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Rep:Mod:ts.scc215

2017-11-08T11:58:21Z

Scc215: /* Calculation */

== Third Year Computational Lab: Transitional States and Reactivity ==
=== Introduction ===
[[File:Potential Energy Surface and Corresponding Reaction Coordinate Diagram scc215.png|thumb|450x450px|Fig. 1 Example of Potential Energy Surface describing reaction of A+B to C]]
A Potential Energy Surface (Fig. 1) is a landscape about that shows various reaction pathway of completing a reaction from reactants to materials. It always possesses dimension numbers of 3N-6 for N standing for the number of molecules involved. A minimum could be divided into two categories, local minima and global minimum under the context of PES. Multiple local minima could exist on the PES, and reactants are normally located on one of them, while global minimum on PES often refers to the location of the most thermodynamic stable product. For a local minimum, it satisfies the following prerequisites: <math>{ \partial V\over \partial (r_i)} = 0</math> and <math>{ \partial^2 V\over \partial (r_i)^2} > 0</math>, which also defines minimum as one of the critical points of the function.

The transition state is one of the local maximum located on minimum energy pathway, and it is the position which most of the reaction pathways passes through. The derivative of the function at TS also showed <math>{ \partial V\over \partial (r_i)} = 0</math> since it is also one of the critical points of the function. <math> V=f(r_i) </math>. However, TS could be distinguished from local minimums since it has a negative second derivative <math>{ \partial^2 V\over \partial (r_i)^2} < 0</math>and thus indicated a correctly optimized reactant and product should have all positive frequencies while a TS should show one imaginary frequency as the result.

== Exercise 1: Reaction of Butadiene with Ethylene ==
[[File:D-a ex1 reaction scheme scc215.png|centre|thumb|826x826px|Fig. 2 Reaction Scheme of Diels-Alder reaction between Butadiene and Ethylene]]

In this reaction, a [4+2] cycloaddition was simulated on Gaussian and the interactions between frontier orbitals have been investigated to determine if the reaction is normal demand or inverse demand DA reaction.

=== MO diagram of frontier orbitals and qualitative energy levels of reaction ===
[[File:Normal demad d-a mo diagram scc215.png|thumb|490x490px|Fig. 3 The qualitative MO diagram showing the frontier orbitals of TS and all molecules involved]]
Using the energy levels listed in checkpoint files of molecules and transition states, a molecule diagram was produced. It has clearly shown that the reaction is normal demand since the gap between LUMO of butadiene and HOMO of ethylene is large such that the overlap between these two is poor. As a result, the reaction is completed through the domination of better-overlapped HOMO of butadiene and LUMO of ethylene. For such bond-forming reaction to proceed, the positive phase of molecular orbitals must overlap, i.e. only symmetric-symmetric reactions and asymmetric-asymmetric overlap are allowed and the rest are forbidden. This means the orbital overlap integrals of symmetric-symmetric and that of asymmetric-asymmetric interactions are non-zero while that of asymmetric-symmetric interactions are zero.

=== Variation of C-C bond length and their comparison to different types of C-C bond ===
[[File:Product bond length scc215.png|left|thumb|Fig. 4 Legend of each corresponding carbon atom]]

{| class="wikitable"
|+Table 1 Variation of the 6 C-C bonds involved in the reaction
!Bond Length (Å)
!C1-C4
!C4-C5
!C5-C6
!C6-C11
!C11-C14
!C14-C1
|-
|Butadiene
|1.335
|1.468
|1.335
|
|
|
|-
|Ethylene
|
|
|
|
|1.331
|
|-
|Transition State
|1.379
|1.411
|1.379
|2.115
|1.381
|2.115
|-
|Product
|1.492
|1.331
|1.492
|1.536
|1.537
|1.536
|}
The two tables have summarized the change of bond length throughout the reaction. Three double bonds in original reactants (C1-C4, C5-C6, C11-C14) has increased the bond length to 1.492 Å and 1.537 Å respectively since their bond order has been reduced to 1 in the product. Bond C4-C5 has decreased in bond length since it has become a C-C double bond instead of a single bond. C6-C11 and C14-C1 are the two newly formed bonds in the product such that the distance between carbon atoms has decreased from 3.4 Å to 1.536 Å which is similar to the length of a sp3C-sp3 C bond. At TS, the originally existing bonds have their length located between 1.379 to 1.411 Å, which are between a pure sp3C-sp3C bond length and sp2C-sp2C bond length and also shorter than sp3C-sp2C bond.
{| class="wikitable"
|+Table 2 Typical C-C bond and Carbon atom Van der Waals Radius [1][2]
!sp3C-sp3C Bond length (Å)
!Error (Å)
!sp2C-sp2C Bond length (Å)
!Error (Å)
|-
|1.526 (propane) or

1.525 (isobutane)
|0.002
|1.338
|0.002
|-
| colspan="4" |Carbon atom Van der Waals Radius: 1.700 Å
|-
| colspan="4" |
|}
{| class="wikitable"
|+Table 3 Variation of C-C bond length against Intrinsic Reaction Coordinate
! colspan="4" |C-C bond
|-
|C1-C4
|[[File:1,4 scc215.png|frameless|500x500px]]
|C6-C11
|[[File:11,6 scc215.png|frameless|500x500px]]
|-
|C4-C5
|[[File:4,5 scc215.png|frameless|500x500px]]
|C11-C14
|[[File:14,11 scc215.png|frameless|500x500px]]
|-
|C5-C6
|[[File:5,6 scc215.png|frameless|500x500px]]
|C14-C1
|[[File:1,14 scc215.png|frameless|500x500px]]
|}

=== Vibration in Imaginary frequency of TS ===
[[File:Ts scc215.gif|thumb|450x450px|Fig. 5 Bond forming process corresponding to the report imaginary vibration frequency]]
From the processed simulation, only one single imaginary vibration frequency at 948.9i cm-1 was reported, which stands for the synchronous bond formation process during the Diels-Alder reaction.

=== Calculation ===
[[File:Final irc scc215.log]][[File:FINISHED TS FOR IRC scc215.LOG]][[File:ETHENE scc215.LOG]][[File:BUTADIENE scc215.LOG]]

== Exercise 2: Reaction between Cyclohexadiene and 1,3-dioxole ==
[[File:Part 2 reaction scheme scc215.png|centre|thumb|585x585px|Fig. 6 Reaction Scheme for both exo and endo product formation]][[File:Part 2 exo mo diagram scc215.png|left|thumb|496x496px|Fig.7 MO diagram of frontier orbitals during formation of exo product]][[File:Part 2 endo mo diagram scc215.png|thumb|501x501px|Fig. 8 MO diagram of the frontier orbitals forming the endo product]]
=== MO diagram of Exo and Endo reaction pathways ===
Similar to all the other [4+2] cycloaddition, the reaction is controlled by the overlap of frontier orbitals of diene and dienophile molecule respectively. As discussed above, the overlap integral is non-zero (i.e. reaction allowed) only if the symmetrical element is identical. Hence, in this case, the overlap between LUMO of cyclohexadiene and HOMO of 1,3-dioxole dominates the reaction since the energy gap between is much smaller than the other energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Thus this reaction, regardless of endo or exo reaction, is an inverse electron demand DA reaction.
=== Which one is more favourable? Endo product vs Exo product ===
{| class="wikitable"
|+Table 4 Gibbs Free energies of reaction
!Energies (Hatrees/molecule)
!Cyclohexadiene
!1,3-dioxole
!TS
!Product
|-
|'''Sum of electronic and thermal Free Energies of Endo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.395506</nowiki>
|}
|
{|
|<nowiki>-500.436135</nowiki>
|}
|-
|'''Sum of electronic and thermal Free Energies of Exo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.348863</nowiki>
|}
|
{|
|<nowiki>-500.434789</nowiki>
|}
|-

|}

==== Endo Reaction Energies ====
Activation Energy: [-500.395506-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 3.80459075 kJ/mol

Reaction Energy: [-500.436135-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -21.69049711 kJ/mol

==== Exo Reaction Energies ====
Activation Energy: [-500.348863-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 138.379614 kJ/mol

Reaction Energy: [-500.434789-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -87.2191166 kJ/mol

==== Explanation of the result ====
As shown in the calculated result, considering both thermodynamic and kinetic aspect, endo product formation is more favourable in this reaction than the exo form. This could be shown by the lower reaction barrier of endo TS from reactant and the more negative reaction energy of endo product from the reactants. This could possibly be explained by the Secondary Orbital Interaction occurring exclusively in endo transition state. For the endo TS, secondary orbital interaction occurs on the overlap of positive phases between the p-orbitals of newly-formed pi system on diene and empty p-orbital of two oxygen atoms, while the strong primary interaction still occurs on both endo and exo state. As a result, endo state has become a both thermodynamically and kinetically stable product.
[[File:Part 2 energy profile scc215.png|thumb|400x400px|Fig. 9 Qualitative energy profile comparing between the two reaction pathways]]

=== Calculations ===
[[File:Exo ts 631 scc215.log]][[File:Endo 631 scc215.log]][[File:Exo product scc215.log]][[File:13 dioxole scc215.log]][[File:Diene 631 scc215.log]][[File:Endo_ts_631 scc215.log]]

== Exercise 3: Exercise 3: Diels-Alder vs Cheletropic ==
[[File:Part 3 reaction scheme scc215.png|centre|thumb|450x450px|Fig. 10 Reaction scheme of both Diels-Alder Reaction and Cheletropic reaction]]

=== Optimized TS with corresponding frequencies and Product via two pathways ===
{| class="wikitable"
!Pathway
!Vibration
!Shape of product
|-
|Endo Diels-Alder
|[[File:Endo ts scc215.gif|thumb|637x637px|Imaginary frequency at 333.69i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Exo Diels-Alder
|[[File:Exo ts scc215.gif|thumb|637x637px|Imaginary frequency at 351.63i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Cheletropic
|[[File:Cheletropic ts scc215.gif|thumb|637x637px|Imaginary frequency at 486.80i cm]]
|[[File:Cheletropic adduct scc215.gif.png|thumb|426x426px]]
|}

=== IRC calculated for each possible pathway ===
As shown in the IRC animation in Table 5, the C-S and C-O bond formation in Diels-Alder reactions are asynchronous while the formation of two C-S bonds are synchronous. It is possibly believed to be related to the difference of van der waals radius in oxygen and sulphur respectively. Sulphur has a larger radius such that the C-S is easier to form than C-O bond.
{| class="wikitable"
|+Table 5 IRC animation of all possible pathways
!Pathway
!Animation of IRC
|-
|Endo Diels-Alder
|[[File:Endo irc scc215.gif|thumb|637x637px]]
|-
|Exo Diels-Alder
|[[File:Exo irc scc215.gif|thumb|637x637px]]
|-
|Cheletropic
|[[File:Cheletropic irc scc215.gif|thumb|637x637px]]
|}

=== Energy Profile and Energies ===
[[File:Part 3 energy profile scc215.png|thumb|567x567px|Fig.11 Quantitative reaction profile comparing three possible pathways]]
Reaction profiles are constructed using the calculated energy extracted from IRC log files. Since zero was set to be the energy level when the reactant have infinite separation (i.e. reactant energy level = 0 Hatrees), table 6 is showing the corrected relative energy with reference to the zero set.
{| class="wikitable"
|+Table 6 Corrected Energies of each pathway
!Corrected Energies (Hatrees/molecule)
!Reactants
!TS
!Product
|-
|Endo Diels-Alder
|0
|
{|
|0.00764995
|}
|
{|
|<nowiki>-0.06415</nowiki>
|}
|-
|Exo Diels-Alder
|0
|
{|
|0.00955814
|}
|
{|
|<nowiki>-0.06559</nowiki>
|}
|-
|Cheletropic
|0
|
{|
|0.01739184
|}
|
{|
|<nowiki>-0.08815</nowiki>
|}
|}

=== Calculated Reaction energies and Reaction Barrier ===

==== Endo Diels-Alder Reaction ====
Reaction Energy:-0.06415*4.3597439422E-18/1000*6.02E-23 = -168.42715058 kJ/mol

Activation Energy:0.00764995*4.3597439422E-18/1000*6.02E-23 = 20.084945255 kJ/mol

==== Exo Diels-Alder Reaction ====
Reaction Energy: -0.06559*4.3597439422E-18/1000*6.02E-23 = -172.1934306 kJ/mol

Activation Energy: 0.00955814*4.3597439422E-18/1000*6.02E-23 = 25.094898482 kJ/mol

==== Cheletropic Reaction ====
Reaction Energy:-0.08815 *4.3597439422E-18/1000*6.02E-23 = -231.45070758 kJ/mol

Activation Energy: 0.01739184*4.3597439422E-18/1000*6.02E-23 = 45.662279398 kJ/mol

Base on the calculations made above, the endo D-A reaction is found to be the most kinetically stable reaction, while the cheletropic reaction is the most thermodynamically favoured reaction with a reaction energy as negative as -231.45070758 kJ/mol yet with the highest energy barrier to reach the TS. This is due to the synchronous bond formation would reduce the O-S-O bond angle such that they would experience unfavourable electron-electron repulsion. On the other hand, a 5-member heterocycle formation will lead to a less strained ring than a hydrocarbon cyclic structure since the van der waals radius of S is larger than C atom, such that the ring formation becomes more stable.

=== Unstable o-xylylene molecule and second possible site of D-A addition ===
[[File:Xylylene self scc215.png|centre|thumb|772x772px|Fig. 12 Alternative electrocyclic reaction carried out by xylylene molecule]]As shown in Fig. 12, there is a possibility for xylylene molecule to undergo a 4-pi electrocyclic reaction to form benzocyclobutene especially in the presence of heat.[3] This is due to the 6 member ring will turn into a 6-pi delocalised electron system after any reaction take place in the diene position, such that the product is more stabilized and favoured to be formed rather than staying as o-xylylene form.

=== Calculations ===
[[File:CHELETROPIC TS scc215.LOG ]][[File:EXO TS2 scc215.LOG]][[File:ENDO TS scc215.LOG]][[File:final endo irc scc215.log]][[File:final exo irc scc215.log]][[File:final cheletropic scc215.log]]

== Conclusion ==
The experiment has given a brief introduction to use computational environment for simulation of reactions and analysis of PES. It has shown several pros and cons by such method.

Although the computational simulation has been more efficient and accurate than traditional measurement and bench work method to predict and analyze a reaction, like simulate the energy level and structure of TS during a reaction which might be impossible to isolate the reaction, the method still has a strong limitation is that it does not take the practicability of reaction in to account. Take the Diels-Alder reaction in exercise 1 for example, although Gaussian could run a simulation on the reaction given that the orbitals and conformation are correct, it still neglected the presence of heat during the reaction. Hence, it is generally believed that butadiene is a poor diene and ethylene is a poor dienophile with wide energy gap to cause a poor overlap for the formation of product.It is also believed that the butadiene will adopt a trans-conformation to minimize the steric clash such that the reaction is impractical in reality.

== Reference ==
1.D. Lide, ''Tetrahedron'', '''1962''', 17, 125-134.

2.A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.

3. Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.

Rep:Mod:ts.scc215

2017-11-08T11:58:03Z

File:Endo ts 631 scc215.log

2017-11-08T11:52:19Z

Scc215:

Rep:Mod:ts.scc215

2017-11-08T11:44:08Z

Scc215: /* Calculations */

== Third Year Computational Lab: Transitional States and Reactivity ==
=== Introduction ===
[[File:Potential Energy Surface and Corresponding Reaction Coordinate Diagram scc215.png|thumb|450x450px|Fig. 1 Example of Potential Energy Surface describing reaction of A+B to C]]
A Potential Energy Surface (Fig. 1) is a landscape about that shows various reaction pathway of completing a reaction from reactants to materials. It always possesses dimension numbers of 3N-6 for N standing for the number of molecules involved. A minimum could be divided into two categories, local minima and global minimum under the context of PES. Multiple local minima could exist on the PES, and reactants are normally located on one of them, while global minimum on PES often refers to the location of the most thermodynamic stable product. For a local minimum, it satisfies the following prerequisites: <math>{ \partial V\over \partial (r_i)} = 0</math> and <math>{ \partial^2 V\over \partial (r_i)^2} > 0</math>, which also defines minimum as one of the critical points of the function.

The transition state is one of the local maximum located on minimum energy pathway, and it is the position which most of the reaction pathways passes through. The derivative of the function at TS also showed <math>{ \partial V\over \partial (r_i)} = 0</math> since it is also one of the critical points of the function. <math> V=f(r_i) </math>. However, TS could be distinguished from local minimums since it has a negative second derivative <math>{ \partial^2 V\over \partial (r_i)^2} < 0</math>and thus indicated a correctly optimized reactant and product should have all positive frequencies while a TS should show one imaginary frequency as the result.

== Exercise 1: Reaction of Butadiene with Ethylene ==
[[File:D-a ex1 reaction scheme scc215.png|centre|thumb|826x826px|Fig. 2 Reaction Scheme of Diels-Alder reaction between Butadiene and Ethylene]]

In this reaction, a [4+2] cycloaddition was simulated on Gaussian and the interactions between frontier orbitals have been investigated to determine if the reaction is normal demand or inverse demand DA reaction.

=== MO diagram of frontier orbitals and qualitative energy levels of reaction ===
[[File:Normal demad d-a mo diagram scc215.png|thumb|490x490px|Fig. 3 The qualitative MO diagram showing the frontier orbitals of TS and all molecules involved]]
Using the energy levels listed in checkpoint files of molecules and transition states, a molecule diagram was produced. It has clearly shown that the reaction is normal demand since the gap between LUMO of butadiene and HOMO of ethylene is large such that the overlap between these two is poor. As a result, the reaction is completed through the domination of better-overlapped HOMO of butadiene and LUMO of ethylene. For such bond-forming reaction to proceed, the positive phase of molecular orbitals must overlap, i.e. only symmetric-symmetric reactions and asymmetric-asymmetric overlap are allowed and the rest are forbidden. This means the orbital overlap integrals of symmetric-symmetric and that of asymmetric-asymmetric interactions are non-zero while that of asymmetric-symmetric interactions are zero.

=== Variation of C-C bond length and their comparison to different types of C-C bond ===
[[File:Product bond length scc215.png|left|thumb|Fig. 4 Legend of each corresponding carbon atom]]

{| class="wikitable"
|+Table 1 Variation of the 6 C-C bonds involved in the reaction
!Bond Length (Å)
!C1-C4
!C4-C5
!C5-C6
!C6-C11
!C11-C14
!C14-C1
|-
|Butadiene
|1.335
|1.468
|1.335
|
|
|
|-
|Ethylene
|
|
|
|
|1.331
|
|-
|Transition State
|1.379
|1.411
|1.379
|2.115
|1.381
|2.115
|-
|Product
|1.492
|1.331
|1.492
|1.536
|1.537
|1.536
|}
The two tables have summarized the change of bond length throughout the reaction. Three double bonds in original reactants (C1-C4, C5-C6, C11-C14) has increased the bond length to 1.492 Å and 1.537 Å respectively since their bond order has been reduced to 1 in the product. Bond C4-C5 has decreased in bond length since it has become a C-C double bond instead of a single bond. C6-C11 and C14-C1 are the two newly formed bonds in the product such that the distance between carbon atoms has decreased from 3.4 Å to 1.536 Å which is similar to the length of a sp3C-sp3 C bond. At TS, the originally existing bonds have their length located between 1.379 to 1.411 Å, which are between a pure sp3C-sp3C bond length and sp2C-sp2C bond length and also shorter than sp3C-sp2C bond.
{| class="wikitable"
|+Table 2 Typical C-C bond and Carbon atom Van der Waals Radius [1][2]
!sp3C-sp3C Bond length (Å)
!Error (Å)
!sp2C-sp2C Bond length (Å)
!Error (Å)
|-
|1.526 (propane) or

1.525 (isobutane)
|0.002
|1.338
|0.002
|-
| colspan="4" |Carbon atom Van der Waals Radius: 1.700 Å
|-
| colspan="4" |
|}
{| class="wikitable"
|+Table 3 Variation of C-C bond length against Intrinsic Reaction Coordinate
! colspan="4" |C-C bond
|-
|C1-C4
|[[File:1,4 scc215.png|frameless|500x500px]]
|C6-C11
|[[File:11,6 scc215.png|frameless|500x500px]]
|-
|C4-C5
|[[File:4,5 scc215.png|frameless|500x500px]]
|C11-C14
|[[File:14,11 scc215.png|frameless|500x500px]]
|-
|C5-C6
|[[File:5,6 scc215.png|frameless|500x500px]]
|C14-C1
|[[File:1,14 scc215.png|frameless|500x500px]]
|}

=== Vibration in Imaginary frequency of TS ===
[[File:Ts scc215.gif|thumb|450x450px|Fig. 5 Bond forming process corresponding to the report imaginary vibration frequency]]
From the processed simulation, only one single imaginary vibration frequency at 948.9i cm-1 was reported, which stands for the synchronous bond formation process during the Diels-Alder reaction.

=== Calculation ===

== Exercise 2: Reaction between Cyclohexadiene and 1,3-dioxole ==
[[File:Part 2 reaction scheme scc215.png|centre|thumb|585x585px|Fig. 6 Reaction Scheme for both exo and endo product formation]][[File:Part 2 exo mo diagram scc215.png|left|thumb|496x496px|Fig.7 MO diagram of frontier orbitals during formation of exo product]][[File:Part 2 endo mo diagram scc215.png|thumb|501x501px|Fig. 8 MO diagram of the frontier orbitals forming the endo product]]
=== MO diagram of Exo and Endo reaction pathways ===
Similar to all the other [4+2] cycloaddition, the reaction is controlled by the overlap of frontier orbitals of diene and dienophile molecule respectively. As discussed above, the overlap integral is non-zero (i.e. reaction allowed) only if the symmetrical element is identical. Hence, in this case, the overlap between LUMO of cyclohexadiene and HOMO of 1,3-dioxole dominates the reaction since the energy gap between is much smaller than the other energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Thus this reaction, regardless of endo or exo reaction, is an inverse electron demand DA reaction.
=== Which one is more favourable? Endo product vs Exo product ===
{| class="wikitable"
|+Table 4 Gibbs Free energies of reaction
!Energies (Hatrees/molecule)
!Cyclohexadiene
!1,3-dioxole
!TS
!Product
|-
|'''Sum of electronic and thermal Free Energies of Endo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.395506</nowiki>
|}
|
{|
|<nowiki>-500.436135</nowiki>
|}
|-
|'''Sum of electronic and thermal Free Energies of Exo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.348863</nowiki>
|}
|
{|
|<nowiki>-500.434789</nowiki>
|}
|-

|}

==== Endo Reaction Energies ====
Activation Energy: [-500.395506-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 3.80459075 kJ/mol

Reaction Energy: [-500.436135-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -21.69049711 kJ/mol

==== Exo Reaction Energies ====
Activation Energy: [-500.348863-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 138.379614 kJ/mol

Reaction Energy: [-500.434789-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -87.2191166 kJ/mol

==== Explanation of the result ====
As shown in the calculated result, considering both thermodynamic and kinetic aspect, endo product formation is more favourable in this reaction than the exo form. This could be shown by the lower reaction barrier of endo TS from reactant and the more negative reaction energy of endo product from the reactants. This could possibly be explained by the Secondary Orbital Interaction occurring exclusively in endo transition state. For the endo TS, secondary orbital interaction occurs on the overlap of positive phases between the p-orbitals of newly-formed pi system on diene and empty p-orbital of two oxygen atoms, while the strong primary interaction still occurs on both endo and exo state. As a result, endo state has become a both thermodynamically and kinetically stable product.
[[File:Part 2 energy profile scc215.png|thumb|400x400px|Fig. 9 Qualitative energy profile comparing between the two reaction pathways]]

=== Calculations ===

== Exercise 3: Exercise 3: Diels-Alder vs Cheletropic ==
[[File:Part 3 reaction scheme scc215.png|centre|thumb|450x450px|Fig. 10 Reaction scheme of both Diels-Alder Reaction and Cheletropic reaction]]

=== Optimized TS with corresponding frequencies and Product via two pathways ===
{| class="wikitable"
!Pathway
!Vibration
!Shape of product
|-
|Endo Diels-Alder
|[[File:Endo ts scc215.gif|thumb|637x637px|Imaginary frequency at 333.69i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Exo Diels-Alder
|[[File:Exo ts scc215.gif|thumb|637x637px|Imaginary frequency at 351.63i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Cheletropic
|[[File:Cheletropic ts scc215.gif|thumb|637x637px|Imaginary frequency at 486.80i cm]]
|[[File:Cheletropic adduct scc215.gif.png|thumb|426x426px]]
|}

=== IRC calculated for each possible pathway ===
As shown in the IRC animation in Table 5, the C-S and C-O bond formation in Diels-Alder reactions are asynchronous while the formation of two C-S bonds are synchronous. It is possibly believed to be related to the difference of van der waals radius in oxygen and sulphur respectively. Sulphur has a larger radius such that the C-S is easier to form than C-O bond.
{| class="wikitable"
|+Table 5 IRC animation of all possible pathways
!Pathway
!Animation of IRC
|-
|Endo Diels-Alder
|[[File:Endo irc scc215.gif|thumb|637x637px]]
|-
|Exo Diels-Alder
|[[File:Exo irc scc215.gif|thumb|637x637px]]
|-
|Cheletropic
|[[File:Cheletropic irc scc215.gif|thumb|637x637px]]
|}

=== Energy Profile and Energies ===
[[File:Part 3 energy profile scc215.png|thumb|567x567px|Fig.11 Quantitative reaction profile comparing three possible pathways]]
Reaction profiles are constructed using the calculated energy extracted from IRC log files. Since zero was set to be the energy level when the reactant have infinite separation (i.e. reactant energy level = 0 Hatrees), table 6 is showing the corrected relative energy with reference to the zero set.
{| class="wikitable"
|+Table 6 Corrected Energies of each pathway
!Corrected Energies (Hatrees/molecule)
!Reactants
!TS
!Product
|-
|Endo Diels-Alder
|0
|
{|
|0.00764995
|}
|
{|
|<nowiki>-0.06415</nowiki>
|}
|-
|Exo Diels-Alder
|0
|
{|
|0.00955814
|}
|
{|
|<nowiki>-0.06559</nowiki>
|}
|-
|Cheletropic
|0
|
{|
|0.01739184
|}
|
{|
|<nowiki>-0.08815</nowiki>
|}
|}

=== Calculated Reaction energies and Reaction Barrier ===

==== Endo Diels-Alder Reaction ====
Reaction Energy:-0.06415*4.3597439422E-18/1000*6.02E-23 = -168.42715058 kJ/mol

Activation Energy:0.00764995*4.3597439422E-18/1000*6.02E-23 = 20.084945255 kJ/mol

==== Exo Diels-Alder Reaction ====
Reaction Energy: -0.06559*4.3597439422E-18/1000*6.02E-23 = -172.1934306 kJ/mol

Activation Energy: 0.00955814*4.3597439422E-18/1000*6.02E-23 = 25.094898482 kJ/mol

==== Cheletropic Reaction ====
Reaction Energy:-0.08815 *4.3597439422E-18/1000*6.02E-23 = -231.45070758 kJ/mol

Activation Energy: 0.01739184*4.3597439422E-18/1000*6.02E-23 = 45.662279398 kJ/mol

Base on the calculations made above, the endo D-A reaction is found to be the most kinetically stable reaction, while the cheletropic reaction is the most thermodynamically favoured reaction with a reaction energy as negative as -231.45070758 kJ/mol yet with the highest energy barrier to reach the TS. This is due to the synchronous bond formation would reduce the O-S-O bond angle such that they would experience unfavourable electron-electron repulsion. On the other hand, a 5-member heterocycle formation will lead to a less strained ring than a hydrocarbon cyclic structure since the van der waals radius of S is larger than C atom, such that the ring formation becomes more stable.

=== Unstable o-xylylene molecule and second possible site of D-A addition ===
[[File:Xylylene self scc215.png|centre|thumb|772x772px|Fig. 12 Alternative electrocyclic reaction carried out by xylylene molecule]]As shown in Fig. 12, there is a possibility for xylylene molecule to undergo a 4-pi electrocyclic reaction to form benzocyclobutene especially in the presence of heat.[3] This is due to the 6 member ring will turn into a 6-pi delocalised electron system after any reaction take place in the diene position, such that the product is more stabilized and favoured to be formed rather than staying as o-xylylene form.

=== Calculations ===
[[File:CHELETROPIC TS scc215.LOG ]][[File:EXO TS2 scc215.LOG]][[File:ENDO TS scc215.LOG]][[File:final endo irc scc215.log]][[File:final exo irc scc215.log]][[File:final cheletropic scc215.log]]

== Conclusion ==
The experiment has given a brief introduction to use computational environment for simulation of reactions and analysis of PES. It has shown several pros and cons by such method.

Although the computational simulation has been more efficient and accurate than traditional measurement and bench work method to predict and analyze a reaction, like simulate the energy level and structure of TS during a reaction which might be impossible to isolate the reaction, the method still has a strong limitation is that it does not take the practicability of reaction in to account. Take the Diels-Alder reaction in exercise 1 for example, although Gaussian could run a simulation on the reaction given that the orbitals and conformation are correct, it still neglected the presence of heat during the reaction. Hence, it is generally believed that butadiene is a poor diene and ethylene is a poor dienophile with wide energy gap to cause a poor overlap for the formation of product.It is also believed that the butadiene will adopt a trans-conformation to minimize the steric clash such that the reaction is impractical in reality.

== Reference ==
1.D. Lide, ''Tetrahedron'', '''1962''', 17, 125-134.

2.A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.

3. Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.

Rep:Mod:ts.scc215

2017-11-08T11:43:06Z

Scc215: /* Calculations */

== Third Year Computational Lab: Transitional States and Reactivity ==
=== Introduction ===
[[File:Potential Energy Surface and Corresponding Reaction Coordinate Diagram scc215.png|thumb|450x450px|Fig. 1 Example of Potential Energy Surface describing reaction of A+B to C]]
A Potential Energy Surface (Fig. 1) is a landscape about that shows various reaction pathway of completing a reaction from reactants to materials. It always possesses dimension numbers of 3N-6 for N standing for the number of molecules involved. A minimum could be divided into two categories, local minima and global minimum under the context of PES. Multiple local minima could exist on the PES, and reactants are normally located on one of them, while global minimum on PES often refers to the location of the most thermodynamic stable product. For a local minimum, it satisfies the following prerequisites: <math>{ \partial V\over \partial (r_i)} = 0</math> and <math>{ \partial^2 V\over \partial (r_i)^2} > 0</math>, which also defines minimum as one of the critical points of the function.

The transition state is one of the local maximum located on minimum energy pathway, and it is the position which most of the reaction pathways passes through. The derivative of the function at TS also showed <math>{ \partial V\over \partial (r_i)} = 0</math> since it is also one of the critical points of the function. <math> V=f(r_i) </math>. However, TS could be distinguished from local minimums since it has a negative second derivative <math>{ \partial^2 V\over \partial (r_i)^2} < 0</math>and thus indicated a correctly optimized reactant and product should have all positive frequencies while a TS should show one imaginary frequency as the result.

== Exercise 1: Reaction of Butadiene with Ethylene ==
[[File:D-a ex1 reaction scheme scc215.png|centre|thumb|826x826px|Fig. 2 Reaction Scheme of Diels-Alder reaction between Butadiene and Ethylene]]

In this reaction, a [4+2] cycloaddition was simulated on Gaussian and the interactions between frontier orbitals have been investigated to determine if the reaction is normal demand or inverse demand DA reaction.

=== MO diagram of frontier orbitals and qualitative energy levels of reaction ===
[[File:Normal demad d-a mo diagram scc215.png|thumb|490x490px|Fig. 3 The qualitative MO diagram showing the frontier orbitals of TS and all molecules involved]]
Using the energy levels listed in checkpoint files of molecules and transition states, a molecule diagram was produced. It has clearly shown that the reaction is normal demand since the gap between LUMO of butadiene and HOMO of ethylene is large such that the overlap between these two is poor. As a result, the reaction is completed through the domination of better-overlapped HOMO of butadiene and LUMO of ethylene. For such bond-forming reaction to proceed, the positive phase of molecular orbitals must overlap, i.e. only symmetric-symmetric reactions and asymmetric-asymmetric overlap are allowed and the rest are forbidden. This means the orbital overlap integrals of symmetric-symmetric and that of asymmetric-asymmetric interactions are non-zero while that of asymmetric-symmetric interactions are zero.

=== Variation of C-C bond length and their comparison to different types of C-C bond ===
[[File:Product bond length scc215.png|left|thumb|Fig. 4 Legend of each corresponding carbon atom]]

{| class="wikitable"
|+Table 1 Variation of the 6 C-C bonds involved in the reaction
!Bond Length (Å)
!C1-C4
!C4-C5
!C5-C6
!C6-C11
!C11-C14
!C14-C1
|-
|Butadiene
|1.335
|1.468
|1.335
|
|
|
|-
|Ethylene
|
|
|
|
|1.331
|
|-
|Transition State
|1.379
|1.411
|1.379
|2.115
|1.381
|2.115
|-
|Product
|1.492
|1.331
|1.492
|1.536
|1.537
|1.536
|}
The two tables have summarized the change of bond length throughout the reaction. Three double bonds in original reactants (C1-C4, C5-C6, C11-C14) has increased the bond length to 1.492 Å and 1.537 Å respectively since their bond order has been reduced to 1 in the product. Bond C4-C5 has decreased in bond length since it has become a C-C double bond instead of a single bond. C6-C11 and C14-C1 are the two newly formed bonds in the product such that the distance between carbon atoms has decreased from 3.4 Å to 1.536 Å which is similar to the length of a sp3C-sp3 C bond. At TS, the originally existing bonds have their length located between 1.379 to 1.411 Å, which are between a pure sp3C-sp3C bond length and sp2C-sp2C bond length and also shorter than sp3C-sp2C bond.
{| class="wikitable"
|+Table 2 Typical C-C bond and Carbon atom Van der Waals Radius [1][2]
!sp3C-sp3C Bond length (Å)
!Error (Å)
!sp2C-sp2C Bond length (Å)
!Error (Å)
|-
|1.526 (propane) or

1.525 (isobutane)
|0.002
|1.338
|0.002
|-
| colspan="4" |Carbon atom Van der Waals Radius: 1.700 Å
|-
| colspan="4" |
|}
{| class="wikitable"
|+Table 3 Variation of C-C bond length against Intrinsic Reaction Coordinate
! colspan="4" |C-C bond
|-
|C1-C4
|[[File:1,4 scc215.png|frameless|500x500px]]
|C6-C11
|[[File:11,6 scc215.png|frameless|500x500px]]
|-
|C4-C5
|[[File:4,5 scc215.png|frameless|500x500px]]
|C11-C14
|[[File:14,11 scc215.png|frameless|500x500px]]
|-
|C5-C6
|[[File:5,6 scc215.png|frameless|500x500px]]
|C14-C1
|[[File:1,14 scc215.png|frameless|500x500px]]
|}

=== Vibration in Imaginary frequency of TS ===
[[File:Ts scc215.gif|thumb|450x450px|Fig. 5 Bond forming process corresponding to the report imaginary vibration frequency]]
From the processed simulation, only one single imaginary vibration frequency at 948.9i cm-1 was reported, which stands for the synchronous bond formation process during the Diels-Alder reaction.

=== Calculation ===

== Exercise 2: Reaction between Cyclohexadiene and 1,3-dioxole ==
[[File:Part 2 reaction scheme scc215.png|centre|thumb|585x585px|Fig. 6 Reaction Scheme for both exo and endo product formation]][[File:Part 2 exo mo diagram scc215.png|left|thumb|496x496px|Fig.7 MO diagram of frontier orbitals during formation of exo product]][[File:Part 2 endo mo diagram scc215.png|thumb|501x501px|Fig. 8 MO diagram of the frontier orbitals forming the endo product]]
=== MO diagram of Exo and Endo reaction pathways ===
Similar to all the other [4+2] cycloaddition, the reaction is controlled by the overlap of frontier orbitals of diene and dienophile molecule respectively. As discussed above, the overlap integral is non-zero (i.e. reaction allowed) only if the symmetrical element is identical. Hence, in this case, the overlap between LUMO of cyclohexadiene and HOMO of 1,3-dioxole dominates the reaction since the energy gap between is much smaller than the other energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Thus this reaction, regardless of endo or exo reaction, is an inverse electron demand DA reaction.
=== Which one is more favourable? Endo product vs Exo product ===
{| class="wikitable"
|+Table 4 Gibbs Free energies of reaction
!Energies (Hatrees/molecule)
!Cyclohexadiene
!1,3-dioxole
!TS
!Product
|-
|'''Sum of electronic and thermal Free Energies of Endo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.395506</nowiki>
|}
|
{|
|<nowiki>-500.436135</nowiki>
|}
|-
|'''Sum of electronic and thermal Free Energies of Exo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.348863</nowiki>
|}
|
{|
|<nowiki>-500.434789</nowiki>
|}
|-

|}

==== Endo Reaction Energies ====
Activation Energy: [-500.395506-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 3.80459075 kJ/mol

Reaction Energy: [-500.436135-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -21.69049711 kJ/mol

==== Exo Reaction Energies ====
Activation Energy: [-500.348863-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 138.379614 kJ/mol

Reaction Energy: [-500.434789-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -87.2191166 kJ/mol

==== Explanation of the result ====
As shown in the calculated result, considering both thermodynamic and kinetic aspect, endo product formation is more favourable in this reaction than the exo form. This could be shown by the lower reaction barrier of endo TS from reactant and the more negative reaction energy of endo product from the reactants. This could possibly be explained by the Secondary Orbital Interaction occurring exclusively in endo transition state. For the endo TS, secondary orbital interaction occurs on the overlap of positive phases between the p-orbitals of newly-formed pi system on diene and empty p-orbital of two oxygen atoms, while the strong primary interaction still occurs on both endo and exo state. As a result, endo state has become a both thermodynamically and kinetically stable product.
[[File:Part 2 energy profile scc215.png|thumb|400x400px|Fig. 9 Qualitative energy profile comparing between the two reaction pathways]]

=== Calculations ===

== Exercise 3: Exercise 3: Diels-Alder vs Cheletropic ==
[[File:Part 3 reaction scheme scc215.png|centre|thumb|450x450px|Fig. 10 Reaction scheme of both Diels-Alder Reaction and Cheletropic reaction]]

=== Optimized TS with corresponding frequencies and Product via two pathways ===
{| class="wikitable"
!Pathway
!Vibration
!Shape of product
|-
|Endo Diels-Alder
|[[File:Endo ts scc215.gif|thumb|637x637px|Imaginary frequency at 333.69i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Exo Diels-Alder
|[[File:Exo ts scc215.gif|thumb|637x637px|Imaginary frequency at 351.63i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Cheletropic
|[[File:Cheletropic ts scc215.gif|thumb|637x637px|Imaginary frequency at 486.80i cm]]
|[[File:Cheletropic adduct scc215.gif.png|thumb|426x426px]]
|}

=== IRC calculated for each possible pathway ===
As shown in the IRC animation in Table 5, the C-S and C-O bond formation in Diels-Alder reactions are asynchronous while the formation of two C-S bonds are synchronous. It is possibly believed to be related to the difference of van der waals radius in oxygen and sulphur respectively. Sulphur has a larger radius such that the C-S is easier to form than C-O bond.
{| class="wikitable"
|+Table 5 IRC animation of all possible pathways
!Pathway
!Animation of IRC
|-
|Endo Diels-Alder
|[[File:Endo irc scc215.gif|thumb|637x637px]]
|-
|Exo Diels-Alder
|[[File:Exo irc scc215.gif|thumb|637x637px]]
|-
|Cheletropic
|[[File:Cheletropic irc scc215.gif|thumb|637x637px]]
|}

=== Energy Profile and Energies ===
[[File:Part 3 energy profile scc215.png|thumb|567x567px|Fig.11 Quantitative reaction profile comparing three possible pathways]]
Reaction profiles are constructed using the calculated energy extracted from IRC log files. Since zero was set to be the energy level when the reactant have infinite separation (i.e. reactant energy level = 0 Hatrees), table 6 is showing the corrected relative energy with reference to the zero set.
{| class="wikitable"
|+Table 6 Corrected Energies of each pathway
!Corrected Energies (Hatrees/molecule)
!Reactants
!TS
!Product
|-
|Endo Diels-Alder
|0
|
{|
|0.00764995
|}
|
{|
|<nowiki>-0.06415</nowiki>
|}
|-
|Exo Diels-Alder
|0
|
{|
|0.00955814
|}
|
{|
|<nowiki>-0.06559</nowiki>
|}
|-
|Cheletropic
|0
|
{|
|0.01739184
|}
|
{|
|<nowiki>-0.08815</nowiki>
|}
|}

=== Calculated Reaction energies and Reaction Barrier ===

==== Endo Diels-Alder Reaction ====
Reaction Energy:-0.06415*4.3597439422E-18/1000*6.02E-23 = -168.42715058 kJ/mol

Activation Energy:0.00764995*4.3597439422E-18/1000*6.02E-23 = 20.084945255 kJ/mol

==== Exo Diels-Alder Reaction ====
Reaction Energy: -0.06559*4.3597439422E-18/1000*6.02E-23 = -172.1934306 kJ/mol

Activation Energy: 0.00955814*4.3597439422E-18/1000*6.02E-23 = 25.094898482 kJ/mol

==== Cheletropic Reaction ====
Reaction Energy:-0.08815 *4.3597439422E-18/1000*6.02E-23 = -231.45070758 kJ/mol

Activation Energy: 0.01739184*4.3597439422E-18/1000*6.02E-23 = 45.662279398 kJ/mol

Base on the calculations made above, the endo D-A reaction is found to be the most kinetically stable reaction, while the cheletropic reaction is the most thermodynamically favoured reaction with a reaction energy as negative as -231.45070758 kJ/mol yet with the highest energy barrier to reach the TS. This is due to the synchronous bond formation would reduce the O-S-O bond angle such that they would experience unfavourable electron-electron repulsion. On the other hand, a 5-member heterocycle formation will lead to a less strained ring than a hydrocarbon cyclic structure since the van der waals radius of S is larger than C atom, such that the ring formation becomes more stable.

=== Unstable o-xylylene molecule and second possible site of D-A addition ===
[[File:Xylylene self scc215.png|centre|thumb|772x772px|Fig. 12 Alternative electrocyclic reaction carried out by xylylene molecule]]As shown in Fig. 12, there is a possibility for xylylene molecule to undergo a 4-pi electrocyclic reaction to form benzocyclobutene especially in the presence of heat.[3] This is due to the 6 member ring will turn into a 6-pi delocalised electron system after any reaction take place in the diene position, such that the product is more stabilized and favoured to be formed rather than staying as o-xylylene form.

=== Calculations ===
[[File:CHELETROPIC TS scc215.LOG ]][[File:EXO TS2 scc215.LOG]][[ENDO TS scc215.LOG]][[File:final endo irc scc215.log]][[File:final exo irc scc215.log]][[File:final cheletropic scc215.log]]

== Conclusion ==
The experiment has given a brief introduction to use computational environment for simulation of reactions and analysis of PES. It has shown several pros and cons by such method.

Although the computational simulation has been more efficient and accurate than traditional measurement and bench work method to predict and analyze a reaction, like simulate the energy level and structure of TS during a reaction which might be impossible to isolate the reaction, the method still has a strong limitation is that it does not take the practicability of reaction in to account. Take the Diels-Alder reaction in exercise 1 for example, although Gaussian could run a simulation on the reaction given that the orbitals and conformation are correct, it still neglected the presence of heat during the reaction. Hence, it is generally believed that butadiene is a poor diene and ethylene is a poor dienophile with wide energy gap to cause a poor overlap for the formation of product.It is also believed that the butadiene will adopt a trans-conformation to minimize the steric clash such that the reaction is impractical in reality.

== Reference ==
1.D. Lide, ''Tetrahedron'', '''1962''', 17, 125-134.

2.A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.

3. Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.

File:ENDO TS scc215.LOG

2017-11-08T11:42:40Z

Scc215: Scc215 uploaded a new version of File:ENDO TS scc215.LOG

Rep:Mod:ts.scc215

2017-11-08T11:41:48Z

Scc215: /* Calculations */

== Third Year Computational Lab: Transitional States and Reactivity ==
=== Introduction ===
[[File:Potential Energy Surface and Corresponding Reaction Coordinate Diagram scc215.png|thumb|450x450px|Fig. 1 Example of Potential Energy Surface describing reaction of A+B to C]]
A Potential Energy Surface (Fig. 1) is a landscape about that shows various reaction pathway of completing a reaction from reactants to materials. It always possesses dimension numbers of 3N-6 for N standing for the number of molecules involved. A minimum could be divided into two categories, local minima and global minimum under the context of PES. Multiple local minima could exist on the PES, and reactants are normally located on one of them, while global minimum on PES often refers to the location of the most thermodynamic stable product. For a local minimum, it satisfies the following prerequisites: <math>{ \partial V\over \partial (r_i)} = 0</math> and <math>{ \partial^2 V\over \partial (r_i)^2} > 0</math>, which also defines minimum as one of the critical points of the function.

The transition state is one of the local maximum located on minimum energy pathway, and it is the position which most of the reaction pathways passes through. The derivative of the function at TS also showed <math>{ \partial V\over \partial (r_i)} = 0</math> since it is also one of the critical points of the function. <math> V=f(r_i) </math>. However, TS could be distinguished from local minimums since it has a negative second derivative <math>{ \partial^2 V\over \partial (r_i)^2} < 0</math>and thus indicated a correctly optimized reactant and product should have all positive frequencies while a TS should show one imaginary frequency as the result.

== Exercise 1: Reaction of Butadiene with Ethylene ==
[[File:D-a ex1 reaction scheme scc215.png|centre|thumb|826x826px|Fig. 2 Reaction Scheme of Diels-Alder reaction between Butadiene and Ethylene]]

In this reaction, a [4+2] cycloaddition was simulated on Gaussian and the interactions between frontier orbitals have been investigated to determine if the reaction is normal demand or inverse demand DA reaction.

=== MO diagram of frontier orbitals and qualitative energy levels of reaction ===
[[File:Normal demad d-a mo diagram scc215.png|thumb|490x490px|Fig. 3 The qualitative MO diagram showing the frontier orbitals of TS and all molecules involved]]
Using the energy levels listed in checkpoint files of molecules and transition states, a molecule diagram was produced. It has clearly shown that the reaction is normal demand since the gap between LUMO of butadiene and HOMO of ethylene is large such that the overlap between these two is poor. As a result, the reaction is completed through the domination of better-overlapped HOMO of butadiene and LUMO of ethylene. For such bond-forming reaction to proceed, the positive phase of molecular orbitals must overlap, i.e. only symmetric-symmetric reactions and asymmetric-asymmetric overlap are allowed and the rest are forbidden. This means the orbital overlap integrals of symmetric-symmetric and that of asymmetric-asymmetric interactions are non-zero while that of asymmetric-symmetric interactions are zero.

=== Variation of C-C bond length and their comparison to different types of C-C bond ===
[[File:Product bond length scc215.png|left|thumb|Fig. 4 Legend of each corresponding carbon atom]]

{| class="wikitable"
|+Table 1 Variation of the 6 C-C bonds involved in the reaction
!Bond Length (Å)
!C1-C4
!C4-C5
!C5-C6
!C6-C11
!C11-C14
!C14-C1
|-
|Butadiene
|1.335
|1.468
|1.335
|
|
|
|-
|Ethylene
|
|
|
|
|1.331
|
|-
|Transition State
|1.379
|1.411
|1.379
|2.115
|1.381
|2.115
|-
|Product
|1.492
|1.331
|1.492
|1.536
|1.537
|1.536
|}
The two tables have summarized the change of bond length throughout the reaction. Three double bonds in original reactants (C1-C4, C5-C6, C11-C14) has increased the bond length to 1.492 Å and 1.537 Å respectively since their bond order has been reduced to 1 in the product. Bond C4-C5 has decreased in bond length since it has become a C-C double bond instead of a single bond. C6-C11 and C14-C1 are the two newly formed bonds in the product such that the distance between carbon atoms has decreased from 3.4 Å to 1.536 Å which is similar to the length of a sp3C-sp3 C bond. At TS, the originally existing bonds have their length located between 1.379 to 1.411 Å, which are between a pure sp3C-sp3C bond length and sp2C-sp2C bond length and also shorter than sp3C-sp2C bond.
{| class="wikitable"
|+Table 2 Typical C-C bond and Carbon atom Van der Waals Radius [1][2]
!sp3C-sp3C Bond length (Å)
!Error (Å)
!sp2C-sp2C Bond length (Å)
!Error (Å)
|-
|1.526 (propane) or

1.525 (isobutane)
|0.002
|1.338
|0.002
|-
| colspan="4" |Carbon atom Van der Waals Radius: 1.700 Å
|-
| colspan="4" |
|}
{| class="wikitable"
|+Table 3 Variation of C-C bond length against Intrinsic Reaction Coordinate
! colspan="4" |C-C bond
|-
|C1-C4
|[[File:1,4 scc215.png|frameless|500x500px]]
|C6-C11
|[[File:11,6 scc215.png|frameless|500x500px]]
|-
|C4-C5
|[[File:4,5 scc215.png|frameless|500x500px]]
|C11-C14
|[[File:14,11 scc215.png|frameless|500x500px]]
|-
|C5-C6
|[[File:5,6 scc215.png|frameless|500x500px]]
|C14-C1
|[[File:1,14 scc215.png|frameless|500x500px]]
|}

=== Vibration in Imaginary frequency of TS ===
[[File:Ts scc215.gif|thumb|450x450px|Fig. 5 Bond forming process corresponding to the report imaginary vibration frequency]]
From the processed simulation, only one single imaginary vibration frequency at 948.9i cm-1 was reported, which stands for the synchronous bond formation process during the Diels-Alder reaction.

=== Calculation ===

== Exercise 2: Reaction between Cyclohexadiene and 1,3-dioxole ==
[[File:Part 2 reaction scheme scc215.png|centre|thumb|585x585px|Fig. 6 Reaction Scheme for both exo and endo product formation]][[File:Part 2 exo mo diagram scc215.png|left|thumb|496x496px|Fig.7 MO diagram of frontier orbitals during formation of exo product]][[File:Part 2 endo mo diagram scc215.png|thumb|501x501px|Fig. 8 MO diagram of the frontier orbitals forming the endo product]]
=== MO diagram of Exo and Endo reaction pathways ===
Similar to all the other [4+2] cycloaddition, the reaction is controlled by the overlap of frontier orbitals of diene and dienophile molecule respectively. As discussed above, the overlap integral is non-zero (i.e. reaction allowed) only if the symmetrical element is identical. Hence, in this case, the overlap between LUMO of cyclohexadiene and HOMO of 1,3-dioxole dominates the reaction since the energy gap between is much smaller than the other energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Thus this reaction, regardless of endo or exo reaction, is an inverse electron demand DA reaction.
=== Which one is more favourable? Endo product vs Exo product ===
{| class="wikitable"
|+Table 4 Gibbs Free energies of reaction
!Energies (Hatrees/molecule)
!Cyclohexadiene
!1,3-dioxole
!TS
!Product
|-
|'''Sum of electronic and thermal Free Energies of Endo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.395506</nowiki>
|}
|
{|
|<nowiki>-500.436135</nowiki>
|}
|-
|'''Sum of electronic and thermal Free Energies of Exo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.348863</nowiki>
|}
|
{|
|<nowiki>-500.434789</nowiki>
|}
|-

|}

==== Endo Reaction Energies ====
Activation Energy: [-500.395506-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 3.80459075 kJ/mol

Reaction Energy: [-500.436135-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -21.69049711 kJ/mol

==== Exo Reaction Energies ====
Activation Energy: [-500.348863-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 138.379614 kJ/mol

Reaction Energy: [-500.434789-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -87.2191166 kJ/mol

==== Explanation of the result ====
As shown in the calculated result, considering both thermodynamic and kinetic aspect, endo product formation is more favourable in this reaction than the exo form. This could be shown by the lower reaction barrier of endo TS from reactant and the more negative reaction energy of endo product from the reactants. This could possibly be explained by the Secondary Orbital Interaction occurring exclusively in endo transition state. For the endo TS, secondary orbital interaction occurs on the overlap of positive phases between the p-orbitals of newly-formed pi system on diene and empty p-orbital of two oxygen atoms, while the strong primary interaction still occurs on both endo and exo state. As a result, endo state has become a both thermodynamically and kinetically stable product.
[[File:Part 2 energy profile scc215.png|thumb|400x400px|Fig. 9 Qualitative energy profile comparing between the two reaction pathways]]

=== Calculations ===

== Exercise 3: Exercise 3: Diels-Alder vs Cheletropic ==
[[File:Part 3 reaction scheme scc215.png|centre|thumb|450x450px|Fig. 10 Reaction scheme of both Diels-Alder Reaction and Cheletropic reaction]]

=== Optimized TS with corresponding frequencies and Product via two pathways ===
{| class="wikitable"
!Pathway
!Vibration
!Shape of product
|-
|Endo Diels-Alder
|[[File:Endo ts scc215.gif|thumb|637x637px|Imaginary frequency at 333.69i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Exo Diels-Alder
|[[File:Exo ts scc215.gif|thumb|637x637px|Imaginary frequency at 351.63i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Cheletropic
|[[File:Cheletropic ts scc215.gif|thumb|637x637px|Imaginary frequency at 486.80i cm]]
|[[File:Cheletropic adduct scc215.gif.png|thumb|426x426px]]
|}

=== IRC calculated for each possible pathway ===
As shown in the IRC animation in Table 5, the C-S and C-O bond formation in Diels-Alder reactions are asynchronous while the formation of two C-S bonds are synchronous. It is possibly believed to be related to the difference of van der waals radius in oxygen and sulphur respectively. Sulphur has a larger radius such that the C-S is easier to form than C-O bond.
{| class="wikitable"
|+Table 5 IRC animation of all possible pathways
!Pathway
!Animation of IRC
|-
|Endo Diels-Alder
|[[File:Endo irc scc215.gif|thumb|637x637px]]
|-
|Exo Diels-Alder
|[[File:Exo irc scc215.gif|thumb|637x637px]]
|-
|Cheletropic
|[[File:Cheletropic irc scc215.gif|thumb|637x637px]]
|}

=== Energy Profile and Energies ===
[[File:Part 3 energy profile scc215.png|thumb|567x567px|Fig.11 Quantitative reaction profile comparing three possible pathways]]
Reaction profiles are constructed using the calculated energy extracted from IRC log files. Since zero was set to be the energy level when the reactant have infinite separation (i.e. reactant energy level = 0 Hatrees), table 6 is showing the corrected relative energy with reference to the zero set.
{| class="wikitable"
|+Table 6 Corrected Energies of each pathway
!Corrected Energies (Hatrees/molecule)
!Reactants
!TS
!Product
|-
|Endo Diels-Alder
|0
|
{|
|0.00764995
|}
|
{|
|<nowiki>-0.06415</nowiki>
|}
|-
|Exo Diels-Alder
|0
|
{|
|0.00955814
|}
|
{|
|<nowiki>-0.06559</nowiki>
|}
|-
|Cheletropic
|0
|
{|
|0.01739184
|}
|
{|
|<nowiki>-0.08815</nowiki>
|}
|}

=== Calculated Reaction energies and Reaction Barrier ===

==== Endo Diels-Alder Reaction ====
Reaction Energy:-0.06415*4.3597439422E-18/1000*6.02E-23 = -168.42715058 kJ/mol

Activation Energy:0.00764995*4.3597439422E-18/1000*6.02E-23 = 20.084945255 kJ/mol

==== Exo Diels-Alder Reaction ====
Reaction Energy: -0.06559*4.3597439422E-18/1000*6.02E-23 = -172.1934306 kJ/mol

Activation Energy: 0.00955814*4.3597439422E-18/1000*6.02E-23 = 25.094898482 kJ/mol

==== Cheletropic Reaction ====
Reaction Energy:-0.08815 *4.3597439422E-18/1000*6.02E-23 = -231.45070758 kJ/mol

Activation Energy: 0.01739184*4.3597439422E-18/1000*6.02E-23 = 45.662279398 kJ/mol

Base on the calculations made above, the endo D-A reaction is found to be the most kinetically stable reaction, while the cheletropic reaction is the most thermodynamically favoured reaction with a reaction energy as negative as -231.45070758 kJ/mol yet with the highest energy barrier to reach the TS. This is due to the synchronous bond formation would reduce the O-S-O bond angle such that they would experience unfavourable electron-electron repulsion. On the other hand, a 5-member heterocycle formation will lead to a less strained ring than a hydrocarbon cyclic structure since the van der waals radius of S is larger than C atom, such that the ring formation becomes more stable.

=== Unstable o-xylylene molecule and second possible site of D-A addition ===
[[File:Xylylene self scc215.png|centre|thumb|772x772px|Fig. 12 Alternative electrocyclic reaction carried out by xylylene molecule]]As shown in Fig. 12, there is a possibility for xylylene molecule to undergo a 4-pi electrocyclic reaction to form benzocyclobutene especially in the presence of heat.[3] This is due to the 6 member ring will turn into a 6-pi delocalised electron system after any reaction take place in the diene position, such that the product is more stabilized and favoured to be formed rather than staying as o-xylylene form.

=== Calculations ===
[[File:CHELETROPIC TS scc215.LOG ]][[File:EXO TS2 scc215.LOG]][[File:ENDO TS scc215.log]][[File:final endo irc scc215.log]][[File:final exo irc scc215.log]][[File:final cheletropic scc215.log]]

== Conclusion ==
The experiment has given a brief introduction to use computational environment for simulation of reactions and analysis of PES. It has shown several pros and cons by such method.

Although the computational simulation has been more efficient and accurate than traditional measurement and bench work method to predict and analyze a reaction, like simulate the energy level and structure of TS during a reaction which might be impossible to isolate the reaction, the method still has a strong limitation is that it does not take the practicability of reaction in to account. Take the Diels-Alder reaction in exercise 1 for example, although Gaussian could run a simulation on the reaction given that the orbitals and conformation are correct, it still neglected the presence of heat during the reaction. Hence, it is generally believed that butadiene is a poor diene and ethylene is a poor dienophile with wide energy gap to cause a poor overlap for the formation of product.It is also believed that the butadiene will adopt a trans-conformation to minimize the steric clash such that the reaction is impractical in reality.

== Reference ==
1.D. Lide, ''Tetrahedron'', '''1962''', 17, 125-134.

2.A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.

3. Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.

Rep:Mod:ts.scc215

2017-11-08T11:40:28Z

Scc215: /* Calculations */

== Third Year Computational Lab: Transitional States and Reactivity ==
=== Introduction ===
[[File:Potential Energy Surface and Corresponding Reaction Coordinate Diagram scc215.png|thumb|450x450px|Fig. 1 Example of Potential Energy Surface describing reaction of A+B to C]]
A Potential Energy Surface (Fig. 1) is a landscape about that shows various reaction pathway of completing a reaction from reactants to materials. It always possesses dimension numbers of 3N-6 for N standing for the number of molecules involved. A minimum could be divided into two categories, local minima and global minimum under the context of PES. Multiple local minima could exist on the PES, and reactants are normally located on one of them, while global minimum on PES often refers to the location of the most thermodynamic stable product. For a local minimum, it satisfies the following prerequisites: <math>{ \partial V\over \partial (r_i)} = 0</math> and <math>{ \partial^2 V\over \partial (r_i)^2} > 0</math>, which also defines minimum as one of the critical points of the function.

The transition state is one of the local maximum located on minimum energy pathway, and it is the position which most of the reaction pathways passes through. The derivative of the function at TS also showed <math>{ \partial V\over \partial (r_i)} = 0</math> since it is also one of the critical points of the function. <math> V=f(r_i) </math>. However, TS could be distinguished from local minimums since it has a negative second derivative <math>{ \partial^2 V\over \partial (r_i)^2} < 0</math>and thus indicated a correctly optimized reactant and product should have all positive frequencies while a TS should show one imaginary frequency as the result.

== Exercise 1: Reaction of Butadiene with Ethylene ==
[[File:D-a ex1 reaction scheme scc215.png|centre|thumb|826x826px|Fig. 2 Reaction Scheme of Diels-Alder reaction between Butadiene and Ethylene]]

In this reaction, a [4+2] cycloaddition was simulated on Gaussian and the interactions between frontier orbitals have been investigated to determine if the reaction is normal demand or inverse demand DA reaction.

=== MO diagram of frontier orbitals and qualitative energy levels of reaction ===
[[File:Normal demad d-a mo diagram scc215.png|thumb|490x490px|Fig. 3 The qualitative MO diagram showing the frontier orbitals of TS and all molecules involved]]
Using the energy levels listed in checkpoint files of molecules and transition states, a molecule diagram was produced. It has clearly shown that the reaction is normal demand since the gap between LUMO of butadiene and HOMO of ethylene is large such that the overlap between these two is poor. As a result, the reaction is completed through the domination of better-overlapped HOMO of butadiene and LUMO of ethylene. For such bond-forming reaction to proceed, the positive phase of molecular orbitals must overlap, i.e. only symmetric-symmetric reactions and asymmetric-asymmetric overlap are allowed and the rest are forbidden. This means the orbital overlap integrals of symmetric-symmetric and that of asymmetric-asymmetric interactions are non-zero while that of asymmetric-symmetric interactions are zero.

=== Variation of C-C bond length and their comparison to different types of C-C bond ===
[[File:Product bond length scc215.png|left|thumb|Fig. 4 Legend of each corresponding carbon atom]]

{| class="wikitable"
|+Table 1 Variation of the 6 C-C bonds involved in the reaction
!Bond Length (Å)
!C1-C4
!C4-C5
!C5-C6
!C6-C11
!C11-C14
!C14-C1
|-
|Butadiene
|1.335
|1.468
|1.335
|
|
|
|-
|Ethylene
|
|
|
|
|1.331
|
|-
|Transition State
|1.379
|1.411
|1.379
|2.115
|1.381
|2.115
|-
|Product
|1.492
|1.331
|1.492
|1.536
|1.537
|1.536
|}
The two tables have summarized the change of bond length throughout the reaction. Three double bonds in original reactants (C1-C4, C5-C6, C11-C14) has increased the bond length to 1.492 Å and 1.537 Å respectively since their bond order has been reduced to 1 in the product. Bond C4-C5 has decreased in bond length since it has become a C-C double bond instead of a single bond. C6-C11 and C14-C1 are the two newly formed bonds in the product such that the distance between carbon atoms has decreased from 3.4 Å to 1.536 Å which is similar to the length of a sp3C-sp3 C bond. At TS, the originally existing bonds have their length located between 1.379 to 1.411 Å, which are between a pure sp3C-sp3C bond length and sp2C-sp2C bond length and also shorter than sp3C-sp2C bond.
{| class="wikitable"
|+Table 2 Typical C-C bond and Carbon atom Van der Waals Radius [1][2]
!sp3C-sp3C Bond length (Å)
!Error (Å)
!sp2C-sp2C Bond length (Å)
!Error (Å)
|-
|1.526 (propane) or

1.525 (isobutane)
|0.002
|1.338
|0.002
|-
| colspan="4" |Carbon atom Van der Waals Radius: 1.700 Å
|-
| colspan="4" |
|}
{| class="wikitable"
|+Table 3 Variation of C-C bond length against Intrinsic Reaction Coordinate
! colspan="4" |C-C bond
|-
|C1-C4
|[[File:1,4 scc215.png|frameless|500x500px]]
|C6-C11
|[[File:11,6 scc215.png|frameless|500x500px]]
|-
|C4-C5
|[[File:4,5 scc215.png|frameless|500x500px]]
|C11-C14
|[[File:14,11 scc215.png|frameless|500x500px]]
|-
|C5-C6
|[[File:5,6 scc215.png|frameless|500x500px]]
|C14-C1
|[[File:1,14 scc215.png|frameless|500x500px]]
|}

=== Vibration in Imaginary frequency of TS ===
[[File:Ts scc215.gif|thumb|450x450px|Fig. 5 Bond forming process corresponding to the report imaginary vibration frequency]]
From the processed simulation, only one single imaginary vibration frequency at 948.9i cm-1 was reported, which stands for the synchronous bond formation process during the Diels-Alder reaction.

=== Calculation ===

== Exercise 2: Reaction between Cyclohexadiene and 1,3-dioxole ==
[[File:Part 2 reaction scheme scc215.png|centre|thumb|585x585px|Fig. 6 Reaction Scheme for both exo and endo product formation]][[File:Part 2 exo mo diagram scc215.png|left|thumb|496x496px|Fig.7 MO diagram of frontier orbitals during formation of exo product]][[File:Part 2 endo mo diagram scc215.png|thumb|501x501px|Fig. 8 MO diagram of the frontier orbitals forming the endo product]]
=== MO diagram of Exo and Endo reaction pathways ===
Similar to all the other [4+2] cycloaddition, the reaction is controlled by the overlap of frontier orbitals of diene and dienophile molecule respectively. As discussed above, the overlap integral is non-zero (i.e. reaction allowed) only if the symmetrical element is identical. Hence, in this case, the overlap between LUMO of cyclohexadiene and HOMO of 1,3-dioxole dominates the reaction since the energy gap between is much smaller than the other energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole. Thus this reaction, regardless of endo or exo reaction, is an inverse electron demand DA reaction.
=== Which one is more favourable? Endo product vs Exo product ===
{| class="wikitable"
|+Table 4 Gibbs Free energies of reaction
!Energies (Hatrees/molecule)
!Cyclohexadiene
!1,3-dioxole
!TS
!Product
|-
|'''Sum of electronic and thermal Free Energies of Endo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.395506</nowiki>
|}
|
{|
|<nowiki>-500.436135</nowiki>
|}
|-
|'''Sum of electronic and thermal Free Energies of Exo reaction'''
|
{|
|<nowiki>-233.333434</nowiki>
|}
|
{|
|<nowiki>-267.068135</nowiki>
|}
|
{|
|<nowiki>-500.348863</nowiki>
|}
|
{|
|<nowiki>-500.434789</nowiki>
|}
|-

|}

==== Endo Reaction Energies ====
Activation Energy: [-500.395506-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 3.80459075 kJ/mol

Reaction Energy: [-500.436135-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -21.69049711 kJ/mol

==== Exo Reaction Energies ====
Activation Energy: [-500.348863-(-233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = 138.379614 kJ/mol

Reaction Energy: [-500.434789-(--233.333434-267.068135)]*4.3597439422E-18/1000*6.02E-23 = -87.2191166 kJ/mol

==== Explanation of the result ====
As shown in the calculated result, considering both thermodynamic and kinetic aspect, endo product formation is more favourable in this reaction than the exo form. This could be shown by the lower reaction barrier of endo TS from reactant and the more negative reaction energy of endo product from the reactants. This could possibly be explained by the Secondary Orbital Interaction occurring exclusively in endo transition state. For the endo TS, secondary orbital interaction occurs on the overlap of positive phases between the p-orbitals of newly-formed pi system on diene and empty p-orbital of two oxygen atoms, while the strong primary interaction still occurs on both endo and exo state. As a result, endo state has become a both thermodynamically and kinetically stable product.
[[File:Part 2 energy profile scc215.png|thumb|400x400px|Fig. 9 Qualitative energy profile comparing between the two reaction pathways]]

=== Calculations ===

== Exercise 3: Exercise 3: Diels-Alder vs Cheletropic ==
[[File:Part 3 reaction scheme scc215.png|centre|thumb|450x450px|Fig. 10 Reaction scheme of both Diels-Alder Reaction and Cheletropic reaction]]

=== Optimized TS with corresponding frequencies and Product via two pathways ===
{| class="wikitable"
!Pathway
!Vibration
!Shape of product
|-
|Endo Diels-Alder
|[[File:Endo ts scc215.gif|thumb|637x637px|Imaginary frequency at 333.69i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Exo Diels-Alder
|[[File:Exo ts scc215.gif|thumb|637x637px|Imaginary frequency at 351.63i cm]]
|[[File:Endo adduct scc215.gif.png|thumb|382x382px]]
|-
|Cheletropic
|[[File:Cheletropic ts scc215.gif|thumb|637x637px|Imaginary frequency at 486.80i cm]]
|[[File:Cheletropic adduct scc215.gif.png|thumb|426x426px]]
|}

=== IRC calculated for each possible pathway ===
As shown in the IRC animation in Table 5, the C-S and C-O bond formation in Diels-Alder reactions are asynchronous while the formation of two C-S bonds are synchronous. It is possibly believed to be related to the difference of van der waals radius in oxygen and sulphur respectively. Sulphur has a larger radius such that the C-S is easier to form than C-O bond.
{| class="wikitable"
|+Table 5 IRC animation of all possible pathways
!Pathway
!Animation of IRC
|-
|Endo Diels-Alder
|[[File:Endo irc scc215.gif|thumb|637x637px]]
|-
|Exo Diels-Alder
|[[File:Exo irc scc215.gif|thumb|637x637px]]
|-
|Cheletropic
|[[File:Cheletropic irc scc215.gif|thumb|637x637px]]
|}

=== Energy Profile and Energies ===
[[File:Part 3 energy profile scc215.png|thumb|567x567px|Fig.11 Quantitative reaction profile comparing three possible pathways]]
Reaction profiles are constructed using the calculated energy extracted from IRC log files. Since zero was set to be the energy level when the reactant have infinite separation (i.e. reactant energy level = 0 Hatrees), table 6 is showing the corrected relative energy with reference to the zero set.
{| class="wikitable"
|+Table 6 Corrected Energies of each pathway
!Corrected Energies (Hatrees/molecule)
!Reactants
!TS
!Product
|-
|Endo Diels-Alder
|0
|
{|
|0.00764995
|}
|
{|
|<nowiki>-0.06415</nowiki>
|}
|-
|Exo Diels-Alder
|0
|
{|
|0.00955814
|}
|
{|
|<nowiki>-0.06559</nowiki>
|}
|-
|Cheletropic
|0
|
{|
|0.01739184
|}
|
{|
|<nowiki>-0.08815</nowiki>
|}
|}

=== Calculated Reaction energies and Reaction Barrier ===

==== Endo Diels-Alder Reaction ====
Reaction Energy:-0.06415*4.3597439422E-18/1000*6.02E-23 = -168.42715058 kJ/mol

Activation Energy:0.00764995*4.3597439422E-18/1000*6.02E-23 = 20.084945255 kJ/mol

==== Exo Diels-Alder Reaction ====
Reaction Energy: -0.06559*4.3597439422E-18/1000*6.02E-23 = -172.1934306 kJ/mol

Activation Energy: 0.00955814*4.3597439422E-18/1000*6.02E-23 = 25.094898482 kJ/mol

==== Cheletropic Reaction ====
Reaction Energy:-0.08815 *4.3597439422E-18/1000*6.02E-23 = -231.45070758 kJ/mol

Activation Energy: 0.01739184*4.3597439422E-18/1000*6.02E-23 = 45.662279398 kJ/mol

Base on the calculations made above, the endo D-A reaction is found to be the most kinetically stable reaction, while the cheletropic reaction is the most thermodynamically favoured reaction with a reaction energy as negative as -231.45070758 kJ/mol yet with the highest energy barrier to reach the TS. This is due to the synchronous bond formation would reduce the O-S-O bond angle such that they would experience unfavourable electron-electron repulsion. On the other hand, a 5-member heterocycle formation will lead to a less strained ring than a hydrocarbon cyclic structure since the van der waals radius of S is larger than C atom, such that the ring formation becomes more stable.

=== Unstable o-xylylene molecule and second possible site of D-A addition ===
[[File:Xylylene self scc215.png|centre|thumb|772x772px|Fig. 12 Alternative electrocyclic reaction carried out by xylylene molecule]]As shown in Fig. 12, there is a possibility for xylylene molecule to undergo a 4-pi electrocyclic reaction to form benzocyclobutene especially in the presence of heat.[3] This is due to the 6 member ring will turn into a 6-pi delocalised electron system after any reaction take place in the diene position, such that the product is more stabilized and favoured to be formed rather than staying as o-xylylene form.

=== Calculations ===
[[File:CHELETROPIC TS scc215.log]][[File:EXO TS2 scc215.log]][[File:ENDO TS scc215.log]][[File:final endo irc scc215.log]][[File:final exo irc scc215.log]][[File:final cheletropic scc215.log]]

== Conclusion ==
The experiment has given a brief introduction to use computational environment for simulation of reactions and analysis of PES. It has shown several pros and cons by such method.

Although the computational simulation has been more efficient and accurate than traditional measurement and bench work method to predict and analyze a reaction, like simulate the energy level and structure of TS during a reaction which might be impossible to isolate the reaction, the method still has a strong limitation is that it does not take the practicability of reaction in to account. Take the Diels-Alder reaction in exercise 1 for example, although Gaussian could run a simulation on the reaction given that the orbitals and conformation are correct, it still neglected the presence of heat during the reaction. Hence, it is generally believed that butadiene is a poor diene and ethylene is a poor dienophile with wide energy gap to cause a poor overlap for the formation of product.It is also believed that the butadiene will adopt a trans-conformation to minimize the steric clash such that the reaction is impractical in reality.

== Reference ==
1.D. Lide, ''Tetrahedron'', '''1962''', 17, 125-134.

2.A. Bondi, ''J. Phys. Chem.'', '''1964''', 68, 441–451.

3. Mehta, G.; Kotha, S., ''Tetrahedron Lett.'', '''2001''',57.

Rep:Mod:ts.scc215

2017-11-08T11:36:38Z

Scc215: /* Which one is more favourable? Endo product vs Exo product */

Rep:Mod:ts.scc215

2017-11-08T00:15:57Z

Scc215: /* Which one is more favourable? Endo product vs Exo product */