ChemWiki - User contributions [en]

Rep:Mod:xm1213

2016-11-17T15:33:15Z

Xm1213: /* MOs and vibrations of the transition state */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-
|}

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bonding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds. However the lowest positive frequency demonstrate asynchronous vibration.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==
===Reactants optimisation===
Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

From the graphs, endo MOs are found to have a better overlap then exo ones. The endo transition state is expected to be more stablised than exo.

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable and lower in energy for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo product is formed rather than exo product.

==Conclusion==
This module shows different computational methods were useful to analyse a variety of pericyclic reactions. The transition states were predicted and the vibrations and energies were used to analyse the selectivity of products. However, factors like solvents and other species exist in real situation and were not included in the calculation, these effects need more calculations or real experiments to be found. In Conclusion, these methods are quite useful for chemist but should be used with caution because it is approximation and other factor could affect the result.

==Reference==

Rep:Mod:xm1213

2016-11-17T15:30:33Z

Xm1213: /* Exercise 2: Reaction of Benzoquinone with Cyclopentadiene */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-
|}

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bonding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==
===Reactants optimisation===
Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

From the graphs, endo MOs are found to have a better overlap then exo ones. The endo transition state is expected to be more stablised than exo.

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable and lower in energy for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo product is formed rather than exo product.

==Conclusion==
This module shows different computational methods were useful to analyse a variety of pericyclic reactions. The transition states were predicted and the vibrations and energies were used to analyse the selectivity of products. However, factors like solvents and other species exist in real situation and were not included in the calculation, these effects need more calculations or real experiments to be found. In Conclusion, these methods are quite useful for chemist but should be used with caution because it is approximation and other factor could affect the result.

==Reference==

Rep:Mod:xm1213

2016-11-17T15:28:58Z

Xm1213: /* MOs of the transition states */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-
|}

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bonding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

From the graphs, endo MOs are found to have a better overlap then exo ones. The endo transition state is expected to be more stablised than exo.

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable and lower in energy for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo product is formed rather than exo product.

==Conclusion==
This module shows different computational methods were useful to analyse a variety of pericyclic reactions. The transition states were predicted and the vibrations and energies were used to analyse the selectivity of products. However, factors like solvents and other species exist in real situation and were not included in the calculation, these effects need more calculations or real experiments to be found. In Conclusion, these methods are quite useful for chemist but should be used with caution because it is approximation and other factor could affect the result.

==Reference==

Rep:Mod:xm1213

2016-11-17T15:22:11Z

Xm1213: /* Energies of the TSs and selectivity */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-
|}

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bonding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable and lower in energy for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo product is formed rather than exo product.

==Conclusion==
This module shows different computational methods were useful to analyse a variety of pericyclic reactions. The transition states were predicted and the vibrations and energies were used to analyse the selectivity of products. However, factors like solvents and other species exist in real situation and were not included in the calculation, these effects need more calculations or real experiments to be found. In Conclusion, these methods are quite useful for chemist but should be used with caution because it is approximation and other factor could affect the result.

==Reference==

Rep:Mod:xm1213

2016-11-17T15:17:59Z

Xm1213:

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-
|}

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bonding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Conclusion==
This module shows different computational methods were useful to analyse a variety of pericyclic reactions. The transition states were predicted and the vibrations and energies were used to analyse the selectivity of products. However, factors like solvents and other species exist in real situation and were not included in the calculation, these effects need more calculations or real experiments to be found. In Conclusion, these methods are quite useful for chemist but should be used with caution because it is approximation and other factor could affect the result.

==Reference==

Rep:Mod:xm1213

2016-11-17T15:16:05Z

Xm1213: /* MOs and vibrations of the transition state */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bonding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Conclusion==
This module shows different computational methods were useful to analyse a variety of pericyclic reactions. The transition states were predicted and the vibrations and energies were used to analyse the selectivity of products. However, factors like solvents and other species exist in real situation and were not included in the calculation, these effects need more calculations or real experiments to be found. In Conclusion, these methods are quite useful for chemist but should be used with caution because it is approximation and other factor could affect the result.

==Reference==

Rep:Mod:xm1213

2016-11-17T15:14:53Z

Xm1213:

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Conclusion==
This module shows different computational methods were useful to analyse a variety of pericyclic reactions. The transition states were predicted and the vibrations and energies were used to analyse the selectivity of products. However, factors like solvents and other species exist in real situation and were not included in the calculation, these effects need more calculations or real experiments to be found. In Conclusion, these methods are quite useful for chemist but should be used with caution because it is approximation and other factor could affect the result.

==Reference==

Rep:Mod:xm1213

2016-11-17T15:00:01Z

Xm1213:

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table : Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table : ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table : Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table : exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table : endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table : Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

Rep:Mod:xm1213

2016-11-17T14:59:13Z

Xm1213: /* IRC analysis */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table : MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==
==Reference==

File:Exo TS IRC PM6 N200.log

2016-11-17T14:58:58Z

Xm1213: Xm1213 uploaded a new version of File:Exo TS IRC PM6 N200.log

File:Exo TS IRC PM6 N200.log

2016-11-17T14:58:53Z

Xm1213:

File:Endo TS IRC PM6 N200.log

2016-11-17T14:58:34Z

Xm1213:

Rep:Mod:xm1213

2016-11-17T14:58:16Z

Xm1213: /* IRC analysis */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===
{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| orientation
| endo
| exo
|-
| graph
| [[File:xmendoirc.gif|250px]]
| [[File:xmexoirc.gif|250px]]
|-
| IRC log file
| [[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
| [[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]
|-
|}
The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==
==Reference==

File:Xmexoirc.gif

2016-11-17T14:56:15Z

Xm1213:

File:Xmendoirc.gif

2016-11-17T14:55:56Z

Xm1213:

Rep:Mod:xm1213

2016-11-17T14:55:13Z

Xm1213: /* Exercise 2: Reaction of Benzoquinone with Cyclopentadiene */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===IRC analysis===

[[File:xmendoirc.gif|250px]]
[[File:xmexoirc.gif|250px]]
[[Media:endo TS IRC PM6 N200.log|endo TS IRC PM6 N200.log]]
[[Media:exo TS IRC PM6 N200.log|exo TS IRC PM6 N200.log]]

The endo IRC graph shows that after 200 points, the geometry of minimum energy has been found, the RMS gradient gets zero and the reaction has reached the minimum.
The exo IRC was ran for three times and all ended abnormally with error link 2070, and from the graph the minimum has not been found.
===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==
==Reference==

Rep:Mod:xm1213

2016-11-17T14:34:34Z

Xm1213: /* Energies of the Transition States */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==
==Reference==

Rep:Mod:xm1213

2016-11-17T14:27:48Z

Xm1213: /* Reference */

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==
==Reference==

Rep:Mod:xm1213

2016-11-17T14:27:33Z

Xm1213:

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
| sp3 lit.<ref>''CRC Handbook of chemistry and physics'', 2005, '''86th edition''', pp. 9-19</Ref>
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius 1.7Ǎ of Carbon atom<ref> http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4 [Accessed 30/10/12] </ref>, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==
==Reference==
1 CRC Handbook of chemistry and physics, 2005, 86th edition, pp. 9-19
2http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4

Rep:Mod:xm1213

2016-11-17T14:19:33Z

Xm1213:

=Computational Chemistry:Transition States=
==Introduction==
During this module, transition states of a variety of pericyclic reactions at different levels will be located and characterised with GaussView. The mechanism and selectivity will be explained with vibrations and energies of the transition state.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-17T14:08:50Z

Xm1213: /* Energies of the Transition States */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the TSs and selectivity===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T16:07:45Z

Xm1213: /* Energies of the Transition States */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS(Kinetic)
| -575.383855
|-
| Exo TS(Thermodynamic)
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T16:05:19Z

Xm1213: /* Exercise 2: Reaction of Benzoquinone with Cyclopentadiene */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(d).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS
| -575.383855
|-
| Exo TS
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:55:23Z

Xm1213: /* Energies of the Transition States */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS
| -575.383855
|-
| Exo TS
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}
-0.002548 a.u.=-6.68977451 kJ/mol

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable by 6.68977451 kJ/mol. And exo product is known to be more stable for being less sterically hindered, however despite being more thermodynamically stable, the Diels-Alder reaction is controlled by the kinetics which means the low energy transition state is prefered and endo adduct is formed.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:46:57Z

Xm1213: /* Optimised transition states */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90 cm-1
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80 cm-1
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS
| -575.383855
|-
| Exo TS
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable

By directly comparing the total energies of the TS at the HF/3-21G level, the Endo TS is more stable by 4.25 kcal mol-1, and therefore the activation energy of this reaction path is much lower, which would mean that the rate of reaction towards the Endo product is much faster than that of the Exo adduct. In fact, the Exo adduct, despite being the thermodynamically more stable product [3], is rarely formed at all. This is known as the Diels-Alder Endo rule, and shows that this reaction is under kinetic, rather than thermodynamic control.

==Exercise 3: Diels-Alder vs Cheletropic==

File:Exo TS b3lypd.log

2016-11-16T15:46:21Z

Xm1213:

File:Endo TS b3lypd.log

2016-11-16T15:45:58Z

Xm1213:

Rep:Mod:xm1213

2016-11-16T15:45:09Z

Xm1213: /* Exercise 2: Reaction of Benzoquinone with Cyclopentadiene */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

[[Media:endo TS b3lypd.log|endo TS b3lypd.log]]
[[Media:exo TS b3lypd.log|exo TS b3lypd.log]]

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS
| -575.383855
|-
| Exo TS
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable

By directly comparing the total energies of the TS at the HF/3-21G level, the Endo TS is more stable by 4.25 kcal mol-1, and therefore the activation energy of this reaction path is much lower, which would mean that the rate of reaction towards the Endo product is much faster than that of the Exo adduct. In fact, the Exo adduct, despite being the thermodynamically more stable product [3], is rarely formed at all. This is known as the Diels-Alder Endo rule, and shows that this reaction is under kinetic, rather than thermodynamic control.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:43:59Z

Xm1213: /* Energies of the Transition States */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

The thermodynamics is compared by the Gibbs free energy, which is labelled "Sum of electronic and thermal Free Energies" in the log file.

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS
| -575.383855
|-
| Exo TS
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable

By directly comparing the total energies of the TS at the HF/3-21G level, the Endo TS is more stable by 4.25 kcal mol-1, and therefore the activation energy of this reaction path is much lower, which would mean that the rate of reaction towards the Endo product is much faster than that of the Exo adduct. In fact, the Exo adduct, despite being the thermodynamically more stable product [3], is rarely formed at all. This is known as the Diels-Alder Endo rule, and shows that this reaction is under kinetic, rather than thermodynamic control.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:41:50Z

Xm1213: /* Energies of the Transition States */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
| Orientation
| Gibb's Free Energy(a.u.)
|-
| Endo TS
| -575.383855
|-
| Exo TS
| -575.381307
|-
| Difference in Energies(a.u.)
| -0.002548
|}

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable

By directly comparing the total energies of the TS at the HF/3-21G level, the Endo TS is more stable by 4.25 kcal mol-1, and therefore the activation energy of this reaction path is much lower, which would mean that the rate of reaction towards the Endo product is much faster than that of the Exo adduct. In fact, the Exo adduct, despite being the thermodynamically more stable product [3], is rarely formed at all. This is known as the Diels-Alder Endo rule, and shows that this reaction is under kinetic, rather than thermodynamic control.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:38:04Z

Xm1213: /* MOs of the transition states */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

===Energies of the Transition States===

{| class="wikitable" border="1"
|+ ''Table 3: Gibbs Free Energy of TSs''
|Endo TS
|Sum of electronic and thermal Free Energies= -575.383855
|-
|Exo TS
|Sum of electronic and thermal Free Energies= -575.381307
|-
|}

After comparing transition states at B3LYP/6-31G(d) level, endo TS is found to be more stable

By directly comparing the total energies of the TS at the HF/3-21G level, the Endo TS is more stable by 4.25 kcal mol-1, and therefore the activation energy of this reaction path is much lower, which would mean that the rate of reaction towards the Endo product is much faster than that of the Exo adduct. In fact, the Exo adduct, despite being the thermodynamically more stable product [3], is rarely formed at all. This is known as the Diels-Alder Endo rule, and shows that this reaction is under kinetic, rather than thermodynamic control.

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:30:49Z

Xm1213: /* MOs and vibrations of the transition state */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds.

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:24:20Z

Xm1213: /* C-C bonds length and hybirdisation */

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in reactants, TS and product(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds

The vibration shows a synchronous formation of the bonds, something characteristic of a pericyclic reaction - both bonds are formed at the same time, on the same side of the molecule.
The calculation yielded an imaginary frequency of -956.1cm-1, corresponding to the transitional reaction path. The motion shows each terminal carbon pair coming together synchronously as the bonds form. This agrees with the known fact that Diels-Alder type reactions occur in concerted manner, with all the electronic transitions occuring simultaneously. The previously sp2 carbons change geometry to sp3 hybridisation. The first positive frequency involves asynchronous motion of the ethene with respect to the butadiene

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:23:21Z

Xm1213:

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in TS(Å)''
|-
| Bond of Molecule
| Length in reactant
| Length in TS
| Length in product
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.33
| 1.38
| 1.50
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.50
| 1.41
| 1.33
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.33
| 1.38
| 1.54
| 1.33
| 1.54
|-
| partially formed bond in TS
| n/a
| 2.11
| 1.54
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.
The optimised product cyclohexene has similar value to the literature, indicating that the reaction is completed.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

The characteristic vibration which with an imaginary frequency of -948.56cm-1, shows the a synchronous formation of the bonds

The vibration shows a synchronous formation of the bonds, something characteristic of a pericyclic reaction - both bonds are formed at the same time, on the same side of the molecule.
The calculation yielded an imaginary frequency of -956.1cm-1, corresponding to the transitional reaction path. The motion shows each terminal carbon pair coming together synchronously as the bonds form. This agrees with the known fact that Diels-Alder type reactions occur in concerted manner, with all the electronic transitions occuring simultaneously. The previously sp2 carbons change geometry to sp3 hybridisation. The first positive frequency involves asynchronous motion of the ethene with respect to the butadiene

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

==Exercise 3: Diels-Alder vs Cheletropic==

Rep:Mod:xm1213

2016-11-16T15:09:53Z

Xm1213:

=Computational Chemistry:Transition States=
During this module, transition structures of a variety of pericyclic reactions will be located and characterised with GaussView.

==Exercise 1: Reaction of Butadiene with Ethylene==
===Molecular Orbitals of cis-Butadiene and ethene===

Molecules of cis-Butadiene and ethene were optimised to a minimum at PM6 level and Molecular Orbitals were generated.

{| class="wikitable" border="1"
|+ ''Table 1: Cis-butadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.04691424 a.u.
|-
|RMS Gradient Norm = 0.00003580 a.u.
|-
|Dipole Moment = 0.0732 Debye
|}
[[Media:cis-butadiene.chk|Cis-butadiene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 2: ethene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RPM6
|-
|Basis Set = ZDO
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = 0.02511137 a.u.
|-
|RMS Gradient Norm = 0.00002852 a.u.
|-
|Dipole Moment = 0.0000 Debye
|}
[[Media:ethene.chk|ethene opt.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: Cis-butadiene and ethene HOMO and LUMO''
| Molecule
| Cis-butadiene
| Cis-butadiene
| Ethene
| Ethene
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmbutadienehomo.gif|250px]]
| [[File:xmbutadienelomo.gif|250px]]
| [[File:xmethenehomo.gif|250px]]
| [[File:xmethenelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.35168
| 0.01103
| -0.39228
| 0.04256
|}

===Straight optimise a guess TS===
The planes of the molecules were kept parallel and distance between the carbon pairs 1-14 and 8-11 were set around 2.2Å.
The TS optimisation was calculated at PM6 level with a force constant.

[[File:xmtsgif.gif|250px]]

[[Media:xmtsgjf.gjf|TS.gjf]]

===C-C bonds length and hybirdisation===
{| class="wikitable" border="1"
|+ ''Bond-lengths in TS''
|-
| Bond of Molecule
| Length
| sp2 lit.
| sp3 lit.
|-
| cis-Butadiene C=C in TS
| 1.38
| 1.33
| 1.54
|-
| cis-Butadiene C-C in TS
| 1.41
| 1.33
| 1.54
|-
| ethene C=C in TS
| 1.38
| 1.33
| 1.54
|-
| partially formed bond in TS
| 2.11
| 1.33
| 1.54
|-
| ethene C=C
| 1.33
| 1.33
| 1.54
|-
| cis-Butadiene C-C
| 1.46
| 1.33
| 1.54
|-
| cis-Butadiene C=C
| 1.33
| 1.33
| 1.54
|-
| product C=C
| 1.33
| 1.33
| 1.54
|-
| product C-C- (1)
| 1.54
| 1.33
| 1.54
|-
| product C-C= (2)
| 1.50
| 1.33
| 1.54
|-
|}

The partially formed bond is longer than either bond of hybirdisation and the bond length is larger than the Van der Waals radius of Carbon atom, indicates the the bond is forming.
The length of double bond in both cis-butadiene and ethene is longer than literature value, and the length of the single bond of cis-butadiene is smaller. Both indicate that the bonds are on its midway to new hybirdisations.

===MOs and vibrations of the transition state===

{| class="wikitable" border="1"
|+ ''Table 3: Transition state HOMO and LUMO''
| Molecule
| TS cyclohexene
| TS cyclohexene
|-
| MO
| HOMO
| LUMO
|-
|
| [[File:xmtshomo.gif|250px]]
| [[File:xmtslomo.gif|250px]]
|-
| Symmetry
| Symmetric
| Symmetric
|-
| Energy a.u.
| -0.32533
| 0.01732
|-

The HOMO of the TS showed the symmetric π-orbitals of the butadiene interacting with the symmetric π orbital of ethene. The symmetries of the orbitals indicate the reaction is allowed.
The LUMO of the TS showed the symmetric π*-orbitals of the butadiene interacting with the symmetric π orbital of ethene. Also the symmetries of the orbitals indicate the reaction is allowed. Since there were more antibonding component in the LUMO and more bongding component in HOMO, HOMO is more stablised and lower in energy.

===Vibration of the Transition State===

==Exercise 2: Reaction of Benzoquinone with Cyclopentadiene==

Molecules of the reactant Benzoquinone and Cyclopentadiene were optimised at PM6 level and then refined with B3LYP/6-31G(D).

{| class="wikitable" border="1"
|+ ''Table 1: cyclopentadiene optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -194.10106256 a.u.
|-
|RMS Gradient Norm = 0.00006295 a.u.
|-
|Dipole Moment = 0.4371 Debye
|-
|}
[[Media:cyclopentadiene b3lypd.chk|cyclopentadiene b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: Benzoquinone optimisation summary''
|-
|File Type = .chk
|-
|Calculation Type = FOPT
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -381.45168107 a.u.
|-
|RMS Gradient Norm = 0.00013109 a.u.
|-
|Dipole Moment = 0.0001 Debye
|-
|}
[[Media:Benzoquinone b3lypd.chk|Benzoquinone b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 3: cyclopentadiene and Benzoquinone HOMO and LUMO''
| Molecule
| cyclopentadiene
| cyclopentadiene
| Benzoquinone
| Benzoquinone
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmcyclopentadienehomo.gif|250px]]
| [[File:xmcyclopentadienelomo.gif|250px]]
| [[File:xmBenzoquinonehomo.gif|250px]]
| [[File:xmBenzoquinonelomo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Symmetric
| Symmetric
| Asymmetric
|-
| energy/a.u.
| -0.21154
| -0.00984
| -0.27056
| -0.12991
|}
===Pre-Guess Transition States and freeze reacting pair===
Frozen Coordinate Method was used for this exercise and the molecules of reactant were placed in either the endo or exo orientation. The reacting carbon pairs were frozen with redundant and the geometries were optimised to minimum at PM6 level. After that, both geometries were optimised as transition state with force constant at PM6 level and refined at B3LYP/6-31G(d) level

===Optimised transition states===

{| class="wikitable" border="1"
|+ ''Table 1: exo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52653489 a.u.
|-
|RMS Gradient Norm = 0.00000373 a.u.
|-
|Imaginary Freq = -440.90
|-
|Dipole Moment = 2.7679 Debye
|-
|}
[[Media:exo TS b3lypd.chk|exo TS b3lypd.chk]]

{| class="wikitable" border="1"
|+ ''Table 1: endo transition state summary''
|-
|File Type = .chk
|-
|Calculation Type = FREQ
|-
|Calculation Method = RB3LYP
|-
|Basis Set = 6-31G(D)
|-
|Charge = 0
|-
|Spin = Singlet
|-
|Total Energy = -575.52914752 a.u.
|-
|RMS Gradient Norm = 0.00000433 a.u.
|-
|Imaginary Freq = -439.80
|-
|Dipole Moment = 3.1960 Debye
|-
|}

[[Media:endo TS b3lypd.chk|endo TS b3lypd.chk]]

===MOs of the transition states===

{| class="wikitable" border="1"
|+ ''Table 3: MOs of TS of exo and endo orientations''
| Orientation
| exo
| exo
| endo
| endo
|-
| MO
| HOMO
| LUMO
| HOMO
| LUMO
|-
|
| [[File:xmexotshomo.gif|250px]]
| [[File:xmexotslumo.gif|250px]]
| [[File:xmendotshomo.gif|250px]]
| [[File:xmendotslumo.gif|250px]]
|-
| Symmetry
| Asymmetric
| Asymmetric
| Asymmetric
| Asymmetric
|-
| energy/a.u.
| -0.24350
| -0.09990
| -0.24114
| -0.09090
|}

==Exercise 3: Diels-Alder vs Cheletropic==

File:Xmtslomo.gif

2016-11-16T14:23:10Z

Xm1213:

File:Xmtshomo.gif

2016-11-16T14:22:42Z

Xm1213:

Rep:Mod:xm1213

2016-11-16T14:22:21Z

Xm1213:

Rep:Mod:xm1213

2016-11-16T14:21:38Z

Xm1213:

Rep:Mod:xm1213

2016-11-15T17:16:21Z

Xm1213: /* C-C bonds length and hybirdisation */

Rep:Mod:xm1213

2016-11-15T17:04:42Z

Xm1213:

File:Xmendotslumo.gif

2016-11-15T16:42:46Z

Xm1213:

File:Xmendotshomo.gif

2016-11-15T16:42:33Z

Xm1213:

File:Xmexotslumo.gif

2016-11-15T16:42:20Z

Xm1213:

File:Endo TS b3lypd.chk

2016-11-15T16:42:06Z

Xm1213:

File:Exo TS b3lypd.chk

2016-11-15T16:41:51Z

Xm1213:

File:Xmexotshomo.gif

2016-11-15T16:41:32Z

Xm1213:

Rep:Mod:xm1213

2016-11-15T16:39:37Z

Xm1213:

Rep:Mod:xm1213

2016-11-15T16:26:30Z

Xm1213:

Rep:Mod:xm1213

2016-11-15T16:24:15Z

Xm1213: