==1,5-Hexadiene Hartree-Fock 3-21G Optimisation==

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised 1,5-hexadiene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_HEXADIENE.mol </uploadedFileContents>
</jmolApplet></jmol>
|}
Point group: C2

The optimised molecule is found to be anti 1, from table 1.

===1,5-Hexadiene Hartree-Fock 3-21G gauche Optimisation===

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene_gauche.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised 1,5-hexadiene gauche</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_HEXADIENE_GAUCHE.mol</uploadedFileContents>
</jmolApplet></jmol>
|}
Point group: C2

The optimised molecule is found to be gauche 2, from table 1.

The anti arrangement gives places the C-C σ the neighboring C-C σ* orbitals at 180 degrees to each other and are anti-peri planar. This allows the two orbitals to interact and lowers the energy of the σ orbital and raises the energy of the σ*. Since only the bonding orbital between the two carbons are occupied, the anti molecule is stabilised by this orbital interaction. This is not possible in the gauche arrangement as the geometry of the two orbitals disfavor interactions.

===1,5-Hexadiene Hartree-Fock 3-21G gauche Optimisation, Ci symmetry===

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene_ci.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised anti 1,5-hexadiene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_HEXADIENE_CI.mol</uploadedFileContents>
</jmolApplet></jmol>
|}
The optimised 1,5-hexadiene molecule with a Ci symmetry and energy-231.69254 hartrees is the anti 2 molecule, found in table 1.

===1,5-Hexadiene DFT B3LYP/6-31G gauche Optimisation, Ci symmetry===

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene_ciB3LYP.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised anti 1,5-hexadiene </title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_hexadiene_ci_B3LYP.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

A higher level of theory is used to optimise the anti 2 conformer. The energy value of the reactant will have to be found in order to calculate the activation energy of the Cope rearrangement. The DTF B3LYP 6-31G basis set will give more accurate energies than the Hartree-Fock 3-21G basis set as 6 functions are used to model the orbitals in 6-21G as opposed to 3 functions used in the 3-21G basis set. Furthermore DTF better represents exchange energy and also include contribution from electron correlation.

{| class="wikitable" border="1"
|+ Table 2. Comparison of HF/3-21G and B3LYP/6-31G Geometries for Anti 2 Conformation.
! ''' ''' !! '''C=C bond (pm)''' !! '''C-C bond (pm)(carbon 3 and 4)''' !! '''C=C-H angle'''
|-
| HF/3-21G || 131.6 || 1.55.3 || 121.9
|-
| B3LYP/6-31G || 133.8 || 155.5 || 121.7
|}

Hartree-Fock gives shorter bond lengths, with DTF giving the sp3-sp2 carbon bond a bond angle closer to 120 degrees.

==1,5-Hexadiene DFT B3LYP/6-31G frequency calculation==
{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 3. Calculated Thermochemical Parameters of B3LYP/6-31G Optimised anti 2 1,5-Hexadiene.
! Parameter !! Calculation at 298.15K (Hartrees)||Calculation at 0.01K (Hartrees)
|-
|Sum of Electronic + Zero-point Energies||-234.401704||-234.40170
|-
|Sum of Electronic and Thermal Energies||-234.396081||-234.401702
|-
|Sum of Electronic and Thermal Enthalpies|| -234.395137||-234.401702
|-
|Sum of Electronic and Thermal Free Energies|| -234.430821||-234.401702
|}

The frequency calculation was carried out at 298.15k and 0.01k at 1 atmospheric pressure. The energies carried out at 0.01K were of the same value as the thermal contribution was too small to have any significant effect on enthalpy and free energy.

===Optimising chair TS - Berny vs frozen coordinate method===
[[File:Chair_TS_numbers.PNG|thumb|upright=2.0| Atom numbers used for table 4.]]
<jmol><jmolApplet>
<title>Chair TS of the Cope rearrangement</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>CHAIR_TS_GCKberny.mol</uploadedFileContents>
</jmolApplet></jmol>
Two allyl fragment was optimised at the Hartree-Fock/3-21G level of theory. Force constants was calculated once. The Berny optimisation gave a chair transition state with the imaginary frequency at 818cm-1.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 4. Comparison of the geometries of the chair transition structure using berny and forzen coordinate method.
! Atom Labels !! Berny Optimisation (Å)||Frozen Coordinate Optimisation (Å)
|-
|C14-C6||2.02044||2.02045
|-
|C3-C11||2.02072||2.02067
|-
|H4-H12||2.63160||2.63199
|-
|H-H||2.43748||2.43728
|}

===Optimising boat TS - QST2===
Imaginary frequency is located at 840cm-1
<jmol><jmolApplet>
<title>Boat TS of the Cope rearrangement</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BOATTS_QST2GCKCORRECT.mol</uploadedFileContents>
</jmolApplet></jmol>

===IRC on chair transition structure===
[[File:IRCGCKCOPE.PNG|thumb|upright=2.0| IRC from chair TS]]

==Diels-Alder Cycloaddition==
===Cis-Butadiene===
[[File:Homolumo_butadiene.png|thumb|upright=2.0| HOMO of butadiene on the left and LUMO of butadiene on the right.]]

The HOMO and LUMO of the reactant cis-butadiene were shown from the optimisation of the molecule using AM1 semi-empirical level of theory. The HOMO and LUMO of butadiene are anti-symmetric with respect to the plane of symmetry in the molecule, which bisects the central C-C bond.

===Prototype Diels-Alder reaction===
[[File:Homo_dielsaldergck.PNG|thumb|upright=2.0| HOMO of the transition state structure.]]
[[File:Lumo_dielsaldergck.PNG|thumb|upright=2.0| LUMO of the transition state structure.]]
[[File:Diels_alder_TSimagineryvibration.PNG ‎|thumb|upright=2.0| Imaginary frequency of the bond forming in the TS.]]
[[File:Diels_alder_TSlowestvibration.PNG ‎|thumb|upright=2.0| Lowest frequency vibration in the TS.]]
[[File:HOMO_DAadductgck.PNG ‎|thumb|upright=2.0| HOMO of the Diels-Alder adduct]]
<jmol><jmolApplet>
<title>Diels-Alder TS</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Diels_alder_TSgck.mol</uploadedFileContents>
</jmolApplet></jmol>
{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 9. Geometry of Diels-Alder Transition Structure with carcon numbered 1 to 6, with 1-6 and 4-5 being the partially formed carbon sigma bonds.
! Atom Labels !! Bond Lengths(Å)
|-
| C1-C2 || 1.38
|-
| C2-C3 || 1.40
|-
| C3-C4 || 1.38
|-
| C4-C5 || 2.12
|-
| C5-C6 || 1.38
|-
| C6-C1 || 2.12
|-
| H7-H15 || 2.60
|-
| H7-H6 || 2.55
|}

The prototype Diels-Alder reaction in this case is the reaction of cis-butadiene with ethylene to give cyclohexene as the adduct. The HOMO and LUMO of the adduct is calculated from the AM1 semi-empirical level of theory. As seen from figurex the HOMO is found to be anti-symmetric with respect to the plane of symmetry, whereas the LUMO is determined to symmetric about the central carbon-carbon sigma bond.

Typical spЗ-spЗ carbon bond lengths, sp2-sp2 lengths and Van der Waals radii for a carbon atom is approximately 1.54Å, 1.34Å and 1.70Å respectively. The forming carbon-carbon bonds has a length of 2.12Å, which is within twice the Van de Waals radii. This shows there is an attractive interaction between the two forming carbon atoms, favoring bond formation. Figurex shows the imaginary frequency of the formation of the carbon-carbon sigma bond in the transition state is synchronous. The HOMO of the Diels-Alder adduct is anti-symmetric with respect to the plane of symmetry. A set of rules concerning the conservation of orbital symmetry formed by Woodward and Hoffmann is used to predict if a pericyclic reaction is allowed or not. the prototype reaction is a thermally allowed 4n+2 cycloaddition, with suprafacial rotation. the HOMO of cis-butadiene and LUMO of ethylene are on the same face of the fragment and are also in the same phase, which gives a favorable and low energy interaction. As a result the reaction is allowed.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 10. Activation Energy of Prototype Reaction.
|Structure||AM1 Sum of Electronic and Thermal Energies at 298.15 K (Hartrees)||AM1 Activation Energy (kcal/mol)||B3LYP/6-31G Sum of Electronic and Thermal Energies at 298.15 K (Hartrees)|| B3LYP/6-31G Activation Energy (kcal/mol)||Experimental (kcal/mol) 22
|-
| Ethylene || 0.080255||25.4938328||-78.539630||20.739193||27.5 (2)
|-
|Cis Butadiene||0.138571||25.4938328||-155.906508||20.739193||27.5 (2)
|-
|DA Transition State||0.259453||25.4938328|| -234.413088||20.739193||27.5 (2)
|}

