ChemWiki - User contributions [en]

User:St908(module3)

2011-02-18T16:01:04Z

St908: /* Activation Energy */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {{DOI|10.1021/ja00111a016}}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å. The imaginary vibrational frequency is observed at -806cm<sup>-1</sup> tells us the reaction is concerted formation as the vibration is symmetrical.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! sp<sup>2</sup>-sp<sup>2</sup> C-C single bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|-
! New σ bond formed in transition state(Å)
| colspan="4" style="text-align: center;" | 2.12
|}

C-C single bond in TS is longer than literature while C=C double bond is shorter than literature. In transition state, all the bonds involved in the reaction are transient bond whose nature is a mixture of double and single bond. The new σ bond formed in transition state is 2.12Å which is much longer than the covalent C-C bond length.

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

<references/>

User:St908(module3)

2011-02-18T16:00:24Z

St908:

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å. The imaginary vibrational frequency is observed at -806cm<sup>-1</sup> tells us the reaction is concerted formation as the vibration is symmetrical.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! sp<sup>2</sup>-sp<sup>2</sup> C-C single bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|-
! New σ bond formed in transition state(Å)
| colspan="4" style="text-align: center;" | 2.12
|}

C-C single bond in TS is longer than literature while C=C double bond is shorter than literature. In transition state, all the bonds involved in the reaction are transient bond whose nature is a mixture of double and single bond. The new σ bond formed in transition state is 2.12Å which is much longer than the covalent C-C bond length.

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

<references/>

User:St908(module3)

2011-02-18T15:59:06Z

St908:

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å. The imaginary vibrational frequency is observed at -806cm<sup>-1</sup> tells us the reaction is concerted formation as the vibration is symmetrical.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! sp<sup>2</sup>-sp<sup>2</sup> C-C single bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|-
! New σ bond formed in transition state(Å)
| colspan="4" style="text-align: center;" | 2.12
|}

C-C single bond in TS is longer than literature while C=C double bond is shorter than literature. In transition state, all the bonds involved in the reaction are transient bond whose nature is a mixture of double and single bond. The new σ bond formed in transition state is 2.12Å which is much longer than the covalent C-C bond length.

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

</ref>

User:St908(module3)

2011-02-18T15:58:00Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å. The imaginary vibrational frequency is observed at -806cm<sup>-1</sup> tells us the reaction is concerted formation as the vibration is symmetrical.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! sp<sup>2</sup>-sp<sup>2</sup> C-C single bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|-
! New σ bond formed in transition state(Å)
| colspan="4" style="text-align: center;" | 2.12
|}

C-C single bond in TS is longer than literature while C=C double bond is shorter than literature. In transition state, all the bonds involved in the reaction are transient bond whose nature is a mixture of double and single bond. The new σ bond formed in transition state is 2.12Å which is much longer than the covalent C-C bond length.

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:53:36Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! sp<sup>2</sup>-sp<sup>2</sup> C-C single bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|-
! New σ bond formed in transition state(Å)
| colspan="4" style="text-align: center;" | 2.12
|}

C-C single bond in TS is longer than literature while C=C double bond is shorter than literature. In transition state, all the bonds involved in the reaction are transient bond whose nature is a mixture of double and single bond. The new σ bond formed in transition state is 2.12Å which is much longer than the covalent C-C bond length.

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:52:31Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! sp<sup>2</sup>-sp<sup>2</sup> C-C single bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|-
! New σ bond formed in transition state(Å)
| colspan="4" style="text-align: center;" | 2.12
|}

C-C single bond in TS is longer than literature while C=C double bond is shorter than literature. In transition state, all the bonds involved in the reaction are transient bond whose nature is a mixture of double and single bond.
[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:52:06Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! sp<sup>2</sup>-sp<sup>2</sup> C-C single bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
! sp<sup>2</sup>-sp<sup>2</sup> C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|-
! New σ bond formed in transition state(Å)
| 2.12
|}

C-C single bond in TS is longer than literature while C=C double bond is shorter than literature. In transition state, all the bonds involved in the reaction are transient bond whose nature is a mixture of double and single bond.
[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:46:25Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! C-C single bond
! C=C double bond
! C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
|-
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|}

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:46:11Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

{| style="width: 60%" border="1"
|+ '''Bond length in TS'''
|-
!
! colspan="2" style="text-align: center;" | Butadiene
! Ethene
|-
!
! C-C single bond
! C=C double bond
! C=C double bond
|-
! Calculated bond length in TS(Å)
| 1.40
| 1.38
| 1.38
! Normal bond length(Å)
| 1.47
| 1.34
| 1.34
|}

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:40:42Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:39:54Z

St908: /* Examine the transition state */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

{| style="width: 50%" border="1"
|+ '''Bond length'''
|-
!
! C=C
! C-C

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:35:39Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

For ''exo'' TS, the immaginary frequency is observed at -811.53cm<sup>-1</sup> while 6 immaginary modes from -38 to-989cm<sup>-1</sup> are observed in endo TS. This attribute to plenty of orbital interactions other than the interaction used for forming new bond in diels alder reaction. The immaginary vibration in ''exo'' shows concerted bond formation.

User:St908(module3)

2011-02-18T15:25:28Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal sp<sup>3</sup> C-C bond length and sp<sup>2</sup> C=C bond length are about 1.54Å and 1.34Å respectively. The C-C bonds in cyclohexadiene that involved in the reaction in transtion state are around 1.39Å for both ''endo'' and ''exo'' TS while the C-C bond in maleic anhydride is about 1.41Å. These bond length are in the middle of length of single and double bond. The C-C new bond being formed in TS are 2.16Å and 2.17Ά which are much larger than the covalent C-C bond length. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap. If we compare the overlap between ''endo'' and ''exo'', the interaction distance indicate the ''exo'' has weaker overlap due to longer distance. In addition, both HOMO and HOMO-1 in ''endo'' transition state have overlap with same symmetry. The ''exo'' transition sate only has interaction between σC-H and πC=O in its HOMO.

User:St908(module3)

2011-02-18T14:56:59Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|-
! Bond length between transition state C-C interaction
| 2.16Å
| 2.17Å
|}

Normal C-C single bond length is about 1.54Å compared with 2.16Å and 2.17Ά in transition states. If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
|
! ''endo''
! ''exo''
|-
!
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|-
! Interaction distance(''endo'':-C=O and -CH=CH- distance through space, ''exo'':-CH<sub>2</sub>-CH<sub>2</sub>- and -C=O)
| 2.89Å
| 2.94Å
|}

We can see that all the C=O π or π* orbital has same symmetry as its face to face orbital through space. This interaction distance is about 0.8Å longer than primary interaction in transition state(2.16-2.17Å). Therefore the secondary overlap is much weaker than the primary overlap.

User:St908(module3)

2011-02-18T13:57:34Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ '''transition structure and their Orbitals'''
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|}

If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

{| style="width: 50%" border="1"
|+ '''Secondary orbital overlap'''
|-
! ''endo''
! ''exo''
|-
| [[Image:endo TS 2nd stang.jpg]]
| [[Image:exo TS 2nd stang.jpg]]
|}

User:St908(module3)

2011-02-18T13:53:06Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ transition structure and their Orbitals
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

From the illustration in the table above, we can conclude the HOMO of cyclohexadiene overlap with LUMO of maleic anhydride for both ''endo'' and ''exo'' transition state. This is consistent with the face that oxygen atom is electronegative and lower the energy of maleic anhydrous compared to ethene. Therefore the cyclohexadiene is acting as electron donor.

{| style="width: 50%" border="1"
|+ '''Energy Summary of TS'''
|-
!
! ''endo''
! ''exo''
|-
! electronic energy(Hartree)
| -0.051594
| -0.050503
|}

If we compare the electronic energy between ''endo'' and ''exo'' TS, ''endo'' TS is about 0.68kcal/mol more stable than ''exo'' TS. If we only consider that the ''exo'' TS conformation has less steric effect than ''endo'' TS, then ''exo'' have to be stablet than ''endo'' conformation. However, the secondary orbital overlap is a stronger influence than steric reason.

User:St908(module3)

2011-02-18T13:34:07Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ transition structure and their Orbitals
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|300px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|300px]]
|}

User:St908(module3)

2011-02-18T13:33:45Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ transition structure and their Orbitals
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:haxadiene HOMO stang.jpg|150px]]
| [[Image:haxadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|250px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|250px]]
|}

User:St908(module3)

2011-02-18T13:33:18Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ transition structure and their Orbitals
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:hexadiene HOMO stang.jpg|150px]]
| [[Image:hexadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS stang.jpg|150px]]
| [[Image:endo TS HOMO stang.jpg|150px]]
|-
! ''exo'' TS[[Image:exo TS stang.jpg|150px]]
| [[Image:exo TS HOMO stang.jpg|150px]]
|}

User:St908(module3)

2011-02-18T13:32:10Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ transition structure and their Orbitals
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg|150px]]
| [[Image:maleic acid HOMO stang.jpg|150px]]
| [[Image:maleic acid LUMO stang.jpg|150px]]
|-
! Cyclohaxa-1,3-diene[[Image:haxadiene stang.jpg|150px]]
| [[Image:hexadiene HOMO stang.jpg|150px]]
| [[Image:hexadiene LUMO stang.jpg|150px]]
|-
! ''endo'' TS[[Image:endo TS.jpg|150px]]
| [[Image:endo TS HOMO.jpg|150px]]
|-
! ''exo'' TS[[Image:exo TS.jpg|150px]]
| [[Image:exo TS HOMO.jpg|150px]]
|}

User:St908(module3)

2011-02-18T13:28:51Z

St908: /* Diels alder(maleic anhydride and cyclohexa-1,3-diene */

The module2 is moved to [https://wiki.ch.ic.ac.uk/wiki/index.php?title=User:St908%28module2%29 module2]

===Tutorial===

====Optimizing the Reactants and Products====

{| style="width: 45%" border="1"
|+ '''Results of Optimisation'''
|-
!
! colspan="4" style="text-align: center;" | Anti conformation
! colspan="6" style="text-align: center;" | gauche conformation
|-
|
| Anti 1
| Anti 2
| Anti 3
| Gauche 1
| Gauche 2
| Gauche 3
|-
|
| [[Image:anti 1 s tang.jpg]]
| [[Image:anti 2 s tang.jpg]]
| [[Image:anti 3 s tang.jpg]]
| [[Image:gauche 1 s tang.jpg]]
| [[Image:gauche 2 s tang.jpg]]
| [[Image:gauche 3 s tang.jpg]]
|-
! Energy(Hatree)
| -231.692535
| -231.690971
| -231.689071
| -231.692661
| -231.691530
| -231.687716
|-
! Symmetry
| Ci
| C1
| C2h
| C1
| C2
| C2
|}

'''Anti 1 Ci''' conformation is optimised using more precise method,DFT with basis set 6-31G*. The energy of this optimised structure is -234.61171 Hatree which is 3 about hartree higher than the energy(-231.692535) obtained with HF/3-21G. These two structure has nearly no difference but the dihedral angles slightly differs with each other. (Note: The dihedral angle of centre four atoms calculated from 6-31G is exactly 180° which shows strict anti-conformation compared to a small deviation of dihedral angle obtained from 3-21G)

=====Thermodynamic=====

Procedure: The optimised Ci anti2 conformation of 1,5-hexadiene is confirmed by frequency analysis. Its thermodynamic properties is extracted from the log file.

{| style="width: 55%" border="1"
|+ '''Thermodynamic properties'''
|-
! Sum of electronic and zero point energies(0K)
| -234.4692 Hatree
|-
! Sum of electronic and thermal energies(298.15K and 1atm)
| -234.4619 Hatree
|-
! Sum of electronic and thermal enthalpies(298.15K and 1atm)
| -234.4609 Hatree
|-
! Sum of electronic and thermal Free energies(298.15K and 1atm)
| -234.5008 Hatree
|}

====Transition State Optimisation====

=====Chair transition state=====

<jmol><jmolApplet><title>Chair TS by one step calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''ONE step''' calculation

<jmol><jmolApplet><title>Chair TS by two steps calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>DERIVATIVE OPT stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Chair TS by '''TWO steps''' calculation

{| style="width: 55%" border="1"
|+ '''Comparison of structures of chair TS'''
|-
! Method use
! (b)one step Method
! (c)(d)Two steps Method
|-
! Bond length between terminal C-C(Å)
| 2.0199
| 2.0206
|-
! Energy(Hatree)
| -231.61932231
| -231.61932247
|-
! Imaginary Frequency(cm<sup>-1</sup>)
| -817.854
| -817.926
|}

The Transition states of cope rearrangement reaction calculated using two methods are very similar in structures, energy and vibrational frequency. For the one step calculation method, as the accuracy of prediction can be enhanced by drawing the structure of transition state closer to ideal structure, the calculated result becomes less reliable if the structure transition state is not well defined. The two steps method has similar limitation but its calculation is simple as optimisation of the conformation of two allyl fragments are not involved in the optimisation of the transient bonds between two fragments. The results produced illustrates that the two steps method performs a good approximation compared to one step method. It can be introduced to optimise larger molecule which would consume more ICT system resources.

=====Boat transition state=====

<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>boat QTS2 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
Boat transition structure by QTS2 calculation

'''IRC calculation:''' Find the conformation relaxing from transition state with lowest energy path.(forward reaction here)

The transition structure can be predicted by providing guessed reactant and product using QTS2 calculating methods. However, the product may not be the most favourable product forming from predicted transition state. The IRC method can predict the favourable product in either direction. The transition structure was performed IRC calculation with N(number of reaction coordinates) equals to 50. The resultant energy did not reach minimum since the IRC gradient did not converge to zero. Since the gradient for the last structure was very close to zero(gradient=0.00087), it got optimised using DFT/BL3YP with basis set 6-31G*. I also repeated the calculation but this time the N point was set to 70. The IRC results showed that minimum energy was achieved at the 69th structure.

{| style="width: 55%" border="1"
|+ '''IRC results comparison'''
|-
!
! 50<sup>th</sup> structure followed by optimisation
<jmol><jmolApplet><title>irc50</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 50 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
! 69<sup>th</sup> structure
<jmol><jmolApplet><title>Boat QTS2 calculation</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>irc 70 stang.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
! Energy(Hatree)
| -234.611329
| -234.611177
|-
! Gradient
| 0.0000077
| 0.0001
|}

Using two methods shown above, the two product has similar structure resembling the Gauche3/C1 structure which is also the lowest energy conformation in Appendix2. As two predictions are similar, the first method, optimisation of the last structure provides precision rather than accuracy as the gradient is 0.0000077, much more precise than 0.0001. The most favourable conformation can be only obtained in ideal condition(ie. zero point energy) as interconversion of different conformations occurs in experimental condition(ie. high temperature)

====Activation Energy====

Using higher level calculation method, dft/b3lyp with basis set 6-31G*, the transition structure and its related reactant got further optimised. This process can enhance the accuracy of predicting the activation energy. The strategy of choosing reactant for comparison is to choose the one resembles the transtion state. The energy differences between the reactants with different conformations are less than 3kcal/mol that will not affect the results strongly. The activation energy required for interconversion between different conformation is around 4-6kcal/mol<ref>Benjamin W. Gung, Zhaohai Zhu, and Rebecca A. Fouch, ''J. Am. Chem. SOC.'' 1995,117, 1783-1788 {DOI|10.1021/ja00111a016}</ref> At elevated temperature where the Cope rearrangement reaction can proceed, all the conformations will convert to the conformation close to the transition states(boat or chair).

{| style="width: 60%" border="1"
|+ '''Energy of reactants and product Summary (All the data below is based on B3LYP/6-31G*)'''
|-
!
! colspan="2" style="text-align: center;" | Reactants
! colspan="2" style="text-align: center;" | Transition states
|-
!
! Anti2(Ci)[[Image:Anti2.jpg|120px]]
! Gauche3 (C1)[[Image:Gauche3.jpg|120px]]
! Chair[[Image:Appendix2a.jpg|200px]]
! Boat[[Image:Appendix2b.jpg|200px]]
|-
! Energy(T=0K, zero-point energy, Hartree)
| -234.469204
| -234.468693
| -234.414929
| -234.402341
|-
! Energy(T=298.15K, Hartree)
| -234.461857
| -234.461464
| -234.409008
| -234.396007
|}

The energy difference between conformation of two reactant(3kcal/mol) is smaller compared with difference between two transition states(8kcal/mol)

{| style="width: 60%" border="1"
|+ '''Activation energy estimation'''
|-
!
! Anti2(reactant) → Chair(TS)
! Gauche3(reactant) → Boat(TS)
|-
! Activation energy(0K, kcal/mol)
| 34.05(4s.f)
| 41.63(4s.f)
|-
! Activation energy(298.15K, kcal/mol)
| 33.17(4s.f)
| 41.08(4s.f)
|-
! Experimental activation energy at 0K(kcal/mol)
| 33.5±0.5
| 44.7±2.0
|}

For activation energy via chair transition structure at 0K, the calculated value is 0.05kcal/mol higher than the experimental results including error which the prediction is acceptable. For boat transition structure, the calculated results is 1.07kcal/mol lower than the experimental value including error. This deviation from experimental is caused by the limitation of methods and basis set used for molecular modelling. The activation energy via both transition states at room temperature and pressure are lower than that at zero point energy. We can deduce that the energy increase of the transition state is less than the energy increase of the corresponding reactant.

===Diels Alder Reaction===

=====Butadiene HOMO and LUMO symmetry=====

<jmol><jmolApplet><title>Butadiene</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>butadiene stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Cis-Butadiene structure''

{| style="width: 50%" border="1"
| style="text-align: center;" | '''LUMO'''
| style="text-align: center;" | '''HOMO'''
|-
| [[Image:butadiene LUMO stang.jpg]]
| [[Image:butadiene HOMO stang.jpg]]
|}

=====Examine the transition state=====

The transient double bond is used to plot the butadiene fragment for gaussian input file as all three bonds are involved in the reaction. Therefore the bond length of transient double bond is close to the length of bond being formed and broken during transition state. The distance between the terminal carbon of two reactants is adjust approximately to 2Å. The optimised transition structure shows the distance of bond being formed is about 2.12Å.

<jmol><jmolApplet><title>Diels alder TS</title><color>black</color>
<size>180</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>diels alder TS stang.mol</uploadedFileContents>
</jmolApplet></jmol>
''Optimised Transition structure''

[[Image:HOMO TS stang.jpg]]

====Diels alder(maleic anhydride and cyclohexa-1,3-diene====

Using optimisation of TS(berny) with semiempirical AM1 methods, the transition state of diels alder reaction bewteen maleic anhyride and cylcohexa-1,3-diene is calculated with MO information. As this reaction is normally governed by kinetic aspects, ''endo'' and ''exo'' transition state are calculated for analysis.

{| style="width: 50%" border="1"
|+ transition structure and their Orbitals
|-
!
! HOMO
! LUMO
|-
! Maleic anhydride[[Image:maleic acid stang.jpg]]
| [[Image:maleic acid HOMO stang.jpg]]
| [[Image:maleic acid LUMO stang.jpg]]
|-
! Cyclohaxa-1,3-diene[[Image:hexadiene stang.jpg]]
| [[Image:hexadiene HOMO stang.jpg]]
| [[Image:hexadiene LUMO stang.jpg]]
|-
! ''endo'' TS[[Image:endo TS.jpg]]
| [[Image:endo TS HOMO.jpg]]
|-
! ''exo'' TS[[Image:exo TS.jpg]]
| [[Image:exo TS HOMO.jpg]]
|}

File:Maleic acid stang.jpg

2011-02-18T13:24:18Z

St908:

File:Maleic acid LUMO stang.jpg

2011-02-18T13:24:12Z

St908:

File:Maleic acid HOMO stang.jpg

2011-02-18T13:24:06Z

St908:

File:Haxadiene stang.jpg

2011-02-18T13:23:36Z

St908:

File:Haxadiene LUMO stang.jpg

2011-02-18T13:23:28Z

St908:

File:Haxadiene HOMO stang.jpg

2011-02-18T13:23:22Z

St908:

File:Exo TS stang.jpg

2011-02-18T13:23:16Z

St908:

File:Exo TS HOMO stang.jpg

2011-02-18T13:23:10Z

St908:

File:Exo TS 2nd stang.jpg

2011-02-18T13:23:04Z

St908:

File:Endo TS stang.jpg

2011-02-18T13:22:57Z

St908:

File:Endo TS HOMO stang.jpg

2011-02-18T13:22:49Z

St908:

File:Endo TS 2nd stang.jpg

2011-02-18T13:22:41Z

St908:

User:St908(module3)

2011-02-18T12:40:16Z

St908: /* Examine the transition state */

User:St908(module3)

2011-02-18T12:36:05Z

St908: /* Examine the transition state */

User:St908(module3)

2011-02-17T15:21:56Z

St908: /* Examine the transition state */

User:St908(module3)

2011-02-17T15:21:44Z

St908: /* Examine the transition state */

File:HOMO TS stang.jpg

2011-02-17T15:21:26Z

St908:

User:St908(module3)

2011-02-17T15:17:24Z

St908: /* Examine the transition state */

User:St908(module3)

2011-02-17T15:06:42Z

St908: /* Butadiene HOMO and LUMO symmetry */

File:Diels alder TS stang.mol

2011-02-17T15:06:09Z

St908:

User:St908(module3)

2011-02-17T14:29:00Z

St908: /* Butadiene HOMO and LUMO symmetry */

User:St908(module3)

2011-02-17T14:28:47Z

St908: /* Butadiene HOMO and LUMO symmetry */

User:St908(module3)

2011-02-17T14:28:08Z

St908: /* Butadiene HOMO and LUMO symmetry */

User:St908(module3)

2011-02-17T14:26:29Z

St908: /* Butadiene HOMO and LUMO symmetry */

User:St908(module3)

2011-02-17T14:26:15Z

St908: /* Butadiene HOMO and LUMO symmetry */

User:St908(module3)

2011-02-17T14:22:13Z

St908: /* Butadiene HOMO and LUMO symmetry */

User:St908(module3)

2011-02-17T14:21:58Z

St908: /* Butadiene HOMO and LUMO symmetry */

User:St908(module3)

2011-02-17T14:20:32Z

St908:

User:St908(module3)

2011-02-17T14:19:49Z

St908: