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Rep:MOD:rs5215TS

2017-11-22T00:04:25Z

Rs5215: /* Thermochemistry */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation which allows for the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows fewer calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this optimisation is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, fewer approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the transition state and optimising it immediately. The second method is also fast but more reliable: this involves estimating the transition state, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethene is explored. The reactants, butadiene and ethene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. In the transition state, the bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of C2 to C3, which is also a typical length for a carbon-carbon double bond.

=== Imaginary Frequencies ===

As mentioned in the introduction, transition states are characterized by a single imaginary frequency as a result of the square root of the negative force constant. This appears as a negative frequency in GaussView. Figure 6 shows an animation of this.

[[File:RS5215_Ethene_Butadiene_Cyclohexene_Transition_State_Imaginary_Frequency_Animation.gif|thumb|centre|Figure 6: Animation of the Imaginary Frequency]]

From the animation, it can be seen that the formation of the two new bonds is synchronous.

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

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 7 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 7: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 8.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 8: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states are shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.<ref name="WoodwardHoffman">[http://pubs.acs.org/doi/abs/10.1021/ja00947a033 R. Hoffmann, R. B. Woodward, J. Am. Chem. Soc. 1965, 87, 4388.]</ref>

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table 6.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 9 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 9: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 10-12 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 12: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The formation of the endo and exo products can be seen to be asynchronous as the C-O bond is formed before the S-O bond.

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|center|Figure 13: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways|917px]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3 ==

[https://wiki.ch.ic.ac.uk/wiki/images/e/e9/RS5215_XYLYLENE_MINIMUM_PM6_OPT_TRY_1.LOG Xylylene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/65/RS5215_SO2_MINIMUM_PM6_OPT_TRY_1.LOG SO2 PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/e7/RS5215_ENDO_TS_PM6_TS_TRY_1.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/67/RS5215_ENDO_TS_PM6_IRC.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/96/RS5215_EXO_TS_PM6_TS_OPT_TRY_1.LOG Exo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/RS5215_EXO_TS_PM6_IRC.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/b/b1/RS5215_CHELETROPIC_TS_BERNY_PM6_OPT_TRY_1.LOG Cheletropic Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ee/RS5215_CHELETROPIC_TS_PM6_IRC_TRY_2.LOG Cheletropic Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/1/12/RS5215_ENDO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Endo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/3/37/RS5215_EXO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Exo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/f/fd/RS5215_CHELETROPIC_PRODUCT_MINIMUM_PM6_OPT.LOG Cheletropic Product PM6]

= References =

Rep:MOD:rs5215TS

2017-11-22T00:00:28Z

Rs5215: /* Thermochemistry */

Rep:MOD:rs5215TS

2017-11-21T23:59:29Z

Rs5215:

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation which allows for the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows fewer calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this optimisation is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, fewer approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the transition state and optimising it immediately. The second method is also fast but more reliable: this involves estimating the transition state, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethene is explored. The reactants, butadiene and ethene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. In the transition state, the bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of C2 to C3, which is also a typical length for a carbon-carbon double bond.

=== Imaginary Frequencies ===

As mentioned in the introduction, transition states are characterized by a single imaginary frequency as a result of the square root of the negative force constant. This appears as a negative frequency in GaussView. Figure 6 shows an animation of this.

[[File:RS5215_Ethene_Butadiene_Cyclohexene_Transition_State_Imaginary_Frequency_Animation.gif|thumb|centre|Figure 6: Animation of the Imaginary Frequency]]

From the animation, it can be seen that the formation of the two new bonds is synchronous.

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

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 7 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 7: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 8.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 8: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states are shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.<ref name="WoodwardHoffman">[http://pubs.acs.org/doi/abs/10.1021/ja00947a033 R. Hoffmann, R. B. Woodward, J. Am. Chem. Soc. 1965, 87, 4388.]</ref>

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table 6.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 9 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 9: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 10-12 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 12: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The formation of the endo and exo products can be seen to be asynchronous as the C-O bond is formed before the S-O bond.

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 13: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3 ==

[https://wiki.ch.ic.ac.uk/wiki/images/e/e9/RS5215_XYLYLENE_MINIMUM_PM6_OPT_TRY_1.LOG Xylylene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/65/RS5215_SO2_MINIMUM_PM6_OPT_TRY_1.LOG SO2 PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/e7/RS5215_ENDO_TS_PM6_TS_TRY_1.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/67/RS5215_ENDO_TS_PM6_IRC.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/96/RS5215_EXO_TS_PM6_TS_OPT_TRY_1.LOG Exo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/RS5215_EXO_TS_PM6_IRC.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/b/b1/RS5215_CHELETROPIC_TS_BERNY_PM6_OPT_TRY_1.LOG Cheletropic Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ee/RS5215_CHELETROPIC_TS_PM6_IRC_TRY_2.LOG Cheletropic Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/1/12/RS5215_ENDO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Endo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/3/37/RS5215_EXO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Exo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/f/fd/RS5215_CHELETROPIC_PRODUCT_MINIMUM_PM6_OPT.LOG Cheletropic Product PM6]

= References =

Rep:MOD:rs5215TS

2017-11-21T23:50:55Z

Rs5215:

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation which allows for the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows fewer calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this optimisation is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, fewer approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the transition state and optimising it immediately. The second method is also fast but more reliable: this involves estimating the transition state, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethene is explored. The reactants, butadiene and ethene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. In the transition state, the bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of C2 to C3, which is also a typical length for a carbon-carbon double bond.

=== Imaginary Frequencies ===

As mentioned in the introduction, transition states are characterized by a single imaginary frequency as a result of the square root of the negative force constant. This appears as a negative frequency in GaussView. Figure 6 shows an animation of this.

[[File:RS5215_Ethene_Butadiene_Cyclohexene_Transition_State_Imaginary_Frequency_Animation.gif|thumb|centre|Figure 6: Animation of the Imaginary Frequency]]

From the animation, it can be seen that the formation of the two new bonds is synchronous.

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

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 7 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 7: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 8.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 8: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states are shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table 6.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 9 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 9: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 10-12 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 12: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The formation of the endo and exo products can be seen to be asynchronous as the C-O bond is formed before the S-O bond.

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 13: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3 ==

[https://wiki.ch.ic.ac.uk/wiki/images/e/e9/RS5215_XYLYLENE_MINIMUM_PM6_OPT_TRY_1.LOG Xylylene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/65/RS5215_SO2_MINIMUM_PM6_OPT_TRY_1.LOG SO2 PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/e7/RS5215_ENDO_TS_PM6_TS_TRY_1.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/67/RS5215_ENDO_TS_PM6_IRC.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/96/RS5215_EXO_TS_PM6_TS_OPT_TRY_1.LOG Exo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/RS5215_EXO_TS_PM6_IRC.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/b/b1/RS5215_CHELETROPIC_TS_BERNY_PM6_OPT_TRY_1.LOG Cheletropic Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ee/RS5215_CHELETROPIC_TS_PM6_IRC_TRY_2.LOG Cheletropic Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/1/12/RS5215_ENDO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Endo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/3/37/RS5215_EXO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Exo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/f/fd/RS5215_CHELETROPIC_PRODUCT_MINIMUM_PM6_OPT.LOG Cheletropic Product PM6]

= References =

Rep:MOD:rs5215TS

2017-11-21T16:17:59Z

Rs5215:

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

=== Imaginary Frequencies ===

As mentioned in the introduction, transition states are characterized by a single imaginary frequency as a result of the square root of the negative force constant. This appears as a negative frequency in GaussView. Figure 6 shows an animation of this.

[[File:RS5215_Ethene_Butadiene_Cyclohexene_Transition_State_Imaginary_Frequency_Animation.gif|thumb|centre|Figure 6: Animation of the Imaginary Frequency]]

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 7 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 7: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 8.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 8: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 9 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 9: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 10-12 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 12: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 13: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3 ==

[https://wiki.ch.ic.ac.uk/wiki/images/e/e9/RS5215_XYLYLENE_MINIMUM_PM6_OPT_TRY_1.LOG Xylylene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/65/RS5215_SO2_MINIMUM_PM6_OPT_TRY_1.LOG SO2 PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/e7/RS5215_ENDO_TS_PM6_TS_TRY_1.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/67/RS5215_ENDO_TS_PM6_IRC.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/96/RS5215_EXO_TS_PM6_TS_OPT_TRY_1.LOG Exo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/RS5215_EXO_TS_PM6_IRC.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/b/b1/RS5215_CHELETROPIC_TS_BERNY_PM6_OPT_TRY_1.LOG Cheletropic Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ee/RS5215_CHELETROPIC_TS_PM6_IRC_TRY_2.LOG Cheletropic Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/1/12/RS5215_ENDO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Endo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/3/37/RS5215_EXO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Exo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/f/fd/RS5215_CHELETROPIC_PRODUCT_MINIMUM_PM6_OPT.LOG Cheletropic Product PM6]

= References =

Rep:MOD:rs5215TS

2017-11-21T16:16:54Z

Rs5215: /* Exercise 1ː Diels Alder with Butadiene and Ethylene */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

=== Imaginary Frequencies ===

As mentioned in the introduction, transition states are characterized by a single imaginary frequency as a result of the square root of the negative force constant. This appears as a negative frequency in GaussView. Figure 6 shows an animation of this.

[[File:RS5215_Ethene_Butadiene_Cyclohexene_Transition_State_Imaginary_Frequency_Animation.gif|thumb|centre|Figure 6: Animation of the Imaginary Frequency]]

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 6 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 6: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 7.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 7: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 8 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 8: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 9-11 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 9: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 12: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3 ==

[https://wiki.ch.ic.ac.uk/wiki/images/e/e9/RS5215_XYLYLENE_MINIMUM_PM6_OPT_TRY_1.LOG Xylylene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/65/RS5215_SO2_MINIMUM_PM6_OPT_TRY_1.LOG SO2 PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/e7/RS5215_ENDO_TS_PM6_TS_TRY_1.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/67/RS5215_ENDO_TS_PM6_IRC.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/96/RS5215_EXO_TS_PM6_TS_OPT_TRY_1.LOG Exo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/RS5215_EXO_TS_PM6_IRC.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/b/b1/RS5215_CHELETROPIC_TS_BERNY_PM6_OPT_TRY_1.LOG Cheletropic Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ee/RS5215_CHELETROPIC_TS_PM6_IRC_TRY_2.LOG Cheletropic Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/1/12/RS5215_ENDO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Endo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/3/37/RS5215_EXO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Exo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/f/fd/RS5215_CHELETROPIC_PRODUCT_MINIMUM_PM6_OPT.LOG Cheletropic Product PM6]

= References =

File:RS5215 Ethene Butadiene Cyclohexene Transition State Imaginary Frequency Animation.gif

2017-11-21T16:14:05Z

Rs5215:

Rep:MOD:rs5215TS

2017-11-21T16:11:02Z

Rs5215:

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 6 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 6: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 7.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 7: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 8 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 8: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 9-11 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 9: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 12: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3 ==

[https://wiki.ch.ic.ac.uk/wiki/images/e/e9/RS5215_XYLYLENE_MINIMUM_PM6_OPT_TRY_1.LOG Xylylene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/65/RS5215_SO2_MINIMUM_PM6_OPT_TRY_1.LOG SO2 PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/e7/RS5215_ENDO_TS_PM6_TS_TRY_1.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/67/RS5215_ENDO_TS_PM6_IRC.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/96/RS5215_EXO_TS_PM6_TS_OPT_TRY_1.LOG Exo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/RS5215_EXO_TS_PM6_IRC.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/b/b1/RS5215_CHELETROPIC_TS_BERNY_PM6_OPT_TRY_1.LOG Cheletropic Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ee/RS5215_CHELETROPIC_TS_PM6_IRC_TRY_2.LOG Cheletropic Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/1/12/RS5215_ENDO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Endo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/3/37/RS5215_EXO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Exo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/f/fd/RS5215_CHELETROPIC_PRODUCT_MINIMUM_PM6_OPT.LOG Cheletropic Product PM6]

= References =

Rep:MOD:rs5215TS

2017-11-21T16:10:32Z

Rs5215: /* Appendix */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 6 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 6: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 7.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 7: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 8 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 8: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 9-11 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 9: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 12: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

Cyclohexadiene, 1,3-Dioxole, Exo TS, Endo TS, Exo Product, Endo Product

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3 ==

Xylylene and SO2 Reactants, Endo Transition State, Endo IRC, Exo Transition State, Exo IRC, Cheletropic Transition State, Cheletropic IRC, Endo Product, Exo Product, Cheletropic Product

[https://wiki.ch.ic.ac.uk/wiki/images/e/e9/RS5215_XYLYLENE_MINIMUM_PM6_OPT_TRY_1.LOG Xylylene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/65/RS5215_SO2_MINIMUM_PM6_OPT_TRY_1.LOG SO2 PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/e7/RS5215_ENDO_TS_PM6_TS_TRY_1.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/6/67/RS5215_ENDO_TS_PM6_IRC.LOG Endo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/96/RS5215_EXO_TS_PM6_TS_OPT_TRY_1.LOG Exo Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/RS5215_EXO_TS_PM6_IRC.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/b/b1/RS5215_CHELETROPIC_TS_BERNY_PM6_OPT_TRY_1.LOG Cheletropic Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ee/RS5215_CHELETROPIC_TS_PM6_IRC_TRY_2.LOG Cheletropic Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/1/12/RS5215_ENDO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Endo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/3/37/RS5215_EXO_PRODUCT_MINIMUM_PM6_OPT_TRY_1.LOG Exo Product PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/f/fd/RS5215_CHELETROPIC_PRODUCT_MINIMUM_PM6_OPT.LOG Cheletropic Product PM6]

= References =

File:RS5215 CHELETROPIC PRODUCT MINIMUM PM6 OPT.LOG

2017-11-21T16:10:17Z

Rs5215:

File:RS5215 EXO PRODUCT MINIMUM PM6 OPT TRY 1.LOG

2017-11-21T16:09:52Z

Rs5215:

File:RS5215 ENDO PRODUCT MINIMUM PM6 OPT TRY 1.LOG

2017-11-21T16:09:21Z

Rs5215:

File:RS5215 CHELETROPIC TS PM6 IRC TRY 2.LOG

2017-11-21T16:08:49Z

Rs5215:

File:RS5215 CHELETROPIC TS BERNY PM6 OPT TRY 1.LOG

2017-11-21T16:08:15Z

Rs5215:

File:RS5215 EXO TS PM6 IRC.LOG

2017-11-21T16:07:48Z

Rs5215:

File:RS5215 EXO TS PM6 TS OPT TRY 1.LOG

2017-11-21T16:05:56Z

Rs5215:

File:RS5215 ENDO TS PM6 IRC.LOG

2017-11-21T16:05:03Z

Rs5215:

File:RS5215 ENDO TS PM6 TS TRY 1.LOG

2017-11-21T16:04:01Z

Rs5215:

File:RS5215 SO2 MINIMUM PM6 OPT TRY 1.LOG

2017-11-21T16:03:22Z

Rs5215:

File:RS5215 XYLYLENE MINIMUM PM6 OPT TRY 1.LOG

2017-11-21T16:02:44Z

Rs5215:

Rep:MOD:rs5215TS

2017-11-21T15:58:11Z

Rs5215: /* Appendix */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 6 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 6: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 7.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 7: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 8 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 8: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 9-11 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 9: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 12: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c4/Rs5215_BUTADIENE_ETHENE_TS_IRC_PM6.LOG Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/Rs5215_CYCLOHEXENE_OPT_PM6_TRY_2.LOG Cyclohexene]

== Exercise 2 ==

Cyclohexadiene, 1,3-Dioxole, Exo TS, Endo TS, Exo Product, Endo Product

[https://wiki.ch.ic.ac.uk/wiki/images/5/54/RS5215_CYCLOHEXADIENE_OPTIMISATION_B3LYP.LOG Cyclohexadiene B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/8/8c/RS5215_DIOXOLE_OPT_B3LYP_TRY_1.LOG 1,3-Dioxole B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_CYCLOHEXADIENE_DIOXOLE_OPT_B3LYP_TRY_1.LOG Endo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/64/RS5215_CYCLOHEXADIENE_DIOXOLE_ENDO_IRC_PM6_TRY_1.LOG Endo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/RS5215_EXO_B3LYP_TS_TRY_2.LOG Exo Transition State B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/6/6b/RS5215_EXO_PM6_TS_IRC_LAST_TRY_2.LOG Exo Transition State IRC PM6]
[https://wiki.ch.ic.ac.uk/wiki/images/e/ec/RS5215_ENDO_PRODUCT_OPT_B3LYP.LOG Endo Product B3LYP]
[https://wiki.ch.ic.ac.uk/wiki/images/2/26/RS5215_EXO_PRODUCT_MINIMUM_B3LYP_TRY_1.LOG Exo Product B3LYP]

== Exercise 3

Xylylene and SO2

= References =

File:RS5215 EXO PRODUCT MINIMUM B3LYP TRY 1.LOG

2017-11-21T15:57:49Z

Rs5215:

File:RS5215 ENDO PRODUCT OPT B3LYP.LOG

2017-11-21T15:57:19Z

Rs5215:

File:RS5215 EXO PM6 TS IRC LAST TRY 2.LOG

2017-11-21T15:56:53Z

Rs5215:

File:RS5215 EXO B3LYP TS TRY 2.LOG

2017-11-21T15:56:18Z

Rs5215:

File:RS5215 CYCLOHEXADIENE DIOXOLE ENDO IRC PM6 TRY 1.LOG

2017-11-21T15:55:44Z

Rs5215:

File:RS5215 CYCLOHEXADIENE DIOXOLE OPT B3LYP TRY 1.LOG

2017-11-21T15:55:06Z

Rs5215:

File:RS5215 DIOXOLE OPT B3LYP TRY 1.LOG

2017-11-21T15:53:45Z

Rs5215:

File:RS5215 CYCLOHEXADIENE OPTIMISATION B3LYP.LOG

2017-11-21T15:53:11Z

Rs5215:

File:Rs5215 BUTADIENE ETHENE TS IRC PM6.LOG

2017-11-21T15:45:36Z

Rs5215:

File:Rs5215 CYCLOHEXENE OPT PM6 TRY 2.LOG

2017-11-21T15:42:27Z

Rs5215:

Rep:MOD:rs5215TS

2017-11-21T15:37:05Z

Rs5215: /* Bond Lengths */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg|thumb|Figure 5: A Labelled Diagram of the Reactants]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 6 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 6: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 7.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 7: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 8 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 8: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 9-11 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 9: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 12: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T15:33:58Z

Rs5215: /* MO Diagram */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_diels_alders.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]|thumb|Figure 5: A Labelled Diagram of the Reactants]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 6 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 6: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 7.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 7: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 8 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 8: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 9-11 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 9: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 12: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

File:Rs5215 MO Diagram butadiene ethene diels alders.jpg

2017-11-21T15:30:47Z

Rs5215: Rs5215 uploaded a new version of File:Rs5215 MO Diagram butadiene ethene diels alders.jpg

Rep:MOD:rs5215TS

2017-11-21T15:28:05Z

Rs5215: /* Transition Structures */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure 1: An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 2: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 2, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 2 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level. Figure 3 shows the reaction scheme.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure 3: Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

Figure 4 shows the MO diagram for the formation of the butadiene/ethene transition state, including basic symmetry labels. This is a normal Diels-Alder reaction, in which the HOMO of the diene reacts with the LUMO of the dienophile.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure 4: An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed' as an orbital overlap is necessary for interaction.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]|thumb|Figure 5: A Labelled Diagram of the Reactants]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. Figure 6 shows the reaction scheme including both products and transition states.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure 6: Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure 7.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure 7: MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table 6: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. Figure 8 shows the reaction scheme for all three.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure 8: Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

Figures 9-11 show the visualisation of the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure 9: Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure 10: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure 11: Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table 7: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table 8: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg|thumb|Figure 12: A Reaction Profile showing the Endo, Exo and Cheletropic Pathways]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T15:17:29Z

Rs5215: /* Conclusion */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. The reaction scheme including both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure X.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3. Alternative pathways, such as the cheletropic reaction, were shown to be disfavoured due to the high energy of the transition state and the product.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T15:14:41Z

Rs5215: /* Conclusion */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. The reaction scheme including both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure X.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

The transition states of multiple Diels-Alder reactions were found using two computational methods, PM6 and B3LYP, depending on the accuracy needed.

The reaction barriers and reaction energies were found through the use of these methods, allowing for comparison of the exo and endo transition states and products. The endo transition state and product were found to be lower in energy than the exo for both exercises 2 and 3.

MO theory was explored in relation to the transition states, offering explanations for the increased stability of the endo product by showing the favourable secondary orbital interactions.

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T15:07:38Z

Rs5215: /* Thermochemistry */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. The reaction scheme including both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure X.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

This shows that the kinetic and thermodynamic product is the endo product.

== Conclusion ==

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T15:07:04Z

Rs5215: /* IRC */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. The reaction scheme including both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure X.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

The lack of stability of xylylene can be explained through the visualisation of the IRCs. As the xylylene reacts, the bond lengths of the six-membered ring equalize as it becomes aromatic. This is a much more stable configuration. Hence, xylylene would prefer to react to form an aromatic ring instead of two diene sites.

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

== Conclusion ==

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T14:58:42Z

Rs5215: /* Secondary Orbital Interactions */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. The reaction scheme including both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure X.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

This favourable bonding interaction means the reaction barrier for the endo transition state will be lower than that of the exo.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

== Conclusion ==

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T14:57:57Z

Rs5215: /* Exercise 2ː Cyclohexadiene and Dioxole */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. The reaction scheme including both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure X.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

== Conclusion ==

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T14:51:51Z

Rs5215:

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

These are shown by the MOs of the optimised reactants below.

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation - these are the HOMO-1, HOMO, LUMO and LUMO+1.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products depending on the trajectory of approach to the transition state. The possible products are the endo product and the exo product. The reaction scheme including both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

Using the information from the PM6 optimisation, the MO diagram from exercise 1 was adjusted to apply to this reaction. The addition of the oxygen atoms results in a higher energy dienophile, resulting in an inverse demand Diels-Alder reaction. This is shown in Figure X.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

The corresponding MOs from the optimised transition states is shown below.

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

As the reaction barrier is smaller for the endo transition state, it is the kinetically favourable pathway. The reaction energy is also lower for the endo product, hence it is the thermodynamically favourable product as well.

=== Secondary Orbital Interactions ===

The 'endo rule' is generally applicable to irreversible Diels-Alder reactions. The endo product is more favoured due to the presence of secondary orbital interactions. The p orbitals of the oxygen atoms can interact with the pi system of the diene resulting in favourable bonding interactions for the endo transition state and product. This is shown in the HOMO of the endo transition state above.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

== Conclusion ==

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Cyclohexadiene and 1,3-Dioxole

== Exercise 3

Xylylene and SO2

= References =

Rep:MOD:rs5215TS

2017-11-21T14:39:19Z

Rs5215: /* Transition Structures */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features<ref name="ChemLibreTexts">[https://www.google.co.uk/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwji15re8c_XAhWIyRQKHYGoA0EQjB0IBg&url=https%3A%2F%2Fchem.libretexts.org%2FCore%2FPhysical_and_Theoretical_Chemistry%2FQuantum_Mechanics%2F11%253A_Molecules%2FPotential_Energy_Surface&psig=AOvVaw2TxKMtJZyLuqMEZpe8Pn3M&ust=1511361302218508 Chemistry LibreTexts, accessed November 2017]</ref>|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.<ref name="GaussianMethods">[https://link.springer.com/protocol/10.1007%2F978-1-62703-017-5_1 Monticelli, L. and Salonen, E. (2013). Biomolecular Simulations. Totowa, NJ: Humana Press, pp.3-27.]</ref>

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products: the endo product and the exo product. The reaction scheme for both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

The occupied and unoccupied orbitals associated with the Diels-Alder reaction were located for both transition states by symmetry.

The relevant MOs are also given.

Another MO diagram is constructed using these new orbitals. This is a [normal/inverse-demand]? Diels Alder reaction.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

The kinetically and thermodynamically favourable products can be inferred from this.

The HOMO of the transition states show us the secondary orbital interactions and steric effects that might affect the reaction barrier energy.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

== Conclusion ==

= References =

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Rep:MOD:rs5215TS

2017-11-21T14:27:22Z

Rs5215: /* Computational Methods */

= Transition Structures =

== Introduction ==

=== Diels-Alder Reactions ===

In the course of this investigation, the transition states of several Diels-Alder reactions are explored.

Diels-Alder reactions are 4+2 cycloadditions between a diene and a dienophile.

Some Diels-Alder reactions can result in either endo or exo products, depending on the trajectory of approach of the dienophile. These alternative paths have different reaction energies and barriers, which are tabulated below.

Normal Diels-Alder reactions involve the interaction of the HOMO of the diene and the LUMO of the dienophile, as shown in Figure 1. However, as Figure 1 also shows, there is an inverse-demand Diels-Alder, in which the LUMO of the diene and the HOMO of the dienophile interact. This tends to happen when there are electron-donating groups on the dienophile, increasing the energy, and electron-withdrawing groups on the diene, decreasing the energy.

[[File:Rs5215_diels_alders_normal_inverse_demand.jpg|thumb|center|Figure : An MO Diagram showing Normal and Inverse Demand Diels Alder Reactions|792px]]

Both normal and inverse-demand Diels-Alder reactions will be looked at.

=== Potential Energy Surfaces ===

Potential energy surfaces (PES) are quantum mechanical conceptual tools that relate the potential energy of a system with its geometry. The degrees of freedom dictate the dimensions of the potential energy surface. PESs rely upon the Born-Oppenheimer approximation. This allows the separation of the nuclear degrees of freedom and the electronic degrees of freedom by stating that the nuclei are fixed in motion relative to the electrons.

[[File:Rs5215_PES_mod_TS.gif|thumb|center|Figure 1: A PES showing Relevant Features|558px]]

The minima relate to chemically stable configurations. Conversely, the maxima relate to chemically unstable configurations.

As shown in Figure 1, transition states are first order saddle points on the potential energy surface. The transition state, as a saddle point, is a minimum between two maxima (second order saddle points) and a maximum between the two minima of the reactants and products. The geometry at the transition state will result in an imaginary frequency, appearing as a negative number, due to the square root of a negative force constant in the harmonic oscillator.

Figure 1 also shows the concept of alternative pathways, transition state A and transition state B could correspond to the endo and exo pathways discussed above.

=== Computational Methods ===

The two methods used are the semi-empirical PM6 method and the DFT-hybrid B3LYP method which uses a 6-31G(d) basis set.

The simplest ab initio method (when the energies are derived from first principles) is based on the Hartree-Fock (HF) method, in which the wavefunction of the system is expressed through the use of a linear combination of Slater determinants with fixed coefficients. The Hartree-Fock method neglects to account for electron correlation and hence is discouraged for large systems.

The PM6 method is based on the same MO theory as the HF ab initio method but it also incorporates empirical data as approximations for certain integrals. This allows less calculations to be made and results in a less computationally expensive method. However, these approximations mean the accuracy of this method is compromised.

The B3LYP method is a DFT-hybrid method. DFT methods are based on electron density, an observable physical property, as opposed to wavefunctions. The DFT-hybrid method incorporates both the HF method, which can find the exact exchange energy when ignoring correlation effects, with the DFT method, which does include the electron correlation effects. DFT-hybrid methods are much more accurate than non-hybrid DFT methods at the cost of computational power. In comparison to the PM6 method, less approximations are used in the B3LYP method resulting in a more accurate optimisation but it is more computationally expensive.

For exercises 1 and 3, the PM6 level was used, while exercise 2 used the B3LYP method.

=== Finding the Transition State ===

Three methods were used to find the transition state. The first method is the fastest and involves estimating the TS and optimising it immediately. The second method is also fast but more reliable: this involves estimating the TS, freezing the atoms involved in bond formations and optimising the structure to a minimum before optimising the transition state. The third method is the most reliable as it involves the least amount of guesswork but requires additional steps and hence the most computational effort. The third method involves optimising the reactants or the products and finding the transition state by changing bond lengths.

For exercise 1, method 2 was used due to the relative simplicity of the reactants, allowing the transition state to be guessed easily.

For exercises 2 and 3, method 3 was the most successful as the transition state was more complex.

== Exercise 1ː Diels Alder with Butadiene and Ethylene ==

In this exercise, the transition state of a π4s + π2s cycloaddition using the reactants butadiene and ethylene is explored. The reactants, butadiene and ethylene, and the transition state were optimised at the PM6 level. The transition state was confirmed with a frequency calculation and an IRC. The products were optimised at the PM6 level.

[[File:Rs5215_butadiene_ethene_cyclohexene_reaction_scheme.jpg|thumb|center|Figure : Reaction Scheme showing the formation of Cyclohexene through a 4+2 cycloaddition reaction|630px]]

=== MO Diagram ===

An MO diagram for the formation of the butadiene/ethene transition state is shown below, including basic symmetry labels.

[[File:Rs5215_MO_Diagram_butadiene_ethene_transition_state.jpg|thumb|center|Figure : An MO Diagram showing the transition state formed from butadiene and ethene|571px]]

{| class="wikitable" border="1" align="center"
|+ Table 1: A Table showing the corresponding MOs to the HOMO and LUMO of both butadiene and ethene
|-
| [[File:Rs5215_butadiene_HOMO_asymmetric.jpg]] Butadiene HOMO Asymmetric || [[File:Rs5215_butadiene_HOMO_MO_opt.png|150px]] || [[File:Rs5215_butadiene_LUMO_symmetric.jpg]] Butadiene LUMO Symmetric || [[File:Rs5215_butadiene_LUMO_MO_opt.png|150px]]
|-
| [[File:Rs5215_ethene_HOMO_symmetric.jpg]] Ethene HOMO Symmetric || [[File:Rs5215_ethene_HOMO_opt.png|150px]] || [[File:Rs5215_ethene_LUMO_asymmetric.jpg]] Ethene LUMO Asymmetric || [[File:Rs5215_ethene_LUMO_opt.png|150px]]
|}

The four MOs that the reactant MOs produce for the transition state are shown in Table 2 along with their corresponding MOs from the transition state after optimisation.

{| class="wikitable" border="1" align="center"
|+ Table 2: A Table showing the MOs produced for the Transition State
|-
| [[File:Rs5215_transition_state_LUMO_plus_1.jpg]] LUMO+1 Asymmetric || [[File:Rs5215_transition_state_LUMO_plus_1_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_LUMO.jpg]] LUMO Symmetric || [[File:Rs5215_transition_state_LUMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_homo_minus_1.jpg]] HOMO Asymmetric || [[File:Rs5215_transition_state_HOMO_opt.png|150px]]
|-
| [[File:Rs5215_transition_state_HOMO.jpg]] HOMO-1 Symmetric || [[File:Rs5215_transition_state_HOMO_minus_1_opt.png|150px]]
|}

As shown, the symmetry of the combining orbitals must be the same. This is because the orbital overlap integral is zero for symmetric-antisymmetric interactions and is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions. Hence, symmetric-antisymmetric combinations are 'forbidden' and only same-symmetry combinations are 'allowed'.

=== Bond Lengths ===

The measurements of the C-C bond lengths of the reactants, products and transition state are shown below.

[[File:Rs5215_butadiene_ethene_labelled_carbon_carbon_bonds.jpg]]

{| class="wikitable" border="1" align="center"
|+ Table 3: A Table showing the Bond Lengths between Carbons for the Reactants, Transition State and Product
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.34 || 1.38 || 1.50
|-
| C2 to C3 || 1.47 || 1.41 || 1.34
|-
| C3 to C4 || 1.34 || 1.38 || 1.50
|-
| C4 to C5 || || 2.11 || 1.54
|-
| C5 to C6 || 1.33 || 1.38 || 1.53
|-
| C6 to C1 || || 2.11 || 1.54
|}

The van der Waals radius of carbon is 1.7 Å, the bond length of an sp2 hybridised carbon is 1.3 Å and the bond length of an sp3 hybridised carbon is 1.5 Å.

From the data in the table, the changes of bond length as the reaction proceeds can be seen.
The double bonds in the diene (C1 to C2 and C3 to C4) are shown to elongate throughout the process as they become single bonds, while the single bond in the diene (C2 to C3) decreases in length as it becomes a double bond. Similarly, the double bond in the dienophile increases in bond length as it becomes a single bond.

For interaction to occur between two carbon atoms, they must be closer than two van der Waals radii - 3.4 Å. The bond lengths between C4 to C5 and C6 to C1 show a length of 2.11 Å. This is within double the van der Waals radius for carbon and hence the two atoms can be said to be interacting.

In the product, all carbon-carbon bonds are around 1.5 Å, the typical bond length of a carbon-carbon single bond, with the exception of the double bond, which is also a typical length for a carbon-carbon double bond.

== Exercise 2ː Cyclohexadiene and Dioxole ==

Exercise 2 explores another 4+2 cycloaddition involving the reactants cyclohexadiene and dioxole. In this case, there are two possible products: the endo product and the exo product. The reaction scheme for both is shown below.

[[File:Rs5215_reaction_scheme_exercise_2_endo_exo_cyclohexadiene.jpg|thumb|center|Figure : Reaction Scheme showing Exo and Endo Products of a Cycloaddition invovling Cyclohexadiene and a 1,3-dioxole|685px]]

The endo and exo transition states were located using method 3. They were optimised to the B3LYP/6-31G(d) level. Frequency calculations and an IRC were taken for both, confirming the transition state.The endo and exo products as well as the reactants were also optimised to the B3LYP/6-31G(d) level.

=== MO Diagram ===

The occupied and unoccupied orbitals associated with the Diels-Alder reaction were located for both transition states by symmetry.

The relevant MOs are also given.

Another MO diagram is constructed using these new orbitals. This is a [normal/inverse-demand]? Diels Alder reaction.

[[File:Rs5215_MO_diagram_cyclohexadiene_dioxole.jpg|thumb|center|Figure : MO Diagram showing the Exo and Endo Transition States|680px]]

{| class="wikitable" border="1" align="center"
|+ Table 4: A Table showing the corresponding MOs to the HOMO and LUMO of both the Exo and Endo Transition States
|-
| [[File:Rs5215_exo_TS_HOMO_symmetric.jpg]] Exo Transition State HOMO Symmetric || [[File:Rs5215_exo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_exo_TS_LUMO_symmetric.jpg]] Exo Transition State LUMO Symmetric || [[File:Rs5215_exo_TS_LUMO_opt.png|175px]]
|-
| [[File:Rs5215_endo_TS_HOMO_symmetric.jpg]] Endo Transition State HOMO Symmetric || [[File:Rs5215_endo_TS_HOMO_opt.png|175px]] || [[File:Rs5215_endo_TS_LUMO_symmetric.jpg]] Endo Transition State LUMO Symmetric || [[File:Rs5215_endo_TS_LUMO_opt.png|175px]]
|}

=== Thermochemistry ===

The table below shows the energies of the reactants, products and transition states in Hartrees and kJ/mol.

{| class="wikitable" border="1" align="center"
|+ Table 5: A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene || -233.321033 || -701187.4340
|-
| 1,3-Dioxole || -267.068132 || -612584.4188
|-
| Reactants || -500.389165 || -1313771.8528
|-
| Endo Transition State || -500.332152 || -1313622.1651
|-
| Exo Transition State || -500.329168 || -1313614.3307
|-
| Endo Product || -500.418691 || -1313849.3733
|-
| Exo Product || -500.417322 || -1313845.7790
|}

From this, the reaction barriers and reaction energies are tabulated at room temperature, shown in Table X.

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 149.688 || -77.521
|-
| Exo || 157.522 || -73.962
|}

The kinetically and thermodynamically favourable products can be inferred from this.

The HOMO of the transition states show us the secondary orbital interactions and steric effects that might affect the reaction barrier energy.

== Exercise 3ː Diels Alder vs Cheletopic ==

In this exercise, three different transition states were investigated. Two of these were the endo and exo transition states and products of a Diels Alder reaction. The third was a cheletropic reaction. The reaction scheme for all three is shown below.

[[File:Rs5215_reaction_scheme_diels_alders_vs_cheletropic.jpg|thumb|center|Figure : Reaction Scheme showing the transition states for the exo product, the endo product and the cheletropic product|690px]]

These were optimised to the PM6 level. The transition states were confirmed using IRCs and frequency calculations.

=== IRC ===

The gif files below show the reaction coordinates for all three paths.

[[File:Rs5215_exo_TS_IRC_exercise_3_try_2.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Exo Product|300px]] 
[[File:Rs5215_exercise_3_endo_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 
[[File:Rs5215_exercise_3_cheletropic_TS_IRC_gif.gif|thumb|center|Figure : Visualisation of the Reaction Coordinate of the Formation of the Endo Product|300px]] 

=== Thermochemistry ===

{| class="wikitable" border="1" align="center"
|+ Table : A Table showing the Energies of the Reactants, Products and Transition States
! Compound !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| SO2 || -0.11861 || -311.4211
|-
| Xylylene || 0.1781 || 467.6331
|-
| Reactants || 0.0595 || 156.2120
|-
| Endo Transition State || 0.0906 || 237.7653
|-
| Exo Transition State || 0.0923 || 241.7508
|-
| Cheletropic Transition State || 0.0997 || 260.0847
|-
| Endo Product || 0.0216 || 56.3301
|-
| Exo Product || 0.0217 || 56.9865
|-
| Cheletropic Product || -0.000002 || -0.0053
|}

From this, the reaction energies and barriers can be calculated:

{| class="wikitable" border="1"
|+ Table X: Showing the Energies of the Reactants, Products and Transition States
! Product Conformation !! Reaction Barrier(kJ mol-1) !! Reaction Energy (kJ mol-1)
|-
| Endo || 81.55 || -99.88
|-
| Exo || 85.54 || -99.23
|-
| Cheletropic || 103.87 || -156.22
|}

From this information, a reaction profile showing all three paths can be configured.

[[File:Rs5215_reaction_coordinate_endo_exo.jpg]]

== Conclusion ==

= References =

= Appendix =

== Exercise 1 ==

[https://wiki.ch.ic.ac.uk/wiki/images/c/c3/Rs5215_butadiene_opt_pm6_jmol.LOG Butadiene]
[https://wiki.ch.ic.ac.uk/wiki/images/9/98/Rs5215_diels_alders_ethene_butadieneTS_Berny_opt_jmol_pm6.LOG Transition State]
[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/Rs5215_ethene_pm6_opt_jmol.LOG Ethene]

== Exercise 2 ==

Rep:MOD:rs5215TS

2017-11-21T14:12:42Z

Rs5215: /* Introduction */

Rep:MOD:rs5215TS

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Rs5215: /* Computational Methods */

Rep:MOD:rs5215TS

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Rs5215: /* Introduction */

Rep:MOD:rs5215TS

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Rs5215: /* Potential Energy Surfaces */

Rep:MOD:rs5215TS

2017-11-21T10:45:18Z

Rs5215:

File:Rs5215 diels alders normal inverse demand.cdx

2017-11-21T10:20:55Z

Rs5215: