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Rep:Mod:usagiphysical

2014-11-07T09:17:41Z

Myh11: /* The Transition State of prototype reaction between ethylene and butadiene */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

**1Ha = 627.509 kcal/mol

{| class="wikitable" border="1"
|+ Summary of Activation Energies / kcal/mol
! ||HF/3-21G||HF/3-21G||B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
!
| at 0 K||at 298.15 K||at 0 K||at 298.15 K||at 0 K
|-
! ΔE (Chair)
|45.70||44.70||34.07||33.16||33.5 ± 0.5
|-
!ΔE (Boat)
|55.60||54.76||41.95||41.32||44.7 ± 2.0
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
[[File:Cis butadiene structure.JPG|thumbnail]]
|-
|HOMO||[[File:Antis HOMO of cis-butadiene.JPG |200px|thumb|left|anti-symmetric]]
|-
|LUMO||[[File:Symmetric LUMO of cis-butadiene.JPG |200px|thumb|left|symmetric]]
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879719
|-
| .log file||
[[File:CIS BUTADIENE 1.LOG|thumbnail]]
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

[[File:Ii)freq.gif|frame|'''Figure 11.'''animation of the butadiene and ethylene cycloaddtion TS [[File:II)FREQ.LOG]]]]

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==
<references/>

Rep:Mod:usagiphysical

2014-11-07T08:25:39Z

Myh11: /* The Transition State of prototype reaction between ethylene and butadiene */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

**1Ha = 627.509 kcal/mol

{| class="wikitable" border="1"
|+ Summary of Activation Energies / kcal/mol
! ||HF/3-21G||HF/3-21G||B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
!
| at 0 K||at 298.15 K||at 0 K||at 298.15 K||at 0 K
|-
! ΔE (Chair)
|45.70||44.70||34.07||33.16||33.5 ± 0.5
|-
!ΔE (Boat)
|55.60||54.76||41.95||41.32||44.7 ± 2.0
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
[[File:Cis butadiene structure.JPG|thumbnail]]
|-
|HOMO||[[File:Antis HOMO of cis-butadiene.JPG |200px|thumb|left|anti-symmetric]]
|-
|LUMO||[[File:Symmetric LUMO of cis-butadiene.JPG |200px|thumb|left|symmetric]]
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879719
|-
| .log file||
[[File:CIS BUTADIENE 1.LOG|thumbnail]]
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

[[File:Ii)freq.gif|frame|animation of the butadiene and ethylene cycloaddtion TS [[File:II)FREQ.LOG]]]]

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==
<references/>

Rep:Mod:usagiphysical

2014-11-07T08:25:10Z

Myh11: /* The Transition State of prototype reaction between ethylene and butadiene */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

**1Ha = 627.509 kcal/mol

{| class="wikitable" border="1"
|+ Summary of Activation Energies / kcal/mol
! ||HF/3-21G||HF/3-21G||B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
!
| at 0 K||at 298.15 K||at 0 K||at 298.15 K||at 0 K
|-
! ΔE (Chair)
|45.70||44.70||34.07||33.16||33.5 ± 0.5
|-
!ΔE (Boat)
|55.60||54.76||41.95||41.32||44.7 ± 2.0
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
[[File:Cis butadiene structure.JPG|thumbnail]]
|-
|HOMO||[[File:Antis HOMO of cis-butadiene.JPG |200px|thumb|left|anti-symmetric]]
|-
|LUMO||[[File:Symmetric LUMO of cis-butadiene.JPG |200px|thumb|left|symmetric]]
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879719
|-
| .log file||
[[File:CIS BUTADIENE 1.LOG|thumbnail]]
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

[[File:Ii)freq.gif|thumbnail|animation of the butadiene and ethylene cycloaddtion TS [[File:II)FREQ.LOG]]]]

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==
<references/>

File:II)FREQ.LOG

2014-11-07T08:24:21Z

Myh11:

File:Ii)freq.gif

2014-11-07T08:19:39Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T08:17:56Z

Myh11: /* Reference */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

**1Ha = 627.509 kcal/mol

{| class="wikitable" border="1"
|+ Summary of Activation Energies / kcal/mol
! ||HF/3-21G||HF/3-21G||B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
!
| at 0 K||at 298.15 K||at 0 K||at 298.15 K||at 0 K
|-
! ΔE (Chair)
|45.70||44.70||34.07||33.16||33.5 ± 0.5
|-
!ΔE (Boat)
|55.60||54.76||41.95||41.32||44.7 ± 2.0
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
[[File:Cis butadiene structure.JPG|thumbnail]]
|-
|HOMO||[[File:Antis HOMO of cis-butadiene.JPG |200px|thumb|left|anti-symmetric]]
|-
|LUMO||[[File:Symmetric LUMO of cis-butadiene.JPG |200px|thumb|left|symmetric]]
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879719
|-
| .log file||
[[File:CIS BUTADIENE 1.LOG|thumbnail]]
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==
<references/>

Rep:Mod:usagiphysical

2014-11-07T08:03:41Z

Myh11: /* Cis Butadiene */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

**1Ha = 627.509 kcal/mol

{| class="wikitable" border="1"
|+ Summary of Activation Energies / kcal/mol
! ||HF/3-21G||HF/3-21G||B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
!
| at 0 K||at 298.15 K||at 0 K||at 298.15 K||at 0 K
|-
! ΔE (Chair)
|45.70||44.70||34.07||33.16||33.5 ± 0.5
|-
!ΔE (Boat)
|55.60||54.76||41.95||41.32||44.7 ± 2.0
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
[[File:Cis butadiene structure.JPG|thumbnail]]
|-
|HOMO||[[File:Antis HOMO of cis-butadiene.JPG |200px|thumb|left|anti-symmetric]]
|-
|LUMO||[[File:Symmetric LUMO of cis-butadiene.JPG |200px|thumb|left|symmetric]]
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879719
|-
| .log file||
[[File:CIS BUTADIENE 1.LOG|thumbnail]]
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

User:Myh11

2014-11-07T08:02:56Z

Myh11: Blanked the page

File:CIS BUTADIENE 1.LOG

2014-11-07T08:02:18Z

Myh11:

File:Symmetric LUMO of cis-butadiene.JPG

2014-11-07T08:00:38Z

Myh11:

File:Antis HOMO of cis-butadiene.JPG

2014-11-07T07:59:15Z

Myh11:

File:Cis butadiene structure.JPG

2014-11-07T07:58:14Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T07:57:10Z

Myh11: /* Activation Energies */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

**1Ha = 627.509 kcal/mol

{| class="wikitable" border="1"
|+ Summary of Activation Energies / kcal/mol
! ||HF/3-21G||HF/3-21G||B3LYP/6-31G* || B3LYP/6-31G* ||Expt.
|-
!
| at 0 K||at 298.15 K||at 0 K||at 298.15 K||at 0 K
|-
! ΔE (Chair)
|45.70||44.70||34.07||33.16||33.5 ± 0.5
|-
!ΔE (Boat)
|55.60||54.76||41.95||41.32||44.7 ± 2.0
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T07:42:54Z

Myh11: /* Activation Energies */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

**1Ha = 627.509 kcal/mol

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T07:38:07Z

Myh11: /* Activation Energies */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450929||align="center"|-231.445301|| align="center"|
[[File:G) BOAT HF NEW.LOG|thumbnail]]
||-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539537||align="center"|-231.532565||align="center"|
[[File:OPTI ANTI 2 NEW.LOG|thumbnail]]
||-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

File:G) BOAT HF NEW.LOG

2014-11-07T07:36:17Z

Myh11:

File:OPTI ANTI 2 NEW.LOG

2014-11-07T07:23:46Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T07:22:41Z

Myh11: /* Activation Energies */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====
{| class="wikitable" border="1"
|+ Table 8 Summary of Energies / Ha
!
!colspan="4" style="text-align: center;"|HF/3-21G
!colspan="4" style="text-align: center;"|HF/6-31G<sup>*</sup>
|-
!
|align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file||align="center"|Electronic Energy||align="center"|Sum of Electronic and Zero-point Energies||align="center"|Sum of Electronic and Thermal Energies||align="center"|.log file
|-
!
| ||align="center"|at 0 K||align="center"|at 298.15 K|| || || align="center"|at 0 K||align="center"|at 298.15 K||
|-
!Chair T.S.
|align="center"|-231.619322||align="center"|-231.466709||align="center"|-231.461351|| align="center"|
[[File:G) CHAIR HF321 NEWNEW.LOG|thumbnail]]
||-234.556983||align="center"| -234.414919||align="center"| -234.408998||align="center"|
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
|-
!Boat T.S.
|align="center"|-231.602802||align="center"|-231.450930||align="center"|-231.445302|| align="center"|[[Media:BN711ANTI2QST2.LOG| here]] ||align="center"|-234.543093||align="center"|-234.402338||align="center"|-234.396004||align="center"|
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|-
!Reactant (anti2)
|align="center"|-231.692535||align="center"|-231.539540||align="center"|-231.532566||align="center"|[[Media:BN711HEXANTI2.LOG| here]] ||align="center"|-234.611710||align="center"|-234.469202||align="center"|-234.461856 ||align="center"|
[[File:G) ANTI2 B3LYP-631G.LOG|thumbnail]]
|}

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

File:G) ANTI2 B3LYP-631G.LOG

2014-11-07T07:18:57Z

Myh11:

File:G) BOAT B3LYP-631G.LOG

2014-11-07T07:14:26Z

Myh11: Myh11 uploaded a new version of "File:G) BOAT B3LYP-631G.LOG"

File:G) CHAIR B3LYP-631G.LOG

2014-11-07T07:11:53Z

Myh11: Myh11 uploaded a new version of "File:G) CHAIR B3LYP-631G.LOG"

File:G) CHAIR HF321 NEWNEW.LOG

2014-11-07T07:07:07Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T06:45:13Z

Myh11: /* Reoptimization of Chair and Boat Transition States */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table 7 Reoptimize Boat and Chair T.S.
! Structure
||[[Image:G chair.JPG|thumb|200px]]||[[Image:G boat.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G*|| 6-31G*
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698303||-234.54309304
|-
!.log File
||
[[File:G) CHAIR B3LYP-631G.LOG|thumbnail]]
||
[[File:G) BOAT B3LYP-631G.LOG|thumbnail]]
|}

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

File:G) BOAT B3LYP-631G.LOG

2014-11-07T06:44:17Z

Myh11:

File:G) CHAIR B3LYP-631G.LOG

2014-11-07T06:43:58Z

Myh11:

File:G boat.JPG

2014-11-07T06:43:04Z

Myh11:

File:G chair.JPG

2014-11-07T06:42:44Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T06:39:49Z

Myh11: /* Intrinsic Reaction Coordinate */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ Table 6 IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table Reoptimize Boat and Chair T.S.
! Structure
||[[Image:Bn711ChairReOPT.JPG|thumb|200px]]||[[Image:Bn711boatReOPT.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G(d)|| 6-31G(d)
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698249||-234.54309287
|-
!.log File
|| [[Media:Bn711CHAIR631g.LOG| here]]|| [[Media:BN711BOAT_631.LOG| here]]
|}

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T06:39:22Z

Myh11: /* Activation Energies */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Reoptimization of Chair and Boat Transition States ====
The transition states were reoptimized at '''B3LYP/6-31G*'''

{| class="wikitable" border="1"
|+ Table Reoptimize Boat and Chair T.S.
! Structure
||[[Image:Bn711ChairReOPT.JPG|thumb|200px]]||[[Image:Bn711boatReOPT.JPG|thumb|200px]]
|-
!Calculation type
||FREQ||FREQ
|-
!Calculation Method
|| RB3LYP || RB3LYP
|-
!Basis Set
|| 6-31G(d)|| 6-31G(d)
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2v</sub>
|-
! Energy/ a.u.
|| -234.55698249||-234.54309287
|-
!.log File
|| [[Media:Bn711CHAIR631g.LOG| here]]|| [[Media:BN711BOAT_631.LOG| here]]
|}

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T06:31:46Z

Myh11: /* The "Chair" and "Boat" Transition State */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 8''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T06:31:07Z

Myh11: /* Intrinsic Reaction Coordinate */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 7''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

From the structure we got from the initial IRC, it is clear that the transition state has not reached to its minimum as neither its energy nor structure corresponds to any of the conformers listed in Appendix 1. Hence the last point of the initial IRC was optimised to proceed further. The energy of the optimized structure (-231.69166699a.u) matches with the energy of gauche2 in Appendix 1. The IRC method suggests that gauche2 is the conformer of 1,5-hexadiene that leads to the chair transition state structure in the Cope Rearrangement of 1,5-hexadiene.

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T06:21:07Z

Myh11: /* Intrinsic Reaction Coordinate */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 7''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

IRC for the chair transition state was computed on the '''HF/3-21G''' basis set, the reaction coordinate was only computed in the forward direction because it is symmetrical. The force constant setting was set to 'calculate always' and the number of points along the IRC is set to 50.

{| class="wikitable" border="1"
|+ IRC
! Structure
||[[Image:IRC1.JPG|thumb|200px|chair,initial IRC]]||[[Image:IRC2.JPG|thumb|200px|chair,further IRC from end point]]
|-
!Calculation type
||FREQ||FOPT
|-
!Calculation Method
|| RHF || RHF
|-
!Basis Set
|| 3-21G|| 3-21G
|-
! Point Group
|| C<sub>2</sub>|| C<sub>2</sub>
|-
! Dihedral Angle
||67.1||64.2
|-
! Energy/ a.u.
|| -231.69121449||-231.69166699
|-
!.log File
||
[[File:F) CHAIR IRC.LOG|thumbnail]]
||
[[File:F) CHAIR IRC OPT MIN 51.LOG|thumbnail]]
|}

[[File:IRC graph1.JPG|left|thumbnail]]
'''Figure 10.''' Initial IRC plot

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

File:IRC graph1.JPG

2014-11-07T06:06:32Z

Myh11:

File:F) CHAIR IRC OPT MIN 51.LOG

2014-11-07T05:56:19Z

Myh11:

File:F) CHAIR IRC.LOG

2014-11-07T05:55:46Z

Myh11:

File:IRC2.JPG

2014-11-07T05:53:59Z

Myh11:

File:IRC1.JPG

2014-11-07T05:53:45Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T05:40:43Z

Myh11: /* The "Chair" and "Boat" Transition State */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering2.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 8 and Figure 9 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 8.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 8''']]]

As seen from '''Figure 7''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 9''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 9''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T05:39:36Z

Myh11: /* Optimizing the "Chair" and "Boat" Transition Structures */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''

In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°.

[[File:E)numbering.JPG|center|'''Figure 7''']]
'''Figure 7''' The resultant geometries of the reactant (left) and the product (right) after modification.

These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 5'''.

{| class="wikitable" border="1"
|+ Table 5 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 7 and Figure 8 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 7.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 7''']]]

As seen from '''Figure 7''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 8''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 8''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T05:34:52Z

Myh11: /* Summary of Results and Discussion */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Table 4. Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''
In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°. These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 4'''.

{| class="wikitable" border="1"
|+ Table 4 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 7 and Figure 8 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 7.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 7''']]]

As seen from '''Figure 7''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 8''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 8''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

Rep:Mod:usagiphysical

2014-11-07T05:33:57Z

Myh11: /* The "Chair" and "Boat" Transition State */

== The Cope Rearrangement of 1,5-hexadiene ==

1,5-hexadiene undergoes [3,3]-sigmatropioc rearrangement reaction as shown in '''Figure 1'''. For a long time its actual mechanism was the subject of some controversy and was studied by a large number of experimental and computational researches, but it is recently believed that this reaction is a concerted reaction via either a 'chair' or 'boat' conformation. The transition state with a 'boat' conformation is believed to be higher in energy than that with the 'chair' conformation. The objectives of this exercise are to locate the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface by Gaussian calculation, in order to determine the preferred reaction mechanism.

[[File:Myh CR.jpg|framed|center|'''Figure 1.''' Cope Rearrangement of 1,5-hexadiene]]

=== Optimizing the Reactants and Products ===

====Optimization via HF/3-21G====

Four conformers (2 with "anti" linkage and 2 with "gauche" linkage) are 1,5-hexadiene were optimized and were confirmed to be anti2, anti4, gauche1 and gauche3 in [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1 Appendix 1] by matching the energies.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 1.
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure|| <jmol><jmolApplet><title>anti 2.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 2.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>anti 4.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>anti 4.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche1.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche1.mol</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet><title>gauche3.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>gauche3.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RHF||RHF||RHF||RHF
|-
| Basis Set||3-21G||3-21G||3-21G||3-21G
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-231.69254 ||-231.69097 ||-231.68772 ||-231.69266
|-
| .log file||
[[File:ANTI2.LOG|thumbnail]]
||
[[File:ANTI4.LOG|thumbnail]]
||
[[File:GAUCHE1.LOG|thumbnail]]
||
[[File:GAUCHE3.LOG|thumbnail]]
|}

====Optimization via B3LYP/6-31G*====
The four comformers were then reoptimized at '''B3LYP/6-31G*'''.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 2.
|+
! scope="col" | Name
! scope="col" | anti2 (C<sub>i</sub>)
! scope="col" | anti4 (C<sub>1</sub>)
! scope="col" | gauche1 (C<sub>2</sub>)
! scope="col" | gauche3 (C<sub>1</sub>)
|-
|Structure||<jmol><jmolApplet><title>anti 2631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Opti anti 2631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Anti4-631g.mol </title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti4-631g.mol </uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche1-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche1-631g.mol</uploadedFileContents>
</jmolApplet></jmol>||<jmol><jmolApplet><title>Gauche3-631g.mol</title><color>white</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche3-631g.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set||6-31G*||6-31G*||6-31G*||6-31G*
|-
| Point Group||C<sub>i</sub>||C<sub>1</sub>||C<sub>2</sub>||C<sub>1</sub>
|-
| Energy/Ha||-234.61071 ||-234.61079 ||-234.60786 ||-234.61133
|-
| .log file||
[[File:OPTI ANTI 2631G.LOG|thumbnail]]
||
[[File:ANTI4-631G.LOG|thumbnail]]
||
[[File:GAUCHE1-631G.LOG|thumbnail]]
||
[[File:GAUCHE3-631G.LOG|thumbnail]]
|}

Optimizing at B3LYP/6-31G* level of theory would add polarisation to atoms and improve the modelling of core electrons, producing more accurate description of orbitals as a result.<ref name="soo">''Nigerian Journal of Chemical Research'', 2007, '''12'''. {{DOI|10.4314/njcr.v12i1.}}</ref>

====Summary of Results and Discussion====

{| class="wikitable" border="1"
|+ Table 3
. Optimization and Frequency Calculation Data
! Structure !! Point Group !! Energy 3-21G (Ha) !! Energy 6-31G* (Ha) !! Sum of electronic and zero-point Energies (Ha) !! Sum of electronic and thermal Energies (Ha) !! Sum of electronic and thermal Enthalpies (Ha) !! Sum of electronic and thermal Free Energies (Ha)
|-
| anti2 || Ci || -231.69254 || -234.61071 || -234.41613 || -234.40864 || -234.407694 || -234.45061
|-
| anti4 || C1 || -231.69097 || -234.61079 || -234.42592 || -234.44740 || -234.44646 || -234.48194
|-
| gauche1 || C2 || -231.68772 || -234.60786 || -234.46522 || -234.45810 || -234.45715 || -234.49541
|-
| gauche3|| C1 || -231.69266 || -234.61133 || -234.46869 || -234.46146 || -234.46052 || -234.50011
|}
log files:
[[File:FREQ ANTI 2 631GD.LOG|thumbnail]],
[[File:ANTI4-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE1-631G FREQ.LOG|thumbnail]],
[[File:GAUCHE3-631G FREQ.LOG|thumbnail]]

Based on the information in the tables above, the '''HF/3-21G''' and '''B3LYP/6-31G*''' basis set produced conformers with same point group.

The 'anti' conformers were expected to be more stable than the 'gauche' ones because of APP orbital interactions and steric repulsions. πC-C is a higher energy donor than σC-H, therefore the πC-C interacts better with the π*C-C app. Hence APP arrangement of the two vinyl groups is favorable. However unexpectedly the most stable conformer among the four is gauche3, as it is the conformation which possesses the lowest energy. Anti2 is more stable than anti4 and gauche3 is more stable than gauche1 because the two vinyl groups are further apart from each other.

[[File:IR spectrum anti2.JPG|thumbnail|'''Figure 2.''' IR spectrum of '''B3LYP/6-31G*''' optimized anti2]]

'''Geometry Discussion'''

[[File:Geometry.JPG|'''Figure 3.''' Anti2 with atoms labelled]]
'''Figure 3.''' Anti2 with atoms labelled

{| class="wikitable" border="1"
|+ Bond Lengths & Angles of Anti2
! Bond !! '''HF/3-21G''' (Å ) !! '''B3LYP/6-31G*''' (Å ) !!Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref> !! Angle !! '''HF/3-21G''' !! '''B3LYP/6-31G*''' !! Literature <ref>I. H. Gyorgy Schultz, ''Journal of Molecular Structure,'' 1994, '''''346,''''' 63-69.</ref>
|-
| C1-C2, C5-C6 || 1.323 || 1.334 || 1.3412 || C1-C2-C3, C4-C5-C6 || 124.8 || 121.8 ||122.5
|-
| C2-C3, C4-C5 || 1.514 || 1.504 || 1.5077 || C2-C3-C4, C3-C4-C5 || 111.3 || 112.7 || 111.0
|-
| C3-C4 || 1.548 || 1.548 || 1.5362 || C3-C2-H || 119.7 || 119.00 || 118.4
|-
|C-H||1.075||1.100||1.108||C2-C3-C4-C5||-179.989||-180.000||-178.3
|}

It could be concluded that '''B3LYP/6-31G*''' was more accurate than the '''HF/3-21G''' as the bond length and angles were closer to the literature values.

=== Optimizing the "Chair" and "Boat" Transition Structures ===

==== The "Chair" and "Boat" Transition State ====
An allyl fragment was optimized at ''''HF/3-21G'''('''Figure 4'''), then two of these fragements were used to assemble the "chair" transition state with the terminal ends of the fragments 2.2Å apart ('''Figure 5'''). This "chair" structure was then optimised by a various methods i.e. '''Hessian''' and '''Frozen coordinates'''.
[[File:Allyl fragment.JPG|left|frame|'''Figure 4.''' Allyl Fragment]]
[[File:Chair ts.JPG|center|frame|'''Figure 5.''' Chair Transition State]]

For the "boat" transition state, the '''QST2''' method was used. In order to build a "boat" structure, all the atoms of the reactant and the product were numbered as shown in '''Figure 6'''.

[[File:E)numbering.JPG|center|'''Figure 6''']]
'''Figure 6'''
In order to assemble molecules into the desired boat form. The central C-C-C-C dihedral angeles (C2-5 for the reactant, C2-C1-C6-C5 for the product) of both molecules were modified from 180° to 0° and the C-C-C angles (C2-C3-C4 & C3-C4-C5 for the reactant, C2-C1-C6 & C1-C6-C5 for the product) were reduced from 113° to 100°. These were then optimized at '''HF/3-21G''' using the '''QST2''' method. The resultant structure in shown in '''Table 4'''.

{| class="wikitable" border="1"
|+ Table 4 "Chair" and "Boat" Transtion State Optimization
!Method||Hessian|| Frozen coordinate method (Bond)||Frozen coordinate method (Derivative)||TS (QST2)
|-
! Structure
||[[Image:Chair ts2.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen.JPG|thumb|200px|chair]]||[[Image:Chair ts frozen d.JPG|thumb|200px|chair]]|| [[Image:Boat ts.JPG|thumb|200px|boat]]
|-
!Calculation type
||FREQ||FREQ|| FREQ||FREQ
|-
!Calculation Method
|| RHF || RHF || RHF ||RHF
|-
!Basis Set
|| 3-21G|| 3-21G||3-21G ||3-21G
|-
! Point Group
|| C<sub>2h</sub>|| C<sub>2h</sub> ||C<sub>2h</sub>||C<sub>2v</sub>
|-
! Energy/ a.u.
|| -231.619322224||-231.61932247||-231.61932246||-231.60280200
|-
!Transition bond distances/ Å
||2.02039||2.02043||2.02041||2.14000
|-
!.log File
||
[[File:B)OPT=TS.LOG|thumbnail]]
||
[[File:C) OPT CHAIR FREEZE.LOG|thumbnail]]
||
[[File:D) CHAIR DERIVATIVE.LOG|thumbnail]]
||
[[File:E) OPT FREQ NUMBERING TS BOAT.LOG|thumbnail]]
|}

'''***Please click the links provided below to see the original file of Figure 7 and Figure 8 for the animation***'''
[[Image:Opt chair ts freq.gif|left|thumb|200px|'''Figure 7.''' Hessian: Vibration at 817.97cm<sup>-1</sup> (imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/b/b3/Opt_chair_ts_freq.gif '''Figure 7''']]]

As seen from '''Figure 7''', the Hessian method gives an imaginary frequency of 817.97cm<sup>-1</sup> and the vibration mode corresponding to the Cope rearrangement. Both Hessian and the frozen coordinate methods give the tranistion bond lengths of about 2.02Å because of the reasonable assumption of the transition structure. For a molecule which is more complex, it will be more difficult to predict its transition structure by the Hessian method hence the frozen coordinate method would be preferable.

[[Image:Opt boat ts freq.gif|left|thumb|200px|'''Figure 8''' QST2: Vibration at 839.94cm<sup>-1</sup>(imaginary)[https://wiki.ch.ic.ac.uk/wiki/images/2/27/Opt_boat_ts_freq.gif '''Figure 8''']]]

QST2 method gives an imaginary frequency of 839.94cm<sup>-1</sup>.

==== Intrinsic Reaction Coordinate ====

==== Activation Energies ====

== The Diels Alder Cycloaddtion ==

=== Cis Butadiene ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+
|-
|Structure||
|-
|HOMO||
|-
|LUMO||
|-
|Calculation Type||FOPT
|-
|Calculation Method||RAM1
|-
| Basis Set||ZDO
|-
| Point Group||C2V
|-
| Energy/Ha||0.04879
|-
| .log file||LOG
|}

=== The Transition State of prototype reaction between ethylene and butadiene ===

=== The cyclohexa-1,3-diene reaction with maleic anhydride ===

=== Further work ===

== Reference ==

File:E)numbering2.JPG

2014-11-07T05:29:39Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T05:00:49Z

Myh11: /* The "Chair" and "Boat" Transition State */

File:E)numbering.JPG

2014-11-07T04:56:51Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T04:45:33Z

Myh11: /* The "Chair" and "Boat" Transition State */

Rep:Mod:usagiphysical

2014-11-07T04:37:49Z

Myh11: /* The "Chair" and "Boat" Transition State */

File:Opt boat ts freq.gif

2014-11-07T04:28:40Z

Myh11:

File:Opt chair ts freq.gif

2014-11-07T04:28:22Z

Myh11:

Rep:Mod:usagiphysical

2014-11-07T04:27:17Z

Myh11: /* The "Chair" and "Boat" Transition State */

File:E) OPT FREQ NUMBERING TS BOAT.LOG

2014-11-07T04:24:59Z

Myh11: