotropic_TS.log]]<br>

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T02:07:29Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

For each of your calculations, upload the log file and include a link in the wiki (this is not necessary if you have included a JMol for that calculation).

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE.LOG]] [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T02:06:16Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

For each of your calculations, upload the log file and include a link in the wiki (this is not necessary if you have included a JMol for that calculation).

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE2.LOG]] [[File:JED15-ETHENE.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T02:04:57Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

For each of your calculations, upload the log file and include a link in the wiki (this is not necessary if you have included a JMol for that calculation).

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Log files: [[File:JED15-BUTADIENE2.LOG]]

Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T01:59:46Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

For each of your calculations, upload the log file and include a link in the wiki (this is not necessary if you have included a JMol for that calculation).

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

==Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole==

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

==Conclusion==

There are examples of several electrocyclic reactions on this page that you can try. These are a subset of pericyclic reactions like the ones above. For each case, find the IRC of the TS, which corresponds to the ground state or thermal reaction. Have a look at the HOMO and LUMO of the reactants, TS and products to justify why the reaction proceeds with either conrotation or disrotation.

Rep:Jed159827

2017-12-17T01:51:05Z

Jed15:

==Y3C - Third Year Computational Laboratory<br>Transition States and Reactivity - Jacob Davies==

==Introduction==

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole===

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:50:09Z

Jed15:

==Y3C - Third Year Computational Laboratory==
===Transition States and Reactivity - Jacob Davies===

==Introduction==

==Exercise 1: Reaction of Butadiene with Ethylene==

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole===

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
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<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
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<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
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LUMO

<jmol>
<jmolApplet>
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<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:49:28Z

Jed15:

==Y3C - Third Year Computational Laboratory==
===Transition States and Reactivity===
===Jacob Davies===

[[''===Introduction==='']]

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
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Transition State 2 (s4)
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<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s5)
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<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole===

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
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<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
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<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
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LUMO

<jmol>
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<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
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'''Endo Product MOs
'''
HOMO

<jmol>
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<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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LUMO

<jmol>
<jmolApplet>
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<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:42:12Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole===

'''Cyclohexadiene HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Cyclohexadiene LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole HOMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

'''Dioxole LUMO'''

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''
Exo Transition State MO Diagram'''

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

'''Exo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Exo Product MOs'''

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Product MOs
'''
HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

'''Dioxole''' <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

'''Cyclohexadiene -233.321033''' <br>
'''Dioxole -267.068132'''<br>
'''Endo Product -500.418691'''<br>
'''Exo Product -500.417323'''

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

'''Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol'''<br>
'''Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol'''

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

'''Gibbs free energy of endo transition state = -500.332149''' <br>
'''Gibbs free energy of exo transition state = -500.329163'''<br>
'''Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol'''<br>
'''Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol'''

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

==Exercise 3: Diels-Alder vs Cheletropic==

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

''Sum of electronic and thermal Free Energies
''

'''Xylyene= 0.178186''' <br>
'''SO2= -0.112724'''<br>
'''Diels-Alder endo= 0.056109'''<br>
'''Diels-Alder exo= 0.021696'''<br>
'''Diels-Alder TS endo = 0.092078'''<br>
'''Diels-Alder TS exo = 0.090556'''<br>
'''Chelotropic adduct = -0.000002'''<br>
'''Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:35:50Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole

Cyclohexadiene HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

Cyclohexadiene LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

Dioxole HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Dioxole LUMO

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Exo Transition State MO Diagram

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

Exo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Exo Product MOs

HOMO

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LUMO

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Endo Product MOs

HOMO

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LUMO

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WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG

EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG

EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_TS.LOG

EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_TS.LOG

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

Dioxole <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

Cyclohexadiene -233.321033 <br>
Dioxole -267.068132<br>
Endo Product -500.418691<br>
Exo Product -500.417323

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol<br>
Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

Gibbs free energy of endo transition state = -500.332149 <br>
Gibbs free energy of exo transition state = -500.329163<br>
Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol<br>
Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

Exercise 3: Diels-Alder vs Cheletropic

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

[[File:Jed15_dielsalder_endo_irc.gif|center|300px|frame||Diels Alder - Endo IRC]]<br>
[[File:Jed15_dielsalder_exo_irc.gif|center|300px|frame|Diels Alder - ExoIRC]]<br>
[[File:Jed15_chelotropic_irc.gif|centre|300px|frame|Chelotropic IRC]]<br>

'''Sum of electronic and thermal Free Energies'''

'''Xylyene= 0.178186 <br>
SO2= -0.112724<br>
Diels-Alder endo= 0.056109<br>
Diels-Alder exo= 0.021696<br>
Diels-Alder TS endo = 0.092078<br>
Diels-Alder TS exo = 0.090556<br>
Chelotropic adduct = -0.000002<br>
Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462''' <br />
'''Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol''' <br />
'''Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol''' <br />
'''Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

'''Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol''' <br />
'''Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol''' <br />
'''Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol'''

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302'''
'''Exo product = 0.065608'''

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:31:09Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
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Ethene Bond Lengths
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Transition State Bond Lengths
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Product Bond Lengths
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Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

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Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole

Cyclohexadiene HOMO

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Cyclohexadiene LUMO

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Dioxole HOMO

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Dioxole LUMO

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Exo Transition State MO Diagram

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

Exo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Exo Product MOs

HOMO

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LUMO

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Endo Product MOs

HOMO

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LUMO

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WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG

EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG

EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_TS.LOG

EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_TS.LOG

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

Dioxole <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

Cyclohexadiene -233.321033 <br>
Dioxole -267.068132<br>
Endo Product -500.418691<br>
Exo Product -500.417323

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol<br>
Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

Gibbs free energy of endo transition state = -500.332149 <br>
Gibbs free energy of exo transition state = -500.329163<br>
Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol<br>
Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

Exercise 3: Diels-Alder vs Cheletropic

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

Diels Alder - Endo IRC
[[File:Jed15_dielsalder_endo_irc.gif|300px]]<br>
Diels Alder - Exo IRC
[[File:Jed15_dielsalder_exo_irc.gif|300px]]<br>
Chelotropic - IRC
[[File:Jed15_chelotropic_irc.gif|300px]]<br>

'''Sum of electronic and thermal Free Energies'''

'''Xylyene= 0.178186 <br>
SO2= -0.112724<br>
Diels-Alder endo= 0.056109<br>
Diels-Alder exo= 0.021696<br>
Diels-Alder TS endo = 0.092078<br>
Diels-Alder TS exo = 0.090556<br>
Chelotropic adduct = -0.000002<br>
Chelotropic TS = 0.099062'''

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

'''Free energy of reactants = 0.065462 <br />
Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol <br />
Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol <br />
Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol'''

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol <br />
Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol <br />
Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]<br>
[[File:Jed15_exo_extra.PNG|300px]]

'''Endo product = 0.067302
Exo product = 0.065608
'''
The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:28:28Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

From the bond measurements below, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole

Cyclohexadiene HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

Cyclohexadiene LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

Dioxole HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

Dioxole LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Exo Transition State MO Diagram

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

Exo Transition States

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

'''Endo Transition State MO Diagram'''

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

'''Endo Transition States'''

Transition State 1 (a3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Exo Product MOs

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Endo Product MOs

HOMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG

EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG

EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_TS.LOG

EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_TS.LOG

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

'''Normal or Inverse Demand Diels Alder'''

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

'''Cyclohexadiene''' <br>
HOMO -0.20104 Hartrees<br>
LUMO -0.01511 Hartrees

Dioxole <br>
HOMO -0.19197<br>
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

'''Thermochemistry'''

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal free energies were extracted, and tabulated below:

Cyclohexadiene -233.321033 <br>
Dioxole -267.068132<br>
Endo Product -500.418691<br>
Exo Product -500.417323

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol<br>
Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

Gibbs free energy of endo transition state = -500.332149 <br>
Gibbs free energy of exo transition state = -500.329163<br>
Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol<br>
Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

Exercise 3: Diels-Alder vs Cheletropic

Each reaction path was visualised with an IRC (PM6) calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

Diels Alder - Endo IRC
[[File:Jed15_dielsalder_endo_irc.gif|300px]]
Diels Alder - Exo IRC
[[File:Jed15_dielsalder_exo_irc.gif|300px]]
Chelotropic - IRC
[[File:Jed15_chelotropic_irc.gif|300px]]

'''Sum of electronic and thermal Free Energies'''

Xylyene= 0.178186
SO2= -0.112724
Diels-Alder endo= 0.056109
Diels-Alder exo= 0.021696
Diels-Alder TS endo = 0.092078
Diels-Alder TS exo = 0.090556
Chelotropic adduct = -0.000002
Chelotropic TS = 0.099062

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

Free energy of reactants = 0.065462 <br />
Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol <br />
Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol <br />
Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol <br />
Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol <br />
Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]
[[File:Jed15_exo_extra.PNG|300px]]

Endo product = 0.067302
Exo product = 0.065608

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:18:48Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 22; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 2 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a5)
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 25;mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State Bond Lengths
<jmol>
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Product Bond Lengths
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From the bond measurements above, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

<jmol>
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Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole

Cyclohexadiene HOMO

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Cyclohexadiene LUMO

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Dioxole HOMO

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Dioxole LUMO

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Exo Transition State MO Diagram

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

Exo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Endo Transition State MO Diagram

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

Endo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Exo Product MOs

HOMO

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LUMO

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Endo Product MOs

HOMO

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LUMO

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WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG

EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG

EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_TS.LOG

EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_TS.LOG

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

Normal or Inverse Demand Diels Alder

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

Cyclohexadiene
HOMO -0.20104 Hartrees
LUMO -0.01511 Hartrees

Dioxole
HOMO -0.19197
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

Thermochemistry

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal energies, enthalpies and free energies were extracted, and are tabulated below in hartrees:

Energy Enthalpy Free Energy
Cyclohexadiene -233.288624 -233.287680 -233.321033
Dioxole -267.038104 -267.037160 -267.068132
Endo Product -500.377578 -500.376634 -500.418691
Exo Product -500.376556 -500.375611 -500.417323

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol

Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

Gibbs free energy of endo transition state = -500.332149

Gibbs free energy of exo transition state = -500.329163

Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol

Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

Exercise 3: Diels-Alder vs Cheletropic

Each reaction path was visualised with an IRC calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

Diels Alder - Endo IRC
[[File:Jed15_dielsalder_endo_irc.gif|300px]]
Diels Alder - Exo IRC
[[File:Jed15_dielsalder_exo_irc.gif|300px]]
Chelotropic - IRC
[[File:Jed15_chelotropic_irc.gif|300px]]

Sum of electronic and thermal Free Energies

Xylyene= 0.178186
SO2= -0.112724
Diels-Alder endo= 0.056109
Diels-Alder exo= 0.021696
Diels-Alder TS endo = 0.092078
Diels-Alder TS exo = 0.090556
Chelotropic adduct = -0.000002
Chelotropic TS = 0.099062

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

Free energy of reactants = 0.065462 <br />
Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol <br />
Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol <br />
Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol <br />
Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol <br />
Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]
[[File:Jed15_exo_extra.PNG|300px]]

Endo product = 0.067302
Exo product = 0.065608

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:10:48Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

'''Bond Lengths'''

Butadiene Bond Lengths
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Ethene Bond Lengths
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Transition State Bond Lengths
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Product Bond Lengths
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From the bond measurements above, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

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Shown above is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole

Cyclohexadiene HOMO

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Cyclohexadiene LUMO

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Dioxole HOMO

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Dioxole LUMO

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Exo Transition State MO Diagram

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

Exo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Endo Transition State MO Diagram

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

Endo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Exo Product MOs

HOMO

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LUMO

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Endo Product MOs

HOMO

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<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

LUMO

<jmol>
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WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG

EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG

EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_TS.LOG

EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_TS.LOG

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

Normal or Inverse Demand Diels Alder

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

Cyclohexadiene
HOMO -0.20104 Hartrees
LUMO -0.01511 Hartrees

Dioxole
HOMO -0.19197
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

Thermochemistry

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal energies, enthalpies and free energies were extracted, and are tabulated below in hartrees:

Energy Enthalpy Free Energy
Cyclohexadiene -233.288624 -233.287680 -233.321033
Dioxole -267.038104 -267.037160 -267.068132
Endo Product -500.377578 -500.376634 -500.418691
Exo Product -500.376556 -500.375611 -500.417323

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol

Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

Gibbs free energy of endo transition state = -500.332149

Gibbs free energy of exo transition state = -500.329163

Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol

Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

Exercise 3: Diels-Alder vs Cheletropic

Each reaction path was visualised with an IRC calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

Diels Alder - Endo IRC
[[File:Jed15_dielsalder_endo_irc.gif|300px]]
Diels Alder - Exo IRC
[[File:Jed15_dielsalder_exo_irc.gif|300px]]
Chelotropic - IRC
[[File:Jed15_chelotropic_irc.gif|300px]]

Sum of electronic and thermal Free Energies

Xylyene= 0.178186
SO2= -0.112724
Diels-Alder endo= 0.056109
Diels-Alder exo= 0.021696
Diels-Alder TS endo = 0.092078
Diels-Alder TS exo = 0.090556
Chelotropic adduct = -0.000002
Chelotropic TS = 0.099062

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

Free energy of reactants = 0.065462 <br />
Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol <br />
Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol <br />
Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol <br />
Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol <br />
Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]
[[File:Jed15_exo_extra.PNG|300px]]

Endo product = 0.067302
Exo product = 0.065608

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:08:01Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
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Transition State 2 (s4)
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<script>frame 8; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s5)
<jmol>
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<script>frame 8; mo 24; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 4 (a5)
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

Butadiene Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>600</size>
<script>measure 3 1; measure 1 6;measure 6 7</script>
<uploadedFileContents>JED15-BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Ethene Bond Lengths
<jmol>
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<color>white</color>
<size>600</size>
<script>measure 1 4 </script>
<uploadedFileContents>JED15-ETHENE.LOG</uploadedFileContents>
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Transition State Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>600</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Product Bond Lengths
<jmol>
<jmolApplet>
<color>white</color>
<size>600</size>
<script>measure 1 2; measure 2 3;measure 3 4; measure 4 5; measure 5 6; measure 6 1 </script>
<uploadedFileContents>jed15-EXERCISE1_-_PRODUCT_-_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

From the bond measurements above, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 9; vibration 1;rotate x -20; </script>
<uploadedFileContents>JED15_-_EX1TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Shown below is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole

Cyclohexadiene HOMO

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Cyclohexadiene LUMO

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<uploadedFileContents>EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG </uploadedFileContents>
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</jmol>

Dioxole HOMO

<jmol>
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<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG </uploadedFileContents>
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Dioxole LUMO

<jmol>
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<uploadedFileContents>EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG</uploadedFileContents>
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Exo Transition State MO Diagram

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

Exo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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Transition State 4 (a4)
<jmol>
<jmolApplet>
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<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_EXO_TS.LOG</uploadedFileContents>
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Endo Transition State MO Diagram

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

Endo Transition States

Transition State 1 (a3)
<jmol>
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<script>frame 6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
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</jmol>

Transition State 2 (s3)
<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 3 (s4)
<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Transition State 4 (a4)
<jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<script>frame 6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JED15-_ENDO_TS.LOG</uploadedFileContents>
</jmolApplet>
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Exo Product MOs

HOMO

<jmol>
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<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG </uploadedFileContents>
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LUMO

<jmol>
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<script>frame 14; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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Endo Product MOs

HOMO

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</jmolApplet>
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LUMO

<jmol>
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<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG</uploadedFileContents>
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WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG

EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG

EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_TS.LOG

EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_TS.LOG

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

Normal or Inverse Demand Diels Alder

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

Cyclohexadiene
HOMO -0.20104 Hartrees
LUMO -0.01511 Hartrees

Dioxole
HOMO -0.19197
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

Thermochemistry

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal energies, enthalpies and free energies were extracted, and are tabulated below in hartrees:

Energy Enthalpy Free Energy
Cyclohexadiene -233.288624 -233.287680 -233.321033
Dioxole -267.038104 -267.037160 -267.068132
Endo Product -500.377578 -500.376634 -500.418691
Exo Product -500.376556 -500.375611 -500.417323

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol

Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

Gibbs free energy of endo transition state = -500.332149

Gibbs free energy of exo transition state = -500.329163

Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol

Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

Exercise 3: Diels-Alder vs Cheletropic

Each reaction path was visualised with an IRC calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

Diels Alder - Endo IRC
[[File:Jed15_dielsalder_endo_irc.gif|300px]]
Diels Alder - Exo IRC
[[File:Jed15_dielsalder_exo_irc.gif|300px]]
Chelotropic - IRC
[[File:Jed15_chelotropic_irc.gif|300px]]

Sum of electronic and thermal Free Energies

Xylyene= 0.178186
SO2= -0.112724
Diels-Alder endo= 0.056109
Diels-Alder exo= 0.021696
Diels-Alder TS endo = 0.092078
Diels-Alder TS exo = 0.090556
Chelotropic adduct = -0.000002
Chelotropic TS = 0.099062

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

Free energy of reactants = 0.065462 <br />
Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol <br />
Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol <br />
Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol <br />
Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol <br />
Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]
[[File:Jed15_exo_extra.PNG|300px]]

Endo product = 0.067302
Exo product = 0.065608

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed159827

2017-12-17T01:06:37Z

Jed15:

Y3C - Third Year Computational Laboratory
Transition States and Reactivity
Jacob Davies

Introduction

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">
Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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It can be seen that for an MO on butadiene to interact with an MO on ethene, both are required to have similar symmetry. Only symmetric-symmetric and antisymmetric-antisymmetric interactions are allowed, and symmetric-antisymmetric interactions are forbidden. The orbital overlap integral is therefore non-zero for these interactions, but zero for a symmetric-antisymmetric interaction.

Butadiene Bond Lengths
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Ethene Bond Lengths
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Transition State Bond Lengths
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Product Bond Lengths
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From the bond measurements above, it can be seen that the distance between the two carbon atoms forming bond on either side of the molecule decreases from 0.227nm in the transition state to 0.158nm in the final product. This is comparable to the bond expected 0.155nm sp3 C-C bond length. The Van der Waals radius of a carbon atom is equal to 0.17nm. Therfore the minimum distance required for a C-C bond to form is 0.34nm. the partly formed C-C bonds in the transition state are short enough to easily fall within this distance, allowing bond formation. The ethene double bond increases from the typical C-C double bond length of 0.133nm to a slightly longer 0.139nm in the transition state. This bond becomes a single bond in the final product, and has the expected 0.156nm bond length of an sp3 carbon. The butadiene double bonds increase to 0.138nm in the transition state and are 0.151nm in the final product. This is slightly shorter than the expected sp3 bond length, which could be attributed to the presence of the newly formed C-C double bond adjacent to these bonds.

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Shown below is the vibration that corresponds to the reaction path at the transition state. It corresponds to the imaginary frequency at -529.27 Hz. The formation of the two bonds is synchronous, as the carbon atoms on either side of the butadiene and ethene are moving in unison, so the bonds will be formed at the same time.

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole

Cyclohexadiene HOMO

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Cyclohexadiene LUMO

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Dioxole HOMO

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Dioxole LUMO

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Exo Transition State MO Diagram

[[File:Jed15_exercise_2_exo_mo_(EXO).PNG|600px]]

Exo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Endo Transition State MO Diagram

[[File:Jed15_exercise_2_endo_mo.PNG|600px]]

Endo Transition States

Transition State 1 (a3)
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Transition State 2 (s3)
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Transition State 3 (s4)
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Transition State 4 (a4)
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Exo Product MOs

HOMO

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LUMO

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Endo Product MOs

HOMO

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LUMO

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WIKI_-_EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_-_OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_-_OPT.LOG

EXERCISE2_-_JED15_-_DIOXOLE_631_OPT.LOG

EXERCISE2 - JED15 - CYCLOHEXADIENE 631 OPT.LOG

WIKI_-_EXERCISE2_-_JED15_-_EXOPRODUCT_-_631_TS.LOG

EXERCISE2_-_JED15_-_ENDOPRODUCT_-_631_TS.LOG

The diagram below shows that the HOMO of the endo transition state contains secondary orbital interactions between the carbon atoms at the back of cyclohexadiene and the orbitals on the oxygen atoms on dioxole. This makes the endo product the kinetic product of the reaction. The exo transition state only contains primary orbital interactions.

[[File:Exo_vs_endo_interactions_jed15.PNG|300px]]

Normal or Inverse Demand Diels Alder

The relative energy levels of the HOMO and LUMO for both reactants were calculated to determine whether the reaction is a normal or inverse Diels Alder reaction. The reaction is a 'normal demand' reaction when the HOMO is found on the diene (cyclohexadiene). The energy levels for the HOMOs and LUMOs are found below:

Cyclohexadiene
HOMO -0.20104 Hartrees
LUMO -0.01511 Hartrees

Dioxole
HOMO -0.19197
LUMO 0.04242

Therefore, it can be seen that the HOMO for this reaction is found on the dienophile reactant, and the LUMO is found on the diene reactant. This is an inverse demand Diels Alder reaction. This can be attributed to the mesomeric effect of the two oxygen atoms on dioxole. The ether oxygen atoms can donate electrons an leads to conjugation with the carbon carbon double bond on the molecule. This leads to an increase in dioxole's π orbital's energy, making this orbital the HOMO for the reaction.

Thermochemistry

The reactants and both the exo and endo products were optimised (B3LYP/6-31G(d)) and values for the sum of electronic and thermal energies, enthalpies and free energies were extracted, and are tabulated below in hartrees:

Energy Enthalpy Free Energy
Cyclohexadiene -233.288624 -233.287680 -233.321033
Dioxole -267.038104 -267.037160 -267.068132
Endo Product -500.377578 -500.376634 -500.418691
Exo Product -500.376556 -500.375611 -500.417323

The difference in Gibbs free energy between products and reactants will give the Gibbs free energy for the formation of the endo and exo product, revealing which is thermodynamically favoured.

Gibbs free energy for formation of endo product = -0.029559 * 2625.5 = -77.61 kJ/mol

Gibbs free energy for formation of exo product = -0.028158 * 2625.5 = -73.93 kJ/mol

The Gibbs free energy for the formation of the endo product is more negative, so this product is thermodynamically favoured.

In order to find which product is kinetically favoured, the Gibbs free energy barrier between the products and each transition state was calculated:

Gibbs free energy of endo transition state = -500.332149

Gibbs free energy of exo transition state = -500.329163

Gibbs free energy barrier for formation of endo product = 0.057016 * 2625.5 = 149.70 kJ/mol

Gibbs free energy barrier for formation of exo product = 0.060002 * 2625.5 = 157.54 kJ/mol

It can be seen that the energy barrier for the formation of the exo product is greater than for the endo product, indicating that the endo product is favoured kinetically as well as thermodynamically.

Exercise 3: Diels-Alder vs Cheletropic

Each reaction path was visualised with an IRC calculation. .gif files for each IRC are found below, and the animations can be viewed by clicking on each image.

Diels Alder - Endo IRC
[[File:Jed15_dielsalder_endo_irc.gif|300px]]
Diels Alder - Exo IRC
[[File:Jed15_dielsalder_exo_irc.gif|300px]]
Chelotropic - IRC
[[File:Jed15_chelotropic_irc.gif|300px]]

Sum of electronic and thermal Free Energies

Xylyene= 0.178186
SO2= -0.112724
Diels-Alder endo= 0.056109
Diels-Alder exo= 0.021696
Diels-Alder TS endo = 0.092078
Diels-Alder TS exo = 0.090556
Chelotropic adduct = -0.000002
Chelotropic TS = 0.099062

Once again, the free energy change from reactants to products can be calculated by subtracting the sum of electronic and thermal free energies of the reactants from the products:

Free energy of reactants = 0.065462 <br />
Free energy change for Diels Alder endo = -0.009353 * 2625.5 = -24.56 kJ/mol <br />
Free energy change for Diels Alder exo = -0.043766 * 2625.5 = -144.91 kJ/mol <br />
Free energy change for Chelotropic adduct = -0.065464 * 2625.5 = -171.88 kJ/mol

The formation of the chelotropic adduct is the most thermodynamically favoured of the three reaction paths, with the most negative Gibbs free energy change. The formation of the exo product is slightly less favoured, and the formation of the endo product is highly disfavoured.

The height of the reaction barrier can be used to find the kinetically favoured reaction pathway:

Barrier for formation of Diels Alder endo product = 0.026616 * 2625.5 = 69.88 kJ/mol <br />
Barrier for formation of Diels Alder exo product = 0.025094 * 2625.5 = 65.88 kJ/mol <br />
Barrier for formation of chelotropic adduct = 0.033600 * 2625.5 = 88.22 kJ/mol

The smallest reaction barrier is found for the formation of the Diels Alder exo product, which is therefore the kinetically favoured reaction pathway. The endo product has a slightly larger barrier, but the chelotropic adduct has considerably larger barrier, making this reaction the most thermodynamically favoured, but least kinetically favoured reaction. The reaction profile for each reaction is shown below:

[[File:Jed15_exercise_3_reaction_coordinate.PNG|600px]]

For each reaction, the six membered ring on xylyene is aromatised, due to the availability of pi electrons on the two double bonds outside the ring. There is a second cis-butadiene fragment in o-xylylene, on the side of the six membered ring. The two final products that can be formed are shown below:

[[File:Jed15_endo_extra.PNG|300px]]
[[File:Jed15_exo_extra.PNG|300px]]

Endo product = 0.067302
Exo product = 0.065608

The Gibbs free energy of both of the products for this reaction pathway are higher than the Gibbs free energy of the reactants. The reaction is therefore endothermic, so is thermodynamically unfavoured. The transition state of the endo and exo product could not be optimised. However, it would be expected that the kinetic barrier would be very high, making the reaction kinetically unfavoured. The unfavourability of this mechanism can likely be attributed to the lack of an aromatic system being formed in the final product.

We expect to see:
key information about the calculation, such as method (eg B3LYP) basis set (eg 6-31G(d,p) and symmetry (eg C3v)
the Item table copied and pasted into your wiki
a rotatable 3d jmol file/image of the optimised structure
a link to the final file of the optimisation/frequency

Conclusion

Rep:Jed15Yr3TS

2017-12-17T01:05:34Z

Jed15:

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

<br style="clear:right">

Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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Rep:Jed15Yr3TS

2017-12-16T22:48:52Z

Jed15:

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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</jmol>

Rep:Jed15Yr3TS

2017-12-16T22:47:10Z

Jed15:

===Exercise 1: Reaction of Butadiene with Ethylene===

Found below is a simple MO diagram for the formation of the butadiene/ethene transition state, containing simple 'symmetric' or antisymmetric' labels, with images for the HOMO and LUMO of each of the starting reactants. The four molecular orbitals in the transition state formed from these MOs can be visualised as Jmol images below.

[[File:Jed15 exercise1 MO diagram final.PNG|700px|left]]

[[File:Jed15_-_butadiene_HOMO.PNG|1px|right|frame|Butadiene HOMO (a1)]]
[[File:Jed15_Ethene_HOMO.PNG|1px|right|right|Ethene HOMO (s3)]]
[[File:Jed15_butadiene_LUMO.PNG|1px|right||frame|Butadiene LUMO (s2)]]
[[File:Jed15_Ethene_LUMO.PNG|1px|right|frame|Ethene LUMO (a3)]]

Transition State 1 (a4)
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Transition State 2 (s4)
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Transition State 3 (s5)
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Transition State 4 (a5)
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Rep:Jed15Yr3TS

2017-12-16T22:41:51Z

Jed15:

Rep:Jed15Yr3TS

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Jed15:

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Jed15:

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Jed15:

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2017-12-16T22:40:59Z

Jed15:

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Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:39:23Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:38:39Z

Jed15:

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Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:31:18Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:30:55Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:30:05Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:29:26Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:28:40Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:28:08Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:27:33Z

Jed15:

Rep:Jed15Yr3TS

2017-12-16T22:26:07Z

Jed15: