2017-12-17T02:16:45Z

Ct1515: /* Exercise 2 */

==TRANSITION STATES AND REACTIVITY==
===INTRODUCTION===
====Potential Energy Surfaces====
A potential energy surface describes the different energies of different conformation of molecules involved in a reaction. They usually will have a maximum where the energy is at its highest, this is usually its transition state and a minimum where the product exists in its lowest energy conformation. At the maximum and minimum the derivative of the curve is zero but the 2nd differential is less than zero for a maximum and greater than zero for a minimum. During this report the Transition states of Diels-Alder reaction will be investigated.
====The Diels-Alder reaction====
This reaction is concerted combination of two molecules to form a ring structure. The 4+2 cycloadditions can either take the conformation of an exo or endo transition state depending on the way in which the reacting molecules collide. The transition states have a corresponding energy and are different for the exo and endo approach.

==Exercise 1==
During this exercise the Diels-Alder reaction of 1,3-Butadiene and Ethene were investigated. It is a π4s + π2s cycloaddition reaction that give cyclohexene. The reactants, transition state and products were all optimised at a PM6 level and conduction of a frequency calculation and an IRC for the transition state was done to confirm the presences of a true transition state. The presence of only one negative vibration frequency (and imaginary frequency) and the correct IRC pathway confirmed the presence of the transition state.
[[File:Ct1515Exercise 1 reaction scheme.png|649x649px|thumb|Figure 1: Reaction scheme for the reaction of butadiene and ethene|centre]]

===Molecular Oribtal Visualisations of Reactants===
The visualisation of the Molecular Orbitals (MOs) for the reactants can be found in the JMOLs added below.
{| class="wikitable"
|+Table 1: A table containing JMOLs of the reactants to be able to visualise the MOs
| <jmol>
<jmolApplet>
<color>white</color>
<title>Butadiene</title>
<size>400</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT1515_BUTADIENE_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<title>Ethene</title>
<size>400</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CT1515_ETHENE_OPT_PM6_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===MO Diagram for the reaction between 1,3-Butadiene and Ethene===
[[File:Ct1515_MO_Diagram_Exercise_1.png|649x649px|thumb|Figure 2: Molecular Orbital (MO) Diagram for the reactants and transition state in the reaction of the Diels-Alder reaction of 1,3-Butadiene and Ethene|centre]]
In Figure 2 the MO diagram for the reaction can be seen. Basic symmetry labels have been added to the orbitals which show the composite MOs which make up the overall MO at each stage. Due to the symmetries of the reacting orbitals, the HOMO of the diene reacts with the LUMO of the dieneophile making it a normal Diels-Alder reaction.

===JMOL of Transition State of the reaction===
Below is the JMOL of the optimised transition state at the PM6 level where the molecular orbitals that participate in the reaction can be visualised.
<jmol>
<jmolApplet>
<color>white</color>
<title>Transition state</title>
<size>400</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ct1515_CYCLOHEXENE_OPT_TO_TS_PM6_2-1_JMOL2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Table 2 below shows a frozen image of the PM6 level optimised transition state orbitals in the HOMO+1, HOMO, LUMO & LUMO-1 states.
{|centre| class="wikitable" border="1" align="center"
|+ Table 2: The molecular orbitals of the transition states
|-
| [[File:Ct1515_Cyclohexene_Transition_State_Orbital_16-2_HOMO-1.jpg|300px]] MO 16 - HOMO -1 Symmetric ||[[File:Ct1515_HOMO-1.png|300px]] MO 16 - HOMO -1 Symmetric || [[File:Ct1515_Cyclohexene_Transition_State_Orbital_17HOMO.jpg|290px]] MO 17 HOMO Asymmetric || [[File:Ct1515_HOMO.png|280px]] MO 17 HOMO Asymmetric 
|-
| [[File:Ct1515_Cyclohexene__Transition_State_Orbital_18LUMO.jpg|300px]] MO 18 - LUMO Symmetric ||[[File:Ct1515_LUMO.png|300px]] MO 18 - LUMO Symmetric || [[File:Ct1515_Cyclohexene_Transition_State_Orbital_19LUMO__+1.jpg|300px]] MO 19 LUMO +1 Asymmetric || [[File:Ct1515_LUMO_+1.png|300px]] MO 19 LUMO +1 Asymmetric 
|}
Table 2 also shows the corresponding atomic orbitals that are used to make up these optimized transition state orbitals. They also correspond to the same named orbitals in the MO diagram in Figure 2.

The reacting orbitals must have the same symmetry in order to react. This is so that the orbital overlap integral is non-zero. Symmetric-Asymmetric orbital overlaps are forbidden due to the fact that this integral becomes zero and therefore not overlapping. In order for a reaction to happen the orbitals must overlap and therefore only orbitals with the same symmetry can react.

===Investigation of Bond length change during the reaction===
[[File:Ct1515Labelled_diagram_of_products_and_reactants.jpg|300px|thumb|Figure 3: Labelled carbons in Ethene and Butadiene]]
Table 3 shows the change in bond length over the course of the reaction. The labelled carbons correspond to the carbons labelled in Figure 3.
{| class="wikitable" border="1" align="center"
|+ Table 3: Bond lengths in the different stages of the reaction of butadiene and ethene
! Carbon-Carbon Bond !! Reactants (Å) !! Transition State (Å) !! Product (Å)
|-
| C1 to C2 || 1.33534 || 1.37970 || 1.50034
|-
| C2 to C3 ||1.46848 || 1.41114 || 1.33766
|-
| C3 to C4 || 1.33534 ||1.37979 || 1.50034
|-
| C4 to C5 || || 2.11412 || 1.54003
|-
| C5 to C6 || 1.32731 || 1.38173 || 1.54076
|-
| C6 to C1 || || 2.11526 || 1.54003
|}

{| class="wikitable" border="1" align="center"
|+ Table 4: Info about carbon lengths
! Description!! Length (Å)
|-
| Typical sp2 hybridsed C-C bond|| 1.3
|-
| Typical sp3 hybridsed C-C bond|| 1.5
|-
| VDW Radius of carbon || 1.7
|}

During this reaction it can be seen in Table 3 that the bond between C1 and C2, C3 and C4 and C6 and C5, ie the sp2 hybridised carbons, elongated as they changed from a a double to a single bond during the reaction. The forming alkene bond between C2 and C3 can be seen to shorten as it changes from sp3 hybridised character to sp2 character.

In the transition state the bond length between the forming bond is less that 2 VDW radii away from each other meaning that the orbitals will be interacting. It is longer than a typical single bond so in the transition state the bond hasn't completely formed.

In the product molecule the bond lengths between each of the carbons are close to their corresponding bond typical lengths. This is to say that the bonds of around 1.5Å are all sp3-sp3 hybridised and the onle sp2-sp2 hybridised bond between C2 and C3 is close to 1.3Å.

===Imaginary/Negative Vibrational Frequencies in the Transition State===
In the frequency analysis of the optimised transition state structure a one negative frequency appears. This frequency corresponds to the formation of the new bonds in the product molecules. This vibration is shown in the gif in Figure 4. As the formation of the 2 bonds is at the same time it can be describes and a synchronous reaction.
[[File:Ct1515_Imaginary_Frequency.gif|300px|thumb|centre|Figure 4: Animation of the Imaginary Frequency]]

==Exercise 2==
In Exercise 2 an investigation of the reaction between Cyclohexadiene and 1,3-Dioxoloe was undertaken. The reactants, transition state and products were all optimized at the B3LYP level using the basis set of 631G-(d). And IRC at the PM6 level was also conducted in order to see whether the transition state was correct and to investigate the two reaction pathways.
[[File:Ct1515Exercise_2_Reaction_Scheme.png|649x649px|thumb|Figure 5: Reaction scheme for the reaction Cyclohexadiene and 1,3-Dioxole|centre]]
In Figure 5 the two reaction pathways are shown the exothermic (exo) and endothermic (endo) routes in which the reaction can proceed. The resulting product depends on the trajectory of the reacting molecules and their position in regards to one another. The exo route has the oxygen atoms in the dioxole facing away from the sp2 bond in the cyclohexadiene. The endo pathway has the oxygen atoms over the top of the sp2 hybridized bond and this therefore means an interaction can take place between the p orbitals of the oxygen and the π orbital stabilizing the transition state. This is what's known as secondary orbital interactions when stabilisation occurs but not through the bonding orbitals.

[[File:Ct1515_MO_Diagram_Exercise_2.png|1000px|thumb|Figure 6: MO diagram showing the exo and endo paths and their transition state structure MOs in the reaction between Cyclohexadiene and 1,3-Dioxole|centre]]
Due to the symmetry of the MOs of the reactants and and of the transition state, this reaction is an inverse Diels-Alder reaction due to the fact the HOMO of the dieneophile is higher in energy than the HOMO of the diene. This is due to the presence of the electron withdrawing oxygen molecule adjacent to reacting alkene bond.

In Table 5 a frozen image of the transition state molecular orbitals can be found. These correspond to the same labelled molecular oribitals in the Molecular Orbital Diagram in Figure 6.
{| class="wikitable" border="1" align="center"
|+ Table 5: The molecular orbitals of the transition states
|-
| [[File:Ct1515Exo_TS_MO_HOMO.jpg|200px]] Exo Transition State HOMO Symmetric || [[File:CT1515_Exo_TS_MO_LUMO.jpg|200px]] Exo Transition State LUMO Symmetric 
|-
| [[File:Ct1515_Endo_TS_HOMO_(Orbital_41).jpg|200px]] Endo Transition State HOMO Symmetric || [[File:Ct1515_Endo_TS_LUMO_(Orbital_42).jpg|200px]] Endo Transition State LUMO Symmetric 
|}
The secondary orbital interactions of the Endothermic Reaction can be clearly seen in the HOMO of the transition state as there is significant overlap between the oxygen's p orbitals.

===JMOL for the Transition States===
{| class="wikitable"
|+Table 1: A table containing JMOLs of the Transition States to be able to visualise the MOs
| <jmol>
<jmolApplet>
<color>white</color>
<title>Exo Transition State </title>
<size>400</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ct1515_Q2_OPT_TO_TS_B3613G_1-3_JMOL3.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<title>Endo Transition State </title>
<size>400</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ct1515OPT_ENDO_TO_TS_B31G_2-2_JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

===Thermochemistry===
Table 6 shows the Sum of electronic and thermal Free Energies of the reactants, transition states and the products of the endo and exo reactions.
{| class="wikitable" border="1" align="center"
|+ Table 6: Table of Energies
! Molecule !! Energy (Hartrees) !! Energy (kJ mol-1)
|-
| Cyclohexadiene (reactant) ||-233.321033|| -612584.4188
|-
| 1,3-Dioxole (reactant) ||-267.068145 || -701187.4681
|-
|Combined Reactant Energy ||-500.389178 ||-1313771.8869
|-
| Exo Transition State || -500.329163 || -1313614.3175
|-
| Endo Transition State ||-500.332149 || -1313622.1573
|-
| Exo Product || -500.417322 || -1313845.7790
|-
| Endo Product ||-500.418691 ||-1313849.3733
|}

From their the activation energy of the reaction can be calculated along with the energy of the reaction. The activation energy was calculated by Σ(energy of reactants)+(energy of transition state).

{| class="wikitable" border="1" align="center"
|+ Table 7: Table of Energies
! Type of reaction path !! Activation Energy (kJ mol-1)!! Energy of the Reaction (kJ mol-1)
|-
| Exothermic Route || 157.57 || -73.89
|-
| Endothermic Route || 149.73 || -77.49
|}

What can be determined from the calculated energies is that the Endothermic route has a lower activation energy. This is as predicted due to the secondary orbital interactions. It is therefore the kinetic product of the reaction.
When comparing the energies of the products it is also true that the endothermic product is lower in energy and therefore a more stabilised molecule. It this therefore the thermodynamic product as well.

==Exercise 3==

[[File:Ct1515_Exercise_3_Reaction_Scheme.png|717x717px|thumb|Figure 7: Reaction scheme for the reaction Cyclohexadiene and 1,3-Dioxole|centre]]

===Visualisation of the three reaction Pathways===

{| class="wikitable" border="1" align="center"
|+ Table 8: IRC
|-
| [[File:Ct1515_chelotropic_reaction_pathway.gif|300px|thumb|centre|Figure 8: Animation of the Reaction Pathway of the Chelotropic reaction]] || [[File:Ct1515_IRC_ENDO_Reaction_Pathway.gif|300px|thumb|centre|Figure 9: Animation of the Reaction Pathway of the Endothermic Reaction]] || [[File:Exo_IRC_Pathway_Ct1515.gif|300px|thumb|centre|Figure 10: Animation of the Reaction Pathway of the Exothermic Reaction]]
|}

The exo and endothermic reactions are both asynchronous as the bond with the oxygen forms with the carbon before the bond with the sulphur. The chelotropic reaction is however synchronous as the bonds form at the same time.
Xylylene is a very unstable molecule due to its lack of aromaticity across the molecule. Upon reaction in each of these pathways the product molecule has an aromatic 6 membered ring which greatly stabilizes the overall molecule. This can be seen in each of the IRC animations as the bond lengths and type of bonds change from the reactants to products. The double bond elongates to become an intermediate length between single and double bond character, characteristic of an aromatic bond length in a six membered ring.

===Thermochemistry===
[[File:Reaction_Diagram_Q3_ct1515.jpg|717x717px|thumb|Figure 7: Reaction scheme for the reaction Cyclohexadiene and 1,3-Dioxole|right]]
{| class="wikitable" border="1" align="center"
|+ Table 9: Table of Energies
! Molecule !! Energy (Hartrees) !! Energy (kJmol-1)
|-
| Xylylene (reactant) || 0.178279|| 468.072
|-
| SO2 (reactant)|| -0.118614 || -311.421
|-
|Combined Reactant Energy ||0.059665||156.651
|-
| Exo Transition State || 0.092077 || 241.748
|-
| Endo Transition State ||0.090559 || 237.763
|-
|Chelotropic Transition State ||0.099062 || 260.087
|-
| Exo Product ||0.021455 || 56.330
|-
| Endo Product ||0.021702 ||56.979
|-
| Chelotropic Product ||0.000000 || 0.000
|}

{| class="wikitable" border="1" align="center"
|+ Table 10: Table of Energies
! Type of reaction path !! Activation Energy (kJ mol-1)!! Energy of the Reaction (kJ mol-1)
|-
| Exothermic Route || 85.10 || -100.32
|-
| Endothermic Route || 81.11 || -99.68
|-
| Chelotropic Route || 94.44 || -156.65
|}

From these energies it can be noted that the reaction with the lowest activation barrier is the endothermic reaction. This is therefore the kinetic product of the reaction. The exothermic pathway gives a product with lower energy and therefore is the thermodynamic product.
When comparing all three however the chelotropic reaction has the lowest energy products.

===Further Investigation===
An investigation of the reaction of the other cis-butadiene molecule in the Xylylene was investigated and a comparison of the energies was under taken.
{|+ Table 11: IRC
|-
| [[File:Ct1515_Endo_IRC.gif|300px|thumb|centre|Figure 9: Animation of the Reaction Pathway of the Endothermic Reaction]] || [[File:Ct1515_Exo_IRC.gif|300px|thumb|centre|Figure 10: Animation of the Reaction Pathway of the Exothermic Reaction]]
|}

{| class="wikitable" border="1" align="center"
|+ Table 12: Table of Energies
! Molecule !! Energy (Hartrees) !! Energy (kJmol-1)
|-
|Combined Reactant Energy ||0.059665||156.651
|-
| Exo Transition State || 0.105052 ||
|-
| Endo Transition State || 0.102071 ||
|-
| Exo Product ||0.067304 ||
|-
| Endo Product ||0.102074 ||
|}

{| class="wikitable" border="1" align="center"
|+ Table 13: Table of Energies
! Type of reaction path !! Activation Energy (kJ mol-1)!! Energy of the Reaction (kJ mol-1)
|-
| Exothermic Route || ||
|-
| Endothermic Route || ||
|}

==Appendix==
===Exercise 1 (log files)===
[[Media:CT1515_BUTADIENE_OPT_PM6.LOG| Butadiene (Opt to Minimum (reactant)) PM6]]

[[Media:CT1515_ETHENE_OPT_PM6.LOG| Ethene (Opt to Minimum (reactant)) PM6]]

[[Media:CT1515_CYCLOHEXENE_OPT_TO_MIN_PM6_2-1.LOG| Cyclohexene (Opt to minimum) PM6]]

[[Media:CT1515 CYCLOHEXENE OPT TO TS PM6 2-1.LOG| Cyclohexene (Opt to TS) PM6]]

[[Media:CT1515_CYCLOHEXENE_IRC_PM6_2-1.LOG| Cyclohexene (IRC) PM6]]

===Exercise 2 (log files)===
[[Media:CT1515MOLECULE 1 OPT B3LYP 1-1.LOG| Cyclohexadiene (Reactant) B3LYP]]

[[Media:Ct1515_1-3_DIOXOLE_B3LYP.LOG| 1,3-Dioxole (Reactant) B3LYP]]

[[Media:Ct1515_OPT_ENDO_TO_TS_B31G_2-2.LOG| Endothermic (TS) B3LYP]]

[[Media:Ct1515_IRC_PM6_ENDO_2-2.LOG| Endothermic (IRC) PM6]]

[[Media:Q2_exo_CT1515_OPT_TO_TS_B3613G_1-3.LOG| Exothermic (TS) B3LYP]]

[[Media:Ct1515_exo_IRC_100_NEVER_TS_1-1.LOG| Exothermic (IRC) PM6]]

[[Media:Ct1515_(GOOD)_Q2_PRODUCT_OPT_B3LYP_1-3.LOG| Exothermic (Product) B3LYP]]

[[Media:CT1515_ENDO_PRODUCT_OPT_B3LYP.LOG| Endothermic (Product) B3LYP]]

===Exercise 3 (log files)===
[[Media:Ct1515_SO2_OPT_TO_MINPM6.LOG| SO2 (Reactant) PM6]]

[[Media:Ct1515_XYLYLENE_OPT_TO_MIN.LOG| Xylylene (Reactant) PM6]]

[[Media:CT1515OPT_TO_TS_Endo_PM6_XYL_1-1.LOG| Endothermic (TS) PM6]]

[[Media:Ct1515IRC_TS_ENDO_PM6_XYL_1-1.LOG| Endothermic (IRC) PM6]]

[[Media:Ct1515OPT_TO_TS_EXO_PM6_XYL_1-1.LOG| Exothermic (TS) PM6]]

[[Media:Ct1515_IRC_TS_EXO_PM6_XYL_1-1.LOG| Exothermic (IRC) PM6]]

[[Media:Ct1515OPT_TO_TS_C_3-1.LOG| Chelotropic (TS) PM6]]

[[Media:Ct1515_IRC_TS_C_3-1.LOG| Chelotropic (IRC) PM6]]

[[Media:PRODUCTS_TS_EXO_PM6_XYL_1-1.LOG| Exothermic (Product) PM6]]

[[Media:CT1515 PRODUCT ENDO PM6 XYL 1-1.LOG| Endothermic (Product) PM6]]

[[Media:Ct1515_PRODUCT_OPT_TO_MIN_PM6_C_3-1.LOG| Chelotropic (Product) PM6]]

====Futher investigation (log files)====
[[Media:Ct1515_Exo_TOWARDS_REST_OF_MOLECULE_TS_OPT.LOG| Exothermic (TS) PM6]]

[[Media:Ct1515_Exo_TOWARDS_REST_OF_MOLECULE_TS_IRC.LOG| Exothermic (IRC) PM6]]

[[Media:Ct1515_Endo_AWAY_FROM_REST_OF_MOLECULE_OPT_TS_1-2.LOG| Endothermic (TS) PM6]]

[[Media:Ct1515_Endo_AWAY_FROM_REST_OF_MOLECULE_IRC_TS_1-2.LOG| Endothermic (IRC) PM6]]

[[Media:Ct1515Exo_TOWARDS_REST_OF_MOLECULE_PRODUCT_OPT1.LOG| Exothermic (Product) PM6]]

[[Media:Ct1515_Endo_AWAY_FROM_REST_OF_MOLECULE_PRODUCT_OPT.LOG| Endothermic (Product) PM6]]