File:IRC exo extension dp2615.PNG

2017-11-22T09:22:21Z

Dp2615:

File:IRC cheletropic dp2615.PNG

2017-11-22T09:21:39Z

Dp2615:

File:IRC endo dp2615.PNG

2017-11-22T09:21:22Z

Dp2615:

File:IRC exo dp2615.PNG

2017-11-22T09:20:04Z

Dp2615:

2017-11-21T14:49:11Z

Dp2615:

File:ENDO FINAL IRC dp2615.LOG

2017-11-21T14:43:19Z

Dp2615:

Rep:Mod:dp2615

2017-11-21T14:41:53Z

Dp2615: /* Thermochemistry of Diels-Alder and Chelatropic reactions */

TRANSITION STRUCTURES AND REACTIVITY

== Introduction ==

===Linking potential energy, transition state and reaction path===

Chemical reactions can be explored by examination of relative energies of reactants, transition states and products. The point of focus during a chemical reaction is the transition state as it offers information on the energy barrier of the reaction which can lead to other crucial conclusions about reaction dynamics.

The potential energy of a chemical reaction is a function of the internuclear distances between all the atoms. This function is hard to calculate and can be simplified to fewer and specific internculear distances as a simplification. On a potential energy surface the transition state is considered as the saddle point. All reactive pathways are calculated to go through a crossing, sometimes called "mountain pass", i.e. the transition state.

Mathematically speaking, the height of this saddle point corresponds to the maximum energy point on the minimum energy reaction path. The gradient and curvature of a saddle point are zero, meaning both the first and second derivatives are zero. It can be also identified as the lowest local maximum of the energy plot. https://arxiv.org/pdf/1405.4604.pdf

The minimum energy reaction path goes straight up through the transition state and then falls down to the products. In this non-ideal reality many reactions go through the region around the transition state and therefore do not cross directly on the saddle point. This can be rationalised by assuming that more kinetic energy than precisely the activation energy has been given to the molecules resulting in a slightly higher energy reaction path.

It is possible to confirm from a frequency calculation that a structure is at the transition state, and so at the saddle point, because the first frequency will result as negative while all the other ones will be positive. This is because at a transition state there is one vibration toward the products which lowers the energy rather than increasing it which gives a negative frequency.

== Exercise 1 ==

===Comparing bond lengths of a Diels-Alder reaction===

A Diels-Alder reaction is a [4+2]-cycloaddition which proceeds via a cyclic transition state to create two new sigma bonds.

[[File:Reaction 1 dp2615.png|thumb|center|Diels-Alder reaction between butadiene and ethene.]]

In this concerted pericyclic reaction, the formation of the two sigma bonds is synchronous as illustrated below where the vibration of the transition state corresponding to the reaction pathway is shown:

[[File:Vibration_ts_dp2615.gif|thumb|center|Diels-Alder reaction between butadiene and ethene.]]

Literature (http://pubs.rsc.org/-/content/articlepdf/1987/p2/p298700000s1) reports by means of X-ray and neutron diffraction the following typical bond lengths (Å):

{| class="wikitable" border="1"
|+ C-C bond lengths
! Type of bond!! Bond length (Å)
|-
| C sp3- C sp3|| 1.51
|-
| C sp3- C sp2|| 1.50
|-
| C sp2- C sp2|| 1.46
|}

The Van der Waals radius of C atom is reported (http://pubs.acs.org/doi/pdf/10.1021/j100785a001) as : 1.70

The C-C bond lengths of reactants(Å), transition state and product are listed below to show their progression throughout the reaction:

{| class="wikitable" border="1"
|+ C-C bond lengths of reactants
! Molecule!! Bond length (Å)
|-
| Butadiene|| 1.34 (double bonds); 1.47 (single bond)
|-
| Ethene|| 1.36
|}

{| class="wikitable" border="1"
|+ C-C bond lengths at transition state
! Molecule!! length (Å)
|-
| Butadiene|| 1.36 (end bonds); 1.44 (central bond)
|-
| Ethene|| 1.36
|-
| New sigma bonds|| 2.11
|}

{| class="wikitable" border="1"
|+ C-C bond lengths of product
! New sigma bond!! length (Å)
|-
| Single bonds|| 1.54
|-
| Double bond|| 1.34
|}

The most significant change of bond length between the reactants and transition state is that of the butadiene molecule. The bond compresses from 1.47 Å to 1.44 Å, thus resulting in a change of the angle between the carbons from 125° to 120° as the molecule adapts its conformation to align the orbitals for the interaction with ethene at the transition state which will lead to the formation of cyclohexene. The end bonds of butadiene present no change in length. Ethene shows no change of conformation between reactant and transition state.

The product shows an elongation of single bonds to 1.54 Å, but the same double bond length as the original butadiene molecule.

It is clear from all the bond lengths observed in these molecules that a covalent C-C bond is not the sum of the Van der Waals radii of the two carbon atoms (2.4 Å), but instead a length produced from a strong interaction which results in a closer approach of the two atoms to each other.

===Molecular Orbital Theory===

Molecular Orbital Theory allows us to represent chemical bonds by combining the orbitals of the reactants to make new complex molecular orbitals (MOs). Only fragment orbitals of the same symmetry can interact to form a bonding/antibonding pair. The strong interaction that is usually present between a HOMO (Highest Occupied MO) and LUMO (Lowest Unoccupied MO) pair results in stabilised MOs. Both the atomic orbitals must have the same symmetry label in order to form new orbitals. In the case of a Diels-Alder reaction, this pair of orbitals must either be symmetric or anti-symmetric for the reaction to be allowed. Any other combination of symmetry would result in a forbidden reaction as the overall stabilisation is not more than that of the starting orbitals.

[[File:MO_1_dp2615.png|500x500px|thumb|center|MO diagram of this Diels-Alder reaction.]]

MOs can be defined as many electron wavefunctions governed by their variant of the Schrödinger equation. This equation has a component Sab called the orbital overlap integral which measures the extent to which the two atomic orbitals overlap. This integral is zero for interactions between orbitals with different symmetry, and not zero for a symmetric—anti-symmetric interaction. This agrees with the symmetry requirement of MO theory.

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO ethene dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO butadiene dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO1 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO2 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO3 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO4 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

LOG FILES

[[:File:ETHYLENE MOS dp2615.LOG]]

[[:File:BUTADIENE MOS dp2615.LOG]]

[[:File:TS WITH MOS FOR JMOL dp2615.LOG]]

[[:File:TS FREQ dp2615.LOG]]

[[:File:IRC dp2615.LOG]]

[[:File:PRODUCT OPT 3 dp2615.LOG]]

== Exercise 2 ==

===Molecular Orbitals in a Diels-Alder reaction===

[[File:Reaction 2 dp2615.png|thumb|center|Diels-ALder reaction between cyclohexadiene and 1,3-dioxole.]]

A Diels-Alder reaction between an electron deficient diene and an electron rich dienophile is an inverse electron demand pericyclic reaction. In this case, the diene is not completely electron deficient as there is a small extent of positive inductive effect from the carbon group attached to the diene. However, the dienophile is under strong effect of two ether groups which are highly electron donating therefore pushing this reaction towards an inverse electron demand interaction rather than a normal electron demand reaction. This is proven by the observed symmetry of the MOs of the two reagents at the transition state where both the HOMO and LUMO appear to be symmetric:

[[File:MO_reac2_dp2615.png|500x500px|thumb|center|MO diagram of this Diels-Alder reaction.]]

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO_dioxole_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO_cyclohexadiene_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO1_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO2_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO3_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO4_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO_dioxole_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO_cyclohexadiene_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO1_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO2_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO3_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO4_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

===Thermochemistry===

Below is a table showing the sum of the electronic and thermal free energies of both the endo and exo reaction pathways calculated using B3YLP calculations:

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| cyclohexadiene|| -233.321033||-612584.418806
|-
| 1,3-dioxole||-267.068132||-701187.43398
|-
| sum of reactants|| -500.389165||-1313771.85279
|}

{| class="wikitable" border="1"
|+ ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| -500.332151|| -1313622.16252
|-
| product|| -500.418691|| -1313849.3733
|}

{| class="wikitable" border="1"
|+ EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| -500.329165 || -1313614.32277
|-
| product|| -500.417322|| -1313845.77899
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct
|-
| in hartrees ||-0.057014|| -149.6902684
|-
| in kJ/mol ||-0.06|| -157.53
|}

Is it deduced from these energies that the thermodynamically favourable reaction path is the one that leads to the endo product, whereas the kinetically favourable path is the one leading to the exo product. The difference in energies between the to energy barriers is 2.986 hartrees, and the difference in energy between the two products is almost insignificant.

The thermodynamically favourbale product is the endo product which literature says requires a higher activation energy for its transition state, but in this case carries a lower more negative kinetic energy barrier. However, it has only a 0.001369 hartrees energetic difference with the exo product, so could be considered a non-significant diversion form typical Diels-Alder behaviour.

This goes to show that both reaction pathways are somewhat favourable and only slightly differ for thermodynamic and kinetic favourability.

Literature reports the endo product of this Diels-Alder reaction as being the kinetic product, thus partly agreeing with these findings and so the predicted pathways partly validates these results.

The diversion of stereosectivity can be rationalised by considering the secondary orbital overlap of the p orbitals of the oxygen atoms with the π orbitals of the diene which stabilises the transition state of the endo adduct, in this case enough to pull it down to a kinetic barrier as for the case of cyclopentadiene and maleic anhydride. This secondary orbital overlap is shown below:

"Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy (Hint: in GaussView, set the isovalue to 0.01. In Jmol, change the mo cutoff to 0.01)?"

LOG FILES

[[:File:DIOXOLE OPT B3YLP dp2615.LOG]]

[[:File:CYCLOHEXADIENE OPT B3YLP dp2615.LOG]]

ENDO

[[:File:ENDO PRODUCT B3YLP OPT dp2615.LOG]]

[[:File:ENDO PM6 IRC OF PM6 dp2615.LOG]]

[[:File:ENDO TS B3LYP dp2615.LOG]]

[[:File:ENDO TS PM6 dp2615.LOG]]

[[:File:ENDO OPT PM6 2 dp2615.LOG]]

EXO

[[:File:EXO PRODUCT OPT B3YLP dp2615.LOG]]

[[:File:EXO FROM TS PM6 IRC dp2615.LOG]]

[[:File:EXO TRANSITION STATE B3YLP dp2615.LOG]]

[[:File:EXO TRANSITION STATE PM6 dp2615.LOG]]

[[:File:EXO OPT PM6 dp2615.LOG]]

== Exercise 3 ==

=== Background chemistry===

A Diels-Alder reaction is a [4+2]-cycloaddition, whereas a cheletropic reaction is a pericyclic reaction considered as a subclass of cycloadditions in which a reorganisation of σ and π bonds occurs at the same atom in the cyclic array of atoms at the transition state.
In many cases, the cheletropic five-membered ring product is the thermodynamic product while the Diels-Alder adduct is the kinetically favoured one. An example is the addition of SO2 to 1,2-dimethylidenecyclohexane. In the case presented here, however, the conjugation of the hexane ring iplays an important part in the lowering of the energy of both the Diels-Alder adducts by aromatisation in comparison to the cheletropic product.

[[File:Reaction 3 dp2615.png|400x400px|thumb|center|Diels-Alder and Cheletropic o-xylylene-SO2 cycloaddition.]]

===Thermochemistry of Diels-Alder and Chelatropic reactions===

Below is a table showing the sum of the electronic and thermal free energies of both the endo, exo and cheletropic reaction pathways calculated using PM6 optimisations:

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| o-xylylene|| 0.178764||469.344918
|-
| SO2|| -0.119268||-313.1381579
|-
| sum of reactants|| 0.059496||156.20676
|}

{| class="wikitable" border="1"
|+ Diels-Alder ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.090558|| 237.760047
|-
| product|| 0.021711|| 57.0022348
|}

{| class="wikitable" border="1"
|+ Diels-Alder EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.092078|| 241.750807
|-
| product|| 0.021455 || 56.3301068
|}

{| class="wikitable" border="1"
|+ Cheletropic adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.099054||260.066297
|-
| product|| 0.063328||166.267677
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct!!chelatropic adduct
|-
| in hartrees || 0.031062|| 0.032582|| 0.039558
|-
| in kJ/mol || 81.5532872|| 85.5440475|| 103.859537
|}

{| class="wikitable" border="1"
|+ Reaction energies
! !!endo adduct!! exo adduct!!chelatropic adduct
|-
| in hartrees || -0.037785|| -0.038041|| 0.003832
|-
| in kJ/mol || -99.20452506|| 99.87665311|| 10.0609168
|}

Is it deduced from these energies that the thermodynamically favourable reaction path is the one that leads to the exo product as it has a larger reaction energy requirement, whereas the kinetically favourable path is the one leading to the endo product with a smaller energy barrier. The endo product also shows a higher product energy proving it is the kinetic product.

The cheletropic product has a higher energy and a higher transition state energy than both the Diels-Alder adducts. It has negative reaction energy, meaning it is an endothermic reaction and requires an input of energy for its completion unlike the exothermic Diels-Alder reactions.

[[File:Reaction_profile_final_2_dp2615.png|500x500px|thumb|center|Reaction profile of Diels-Alder and Cheletropic reactions.]]

This reaction profile shows the relative enrgies of the Diels-Alder and cheletropic cycloadditions. The reactant energy level has been set to 0 as the molecules are being considered at infinite separation, and the energy barriers for the transition states as well as the energies of the products are reported to demonstrate thermodynamic and kinetic favourability of these reactions.

"Include a .gif file in the wiki of these IRCs.

Looking at the IRCs of the Diels-Alder reactions it can be observed that the double bonds of the six-membered ring of o-xylylene delocalise across the entire ring during the course of the reaction and then go to the make the final aromatic product.

LOG FILES:

[[:File:OPT OF SO2 dp2615.LOG]]

[[:File:STARTING MATERIAL OPT dp2615.LOG]]

[[:File:OPTIMISATION OF PRODUCT dp2615.LOG]]

EXO

[[:File:OPTIMISATION PRE-TS 2 dp2615.LOG]]

[[:File:EXO TS PM6 6 dp2615.LOG]]

[[:File:EXO FROM TS PM6 6 IRC dp2615.LOG]]

[[:File:EXO PRODUCT OPT dp2615.LOG]]

ENDO

[[:File:ENDO OPTIMISATION PRE TS dp2615.LOG]]

[[:File:ENDO TRANS STATE dp2615.LOG]]

CHELETROPIC

[[:File:OPTIMISATION PRODUCT dp2615.LOG]]

[[:File:EXO OPTIMISATION PRE-TS dp2615.LOG]]

[[:File:EXO TRANSITION STATE dp2615.LOG]]

[[:File:EXO IRC dp2615.LOG]]

===Thermochemistry of the secondary Diels-Alder reactions===

o-xylylene contains a second cis-butadiene fragment within the hexadiene ring which can undergo Diels-Alder reactions. Below is a table showing the sum of the electronic and thermal free energies of both the endo and exo reaction pathways calculated using PM6 optimisations:

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. If you have time, prove that the endo and exo Diels-Alder reactions are very thermodynamically and kinetically unfavourable at this site."

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| o-xylylene|| 0.178764|| 469.344918
|-
| SO2|| -0.119268|| -313.1381579
|-
| sum of reactants|| 0.059496|| 156.20676
|}

{| class="wikitable" border="1"
|+ Diels-Alder ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.102070|| 267.984805
|-
| product|| 0.065610|| 172.259068
|}

{| class="wikitable" border="1"
|+ Diels-Alder EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.105054|| 275.819298
|-
| product|| 0.067304|| 176.706665
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct
|-
| in hartrees || 0.042574|| 0.045558
|-
| in kJ/mol || 111.778046||119.612538
|}

{| class="wikitable" border="1"
|+ Reaction energies
! !!endo adduct!! exo adduct
|-
| in hartrees || 0.006114||0.007808
|-
| in kJ/mol || 16.0523082|| 20.4999056
|}

Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.

From these energies it can be deduced that the endo adduct is both the thermodynamic and kinetic product as it holds a lower reaction energy barrier but also a lower product energy. However, this reaction is extremely unfavourbale when comparing these energies to the lower ones of the Diels-Alder reactions on the external diene. Is it thermodynamically and kinetically unfavourbale because the energy barrier is extremely high and the final products' energies are higher than the reactants making this an endothermic process.

LOG FILES:

EXO

[[:File:EXO EXTENSION PRODUCT OPT dp2615.LOG]]

[[:File:EXO IRC EXTENSION dp2615.LOG]]

[[:File:EXO TS EXTENSION dp2615.LOG]]

[[:File:EXO OPTIMISATION EXTENSION dp2615.LOG]]

<nowiki> </nowiki>ENDO

[[:File:ENDO EXTENSION PRODUCT OPT dp2615.LOG]]

[[:File:ENDO IRC EXTENSION dp2615.LOG]]

[[:File:ENDO TS EXTENSION dp2615.LOG]]

[[:File:ENDO OPT EXTENSION dp2615.LOG]]

== References ==

Rep:Mod:dp2615

2017-11-21T14:39:38Z

2017-11-21T14:18:05Z

Dp2615: /* Thermochemistry of the secondary Diels-Alder reactions */

TRANSITION STRUCTURES AND REACTIVITY

== Introduction ==

===Linking potential energy, transition state and reaction path===

Chemical reactions can be explored by examination of relative energies of reactants, transition states and products. The point of focus during a chemical reaction is the transition state as it offers information on the energy barrier of the reaction which can lead to other crucial conclusions about reaction dynamics.

The potential energy of a chemical reaction is a function of the internuclear distances between all the atoms. This function is hard to calculate and can be simplified to fewer and specific internculear distances as a simplification. On a potential energy surface the transition state is considered as the saddle point. All reactive pathways are calculated to go through a crossing, sometimes called "mountain pass", i.e. the transition state.

Mathematically speaking, the height of this saddle point corresponds to the maximum energy point on the minimum energy reaction path. The gradient and curvature of a saddle point are zero, meaning both the first and second derivatives are zero. It can be also identified as the lowest local maximum of the energy plot. https://arxiv.org/pdf/1405.4604.pdf

The minimum energy reaction path goes straight up through the transition state and then falls down to the products. In this non-ideal reality many reactions go through the region around the transition state and therefore do not cross directly on the saddle point. This can be rationalised by assuming that more kinetic energy than precisely the activation energy has been given to the molecules resulting in a slightly higher energy reaction path.

It is possible to confirm from a frequency calculation that a structure is at the transition state, and so at the saddle point, because the first frequency will result as negative while all the other ones will be positive. This is because at a transition state there is one vibration toward the products which lowers the energy rather than increasing it which gives a negative frequency.

== Exercise 1 ==

===Comparing bond lengths of a Diels-Alder reaction===

A Diels-Alder reaction is a [4+2]-cycloaddition which proceeds via a cyclic transition state to create two new sigma bonds.

[[File:Reaction 1 dp2615.png|thumb|center|Diels-Alder reaction between butadiene and ethene.]]

In this concerted pericyclic reaction, the formation of the two sigma bonds is synchronous as illustrated below where the vibration of the transition state corresponding to the reaction pathway is shown:

[[File:Vibration_ts_dp2615.gif|thumb|center|Diels-Alder reaction between butadiene and ethene.]]

Literature (http://pubs.rsc.org/-/content/articlepdf/1987/p2/p298700000s1) reports by means of X-ray and neutron diffraction the following typical bond lengths (Å):

{| class="wikitable" border="1"
|+ C-C bond lengths
! Type of bond!! Bond length (Å)
|-
| C sp3- C sp3|| 1.51
|-
| C sp3- C sp2|| 1.50
|-
| C sp2- C sp2|| 1.46
|}

The Van der Waals radius of C atom is reported (http://pubs.acs.org/doi/pdf/10.1021/j100785a001) as : 1.70

The C-C bond lengths of reactants(Å), transition state and product are listed below to show their progression throughout the reaction:

{| class="wikitable" border="1"
|+ C-C bond lengths of reactants
! Molecule!! Bond length (Å)
|-
| Butadiene|| 1.34 (double bonds); 1.47 (single bond)
|-
| Ethene|| 1.36
|}

{| class="wikitable" border="1"
|+ C-C bond lengths at transition state
! Molecule!! length (Å)
|-
| Butadiene|| 1.36 (end bonds); 1.44 (central bond)
|-
| Ethene|| 1.36
|-
| New sigma bonds|| 2.11
|}

{| class="wikitable" border="1"
|+ C-C bond lengths of product
! New sigma bond!! length (Å)
|-
| Single bonds|| 1.54
|-
| Double bond|| 1.34
|}

The most significant change of bond length between the reactants and transition state is that of the butadiene molecule. The bond compresses from 1.47 Å to 1.44 Å, thus resulting in a change of the angle between the carbons from 125° to 120° as the molecule adapts its conformation to align the orbitals for the interaction with ethene at the transition state which will lead to the formation of cyclohexene. The end bonds of butadiene present no change in length. Ethene shows no change of conformation between reactant and transition state.

The product shows an elongation of single bonds to 1.54 Å, but the same double bond length as the original butadiene molecule.

It is clear from all the bond lengths observed in these molecules that a covalent C-C bond is not the sum of the Van der Waals radii of the two carbon atoms (2.4 Å), but instead a length produced from a strong interaction which results in a closer approach of the two atoms to each other.

===Molecular Orbital Theory===

Molecular Orbital Theory allows us to represent chemical bonds by combining the orbitals of the reactants to make new complex molecular orbitals (MOs). Only fragment orbitals of the same symmetry can interact to form a bonding/antibonding pair. The strong interaction that is usually present between a HOMO (Highest Occupied MO) and LUMO (Lowest Unoccupied MO) pair results in stabilised MOs. Both the atomic orbitals must have the same symmetry label in order to form new orbitals. In the case of a Diels-Alder reaction, this pair of orbitals must either be symmetric or anti-symmetric for the reaction to be allowed. Any other combination of symmetry would result in a forbidden reaction as the overall stabilisation is not more than that of the starting orbitals.

[[File:MO_1_dp2615.png|500x500px|thumb|center|MO diagram of this Diels-Alder reaction.]]

MOs can be defined as many electron wavefunctions governed by their variant of the Schrödinger equation. This equation has a component Sab called the orbital overlap integral which measures the extent to which the two atomic orbitals overlap. This integral is zero for interactions between orbitals with different symmetry, and not zero for a symmetric—anti-symmetric interaction. This agrees with the symmetry requirement of MO theory.

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO ethene dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO butadiene dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO1 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO2 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO3 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO4 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

LOG FILES

[[:File:ETHYLENE MOS dp2615.LOG]]

[[:File:BUTADIENE MOS dp2615.LOG]]

[[:File:TS WITH MOS FOR JMOL dp2615.LOG]]

[[:File:TS FREQ dp2615.LOG]]

[[:File:IRC dp2615.LOG]]

[[:File:PRODUCT OPT 3 dp2615.LOG]]

== Exercise 2 ==

===Molecular Orbitals in a Diels-Alder reaction===

[[File:Reaction 2 dp2615.png|thumb|center|Diels-ALder reaction between cyclohexadiene and 1,3-dioxole.]]

A Diels-Alder reaction between an electron deficient diene and an electron rich dienophile is an inverse electron demand pericyclic reaction. In this case, the diene is not completely electron deficient as there is a small extent of positive inductive effect from the carbon group attached to the diene. However, the dienophile is under strong effect of two ether groups which are highly electron donating therefore pushing this reaction towards an inverse electron demand interaction rather than a normal electron demand reaction. This is proven by the observed symmetry of the MOs of the two reagents at the transition state where both the HOMO and LUMO appear to be symmetric:

[[File:MO_reac2_dp2615.png|500x500px|thumb|center|MO diagram of this Diels-Alder reaction.]]

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO_dioxole_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO_cyclohexadiene_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO1_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO2_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO3_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO4_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO_dioxole_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO_cyclohexadiene_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO1_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO2_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO3_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO4_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

===Thermochemistry===

Below is a table showing the sum of the electronic and thermal free energies of both the endo and exo reaction pathways calculated using B3YLP calculations:

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| cyclohexadiene|| -233.321033||-612584.418806
|-
| 1,3-dioxole||-267.068132||-701187.43398
|-
| sum of reactants|| -500.389165||-1313771.85279
|}

{| class="wikitable" border="1"
|+ ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| -500.332151|| -1313622.16252
|-
| product|| -500.418691|| -1313849.3733
|}

{| class="wikitable" border="1"
|+ EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| -500.329165 || -1313614.32277
|-
| product|| -500.417322|| -1313845.77899
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct
|-
| in hartrees ||-0.057014|| -149.6902684
|-
| in kJ/mol ||-0.06|| -157.53
|}

Is it deduced from these energies that the thermodynamically favourable reaction path is the one that leads to the endo product, whereas the kinetically favourable path is the one leading to the exo product. The difference in energies between the to energy barriers is 2.986 hartrees, and the difference in energy between the two products is almost insignificant.

The thermodynamically favourbale product is the endo product which literature says requires a higher activation energy for its transition state, but in this case carries a lower more negative kinetic energy barrier. However, it has only a 0.001369 hartrees energetic difference with the exo product, so could be considered a non-significant diversion form typical Diels-Alder behaviour.

This goes to show that both reaction pathways are somewhat favourable and only slightly differ for thermodynamic and kinetic favourability.

Literature reports the endo product of this Diels-Alder reaction as being the kinetic product, thus partly agreeing with these findings and so the predicted pathways partly validates these results.

The diversion of stereosectivity can be rationalised by considering the secondary orbital overlap of the p orbitals of the oxygen atoms with the π orbitals of the diene which stabilises the transition state of the endo adduct, in this case enough to pull it down to a kinetic barrier as for the case of cyclopentadiene and maleic anhydride. This secondary orbital overlap is shown below:

"Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy (Hint: in GaussView, set the isovalue to 0.01. In Jmol, change the mo cutoff to 0.01)?"

LOG FILES

[[:File:DIOXOLE OPT B3YLP dp2615.LOG]]

[[:File:CYCLOHEXADIENE OPT B3YLP dp2615.LOG]]

ENDO

[[:File:ENDO PRODUCT B3YLP OPT dp2615.LOG]]

[[:File:ENDO PM6 IRC OF PM6 dp2615.LOG]]

[[:File:ENDO TS B3LYP dp2615.LOG]]

[[:File:ENDO TS PM6 dp2615.LOG]]

[[:File:ENDO OPT PM6 2 dp2615.LOG]]

EXO

[[:File:EXO PRODUCT OPT B3YLP dp2615.LOG]]

[[:File:EXO FROM TS PM6 IRC dp2615.LOG]]

[[:File:EXO TRANSITION STATE B3YLP dp2615.LOG]]

[[:File:EXO TRANSITION STATE PM6 dp2615.LOG]]

[[:File:EXO OPT PM6 dp2615.LOG]]

== Exercise 3 ==

=== Background chemistry===

A Diels-Alder reaction is a [4+2]-cycloaddition, whereas a cheletropic reaction is a pericyclic reaction considered as a subclass of cycloadditions in which a reorganisation of σ and π bonds occurs at the same atom in the cyclic array of atoms at the transition state.
In many cases, the cheletropic five-membered ring product is the thermodynamic product while the Diels-Alder adduct is the kinetically favoured one. An example is the addition of SO2 to 1,2-dimethylidenecyclohexane. In the case presented here, however, the conjugation of the hexane ring iplays an important part in the lowering of the energy of both the Diels-Alder adducts by aromatisation in comparison to the cheletropic product.

[[File:Reaction 3 dp2615.png|400x400px|thumb|center|Diels-Alder and Cheletropic o-xylylene-SO2 cycloaddition.]]

===Thermochemistry of Diels-Alder and Chelatropic reactions===

Below is a table showing the sum of the electronic and thermal free energies of both the endo, exo and cheletropic reaction pathways calculated using PM6 optimisations:

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| o-xylylene|| 0.178764||469.344918
|-
| SO2|| -0.119268||-313.1381579
|-
| sum of reactants|| 0.059496||156.20676
|}

{| class="wikitable" border="1"
|+ Diels-Alder ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.090558|| 237.760047
|-
| product|| 0.021711|| 57.0022348
|}

{| class="wikitable" border="1"
|+ Diels-Alder EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.092078|| 241.750807
|-
| product|| 0.021455 || 56.3301068
|}

{| class="wikitable" border="1"
|+ Cheletropic adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.099054||260.066297
|-
| product|| 0.063328||166.267677
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct!!chelatropic adduct
|-
| in hartrees || 0.031062|| 0.032582|| 0.039558
|-
| in kJ/mol || 81.5532872|| 85.5440475|| 103.859537
|}

{| class="wikitable" border="1"
|+ Reaction energies
! !!endo adduct!! exo adduct!!chelatropic adduct
|-
| in hartrees || -0.037785|| -0.038041|| 0.003832
|-
| in kJ/mol || -99.20452506|| 99.87665311|| 10.0609168
|}

Is it deduced from these energies that the thermodynamically favourable reaction path is the one that leads to the exo product as it has a larger reaction energy requirement, whereas the kinetically favourable path is the one leading to the endo product with a smaller energy barrier. The endo product also shows a higher product energy proving it is the kinetic product.

The cheletropic product has a higher energy and a higher transition state energy than both the Diels-Alder adducts. It has negative reaction energy, meaning it is an endothermic reaction and requires an input of energy for its completion unlike the exothermic Diels-Alder reactions.

[[File:Reaction_profile_final_2_dp2615.png|500x500px|thumb|center|Reaction profile of Diels-Alder and Cheletropic reactions.]]

This reaction profile shows the relative enrgies of the Diels-Alder and cheletropic cycloadditions. The reactant energy level has been set to 0 as the molecules are being considered at infinite separation, and the energy barriers for the transition states as well as the energies of the products are reported to demonstrate thermodynamic and kinetic favourability of these reactions.

"Include a .gif file in the wiki of these IRCs.

Looking at the IRCs of the Diels-Alder reactions it can be observed that the double bonds of the six-membered ring of o-xylylene delocalise across the entire ring during the course of the reaction and then go to the make the final aromatic product.

LOG FILES:

EXO

ENDO

CHELETROPIC

===Thermochemistry of the secondary Diels-Alder reactions===

o-xylylene contains a second cis-butadiene fragment within the hexadiene ring which can undergo Diels-Alder reactions. Below is a table showing the sum of the electronic and thermal free energies of both the endo and exo reaction pathways calculated using PM6 optimisations:

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. If you have time, prove that the endo and exo Diels-Alder reactions are very thermodynamically and kinetically unfavourable at this site."

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| o-xylylene|| 0.178764|| 469.344918
|-
| SO2|| -0.119268|| -313.1381579
|-
| sum of reactants|| 0.059496|| 156.20676
|}

{| class="wikitable" border="1"
|+ Diels-Alder ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.102070|| 267.984805
|-
| product|| 0.065610|| 172.259068
|}

{| class="wikitable" border="1"
|+ Diels-Alder EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.105054|| 275.819298
|-
| product|| 0.067304|| 176.706665
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct
|-
| in hartrees || 0.042574|| 0.045558
|-
| in kJ/mol || 111.778046||119.612538
|}

{| class="wikitable" border="1"
|+ Reaction energies
! !!endo adduct!! exo adduct
|-
| in hartrees || 0.006114||0.007808
|-
| in kJ/mol || 16.0523082|| 20.4999056
|}

Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.

From these energies it can be deduced that the endo adduct is both the thermodynamic and kinetic product as it holds a lower reaction energy barrier but also a lower product energy. However, this reaction is extremely unfavourbale when comparing these energies to the lower ones of the Diels-Alder reactions on the external diene. Is it thermodynamically and kinetically unfavourbale because the energy barrier is extremely high and the final products' energies are higher than the reactants making this an endothermic process.

LOG FILES:

EXO

[[:File:EXO EXTENSION PRODUCT OPT dp2615.LOG]]

[[:File:EXO IRC EXTENSION dp2615.LOG]]

[[:File:EXO TS EXTENSION dp2615.LOG]]

[[:File:EXO OPTIMISATION EXTENSION dp2615.LOG]]

<nowiki> </nowiki>ENDO

[[:File:ENDO EXTENSION PRODUCT OPT dp2615.LOG]]

[[:File:ENDO IRC EXTENSION dp2615.LOG]]

[[:File:ENDO TS EXTENSION dp2615.LOG]]

[[:File:ENDO OPT EXTENSION dp2615.LOG]]

== References ==

Rep:Mod:dp2615

2017-11-21T14:16:33Z

Rep:Mod:dp2615

2017-11-21T14:02:44Z

Dp2615: /* Exercise 2 */

TRANSITION STRUCTURES AND REACTIVITY

== Introduction ==

===Linking potential energy, transition state and reaction path===

Chemical reactions can be explored by examination of relative energies of reactants, transition states and products. The point of focus during a chemical reaction is the transition state as it offers information on the energy barrier of the reaction which can lead to other crucial conclusions about reaction dynamics.

The potential energy of a chemical reaction is a function of the internuclear distances between all the atoms. This function is hard to calculate and can be simplified to fewer and specific internculear distances as a simplification. On a potential energy surface the transition state is considered as the saddle point. All reactive pathways are calculated to go through a crossing, sometimes called "mountain pass", i.e. the transition state.

Mathematically speaking, the height of this saddle point corresponds to the maximum energy point on the minimum energy reaction path. The gradient and curvature of a saddle point are zero, meaning both the first and second derivatives are zero. It can be also identified as the lowest local maximum of the energy plot. https://arxiv.org/pdf/1405.4604.pdf

The minimum energy reaction path goes straight up through the transition state and then falls down to the products. In this non-ideal reality many reactions go through the region around the transition state and therefore do not cross directly on the saddle point. This can be rationalised by assuming that more kinetic energy than precisely the activation energy has been given to the molecules resulting in a slightly higher energy reaction path.

It is possible to confirm from a frequency calculation that a structure is at the transition state, and so at the saddle point, because the first frequency will result as negative while all the other ones will be positive. This is because at a transition state there is one vibration toward the products which lowers the energy rather than increasing it which gives a negative frequency.

== Exercise 1 ==

===Comparing bond lengths of a Diels-Alder reaction===

A Diels-Alder reaction is a [4+2]-cycloaddition which proceeds via a cyclic transition state to create two new sigma bonds.

[[File:Reaction 1 dp2615.png|thumb|center|Diels-Alder reaction between butadiene and ethene.]]

In this concerted pericyclic reaction, the formation of the two sigma bonds is synchronous as illustrated below where the vibration of the transition state corresponding to the reaction pathway is shown:

[[File:Vibration_ts_dp2615.gif|thumb|center|Diels-Alder reaction between butadiene and ethene.]]

Literature (http://pubs.rsc.org/-/content/articlepdf/1987/p2/p298700000s1) reports by means of X-ray and neutron diffraction the following typical bond lengths (Å):

{| class="wikitable" border="1"
|+ C-C bond lengths
! Type of bond!! Bond length (Å)
|-
| C sp3- C sp3|| 1.51
|-
| C sp3- C sp2|| 1.50
|-
| C sp2- C sp2|| 1.46
|}

The Van der Waals radius of C atom is reported (http://pubs.acs.org/doi/pdf/10.1021/j100785a001) as : 1.70

The C-C bond lengths of reactants(Å), transition state and product are listed below to show their progression throughout the reaction:

{| class="wikitable" border="1"
|+ C-C bond lengths of reactants
! Molecule!! Bond length (Å)
|-
| Butadiene|| 1.34 (double bonds); 1.47 (single bond)
|-
| Ethene|| 1.36
|}

{| class="wikitable" border="1"
|+ C-C bond lengths at transition state
! Molecule!! length (Å)
|-
| Butadiene|| 1.36 (end bonds); 1.44 (central bond)
|-
| Ethene|| 1.36
|-
| New sigma bonds|| 2.11
|}

{| class="wikitable" border="1"
|+ C-C bond lengths of product
! New sigma bond!! length (Å)
|-
| Single bonds|| 1.54
|-
| Double bond|| 1.34
|}

The most significant change of bond length between the reactants and transition state is that of the butadiene molecule. The bond compresses from 1.47 Å to 1.44 Å, thus resulting in a change of the angle between the carbons from 125° to 120° as the molecule adapts its conformation to align the orbitals for the interaction with ethene at the transition state which will lead to the formation of cyclohexene. The end bonds of butadiene present no change in length. Ethene shows no change of conformation between reactant and transition state.

The product shows an elongation of single bonds to 1.54 Å, but the same double bond length as the original butadiene molecule.

It is clear from all the bond lengths observed in these molecules that a covalent C-C bond is not the sum of the Van der Waals radii of the two carbon atoms (2.4 Å), but instead a length produced from a strong interaction which results in a closer approach of the two atoms to each other.

===Molecular Orbital Theory===

Molecular Orbital Theory allows us to represent chemical bonds by combining the orbitals of the reactants to make new complex molecular orbitals (MOs). Only fragment orbitals of the same symmetry can interact to form a bonding/antibonding pair. The strong interaction that is usually present between a HOMO (Highest Occupied MO) and LUMO (Lowest Unoccupied MO) pair results in stabilised MOs. Both the atomic orbitals must have the same symmetry label in order to form new orbitals. In the case of a Diels-Alder reaction, this pair of orbitals must either be symmetric or anti-symmetric for the reaction to be allowed. Any other combination of symmetry would result in a forbidden reaction as the overall stabilisation is not more than that of the starting orbitals.

[[File:MO_1_dp2615.png|500x500px|thumb|center|MO diagram of this Diels-Alder reaction.]]

MOs can be defined as many electron wavefunctions governed by their variant of the Schrödinger equation. This equation has a component Sab called the orbital overlap integral which measures the extent to which the two atomic orbitals overlap. This integral is zero for interactions between orbitals with different symmetry, and not zero for a symmetric—anti-symmetric interaction. This agrees with the symmetry requirement of MO theory.

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO ethene dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO butadiene dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO1 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO2 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO3 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Resulting MO4 dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

LOG FILES

[[:File:ETHYLENE MOS dp2615.LOG]]

[[:File:BUTADIENE MOS dp2615.LOG]]

[[:File:TS WITH MOS FOR JMOL dp2615.LOG]]

[[:File:TS FREQ dp2615.LOG]]

[[:File:IRC dp2615.LOG]]

[[:File:PRODUCT OPT 3 dp2615.LOG]]

== Exercise 2 ==

===Molecular Orbitals in a Diels-Alder reaction===

[[File:Reaction 2 dp2615.png|thumb|center|Diels-ALder reaction between cyclohexadiene and 1,3-dioxole.]]

A Diels-Alder reaction between an electron deficient diene and an electron rich dienophile is an inverse electron demand pericyclic reaction. In this case, the diene is not completely electron deficient as there is a small extent of positive inductive effect from the carbon group attached to the diene. However, the dienophile is under strong effect of two ether groups which are highly electron donating therefore pushing this reaction towards an inverse electron demand interaction rather than a normal electron demand reaction. This is proven by the observed symmetry of the MOs of the two reagents at the transition state where both the HOMO and LUMO appear to be symmetric:

[[File:MO_reac2_dp2615.png|500x500px|thumb|center|MO diagram of this Diels-Alder reaction.]]

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO_dioxole_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO_cyclohexadiene_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO1_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO2_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO3_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:Final_MO4_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

{| class="Images"
|-
!
!
!
|-
| [[File:HOMO_dioxole_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:LUMO_cyclohexadiene_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO1_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO2_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO3_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
| [[File:ENDO_MO4_dp2615.PNG|thumb|center|Diels-Alder reaction between butadiene and ethene.]]
|-
|}

===Thermochemistry===

Below is a table showing the sum of the electronic and thermal free energies of both the endo and exo reaction pathways calculated using B3YLP calculations:

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| cyclohexadiene|| -233.321033||-612584.418806
|-
| 1,3-dioxole||-267.068132||-701187.43398
|-
| sum of reactants|| -500.389165||-1313771.85279
|}

{| class="wikitable" border="1"
|+ ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| -500.332151|| -1313622.16252
|-
| product|| -500.418691|| -1313849.3733
|}

{| class="wikitable" border="1"
|+ EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| -500.329165 || -1313614.32277
|-
| product|| -500.417322|| -1313845.77899
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct
|-
| in hartrees ||-0.057014|| -149.6902684
|-
| in kJ/mol ||-0.06|| -157.53
|}

Is it deduced from these energies that the thermodynamically favourable reaction path is the one that leads to the endo product, whereas the kinetically favourable path is the one leading to the exo product. The difference in energies between the to energy barriers is 2.986 hartrees, and the difference in energy between the two products is almost insignificant.

The thermodynamically favourbale product is the endo product which literature says requires a higher activation energy for its transition state, but in this case carries a lower more negative kinetic energy barrier. However, it has only a 0.001369 hartrees energetic difference with the exo product, so could be considered a non-significant diversion form typical Diels-Alder behaviour.

This goes to show that both reaction pathways are somewhat favourable and only slightly differ for thermodynamic and kinetic favourability.

Literature reports the endo product of this Diels-Alder reaction as being the kinetic product, thus partly agreeing with these findings and so the predicted pathways partly validates these results.

The diversion of stereosectivity can be rationalised by considering the secondary orbital overlap of the p orbitals of the oxygen atoms with the π orbitals of the diene which stabilises the transition state of the endo adduct, in this case enough to pull it down to a kinetic barrier as for the case of cyclopentadiene and maleic anhydride. This secondary orbital overlap is shown below:

"Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy (Hint: in GaussView, set the isovalue to 0.01. In Jmol, change the mo cutoff to 0.01)?"

LOG FILES

File:DIOXOLE OPT B3YLP dp2615.LOG
File:CYCLOHEXADIENE OPT B3YLP dp2615.LOG

ENDO
File:ENDO PRODUCT B3YLP OPT dp2615.LOG
File:ENDO PM6 IRC OF PM6 dp2615.LOG
File:ENDO TS B3LYP dp2615.LOG
File:ENDO TS PM6 dp2615.LOG
File:ENDO OPT PM6 2 dp2615.LOG

EXO

File:EXO PRODUCT OPT B3YLP dp2615.LOG
File:EXO FROM TS PM6 IRC dp2615.LOG
File:EXO TRANSITION STATE B3YLP dp2615.LOG
File:EXO TRANSITION STATE PM6 dp2615.LOG
File:EXO OPT PM6 dp2615.LOG

== Exercise 3 ==

=== Background chemistry===

A Diels-Alder reaction is a [4+2]-cycloaddition, whereas a cheletropic reaction is a pericyclic reaction considered as a subclass of cycloadditions in which a reorganisation of σ and π bonds occurs at the same atom in the cyclic array of atoms at the transition state.
In many cases, the cheletropic five-membered ring product is the thermodynamic product while the Diels-Alder adduct is the kinetically favoured one. An example is the addition of SO2 to 1,2-dimethylidenecyclohexane. In the case presented here, however, the conjugation of the hexane ring iplays an important part in the lowering of the energy of both the Diels-Alder adducts by aromatisation in comparison to the cheletropic product.

[[File:Reaction 3 dp2615.png|400x400px|thumb|center|Diels-Alder and Cheletropic o-xylylene-SO2 cycloaddition.]]

===Thermochemistry of Diels-Alder and Chelatropic reactions===

Below is a table showing the sum of the electronic and thermal free energies of both the endo, exo and cheletropic reaction pathways calculated using PM6 optimisations:

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| o-xylylene|| 0.178764||469.344918
|-
| SO2|| -0.119268||-313.1381579
|-
| sum of reactants|| 0.059496||156.20676
|}

{| class="wikitable" border="1"
|+ Diels-Alder ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.090558|| 237.760047
|-
| product|| 0.021711|| 57.0022348
|}

{| class="wikitable" border="1"
|+ Diels-Alder EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.092078|| 241.750807
|-
| product|| 0.021455 || 56.3301068
|}

{| class="wikitable" border="1"
|+ Cheletropic adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.099054||260.066297
|-
| product|| 0.063328||166.267677
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct!!chelatropic adduct
|-
| in hartrees || 0.031062|| 0.032582|| 0.039558
|-
| in kJ/mol || 81.5532872|| 85.5440475|| 103.859537
|}

{| class="wikitable" border="1"
|+ Reaction energies
! !!endo adduct!! exo adduct!!chelatropic adduct
|-
| in hartrees || -0.037785|| -0.038041|| 0.003832
|-
| in kJ/mol || -99.20452506|| 99.87665311|| 10.0609168
|}

Is it deduced from these energies that the thermodynamically favourable reaction path is the one that leads to the exo product as it has a larger reaction energy requirement, whereas the kinetically favourable path is the one leading to the endo product with a smaller energy barrier. The endo product also shows a higher product energy proving it is the kinetic product.

The cheletropic product has a higher energy and a higher transition state energy than both the Diels-Alder adducts. It has negative reaction energy, meaning it is an endothermic reaction and requires an input of energy for its completion unlike the exothermic Diels-Alder reactions.

[[File:Reaction_profile_final_2_dp2615.png|500x500px|thumb|center|Reaction profile of Diels-Alder and Cheletropic reactions.]]

This reaction profile shows the relative enrgies of the Diels-Alder and cheletropic cycloadditions. The reactant energy level has been set to 0 as the molecules are being considered at infinite separation, and the energy barriers for the transition states as well as the energies of the products are reported to demonstrate thermodynamic and kinetic favourability of these reactions.

"Include a .gif file in the wiki of these IRCs.

Looking at the IRCs of the Diels-Alder reactions it can be observed that the double bonds of the six-membered ring of o-xylylene delocalise across the entire ring during the course of the reaction and then go to the make the final aromatic product.

===Thermochemistry of the secondary Diels-Alder reactions===

o-xylylene contains a second cis-butadiene fragment within the hexadiene ring which can undergo Diels-Alder reactions. Below is a table showing the sum of the electronic and thermal free energies of both the endo and exo reaction pathways calculated using PM6 optimisations:

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. If you have time, prove that the endo and exo Diels-Alder reactions are very thermodynamically and kinetically unfavourable at this site."

{| class="wikitable" border="1"
|+ Reactants
! Molecule!! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| o-xylylene|| 0.178764|| 469.344918
|-
| SO2|| -0.119268|| -313.1381579
|-
| sum of reactants|| 0.059496|| 156.20676
|}

{| class="wikitable" border="1"
|+ Diels-Alder ENDO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.102070|| 267.984805
|-
| product|| 0.065610|| 172.259068
|}

{| class="wikitable" border="1"
|+ Diels-Alder EXO adduct
! Molecule !! Gibbs Free Energies (hartrees) !! Gibbs Free Energies (kJ/mol)
|-
| transition state|| 0.105054|| 275.819298
|-
| product|| 0.067304|| 176.706665
|}

{| class="wikitable" border="1"
|+ Activation energies
! !!endo adduct!! exo adduct
|-
| in hartrees || 0.042574|| 0.045558
|-
| in kJ/mol || 111.778046||119.612538
|}

{| class="wikitable" border="1"
|+ Reaction energies
! !!endo adduct!! exo adduct
|-
| in hartrees || 0.006114||0.007808
|-
| in kJ/mol || 16.0523082|| 20.4999056
|}

Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.

From these energies it can be deduced that the endo adduct is both the thermodynamic and kinetic product as it holds a lower reaction energy barrier but also a lower product energy. However, this reaction is extremely unfavourbale when comparing these energies to the lower ones of the Diels-Alder reactions on the external diene. Is it thermodynamically and kinetically unfavourbale because the energy barrier is extremely high and the final products' energies are higher than the reactants making this an endothermic process.

== References ==

File:ENDO OPT PM6 2 dp2615.LOG

2017-11-21T14:02:34Z

Dp2615: