ChemWiki - User contributions [en]

User:Dk1814

2017-02-24T08:59:30Z

Dk1814: /* Instability of o-xylylene */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x500px|thumb|left|Molecular Orbital diagram for formation of transition state]]
Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" heights = 160px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" heights = 160px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 160px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 160px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|320px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character). The gain in aromaticity drive the reactions thermodynamically.
 

=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:33:44Z

Dk1814: /* Orbitals with the same symmetry label have non-zero overlap integral */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x500px|thumb|left|Molecular Orbital diagram for formation of transition state]]
Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" heights = 160px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" heights = 160px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 160px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 160px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|320px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:32:11Z

Dk1814: /* Calculations */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x500px|thumb|left|Molecular Orbital diagram for formation of transition state]]
Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" heights = 160px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" heights = 160px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 160px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 160px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|320px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:31:21Z

Dk1814: /* Orbitals with the same symmetry label have non-zero overlap integral */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x500px|thumb|left|Molecular Orbital diagram for formation of transition state]]
Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" heights = 160px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" heights = 160px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 160px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 160px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|320px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:30:25Z

Dk1814: /* Orbitals with the same symmetry label have non-zero overlap integral */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x500px|thumb|left|Molecular Orbital diagram for formation of transition state]]
Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" heights = 160px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" heights = 160px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 160px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 160px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|320px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:29:00Z

Dk1814: /* Inverse electron demand Diels-Alder cycloaddition is synchronous */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 160px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 160px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|320px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:27:37Z

Dk1814: /* Secondary orbital interactions stabilise the endo transition state */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
<gallery mode=nolines widths = 300px>
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|320px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:25:48Z

Dk1814: /* Asynchronous Diels-Alder cycloaddition */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|160px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|160px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|160px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|160px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|160px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|160px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
[[File:Dk1814-ex3energydiagram.png|300px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|}
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 200px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 200px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-21T12:21:45Z

Dk1814: /* Alternate Diels-Alder reaction */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.

{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|200px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|200px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|200px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|200px|Concerted, asynchronous cycloaddition to form exo product]]
|}
[[File:Dk1814-ex3otherenergydiagram.png|x300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-17T11:04:04Z

Dk1814: /* Conclusion */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|x360px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
 
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
 
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
 
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
 
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-17T11:01:45Z

Dk1814: /* Conclusion */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|x360px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

Two different computational methods were used to investigate the transition state as well as kinetic & thermodynamic products for pericyclic reactions. While the semi-empirical PM6 method utilises experimental data and allows for faster calculations, the Density Functional Theory based B3LYP/6-31G(d) method yields better optimization by using a higher split-valence basis set to generate molecular orbitals.
The concerted Diels-Alder reaction between butadiene and ethene was shown to proceed via a symmetrical transition state with synchronous C-C bond formation to generate cyclohexene.
For the inverse electron demand Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the endo adduct was the kinetic and thermodynamic product due to electronic (secondary orbital overlap) & steric (less steric clashes) effects.
Of the two feasible pericyclic reactions between ''o''-xylylene and sulphur dioxide, the cheletropic reaction yielded the thermodynamic product (more stable 5-membered sulfolene ring) while the kinetic product was the endo Diels-Alder adduct (possible secondary orbital overlap). The hetero-Diels-Alder reaction involving the endocyclic diene was shown to be kinetically and thermodynamically unfeasible.
As transition states are difficult to analyze in conventional experiments as they are not isolated, computational chemistry is extremely useful for modelling the progression of chemical reactions and providing valuable information about transition states.

==References==

User:Dk1814

2017-02-17T09:49:48Z

Dk1814:

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|x360px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==Conclusion==

==References==

User:Dk1814

2017-02-14T13:20:25Z

Dk1814: /* Orbitals with the same symmetry label have non-zero overlap integral */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state.
The HOMO and LUMO of the transition state are the bonding and anti-bonding molecular orbitals produced via overlap of the LUMO of butadiene and the HOMO of ethene (due to the smaller energy gap between these orbitals leading to a stronger orbital interaction). Thus, the [4+2] cycloaddition can be characterised as an inverse electron demand Diels-Alder reaction.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|x360px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:24:21Z

Dk1814: /* Exercise 1: Diels-Alder reaction between butadiene and ethene */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill opaque; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|x360px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:22:37Z

Dk1814: /* Inverse electron demand Diels-Alder cycloaddition is synchronous */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|x360px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:21:43Z

Dk1814: /* Alternate Diels-Alder reaction */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|x360px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:19:27Z

Dk1814: /* Alternate Diels-Alder reaction */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
{|style="margin: 0;"
| [[File:Dk1814otherendots.gif|thumb|240px|453.4i cm-1 vibration for endo TS]]
| [[File:Dk1814otherexots.gif|thumb|240px|482.8i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3otherendoIRC.gif|thumb|240px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3otherexoirc.gif|thumb|240px|Concerted, asynchronous cycloaddition to form exo product]]
|}
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:16:21Z

Dk1814: /* Asynchronous Diels-Alder cycloaddition */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:14:23Z

Dk1814: /* Asynchronous Diels-Alder cycloaddition */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
{|style="margin: 0;"
| [[File:Dk1814ex3exoTS.gif|thumb|180px|351.9i cm-1 vibration for exo TS]]
| [[File:Dk1814--ex3exoIRC.gif|thumb|180px|Concerted, asynchronous cycloaddition to form exo product]]
| [[File:Dk1814ex3endots.gif|thumb|180px|333.9i cm-1 vibration for endo TS]]
| [[File:Dk1814ex3endoirc.gif|thumb|180px|Concerted, asynchronous cycloaddition to form endo product]]
| [[File:Dk1814ex3chelevib.gif|thumb|180px|486.6i cm-1 vibration for cheletropic reaction TS]]
| [[File:Dk1814ex3cheleirc.gif|thumb|180px|Concerted, synchronous cheletropic reaction]]
|}
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

File:Dk1814--ex3exoIRC.gif

2017-02-09T17:13:13Z

Dk1814:

User:Dk1814

2017-02-09T17:09:06Z

Dk1814: /* Inverse electron demand Diels-Alder cycloaddition is synchronous */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:08:25Z

Dk1814: /* Orbitals with the same symmetry label have non-zero overlap integral */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" widths = 240px heights = 120px >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" widths = 240px heights = 120px>
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T17:07:24Z

Dk1814: /* Inverse electron demand Diels-Alder cycloaddition is synchronous */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" style="text-align: left;">
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines widths = 240 px heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines widths = 240 px heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

File:Dk1814ex3chelevib.gif

2017-02-09T17:05:59Z

Dk1814:

File:Dk1814ex3endoirc.gif

2017-02-09T17:05:42Z

Dk1814:

File:Dk1814ex3endots.gif

2017-02-09T17:05:34Z

Dk1814:

File:Dk1814ex3exoTS.gif

2017-02-09T17:05:07Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814ex3exoTS.gif

File:Dk1814ex3otherendoIRC.gif

2017-02-09T17:04:57Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814ex3otherendoIRC.gif

File:Dk1814otherendots.gif

2017-02-09T17:04:49Z

Dk1814:

File:Dk1814ex3otherexoirc.gif

2017-02-09T17:04:41Z

Dk1814:

File:Dk1814otherexots.gif

2017-02-09T17:04:26Z

Dk1814:

User:Dk1814

2017-02-09T16:51:38Z

Dk1814: /* Inverse electron demand Diels-Alder cycloaddition is synchronous */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" style="text-align: left;">
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{|style="margin: 0;"
| [[File:Dk1814ex2exots.gif|x200px|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|x200px|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|x200px|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T16:43:12Z

Dk1814: /* Inverse electron demand Diels-Alder cycloaddition is synchronous */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" style="text-align: left;">
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
{| class="wikitable"
| style = "colour:white";
| [[File:Dk1814ex2exots.gif|thumb|528.9i cm-1 vibration for exo TS corresponding to reaction]]
| [[File:Dk1814ex2exoirc.gif|thumb|Concerted, synchronous cycloaddition to form exo product]]
| [[File:Dk1814ex2endots.gif|thumb|520.9i cm-1 vibration for endo TS corresponding to reaction]]
| [[File:Dk1814ex2endoirc.gif|thumb|Concerted, synchronous cycloaddition to form endo product]]
|}
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

File:Dk1814ex3cheleirc.gif

2017-02-09T16:26:58Z

Dk1814:

User:Dk1814

2017-02-09T16:24:51Z

Dk1814: /* Inverse electron demand Diels-Alder cycloaddition is synchronous */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" style="text-align: left;">
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
<gallery mode=nolines widths = 220px>
File:Dk1814ex2exots.gif|528.9i cm-1 vibration for exo TS corresponding to reaction
File:Dk1814ex2exoirc.gif|Concerted, synchronous cycloaddition to form exo product
File:Dk1814ex2endots.gif|520.9i cm-1 vibration for endo TS corresponding to reaction
File:Dk1814ex2endoirc.gif|Concerted, synchronous cycloaddition to form endo product
</gallery>
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.

===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

File:Dk1814ex2exots.gif

2017-02-09T16:24:14Z

Dk1814:

File:Dk1814ex2exoirc.gif

2017-02-09T16:24:06Z

Dk1814:

File:Dk1814ex2endots.gif

2017-02-09T16:23:58Z

Dk1814:

File:Dk1814ex2endoirc.gif

2017-02-09T16:23:45Z

Dk1814:

File:Dk1814-endoIRC.gif

2017-02-09T16:14:21Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-endoIRC.gif

File:Dk1814-exoTS.gif

2017-02-09T16:11:36Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-exoTS.gif

File:Dk1814-endoIRC.gif

2017-02-09T16:11:27Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-endoIRC.gif

File:Dk1814-endoTS.gif

2017-02-09T16:11:18Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-endoTS.gif

File:Dk1814-exoIRC.gif

2017-02-09T16:11:04Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-exoIRC.gif

File:Dk1814-ex1irc.gif

2017-02-09T16:03:11Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-ex1irc.gif

File:Dk1814-ex1vib.gif

2017-02-09T16:00:48Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-ex1vib.gif

File:Dk1814-ex1vib.gif

2017-02-09T15:57:23Z

Dk1814: Dk1814 uploaded a new version of File:Dk1814-ex1vib.gif

User:Dk1814

2017-02-09T15:54:03Z

Dk1814: /* Exercise 1: Diels-Alder reaction between butadiene and ethene */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" style="text-align: left;">
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
<gallery mode=nolines widths = 220px>
File:Dk1814-exoTS.gif|528.9i cm-1 vibration for exo TS corresponding to reaction
File:Dk1814-exoIRC.gif|Concerted, synchronous cycloaddition to form exo product
File:Dk1814-endoTS.gif|520.9i cm-1 vibration for endo TS corresponding to reaction
File:Dk1814-endoIRC.gif|Concerted, synchronous cycloaddition to form endo product
</gallery>
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.
===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T15:52:09Z

Dk1814: /* Orbitals with the same symmetry label have non-zero overlap integral */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Corresponding MOs for reactants" >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Corresponding MOs for transition state" style="text-align: left;">
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
<gallery mode=nolines widths = 220px>
File:Dk1814-exoTS.gif|528.9i cm-1 vibration for exo TS corresponding to reaction
File:Dk1814-exoIRC.gif|Concerted, synchronous cycloaddition to form exo product
File:Dk1814-endoTS.gif|520.9i cm-1 vibration for endo TS corresponding to reaction
File:Dk1814-endoIRC.gif|Concerted, synchronous cycloaddition to form endo product
</gallery>
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.
===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==

User:Dk1814

2017-02-09T15:36:59Z

Dk1814: /* Exercise 1: Diels-Alder reaction between butadiene and ethene */

== Introduction ==

[[File:dk1814-potes.png|x250px|left|thumb|PES for A-B-C system<ref>Wales, David., ''Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses.'', '''2003''', Cambridge University Press</ref>]] [[File:dk1814rc.png|x250px|right]]A potential energy surface (PES) plots the potential energy of a chemical system (such as the A-B-C system) as a function of internuclear separation for atoms comprising the system. It takes into account interatomic interactions such as Van Der Waals forces using mathematical functions such as the Lennard-Jones (12-6) potential.
A '''minimum''' on the potential energy surface has a gradient (first derivative) of zero and a positive second derivative.
[[File:dk1814min.PNG|60px|none]]
A series of minima form a minimum energy path (red bold line in PES) or reaction pathway which allow for chemical reactions to occur.
The '''transition state''' (TS) is the state with maximum energy along a minimum energy pathway. While the gradient at the transition state is also zero, the second derivative with respect to reaction coordinates is negative.
[[File:dk1814secderiv.PNG|70px|none]] 

===Vibrational analysis to confirm TS structure===
[[File:dk1814pot.PNG|x300px|right]]
The semi-empirical PM6 & Density Functional Theory-based B3LYP methods were used to compute optimized structures of chemical species. A frequency calculation for an optimised structure generate the normal vibration modes (3N-5 for linear molecules, 3N-6 for non-linear molecules where N is the total number of atoms). Molecular vibrations can be modelled using a Morse Potential which takes into account interatomic attractions/repulsions between adjacent nuclei. For small displacements about the equilibrium distance between two nuclei, the harmonic oscillator approximation can be used:[[File:dk1814ho.PNG|x100px]]where k is a force constant.

A Taylor expansion about the equilibrium internuclear separation (bottom of potential energy well) yields an expression for the force constant. 
[[File:dk1814-taylorexp.PNG|280px|none]]
[[File:dk1814-forceconstant.PNG|100px|none]]
[[File:dk1814-vibfreq.PNG|85px|none]]
A transition state has a negative second derivative along the reaction pathway (negative force constant). Since the frequency of vibration is proportional to the square root of the force constant, a vibration corresponding to the transition state has an imaginary frequency (negative frequency in GaussView).
 

== Exercise 1: Diels-Alder reaction between butadiene and ethene ==

[[File:Dk1814-ex1.png|500px|left]]
 

The Diels-Alder reaction is a [4+2] cycloaddition between a s-cis diene and a dienophile which proceeds via a transition state with 6π electrons. Using the frontier orbitals or the highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO) of the diene and dienophile, the reaction occurs via a suprafacial-suprafacial interaction of orbitals with the correct symmetry.

The thermally allowed Diels-Alder reaction proceeds in 2 ways:
# Overlap of the HOMO of diene with the LUMO of dienophile (Normal electron demand)
# Overlap of the LUMO of diene with the HOMO of dienophile (Inverse electron demand)
{| class="wikitable"
|+ Molecular Orbitals of butadiene and ethene
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | Butadiene
! style="background: #000000; color: white;" | Ethene
|-
! style="background: #000000; color: white;"| HOMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene HOMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 11; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene HOMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 6; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|-
! style="background: #000000; color: white;"| LUMO
|style="text-align: center;"| <jmol><jmolApplet>
<title>Butadiene LUMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814BUTADIENEMO.LOG</uploadedFileContents>
<script>frame 6;mo 12; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate z 75; rotate x 180</script>
</jmolApplet></jmol>
|style="text-align: center;"| <jmol><jmolApplet>
<title>Ethene LUMO</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Dk1814-ETHENE.LOG</uploadedFileContents>
<script>frame 6;mo 7; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02; rotate x 90; rotate y 90</script>
</jmolApplet></jmol>
|}

===Orbitals with the same symmetry label have non-zero overlap integral===
[[File:Dk1814-modiagram.png|x400px|thumb|left|Molecular Orbital diagram for formation of transition state]]

Only orbitals with the same symmetry (symmetric/symmetric or asymmetric/asymmetric) have a non-zero orbital overlap to allow for a reaction to occur.
Orbitals with different symmetry have zero orbital overlap; reaction is forbidden.
Hence, the interactions between HOMO of butadiene with LUMO of ethene as well as LUMO of butadiene with HOMO of ethene generate 4 molecular orbitals for the transition state. As butadiene is not especially electron-rich and ethene is not especially electron-poor, aspects of both normal & inverse electron demand are observed. The computed MOs corresponding to the MOs in the diagram make up the frontier orbitals for the transition state.
<gallery mode=nolines caption="Computed MOs for reactants" >
File:Dk1814-butadienehomo.PNG|HOMO of butadiene.
File:Dk1814-butadienelumo.PNG|LUMO of butadiene.
File:Dk1814-ethenehomo.PNG|HOMO of ethene.
File:Dk1814-ethenelumo.PNG|LUMO of ethene.
</gallery>
<gallery mode=nolines caption="Computed MOs for transition state" style="text-align: left;">
File:Dk1814-mo16.PNG|HOMO-1; MO1
File:Dk1814-mo17.PNG|HOMO; MO2
File:Dk1814-mo18.PNG|LUMO; MO3
File:Dk1814-mo19.PNG|LUMO+1; MO4
</gallery>
 
[[File:Dk1814-ccgraph.PNG|x280px|thumb|right|Changes in C-C internuclear distances as reaction progresses]]
{| class="wikitable"
|+ C-C Internuclear Distances (Å)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | C1-C2
! style="background: #000000; color: white;" | C2-C3
! style="background: #000000; color: white;" | C1-C6
! style="background: #000000; color: white;" | C5-C6
! style="background: #000000; color: white;" | C3-C4
! style="background: #000000; color: white;" | C4-C5
|-
! style="background: #000000; color: white;"| Ethene + Butadiene
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 1.39
|style="text-align: center;"| 2.08
|style="text-align: center;"| 2.08
|style="text-align: center;"| 1.39
|-
! style="background: #000000; color: white;"| Cyclohexene
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}
Van Der Waals radius of carbon atom<ref>1 A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.</ref>: 1.70 Å
 
Typical sp3-sp3 C-C bond length: 1.54 Å
 
Typical sp2-sp2 C=C bond length: 1.34 Å

As the reaction progress, 3 C=C bonds are broken while 2 C-C bonds & 1 new C=C bond forms. The symmetric transition state has 4 carbon-carbon bonds with the same lengths (1.39 Å) corresponding to the partially formed/broken C=C bonds. This bond has a bond order between 1 & 2 and hence an intermediate bond length between a single bond and a double bond.
The distance between the reacting termini carbon atoms in butadiene & ethene (2.08 Å) is significantly smaller than twice the Van Der Waals radius of a carbon atom (3.40 Å), indicating a bonding interaction and the 2 C-C bonds eventually form.
 
 
[[File:Dk1814-ex1vib.gif|left|300x200px|thumb|Vibration at 948.6i cm-1]][[File:Dk1814-ex1irc.gif|right|300x200px|thumb|Synchronous & concerted cycloaddition]]
 
The vibration of the transition state which corresponds to the Diels Alder reaction shows that the formation of the 2 C-C bonds is synchronous and concerted.
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814BUTADIENE.LOG Butadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENE.LOG Ethene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ETHENEBUTADIENE1.LOG TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814CYCLOHEXENE.LOG Cyclohexene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex1IRC.LOG IRC]]
 

== Exercise 2: Diels-Alder reaction between cyclohexadiene and 1,3-dioxole ==
[[File:Dk1814-ex2.png|400px|left]]
 

The Diels-Alder reaction between cyclohexadiene & 1,3-dioxole results in the formation of exo & endo diastereoisomers via different transition states.
 
=== Inverse electron demand Diels-Alder cycloaddition is synchronous===
1,3-dioxole is a relatively electron-rich dienophile due to the donation of lone pairs on the oxygen atoms into the π/π* molecular orbitals of the alkene. This raises the energy of both the HOMO and LUMO of the dienophile. The HOMO lies closer in energy to the LUMO of cyclohexadiene and the Diels-Alder reaction is driven by an inverse electron demand.
 
[[File:Dk1814-ex2modiagram.png|x400px|thumb|left|MO diagram for an inverse electron demand Diels-Alder reaction]]
<gallery style="text-align:left" mode=nolines heights= 150px caption="Computed MOs for exo TS" >
File:Dk1814-exomo40.PNG|HOMO-1
File:Dk1814-exomo41.PNG|HOMO
File:Dk1814-exomo42.PNG|LUMO
File:Dk1814-exomo43.PNG|LUMO+1
</gallery>
<gallery style="text-align:left" mode=nolines heights = 150px caption="Computed MOs for endo TS" >
File:Dk1814-endomo40.PNG|HOMO-1
File:Dk1814-endomo41-sec.PNG|HOMO
File:Dk1814-endomo42.PNG|LUMO
File:Dk1814-endomo43.PNG|LUMO+1
</gallery>
 
<gallery mode=nolines widths = 220px>
File:Dk1814-exoTS.gif|528.9i cm-1 vibration for exo TS corresponding to reaction
File:Dk1814-exoIRC.gif|Concerted, synchronous cycloaddition to form exo product
File:Dk1814-endoTS.gif|520.9i cm-1 vibration for endo TS corresponding to reaction
File:Dk1814-endoIRC.gif|Concerted, synchronous cycloaddition to form endo product
</gallery>
The concerted Diels-Alder reaction between cyclohexadiene and 1,3-dioxole involves the synchronous formation of 2 C-C bonds to generate a new 6-membered ring in the product.
===Secondary orbital interactions stabilise the endo transition state===
By comparing the HOMO of the exo and endo transition states, there is an additional interaction between the O2p orbitals and the LUMO of the diene. Both transition states suffer from similar steric repulsions - Van der Waals strain due to the distance between neighboring C & O atoms (~ 3 Å) being less than the sum of their Van der Waals radii; Van der Waals radius of Oxygen is 1.52 Å[2], sum of radii = 3.22 Å. Hence, the secondary orbital interaction stabilises the endo TS and lowers the activation energy for formation of the endo product.
<gallery mode=nolines widths = 240px>
File:Dk1814-ex2endots.PNG|endo TS
File:Dk1814-endomo41-sec.PNG|endo TS HOMO
File:Dk1814-ex2endotssteric.PNG|Van der Waals repulsion between C & O
File:Dk1814-ex2exots.PNG|exo TS
File:Dk1814-exomo41.PNG|exo TS HOMO
File:Dk1814-ex2exotssteric.PNG|Van der Waals repulsion between C & O
</gallery>
[[File:Dk1814-ex2energydiagram.png|right|300px|thumb|The endo Diels-Alder adduct is both the kinetic and thermodynamic product.]]
{| class="wikitable"
|+ Free Energies (kJ mol-1)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| -1313780.63
|style="text-align: center;"| -1313780.63
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| -1313614.33
|style="text-align: center;"| -1313622.16
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| -1313845.75
|style="text-align: center;"| -1313849.37
|}
The endo product is kinetically favored (endo TS 7.83 kJ mol-1 lower in energy than exo TS) due to stabilising secondary orbital interactions between oxygens and the diene. It is thermodynamically favored due to less destabilising steric clashes; the exo product is relatively congested on its top face and suffers from steric repulsions between the ethylene bridge and the dioxane ring.
<gallery mode=nolines widths = 400px>
File:Dk1814-exoproduct.PNG|Exo product suffers from steric congestion on its top face
File:Dk1814-endoproduct.PNG|Endo product has less steric clashes
</gallery>
 

===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2DIENEB3LYP.LOG Cyclohexadiene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814DIOXOLEB3LYP.LOG 1,3-dioxole]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOTSB3LYP.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOPRODUCTB3LYP.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOTSB3LYP.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOPRODUCTB3LYP.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-EX2EXOIRC.LOG Exo Diels-Alder IRC]]

== Exercise 3: Reactions between o-xylylene and sulphur dioxide: Hetero Diels-Alder vs Cheletropic ==
[[File:Ts tutorial xylylene so2 scheme.png|600px|none]]
 
=== Asynchronous Diels-Alder cycloaddition ===
<gallery mode=nolines widths = 220px>
File:Dk1814ex3exoTS.gif|351.9i cm-1 vibration for exo TS
File:Dk1814ex3exoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814-ex3endoTS.gif|333.9i cm-1 vibration for endo TS
File:Dk1814-ex3endoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
File:Dk1814-ex3cheleTS.gif|486.6i cm-1 vibration for cheletropic reaction TS
File:Dk1814-ex3cheleirc.gif|Concerted, synchronous cheletropic reaction
</gallery>
The Diels-Alder reaction between ortho-xylylene and SO2 involves the asynchronous formation of C-O and C-S bonds to generate a 6-membered ring. The C-O bond forms first, followed by the C-S bond. The cheletropic reaction involves synchronous formation of 2 C-S bonds to generate a 5-membered ring.
 
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
! style="background: #000000; color: white;" | cheletropic
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 241.75
|style="text-align: center;"| 237.77
|style="text-align: center;"| 260.09
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 57.92
|style="text-align: center;"| 56.32
|style="text-align: center;"| -0.01
|} 
[[File:Dk1814-ex3energydiagram.png|x400px|right|thumb|Kinetic product: endo Diels-Alder adduct. Thermodynamic product: Cheletropic product.]]
The endo product is kinetically and thermodynamically favored over the exo product. The lower activation energy is likely due to additional interactions between O2p orbitals and the diene HOMO stabilising the endo transition state. While both products are similar in steric requirement, the endo product is likely to be stabilized by through space bonding interactions involving the O2p orbitals.

<gallery mode=nolines widths = 240px>
File:Dk1814endots.PNG|Endo TS
File:Dk1814endohomo.PNG|HOMO - Secondary orbital interaction with O2p
File:Dk1814exots.PNG|Exo TS
File:Dk1814exohomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
<gallery mode=nolines widths = 240px>
File:Dk1814endoproduct.PNG|Endo product
File:Dk1814endoproducthomo.PNG|HOMO - Additional orbital overlap with O2p
File:Dk1814exoproduct.PNG|Exo product
File:Dk1814exoproducthomo.PNG|HOMO - No interaction with exo oxygen
</gallery>
The cheletropic product is the most thermodynamically stable. Due to the larger S atom (VDW radius of 1.8 Å compared to 1.7 Å for carbon), the 5-membered sulfolane heterocycle is likely to suffer from less ring strain than the 6-membered heterocycles in the Diels-Alder products. However, it forms the slowest (highest activation energy); this is likely due to destabilizing repulsions between the oxygen lone pairs as the oxygen atoms are closer in proximity in the transition state (O-S-O angle decreases from 120 o to ~109 o as the reaction progresses).

=== Instability of ''o''-xylylene ===
[[File:dk1814xylylene.png|none|400px]]
ortho-xylylene is highly unstable and undergoes electrocyclic ring closure to generate the aromatic product, benzocyclobutene<ref>Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.</ref>.

Both reaction pathways with sulphur dioxide generate an aromatic product with a phenyl group. As the reaction progresses, 6π electrons become delocalised in the 6-membered ring and all 6 C-C bonds are equivalent (bond lengths of 1.4 Å; partial double bond character).
 
=== Alternate Diels-Alder reaction ===
[[File:dk1814otherda.png|none|400px]]
ortho-xylylene has an endocyclic diene component which can undergo a Diels-Alder reaction with sulphur dioxide.
[[File:Dk1814-ex3otherenergydiagram.png|300px|right|thumb|Diels-Alder reaction at this diene is both kinetically and thermodynamically unfavourable.]]
{| class="wikitable"
|+ Free Energies (kJ/ mol)
|-
! style="background: #ffffff; color: white;" |
! style="background: #000000; color: white;" | exo-
! style="background: #000000; color: white;" | endo-
|-
! style="background: #000000; color: white;"| Reactants
|style="text-align: center;"| 154.37
|style="text-align: center;"| 154.37
|-
! style="background: #000000; color: white;"| Transition State
|style="text-align: center;"| 275.82
|style="text-align: center;"| 267.99
|-
! style="background: #000000; color: white;"| Product
|style="text-align: center;"| 176.71
|style="text-align: center;"| 172.26
|}
<gallery mode=nolines widths = 220px>
File:Dk1814ex3otherexoTS.gif|482.8i cm-1 vibration for exo TS
File:Dk1814ex3otherexoIRC.gif|Concerted, asynchronous cycloaddition to form exo product
File:Dk1814ex3otherendoTS.gif|453.4i cm-1 vibration for endo TS
File:Dk1814ex3otherendoIRC.gif|Concerted, asynchronous cycloaddition to form endo product
</gallery>
A Diels-Alder reaction at the second cis-butadiene is both kinetically & thermodynamically unfavourable due to the loss of conjugation as the reaction progresses (exocyclic C=Cs no longer planar with partially broken endocyclic C=Cs in the transition state) and lack of aromaticity in the product (localised C=C in 6-membered ring leads to a higher energy product relative to reactants).
 
 
===Calculations===
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814ex3XYLYLENE.LOG o-xylylene]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3DIENOPHILE.LOG SO2]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOTS.LOG Endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOPRODUCT.LOG Endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOTS.LOG Exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOPRODUCT.LOG Exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELETS.LOG Cheletropic TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEPRODUCT.LOG Cheletropic product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOTS.LOG Other exo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOPRODUCT.LOG Other exo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOTS.LOG Other endo TS]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOPRODUCT.LOG Other endo product]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3ENDOIRC.LOG Endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3EXOIRC.LOG Exo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3CHELEIRC.LOG Cheletropic IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHERENDOIRC.LOG Other endo Diels-Alder IRC]]
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Dk1814-ex3OTHEREXOIRC.LOG Other exo Diels-Alder IRC]]

==References==