===Cycloaddition of cyclohexa-1,3-diene with maleic anhydride===
[[File:Endo_atomnumber.PNG|thumb|upright=2.0|Figurex. atom number of the endo TS.]]
[[File:Exo_atomnumber.PNG|thumb|upright=2.0|Figurex. atom number of the exo TS.]]
[[File:Endo_homo.PNG|thumb|upright=2.0|Figurex. HOMO of endo TS.]]
[[File:Exo_homo.PNG|thumb|upright=2.0|Figurex. HOMO of exo TS.]]
The exo and endo transition state was located at the AM1 level of theory. The imaginary frequency for the endo transition and exo transition state is 806cm-1 and 812cm-1 respectively with the oscillation of the bond forming carbons as proof of the transition state structure. The vibrations of the endo and exo product is synchronous. As seen in tableX, the forming C-C bond length is shorter in the endo transition structure than the forming C-C bond in the exo structure. This is due to the steric repulsion of bridging -CH2-CH2- group with the carbonyl-oxygen-carbonyl fragment as the two groups are comparable in size. Another contribution to the different bond lengths is from secondary orbital effects. Since the double bonds in the maleic andyhride and cyclohexadiene are placed directly above each other, the orbitals can overlap favorably to form sigma bonds. As orbitals from the double bond in cyclohexadiene overlap with orbitals in the carbonyl fragment, the diene will lose some double bond character. This is evident from the longer bond between C1 and C4 in the endo transition structure. It is this secondary orbital effect that result in the endo transition structure having a lower energy than the exo transition structure. Hence the endo product is normally formed first; giving the kinetic product. The exo product is "anti" to the largest cyclic bridge which in turn gives less steric strain and is the lower energy product, giving the thermodynamic product.

<jmol><jmolApplet>
<title>endo transition state</title>
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<size>200</size>
<uploadedFileContents>DA_TS_endogck.mol</uploadedFileContents>
</jmolApplet></jmol>

<jmol><jmolApplet>
<title>exo transition state</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>DA_TS_EXOgck.mol</uploadedFileContents>
</jmolApplet></jmol>

The endo transition state has been found to have a lower energy then the exo transition state, with a difference of 0.00108495 hartrees.

Absolute energy of exo TS(hartress): -0.05041985 hartrees

Absolute energy of endo TS(hartress): -0.05150480

Absolute relative energy(hartress): 0.00108495

Absolute relative energy(kcal/mol): 0.68081654923

Endo - sum of electronic and thermal Energies(hartrees)= 0.143683

Exo - sum of electronic and thermal Energies(hartrees)= 0.144881

Relative sum of electronic and thermal Energies(hartrees)= 0.001198

relative energy(kcal/mol): 0.75175651

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table x. geometry of endo and exo TS.
|Atom Labels Exo||Bond Lengths (Å)||Atom Labels Endo|| Bond Lengths (Å)
|-
|C3-C17||2.17040||C2-C17||2.16239
|-
|C2-C16||2.17040||C3-C16||2.16239
|-
|C1-C4||1.39676||C1-C4||1.39724
|-
|C3-C4||1.39438||C1-C2|| 1.39305
|-
|C16-C17||1.41011||C16-C17||1.40849
|-
|C12-C18 || 2.17048||C2-C8||2.16238
|-
|C12-C18||2.94508||C1-C18||2.89222
|}

===secondary orbital overlap effect?===
The HOMO of the endo and exo transition state were plotted as shown in figureX and figurex. It is expected that secondary orbital effect will be observed in the HOMO of the endo Transition state. This is not the case for the plotted HOMO. There are no in-phase overlap between the carbonyl orbitals and the orbital from the double bond in cyclohexadiene. However seondary orbital effect is present in lower energy orbitals below the HOMO.

===AM1 neglected effects===
The semi-empirical AM1 method has a few setbacks which effects the accuracy of the calculations. The AM1 greatly underestimates the barrier of bond rotation with partial double bond character and predicts alkyl groups to be more stable than reality. The calculated hydrogen bond strength is close to experimental results, but the geometry of the hydrogen bonds is often misrepresented. Van der Waals interactions are also poorly predicted. This could provide an explanation to why the secondary orbital effect is not observed in the HOMO of the endo transition structure.

File:IRCGCKCOPE.PNG

2015-02-27T11:21:43Z

Gck12:

Rep:Mod:gck12

2015-02-27T11:20:50Z

2015-02-27T10:52:27Z

Gck12: /* Optimising chair TS - Berny */

==1,5-Hexadiene Hartree-Fock 3-21G Optimisation==

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised 1,5-hexadiene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_HEXADIENE.mol </uploadedFileContents>
</jmolApplet></jmol>
|}
Point group: C2

The optimised molecule is found to be anti 1, from table 1.

===1,5-Hexadiene Hartree-Fock 3-21G gauche Optimisation===

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene_gauche.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised 1,5-hexadiene gauche</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_HEXADIENE_GAUCHE.mol</uploadedFileContents>
</jmolApplet></jmol>
|}
Point group: C2

The optimised molecule is found to be gauche 2, from table 1.

The anti arrangement gives places the C-C σ the neighboring C-C σ* orbitals at 180 degrees to each other and are anti-peri planar. This allows the two orbitals to interact and lowers the energy of the σ orbital and raises the energy of the σ*. Since only the bonding orbital between the two carbons are occupied, the anti molecule is stabilised by this orbital interaction. This is not possible in the gauche arrangement as the geometry of the two orbitals disfavor interactions.

===1,5-Hexadiene Hartree-Fock 3-21G gauche Optimisation, Ci symmetry===

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene_ci.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised anti 1,5-hexadiene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_HEXADIENE_CI.mol</uploadedFileContents>
</jmolApplet></jmol>
|}
The optimised 1,5-hexadiene molecule with a Ci symmetry and energy-231.69254 hartrees is the anti 2 molecule, found in table 1.

===1,5-Hexadiene DFT B3LYP/6-31G gauche Optimisation, Ci symmetry===

{| class="wikitable"
|+
! summary data || Jmol
|-
|[[File:1_5_hexadiene_ciB3LYP.PNG|300px]]
|
<jmol><jmolApplet>
<title>optimised anti 1,5-hexadiene </title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>1_5_hexadiene_ci_B3LYP.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

A higher level of theory is used to optimise the anti 2 conformer. The energy value of the reactant will have to be found in order to calculate the activation energy of the Cope rearrangement. The DTF B3LYP 6-31G basis set will give more accurate energies than the Hartree-Fock 3-21G basis set as 6 functions are used to model the orbitals in 6-21G as opposed to 3 functions used in the 3-21G basis set. Furthermore DTF better represents exchange energy and also include contribution from electron correlation.

{| class="wikitable" border="1"
|+ Table 2. Comparison of HF/3-21G and B3LYP/6-31G Geometries for Anti 2 Conformation.
! ''' ''' !! '''C=C bond (pm)''' !! '''C-C bond (pm)(carbon 3 and 4)''' !! '''C=C-H angle'''
|-
| HF/3-21G || 131.6 || 1.55.3 || 121.9
|-
| B3LYP/6-31G || 133.8 || 155.5 || 121.7
|}

Hartree-Fock gives shorter bond lengths, with DTF giving the sp3-sp2 carbon bond a bond angle closer to 120 degrees.

==1,5-Hexadiene DFT B3LYP/6-31G frequency calculation==
{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 3. Calculated Thermochemical Parameters of B3LYP/6-31G Optimised anti 2 1,5-Hexadiene.
! Parameter !! Calculation at 298.15K (Hartrees)||Calculation at 0.01K (Hartrees)
|-
|Sum of Electronic + Zero-point Energies||-234.401704||-234.40170
|-
|Sum of Electronic and Thermal Energies||-234.396081||-234.401702
|-
|Sum of Electronic and Thermal Enthalpies|| -234.395137||-234.401702
|-
|Sum of Electronic and Thermal Free Energies|| -234.430821||-234.401702
|}

The frequency calculation was carried out at 298.15k and 0.01k at 1 atmospheric pressure. The energies carried out at 0.01K were of the same value as the thermal contribution was too small to have any significant effect on enthalpy and free energy.

===Optimising chair TS - Berny===
<jmol><jmolApplet>
<title>Chair TS of the Cope rearrangement</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>CHAIR_TS_GCKberny.mol</uploadedFileContents>
</jmolApplet></jmol>
Two allyl fragment was optimised at the Hartree-Fock/3-21G level of theory. Force constants was calculated once. The Berny optimisation gave a chair transition state with the imaginary frequency at 818cm-1.

==Diels-Alder Cycloaddition==
===Cis-Butadiene===
[[File:Homolumo_butadiene.png|thumb|upright=2.0| HOMO of butadiene on the left and LUMO of butadiene on the right.]]

The HOMO and LUMO of the reactant cis-butadiene were shown from the optimisation of the molecule using AM1 semi-empirical level of theory. The HOMO and LUMO of butadiene are anti-symmetric with respect to the plane of symmetry in the molecule, which bisects the central C-C bond.

===Prototype Diels-Alder reaction===
[[File:Homo_dielsaldergck.PNG|thumb|upright=2.0| HOMO of the transition state structure.]]
[[File:Lumo_dielsaldergck.PNG|thumb|upright=2.0| LUMO of the transition state structure.]]
[[File:Diels_alder_TSimagineryvibration.PNG ‎|thumb|upright=2.0| Imaginary frequency of the bond forming in the TS.]]
[[File:Diels_alder_TSlowestvibration.PNG ‎|thumb|upright=2.0| Lowest frequency vibration in the TS.]]
[[File:HOMO_DAadductgck.PNG ‎|thumb|upright=2.0| HOMO of the Diels-Alder adduct]]
<jmol><jmolApplet>
<title>Diels-Alder TS</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Diels_alder_TSgck.mol</uploadedFileContents>
</jmolApplet></jmol>
{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 9. Geometry of Diels-Alder Transition Structure with carcon numbered 1 to 6, with 1-6 and 4-5 being the partially formed carbon sigma bonds.
! Atom Labels !! Bond Lengths(Å)
|-
| C1-C2 || 1.38
|-
| C2-C3 || 1.40
|-
| C3-C4 || 1.38
|-
| C4-C5 || 2.12
|-
| C5-C6 || 1.38
|-
| C6-C1 || 2.12
|-
| H7-H15 || 2.60
|-
| H7-H6 || 2.55
|}

The prototype Diels-Alder reaction in this case is the reaction of cis-butadiene with ethylene to give cyclohexene as the adduct. The HOMO and LUMO of the adduct is calculated from the AM1 semi-empirical level of theory. As seen from figurex the HOMO is found to be anti-symmetric with respect to the plane of symmetry, whereas the LUMO is determined to symmetric about the central carbon-carbon sigma bond.

Typical spЗ-spЗ carbon bond lengths, sp2-sp2 lengths and Van der Waals radii for a carbon atom is approximately 1.54Å, 1.34Å and 1.70Å respectively. The forming carbon-carbon bonds has a length of 2.12Å, which is within twice the Van de Waals radii. This shows there is an attractive interaction between the two forming carbon atoms, favoring bond formation. Figurex shows the imaginary frequency of the formation of the carbon-carbon sigma bond in the transition state is synchronous. The HOMO of the Diels-Alder adduct is anti-symmetric with respect to the plane of symmetry. A set of rules concerning the conservation of orbital symmetry formed by Woodward and Hoffmann is used to predict if a pericyclic reaction is allowed or not. the prototype reaction is a thermally allowed 4n+2 cycloaddition, with suprafacial rotation. the HOMO of cis-butadiene and LUMO of ethylene are on the same face of the fragment and are also in the same phase, which gives a favorable and low energy interaction. As a result the reaction is allowed.

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table 10. Activation Energy of Prototype Reaction.
|Structure||AM1 Sum of Electronic and Thermal Energies at 298.15 K (Hartrees)||AM1 Activation Energy (kcal/mol)||B3LYP/6-31G Sum of Electronic and Thermal Energies at 298.15 K (Hartrees)|| B3LYP/6-31G Activation Energy (kcal/mol)||Experimental (kcal/mol) 22
|-
| Ethylene || 0.080255||25.4938328||-78.539630||20.739193||27.5 (2)
|-
|Cis Butadiene||0.138571||25.4938328||-155.906508||20.739193||27.5 (2)
|-
|DA Transition State||0.259453||25.4938328|| -234.413088||20.739193||27.5 (2)
|}

===Cycloaddition of cyclohexa-1,3-diene with maleic anhydride===
[[File:Endo_atomnumber.PNG|thumb|upright=2.0|Figurex. atom number of the endo TS.]]
[[File:Exo_atomnumber.PNG|thumb|upright=2.0|Figurex. atom number of the exo TS.]]
[[File:Endo_homo.PNG|thumb|upright=2.0|Figurex. HOMO of endo TS.]]
[[File:Exo_homo.PNG|thumb|upright=2.0|Figurex. HOMO of exo TS.]]
The exo and endo transition state was located at the AM1 level of theory. The imaginary frequency for the endo transition and exo transition state is 806cm-1 and 812cm-1 respectively with the oscillation of the bond forming carbons as proof of the transition state structure. The vibrations of the endo and exo product is synchronous. As seen in tableX, the forming C-C bond length is shorter in the endo transition structure than the forming C-C bond in the exo structure. This is due to the steric repulsion of bridging -CH2-CH2- group with the carbonyl-oxygen-carbonyl fragment as the two groups are comparable in size. Another contribution to the different bond lengths is from secondary orbital effects. Since the double bonds in the maleic andyhride and cyclohexadiene are placed directly above each other, the orbitals can overlap favorably to form sigma bonds. As orbitals from the double bond in cyclohexadiene overlap with orbitals in the carbonyl fragment, the diene will lose some double bond character. This is evident from the longer bond between C1 and C4 in the endo transition structure. It is this secondary orbital effect that result in the endo transition structure having a lower energy than the exo transition structure. Hence the endo product is normally formed first; giving the kinetic product. The exo product is "anti" to the largest cyclic bridge which in turn gives less steric strain and is the lower energy product, giving the thermodynamic product.

<jmol><jmolApplet>
<title>endo transition state</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>DA_TS_endogck.mol</uploadedFileContents>
</jmolApplet></jmol>

<jmol><jmolApplet>
<title>exo transition state</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>DA_TS_EXOgck.mol</uploadedFileContents>
</jmolApplet></jmol>

The endo transition state has been found to have a lower energy then the exo transition state, with a difference of 0.00108495 hartrees.

Absolute energy of exo TS(hartress): -0.05041985 hartrees

Absolute energy of endo TS(hartress): -0.05150480

Absolute relative energy(hartress): 0.00108495

Absolute relative energy(kcal/mol): 0.68081654923

Endo - sum of electronic and thermal Energies(hartrees)= 0.143683

Exo - sum of electronic and thermal Energies(hartrees)= 0.144881

Relative sum of electronic and thermal Energies(hartrees)= 0.001198

relative energy(kcal/mol): 0.75175651

{| class="wikitable" style="margin: 1em auto 1em auto;"
|+ Table x. geometry of endo and exo TS.
|Atom Labels Exo||Bond Lengths (Å)||Atom Labels Endo|| Bond Lengths (Å)
|-
|C3-C17||2.17040||C2-C17||2.16239
|-
|C2-C16||2.17040||C3-C16||2.16239
|-
|C1-C4||1.39676||C1-C4||1.39724
|-
|C3-C4||1.39438||C1-C2|| 1.39305
|-
|C16-C17||1.41011||C16-C17||1.40849
|-
|C12-C18 || 2.17048||C2-C8||2.16238
|-
|C12-C18||2.94508||C1-C18||2.89222
|}

===secondary orbital overlap effect?===
The HOMO of the endo and exo transition state were plotted as shown in figureX and figurex. It is expected that secondary orbital effect will be observed in the HOMO of the endo Transition state. This is not the case for the plotted HOMO. There are no in-phase overlap between the carbonyl orbitals and the orbital from the double bond in cyclohexadiene. However seondary orbital effect is present in lower energy orbitals below the HOMO.

===AM1 neglected effects===
The semi-empirical AM1 method has a few setbacks which effects the accuracy of the calculations. The AM1 greatly underestimates the barrier of bond rotation with partial double bond character and predicts alkyl groups to be more stable than reality. The calculated hydrogen bond strength is close to experimental results, but the geometry of the hydrogen bonds is often misrepresented. Van der Waals interactions are also poorly predicted. This could provide an explanation to why the secondary orbital effect is not observed in the HOMO of the endo transition structure.

Rep:Mod:gck12

2015-02-26T19:53:51Z

Gck12: /* Cycloaddition of cyclohexa-1,3-diene with maleic anhydride */

Rep:Mod:gck12

2015-02-26T19:53:41Z

Gck12: /* Cycloaddition of cyclohexa-1,3-diene with maleic anhydride */

Rep:Mod:gck12

2015-02-26T19:53:25Z

Gck12: /* Cycloaddition of cyclohexa-1,3-diene with maleic anhydride */