ChemWiki - User contributions [en]

Rep:MOD:SY3814

2016-12-16T11:43:09Z

Sy3814:

=='''Introduction''' ==
=== '''Potential Energy Surface''' ===
A potential energy surface(PES) is a mathematical function that describes molecule as a function of its geometry. It is commonly applied in Chemistry to theoretically explore properties of atomic structures and rates of chemical reactions.
==='''stationary points''' ===
There are two stationary points(points with zero gradient) in PES, minimum state point and transition state point. Minimum state is where the molecule in its minimum energy shape(physically stable) and the transition state is the highest energy point along a reaction coordinate.
==='''gradient and the curvature'''===
As the point is evaluated in the PES, the point can be identified by its gradient(first derivatives) and curvature(second derivatives) of the energy related to the position.
===='''Gradient''' ====
For a given molecule, '''r''' describes the position of molecule and the Function E('''r''') can be introduced as the energy of the position. The first derivative of the energy corresponds to the position of the molecule is calculated as gradient.
===Gradient = ∂E/∂r===
==== '''Curvature''' ====
In the case that the gradient is a zero vector(stationary points), second derivative matrix is used, which describes the PES curvature at '''r''' position.
===Curvature = ∂∂E/∂ri∂rj===
=='''Exercise 1'''==
==='''Reaction of Butadiene with Ethylene'''===
[[File:Buata2.PNG]]
==='''Visualised MOs'''===
{| class="wikitable" border="1"
|+ Ethylene and Butadiene MOs
! Ethylene HOMO(A) !! Ethylene LUMO(S) !! Butadiene HOMO(S) !! Butadiene LUMO(A)
|-
| [[File:Ethylene homo11.jpg|150px]] || [[File:Ethylene lumo11.jpg|150px]] || [[File:Butadiene homo11.jpg|150px]] || [[File:Butadiene lumo11.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Transition states MOs
! Occupied orbital(S) !! TS HOMO(A) !! TS LUMO(A) !! Unoccupied orbital(S)
|-
| [[File:Ts1 hohomo.jpg|150px]] || [[File:Ts1 homo.jpg|150px]] || [[File:Ts1 lumo.jpg|150px]] || [[File:Ts1 lulumo.jpg|150px]]
|}

====MO diagram for the formation of the butadiene/ethene Transition state====
[[File:Capture graham.PNG]]

The Mo diagram demonstrate that 4 TS orbital are produced by interaction between LUMO and HOMO orbitals. Correlated with Mos computed, only butadiene HOMO orbital interacts with ethylene LUMO orbital and butadiene LUMO orbital interacts with HOMO orbital in ethylene. It testifies that the reaction is allowed only when reactants in the same symmetry. The orbital overlap integral is zero in an asymmetric-asymmetric interaction and non-zero in interaction with same symmetries.
==='''bond length change in the reaction'''===
{| class="wikitable" border="1"
|+ C-C Bond Length Change
! !!Reactants !! Transition state !! Product
|-
| Ethylene C=C || 1.327Å || 1.381Å || 1.54Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| Butadiene C=C || 1.47Å || 1.41Å || 1.34Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|}
The ethylene C=C double bond length is 1.327Å and the C=C bond lengths in Butadiene are at 1.33Å, 1.47Å and 1.33Å respectively. In Transition state, the C-C bond length in ethylene is extended to 1.381Å, the C-C bond lengths in butadiene are shifted to 1.38Å, 1.41Å and 1.38Å. The C-C bond length between reactants is around 2.11Å. In the product, the reactants C-C bond length are changed to 1.54Å (Ethylene C-C), 1.50Å, 1.34Å and 1.50Å (Butadiene C-C). The C-C bond length between reactants is shortened to 1.54Å. As the data shown, the C-C bond length between reactants shorten as the reaction progresses. The butadiene C-C single bond length decreases and turns into double bond in the reaction. All reactants double bonds, in contrast, move longer and change to single bonds in the product.
==='''Vibrations'''===
In the TS vibration, the two reacting carbons from Ethylene and Butadiene vibrate vertically and move aproaching each other. The formation of the two bonds are synchronous, and the transition movement can be testified by the negative frequency (negative second derivative for the saddle point). From the computed MOs, the vibration for the lowest positive frequency is twisting around the reaction center.
=='''Exercise 2'''==
[[File:Capture 120.PNG]]
{| class="wikitable" border="1"
|+ Endo Transition state MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Hohomo ex2 endo.jpg|150px]] || [[File:Homo ex2 endo11.jpg|150px]] || [[File:Lumo ex2 endo11.jpg|150px]] || [[File:Lulumo ex2 endo.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Exo Transition State MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Ex2 hohomo exo ts.jpg|150px]] || [[File:Ex2 homo exo ts.jpg|150px]] || [[File:Ex2 ts exo lumo.jpg|150px]] || [[File:Ex2 ts exo lulumo.jpg|150px]]
|}
It's a inverse electron demand DA reaction due to the electron donating oxygen subsituents on dienophile. The electron richer dienophile makes the diene LUMO and dienophile HOMO more closer in energy and be the frontier orbitals.
==='''Reaction Barriers and Reaction Energies'''===
'''Barrier energy = transition state free energy- sum of reactant free energies'''
'''Reaction free energy = sum of product free energies - sum of reactant free energies'''

Extract the "Sum of electronic and thermal Free Energies" data from the Log file and substitute into the equation.

Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-267.068643+-233.324375))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction barrier energy:ΔrG0(298K)=(-500.073175-(-267.068643+-233.324375))*627.5095= 17.51Kcal = 73.262KJ/mol

Exo reaction barrier energy:ΔrG0(298K)=(-500.072282-(-267.068643+-233.324375))*627.5095= 18.07Kcal = 75.605KJ/mol

Endo is the more kinetic product due to the relative lower barrier energy, and the higher reaction free energy makes the exo product more thermodynamic favoured.
===Secondary orbitals and steric effects'''===
The secondary orbital interaction (non-bonding) in endo structure makes it with lower energy and react faster towards endo product. This can be testified by the oxygen-carbon overlap in the HOMO transition state MO. The oxygen in 1,3-Dioxole interacts with the carbon in cyclohexadiene so that to lower the energy barrier and make the reaction proceed faster. The smaller crossing between two rings in exo structure makes it less steric hindered thermodynamically stable.
=='''Exercise 3'''==
[[File:Capture ex3.PNG]]
{| class="wikitable" border="1"
|+ IRC Calculation for reaction path
! Exo- Diels-Alder Reaction !! Endo- Diels-Alder Reaction !! Cheletropic Reaction
|-
| [[File:Exo movie111.gif|400px]] || [[File:Endo movie111.gif|400px]] || [[File:Chele movie.gif|400px]]
|-
| [[File:Capture exo.PNG|400px]] || [[File:Capture endo.PNG|400px]] || [[File:Capture chele.PNG|400px]]
|}

The IRC reaction paths move from product to reactants in exo and endo reaction diagrams, while for Cheletropic, it's from reactants to product.
==='''Activation and Reaction Energies for Each Route'''===
Endo reaction free energy:ΔrG0(298K)=(0.021699-(-0.113379+0.178117))*627.5095= -27.01Kcal = -112.999KJ/mol

Exo reaction free energy:ΔrG0(298K)=(0.021455-(-0.113379+0.178117))*627.5095= -27.16Kcal = -113.637KJ/mol

Cheletropic reaction free energy:ΔrG0(298K)=(-0.000002-(-0.113379+0.178117))*627.5095= -40.63Kcal = -169.996KJ/mol

Endo reaction activation energy:ΔrG0(298K)=(0.090560-(-0.113379+0.178117))*627.5095= 16.20Kcal = 67.796KJ/mol

Exo reaction activation energy:ΔrG0(298K)=(0.092076-(-0.113379+0.178117))*627.5095= 17.15Kcal = 71.756KJ/mol

Cheletropic activation free energy:ΔrG0(298K)=(0.099061-(-0.113379+0.178117))*627.5095= 21.53Kcal = 90.082KJ/mol

From the calculation, the endo route is the most preferred one due to its lowest activation energy, which makes the reaction progresses faster towards endo product(kinetic product). However, as the Diels-Alder reaction move towards the equilibrium, more relatively thermodynamic exo product will be formed. The Cheletropic product has the lowest energy level, so it's most thermodynamically favoured and can be formed in the reversible reaction.
===''' Reaction Profile'''===
[[File:Capture profile.PNG]]
==='''Xylylene bonding change in the reaction'''===
From the IRC animation, the C-C single bonds in 6 membered ring shorten and with more double bond character as the reaction progresses. The C=C double bond length moves longer and shares the π character across the ring.
=='''Conclusion'''==
Transition states of three Diels-Alder reaction have been investigated in this experiment, the bond length changes and free energy level are clearly shown in the Gaussview files. From the computed MOs and data, the endo adduct is usually the kinetic product, which is influenced by secondary orbital interaction to lower its barrier energy. While the less steric congestion makes the exo adduct more thermodynamic favourable and will be the final product in the equilibrium.

Rep:MOD:SY3814

2016-12-16T11:21:21Z

Sy3814:

Rep:MOD:SY3814

2016-12-16T10:27:13Z

Sy3814:

=='''Introduction''' ==
=== '''Potential Energy Surface''' ===
A potential energy surface(PES) is a mathematical function that describes molecule as a function of its geometry. It is commonly applied in Chemistry to theoretically explore properties of atomic structures and rates of chemical reactions.
==='''stationary points''' ===
There are two stationary points(points with zero gradient) in PES, minimum state point and transition state point. Minimum state is where the molecule in its minimum energy shape(physically stable) and the transition state is the highest energy point along a reaction coordinate.
==='''gradient and the curvature'''===
As the point is evaluated in the PES, the point can be identified by its gradient(first derivatives) and curvature(second derivatives) of the energy related to the position.
===='''Gradient''' ====
For a given molecule, '''r''' describes the position of molecule and the Function E('''r''') can be introduced as the energy of the position. The first derivative of the energy corresponds to the position of the molecule is calculated as gradient.
===Gradient = ∂E/∂r===
==== '''Curvature''' ====
In the case that the gradient is a zero vector(stationary points), second derivative matrix is used, which describes the PES curvature at '''r''' position.
===Curvature = ∂∂E/∂ri∂rj===
=='''Exercise 1'''==
==='''Reaction of Butadiene with Ethylene'''===
[[File:Buata2.PNG]]
==='''Visualised MOs'''===
{| class="wikitable" border="1"
|+ Ethylene and Butadiene MOs
! Ethylene HOMO(A) !! Ethylene LUMO(S) !! Butadiene HOMO(S) !! Butadiene LUMO(A)
|-
| [[File:Ethylene homo11.jpg|150px]] || [[File:Ethylene lumo11.jpg|150px]] || [[File:Butadiene homo11.jpg|150px]] || [[File:Butadiene lumo11.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Transition states MOs
! Occupied orbital(S) !! TS HOMO(A) !! TS LUMO(A) !! Unoccupied orbital(S)
|-
| [[File:Ts1 hohomo.jpg|150px]] || [[File:Ts1 homo.jpg|150px]] || [[File:Ts1 lumo.jpg|150px]] || [[File:Ts1 lulumo.jpg|150px]]
|}

====MO diagram for the formation of the butadiene/ethene Transition state====
[[File:Capture graham.PNG]]

The Mo diagram demonstrate that 4 TS orbital are produced by interaction between LUMO and HOMO orbitals. Correlated with Mos computed, only butadiene HOMO orbital interacts with ethylene LUMO orbital and butadiene LUMO orbital interacts with HOMO orbital in ethylene. It testifies that the reaction is allowed only when reactants in the same symmetry. The orbital overlap integral is zero in an asymmetric-asymmetric interaction and non-zero in interaction with same symmetries.
==='''bond length change in the reaction'''===
{| class="wikitable" border="1"
|+ C-C Bond Length Change
! !!Reactants !! Transition state !! Product
|-
| Ethylene C=C || 1.327Å || 1.381Å || 1.54Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| Butadiene C=C || 1.47Å || 1.41Å || 1.34Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|}
The ethylene C=C double bond length is 1.327Å and the C=C bond lengths in Butadiene are at 1.33Å, 1.47Å and 1.33Å respectively. In Transition state, the C-C bond length in ethylene is extended to 1.381Å, the C-C bond lengths in butadiene are shifted to 1.38Å, 1.41Å and 1.38Å. The C-C bond length between reactants is around 2.11Å. In the product, the reactants C-C bond length are changed to 1.54Å (Ethylene C-C), 1.50Å, 1.34Å and 1.50Å (Butadiene C-C). The C-C bond length between reactants is shortened to 1.54Å. As the data shown, the C-C bond length between reactants shorten as the reaction progresses. The butadiene C-C single bond length decreases and turns into double bond in the reaction. All reactants double bonds, in contrast, move longer and change to single bonds in the product.
==='''Vibrations'''===
In the TS vibration, the two reacting carbons from Ethylene and Butadiene vibrate vertically and move aproaching each other. The formation of the two bonds are synchronous, and the transition movement can be testified by the negative frequency (negative second derivative for the saddle point). From the computed MOs, the vibration for the lowest positive frequency is twisting around the reaction center.
=='''Exercise 2'''==
[[File:Capture 120.PNG]]
{| class="wikitable" border="1"
|+ Endo Transition state MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Hohomo ex2 endo.jpg|150px]] || [[File:Homo ex2 endo11.jpg|150px]] || [[File:Lumo ex2 endo11.jpg|150px]] || [[File:Lulumo ex2 endo.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Exo Transition State MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Ex2 hohomo exo ts.jpg|150px]] || [[File:Ex2 homo exo ts.jpg|150px]] || [[File:Ex2 ts exo lumo.jpg|150px]] || [[File:Ex2 ts exo lulumo.jpg|150px]]
|}
It's a inverse electron demand DA reaction due to the electron donating oxygen subsituents on dienophile. The electron richer dienophile makes the diene LUMO and dienophile HOMO more closer in energy and be the frontier orbitals.
==='''Reaction Barriers and Reaction Energies'''===
'''Barrier energy = transition state free energy- sum of reactant free energies'''
'''Reaction free energy = sum of product free energies - sum of reactant free energies'''

Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-267.068643+-233.324375))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction barrier energy:ΔrG0(298K)=(-500.073175-(-267.068643+-233.324375))*627.5095= 17.51Kcal = 73.262KJ/mol

Exo reaction barrier energy:ΔrG0(298K)=(-500.072282-(-267.068643+-233.324375))*627.5095= 18.07Kcal = 75.605KJ/mol

Endo is the more kinetic product due to the relative lower barrier energy, and the higher reaction free energy makes the exo product more thermodynamic favoured.
===Secondary orbitals and steric effects'''===
The secondary orbital interaction (non-bonding) in endo structure makes it with lower energy and react faster towards endo product. This can be testified by the oxygen-carbon overlap in the HOMO transition state MO. The oxygen in 1,3-Dioxole interacts with the carbon in cyclohexadiene so that to lower the energy barrier and make the reaction proceed faster. The smaller crossing between two rings in exo structure makes it less steric hindered thermodynamically stable.
=='''Exercise 3'''==
[[File:Capture ex3.PNG]]
{| class="wikitable" border="1"
|+ IRC Calculation for reaction path
! Exo- Diels-Alder Reaction !! Endo- Diels-Alder Reaction !! Cheletropic Reaction
|-
| [[File:Exo movie111.gif|400px]] || [[File:Endo movie111.gif|400px]] || [[File:Chele movie.gif|400px]]
|-
| [[File:Capture exo.PNG|400px]] || [[File:Capture endo.PNG|400px]] || [[File:Capture chele.PNG|400px]]
|}
==='''Activation and Reaction Energies for Each Route'''===
Endo reaction free energy:ΔrG0(298K)=(0.021699-(-0.113379+0.178117))*627.5095= -27.01Kcal = -112.999KJ/mol

Exo reaction free energy:ΔrG0(298K)=(0.021455-(-0.113379+0.178117))*627.5095= -27.16Kcal = -113.637KJ/mol

Cheletropic reaction free energy:ΔrG0(298K)=(-0.000002-(-0.113379+0.178117))*627.5095= -40.63Kcal = -169.996KJ/mol

Endo reaction activation energy:ΔrG0(298K)=(0.090560-(-0.113379+0.178117))*627.5095= 16.20Kcal = 67.796KJ/mol

Exo reaction activation energy:ΔrG0(298K)=(0.092076-(-0.113379+0.178117))*627.5095= 17.15Kcal = 71.756KJ/mol

Cheletropic activation free energy:ΔrG0(298K)=(0.099061-(-0.113379+0.178117))*627.5095= 21.53Kcal = 90.082KJ/mol
From the calculation, the endo route is the most preferred one due to its lowest activation energy, which makes the reaction progresses faster towards endo product(kinetic product). The Cheletropic product has the lowest energy level, which makes it the thermodynamic product,
===''' Reaction Profile'''===
[[File:Capture profile.PNG]]

File:Capture profile.PNG

2016-12-16T10:16:16Z

Sy3814:

File:Capture ex3.PNG

2016-12-16T09:05:49Z

Sy3814:

Rep:MOD:SY3814

2016-12-15T23:51:39Z

Sy3814:

=='''Introduction''' ==
=== '''Potential Energy Surface''' ===
A potential energy surface(PES) is a mathematical function that describes molecule as a function of its geometry. It is commonly applied in Chemistry to theoretically explore properties of atomic structures and rates of chemical reactions.
==='''stationary points''' ===
There are two stationary points(points with zero gradient) in PES, minimum state point and transition state point. Minimum state is where the molecule in its minimum energy shape(physically stable) and the transition state is the highest energy point along a reaction coordinate.
==='''gradient and the curvature'''===
As the point is evaluated in the PES, the point can be identified by its gradient(first derivatives) and curvature(second derivatives) of the energy related to the position.
===='''Gradient''' ====
For a given molecule, '''r''' describes the position of molecule and the Function E('''r''') can be introduced as the energy of the position. The first derivative of the energy corresponds to the position of the molecule is calculated as gradient.
===Gradient = ∂E/∂r===
==== '''Curvature''' ====
In the case that the gradient is a zero vector(stationary points), second derivative matrix is used, which describes the PES curvature at '''r''' position.
===Curvature = ∂∂E/∂ri∂rj===
=='''Exercise 1'''==
==='''Reaction of Butadiene with Ethylene'''===
[[File:Buata2.PNG]]
==='''Visualised MOs'''===
{| class="wikitable" border="1"
|+ Ethylene and Butadiene MOs
! Ethylene HOMO(A) !! Ethylene LUMO(S) !! Butadiene HOMO(S) !! Butadiene LUMO(A)
|-
| [[File:Ethylene homo11.jpg|150px]] || [[File:Ethylene lumo11.jpg|150px]] || [[File:Butadiene homo11.jpg|150px]] || [[File:Butadiene lumo11.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Transition states MOs
! Occupied orbital(S) !! TS HOMO(A) !! TS LUMO(A) !! Unoccupied orbital(S)
|-
| [[File:Ts1 hohomo.jpg|150px]] || [[File:Ts1 homo.jpg|150px]] || [[File:Ts1 lumo.jpg|150px]] || [[File:Ts1 lulumo.jpg|150px]]
|}

====MO diagram for the formation of the butadiene/ethene Transition state====
[[File:Capture graham.PNG]]

The Mo diagram demonstrate that 4 TS orbital are produced by interaction between LUMO and HOMO orbitals. Correlated with Mos computed, only butadiene HOMO orbital interacts with ethylene LUMO orbital and butadiene LUMO orbital interacts with HOMO orbital in ethylene. It testifies that the reaction is allowed only when reactants in the same symmetry. The orbital overlap integral is zero in an asymmetric-asymmetric interaction and non-zero in interaction with same symmetries.
==='''bond length change in the reaction'''===
{| class="wikitable" border="1"
|+ C-C Bond Length Change
! !!Reactants !! Transition state !! Product
|-
| Ethylene C=C || 1.327Å || 1.381Å || 1.54Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| Butadiene C=C || 1.47Å || 1.41Å || 1.34Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|}
The ethylene C=C double bond length is 1.327Å and the C=C bond lengths in Butadiene are at 1.33Å, 1.47Å and 1.33Å respectively. In Transition state, the C-C bond length in ethylene is extended to 1.381Å, the C-C bond lengths in butadiene are shifted to 1.38Å, 1.41Å and 1.38Å. The C-C bond length between reactants is around 2.11Å. In the product, the reactants C-C bond length are changed to 1.54Å (Ethylene C-C), 1.50Å, 1.34Å and 1.50Å (Butadiene C-C). The C-C bond length between reactants is shortened to 1.54Å. As the data shown, the C-C bond length between reactants shorten as the reaction progresses. The butadiene C-C single bond length decreases and turns into double bond in the reaction. All reactants double bonds, in contrast, move longer and change to single bonds in the product.
==='''Vibrations'''===
In the TS vibration, the two reacting carbons from Ethylene and Butadiene vibrate vertically and move aproaching each other. The formation of the two bonds are synchronous, and the transition movement can be testified by the negative frequency (negative second derivative for the saddle point). From the computed MOs, the vibration for the lowest positive frequency is twisting around the reaction center.
=='''Exercise 2'''==
[[File:Capture 120.PNG]]
{| class="wikitable" border="1"
|+ Endo Transition state MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Hohomo ex2 endo.jpg|150px]] || [[File:Homo ex2 endo11.jpg|150px]] || [[File:Lumo ex2 endo11.jpg|150px]] || [[File:Lulumo ex2 endo.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Exo Transition State MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Ex2 hohomo exo ts.jpg|150px]] || [[File:Ex2 homo exo ts.jpg|150px]] || [[File:Ex2 ts exo lumo.jpg|150px]] || [[File:Ex2 ts exo lulumo.jpg|150px]]
|}
It's a inverse electron demand DA reaction due to the electron donating oxygen subsituents on dienophile. The electron richer dienophile makes the diene LUMO and dienophile HOMO more closer in energy and be the frontier orbitals.
==='''Reaction Barriers and Reaction Energies'''===
'''Barrier energy = transition state free energy- sum of reactant free energies'''
'''Reaction free energy = sum of product free energies - sum of reactant free energies'''

Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-267.068643+-233.324375))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction barrier energy:ΔrG0(298K)=(-500.073175-(-267.068643+-233.324375))*627.5095= 17.51Kcal = 73.262KJ/mol

Exo reaction barrier energy:ΔrG0(298K)=(-500.072282-(-267.068643+-233.324375))*627.5095= 18.07Kcal = 75.605KJ/mol

Endo is the more kinetic product due to the relative lower barrier energy, and the higher reaction free energy makes the exo product more thermodynamic favoured.
===Secondary orbitals and steric effects'''===
The secondary orbital interaction (non-bonding) in endo structure makes it with lower energy and react faster towards endo product. This can be testified by the oxygen-carbon overlap in the HOMO transition state MO. The oxygen in 1,3-Dioxole interacts with the carbon in cyclohexadiene so that to lower the energy barrier and make the reaction proceed faster. The smaller eclipse between two rings in exo structure makes it less steric hindered thermodynamically stable.
=='''Exercise 3'''==
{| class="wikitable" border="1"
|+ IRC Calculation for reaction path
! Exo- Diels-Alder Reaction !! Endo- Diels-Alder Reaction !! Cheletropic Reaction
|-
| [[File:Exo movie111.gif|400px]] || [[File:Endo movie111.gif|400px]] || [[File:Chele movie.gif|400px]]
|-
| [[File:Capture exo.PNG|400px]] || [[File:Capture endo.PNG|400px]] || [[File:Capture chele.PNG|400px]]
|}
==='''Activation and Reaction Energies for Each Route'''===
Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-0.113379+0.178117))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-0.113379+0.178117))*627.5095= -15.25Kcal = -63.806KJ/mol

Cheletropic reaction free energy:ΔrG0(298K)=(-500.417317-(-0.113379+0.178117))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction activation energy:ΔrG0(298K)=(0.090560-(-0.113379+0.178117))*627.5095= 16.20Kcal = 67.796KJ/mol

Exo reaction activation energy:ΔrG0(298K)=(0.092076-(-0.113379+0.178117))*627.5095= 17.15Kcal = 71.756KJ/mol

Cheletropic activation free energy:ΔrG0(298K)=(0.099061-(-0.113379+0.178117))*627.5095= 21.53Kcal = 90.082KJ/mol

Rep:MOD:SY3814

2016-12-15T23:49:01Z

Sy3814:

=='''Introduction''' ==
=== '''Potential Energy Surface''' ===
A potential energy surface(PES) is a mathematical function that describes molecule as a function of its geometry. It is commonly applied in Chemistry to theoretically explore properties of atomic structures and rates of chemical reactions.
==='''stationary points''' ===
There are two stationary points(points with zero gradient) in PES, minimum state point and transition state point. Minimum state is where the molecule in its minimum energy shape(physically stable) and the transition state is the highest energy point along a reaction coordinate.
==='''gradient and the curvature'''===
As the point is evaluated in the PES, the point can be identified by its gradient(first derivatives) and curvature(second derivatives) of the energy related to the position.
===='''Gradient''' ====
For a given molecule, '''r''' describes the position of molecule and the Function E('''r''') can be introduced as the energy of the position. The first derivative of the energy corresponds to the position of the molecule is calculated as gradient.
===Gradient = ∂E/∂r===
==== '''Curvature''' ====
In the case that the gradient is a zero vector(stationary points), second derivative matrix is used, which describes the PES curvature at '''r''' position.
===Curvature = ∂∂E/∂ri∂rj===
=='''Exercise 1'''==
==='''Reaction of Butadiene with Ethylene'''===
[[File:Buata2.PNG]]
==='''Visualised MOs'''===
{| class="wikitable" border="1"
|+ Ethylene and Butadiene MOs
! Ethylene HOMO(A) !! Ethylene LUMO(S) !! Butadiene HOMO(S) !! Butadiene LUMO(A)
|-
| [[File:Ethylene homo11.jpg|150px]] || [[File:Ethylene lumo11.jpg|150px]] || [[File:Butadiene homo11.jpg|150px]] || [[File:Butadiene lumo11.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Transition states MOs
! Occupied orbital(S) !! TS HOMO(A) !! TS LUMO(A) !! Unoccupied orbital(S)
|-
| [[File:Ts1 hohomo.jpg|150px]] || [[File:Ts1 homo.jpg|150px]] || [[File:Ts1 lumo.jpg|150px]] || [[File:Ts1 lulumo.jpg|150px]]
|}

====MO diagram for the formation of the butadiene/ethene Transition state====
[[File:Capture graham.PNG]]

The Mo diagram demonstrate that 4 TS orbital are produced by interaction between LUMO and HOMO orbitals. Correlated with Mos computed, only butadiene HOMO orbital interacts with ethylene LUMO orbital and butadiene LUMO orbital interacts with HOMO orbital in ethylene. It testifies that the reaction is allowed only when reactants in the same symmetry. The orbital overlap integral is zero in an asymmetric-asymmetric interaction and non-zero in interaction with same symmetries.
==='''bond length change in the reaction'''===
{| class="wikitable" border="1"
|+ C-C Bond Length Change
! !!Reactants !! Transition state !! Product
|-
| Ethylene C=C || 1.327Å || 1.381Å || 1.54Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| Butadiene C=C || 1.47Å || 1.41Å || 1.34Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|}
The ethylene C=C double bond length is 1.327Å and the C=C bond lengths in Butadiene are at 1.33Å, 1.47Å and 1.33Å respectively. In Transition state, the C-C bond length in ethylene is extended to 1.381Å, the C-C bond lengths in butadiene are shifted to 1.38Å, 1.41Å and 1.38Å. The C-C bond length between reactants is around 2.11Å. In the product, the reactants C-C bond length are changed to 1.54Å (Ethylene C-C), 1.50Å, 1.34Å and 1.50Å (Butadiene C-C). The C-C bond length between reactants is shortened to 1.54Å. As the data shown, the C-C bond length between reactants shorten as the reaction progresses. The butadiene C-C single bond length decreases and turns into double bond in the reaction. All reactants double bonds, in contrast, move longer and change to single bonds in the product.
==='''Vibrations'''===
In the TS vibration, the two reacting carbons from Ethylene and Butadiene vibrate vertically and move aproaching each other. The formation of the two bonds are synchronous, and the transition movement can be testified by the negative frequency (negative second derivative for the saddle point). From the computed MOs, the vibration for the lowest positive frequency is twisting around the reaction center.
=='''Exercise 2'''==
[[File:Capture 120.PNG]]
{| class="wikitable" border="1"
|+ Endo Transition state MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Hohomo ex2 endo.jpg|150px]] || [[File:Homo ex2 endo11.jpg|150px]] || [[File:Lumo ex2 endo11.jpg|150px]] || [[File:Lulumo ex2 endo.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Exo Transition State MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Ex2 hohomo exo ts.jpg|150px]] || [[File:Ex2 homo exo ts.jpg|150px]] || [[File:Ex2 ts exo lumo.jpg|150px]] || [[File:Ex2 ts exo lulumo.jpg|150px]]
|}
It's a inverse electron demand DA reaction due to the electron donating oxygen subsituents on dienophile. The electron richer dienophile makes the diene LUMO and dienophile HOMO more closer in energy and be the frontier orbitals.
==='''Reaction Barriers and Reaction Energies'''===
'''Barrier energy = transition state free energy- sum of reactant free energies'''
'''Reaction free energy = sum of product free energies - sum of reactant free energies'''

Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-267.068643+-233.324375))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction barrier energy:ΔrG0(298K)=(-500.073175-(-267.068643+-233.324375))*627.5095= 17.51Kcal = 73.262KJ/mol

Exo reaction barrier energy:ΔrG0(298K)=(-500.072282-(-267.068643+-233.324375))*627.5095= 18.07Kcal = 75.605KJ/mol

Endo is the more kinetic product due to the relative lower barrier energy, and the higher reaction free energy makes the exo product more thermodynamic favoured.
===Secondary orbitals and steric effects'''===
The secondary orbital interaction (non-bonding) in endo structure makes it with lower energy and react faster towards endo product. This can be testified by the oxygen-carbon overlap in the HOMO transition state MO. The oxygen in 1,3-Dioxole interacts with the carbon in cyclohexadiene so that to lower the energy barrier and make the reaction proceed faster. The smaller eclipse between two rings in exo structure makes it less steric hindered thermodynamically stable.
=='''Exercise 3'''==
{| class="wikitable" border="1"
|+ IRC Calculation for reaction path
! Exo- Diels-Alder Reaction !! Endo- Diels-Alder Reaction !! Cheletropic Reaction
|-
| [[File:Exo movie111.gif|400px]] || [[File:Endo movie111.gif|400px]] || [[File:Chele movie.gif|400px]]
|-
| [[File:Capture exo.PNG|400px]] || [[File:Capture endo.PNG|400px]] || [[File:Capture chele.PNG|400px]]
|}
==='''Activation and Reaction Energies for Each Route'''===
Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-0.113379+0.178117))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-0.113379+0.178117))*627.5095= -15.25Kcal = -63.806KJ/mol

Cheletropic reaction free energy:ΔrG0(298K)=(-500.417317-(-0.113379+0.178117))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction activation energy:ΔrG0(298K)=(0.090560-(-0.113379+0.178117))*627.5095= 16.20Kcal = 73.262KJ/mol

Exo reaction activation energy:ΔrG0(298K)=(0.092076-(-0.113379+0.178117))*627.5095= 17.15Kcal = 75.605KJ/mol

Cheletropic activation free energy:ΔrG0(298K)=(0.099061-(-0.113379+0.178117))*627.5095= 21.53Kcal = -63.806KJ/mol

Rep:MOD:SY3814

2016-12-15T23:22:40Z

Sy3814:

=='''Introduction''' ==
=== '''Potential Energy Surface''' ===
A potential energy surface(PES) is a mathematical function that describes molecule as a function of its geometry. It is commonly applied in Chemistry to theoretically explore properties of atomic structures and rates of chemical reactions.
==='''stationary points''' ===
There are two stationary points(points with zero gradient) in PES, minimum state point and transition state point. Minimum state is where the molecule in its minimum energy shape(physically stable) and the transition state is the highest energy point along a reaction coordinate.
==='''gradient and the curvature'''===
As the point is evaluated in the PES, the point can be identified by its gradient(first derivatives) and curvature(second derivatives) of the energy related to the position.
===='''Gradient''' ====
For a given molecule, '''r''' describes the position of molecule and the Function E('''r''') can be introduced as the energy of the position. The first derivative of the energy corresponds to the position of the molecule is calculated as gradient.
===Gradient = ∂E/∂r===
==== '''Curvature''' ====
In the case that the gradient is a zero vector(stationary points), second derivative matrix is used, which describes the PES curvature at '''r''' position.
===Curvature = ∂∂E/∂ri∂rj===
=='''Exercise 1'''==
==='''Reaction of Butadiene with Ethylene'''===
[[File:Buata2.PNG]]
==='''Visualised MOs'''===
{| class="wikitable" border="1"
|+ Ethylene and Butadiene MOs
! Ethylene HOMO(A) !! Ethylene LUMO(S) !! Butadiene HOMO(S) !! Butadiene LUMO(A)
|-
| [[File:Ethylene homo11.jpg|150px]] || [[File:Ethylene lumo11.jpg|150px]] || [[File:Butadiene homo11.jpg|150px]] || [[File:Butadiene lumo11.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Transition states MOs
! Occupied orbital(S) !! TS HOMO(A) !! TS LUMO(A) !! Unoccupied orbital(S)
|-
| [[File:Ts1 hohomo.jpg|150px]] || [[File:Ts1 homo.jpg|150px]] || [[File:Ts1 lumo.jpg|150px]] || [[File:Ts1 lulumo.jpg|150px]]
|}

====MO diagram for the formation of the butadiene/ethene Transition state====
[[File:Capture graham.PNG]]

The Mo diagram demonstrate that 4 TS orbital are produced by interaction between LUMO and HOMO orbitals. Correlated with Mos computed, only butadiene HOMO orbital interacts with ethylene LUMO orbital and butadiene LUMO orbital interacts with HOMO orbital in ethylene. It testifies that the reaction is allowed only when reactants in the same symmetry. The orbital overlap integral is zero in an asymmetric-asymmetric interaction and non-zero in interaction with same symmetries.
==='''bond length change in the reaction'''===
{| class="wikitable" border="1"
|+ C-C Bond Length Change
! !!Reactants !! Transition state !! Product
|-
| Ethylene C=C || 1.327Å || 1.381Å || 1.54Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| Butadiene C=C || 1.47Å || 1.41Å || 1.34Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|}
The ethylene C=C double bond length is 1.327Å and the C=C bond lengths in Butadiene are at 1.33Å, 1.47Å and 1.33Å respectively. In Transition state, the C-C bond length in ethylene is extended to 1.381Å, the C-C bond lengths in butadiene are shifted to 1.38Å, 1.41Å and 1.38Å. The C-C bond length between reactants is around 2.11Å. In the product, the reactants C-C bond length are changed to 1.54Å (Ethylene C-C), 1.50Å, 1.34Å and 1.50Å (Butadiene C-C). The C-C bond length between reactants is shortened to 1.54Å. As the data shown, the C-C bond length between reactants shorten as the reaction progresses. The butadiene C-C single bond length decreases and turns into double bond in the reaction. All reactants double bonds, in contrast, move longer and change to single bonds in the product.
==='''Vibrations'''===
In the TS vibration, the two reacting carbons from Ethylene and Butadiene vibrate vertically and move aproaching each other. The formation of the two bonds are synchronous, and the transition movement can be testified by the negative frequency (negative second derivative for the saddle point). From the computed MOs, the vibration for the lowest positive frequency is twisting around the reaction center.
=='''Exercise 2'''==
[[File:Capture 120.PNG]]
{| class="wikitable" border="1"
|+ Endo Transition state MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Hohomo ex2 endo.jpg|150px]] || [[File:Homo ex2 endo11.jpg|150px]] || [[File:Lumo ex2 endo11.jpg|150px]] || [[File:Lulumo ex2 endo.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Exo Transition State MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Ex2 hohomo exo ts.jpg|150px]] || [[File:Ex2 homo exo ts.jpg|150px]] || [[File:Ex2 ts exo lumo.jpg|150px]] || [[File:Ex2 ts exo lulumo.jpg|150px]]
|}
It's a inverse electron demand DA reaction due to the electron donating oxygen subsituents on dienophile. The electron richer dienophile makes the diene LUMO and dienophile HOMO more closer in energy and be the frontier orbitals.
==='''Reaction Barriers and Reaction Energies'''===
'''Barrier energy = transition state free energy- sum of reactant free energies'''
'''Reaction free energy = sum of product free energies - sum of reactant free energies'''

Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-267.068643+-233.324375))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction barrier energy:ΔrG0(298K)=(-500.073175-(-267.068643+-233.324375))*627.5095= 17.51Kcal = 73.262KJ/mol

Exo reaction barrier energy:ΔrG0(298K)=(-500.072282-(-267.068643+-233.324375))*627.5095= 18.07Kcal = 75.605KJ/mol

Endo is the more kinetic product due to the relative lower barrier energy, and the higher reaction free energy makes the exo product more thermodynamic favoured.
===Secondary orbitals and steric effects'''===
The secondary orbital interaction (non-bonding) in endo structure makes it with lower energy and react faster towards endo product. This can be testified by the oxygen-carbon overlap in the HOMO transition state MO. The oxygen in 1,3-Dioxole interacts with the carbon in cyclohexadiene so that to lower the energy barrier and make the reaction proceed faster. The smaller eclipse between two rings in exo structure makes it less steric hindered thermodynamically stable.
=='''Exercise 3'''==
{| class="wikitable" border="1"
|+ IRC Calculation for reaction path
! Exo- Diels-Alder Reaction !! Endo- Diels-Alder Reaction !! Cheletropic Reaction
|-
| [[File:Exo movie111.gif|400px]] || [[File:Endo movie111.gif|400px]] || [[File:Chele movie.gif|400px]]
|-
| [[File:Capture exo.PNG|400px]] || [[File:Capture endo.PNG|400px]] || [[File:Capture chele.PNG|400px]]
|}
==='''Activation and Reaction Energies for Each Route'''===
Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-267.068643+-233.324375))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Cheletropic reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction activation energy:ΔrG0(298K)=(-500.073175-(-267.068643+-233.324375))*627.5095= 17.51Kcal = 73.262KJ/mol

Exo reaction activation energy:ΔrG0(298K)=(-500.072282-(-267.068643+-233.324375))*627.5095= 18.07Kcal = 75.605KJ/mol

Cheletropic activation free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

File:Chele movie.gif

2016-12-15T23:20:35Z

Sy3814: Sy3814 uploaded a new version of File:Chele movie.gif

File:Exo movie111.gif

2016-12-15T23:06:06Z

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File:Capture exo.PNG

2016-12-15T23:00:42Z

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File:Endo movie111.gif

2016-12-15T22:52:27Z

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File:Capture endo.PNG

2016-12-15T22:46:33Z

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File:Capture chele.PNG

2016-12-15T22:41:46Z

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File:Chele movie.gif

2016-12-15T22:39:55Z

Sy3814:

Rep:MOD:SY3814

2016-12-15T22:16:22Z

Sy3814:

=='''Introduction''' ==
=== '''Potential Energy Surface''' ===
A potential energy surface(PES) is a mathematical function that describes molecule as a function of its geometry. It is commonly applied in Chemistry to theoretically explore properties of atomic structures and rates of chemical reactions.
==='''stationary points''' ===
There are two stationary points(points with zero gradient) in PES, minimum state point and transition state point. Minimum state is where the molecule in its minimum energy shape(physically stable) and the transition state is the highest energy point along a reaction coordinate.
==='''gradient and the curvature'''===
As the point is evaluated in the PES, the point can be identified by its gradient(first derivatives) and curvature(second derivatives) of the energy related to the position.
===='''Gradient''' ====
For a given molecule, '''r''' describes the position of molecule and the Function E('''r''') can be introduced as the energy of the position. The first derivative of the energy corresponds to the position of the molecule is calculated as gradient.
===Gradient = ∂E/∂r===
==== '''Curvature''' ====
In the case that the gradient is a zero vector(stationary points), second derivative matrix is used, which describes the PES curvature at '''r''' position.
===Curvature = ∂∂E/∂ri∂rj===
=='''Exercise 1'''==
==='''Reaction of Butadiene with Ethylene'''===
[[File:Buata2.PNG]]
==='''Visualised MOs'''===
{| class="wikitable" border="1"
|+ Ethylene and Butadiene MOs
! Ethylene HOMO(A) !! Ethylene LUMO(S) !! Butadiene HOMO(S) !! Butadiene LUMO(A)
|-
| [[File:Ethylene homo11.jpg|150px]] || [[File:Ethylene lumo11.jpg|150px]] || [[File:Butadiene homo11.jpg|150px]] || [[File:Butadiene lumo11.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Transition states MOs
! Occupied orbital(S) !! TS HOMO(A) !! TS LUMO(A) !! Unoccupied orbital(S)
|-
| [[File:Ts1 hohomo.jpg|150px]] || [[File:Ts1 homo.jpg|150px]] || [[File:Ts1 lumo.jpg|150px]] || [[File:Ts1 lulumo.jpg|150px]]
|}

====MO diagram for the formation of the butadiene/ethene Transition state====
[[File:Capture graham.PNG]]

The Mo diagram demonstrate that 4 TS orbital are produced by interaction between LUMO and HOMO orbitals. Correlated with Mos computed, only butadiene HOMO orbital interacts with ethylene LUMO orbital and butadiene LUMO orbital interacts with HOMO orbital in ethylene. It testifies that the reaction is allowed only when reactants in the same symmetry. The orbital overlap integral is zero in an asymmetric-asymmetric interaction and non-zero in interaction with same symmetries.
==='''bond length change in the reaction'''===
{| class="wikitable" border="1"
|+ C-C Bond Length Change
! !!Reactants !! Transition state !! Product
|-
| Ethylene C=C || 1.327Å || 1.381Å || 1.54Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| Butadiene C=C || 1.47Å || 1.41Å || 1.34Å
|-
| Butadiene C-C || 1.33Å || 1.38Å || 1.50Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|-
| New forming C-C bond || || 2.11Å || 1.54Å
|}
The ethylene C=C double bond length is 1.327Å and the C=C bond lengths in Butadiene are at 1.33Å, 1.47Å and 1.33Å respectively. In Transition state, the C-C bond length in ethylene is extended to 1.381Å, the C-C bond lengths in butadiene are shifted to 1.38Å, 1.41Å and 1.38Å. The C-C bond length between reactants is around 2.11Å. In the product, the reactants C-C bond length are changed to 1.54Å (Ethylene C-C), 1.50Å, 1.34Å and 1.50Å (Butadiene C-C). The C-C bond length between reactants is shortened to 1.54Å. As the data shown, the C-C bond length between reactants shorten as the reaction progresses. The butadiene C-C single bond length decreases and turns into double bond in the reaction. All reactants double bonds, in contrast, move longer and change to single bonds in the product.
==='''Vibrations'''===
In the TS vibration, the two reacting carbons from Ethylene and Butadiene vibrate vertically and move aproaching each other. The formation of the two bonds are synchronous, and the transition movement can be testified by the negative frequency (negative second derivative for the saddle point). From the computed MOs, the vibration for the lowest positive frequency is twisting around the reaction center.
=='''Exercise 2'''==
[[File:Capture 120.PNG]]
{| class="wikitable" border="1"
|+ Endo Transition state MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Hohomo ex2 endo.jpg|150px]] || [[File:Homo ex2 endo11.jpg|150px]] || [[File:Lumo ex2 endo11.jpg|150px]] || [[File:Lulumo ex2 endo.jpg|150px]]
|}
{| class="wikitable" border="1"
|+ Exo Transition State MOs
! Occupied orbital(A) !! TS HOMO(S) !! TS LUMO(S) !! Unoccupied orbital(A)
|-
| [[File:Ex2 hohomo exo ts.jpg|150px]] || [[File:Ex2 homo exo ts.jpg|150px]] || [[File:Ex2 ts exo lumo.jpg|150px]] || [[File:Ex2 ts exo lulumo.jpg|150px]]
|}
It's a inverse electron demand DA reaction due to the electron donating oxygen subsituents on dienophile. The electron richer dienophile makes the diene LUMO and dienophile HOMO more closer in energy and be the frontier orbitals.
==='''Reaction Barriers and Reaction Energies'''===
'''Barrier energy = transition state free energy- sum of reactant free energies'''
'''Reaction free energy = sum of product free energies - sum of reactant free energies'''

Endo reaction free energy:ΔrG0(298K)=(-500.418694-(-267.068643+-233.324375))*627.5095= -16.11Kcal = -67.404KJ/mol

Exo reaction free energy:ΔrG0(298K)=(-500.417317-(-267.068643+-233.324375))*627.5095= -15.25Kcal = -63.806KJ/mol

Endo reaction barrier energy:ΔrG0(298K)=(-500.073175-(-267.068643+-233.324375))*627.5095= 17.51Kcal = 73.262KJ/mol

Exo reaction barrier energy:ΔrG0(298K)=(-500.072282-(-267.068643+-233.324375))*627.5095= 18.07Kcal = 75.605KJ/mol

Endo is the more kinetic product due to the relative lower barrier energy, and the higher reaction free energy makes the exo product more thermodynamic favoured.
===Secondary orbitals and steric effects'''===
The secondary orbital interaction (non-bonding) in endo structure makes it with lower energy and react faster towards endo product. This can be testified by the oxygen-carbon overlap in the HOMO transition state MO. The oxygen in 1,3-Dioxole interacts with the carbon in cyclohexadiene so that to lower the energy barrier and make the reaction proceed faster. The smaller eclipse between two rings in exo structure makes it less steric hindered thermodynamically stable.
=='''Exercise 3'''==

Rep:MOD:SY3814

2016-12-15T22:05:36Z

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File:Lulumo ex2 endo.jpg

2016-12-15T21:09:05Z

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File:Lumo ex2 endo11.jpg

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File:Homo ex2 endo11.jpg

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File:Hohomo ex2 endo.jpg

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File:Endo ex hohomo.jpg

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File:Capture graham.PNG

2016-12-15T15:49:45Z

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2016-12-15T15:24:51Z

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File:Ts1 lulumo.jpg

2016-12-15T13:37:26Z

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File:Butadiene lumo11.jpg

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File:Butadiene homo11.jpg

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Sy3814:

File:Ethylene lumo11.jpg

2016-12-15T13:15:08Z

Sy3814:

File:Ethylene homo11.jpg

2016-12-15T13:13:49Z

Sy3814:

File:Butadiene homo.tif

2016-12-15T13:05:04Z

Sy3814: Sy3814 uploaded a new version of File:Butadiene homo.tif

File:TS1 lumo.tif

2016-12-15T12:44:04Z

Sy3814:

File:Ts1 lulumo.tif

2016-12-15T12:43:46Z

Sy3814:

File:Ts1 homo.tif

2016-12-15T12:43:36Z

Sy3814:

File:Ts1 Hohomo.tif

2016-12-15T12:43:22Z

Sy3814:

File:Ethene lumo.tif

2016-12-15T12:43:11Z

Sy3814: