Rep:JSheny3

2017-11-21T22:40:20Z

Js6815: /* Reaction of Butadiene with Ethene */

== 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 Ethene==
===MO analysis of the reaction===
The MO diagram of the formation of transition state is drawn below along with the symmetry symbol (a or s) (fig 1).
[[File:Jsheny3_ex1_MOED_corrected.png|thumb|center|500px|Fig 1: Molecular Orbital Diagram for the formation of the transition state of the reaction.]]

It's worth noticing that all the orbitals from the transition state are higher than the HOMO of the reactants. This is deliberately drawn in this way to show that the transition state has higher energy than the reactants in a reaction.
<br>
<br>
The HOMO and LUMO orbitals of the reactants and the orbits of transition state which they produced are listed below (table 1):

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of some key MOs and their correlation with the MO energy diagram (fig 1)
! colspan="2"| Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state of the reaction
|-
| Fig 2: HOMO || Fig 3: LUMO || Fig 4: HOMO || Fig 5: LUMO || Fig 6: MO 16 of transition state || Fig 7: MO 17 of transition state || Fig 8: MO 18 of transition state || Fig 9: MO 19 of transition state
|-
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|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:Jsheny3 ex1 mo1.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo2.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo3.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo4.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo5.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo6.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo7.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo8.png|100px|]]
|}
''Figure 7 and figure 9 is a bit misleading due to the limitation of the method used for the optimization. The interactions should be between the terminal carbon atoms of butadiene and ethene like the others ''

From the table above, it can be concluded that only orbitals with same symmetry label can interact (either both symmetrical or both antisymmetrical). The interaction between orbitals with different symmetry (one symmetrical and the other antisymmetrical) is forbiddened. Therefore the orbital overlap integral (S) is zero for a symmetric-antisymmetric interaction and non-zero for an antisymmetric-antisymmetric interaction.

===Analysis of C-C bond length and transition state vibration===
The C-C bond lengths of the reactants, transition state as well as the product are listed below:

* Fig 10: C-C bond lengths of ethene (reactant)
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<name>JSHENY3EX1ETHENE</name>
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<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
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* Fig 11: C-C bond lengths of butadiene (reactant)
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<text>C1-C4 Distances</text>
<target>JSHENY3EX1BUTADIENE</target>
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<script>measure 4 6 </script>
<text>C4-C6 Distances</text>
<target>JSHENY3EX1BUTADIENE</target>
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* Fig 12: C-C bond lengths of reaction transition state
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<text>C1-C9 Distances</text>
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<text>C9-C6 Distances</text>

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<text>C6-C11 Distances</text>

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<script>frame 16; measure off;measure 11 14 </script>
<text>C11-C14 Distances</text>

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* Fig 13: C-C bond lengths of cyclohexene (product)
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<text>C3-C14 Distances</text>
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<text>C14-C11 Distances</text>

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<text>C11-C8 Distances</text>

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<text>C8-C5 Distances</text>

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<text>C5-C1 Distances</text>
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Typical sp<sup>3</sup>-sp<sup>3</sup> C-C bond length is 1.54 Å while typical sp<sup>2</sup>-sp<sup>2</sup> C-C bond length 1.47 Å. The Van der Waals radius of the Carbon atom is 1.7 Å.

Since in the transition state, the electrons are delocalized within the two reactants, it is expected that the sp<sup>3</sup>-sp<sup>3</sup> C-C bond of the reactants will possess higher electron density and thus the bond length will be shorter in the transition state. For the same reason, the sp<sup>2</sup>-sp<sup>2</sup> C-C bond lengths of the reactants are weaken and lengthen in the transition state. These expectations for the bond length of transitions state is verified by the above distance measurements:
*C1-C4 distance in Fig 10 (1.33 Å) is shorter than C11-C14 distance in Fig 12 (1.38 Å).
*C1-C4 distance in Fig 11 (1.33 Å) is longer than C9-C6 distance in Fig 12 (1.38 Å).
*C4-C6 distance in Fig 11 (1.47 Å) is longer than C9-C6 distance in Fig 12 (1.41 Å).

The distance between two approaching carbons (C6 and C11 /C3 and C14 in fig 13 ) is 2.11 Å, which is shorter than the Van der Waals radius of two carbon atoms (1.7 + 1.7=3.4 Å).
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<br>
The vibration corresponds to the reaction path at transition state is shown below (fig 14):
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From fig 14, it can be seen that the formation of the two bonds is synchronous, as expected for a concerted pericyclic reactions. One other way to prove this is in the transition state the distances between the two reacting carbon atoms in both ends are the same (in fig 12: C3-14 = C6-C11 = 2.11 Å).

===Calculation for exercise 1===
PM6 optimized reactant: [[Media:JSHENY3_EX1_BUTADIENE.LOG]] [[Media:JSHENY3_EX1_ETHENE.LOG]]

PM6 optimized product: [[Media:JSHENY3_EX1_OPT1_PRODUCT.LOG]]

PM6 optimized transition state:[[Media:JSHENY3_EX1_OPT1_PRODUCT.LOG]]

Using frequency calculation to confirm the transition state: [[Media:JSHENY3_EX1_OPT3_FRE.LOG]]

Using IRC to confirm the transition state: [[Media:JSHENY3_EX1_OPT4_IRC.LOG]]

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
===MO analysis===
The MO diagram for the reaction is shown below (Fig 15 and Fig 16):
[[File:Jsheny3 ex2 endo MOED.png|thumb|left|500px|Fig 14: Molecular Orbital Diagram for endo transition state.]]
[[File:Jsheny3 ex2 exo MOED.png|thumb|right|500px|Fig 15: Molecular Orbital Diagram for exo transition state.]]

<br style="clear:right">

The orbitals for both endo and exo transition states are listed below (table 2):
{| class="wikitable" style="border: none; background: none;"
|+|table 2: table of some key MOs and their correlation with the MO energy diagram (fig 14 and fig 15)
! colspan="4"| Endo transition state !! colspan="4"| Exo transition state
|-
| Fig 17: MO 40 of transition states (occupied) || Fig 18: MO 41 of transition states (occupied) || Fig 19: MO 42 of transition states (unoccupied) || Fig 20: MO 43 of transition states (unoccupied) || Fig 21: MO 40 of transition states (occupied) || Fig 22: MO 41 of transition states (occupied) || Fig 23: MO 42 of transition states (unoccupied) || Fig 24: MO 43 of transition states (unoccupied)
|-
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|-
! colspan="8"| Correlation with MO diagram (Fig 15 and Fig 16)
|-
|align=center|[[File:Jsy3endo ex2 ts1.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts2.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts3.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts4.png|100px|]]
|align=center|[[File:Jsheny3 ex2 exo ts1.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts2.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts3.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts4.png|130px|]]
|}

This is an inverse demand DA reaction. The inverse demand DA reaction is a [4+2] cycloaddition between an electron-rich dienophile and an electron-poor diene. In this case, cyclohexadiene (the diene) is not necessarily electron poor, yet 1,3-dioxole (the dienophile) is definitely electron-rich, due to the π-conjugation by the oxygen atoms in both ends. So 1,3-dioxole has higher energy molecular orbitals than cyclohexadiene. Therefore, it is expected that the LUMO of cyclohexadiene and HOMO of 1,3-dioxole have a smaller energy difference than the HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Hence, the bonding molecular orbital formed from LUMO of cyclohexadiene and HOMO of 1,3-dioxole will be the stronger and more stable one.
<br>
<br>
This is verified by computational calculation. The HOMO, LUMO energy of both diene and dienophile can be calculated to see the energy difference (via B3YLP method). The results are displayed below (table 3).

{| class="wikitable" style="border: none; background: none;"
|+|Table 3: table of energy calculation results to show that this reaction is an inverse demand DA reaction
! HOMO of cyclohexadiene!! LUMO of 1,3-dioxole!! Energy difference (absolute value)
|-
| -0.20554 a.u.|| 0.03795 a.u.|| 0.24349 a.u.
|-
! LUMO of cyclohexadiene!! HOMO of 1,3-dioxole!! Energy difference (absolute value)
|-
| -0.01711 a.u.|| -0.19593 a.u.|| 0.17882 a.u.
|}
So the LUMO of cyclohexadiene and HOMO of 1,3-dioxole have a smaller energy difference and therefore are better overlapped.
<br>
<br>
''Calculation reference:''

Orbital energies of dioxole: [[Media:JSHENY3_EX2_DIOXOLE_B3LYP.LOG]]

Orbital energies of cyclohexadiene: [[Media:JSHENY3_EX2_CYCLOHEXADIENE_B3LYP.LOG]]

===Reaction Barriers and Reaction Energy===

{| class="wikitable"
|+|Table 4: tabulated energies of reactants, transition states and the reaction.
! !!cyclohexadiene!! 1,3-dioxole!! endo transition state!! endo product!! exo transition state!! exo product
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (Hartree/Particle)
| -233.324375 || -267.068643|| -500.332150|| -500.418691|| -500.329168||-500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (KJ/mol)
| -6.12593193227x10<sup>6</sup> || -7.0118877561x10<sup>6</sup> || -1.31362215989x10<sup>7</sup> || -1.3138493733x10<sup>7</sup> || -1.31361433065x10<sup>7</sup> || -1.31384577637x10<sup>7</sup>
|-
|}

*The reaction barrier of a reaction is the energy difference between the transition state and the reactants, the smaller reaction barrier reaction pathway is the kinetically favored one:
**For the endo reaction: -1.31362215989x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= 159.808946 KJ/mol
**For the exo reaction: -1.31361433065x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= 167.638188 KJ/mol

*The reaction energy of a reaction is the energy difference between the product and the reactants.
**For the endo reaction: -1.3138493733x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= -67.40 KJ/mol
**For the exo reaction: -1.31384577637x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= -63.8 KJ/mol

Since the endo product is the one that has lower energy, and the endo pathway has a smaller reaction barrier, endo product is bothe kinetically and thermodynamically favored.

File:Jsheny3 ex2 endo opt3 by3lp.log

The HOMO of the endo and exo transition states are listed below (table 5):
{| class="wikitable" style="border: none; background: none;"
|+|table 5: table of HOMO of endo and exo transition states MO, isovalue set to 0.01

! Endo transition state
! scope="col" style="width: 500px;" | Explanation
|-
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|rowspan="3" style="text-align: left; vertical-align: top;" | The endo transition state is the one possesses secondary orbital effect. The interaction is visualized by the figures on the left. For the endo transition state, the interaction is not just between the four reacting carbon atoms. The MOs of oxygens of 1,3-dioxole can also interact with the diene part of cyclohexadiene. Such interactions result in an overall stabilizing of transition state, and thus lower the reaction barrier of the endo transition state. However for the exo transition state, there is only primary orbital interaction between the two reactants. Therefore the endo product is the kinetically favored one.
|-
! Exo transition state
|-
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== Exercise 3: Diels-Alder vs Cheletropic ==
===IRC analysis===
The TSs for endo,exo and chelectropic transition states and their corresponding IRCs are tabulated below (table 6):

{| class="wikitable" style="border: none; background: none;"
|+|Table 6: Endo, exo and chelectropic (optimized by PM6) and their corresponding IRCs
! Endo transition state (fig 25)!! Exo transition state (fig 26)!! Cheletropic transition state (fig 27)
|-
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|-
! colspan="3"|IRC animation (click the image to see the animated reaction trajectory if it is not moving already)
|-
| [[File:Jsheny3_ex3_endo_irc_ani.gif|500px]]
| [[File:Jsheny3_ex3_exo_irc_ani.gif|500px]]
| [[File:Jsheny3_ex3_che_irc_ani.gif|500px]]
|-
! colspan="3"|TOP: IRC trajectory energy vs reaction coordinate graph, Bottom: gradient variation
|-
| [[File:Jsheny3 ex3 endo irc graph.PNG|500px]]
| [[File:Jsheny3 ex3 exo irc graph.PNG|500px]]
| [[File:Jsheny3 ex3 che irc graph.PNG|500px]]
|}

===Reaction Barriers and Reaction Energy===
{| class="wikitable"
|+|Table 7: tabulated energies of reactants, transition states and the reaction (PM6 optimized)
! style="width: 200px;"| !!o-Xylylene!! SO<sub>2</sub>!! endo transition state!! endo product!! exo transition state!! exo product!! cheletropic transition state !! cheletropic product
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (Hartree/Particle)
| 0.178099 || -0.118614|| 0.090562|| 0.021697|| 0.092078||0.021454||0.099062||-0.000006
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (KJ/mol)
| 467.59896 || -311.4210807 || 237.770549 || 56.9654778 || 241.7508074 || 56.3274813|| 260.087301 || -0.0157530012
|-
|}

*The reaction barrier of a reaction is the energy difference between the transition state and the reactants, the smaller reaction barrier reaction pathway is the kinetically favored one:
**For the endo reaction: 237.770549-(467.59896+(-311.4210807))=81.59 KJ/mol
**For the exo reaction: 241.7508074-(467.59896+(-311.4210807))=85.57 KJ/mol
**For the cheletropic reaction: 260.087301-(467.59896+(-311.4210807))=103.91 KJ/mol

*The reaction energy of a reaction is the energy difference between the product and the reactants.
**For the endo reaction: 56.9654778-(467.59896+(-311.4210807))=-99.21 KJ/mol
**For the exo reaction: 56.3274813-(467.59896+(-311.4210807))=-99.85 KJ/mol
**For the cheletropic reaction: -0.0157530012-(467.59896+(-311.4210807))=-156.19 KJ/mol

The endo transition state has the lowest energy and therefore the endo product is regarded as the kinetic product. The cheletropic reaction requires smallest amount of energy and therefore its product is regarded as the thermodynamically favored product.

The reaction profile is drawn below (fig28):

[[File:Jsheny3 ex3 energy profile.png|center|400px]]

By looking at the IRC of the reactions, it can be found that for all three reactions, the bonding of the six-membered ring changes in the same way----it gains a new double bond and forms an aromatic ring. Here, formation of endo product is used as an example:

{| class="wikitable"
|+|Table 9: using formation of endo product to illustrate gaining of aromaticity by the 6-membered ring
! before the reaction!! after the reaction
|-
|Fig 29: [[File:jsheny3_ex3_endo_before.PNG|200px]]
|Fig 30: [[File:jsheny3_ex3_endo_after.PNG|200px]]
|-
! number of double bonds in 6-membered ring!! number of double bonds in 6-membered ring
|-
| style="text-align: center;"|2 ||style="text-align: center;"| 3 (delocalized, showing aromaticity)
|-
|}

===Conclusion===

File:JSHENY3 EX1 OPT4 IRC.LOG

2017-11-21T22:36:02Z

Js6815:

File:JSHENY3 EX1 OPT3 FRE.LOG

2017-11-21T22:36:01Z

Js6815: Js6815 uploaded a new version of File:JSHENY3 EX1 OPT3 FRE.LOG

File:JSHENY3 EX1 OPT2 TS.LOG

2017-11-21T22:36:00Z

Js6815: Js6815 uploaded a new version of File:JSHENY3 EX1 OPT2 TS.LOG

File:JSHENY3 EX1 OPT1 PRODUCT.LOG

2017-11-21T22:36:00Z

Js6815: Js6815 uploaded a new version of File:JSHENY3 EX1 OPT1 PRODUCT.LOG

File:JSHENY3 EX1 ETHENE.LOG

2017-11-21T22:35:59Z

Js6815: Js6815 uploaded a new version of File:JSHENY3 EX1 ETHENE.LOG

2017-11-21T21:57:47Z

Js6815: /* MO analysis */

== 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?)

==Reaction of Butadiene with Ethene==
===MO analysis of the reaction===
The MO diagram of the formation of transition state is drawn below along with the symmetry symbol (a or s) (fig 1).
[[File:Jsheny3_ex1_MOED_corrected.png|thumb|center|500px|Fig 1: Molecular Orbital Diagram for the formation of the transition state of the reaction.]]

It's worth noticing that all the orbitals from the transition state are higher than the HOMO of the reactants. This is deliberately drawn in this way to show that the transition state has higher energy than the reactants in a reaction.
<br>
<br>
The HOMO and LUMO orbitals of the reactants and the orbits of transition state which they produced are listed below (table 1):

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of some key MOs and their correlation with the MO energy diagram (fig 1)
! colspan="2"| Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state of the reaction
|-
| Fig 2: HOMO || Fig 3: LUMO || Fig 4: HOMO || Fig 5: LUMO || Fig 6: MO 16 of transition state || Fig 7: MO 17 of transition state || Fig 8: MO 18 of transition state || Fig 9: MO 19 of transition state
|-
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|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:Jsheny3 ex1 mo1.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo2.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo3.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo4.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo5.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo6.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo7.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo8.png|100px|]]
|}
''Figure 7 and figure 9 is a bit misleading due to the limitation of the method used for the optimization. The interactions should be between the terminal carbon atoms of butadiene and ethene like the others ''

From the table above, it can be concluded that only orbitals with same symmetry label can interact (either both symmetrical or both antisymmetrical). The interaction between orbitals with different symmetry (one symmetrical and the other antisymmetrical) is forbiddened. Therefore the orbital overlap integral (S) is zero for a symmetric-antisymmetric interaction and non-zero for an antisymmetric-antisymmetric interaction.

===Analysis of C-C bond length and transition state vibration===
The C-C bond lengths of the reactants, transition state as well as the product are listed below:

* Fig 10: C-C bond lengths of ethene (reactant)
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<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
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* Fig 11: C-C bond lengths of butadiene (reactant)
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<text>C4-C6 Distances</text>
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* Fig 12: C-C bond lengths of reaction transition state
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<script>frame 16; measure off;measure 9 6 </script>
<text>C9-C6 Distances</text>

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<script>frame 16; measure off;measure 6 11 </script>
<text>C6-C11 Distances</text>

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<script>frame 16; measure off;measure 11 14 </script>
<text>C11-C14 Distances</text>

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<script>frame 16; measure off;measure 14 3 </script>
<text>C14-C3 Distances</text>
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* Fig 13: C-C bond lengths of cyclohexene (product)
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<text>C3-C14 Distances</text>
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<script>frame 14; measure off;measure 14 11 </script>
<text>C14-C11 Distances</text>

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<text>C11-C8 Distances</text>

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<script>frame 14; measure off;measure 8 5 </script>
<text>C8-C5 Distances</text>

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<script>frame 14; measure off;measure 5 1 </script>
<text>C5-C1 Distances</text>
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Typical sp<sup>3</sup>-sp<sup>3</sup> C-C bond length is 1.54 Å while typical sp<sup>2</sup>-sp<sup>2</sup> C-C bond length 1.47 Å. The Van der Waals radius of the Carbon atom is 1.7 Å.

Since in the transition state, the electrons are delocalized within the two reactants, it is expected that the sp<sup>3</sup>-sp<sup>3</sup> C-C bond of the reactants will possess higher electron density and thus the bond length will be shorter in the transition state. For the same reason, the sp<sup>2</sup>-sp<sup>2</sup> C-C bond lengths of the reactants are weaken and lengthen in the transition state. These expectations for the bond length of transitions state is verified by the above distance measurements:
*C1-C4 distance in Fig 10 (1.33 Å) is shorter than C11-C14 distance in Fig 12 (1.38 Å).
*C1-C4 distance in Fig 11 (1.33 Å) is longer than C9-C6 distance in Fig 12 (1.38 Å).
*C4-C6 distance in Fig 11 (1.47 Å) is longer than C9-C6 distance in Fig 12 (1.41 Å).

The distance between two approaching carbons (C6 and C11 /C3 and C14 in fig 13 ) is 2.11 Å, which is shorter than the Van der Waals radius of two carbon atoms (1.7 + 1.7=3.4 Å).
<br>
<br>
The vibration corresponds to the reaction path at transition state is shown below (fig 14):
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From fig 14, it can be seen that the formation of the two bonds is synchronous, as expected for a concerted pericyclic reactions. One other way to prove this is in the transition state the distances between the two reacting carbon atoms in both ends are the same (in fig 12: C3-14 = C6-C11 = 2.11 Å).

== Exercise 2 ==
===MO analysis===
The MO diagram for the reaction is shown below (Fig 15 and Fig 16):
[[File:Jsheny3 ex2 endo MOED.png|thumb|left|500px|Fig 14: Molecular Orbital Diagram for endo transition state.]]
[[File:Jsheny3 ex2 exo MOED.png|thumb|right|500px|Fig 15: Molecular Orbital Diagram for exo transition state.]]

<br style="clear:right">

The orbitals for both endo and exo transition states are listed below (table 2):
{| class="wikitable" style="border: none; background: none;"
|+|table 2: table of some key MOs and their correlation with the MO energy diagram (fig 1)
! colspan="4"| Endo transition state !! colspan="4"| Exo transition state
|-
| Fig 17: MO 40 of transition states (occupied) || Fig 18: MO 41 of transition states (occupied) || Fig 19: MO 42 of transition states (unoccupied) || Fig 20: MO 43 of transition states (unoccupied) || Fig 21: MO 40 of transition states (occupied) || Fig 22: MO 41 of transition states (occupied) || Fig 23: MO 42 of transition states (unoccupied) || Fig 24: MO 43 of transition states (unoccupied)
|-
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|-
! colspan="8"| Correlation with MO diagram (Fig 15 and Fig 16)
|-
|align=center|[[File:Jsy3endo ex2 ts1.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts2.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts3.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts4.png|100px|]]
|align=center|[[File:Jsheny3 ex2 exo ts1.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts2.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts3.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts4.png|130px|]]
|}

This is an inverse demand DA reaction. The inverse demand DA reaction is a [4+2] cycloaddition between an electron-rich dienophile and an electron-poor diene. In this case, cyclohexadiene (the diene) is not necessarily electron poor, yet 1,3-dioxole (the dienophile) is definitely electron-rich, due to the π-conjugation by the oxygen atoms in both ends. So 1,3-dioxole has higher energy molecular orbitals than cyclohexadiene. Therefore, it is expected that the LUMO of cyclohexadiene and HOMO of 1,3-dioxole have a smaller energy difference than the HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Hence, the bonding molecular orbital formed from LUMO of cyclohexadiene and HOMO of 1,3-dioxole will be the stronger and more stable one.
<br>
<br>
This is verified by computational calculation. The HOMO, LUMO energy of both diene and dienophile can be calculated to see the energy difference (via B3YLP method). The results for both ways are displayed below (table 3).

{| class="wikitable" style="border: none; background: none;"
|+|Table 3: table of energy calculation results to show that this reaction is an inverse demand DA reaction
! HOMO of cyclohexadiene!! LUMO of 1,3-dioxole!! Energy difference (absolute value)
|-
| -0.20554 a.u.|| 0.03795 a.u.|| 0.24349 a.u.
|-
! LUMO of cyclohexadiene!! HOMO of 1,3-dioxole!! Energy difference (absolute value)
|-
| -0.01711 a.u.|| -0.19593 a.u.|| 0.17882 a.u.
|}
So the LUMO of cyclohexadiene and HOMO of 1,3-dioxole have a smaller energy difference and therefore are better overlapped.
<br>
<br>
''Calculation reference:''

Orbital energies of dioxole: [[Media:JSHENY3_EX2_DIOXOLE_B3LYP.LOG]]

Orbital energies of cyclohexadiene: [[Media:JSHENY3_EX2_CYCLOHEXADIENE_B3LYP.LOG]]

===Reaction Barriers and Reaction Energy===

{| class="wikitable"
|+|Table 4: tabulated energies of reactants, transition states and the reaction.
! !!cyclohexadiene!! 1,3-dioxole!! endo transition state!! endo product!! exo transition state!! exo product
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (Hartree/Particle)
| -233.324375 || -267.068643|| -500.332150|| -500.418691|| -500.329168||-500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (KJ/mol)
| -6.12593193227x10<sup>6</sup> || -7.0118877561x10<sup>6</sup> || -1.31362215989x10<sup>7</sup> || -1.3138493733x10<sup>7</sup> || -1.31361433065x10<sup>7</sup> || -1.31384577637x10<sup>7</sup>
|-
|}

*The reaction barrier of a reaction is the energy difference between the transition state and the reactants, the smaller reaction barrier reaction pathway is the kinetically favored one:
**For the endo reaction: -1.31362215989x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= 159.808946 KJ/mol
**For the exo reaction: -1.31361433065x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= 167.638188 KJ/mol

*The reaction energy of a reaction is the energy difference between the product and the reactants.
**For the endo reaction: -1.3138493733x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= -67.40 KJ/mol
**For the exo reaction: -1.31384577637x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= -63.8 KJ/mol

Since the endo product is the one that has lower energy, and the endo pathway has a smaller reaction barrier, endo product is bothe kinetically and thermodynamically favored.

File:Jsheny3 ex2 endo opt3 by3lp.log

The HOMO of the endo and exo transition states are listed below (table 5):
{| class="wikitable" style="border: none; background: none;"
|+|table 5: table of HOMO of endo and exo transition states MO, isovalue set to 0.01

! Endo transition state
! scope="col" style="width: 500px;" | Explanation
|-
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|rowspan="3" | The endo transition state is the one possesses secondary orbital effect. The interaction is visualized by the figures on the left. For the endo transition state, the interaction is not just between the four reacting carbon atoms. The MOs of oxygens of 1,3-dioxole can also interact with the diene part of cyclohexadiene. Such interactions result in an overall stabilizing of transition state, and thus lower the reaction barrier of the endo transition state. Therefore the endo product is the kinetically favored one.
|-
! Exo transition state
|-
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== Exercise 3: ==
===IRC analysis===
The TSs for endo,exo and chelectropic transition states and their corresponding IRCs are tabulated below (table 5):

{| class="wikitable" style="border: none; background: none;"
|+|Table 5: Endo, exo and chelectropic (optimized by PM6) and their corresponding IRCs
! Endo transition state!! Exo transition state!! Cheletropic transition state
|-
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|-
! colspan="3"|IRC animation (click the image to see the animated reaction trajectory if it is not moving already)
|-
| [[File:Jsheny3_ex3_endo_irc_ani.gif|500px]]
| [[File:Jsheny3_ex3_exo_irc_ani.gif|500px]]
| [[File:Jsheny3_ex3_che_irc_ani.gif|500px]]
|-
! colspan="3"|TOP: IRC trajectory energy vs reaction coordinate graph, Bottom: gradient variation
|-
| [[File:Jsheny3 ex3 endo irc graph.PNG|500px]]
| [[File:Jsheny3 ex3 exo irc graph.PNG|500px]]
| [[File:Jsheny3 ex3 che irc graph.PNG|500px]]
|}

===Reaction Barriers and Reaction Energy===
{| class="wikitable"
|+|Table 7: tabulated energies of reactants, transition states and the reaction (PM6 optimized)
! style="width: 200px;"| !!o-Xylylene!! SO<sub>2</sub>!! endo transition state!! endo product!! exo transition state!! exo product!! cheletropic transition state !! cheletropic product
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (Hartree/Particle)
| 0.178099 || -0.118614|| 0.090562|| 0.021697|| 0.092078||0.021454||0.099062||-0.000006
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (KJ/mol)
| 467.59896 || -311.4210807 || 237.770549 || 56.9654778 || 241.7508074 || 56.3274813|| 260.087301 || -0.0157530012
|-
|}

*The reaction barrier of a reaction is the energy difference between the transition state and the reactants, the smaller reaction barrier reaction pathway is the kinetically favored one:
**For the endo reaction: 237.770549-(467.59896+(-311.4210807))=81.59 KJ/mol
**For the exo reaction: 241.7508074-(467.59896+(-311.4210807))=85.57 KJ/mol
**For the cheletropic reaction: 260.087301-(467.59896+(-311.4210807))=103.91 KJ/mol

*The reaction energy of a reaction is the energy difference between the product and the reactants.
**For the endo reaction: 56.9654778-(467.59896+(-311.4210807))=-99.21 KJ/mol
**For the exo reaction: 56.3274813-(467.59896+(-311.4210807))=-99.85 KJ/mol
**For the cheletropic reaction: -0.0157530012-(467.59896+(-311.4210807))=-156.19 KJ/mol

The endo transition state has the lowest energy and therefore the endo product is regarded as the kinetic product. The cheletropic reaction requires smallest amount of energy and therefore its product is regarded as the thermodynamically favored product.

The reaction profile is drawn below (fig):

[[File:Jsheny3 ex3 energy profile.png|center|400px]]

By looking at the IRC of the reactions, it can be found that for all three reactions, the bonding of the six-membered ring changes in the same way----it gains a new double bond and forms an aromatic ring. Here, formation of endo product is used as an example:

{| class="wikitable"
|+|Table 9: using formation of endo product to illustrate gaining of aromaticity by the 6-membered ring
! before the reaction!! after the reaction
|-
|[[File:jsheny3_ex3_endo_before.PNG|200px]]
|[[File:jsheny3_ex3_endo_after.PNG|200px]]
|-
! number of double bonds in 6-membered ring!! number of double bonds in 6-membered ring
|-
| style="text-align: center;"|2 ||style="text-align: center;"| 3 (delocalized, showing aromaticity)
|-
|}

===Conclusion===

File:Jsheny3 ex2 exo MOED.png

2017-11-21T21:54:49Z

Js6815: Js6815 uploaded a new version of File:Jsheny3 ex2 exo MOED.png

File:Jsheny3 ex2 endo MOED.png

2017-11-21T21:54:13Z

Js6815: Js6815 uploaded a new version of File:Jsheny3 ex2 endo MOED.png

Rep:JSheny3

2017-11-21T21:21:15Z

Js6815: /* Reaction Barriers and Reaction Energy */

== 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?)

==Reaction of Butadiene with Ethene==
===MO analysis of the reaction===
The MO diagram of the formation of transition state is drawn below along with the symmetry symbol (a or s) (fig 1).
[[File:Jsheny3_ex1_MOED_corrected.png|thumb|center|500px|Fig 1: Molecular Orbital Diagram for the formation of the transition state of the reaction.]]

It's worth noticing that all the orbitals from the transition state are higher than the HOMO of the reactants. This is deliberately drawn in this way to show that the transition state has higher energy than the reactants in a reaction.
<br>
<br>
The HOMO and LUMO orbitals of the reactants and the orbits of transition state which they produced are listed below (table 1):

{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of some key MOs and their correlation with the MO energy diagram (fig 1)
! colspan="2"| Butadiene !! colspan="2"| Ethene !! colspan="4"| Transition state of the reaction
|-
| Fig 2: HOMO || Fig 3: LUMO || Fig 4: HOMO || Fig 5: LUMO || Fig 6: MO 16 of transition state || Fig 7: MO 17 of transition state || Fig 8: MO 18 of transition state || Fig 9: MO 19 of transition state
|-
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|-
! colspan="8"| Correlation with MO diagram (Fig1)
|-
|align=center|[[File:Jsheny3 ex1 mo1.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo2.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo3.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo4.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo5.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo6.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo7.png|100px|]]
|align=center|[[File:Jsheny3 ex1 mo8.png|100px|]]
|}
''Figure 7 and figure 9 is a bit misleading due to the limitation of the method used for the optimization. The interactions should be between the terminal carbon atoms of butadiene and ethene like the others ''

From the table above, it can be concluded that only orbitals with same symmetry label can interact (either both symmetrical or both antisymmetrical). The interaction between orbitals with different symmetry (one symmetrical and the other antisymmetrical) is forbiddened. Therefore the orbital overlap integral (S) is zero for a symmetric-antisymmetric interaction and non-zero for an antisymmetric-antisymmetric interaction.

===Analysis of C-C bond length and transition state vibration===
The C-C bond lengths of the reactants, transition state as well as the product are listed below:

* Fig 10: C-C bond lengths of ethene (reactant)
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<script>measure 1 4 </script>
<text>C1-C4 Distances</text>
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* Fig 11: C-C bond lengths of butadiene (reactant)
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<text>C4-C6 Distances</text>
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* Fig 12: C-C bond lengths of reaction transition state
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<text>C9-C6 Distances</text>

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<text>C6-C11 Distances</text>

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<script>frame 16; measure off;measure 11 14 </script>
<text>C11-C14 Distances</text>

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<script>frame 16; measure off;measure 14 3 </script>
<text>C14-C3 Distances</text>
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* Fig 13: C-C bond lengths of cyclohexene (product)
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<text>C3-C14 Distances</text>
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<text>C14-C11 Distances</text>

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<text>C11-C8 Distances</text>

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<text>C8-C5 Distances</text>

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<text>C5-C1 Distances</text>
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Typical sp<sup>3</sup>-sp<sup>3</sup> C-C bond length is 1.54 Å while typical sp<sup>2</sup>-sp<sup>2</sup> C-C bond length 1.47 Å. The Van der Waals radius of the Carbon atom is 1.7 Å.

Since in the transition state, the electrons are delocalized within the two reactants, it is expected that the sp<sup>3</sup>-sp<sup>3</sup> C-C bond of the reactants will possess higher electron density and thus the bond length will be shorter in the transition state. For the same reason, the sp<sup>2</sup>-sp<sup>2</sup> C-C bond lengths of the reactants are weaken and lengthen in the transition state. These expectations for the bond length of transitions state is verified by the above distance measurements:
*C1-C4 distance in Fig 10 (1.33 Å) is shorter than C11-C14 distance in Fig 12 (1.38 Å).
*C1-C4 distance in Fig 11 (1.33 Å) is longer than C9-C6 distance in Fig 12 (1.38 Å).
*C4-C6 distance in Fig 11 (1.47 Å) is longer than C9-C6 distance in Fig 12 (1.41 Å).

The distance between two approaching carbons (C6 and C11 /C3 and C14 in fig 13 ) is 2.11 Å, which is shorter than the Van der Waals radius of two carbon atoms (1.7 + 1.7=3.4 Å).
<br>
<br>
The vibration corresponds to the reaction path at transition state is shown below (fig 14):
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From fig 14, it can be seen that the formation of the two bonds is synchronous, as expected for a concerted pericyclic reactions. One other way to prove this is in the transition state the distances between the two reacting carbon atoms in both ends are the same (in fig 12: C3-14 = C6-C11 = 2.11 Å).

== Exercise 2 ==
===MO analysis===
The MO diagram for the reaction is shown below (Fig 14 and Fig 15):
[[File:Jsheny3 ex2 endo MOED.png|thumb|left|500px|Fig 14: Molecular Orbital Diagram for endo product.]]
[[File:Jsheny3 ex2 exo MOED.png|thumb|right|500px|Fig 15: Molecular Orbital Diagram for exo product.]]

<br style="clear:right">

The orbitals for both endo and exo transition states are listed below (table 2):
{| class="wikitable" style="border: none; background: none;"
|+|table 1: table of some key MOs and their correlation with the MO energy diagram (fig 1)
! colspan="4"| Endo transition state !! colspan="4"| Exo transition state
|-
| Fig 16: MO 40 of transition states (occupied) || Fig 17: MO 41 of transition states (occupied) || Fig 18: MO 42 of transition states (unoccupied) || Fig 19: MO 43 of transition states (unoccupied) || Fig 20: MO 40 of transition states (occupied) || Fig 21: MO 41 of transition states (occupied) || Fig 22: MO 42 of transition states (unoccupied) || Fig 23: MO 43 of transition states (unoccupied)
|-
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|-
! colspan="8"| Correlation with MO diagram (Fig 14 and Fig 15)
|-
|align=center|[[File:Jsy3endo ex2 ts1.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts2.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts3.png|100px|]]
|align=center|[[File:Jsy3endo ex2 ts4.png|100px|]]
|align=center|[[File:Jsheny3 ex2 exo ts1.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts2.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts3.png|130px|]]
|align=center|[[File:Jsheny3 ex2 exo ts4.png|130px|]]
|}

This is an inverse demand DA reaction. The inverse demand DA reaction is a [4+2] cycloaddition between an electron-rich dienophile and an electron-poor diene. In this case, cyclohexadiene (the diene) is not necessarily electron poor, yet 1,3-dioxole (the dienophile) is definitely electron-rich, due to the π-conjugation by the oxygen atoms in both ends. So 1,3-dioxole has higher energy molecular orbitals than cyclohexadiene. Therefore, it is expected that the LUMO of cyclohexadiene and HOMO of 1,3-dioxole have a smaller energy difference than the HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Hence, the bonding molecular orbital formed from LUMO of cyclohexadiene and HOMO of 1,3-dioxole will be the stronger and more stable one.
<br>
<br>
This is verified by computational calculation. The HOMO, LUMO energy of both diene and dienophile can be calculated to see the energy difference (via B3YLP method). The results for both ways are displayed below (table 3).

{| class="wikitable" style="border: none; background: none;"
|+|Table 3: table of energy calculation results to show that this reaction is an inverse demand DA reaction
! HOMO of cyclohexadiene!! LUMO of 1,3-dioxole!! Energy difference (absolute value)
|-
| -0.20554 a.u.|| 0.03795 a.u.|| 0.24349 a.u.
|-
! LUMO of cyclohexadiene!! HOMO of 1,3-dioxole!! Energy difference (absolute value)
|-
| -0.01711 a.u.|| -0.19593 a.u.|| 0.17882 a.u.
|}
So the LUMO of cyclohexadiene and HOMO of 1,3-dioxole have a smaller energy difference and therefore are better overlapped.
<br>
<br>
''Calculation reference:''

Orbital energies of dioxole: [[Media:JSHENY3_EX2_DIOXOLE_B3LYP.LOG]]

Orbital energies of cyclohexadiene: [[Media:JSHENY3_EX2_CYCLOHEXADIENE_B3LYP.LOG]]

===Reaction Barriers and Reaction Energy===

{| class="wikitable"
|+|Table 4: tabulated energies of reactants, transition states and the reaction.
! !!cyclohexadiene!! 1,3-dioxole!! endo transition state!! endo product!! exo transition state!! exo product
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (Hartree/Particle)
| -233.324375 || -267.068643|| -500.332150|| -500.418691|| -500.329168||-500.417321
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (KJ/mol)
| -6.12593193227x10<sup>6</sup> || -7.0118877561x10<sup>6</sup> || -1.31362215989x10<sup>7</sup> || -1.3138493733x10<sup>7</sup> || -1.31361433065x10<sup>7</sup> || -1.31384577637x10<sup>7</sup>
|-
|}

*The reaction barrier of a reaction is the energy difference between the transition state and the reactants, the smaller reaction barrier reaction pathway is the kinetically favored one:
**For the endo reaction: -1.31362215989x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= 159.808946 KJ/mol
**For the exo reaction: -1.31361433065x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= 167.638188 KJ/mol

*The reaction energy of a reaction is the energy difference between the product and the reactants.
**For the endo reaction: -1.3138493733x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= -67.40 KJ/mol
**For the exo reaction: -1.31384577637x10<sup>7</sup>-(-6.12593193227x10<sup>6</sup>+(-7.0118877561x10<sup>6</sup>))= -63.8 KJ/mol

Since the endo product is the one that has lower energy, and the endo pathway has a smaller reaction barrier, endo product is bothe kinetically and thermodynamically favored.

File:Jsheny3 ex2 endo opt3 by3lp.log

The HOMO of the endo and exo transition states are listed below (table 5):
{| class="wikitable" style="border: none; background: none;"
|+|table 5: table of HOMO of endo and exo transition states MO, isovalue set to 0.01

! Endo transition state
! scope="col" style="width: 500px;" | Explanation
|-
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|rowspan="3" | The endo transition state is the one possesses secondary orbital effect. The interaction is visualized by the figures on the left. For the endo transition state, the interaction is not just between the four reacting carbon atoms. The MOs of oxygens of 1,3-dioxole can also interact with the diene part of cyclohexadiene. Such interactions result in an overall stabilizing of transition state, and thus lower the reaction barrier of the endo transition state. Therefore the endo product is the kinetically favored one.
|-
! Exo transition state
|-
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|}

== Exercise 3: ==
===IRC analysis===
The TSs for endo,exo and chelectropic transition states and their corresponding IRCs are tabulated below (table 5):

{| class="wikitable" style="border: none; background: none;"
|+|Table 5: Endo, exo and chelectropic (optimized by PM6) and their corresponding IRCs
! Endo transition state!! Exo transition state!! Cheletropic transition state
|-
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|-
! colspan="3"|IRC animation (click the image to see the animated reaction trajectory if it is not moving already)
|-
| [[File:Jsheny3_ex3_endo_irc_ani.gif|500px]]
| [[File:Jsheny3_ex3_exo_irc_ani.gif|500px]]
| [[File:Jsheny3_ex3_che_irc_ani.gif|500px]]
|-
! colspan="3"|TOP: IRC trajectory energy vs reaction coordinate graph, Bottom: gradient variation
|-
| [[File:Jsheny3 ex3 endo irc graph.PNG|500px]]
| [[File:Jsheny3 ex3 exo irc graph.PNG|500px]]
| [[File:Jsheny3 ex3 che irc graph.PNG|500px]]
|}

===Reaction Barriers and Reaction Energy===
{| class="wikitable"
|+|Table 7: tabulated energies of reactants, transition states and the reaction (PM6 optimized)
! style="width: 200px;"| !!o-Xylylene!! SO<sub>2</sub>!! endo transition state!! endo product!! exo transition state!! exo product!! cheletropic transition state !! cheletropic product
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (Hartree/Particle)
| 0.178099 || -0.118614|| 0.090562|| 0.021697|| 0.092078||0.021454||0.099062||-0.000006
|-
!style="text-align: left;"| Sum of electronic and thermal free energies (KJ/mol)
| 467.59896 || -311.4210807 || 237.770549 || 56.9654778 || 241.7508074 || 56.3274813|| 260.087301 || -0.0157530012
|-
|}

*The reaction barrier of a reaction is the energy difference between the transition state and the reactants, the smaller reaction barrier reaction pathway is the kinetically favored one:
**For the endo reaction: 237.770549-(467.59896+(-311.4210807))=81.59 KJ/mol
**For the exo reaction: 241.7508074-(467.59896+(-311.4210807))=85.57 KJ/mol
**For the cheletropic reaction: 260.087301-(467.59896+(-311.4210807))=103.91 KJ/mol

*The reaction energy of a reaction is the energy difference between the product and the reactants.
**For the endo reaction: 56.9654778-(467.59896+(-311.4210807))=-99.21 KJ/mol
**For the exo reaction: 56.3274813-(467.59896+(-311.4210807))=-99.85 KJ/mol
**For the cheletropic reaction: -0.0157530012-(467.59896+(-311.4210807))=-156.19 KJ/mol

The endo transition state has the lowest energy and therefore the endo product is regarded as the kinetic product. The cheletropic reaction requires smallest amount of energy and therefore its product is regarded as the thermodynamically favored product.

The reaction profile is drawn below (fig):

[[File:Jsheny3 ex3 energy profile.png|center|400px]]

By looking at the IRC of the reactions, it can be found that for all three reactions, the bonding of the six-membered ring changes in the same way----it gains a new double bond and forms an aromatic ring. Here, formation of endo product is used as an example:

{| class="wikitable"
|+|Table 9: using formation of endo product to illustrate gaining of aromaticity by the 6-membered ring
! before the reaction!! after the reaction
|-
|[[File:jsheny3_ex3_endo_before.PNG|200px]]
|[[File:jsheny3_ex3_endo_after.PNG|200px]]
|-
! number of double bonds in 6-membered ring!! number of double bonds in 6-membered ring
|-
| style="text-align: center;"|2 ||style="text-align: center;"| 3 (delocalized, showing aromaticity)
|-
|}

===Conclusion===