Rep:MOD:ST3515 TS3

2018-01-30T10:43:01Z

St3515:

===Introduction===

A potential energy surface describes the relationship between the energy of a molecule and its geometry. The transition state is the maximum in a reaction profile while a minimum is a minimum in a potential energy surface, corresponding to either reactants or products. Both maximum and minimum have the same first derivative of energy ie. zero gradient, but their second derivatives are different. a maximum has a negative second derivative while a minimum has a positive second derivative. A frequency analysis can be used to distinguish the two; the transition state can be identified as it has only one negative frequency but a minimum will not have any negative frequencies. Computational methods allow these transitions states that cannot to isolated to be visualised. The computed energies of the TS, reactants and products also allow reaction energies and barriers to be calculated, and hence predict the more favourable reaction pathway. Once the TS has be optimised successfully, an intrinsic reaction coordinate (IRC) calculation can be carried out which, besides giving energy plots, also allows visualisation of the minimum energy pathway from reactants to products.to confirm the correct reaction is taking place.

The semi-empirical method PM6 method involves approximations and the use of atomic and diatomic parameters from experimental data. Calculations using this method are therefore fast and are frequently used to minimise structures before carrying out more expensive calculations. B3LYP calculations, a Density Functional Theory (DFT) method, uses the basis set 6-31G(d) that has added d polarisation functions on atoms other than hydrogen. These calculations take longer but are more accurate than PM6 due to the use of a greater number of basis functions. MOs can also be visualised.

The Cycloaddition reactions of butadiene with ethylene, cyclohexadiene with 1,3-dioxole and o-xylylene with SO2 were studied using the PM6 method, and some also using B3LYP. Firstly, the products of the reactions were optimised to a minimum and the resulting optimised structure was modified to resemble the TS. The modified structure was then optimised to a TS. Reactants were built and optimised to a minimum.

https://books.google.co.uk/books? 6 gaussians for 1s, 3 gaussians for the inner 2s,2p, 1 gaussian for the outer 2s,2p

===Exercise 1: Butadiene and Ethene===

[[File:St3515 TS3 Reaction Scheme 1.jpg|thumb|center|<b>Scheme 1</b>. The Diels Alder reaction between butadiene and ethene to form a six membered ring.]]

Butadiene and ethene undergo a [4+2] Diels Alder reaction (<b>Scheme 1</b>). The semi-empirical PM6 method was used to optimise the reactants, product and TS, and frequency analysis suggests successful optimisation of the structures.

====MO Analysis====

{| class="wikitable" border="1"
|+ Table 1. The computed HOMOs and LUMOs of butadiene and ethene, and the computed butadiene/ethene TS MOs produced as a results of their interaction.
|-
| style="text-align: center;"|MO
| style="text-align: center;"|Butadiene
| style="text-align: center;"|Butadiene/Ethene TS
| style="text-align: center;"|Ethene
|-
| LUMO + 1
|
|<jmol>
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|
|-
| LUMO
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| HOMO
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| HOMO - 1
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[[File:st3515_Exercise_1_TS_MO_2.jpg|thumb|center|<b>Figure 1</b>. MO diagram showing the interaction between the HOMOs and LUMOs of butadiene and ethene to give four TS MOs. The TS MOs corresponding to each TS energy level is indicated using pink arrows. The change in the TS MO energy levels due to mixing is indicated using the blue arrows. The symmetry labels a and s correspond to asymmetric and symmetric respectively.]]

The pi MOs of butadiene and ethene (HOMOs and LUMOs) involved in the formation of the TS were computed. The four TS MOs resulting from the interaction of the HOMO and LUMO of the reactants were also computed (<b>Table 1</b>).

An allowed reaction is one in which the interacting MOs, which are close enough in energy for effective orbital overlap, are of the same symmetry. Hence symmetric-symmetric MO interactions and asymmetric-asymmetric MO interactions are allowed. For these allowed reactions, the orbital overlap integral is non-zero.
The orbital overlap integral is zero when there is a symmetric-asymmetric MO interaction, and this corresponds to a forbidden reaction.

The computed MOs and MO diagram for the Diels Alder reaction between butadiene and ethene show that the MO interactions are allowed (<b>Table 1; Figure 1</b>). The asymmetric HOMO of butadiene interacts with the asymmetric LUMO of ethene to produce two asymmetric TS MOs. The symmetric LUMO of butadiene interacts with the symmetric HOMO of ethene to produce two symmetric TS MOs.

The TS MO energies computed are however not as expected. The bonding TS MOs are higher in energy and the antibonding MOs are lower in energy (<b>Figure 1</b>). This suggests that there is MO mixing in the TS causing a shift in the MO energies.

====Bond Length Analysis====

{| class="wikitable" border="1"
|+ Table 2. The literature values (Å) for the C-C single bond, C=C double bond and carbon Van der Waals radius.
! C-C single bond length !! C=C double bond length !! Carbon Van der Waals radius
|-
| 1.54 || 1.34 || 1.85
|}

{| class="wikitable" border="1"
|+ Table 3. The computed C-C bond lengths (Å) for the reactants, TS and product.
| colspan="3" align="center"|[[File:Benzene_3D.png|256px]]
|-
! Bond !! Reactants !! TS !! Product
|-
| C1 || 1.34 || 1.38 || 1.50
|-
| C2 || 1.47 || 1.41 || 1.34
|-
| C3 || 1.34 || 1.38 || 1.50
|-
| C4 || - || 2.11 || 1.54
|-
| C5 || 1.33 || 1.38 || 1.53
|-
| C6 || - || 2.12 || 1.54
|}

Pi electorn delocalisation in butadiene results in lengthening of the C=C double bond and shortening of the C-C single bond compared to the literature C-C single and double bond lengths (Tables).

As the reaction progresses, the bond lengths C1, C3 and C5 increase from ~1.3 Å in the reactants to ~1.5 Å in the products. This suggests that breaking of the double bond at those positions to form a single bond. The bond length C2 decreases from 1.47 Å in the reactants to 1.34 Å in the product as a double bond forms at that position. In the TS, the bond lengths at these positions are between the literature values for the C-C single bond length and C=C double bond length, suggesting a change in bond order is occurring during the reaction.

In the TS, the bond lengths C4 and C6 are less than twice the Van der Waals radius of carbon, suggesting that bond formation is occurring at those positions. In the product, these bond lengths are close to the lit. C-C single bond length, suggesting that single bonds were formed at those positions.

====TS Vibrational Analysis====

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Frequency analysis of the TS shows one imaginary frequency, suggesting that the TS structure was correctly optimised. This imaginary frequency corresponds to the reaction at the TS and shows synchronous bond formation with both bonds forming to the same extent (Figure). This is in agreement with the concerted mechanism of a Diels Alder reaction.

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

[[File:St3515 TS3 Reaction Scheme 2.jpg|thumb|center|<b>Scheme 2</b>. The Diels Alder reaction between cyclohexadiene and 1,3-dioxole forms either the endo or exo adduct.]]

Cyclohexadiene and 1,3-dioxole can undergo a [4+2] Diels Alder reaction to form either the exo or endo product. The semi-empirical PM6 method was used to obtain initial structures of the reactants, products and TS. These initial structures were then optimised using B3LYP method using the basis set 6-31G(d). Frequency analysis suggests that the TS, reactants and products structures were optimised correctly.

====MO Analysis====

{| class="wikitable" border="1"
|+ Table.
|-
| style="text-align: center;"|MO
| style="text-align: center;"|Cyclohexadiene
| style="text-align: center;"|1,3-Dioxole
|-
| LUMO
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| HOMO
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{| class="wikitable" border="1"
|+ Table.
|-
| style="text-align: center;"|MO
| style="text-align: center;"|Endo TS
| style="text-align: center;"|Exo TS
|-
| LUMO + 1
|[[File:st3515_Endo_above_LUMO.JPG]]
|[[File:st3515_Exo_above_LUMO.JPG]]
|-
| LUMO
|[[File:St3515_TS3_Endo_LUMO.JPG]]
|[[File:St3515_TS3_Exo_LUMO.JPG]]
|-
| HOMO
|[[File:St3515_TS3_Endo_HOMO.JPG]]
|[[File:St3515_TS3_Exo_HOMO.JPG]]
|-
| HOMO -1
|[[File:St3515_TS3_Endo_below_HOMO.JPG]]
|[[File:St3515_TS3_Exo_below_HOMO.JPG]]
|}

The normal demand Diels Alder reaction involves an electron poor dienophile and an electron rich diene. However the Diels Alder reaction can also occur between the an electron rich dienophile and electron poor diene, and this is known as the inverse demand Diels Alder reaction. In such a reaction, the interaction between the HOMO and LUMO of the dienophile and diene respectively is stronger than the interaction between the HOMO and LUMO of the diene and dienophile respectively. The opposite is true for a normal demand Diels Alder reaction.

1,3-dioxole is an electron rich dienophile, while cyclohexadiene is an electron poor diene. The oxygen atoms in dioxole are electron rich and hence raise the energy of the HOMO and LUMO. This results in a stronger interaction between the HOMO of dioxole and the LUMO of cyclohexadiene, making these the frontier molecular orbitals. Hence this is an inverse demand Diels Alder reaction.

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

{| class="wikitable" border="1"
|+ Table
! Adduct !! Reactants !! TS !! Product !! Reaction Energy/ KJ mol<sup>-1</sup> !! Reaction Barrier/ KJ mol<sup>-1</sup>
|-
| Endo|| -1313781 || -1313621 || -1313849 || 67.410 || 167.649
|-
| Exo || -1313781 || -1313614 || -1313845 || 63.808 || 159.809
|}

The HOMO of the endo TS suggests that there is a favourable secondary orbital interaction between the orbitals on oxygen in dioxole and the orbitals on cyclohexadiene. This interaction is not possible in the HOMO of the exo TS as the orbitals involved cannot overlap. The TS also suggests that the endo TS has less steric hindrance between the reactants than the exo TS. The lower steric hindrance and secondary orbital interaction explain why calculations show that the endo TS is lower in energy than the exo TS. Therefore the endo product is the kinetic product. However, the exo product is lower in energy than the endo product, making the exo product thermodynamically favourable. Check steric

===Exercise 3: SO<sub>2</sub> and o-Xylylene===

[[File:St3515_TS3_Reaction_Scheme_3.jpg|thumb|center|<b>Scheme 3</b>. The possible cycloaddition reactions between SO<sub>2</sub> and o-Xylylene. <b>a)</b> The Diels Alder reaction involving the <i>cis</i>-butadiene fragment not in the six-membered ring to form the exo or endo product; <b>b)</b> the Cheletropic reaction and; <b>c)</b> the Diels Alder reaction involving the <i>cis</i>-butadiene fragment in the six-membered ring to form the exo or endo product.]]

SO<sub>2</sub> and o-xylylene can undergo Diels Alder reaction to form the exo or endo product and also a cheletropic reaction to form a five membered ring. The semi-empirical PM6 method was used to optimise the reactants, products and TS.

{| class="wikitable" border="1"
|+ Table. gif. files of the IRCs for the exo and endo Diels Alder reaction, and for the Cheletropic reaction.
|-
|Exo Diel Alder|| Endo Diels Alder|| Cheletropic
|-
|[[File:St3515_DA_Exo_IRC_movie.gif]]||[[File:St3515_DA_Endo_IRC_movie.gif]]||[[File:St3515_C_IRC_movie.gif]]
|}

The IRCs for each path confirm that the reactions are either Diel Alder or Cheletropic. It also shows how an aromatic benzene ring forms as a result of the reaction. This explains the high instability of the non-aromatic o-xylylene that wants to react to form the thermodynamically stable aromatic benzene ring. Besides reaction with another molecule, o-xylylene can also undergo an electrocyclic reaction to form the stable aromatic ring (<b>Scheme 4</b>).

[[File:st3515_TS3_Electrocyclic.jpg|thumb|center|<b>Scheme 4</b>. The electrocyclic reaction of o-xylylene to form the thermodynamically stable aromatic benzene ring.]]

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

[[File:st3515_TS3_Reaction_Profile.jpg|thumb|center|<b>Figure</b>. The reaction profile showing the reaction energies and reaction barriers for the endo and exo Diels Alder reactions and the Cheletropic reaction of SO<sub>2</sub> and o-xylylene. The reactants, endo Diels Alder, exo Diels Alder and Cheletropic reaction are highlighted in green, orange, purple and pink respectively.]]

{| class="wikitable" border="1"
|+ caption
! !! Reactants !! TS !! Product !! Reaction Energy !! Reaction Barrier
|-
| Endo Diels Alder || 154.351 || 237.765 || 56.989 || 97.361 || 83.415
|-
| Exo Diels Alder || 154.351 || 241.748 || 56.325 || 98.026 || 87.398
|-
| Cheletropic || 154.351 || 260.084 || 0.013 || 154.337 || 105.734
|}

{| class="wikitable" border="1"
|+ caption
! !! Reaction Energy !! Reaction Barrier
|-
| Endo || -17.909 || 113.634
|-
| Exo || -22.359 || 121.471
|}

The endo product of the Diels Alder reaction is the kinetic product with the lowest activation energy. The exo product of the Diels Alder reaction is more stable than the endo product as it has a larger reaction energy.

The cheletropic product is the thermodyanamic product with the highest reaction energy. However it has the highest activation energy.

====Reaction with Second <i>cis</i>-Butadiene Fragment====

SO<sub>2</sub> can also undergo [4+2] Diels Alder reaction with a second <i>cis</i>-butadiene fragment in the six-membered ring of o-xylylene. This reaction is however less likely because the resulting products are less stable. This is seen in the computed reaction energies that are much lower than the reaction energies involving reaction with the <i>cis</i>-butadiene fragment not in the six-membered ring. This is because the reaction does not result in the formation of a stable aromatic benzene ring in the products. Furthermore, there is greater steric hindrance in the product.

===Conclusion===

===References===
ex 1

St3515_BUTADIENE_CIS_MIN.LOG
St3515_ETHENE_MIN.LOG
St3515_Ex_1_PRODUCTS_MIN_2.LOG

ex 2

St3515_Ex_2_PRODUCT_ENDO_B3LYP.LOG
St3515_Ex_2_PRODUCT_EXO_B3LYP.LOG
St3515_Ex_2_REACTANTS_ENDO_B3LYP.LOG
St3515_Ex_2_REACTANTS_EXO_B3LYP.LOG

ex 3

St3515_XYLYLENE_MIN.LOG
St3515_XYLYLENE_B3LYP.LOG
St3515_SO2_MIN.LOG
St3515_SO2_B3LYP.LOG
St3515_Ex_3_DA_EXO_PRODUCT_B3LYP_2.LOG
St3515_ex_3_DA_ENDO_PRODUCT_B3LYP.LOG
St3515_ex_3_DA_ENDO_PRODUCT_MIN.LOG
St3515_ex_3_Exo_Product_DA_REOPT.LOG
St3515_ex_3_DA_ENDO_TS_B3LYP.LOG
St3515_ex_3_DA_ENDO_TS.LOG
St3515_ex_3_Exo_DA_REACTANTS_TS.LOG
St3515_ex_3_DA_EXO_TS_B3LYP.LOG
St3515_ex_3_C_PRODUCT_B3LYP_2.LOG
St3515_ex_3_C_Product_min.LOG
St3515_ex_3_C_TS_B3LYP.LOG
St3515_ex_3_C_REACTANTS_TS.LOG

extra

St3515_ex_3_NPRODUCT_ENDO_MIN.LOG
St3515_ex_3_NPRODUCT_EXO_MIN_3.LOG
St3515_ex_3_NREACTANTS_ENDO_TS.LOG
St3515_ex_3_NREACTANTS_EXO_TS_2.LOG

Rep:MOD:ST3515 TS3

File:St3515 TS3 Reaction Scheme 1.jpg

2018-01-29T18:44:50Z

St3515: