File:EX EXO IRC ZZY J.LOG

2018-02-27T22:00:32Z

Zzy15:

File:EX ENDO IRC ZZY J.LOG

2018-02-27T22:00:24Z

Zzy15:

Rep:Mod:ZZY15 TS

2018-02-27T21:59:51Z

2018-02-27T21:54:38Z

Zzy15: /* Exercise 3: Diels-Alder vs Cheletropic */

=''' Transition States and reactivity '''=
== Introduction ==

== Method ==

== Results and Discussion ==

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

[[File:E1_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Butadiene with Ethene reaction.]]

This is a Dials-Alder reaction. The ethene acting as the dienophile, reacts with the s-cis butadiene. Cyclohexene is formed.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Ethene
! center; style="background: #0D4F8B; color: white;" | Butadiene
! center; style="background: #0D4F8B; color: white;" | Transition State
! center; style="background: #0D4F8B; color: white;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 12; measure 1 4</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 3 4; measure 1 2; measure 1 4</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 54; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>E1_PRODUCT_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. Optimized Stuctures at PM6 level.
|}

==== Bond Length Analysis ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" |sp<sup>3</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Double bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Single bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |VDW radius of C
|-
| style="background: #0D4F8B; color: white;" |Typical Bond Length (Å)
| 1.54
| 1.33
| 1.47
| 1.50
| 1.70
|+ Table 2. Typical C-C Bond Length.
|}

{| class="wikitable" style="margin: auto;"
|-
| [[File:ZZY_E1_NUMBERING.png|thumb|none|350px|center|Figure 2. Numbering of TS Carbons.]]
|rowspan="2" |[[File:E1_BONDDISTANCES_ZZY.png|thumb|none|500px|center|Figure 3. Bond distances versus IRC.]]
|-
| [[File:ZZY_E1_DISTANCE_FOCUS.png|thumb|none|350px|center|Figure 4. Zoom-in of Bond distances versus IRC Graph.]]
|-
|+ Table 3. Change in Bond Distances During The Reaction.
|}

The length of the partially formed C-C sigma bonds (C1-C8, C4-C9) in the TS is shorter than 2 x Van Der Waals radius of carbon, indicating formation of bonds between them. As the reaction proceeds, their length shortens and reaches the typical sp<sup>3</sup> C-sp<sup>3</sup>C single bond length at the end of the reation. The bond length between C7-C10 in the TS is shorter compared to the typical sp<sup>2</sup> C-sp<sup>2</sup>C single bond length. This indicating the formation of C-C pi bond between them. The bond length between C1-C4 at TS is longer than the typical C-C double bond length, indicating the pi bond breaking during the reaction. The bond length between C7-C8, C9-C10 is longer than the typical C-C double bond length, indicating the breaking of pi bond between them. It reaches the typical sp<sup>2</sup> C-sp<sup>3</sup>C bond length at the end.

==== Frequency and IRC Analysis ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | TS Bond Forming/Breaking Vibration
! center; style="background: #0D4F8B; color: white;" | Frequency Calculation
|-
| [[File:ZZY_TS_VIBRATION.gif]] || [[File:ZZY_E1_FREQUENCY.PNG|350px|thumb|center |]]
|-
|+ Table 4. Transition State Vibrational Frequencies
|}

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Trajectory
! center; style="background: #0D4F8B; color: white;" | IRC Path
|-
| [[File:ZZY_IRC.gif]] || [[File:ZZY_E1_IRC_PATH.PNG|350px|thumb|center |]]
|-
|+ Table 5. IRC Path of Reaction
|}

There is only one imaginary vibration (negative vibration) for the TS calculated, confirming that the TS is optimized correctly. Transition state corresponds to the highest potential energy along the reaction coordinate. At TS, the first derivative of energy graph is zero and the second derivative is negative. The frequency represents the second derivative of the energy. Therefore a single negative frequency indicates that there is only one maximum point on the reaction coordinate chosen. It is the maximum point in all order parameters. That is the correct transition state. If there are more than one negative frequency, they represent state that is maximum on one order parameter but not on others.

The IRC plots also show the correct optimization of TS. The maximum energy point corresponds to zero RMS gradient,showing the geometry is optimized at that point.

The animation of vibration at -949 cm<sup>-1</sup> shows that the formation of bonds in this reaction is synchronous. They form at the same time.

==== MO Analysis ====
{| class="wikitable" style="margin: auto;"
!
! center; style="background: #0D4F8B; color: white;" | HOMO
! center; style="background: #0D4F8B; color: white;" | LUMO
! colspan="2" center; style="background: #0D4F8B; color: white;" | MO Diagram
|-
| center; style="background: #0D4F8B; color: white;" | Butadiene
|<jmol>
<jmolApplet>
<title>HOMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2" colspan="2"|[[File:E1_MO_ZZY_NEW.png|thumb|none|450px|center|]]

|-
| center; style="background: #0D4F8B; color: white;" | Ethene
|<jmol>
<jmolApplet>
<title>HOMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| center; style="background: #0D4F8B; color: white;" | Transition state
|<jmol>
<jmolApplet>
<title>HOMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
|+ Table 6. MO Diagrams
|}

The MO diagram is constructed based on the energies of MOs calculated at PM6 level. The diene has a smaller HOMO-LUMO energy gap as the HOMO and LUMO are neither the lowest energy bonding MO nor the highest energy antiboning MO, which is the case for the ethene. Noticed that the energy of HOMO/HOMO-1 of TS is higher than expected and the energy of the LUMO/LUMO+1 of TS is lower than expected (real energy levels indicated by red lines in the graph). This is because the MO diagram is based on the transition state MO energies, not on product as we used to do. In the TS, the new bonds are not completely formed. Therefore the "bonding orbitals" are higher in energy and the "anti-bonding orbitals" are lower in energy than expected.

Due to the larger energy gap between interacting MOs of ethene and diene, this reaction is not efficient. This can be improved by adding electron donating groups to the diene and adding electron withdrawing groups to the dienophile. By doing this, the energy leveles of diene are raised and that of the dienophile are lowered. This leads to better overlap as MOs closer in energy. The reaction is more efficient.

As shown by the MO visualization, reactants' MOs of the same symmetry overlap and give the TS MOs. This indicates that only interactions between MOs of the same symmetry are allowed. Mis-symmetry interactions are forbidden, i.e. they don't interact.

The overlap between MOs is described by the orbital overlap integral <math>S</math>. It is defined as:
<center><math>S=\int {\psi_1\psi^*_2 d\tau}</math></center>
<center><small> ''Equation 1: Equation of the Overlap Integral'' </small> </center>
<math>\psi_1</math> and <math>\psi^*_2</math> are the wavefunctions of the interacting MOs.
It is known that integral of asymmetric functions is zero. The product of an asymmetric and a symmetric function is asymmetric as the product of two functions of the same symmetry is symmetric. In conclusion, the overlap integral of two MOs of different symmetry is zero and the overlap integral of two MOs of the same symmetry is non-zero. This is consistent to the symmetry requirement mentioned before as reaction can't happen with zero overlap.

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

[[File:E2_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 5. Reaction Scheme of Cyclohexadiene and 1,3-Dioxole Reaction.]]

This a Diels-Alder reaction. The 1,3-Dioxole acts as the dienophile. There are two possible products: endo and exo.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
|+ Table 7: ''' Optimized Stuctures at PM6 Level and BY3LP 6-31(d) Level '''
!
!center; style="background: #0D4F8B; color: white;" |Cyclohexadiene
!center; style="background: #0D4F8B; color: white;" |1,3-dioxole
!center; style="background: #0D4F8B; color: white;" |Endo TS
!center; style="background: #0D4F8B; color: white;" |Exo TS
!center; style="background: #0D4F8B; color: white;" |Endo Product
!center; style="background: #0D4F8B; color: white;" |Exo Product
|-
|center; style="background: #0D4F8B; color: white;" |PM6
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |B3LYP/6-31G(d)
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |Frequency values at B3LYP/6-31G(d) Level
|[[File:E2_DIENE_ZZY.png|185px|thumb|center |]]
|[[File:E2_OXO_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_ZZY.png|185px|thumb|center |]]
|-
|}

The structures above are optimized as confirmed by the frequency calculation. None of them has more than one negative frequencies. There is only one negative frequency for both TS structures, indicating they are correctly optimized.

==== MO Analysis ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | ENDO MO
! style="background: #0D4F8B; color: white;" | EXO MO
|-
| [[File:E2_ENDO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
| [[File:E2_EXO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
|-
|+ Table 8. MO Diagrams for Endo and Exo Reactions
|}

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene HOMO
! style="background: #0D4F8B; color: white;" | Cyclohexadiene LUMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole HOMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | EXO TS HOMO
! style="background: #0D4F8B; color: white;" | EXO TS LUMO
! style="background: #0D4F8B; color: white;" | EXO TS HOMO-1
! style="background: #0D4F8B; color: white;" | EXO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO-1
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|+ Table 9. Relevant MOs to the MO Diagram
|}

The MO diagram is constructed based on the energies of MOs calculated at BY3LYP/6-31(d) level.

This is an inverse demand DA reaction. The frontier molecular orbitals of the dienophile are higher in energy than that of the diene, i.e. the diene is electron poor while the dienophile is electron rich. In result of that, the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub> are more similar in energy compared to the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub>. The strongest orbital interaction is between FMOs that are closest in energy, in this case, that are the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub>. In a normal demand DA reaction, the strongest orbital interaction is between the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub> and the diene is electron rich as the dienophile is electron poor.

This can be rationalized as the dienophile of this reaction: 1,3-dioxole, is relatively electron rich. The neighbouring oxygen atoms donate electron density into the double bond, raise the energy of the double bond MOs. The reaction proceeds in an inverse demand fashion.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energies Calculated From B3LYP/631G(d) (kJmol<sup>-1</sup>)
| -612584.1026
| -701187.072
| -1313621.484
| -1313613.647
| -1313848.695
| -1313845.101
|-
|+ Table 10. Energies for All Species
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 150
| -77.5
|-
| style="background: #0D4F8B; color: white;" | Exo
| +157
| -73.9
|-
|+ Table 11. Calculated Activation and Reaction Energy
|}

The reaction barrier and the reaction energy were calculated by using the energy data from the BY3LYP/6-31G(d) results.
<center>Reaction barrier = Energy of TS - Sum of energy of reactants</center>
<center>Reaction energy = Energy of product - Sum of energy of reactants</center>

For this reaction, the endo reaction has a more negative reaction energy and a lower activation energy. Therefore the endo product is both the kinetically and thermodynamically favourable products. The endo product is more stable and less energy is required to overcome the reaction barrier of the endo reaction. Noticed both the endo and exo reactions are exothermic, i.e. the products are lower in energy compared to the reactants.

==== Secondary Orbital Interaction ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
|-
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|[[File:ZZY_E2_ENDO_2.png|thumb|center]]
|[[File:ZZY_E2_EXO_steric.png|thumb|center]]
|-
|+ Table 12. Secondary Orbital Interactions
|}

As shown in the graph, only the endo TS has the secondary orbital interactions between diene and dienophile. The lone pair orbitals of oxygen atoms interact with the LUMO of cyclohexadiene. This interaction stabilizes the endo transition state, lowering the reaction barrier. According to the Hammond's Postulate, the transition state of a reaction resembles either the reactants or the products, to whichever it is closer in energy. In this reaction, the energy of both TS are closer in energy to the product, hence the structure of the TS resembles the product. Consequently, the secondary orbital interactions which stabilizes the endo TS, also stabilizes the endo product. This explains the endo selectivity of this reaction.

For the exo TS, there is no secondary orbital interactions and the steric clash between the diene and dienophile destablizes the exo TS and product. This results in disfavouring of the exo reaction.

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

[[File:E3_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 6. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 63; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_TS_ZZY_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 65; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 134; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo Product
! center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 119; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 85; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 13. Optimized stuctures at PM6 level
|}

==== IRC Analysis ====

{| class="wikitable" style="margin: auto;"
|-
| style="background: #0D4F8B; color: white;" | Endo
| [[File:ZZY_E3_ENDO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Exo
| [[File:ZZY_E3_EXO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| [[File:ZZY_E3_CHE_DONG.gif]]
|-
|+ Table 14. Approach Trajectory of xylylene with SO<sub>2</sub>
|}

Ortho-xylylene has 8 <math>pi</math> electrons. According to the Huckle's rule (4n+2), it is not aromatic. However, it is planar as all carbons are sp<sup>2</sup> hybridised. When SO<sub>2</sub> approaches o-xylylene, the two ortho bonds stick out of the 6-membered ring plane towards the SO<sub>2</sub> and form new bonds with it while the <math>pi</math> bonds in the two ortho double bonds break. This leaves 6 <math>pi</math> electrons within the ring and the ring establishes aromaticity. Then the molecule adjusts to such that the original 8 carbons of the o-xylylene back to the same plane. The formation of aromatic ring and new sigma bonds are the driving force for the reactions.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Cheletropic TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
! style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +237.7678009
| +241.7506826
| +260.0871666
| +56.96807393
| +56.32220122
| -0.013127494
|-
|+ Table 15. Energies calculated from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 79.8
| -101.0
|-
| style="background: #0D4F8B; color: white;" | Exo
| +83.8
| -101.6
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| +102.2
| -157.9
|-
|+ Table 16. Calculated Activation and Reaction Energy
|}

[[File:ZZY_E3_ENERGY_PROFILE.PNG|centre|frame|Fig.7: Energy profiles of Endo, Exo and Cheletropic reactions]]

The Diels-Alder reactions have lower reaction barrier than the Cheletropic reaction. They are kinetically favoured. The endo reaction has the lowest reaction barrier and it is the most favoured kinetically. The reaction energy of the endo and exo reactions are very close with the exo one slightly lower (probably due to less steric hindrance). Hence thermodynamically, they are favoured similarly. However, the Cheletropic reaction has a much lower reaction energy, i.e. the Cheletropic product is the most stable. The Cheletropic reaction is thermodynamically the most favoured reaction.

=== Extension: Second Cis-butadiene Fragment in O-xylylene ===

[[File:EX_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 8. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Exo Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 99; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 69; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 101; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 17. Optimized stuctures at PM6 level
|}

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +267.9846671
| +275.8217811
| +172.2537282
| +176.7223272
|-
|+ Table 18. Energies from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 110.1
| +14.3
|-
| style="background: #0D4F8B; color: white;" | Exo
| +117.9
| +18.8
|-
|+ Table 19. Calculated Activation and Reaction Energy
|}

The reaction barrier for both endo and exo reactions is much higher than that of the reactions with the other cis-butadiene fragment in Exercise 3. More energy required to overcome the barrier. In addition, the reaction energy for both endo and exo is positive, i.e. the products are more unstable than the reactants. Thus, this reaction with the cis-butadiene fragment within the ring is thermodynamically and kinetically unfavoured.

== Conclusion ==

In this experiment, the transition structures for three pericyclic reactions were located and characterized using two electronic structure methods: the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP in Gaussian. The structures were visualized in GaussView. An Intrinsic Reaction Coordinate (IRC) calculation on the correctly located TS showed the trajectories of the reactions and the change in physical parameters such as bond lengths and energy during the reaction. The TS MO diagram of these reactions were constructed based on the MO energy calculated from Gaussian. This showed the interacting orbitals and symmetry requirement for the reaction. The demand of the Diel-Alder reactions (normal/inverse) was also determined by analysis of the TS MO. Analysis of energy of optimized products, reactants and transition states demonstrated which products or route of reactions are more kinetically or thermodynamically favoured.

== Reference ==

== Appendix ==

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Ethene
|[[File:E1_SM_ALKENE_OP_PM6.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Butadiene
|[[File:DIENE_OP_PM6_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | TS
|[[File:REACTANT_TS_PM6_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexene
|[[File:E1_PRODUCT_OP_PM6.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | IRC
|[[File:E1_TS_IRC_PM6.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
!center; style="background: #0D4F8B; color: white;" | BY3LYP/6-31(d)
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexadiene
|[[File:ZZY_E2_DIENE_OP_PM6.LOG]]
|[[File:ZZY_E2_DIENE_OP_631.log]]
|-
|center; style="background: #0D4F8B; color: white;" | 1,3-dioxole
|[[File:ZZY_E2_DIOXOLE_OP_PM6.LOG]]
|[[File:ZZY_E2_DIOXOLE_OP_631.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:ZZY_E2_ENDO_TS_PM6_J.LOG]]
|[[File:ZZY_E2_ENDO_TS_631_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:ZZY_E2_EXO_TS_PM6_J.LOG]]
|[[File:ZZY_E2_EXO_TS_631_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:ZZY_E2_ENDO_OP_PM6.LOG]]
|[[File:ZZY_E2_ENDO_OP_631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:ZZY_E2_EXO_OP_PM6.LOG]]
|[[File:ZZY_E2_EXO_OP_631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:ZZY_E2_ENDO_IRC_PM6.LOG]]
|
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:ZZY_E2_EXO_IRC_PM6.LOG]]
|
|-
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:E3_XYLYLENE_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:E3_SO2_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:E3_ENDO_TS_ZZY_2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:E3_EXO_TS_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|[[File:E3_CHE_TS_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:E3_ENDO_Product_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:E3_EXO_Product_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|[[File:E3_CHE_Product_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:E3_ENDO_IRC_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:E3_EXO_IRC_ZZY.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic IRC
|[[File:E3_CHE_IRC_ZZY.LOG]]
|}

=== Extension ===
{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:Xylene.log]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:Endotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:Exotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endoproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCTMIN4.LOG]]
|}

File:ZZY E2 EXO IRC PM6.LOG

2018-02-27T21:52:15Z

Zzy15:

File:ZZY E2 ENDO IRC PM6.LOG

2018-02-27T21:52:06Z

Zzy15:

Rep:Mod:ZZY15 TS

2018-02-27T21:50:27Z

Zzy15: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

=''' Transition States and reactivity '''=
== Introduction ==

== Method ==

== Results and Discussion ==

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

[[File:E1_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Butadiene with Ethene reaction.]]

This is a Dials-Alder reaction. The ethene acting as the dienophile, reacts with the s-cis butadiene. Cyclohexene is formed.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Ethene
! center; style="background: #0D4F8B; color: white;" | Butadiene
! center; style="background: #0D4F8B; color: white;" | Transition State
! center; style="background: #0D4F8B; color: white;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 12; measure 1 4</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 3 4; measure 1 2; measure 1 4</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 54; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>E1_PRODUCT_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. Optimized Stuctures at PM6 level.
|}

==== Bond Length Analysis ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" |sp<sup>3</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Double bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Single bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |VDW radius of C
|-
| style="background: #0D4F8B; color: white;" |Typical Bond Length (Å)
| 1.54
| 1.33
| 1.47
| 1.50
| 1.70
|+ Table 2. Typical C-C Bond Length.
|}

{| class="wikitable" style="margin: auto;"
|-
| [[File:ZZY_E1_NUMBERING.png|thumb|none|350px|center|Figure 2. Numbering of TS Carbons.]]
|rowspan="2" |[[File:E1_BONDDISTANCES_ZZY.png|thumb|none|500px|center|Figure 3. Bond distances versus IRC.]]
|-
| [[File:ZZY_E1_DISTANCE_FOCUS.png|thumb|none|350px|center|Figure 4. Zoom-in of Bond distances versus IRC Graph.]]
|-
|+ Table 3. Change in Bond Distances During The Reaction.
|}

The length of the partially formed C-C sigma bonds (C1-C8, C4-C9) in the TS is shorter than 2 x Van Der Waals radius of carbon, indicating formation of bonds between them. As the reaction proceeds, their length shortens and reaches the typical sp<sup>3</sup> C-sp<sup>3</sup>C single bond length at the end of the reation. The bond length between C7-C10 in the TS is shorter compared to the typical sp<sup>2</sup> C-sp<sup>2</sup>C single bond length. This indicating the formation of C-C pi bond between them. The bond length between C1-C4 at TS is longer than the typical C-C double bond length, indicating the pi bond breaking during the reaction. The bond length between C7-C8, C9-C10 is longer than the typical C-C double bond length, indicating the breaking of pi bond between them. It reaches the typical sp<sup>2</sup> C-sp<sup>3</sup>C bond length at the end.

==== Frequency and IRC Analysis ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | TS Bond Forming/Breaking Vibration
! center; style="background: #0D4F8B; color: white;" | Frequency Calculation
|-
| [[File:ZZY_TS_VIBRATION.gif]] || [[File:ZZY_E1_FREQUENCY.PNG|350px|thumb|center |]]
|-
|+ Table 4. Transition State Vibrational Frequencies
|}

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Trajectory
! center; style="background: #0D4F8B; color: white;" | IRC Path
|-
| [[File:ZZY_IRC.gif]] || [[File:ZZY_E1_IRC_PATH.PNG|350px|thumb|center |]]
|-
|+ Table 5. IRC Path of Reaction
|}

There is only one imaginary vibration (negative vibration) for the TS calculated, confirming that the TS is optimized correctly. Transition state corresponds to the highest potential energy along the reaction coordinate. At TS, the first derivative of energy graph is zero and the second derivative is negative. The frequency represents the second derivative of the energy. Therefore a single negative frequency indicates that there is only one maximum point on the reaction coordinate chosen. It is the maximum point in all order parameters. That is the correct transition state. If there are more than one negative frequency, they represent state that is maximum on one order parameter but not on others.

The IRC plots also show the correct optimization of TS. The maximum energy point corresponds to zero RMS gradient,showing the geometry is optimized at that point.

The animation of vibration at -949 cm<sup>-1</sup> shows that the formation of bonds in this reaction is synchronous. They form at the same time.

==== MO Analysis ====
{| class="wikitable" style="margin: auto;"
!
! center; style="background: #0D4F8B; color: white;" | HOMO
! center; style="background: #0D4F8B; color: white;" | LUMO
! colspan="2" center; style="background: #0D4F8B; color: white;" | MO Diagram
|-
| center; style="background: #0D4F8B; color: white;" | Butadiene
|<jmol>
<jmolApplet>
<title>HOMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2" colspan="2"|[[File:E1_MO_ZZY_NEW.png|thumb|none|450px|center|]]

|-
| center; style="background: #0D4F8B; color: white;" | Ethene
|<jmol>
<jmolApplet>
<title>HOMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| center; style="background: #0D4F8B; color: white;" | Transition state
|<jmol>
<jmolApplet>
<title>HOMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
|+ Table 6. MO Diagrams
|}

The MO diagram is constructed based on the energies of MOs calculated at PM6 level. The diene has a smaller HOMO-LUMO energy gap as the HOMO and LUMO are neither the lowest energy bonding MO nor the highest energy antiboning MO, which is the case for the ethene. Noticed that the energy of HOMO/HOMO-1 of TS is higher than expected and the energy of the LUMO/LUMO+1 of TS is lower than expected (real energy levels indicated by red lines in the graph). This is because the MO diagram is based on the transition state MO energies, not on product as we used to do. In the TS, the new bonds are not completely formed. Therefore the "bonding orbitals" are higher in energy and the "anti-bonding orbitals" are lower in energy than expected.

Due to the larger energy gap between interacting MOs of ethene and diene, this reaction is not efficient. This can be improved by adding electron donating groups to the diene and adding electron withdrawing groups to the dienophile. By doing this, the energy leveles of diene are raised and that of the dienophile are lowered. This leads to better overlap as MOs closer in energy. The reaction is more efficient.

As shown by the MO visualization, reactants' MOs of the same symmetry overlap and give the TS MOs. This indicates that only interactions between MOs of the same symmetry are allowed. Mis-symmetry interactions are forbidden, i.e. they don't interact.

The overlap between MOs is described by the orbital overlap integral <math>S</math>. It is defined as:
<center><math>S=\int {\psi_1\psi^*_2 d\tau}</math></center>
<center><small> ''Equation 1: Equation of the Overlap Integral'' </small> </center>
<math>\psi_1</math> and <math>\psi^*_2</math> are the wavefunctions of the interacting MOs.
It is known that integral of asymmetric functions is zero. The product of an asymmetric and a symmetric function is asymmetric as the product of two functions of the same symmetry is symmetric. In conclusion, the overlap integral of two MOs of different symmetry is zero and the overlap integral of two MOs of the same symmetry is non-zero. This is consistent to the symmetry requirement mentioned before as reaction can't happen with zero overlap.

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

[[File:E2_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 5. Reaction Scheme of Cyclohexadiene and 1,3-Dioxole Reaction.]]

This a Diels-Alder reaction. The 1,3-Dioxole acts as the dienophile. There are two possible products: endo and exo.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
|+ Table 7: ''' Optimized Stuctures at PM6 Level and BY3LP 6-31(d) Level '''
!
!center; style="background: #0D4F8B; color: white;" |Cyclohexadiene
!center; style="background: #0D4F8B; color: white;" |1,3-dioxole
!center; style="background: #0D4F8B; color: white;" |Endo TS
!center; style="background: #0D4F8B; color: white;" |Exo TS
!center; style="background: #0D4F8B; color: white;" |Endo Product
!center; style="background: #0D4F8B; color: white;" |Exo Product
|-
|center; style="background: #0D4F8B; color: white;" |PM6
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |B3LYP/6-31G(d)
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |Frequency values at B3LYP/6-31G(d) Level
|[[File:E2_DIENE_ZZY.png|185px|thumb|center |]]
|[[File:E2_OXO_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_ZZY.png|185px|thumb|center |]]
|-
|}

The structures above are optimized as confirmed by the frequency calculation. None of them has more than one negative frequencies. There is only one negative frequency for both TS structures, indicating they are correctly optimized.

==== MO Analysis ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | ENDO MO
! style="background: #0D4F8B; color: white;" | EXO MO
|-
| [[File:E2_ENDO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
| [[File:E2_EXO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
|-
|+ Table 8. MO Diagrams for Endo and Exo Reactions
|}

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene HOMO
! style="background: #0D4F8B; color: white;" | Cyclohexadiene LUMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole HOMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | EXO TS HOMO
! style="background: #0D4F8B; color: white;" | EXO TS LUMO
! style="background: #0D4F8B; color: white;" | EXO TS HOMO-1
! style="background: #0D4F8B; color: white;" | EXO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO-1
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|+ Table 9. Relevant MOs to the MO Diagram
|}

The MO diagram is constructed based on the energies of MOs calculated at BY3LYP/6-31(d) level.

This is an inverse demand DA reaction. The frontier molecular orbitals of the dienophile are higher in energy than that of the diene, i.e. the diene is electron poor while the dienophile is electron rich. In result of that, the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub> are more similar in energy compared to the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub>. The strongest orbital interaction is between FMOs that are closest in energy, in this case, that are the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub>. In a normal demand DA reaction, the strongest orbital interaction is between the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub> and the diene is electron rich as the dienophile is electron poor.

This can be rationalized as the dienophile of this reaction: 1,3-dioxole, is relatively electron rich. The neighbouring oxygen atoms donate electron density into the double bond, raise the energy of the double bond MOs. The reaction proceeds in an inverse demand fashion.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energies Calculated From B3LYP/631G(d) (kJmol<sup>-1</sup>)
| -612584.1026
| -701187.072
| -1313621.484
| -1313613.647
| -1313848.695
| -1313845.101
|-
|+ Table 10. Energies for All Species
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 150
| -77.5
|-
| style="background: #0D4F8B; color: white;" | Exo
| +157
| -73.9
|-
|+ Table 11. Calculated Activation and Reaction Energy
|}

The reaction barrier and the reaction energy were calculated by using the energy data from the BY3LYP/6-31G(d) results.
<center>Reaction barrier = Energy of TS - Sum of energy of reactants</center>
<center>Reaction energy = Energy of product - Sum of energy of reactants</center>

For this reaction, the endo reaction has a more negative reaction energy and a lower activation energy. Therefore the endo product is both the kinetically and thermodynamically favourable products. The endo product is more stable and less energy is required to overcome the reaction barrier of the endo reaction. Noticed both the endo and exo reactions are exothermic, i.e. the products are lower in energy compared to the reactants.

==== Secondary Orbital Interaction ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
|-
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|[[File:ZZY_E2_ENDO_2.png|thumb|center]]
|[[File:ZZY_E2_EXO_steric.png|thumb|center]]
|-
|+ Table 12. Secondary Orbital Interactions
|}

As shown in the graph, only the endo TS has the secondary orbital interactions between diene and dienophile. The lone pair orbitals of oxygen atoms interact with the LUMO of cyclohexadiene. This interaction stabilizes the endo transition state, lowering the reaction barrier. According to the Hammond's Postulate, the transition state of a reaction resembles either the reactants or the products, to whichever it is closer in energy. In this reaction, the energy of both TS are closer in energy to the product, hence the structure of the TS resembles the product. Consequently, the secondary orbital interactions which stabilizes the endo TS, also stabilizes the endo product. This explains the endo selectivity of this reaction.

For the exo TS, there is no secondary orbital interactions and the steric clash between the diene and dienophile destablizes the exo TS and product. This results in disfavouring of the exo reaction.

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

[[File:E3_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 6. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 63; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_TS_ZZY_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 65; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 134; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo Product
! center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 119; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 85; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 13. Optimized stuctures at PM6 level
|}

==== IRC Analysis ====

{| class="wikitable" style="margin: auto;"
|-
| style="background: #0D4F8B; color: white;" | Endo
| [[File:ZZY_E3_ENDO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Exo
| [[File:ZZY_E3_EXO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| [[File:ZZY_E3_CHE_DONG.gif]]
|-
|+ Table 14. Approach Trajectory of xylylene with SO<sub>2</sub>
|}

Ortho-xylylene has 8 <math>pi</math> electrons. According to the Huckle's rule (4n+2), it is not aromatic. However, it is planar as all carbons are sp<sup>2</sup> hybridised. When SO<sub>2</sub> approaches o-xylylene, the two ortho bonds stick out of the 6-membered ring plane towards the SO<sub>2</sub> and form new bonds with it while the <math>pi</math> bonds in the two ortho double bonds break. This leaves 6 <math>pi</math> electrons within the ring and the ring establishes aromaticity. Then the molecule adjusts to such that the original 8 carbons of the o-xylylene back to the same plane. The formation of aromatic ring and new sigma bonds are the driving force for the reactions.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Cheletropic TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
! style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +237.7678009
| +241.7506826
| +260.0871666
| +56.96807393
| +56.32220122
| -0.013127494
|-
|+ Table 15. Energies calculated from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 79.8
| -101.0
|-
| style="background: #0D4F8B; color: white;" | Exo
| +83.8
| -101.6
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| +102.2
| -157.9
|-
|+ Table 16. Calculated Activation and Reaction Energy
|}

[[File:ZZY_E3_ENERGY_PROFILE.PNG|centre|frame|Fig.7: Energy profiles of Endo, Exo and Cheletropic reactions]]

The Diels-Alder reactions have lower reaction barrier than the Cheletropic reaction. They are kinetically favoured. The endo reaction has the lowest reaction barrier and it is the most favoured kinetically. The reaction energy of the endo and exo reactions are very close with the exo one slightly lower (probably due to less steric hindrance). Hence thermodynamically, they are favoured similarly. However, the Cheletropic reaction has a much lower reaction energy, i.e. the Cheletropic product is the most stable. The Cheletropic reaction is thermodynamically the most favoured reaction.

=== Extension: Second Cis-butadiene Fragment in O-xylylene ===

[[File:EX_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 8. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Exo Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 99; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 69; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 101; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 17. Optimized stuctures at PM6 level
|}

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +267.9846671
| +275.8217811
| +172.2537282
| +176.7223272
|-
|+ Table 18. Energies from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 110.1
| +14.3
|-
| style="background: #0D4F8B; color: white;" | Exo
| +117.9
| +18.8
|-
|+ Table 19. Calculated Activation and Reaction Energy
|}

The reaction barrier for both endo and exo reactions is much higher than that of the reactions with the other cis-butadiene fragment in Exercise 3. More energy required to overcome the barrier. In addition, the reaction energy for both endo and exo is positive, i.e. the products are more unstable than the reactants. Thus, this reaction with the cis-butadiene fragment within the ring is thermodynamically and kinetically unfavoured.

== Conclusion ==

In this experiment, the transition structures for three pericyclic reactions were located and characterized using two electronic structure methods: the semi-empirical method PM6 and the Density Functional Theory (DFT) method B3LYP in Gaussian. The structures were visualized in GaussView. An Intrinsic Reaction Coordinate (IRC) calculation on the correctly located TS showed the trajectories of the reactions and the change in physical parameters such as bond lengths and energy during the reaction. The TS MO diagram of these reactions were constructed based on the MO energy calculated from Gaussian. This showed the interacting orbitals and symmetry requirement for the reaction. The demand of the Diel-Alder reactions (normal/inverse) was also determined by analysis of the TS MO. Analysis of energy of optimized products, reactants and transition states demonstrated which products or route of reactions are more kinetically or thermodynamically favoured.

== Reference ==

== Appendix ==

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Ethene
|[[File:E1_SM_ALKENE_OP_PM6.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Butadiene
|[[File:DIENE_OP_PM6_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | TS
|[[File:REACTANT_TS_PM6_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexene
|[[File:E1_PRODUCT_OP_PM6.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | IRC
|[[File:E1_TS_IRC_PM6.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
!center; style="background: #0D4F8B; color: white;" | BY3LYP/6-31(d)
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexadiene
|[[File:ZZY_E2_DIENE_OP_PM6.LOG]]
|[[File:ZZY_E2_DIENE_OP_631.log]]
|-
|center; style="background: #0D4F8B; color: white;" | 1,3-dioxole
|[[File:ZZY_E2_DIOXOLE_OP_PM6.LOG]]
|[[File:ZZY_E2_DIOXOLE_OP_631.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:ZZY_E2_ENDO_TS_PM6_J.LOG]]
|[[File:ZZY_E2_ENDO_TS_631_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:ZZY_E2_EXO_TS_PM6_J.LOG]]
|[[File:ZZY_E2_EXO_TS_631_J.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:ZZY_E2_ENDO_OP_PM6.LOG]]
|[[File:ZZY_E2_ENDO_OP_631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:ZZY_E2_EXO_OP_PM6.LOG]]
|[[File:ZZY_E2_EXO_OP_631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:ZZY_E2_ENDO_IRC_PM6.LOG]]
|
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:ZZY_E2_EXO_IRC_PM6.LOG]]
|
|-
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:XYLENE3.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:EX3ENDOTS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:XYLYLENE exoex3 TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|[[File:INDENE_TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:ENDOPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCT OPT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|[[File:INDENEPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:EX3ENDOTSIRC.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:Xylene exo ts ir.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic IRC
|[[File:INDENEIRC.LOG]]
|}

=== Extension ===
{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:Xylene.log]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:Endotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:Exotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endoproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCTMIN4.LOG]]
|}

2018-02-27T19:31:07Z

Zzy15: /* Optimization Results */

=''' Transition States and reactivity '''=
== Introduction ==

== Method ==

== Results and Discussion ==

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

[[File:E1_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Butadiene with Ethene reaction.]]

This is a Dials-Alder reaction. The ethene acting as the dienophile, reacts with the s-cis butadiene. Cyclohexene is formed.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Ethene
! center; style="background: #0D4F8B; color: white;" | Butadiene
! center; style="background: #0D4F8B; color: white;" | Transition State
! center; style="background: #0D4F8B; color: white;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 12; measure 1 4</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 3 4; measure 1 2; measure 1 4</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 54; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>E1_PRODUCT_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. Optimized stuctures at PM6 level.
|}

==== Bond Length Analysis ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" |sp<sup>3</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Double bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Single bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |VDW radius of C
|-
| style="background: #0D4F8B; color: white;" |Typical Bond Length (Å)
| 1.54
| 1.33
| 1.47
| 1.50
| 1.70
|+ Table 2. Typical C-C bond Length.
|}

{| class="wikitable" style="margin: auto;"
|-
| [[File:ZZY_E1_NUMBERING.png|thumb|none|350px|center|Figure 2. Numbering of TS Carbons.]]
|rowspan="2" |[[File:E1_BONDDISTANCES_ZZY.png|thumb|none|500px|center|Figure 3. Bond distances versus IRC.]]
|-
| [[File:ZZY_E1_DISTANCE_FOCUS.png|thumb|none|350px|center|Figure 4. Zoom-in of Bond distances versus IRC Graph.]]
|-
|+ Table 3. Change in Bond Distances During The Reaction.
|}

The length of the partially formed C-C sigma bonds (C1-C8, C4-C9) in the TS is shorter than 2 x Van Der Waals radius of carbon, indicating formation of bonds between them. As the reaction proceeds, their length shortens and reaches the typical sp<sup>3</sup> C-sp<sup>3</sup>C single bond length at the end of the reation. The bond length between C7-C10 in the TS is shorter compared to the typical sp<sup>2</sup> C-sp<sup>2</sup>C single bond length. This indicating the formation of C-C pi bond between them. The bond length between C1-C4 at TS is longer than the typical C-C double bond length, indicating the pi bond breaking during the reaction. The bond length between C7-C8, C9-C10 is longer than the typical C-C double bond length, indicating the breaking of pi bond between them. It reaches the typical sp<sup>2</sup> C-sp<sup>3</sup>C bond length at the end.

==== Frequency and IRC Analysis ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | TS Bond Forming/Breaking Vibration
! center; style="background: #0D4F8B; color: white;" | Frequency Calculation
|-
| [[File:ZZY_TS_VIBRATION.gif]] || [[File:ZZY_E1_FREQUENCY.PNG|350px|thumb|center |]]
|-
|+ Table 2. Transition State Vibrational Frequencies.
|}

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Trajectory
! center; style="background: #0D4F8B; color: white;" | IRC Path
|-
| [[File:ZZY_IRC.gif]] || [[File:ZZY_E1_IRC_PATH.PNG|350px|thumb|center |]]
|-
|+ Table 3. IRC Path of Reaction
|}

There is only one imaginary vibration (negative vibration) for the TS calculated, confirming that the TS is optimized correctly. Transition state corresponds to the highest potential energy along the reaction coordinate. At TS, the first derivative of energy graph is zero and the second derivative is negative. The frequency represents the second derivative of the energy. Therefore a single negative frequency indicates that there is only one maximum point on the reaction coordinate chosen. It is the maximum point in all order parameters. That is the correct transition state. If there are more than one negative frequency, they represent state that is maximum on one order parameter but not on others.

The IRC plots also show the correct optimization of TS. The maximum energy point corresponds to zero RMS gradient,showing the geometry is optimized at that point.

The animation of vibration at -949 cm<sup>-1</sup> shows that the formation of bonds in this reaction is synchronous. They form at the same time.

==== MO Analysis ====
{| class="wikitable" style="margin: auto;"
!
! center; style="background: #0D4F8B; color: white;" | HOMO
! center; style="background: #0D4F8B; color: white;" | LUMO
! colspan="2" center; style="background: #0D4F8B; color: white;" | MO Diagram
|-
| center; style="background: #0D4F8B; color: white;" | Butadiene
|<jmol>
<jmolApplet>
<title>HOMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2" colspan="2"|[[File:E1_MO_ZZY_NEW.png|thumb|none|450px|center|Figure 5. MO of diels-alder reaction.]]

|-
| center; style="background: #0D4F8B; color: white;" | Ethene
|<jmol>
<jmolApplet>
<title>HOMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| center; style="background: #0D4F8B; color: white;" | Transition state
|<jmol>
<jmolApplet>
<title>HOMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
|+ Table 4. MO diagrams
|}

The MO diagram is constructed based on the energies of MOs calculated at PM6 level. The diene has a smaller HOMO-LUMO energy gap as the HOMO and LUMO are neither the lowest energy bonding MO nor the highest energy antiboning MO, which is the case for the ethene. Noticed that the energy of HOMO/HOMO-1 of TS is higher than expected and the energy of the LUMO/LUMO+1 of TS is lower than expected (real energy levels indicated by red lines in the graph). This is because the MO diagram is based on the transition state MO energies, not on product as we used to do. In the TS, the new bonds are not completely formed. Therefore the "bonding orbitals" are higher in energy and the "anti-bonding orbitals" are lower in energy than expected.

Due to the larger energy gap between interacting MOs of ethene and diene, this reaction is not efficient. This can be improved by adding electron donating groups to the diene and adding electron withdrawing groups to the dienophile. By doing this, the energy leveles of diene are raised and that of the dienophile are lowered. This leads to better overlap as MOs closer in energy. The reaction is more efficient.

As shown by the MO visualization, reactants' MOs of the same symmetry overlap and give the TS MOs. This indicates that only interactions between MOs of the same symmetry are allowed. Mis-symmetry interactions are forbidden, i.e. they don't interact.

The overlap between MOs is described by the orbital overlap integral <math>S</math>. It is defined as:
<center><math>S=\int {\psi_1\psi^*_2 d\tau}</math></center>
<center><small> ''Equation 1: Equation of the Overlap Integral'' </small> </center>
<math>\psi_1</math> and <math>\psi^*_2</math> are the wavefunctions of the interacting MOs.
It is known that integral of asymmetric functions is zero. The product of an asymmetric and a symmetric function is asymmetric as the product of two functions of the same symmetry is symmetric. In conclusion, the overlap integral of two MOs of different symmetry is zero and the overlap integral of two MOs of the same symmetry is non-zero. This is consistent to the symmetry requirement mentioned before as reaction can't happen with zero overlap.

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

[[File:E2_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 6. Reaction Scheme of Cyclohexadiene and 1,3-Dioxole Reaction.]]

This a Diels-Alder reaction. The 1,3-Dioxole acts as the dienophile. There are two possible products: endo and exo.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
|+ Table 7: ''' Optimized Stuctures at PM6 Level and BY3LP 6-31(d) Level '''
!
!center; style="background: #0D4F8B; color: white;" |Cyclohexadiene
!center; style="background: #0D4F8B; color: white;" |1,3-dioxole
!center; style="background: #0D4F8B; color: white;" |Endo TS
!center; style="background: #0D4F8B; color: white;" |Exo TS
!center; style="background: #0D4F8B; color: white;" |Endo Product
!center; style="background: #0D4F8B; color: white;" |Exo Product
|-
|center; style="background: #0D4F8B; color: white;" |PM6
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |B3LYP/6-31G(d)
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |Frequency values at B3LYP/6-31G(d) Level
|[[File:E2_DIENE_ZZY.png|185px|thumb|center |]]
|[[File:E2_OXO_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_ZZY.png|185px|thumb|center |]]
|-
|}

The structures above are optimized as confirmed by the frequency calculation. None of them has more than one negative frequencies. There is only one negative frequency for both TS structures, indicating they are correctly optimized.

==== MO Analysis ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | ENDO MO
! style="background: #0D4F8B; color: white;" | EXO MO
|-
| [[File:E2_ENDO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
| [[File:E2_EXO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
|-
|+ Table 6. Calculated activation and reaction Energy for Endo Product
|}

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene HOMO
! style="background: #0D4F8B; color: white;" | Cyclohexadiene LUMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole HOMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
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<script> frame 2; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | EXO TS HOMO
! style="background: #0D4F8B; color: white;" | EXO TS LUMO
! style="background: #0D4F8B; color: white;" | EXO TS HOMO-1
! style="background: #0D4F8B; color: white;" | EXO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO-1
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|+ Table 6. Relevant MOs to the MO Diagram
|}

The MO diagram is constructed based on the energies of MOs calculated at BY3LYP/6-31(d) level.

This is an inverse demand DA reaction. The frontier molecular orbitals of the dienophile are higher in energy than that of the diene, i.e. the diene is electron poor while the dienophile is electron rich. In result of that, the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub> are more similar in energy compared to the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub>. The strongest orbital interaction is between FMOs that are closest in energy, in this case, that are the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub>. In a normal demand DA reaction, the strongest orbital interaction is between the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub> and the diene is electron rich as the dienophile is electron poor.

This can be rationalized as the dienophile of this reaction: 1,3-dioxole, is relatively electron rich. The neighbouring oxygen atoms donate electron density into the double bond, raise the energy of the double bond MOs. The reaction proceeds in an inverse demand fashion.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energies Calculated From B3LYP/631G(d) (kJmol<sup>-1</sup>)
| -612584.1026
| -701187.072
| -1313621.484
| -1313613.647
| -1313848.695
| -1313845.101
|-
|+ Table 5. Energies for All Species
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 150
| -77.5
|-
| style="background: #0D4F8B; color: white;" | Exo
| +157
| -73.9
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

The reaction barrier and the reaction energy were calculated by using the energy data from the BY3LYP/6-31G(d) results.
<center>Reaction barrier = Energy of TS - Sum of energy of reactants</center>
<center>Reaction energy = Energy of product - Sum of energy of reactants</center>

For this reaction, the endo reaction has a more negative reaction energy and a lower activation energy. Therefore the endo product is both the kinetically and thermodynamically favourable products. The endo product is more stable and less energy is required to overcome the reaction barrier of the endo reaction. Noticed both the endo and exo reactions are exothermic, i.e. the products are lower in energy compared to the reactants.

==== Secondary Orbital Interaction ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
|-
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|[[File:ZZY_E2_ENDO_2.png|thumb|center]]
|[[File:ZZY_E2_EXO_steric.png|thumb|center]]
|-
|+ Table 7. Secondary Orbital Interactions
|}

As shown in the graph, only the endo TS has the secondary orbital interactions between diene and dienophile. The lone pair orbitals of oxygen atoms interact with the LUMO of cyclohexadiene. This interaction stabilizes the endo transition state, lowering the reaction barrier. According to the Hammond's Postulate, the transition state of a reaction resembles either the reactants or the products, to whichever it is closer in energy. In this reaction, the energy of both TS are closer in energy to the product, hence the structure of the TS resembles the product. Consequently, the secondary orbital interactions which stabilizes the endo TS, also stabilizes the endo product. This explains the endo selectivity of this reaction.

For the exo TS, there is no secondary orbital interactions and the steric clash between the diene and dienophile destablizes the exo TS and product. This results in disfavouring of the exo reaction.

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

[[File:E3_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 63; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_TS_ZZY_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 65; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 134; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo Product
! center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 119; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 85; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 71; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 3. Optimized stuctures at PM6 level
|}

==== IRC Analysis ====

{| class="wikitable" style="margin: auto;"
|-
| style="background: #0D4F8B; color: white;" | Endo
| [[File:ZZY_E3_ENDO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Exo
| [[File:ZZY_E3_EXO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| [[File:ZZY_E3_CHE_DONG.gif]]
|-
|+ Table 6. Approach Trajectory of xylylene with SO<sub>2</sub>
|}

Ortho-xylylene has 8 <math>pi</math> electrons. According to the Huckle's rule (4n+2), it is not aromatic. However, it is planar as all carbons are sp<sup>2</sup> hybridised. When SO<sub>2</sub> approaches o-xylylene, the two ortho bonds stick out of the 6-membered ring plane towards the SO<sub>2</sub> and form new bonds with it while the <math>pi</math> bonds in the two ortho double bonds break. This leaves 6 <math>pi</math> electrons within the ring and the ring establishes aromaticity. Then the molecule adjusts to such that the original 8 carbons of the o-xylylene back to the same plane. The formation of aromatic ring and new sigma bonds are the driving force for the reactions.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Cheletropic TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
! style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +237.7678009
| +241.7506826
| +260.0871666
| +56.96807393
| +56.32220122
| -0.013127494
|-
|+ Table 5. Energies calculated from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 79.8
| -101.0
|-
| style="background: #0D4F8B; color: white;" | Exo
| +83.8
| -101.6
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| +102.2
| -157.9
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

[[File:ZZY_E3_ENERGY_PROFILE.PNG|centre|frame|Fig. 16: Energy profiles of Endo, Exo and Cheletropic reactions]]

The Diels-Alder reactions have lower reaction barrier than the Cheletropic reaction. They are kinetically favoured. The endo reaction has the lowest reaction barrier and it is the most favoured kinetically. The reaction energy of the endo and exo reactions are very close with the exo one slightly lower (probably due to less steric hindrance). Hence thermodynamically, they are favoured similarly. However, the Cheletropic reaction has a much lower reaction energy, i.e. the Cheletropic product is the most stable. The Cheletropic reaction is thermodynamically the most favoured reaction.

=== Extension: Second Cis-butadiene Fragment in O-xylylene ===

[[File:EX_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Exo Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 99; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 69; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 101; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 3. Optimized stuctures at PM6 level
|}

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +267.9846671
| +275.8217811
| +172.2537282
| +176.7223272
|-
|+ Table 5. Energies from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 110.1
| +14.3
|-
| style="background: #0D4F8B; color: white;" | Exo
| +117.9
| +18.8
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

The reaction barrier for both endo and exo reactions is much higher than that of the reactions with the other cis-butadiene fragment in Exercise 3. More energy required to overcome the barrier. In addition, the reaction energy for both endo and exo is positive, i.e. the products are more unstable than the reactants. Thus, this reaction with the cis-butadiene fragment within the ring is thermodynamically and kinetically unfavoured.

== Conclusion ==

== Reference ==

== Appendix ==

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Butadiene
|[[File:BUTADIENEWITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Ethene
|[[File:ETHENE_WITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | TS
|[[File:TS WITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexene
|[[File:Cyclohexeneproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | IRC
|[[File:CYCLOHEXENE TS IRC3.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
!center; style="background: #0D4F8B; color: white;" | BY3LYP/6-31(d)
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexadiene
|[[File:CYCLOHEXADIENE MIN.LOG]]
|[[File:CYCLOHEXADIENE MIN 63.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | 1,3-dioxole
|[[File:DIOXOLE MIN.LOG]]
|[[File:DIOXOLE631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:TS ex2 endo.LOG]]
|[[File:Endots631mo.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:TS ex2 exo.LOG]]
|[[File:Exots631mo2.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endo PRODUCT MIN.LOG]]
|[[File:ENDOPRODUCT 631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:ExoPRODUCT MIN.LOG]]
|[[File:EXOPRODUCT631.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:XYLENE3.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:EX3ENDOTS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:XYLYLENE exoex3 TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|[[File:INDENE_TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:ENDOPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCT OPT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|[[File:INDENEPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:EX3ENDOTSIRC.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:Xylene exo ts ir.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic IRC
|[[File:INDENEIRC.LOG]]
|}

=== Extension ===
{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:Xylene.log]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:Endotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:Exotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endoproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCTMIN4.LOG]]
|}

File:E3 CHE Product ZZY.LOG

2018-02-27T19:25:56Z

Zzy15:

File:E3 EXO Product ZZY.LOG

2018-02-27T19:25:17Z

Zzy15:

File:E3 ENDO Product ZZY.LOG

2018-02-27T19:24:51Z

Zzy15:

Rep:Mod:ZZY15 TS

2018-02-27T19:21:29Z

Zzy15: /* Optimization Results */

=''' Transition States and reactivity '''=
== Introduction ==

== Method ==

== Results and Discussion ==

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

[[File:E1_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Butadiene with Ethene reaction.]]

This is a Dials-Alder reaction. The ethene acting as the dienophile, reacts with the s-cis butadiene. Cyclohexene is formed.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Ethene
! center; style="background: #0D4F8B; color: white;" | Butadiene
! center; style="background: #0D4F8B; color: white;" | Transition State
! center; style="background: #0D4F8B; color: white;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 12; measure 1 4</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 3 4; measure 1 2; measure 1 4</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 54; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>E1_PRODUCT_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. Optimized stuctures at PM6 level.
|}

==== Bond Length Analysis ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" |sp<sup>3</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Double bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Single bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |VDW radius of C
|-
| style="background: #0D4F8B; color: white;" |Typical Bond Length (Å)
| 1.54
| 1.33
| 1.47
| 1.50
| 1.70
|+ Table 2. Typical C-C bond Length.
|}

{| class="wikitable" style="margin: auto;"
|-
| [[File:ZZY_E1_NUMBERING.png|thumb|none|350px|center|Figure 2. Numbering of TS Carbons.]]
|rowspan="2" |[[File:E1_BONDDISTANCES_ZZY.png|thumb|none|500px|center|Figure 3. Bond distances versus IRC.]]
|-
| [[File:ZZY_E1_DISTANCE_FOCUS.png|thumb|none|350px|center|Figure 4. Zoom-in of Bond distances versus IRC Graph.]]
|-
|+ Table 3. Change in Bond Distances During The Reaction.
|}

The length of the partially formed C-C sigma bonds (C1-C8, C4-C9) in the TS is shorter than 2 x Van Der Waals radius of carbon, indicating formation of bonds between them. As the reaction proceeds, their length shortens and reaches the typical sp<sup>3</sup> C-sp<sup>3</sup>C single bond length at the end of the reation. The bond length between C7-C10 in the TS is shorter compared to the typical sp<sup>2</sup> C-sp<sup>2</sup>C single bond length. This indicating the formation of C-C pi bond between them. The bond length between C1-C4 at TS is longer than the typical C-C double bond length, indicating the pi bond breaking during the reaction. The bond length between C7-C8, C9-C10 is longer than the typical C-C double bond length, indicating the breaking of pi bond between them. It reaches the typical sp<sup>2</sup> C-sp<sup>3</sup>C bond length at the end.

==== Frequency and IRC Analysis ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | TS Bond Forming/Breaking Vibration
! center; style="background: #0D4F8B; color: white;" | Frequency Calculation
|-
| [[File:ZZY_TS_VIBRATION.gif]] || [[File:ZZY_E1_FREQUENCY.PNG|350px|thumb|center |]]
|-
|+ Table 2. Transition State Vibrational Frequencies.
|}

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Trajectory
! center; style="background: #0D4F8B; color: white;" | IRC Path
|-
| [[File:ZZY_IRC.gif]] || [[File:ZZY_E1_IRC_PATH.PNG|350px|thumb|center |]]
|-
|+ Table 3. IRC Path of Reaction
|}

There is only one imaginary vibration (negative vibration) for the TS calculated, confirming that the TS is optimized correctly. Transition state corresponds to the highest potential energy along the reaction coordinate. At TS, the first derivative of energy graph is zero and the second derivative is negative. The frequency represents the second derivative of the energy. Therefore a single negative frequency indicates that there is only one maximum point on the reaction coordinate chosen. It is the maximum point in all order parameters. That is the correct transition state. If there are more than one negative frequency, they represent state that is maximum on one order parameter but not on others.

The IRC plots also show the correct optimization of TS. The maximum energy point corresponds to zero RMS gradient,showing the geometry is optimized at that point.

The animation of vibration at -949 cm<sup>-1</sup> shows that the formation of bonds in this reaction is synchronous. They form at the same time.

==== MO Analysis ====
{| class="wikitable" style="margin: auto;"
!
! center; style="background: #0D4F8B; color: white;" | HOMO
! center; style="background: #0D4F8B; color: white;" | LUMO
! colspan="2" center; style="background: #0D4F8B; color: white;" | MO Diagram
|-
| center; style="background: #0D4F8B; color: white;" | Butadiene
|<jmol>
<jmolApplet>
<title>HOMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2" colspan="2"|[[File:E1_MO_ZZY_NEW.png|thumb|none|450px|center|Figure 5. MO of diels-alder reaction.]]

|-
| center; style="background: #0D4F8B; color: white;" | Ethene
|<jmol>
<jmolApplet>
<title>HOMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| center; style="background: #0D4F8B; color: white;" | Transition state
|<jmol>
<jmolApplet>
<title>HOMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
|+ Table 4. MO diagrams
|}

The MO diagram is constructed based on the energies of MOs calculated at PM6 level. The diene has a smaller HOMO-LUMO energy gap as the HOMO and LUMO are neither the lowest energy bonding MO nor the highest energy antiboning MO, which is the case for the ethene. Noticed that the energy of HOMO/HOMO-1 of TS is higher than expected and the energy of the LUMO/LUMO+1 of TS is lower than expected (real energy levels indicated by red lines in the graph). This is because the MO diagram is based on the transition state MO energies, not on product as we used to do. In the TS, the new bonds are not completely formed. Therefore the "bonding orbitals" are higher in energy and the "anti-bonding orbitals" are lower in energy than expected.

Due to the larger energy gap between interacting MOs of ethene and diene, this reaction is not efficient. This can be improved by adding electron donating groups to the diene and adding electron withdrawing groups to the dienophile. By doing this, the energy leveles of diene are raised and that of the dienophile are lowered. This leads to better overlap as MOs closer in energy. The reaction is more efficient.

As shown by the MO visualization, reactants' MOs of the same symmetry overlap and give the TS MOs. This indicates that only interactions between MOs of the same symmetry are allowed. Mis-symmetry interactions are forbidden, i.e. they don't interact.

The overlap between MOs is described by the orbital overlap integral <math>S</math>. It is defined as:
<center><math>S=\int {\psi_1\psi^*_2 d\tau}</math></center>
<center><small> ''Equation 1: Equation of the Overlap Integral'' </small> </center>
<math>\psi_1</math> and <math>\psi^*_2</math> are the wavefunctions of the interacting MOs.
It is known that integral of asymmetric functions is zero. The product of an asymmetric and a symmetric function is asymmetric as the product of two functions of the same symmetry is symmetric. In conclusion, the overlap integral of two MOs of different symmetry is zero and the overlap integral of two MOs of the same symmetry is non-zero. This is consistent to the symmetry requirement mentioned before as reaction can't happen with zero overlap.

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

[[File:E2_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 6. Reaction Scheme of Cyclohexadiene and 1,3-Dioxole Reaction.]]

This a Diels-Alder reaction. The 1,3-Dioxole acts as the dienophile. There are two possible products: endo and exo.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
|+ Table 7: ''' Optimized Stuctures at PM6 Level and BY3LP 6-31(d) Level '''
!
!center; style="background: #0D4F8B; color: white;" |Cyclohexadiene
!center; style="background: #0D4F8B; color: white;" |1,3-dioxole
!center; style="background: #0D4F8B; color: white;" |Endo TS
!center; style="background: #0D4F8B; color: white;" |Exo TS
!center; style="background: #0D4F8B; color: white;" |Endo Product
!center; style="background: #0D4F8B; color: white;" |Exo Product
|-
|center; style="background: #0D4F8B; color: white;" |PM6
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |B3LYP/6-31G(d)
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |Frequency values at B3LYP/6-31G(d) Level
|[[File:E2_DIENE_ZZY.png|185px|thumb|center |]]
|[[File:E2_OXO_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_ZZY.png|185px|thumb|center |]]
|-
|}

The structures above are optimized as confirmed by the frequency calculation. None of them has more than one negative frequencies. There is only one negative frequency for both TS structures, indicating they are correctly optimized.

==== MO Analysis ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | ENDO MO
! style="background: #0D4F8B; color: white;" | EXO MO
|-
| [[File:E2_ENDO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
| [[File:E2_EXO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
|-
|+ Table 6. Calculated activation and reaction Energy for Endo Product
|}

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene HOMO
! style="background: #0D4F8B; color: white;" | Cyclohexadiene LUMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole HOMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | EXO TS HOMO
! style="background: #0D4F8B; color: white;" | EXO TS LUMO
! style="background: #0D4F8B; color: white;" | EXO TS HOMO-1
! style="background: #0D4F8B; color: white;" | EXO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO-1
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|+ Table 6. Relevant MOs to the MO Diagram
|}

The MO diagram is constructed based on the energies of MOs calculated at BY3LYP/6-31(d) level.

This is an inverse demand DA reaction. The frontier molecular orbitals of the dienophile are higher in energy than that of the diene, i.e. the diene is electron poor while the dienophile is electron rich. In result of that, the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub> are more similar in energy compared to the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub>. The strongest orbital interaction is between FMOs that are closest in energy, in this case, that are the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub>. In a normal demand DA reaction, the strongest orbital interaction is between the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub> and the diene is electron rich as the dienophile is electron poor.

This can be rationalized as the dienophile of this reaction: 1,3-dioxole, is relatively electron rich. The neighbouring oxygen atoms donate electron density into the double bond, raise the energy of the double bond MOs. The reaction proceeds in an inverse demand fashion.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energies Calculated From B3LYP/631G(d) (kJmol<sup>-1</sup>)
| -612584.1026
| -701187.072
| -1313621.484
| -1313613.647
| -1313848.695
| -1313845.101
|-
|+ Table 5. Energies for All Species
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 150
| -77.5
|-
| style="background: #0D4F8B; color: white;" | Exo
| +157
| -73.9
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

The reaction barrier and the reaction energy were calculated by using the energy data from the BY3LYP/6-31G(d) results.
<center>Reaction barrier = Energy of TS - Sum of energy of reactants</center>
<center>Reaction energy = Energy of product - Sum of energy of reactants</center>

For this reaction, the endo reaction has a more negative reaction energy and a lower activation energy. Therefore the endo product is both the kinetically and thermodynamically favourable products. The endo product is more stable and less energy is required to overcome the reaction barrier of the endo reaction. Noticed both the endo and exo reactions are exothermic, i.e. the products are lower in energy compared to the reactants.

==== Secondary Orbital Interaction ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
|-
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|[[File:ZZY_E2_ENDO_2.png|thumb|center]]
|[[File:ZZY_E2_EXO_steric.png|thumb|center]]
|-
|+ Table 7. Secondary Orbital Interactions
|}

As shown in the graph, only the endo TS has the secondary orbital interactions between diene and dienophile. The lone pair orbitals of oxygen atoms interact with the LUMO of cyclohexadiene. This interaction stabilizes the endo transition state, lowering the reaction barrier. According to the Hammond's Postulate, the transition state of a reaction resembles either the reactants or the products, to whichever it is closer in energy. In this reaction, the energy of both TS are closer in energy to the product, hence the structure of the TS resembles the product. Consequently, the secondary orbital interactions which stabilizes the endo TS, also stabilizes the endo product. This explains the endo selectivity of this reaction.

For the exo TS, there is no secondary orbital interactions and the steric clash between the diene and dienophile destablizes the exo TS and product. This results in disfavouring of the exo reaction.

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

[[File:E3_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 63; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_TS_ZZY_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 65; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 134; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo Product
! center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 63; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 65; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 134; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_Product_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 3. Optimized stuctures at PM6 level
|}

==== IRC Analysis ====

{| class="wikitable" style="margin: auto;"
|-
| style="background: #0D4F8B; color: white;" | Endo
| [[File:ZZY_E3_ENDO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Exo
| [[File:ZZY_E3_EXO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| [[File:ZZY_E3_CHE_DONG.gif]]
|-
|+ Table 6. Approach Trajectory of xylylene with SO<sub>2</sub>
|}

Ortho-xylylene has 8 <math>pi</math> electrons. According to the Huckle's rule (4n+2), it is not aromatic. However, it is planar as all carbons are sp<sup>2</sup> hybridised. When SO<sub>2</sub> approaches o-xylylene, the two ortho bonds stick out of the 6-membered ring plane towards the SO<sub>2</sub> and form new bonds with it while the <math>pi</math> bonds in the two ortho double bonds break. This leaves 6 <math>pi</math> electrons within the ring and the ring establishes aromaticity. Then the molecule adjusts to such that the original 8 carbons of the o-xylylene back to the same plane. The formation of aromatic ring and new sigma bonds are the driving force for the reactions.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Cheletropic TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
! style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +237.7678009
| +241.7506826
| +260.0871666
| +56.96807393
| +56.32220122
| -0.013127494
|-
|+ Table 5. Energies calculated from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 79.8
| -101.0
|-
| style="background: #0D4F8B; color: white;" | Exo
| +83.8
| -101.6
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| +102.2
| -157.9
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

[[File:ZZY_E3_ENERGY_PROFILE.PNG|centre|frame|Fig. 16: Energy profiles of Endo, Exo and Cheletropic reactions]]

The Diels-Alder reactions have lower reaction barrier than the Cheletropic reaction. They are kinetically favoured. The endo reaction has the lowest reaction barrier and it is the most favoured kinetically. The reaction energy of the endo and exo reactions are very close with the exo one slightly lower (probably due to less steric hindrance). Hence thermodynamically, they are favoured similarly. However, the Cheletropic reaction has a much lower reaction energy, i.e. the Cheletropic product is the most stable. The Cheletropic reaction is thermodynamically the most favoured reaction.

=== Extension: Second Cis-butadiene Fragment in O-xylylene ===

[[File:EX_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Endo Product
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Exo Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 1; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 99; set antialiasdisplay on</script>
<uploadedFileContents>EX_ENDO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 69; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_TS_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 101; set antialiasdisplay on</script>
<uploadedFileContents>EX_EXO_PRODUCT_ZZY_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 3. Optimized stuctures at PM6 level
|}

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +267.9846671
| +275.8217811
| +172.2537282
| +176.7223272
|-
|+ Table 5. Energies from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 110.1
| +14.3
|-
| style="background: #0D4F8B; color: white;" | Exo
| +117.9
| +18.8
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

The reaction barrier for both endo and exo reactions is much higher than that of the reactions with the other cis-butadiene fragment in Exercise 3. More energy required to overcome the barrier. In addition, the reaction energy for both endo and exo is positive, i.e. the products are more unstable than the reactants. Thus, this reaction with the cis-butadiene fragment within the ring is thermodynamically and kinetically unfavoured.

== Conclusion ==

== Reference ==

== Appendix ==

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Butadiene
|[[File:BUTADIENEWITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Ethene
|[[File:ETHENE_WITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | TS
|[[File:TS WITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexene
|[[File:Cyclohexeneproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | IRC
|[[File:CYCLOHEXENE TS IRC3.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
!center; style="background: #0D4F8B; color: white;" | BY3LYP/6-31(d)
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexadiene
|[[File:CYCLOHEXADIENE MIN.LOG]]
|[[File:CYCLOHEXADIENE MIN 63.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | 1,3-dioxole
|[[File:DIOXOLE MIN.LOG]]
|[[File:DIOXOLE631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:TS ex2 endo.LOG]]
|[[File:Endots631mo.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:TS ex2 exo.LOG]]
|[[File:Exots631mo2.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endo PRODUCT MIN.LOG]]
|[[File:ENDOPRODUCT 631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:ExoPRODUCT MIN.LOG]]
|[[File:EXOPRODUCT631.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:XYLENE3.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:EX3ENDOTS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:XYLYLENE exoex3 TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|[[File:INDENE_TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:ENDOPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCT OPT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|[[File:INDENEPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:EX3ENDOTSIRC.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:Xylene exo ts ir.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic IRC
|[[File:INDENEIRC.LOG]]
|}

=== Extension ===
{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:Xylene.log]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:Endotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:Exotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endoproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCTMIN4.LOG]]
|}

Rep:Mod:ZZY15 TS

2018-02-27T19:16:20Z

Rep:Mod:ZZY15 TS

2018-02-27T18:50:21Z

Zzy15: /* MO Analysis */

=''' Transition States and reactivity '''=
== Introduction ==

== Method ==

== Results and Discussion ==

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

[[File:E1_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Butadiene with Ethene reaction.]]

This is a Dials-Alder reaction. The ethene acting as the dienophile, reacts with the s-cis butadiene. Cyclohexene is formed.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Ethene
! center; style="background: #0D4F8B; color: white;" | Butadiene
! center; style="background: #0D4F8B; color: white;" | Transition State
! center; style="background: #0D4F8B; color: white;" | Product
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 12; measure 1 4</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 3 4; measure 1 2; measure 1 4</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 14; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 54; measure 1 4; measure 1 8; measure 7 8; measure 7 10; measure 9 10; measure 4 9</script>
<uploadedFileContents>E1_PRODUCT_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 1. Optimized stuctures at PM6 level.
|}

==== Bond Length Analysis ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" |sp<sup>3</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Double bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>2</sup> C (Single bond)
! style="background: #0D4F8B; color: white;" |sp<sup>2</sup> C- sp<sup>3</sup> C
! style="background: #0D4F8B; color: white;" |VDW radius of C
|-
| style="background: #0D4F8B; color: white;" |Typical Bond Length (Å)
| 1.54
| 1.33
| 1.47
| 1.50
| 1.70
|+ Table 2. Typical C-C bond Length.
|}

{| class="wikitable" style="margin: auto;"
|-
| [[File:ZZY_E1_NUMBERING.png|thumb|none|350px|center|Figure 2. Numbering of TS Carbons.]]
|rowspan="2" |[[File:E1_BONDDISTANCES_ZZY.png|thumb|none|500px|center|Figure 3. Bond distances versus IRC.]]
|-
| [[File:ZZY_E1_DISTANCE_FOCUS.png|thumb|none|350px|center|Figure 4. Zoom-in of Bond distances versus IRC Graph.]]
|-
|+ Table 3. Change in Bond Distances During The Reaction.
|}

The length of the partially formed C-C sigma bonds (C1-C8, C4-C9) in the TS is shorter than 2 x Van Der Waals radius of carbon, indicating formation of bonds between them. As the reaction proceeds, their length shortens and reaches the typical sp<sup>3</sup> C-sp<sup>3</sup>C single bond length at the end of the reation. The bond length between C7-C10 in the TS is shorter compared to the typical sp<sup>2</sup> C-sp<sup>2</sup>C single bond length. This indicating the formation of C-C pi bond between them. The bond length between C1-C4 at TS is longer than the typical C-C double bond length, indicating the pi bond breaking during the reaction. The bond length between C7-C8, C9-C10 is longer than the typical C-C double bond length, indicating the breaking of pi bond between them. It reaches the typical sp<sup>2</sup> C-sp<sup>3</sup>C bond length at the end.

==== Frequency and IRC Analysis ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | TS Bond Forming/Breaking Vibration
! center; style="background: #0D4F8B; color: white;" | Frequency Calculation
|-
| [[File:ZZY_TS_VIBRATION.gif]] || [[File:ZZY_E1_FREQUENCY.PNG|350px|thumb|center |]]
|-
|+ Table 2. Transition State Vibrational Frequencies.
|}

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Trajectory
! center; style="background: #0D4F8B; color: white;" | IRC Path
|-
| [[File:ZZY_IRC.gif]] || [[File:ZZY_E1_IRC_PATH.PNG|350px|thumb|center |]]
|-
|+ Table 3. IRC Path of Reaction
|}

There is only one imaginary vibration (negative vibration) for the TS calculated, confirming that the TS is optimized correctly. Transition state corresponds to the highest potential energy along the reaction coordinate. At TS, the first derivative of energy graph is zero and the second derivative is negative. The frequency represents the second derivative of the energy. Therefore a single negative frequency indicates that there is only one maximum point on the reaction coordinate chosen. It is the maximum point in all order parameters. That is the correct transition state. If there are more than one negative frequency, they represent state that is maximum on one order parameter but not on others.

The IRC plots also show the correct optimization of TS. The maximum energy point corresponds to zero RMS gradient,showing the geometry is optimized at that point.

The animation of vibration at -949 cm<sup>-1</sup> shows that the formation of bonds in this reaction is synchronous. They form at the same time.

==== MO Analysis ====
{| class="wikitable" style="margin: auto;"
!
! center; style="background: #0D4F8B; color: white;" | HOMO
! center; style="background: #0D4F8B; color: white;" | LUMO
! colspan="2" center; style="background: #0D4F8B; color: white;" | MO Diagram
|-
| center; style="background: #0D4F8B; color: white;" | Butadiene
|<jmol>
<jmolApplet>
<title>HOMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Butadiene </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>DIENE_OP_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="2" colspan="2"|[[File:E1_MO_ZZY_NEW.png|thumb|none|450px|center|Figure 5. MO of diels-alder reaction.]]

|-
| center; style="background: #0D4F8B; color: white;" | Ethene
|<jmol>
<jmolApplet>
<title>HOMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of Ethene </title>
<color>white</color>
<size>220</size>
<script> frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>E1_SM_ALKENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| center; style="background: #0D4F8B; color: white;" | Transition state
|<jmol>
<jmolApplet>
<title>HOMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO-1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO+1 of TS </title>
<color>white</color>
<size>220</size>
<script> frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>REACTANT_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|-
|+ Table 4. MO diagrams
|}

The MO diagram is constructed based on the energies of MOs calculated at PM6 level. The diene has a smaller HOMO-LUMO energy gap as the HOMO and LUMO are neither the lowest energy bonding MO nor the highest energy antiboning MO, which is the case for the ethene. Noticed that the energy of HOMO/HOMO-1 of TS is higher than expected and the energy of the LUMO/LUMO+1 of TS is lower than expected (real energy levels indicated by red lines in the graph). This is because the MO diagram is based on the transition state MO energies, not on product as we used to do. In the TS, the new bonds are not completely formed. Therefore the "bonding orbitals" are higher in energy and the "anti-bonding orbitals" are lower in energy than expected.

Due to the larger energy gap between interacting MOs of ethene and diene, this reaction is not efficient. This can be improved by adding electron donating groups to the diene and adding electron withdrawing groups to the dienophile. By doing this, the energy leveles of diene are raised and that of the dienophile are lowered. This leads to better overlap as MOs closer in energy. The reaction is more efficient.

As shown by the MO visualization, reactants' MOs of the same symmetry overlap and give the TS MOs. This indicates that only interactions between MOs of the same symmetry are allowed. Mis-symmetry interactions are forbidden, i.e. they don't interact.

The overlap between MOs is described by the orbital overlap integral <math>S</math>. It is defined as:
<center><math>S=\int {\psi_1\psi^*_2 d\tau}</math></center>
<center><small> ''Equation 1: Equation of the Overlap Integral'' </small> </center>
<math>\psi_1</math> and <math>\psi^*_2</math> are the wavefunctions of the interacting MOs.
It is known that integral of asymmetric functions is zero. The product of an asymmetric and a symmetric function is asymmetric as the product of two functions of the same symmetry is symmetric. In conclusion, the overlap integral of two MOs of different symmetry is zero and the overlap integral of two MOs of the same symmetry is non-zero. This is consistent to the symmetry requirement mentioned before as reaction can't happen with zero overlap.

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

[[File:E2_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 6. Reaction Scheme of Cyclohexadiene and 1,3-Dioxole Reaction.]]

This a Diels-Alder reaction. The 1,3-Dioxole acts as the dienophile. There are two possible products: endo and exo.

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
|+ Table 7: ''' Optimized Stuctures at PM6 Level and BY3LP 6-31(d) Level '''
!
!center; style="background: #0D4F8B; color: white;" |Cyclohexadiene
!center; style="background: #0D4F8B; color: white;" |1,3-dioxole
!center; style="background: #0D4F8B; color: white;" |Endo TS
!center; style="background: #0D4F8B; color: white;" |Exo TS
!center; style="background: #0D4F8B; color: white;" |Endo Product
!center; style="background: #0D4F8B; color: white;" |Exo Product
|-
|center; style="background: #0D4F8B; color: white;" |PM6
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_PM6_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |B3LYP/6-31G(d)
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIENE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_ENDO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>190</size>
<uploadedFileContents>ZZY_E2_EXO_OP_631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|center; style="background: #0D4F8B; color: white;" |Frequency values at B3LYP/6-31G(d) Level
|[[File:E2_DIENE_ZZY.png|185px|thumb|center |]]
|[[File:E2_OXO_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_TS_ZZY.png|185px|thumb|center |]]
|[[File:E2_ENDO_ZZY.png|185px|thumb|center |]]
|[[File:E2_EXO_ZZY.png|185px|thumb|center |]]
|-
|}

The structures above are optimized as confirmed by the frequency calculation. None of them has more than one negative frequencies. There is only one negative frequency for both TS structures, indicating they are correctly optimized.

==== MO Analysis ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | ENDO MO
! style="background: #0D4F8B; color: white;" | EXO MO
|-
| [[File:E2_ENDO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
| [[File:E2_EXO_MO_ZZY_CORRECT.png|450px|thumb|center |]]
|-
|+ Table 6. Calculated activation and reaction Energy for Endo Product
|}

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Cyclohexadiene HOMO
! style="background: #0D4F8B; color: white;" | Cyclohexadiene LUMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole HOMO
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole LUMO
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIENE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_DIOXOLE_OP_631_J.log</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | EXO TS HOMO
! style="background: #0D4F8B; color: white;" | EXO TS LUMO
! style="background: #0D4F8B; color: white;" | EXO TS HOMO-1
! style="background: #0D4F8B; color: white;" | EXO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 16; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO
! style="background: #0D4F8B; color: white;" | ENDO TS HOMO-1
! style="background: #0D4F8B; color: white;" | ENDO TS LUMO+1
|-
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 2; MO 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo titleformat "Energy=%E%U"</script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|+ Table 6. Relevant MOs to the MO Diagram
|}

The MO diagram is constructed based on the energies of MOs calculated at BY3LYP/6-31(d) level.

This is an inverse demand DA reaction. The frontier molecular orbitals of the dienophile are higher in energy than that of the diene, i.e. the diene is electron poor while the dienophile is electron rich. In result of that, the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub> are more similar in energy compared to the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub>. The strongest orbital interaction is between FMOs that are closest in energy, in this case, that are the HOMO<sub>dienophile</sub> and the LUMO<sub>diene</sub>. In a normal demand DA reaction, the strongest orbital interaction is between the HOMO<sub>diene</sub> and the LUMO<sub>dienophile</sub> and the diene is electron rich as the dienophile is electron poor.

This can be rationalized as the dienophile of this reaction: 1,3-dioxole, is relatively electron rich. The neighbouring oxygen atoms donate electron density into the double bond, raise the energy of the double bond MOs. The reaction proceeds in an inverse demand fashion.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energies Calculated From B3LYP/631G(d) (kJmol<sup>-1</sup>)
| -612584.1026
| -701187.072
| -1313621.484
| -1313613.647
| -1313848.695
| -1313845.101
|-
|+ Table 5. Energies for All Species
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 150
| -77.5
|-
| style="background: #0D4F8B; color: white;" | Exo
| +157
| -73.9
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

The reaction barrier and the reaction energy were calculated by using the energy data from the BY3LYP/6-31G(d) results.
<center>Reaction barrier = Energy of TS - Sum of energy of reactants</center>
<center>Reaction energy = Energy of product - Sum of energy of reactants</center>

For this reaction, the endo reaction has a more negative reaction energy and a lower activation energy. Therefore the endo product is both the kinetically and thermodynamically favourable products. The endo product is more stable and less energy is required to overcome the reaction barrier of the endo reaction. Noticed both the endo and exo reactions are exothermic, i.e. the products are lower in energy compared to the reactants.

==== Secondary Orbital Interaction ====

{| class="wikitable" style="margin: auto;"
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
|-
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_ENDO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title> HOMO </title>
<color>white</color>
<size>250</size>
<script> frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on "" </script>
<uploadedFileContents>ZZY_E2_EXO_TS_631_J.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|[[File:ZZY_E2_ENDO_2.png|thumb|center]]
|[[File:ZZY_E2_EXO_steric.png|thumb|center]]
|-
|+ Table 7. Secondary Orbital Interactions
|}

As shown in the graph, only the endo TS has the secondary orbital interactions between diene and dienophile. The lone pair orbitals of oxygen atoms interact with the LUMO of cyclohexadiene. This interaction stabilizes the endo transition state, lowering the reaction barrier. According to the Hammond's Postulate, the transition state of a reaction resembles either the reactants or the products, to whichever it is closer in energy. In this reaction, the energy of both TS are closer in energy to the product, hence the structure of the TS resembles the product. Consequently, the secondary orbital interactions which stabilizes the endo TS, also stabilizes the endo product. This explains the endo selectivity of this reaction.

For the exo TS, there is no secondary orbital interactions and the steric clash between the diene and dienophile destablizes the exo TS and product. This results in disfavouring of the exo reaction.

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

[[File:E3_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

==== Optimization Results ====

{| class="wikitable" style="margin: auto;"
! center; style="background: #0D4F8B; color: white;" | Endo TS
! center; style="background: #0D4F8B; color: white;" | Exo TS
! center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 63; set antialiasdisplay on</script>
<uploadedFileContents>E3_ENDO_TS_ZZY_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 65; set antialiasdisplay on</script>
<uploadedFileContents>E3_EXO_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>220</size>
<script> frame 134; set antialiasdisplay on</script>
<uploadedFileContents>E3_CHE_TS_ZZY.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|+ Table 3. Optimized stuctures at PM6 level
|}

==== IRC Analysis ====

{| class="wikitable" style="margin: auto;"
|-
| style="background: #0D4F8B; color: white;" | Endo
| [[File:ZZY_E3_ENDO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Exo
| [[File:ZZY_E3_EXO_DONG.gif]]
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| [[File:ZZY_E3_CHE_DONG.gif]]
|-
|+ Table 6. Approach Trajectory of xylylene with SO<sub>2</sub>
|}

Ortho-xylylene has 8 <math>pi</math> electrons. According to the Huckle's rule (4n+2), it is not aromatic. However, it is planar as all carbons are sp<sup>2</sup> hybridised. When SO<sub>2</sub> approaches o-xylylene, the two ortho bonds stick out of the 6-membered ring plane towards the SO<sub>2</sub> and form new bonds with it while the <math>pi</math> bonds in the two ortho double bonds break. This leaves 6 <math>pi</math> electrons within the ring and the ring establishes aromaticity. Then the molecule adjusts to such that the original 8 carbons of the o-xylylene back to the same plane. The formation of aromatic ring and new sigma bonds are the driving force for the reactions.

==== Reaction Barriers and Reaction Energies ====

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Cheletropic TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
! style="background: #0D4F8B; color: white;" | Cheletropic Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +237.7678009
| +241.7506826
| +260.0871666
| +56.96807393
| +56.32220122
| -0.013127494
|-
|+ Table 5. Energies calculated from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 79.8
| -101.0
|-
| style="background: #0D4F8B; color: white;" | Exo
| +83.8
| -101.6
|-
| style="background: #0D4F8B; color: white;" | Cheletropic
| +102.2
| -157.9
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

[[File:ZZY_E3_ENERGY_PROFILE.PNG|centre|frame|Fig. 16: Energy profiles of Endo, Exo and Cheletropic reactions]]

The Diels-Alder reactions have lower reaction barrier than the Cheletropic reaction. They are kinetically favoured. The endo reaction has the lowest reaction barrier and it is the most favoured kinetically. The reaction energy of the endo and exo reactions are very close with the exo one slightly lower (probably due to less steric hindrance). Hence thermodynamically, they are favoured similarly. However, the Cheletropic reaction has a much lower reaction energy, i.e. the Cheletropic product is the most stable. The Cheletropic reaction is thermodynamically the most favoured reaction.

=== Extension: Second Cis-butadiene Fragment in O-xylylene ===

[[File:EX_REACTION_SCHEME_ZZY.png|thumb|700px|center|Figure 1. Reaction Scheme of Xylylene-SO2 Cycloaddition.]]

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Endo TS
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo Product
! style="background: #0D4F8B; color: white;" | Exo Product
|-
| style="background: #0D4F8B; color: white;" | Energy (kJmol<sup>-1</sup>)
| +469.3446755
| -311.42092
| +267.9846671
| +275.8217811
| +172.2537282
| +176.7223272
|-
|+ Table 5. Energies from PM6
|}

{| class="wikitable" style="margin: auto;"
!
! style="background: #0D4F8B; color: white;" | Reaction Barrier (kJmol<sup>-1</sup>)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJmol<sup>-1</sup>)
|-
| style="background: #0D4F8B; color: white;" | Endo
| + 110.1
| +14.3
|-
| style="background: #0D4F8B; color: white;" | Exo
| +117.9
| +18.8
|-
|+ Table 6. Calculated Activation and Reaction Energy
|}

The reaction barrier for both endo and exo reactions is much higher than that of the reactions with the other cis-butadiene fragment in Exercise 3. More energy required to overcome the barrier. In addition, the reaction energy for both endo and exo is positive, i.e. the products are more unstable than the reactants. Thus, this reaction with the cis-butadiene fragment within the ring is thermodynamically and kinetically unfavoured.

== Conclusion ==

== Reference ==

== Appendix ==

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Butadiene
|[[File:BUTADIENEWITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Ethene
|[[File:ETHENE_WITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | TS
|[[File:TS WITHMO.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexene
|[[File:Cyclohexeneproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | IRC
|[[File:CYCLOHEXENE TS IRC3.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
!center; style="background: #0D4F8B; color: white;" | BY3LYP/6-31(d)
|-
|center; style="background: #0D4F8B; color: white;" | Cyclohexadiene
|[[File:CYCLOHEXADIENE MIN.LOG]]
|[[File:CYCLOHEXADIENE MIN 63.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | 1,3-dioxole
|[[File:DIOXOLE MIN.LOG]]
|[[File:DIOXOLE631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:TS ex2 endo.LOG]]
|[[File:Endots631mo.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:TS ex2 exo.LOG]]
|[[File:Exots631mo2.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endo PRODUCT MIN.LOG]]
|[[File:ENDOPRODUCT 631.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:ExoPRODUCT MIN.LOG]]
|[[File:EXOPRODUCT631.LOG]]
|}

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

{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:XYLENE3.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:EX3ENDOTS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:XYLYLENE exoex3 TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic TS
|[[File:INDENE_TS.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:ENDOPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCT OPT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic Product
|[[File:INDENEPRODUCT.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo IRC
|[[File:EX3ENDOTSIRC.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo IRC
|[[File:Xylene exo ts ir.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Cheletropic IRC
|[[File:INDENEIRC.LOG]]
|}

=== Extension ===
{| class="wikitable" style="margin: auto;"
!
!center; style="background: #0D4F8B; color: white;" | PM6
|-
|center; style="background: #0D4F8B; color: white;" | Xylylene
|[[File:Xylene.log]]
|-
|center; style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
|[[File:SO2.LOG]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo TS
|[[File:Endotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo TS
|[[File:Exotsextra.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Endo Product
|[[File:Endoproduct.log]]
|-
|center; style="background: #0D4F8B; color: white;" | Exo Product
|[[File:EXOPRODUCTMIN4.LOG]]
|}

File:E2 ENDO MO ZZY CORRECT.png

2018-02-27T18:29:25Z

Zzy15:

File:E2 EXO MO ZZY CORRECT.png

2018-02-27T18:28:43Z

Zzy15: