ChemWiki - User contributions [en]

Rep:Title=Mod:SSH214ts

2017-03-23T19:50:33Z

Ssh214: /* Conclusion: */

==Introduction==

[4+2] cycloaddition reactions between diene and dienophile occur via a concerted mechanism. The transition state is cyclic in nature. 2pi bonds are broken to form to new sigma bonds and one new pi bond. Woodward Hoffman rule is applied to check whether the reactions are thermally allowed. Reactions between the HOMO of the diene and the LUMO of the dienophile is known as normal electron demand, whereas when the LUMO of the diene reacts with the HOMO of the dienophile, it is known as inverse electron demand. This experiment shows the effect on orbitals and transition state state energy as electron withdrawing and donationg groups are altered in the reactants, hence effecting the orbital overlaps in the reactions.
The activation energy of the reaction is the energy required to overcome the barrier to form products from reactants. It depends on a number of factors and can be estimated using the gaussview program. Once the transition state is optimised, the Intrinsic reaction Coordinate can be used to determine the activation energy of the reaction. As the reaction is concerted in nature, no intermediates are involved that makes the computational analysis much more simpler.

Transition state is known to be the maximum peak in a reaction coordinate graph. For this point, the second derivative is a negative value and the first derivative of the graph equation is 0. On the other hand, potential energy is the function of energy vs reaction coordinates. It has dimensions of 3N-6. All dimensions are found to be positive in Gaussian except the transition state. Hence there is a negative frequency in the results, which is an imaginary frequency due to the negative value of the secondary derivative.

Two methods used are SEMI EMPIRICAL PM6 and DFT/B3LYP. "Both method describes the quantum states of many electrron systems and solves the electronic degrees of freedom, using the born oppenheimer approximation, The Hartree-Fock method assumes that the many-electron wavefunction takes the form of a determinant of single-electron wavefunctions, called a Slater determinant. The problem associated with this, is that a general many-electron wavefunction cannot be stated as a single determinant. Hence, electronic correlation is not incorporated by Hartree-Fock methods and the follow-on energies tend to be too high. If the complete basis of single-electron wavefunctions is found, then the express exact many-electron wavefunction can be expressed as a linear combination of all possible determinants made of these wavefunctions. This is called Configuration interaction.

In density functional theory (DFT), the many-electron wavefunction is completely bypassed in favor of the electron density. Due to to the the Hohenberg-Kohn Theorems, the ground state energy of the system depends uniquely on the electron density, for example the total energy is a functional of the electron density. Therefore, the variational principle can be applied to reduce the energy with respect to the electron density. The problem with this technique is that the energy functional is not known. At the first level of approximation, the local density approximation (LDA) could be used, where it is assumed that the energy depends locally on the density in the same way it does for a uniform electron gas. Modern methods use generalized gradient approximations (GGAs) where the gradient of the density is taken into account to produce a more accurate functional. However, the exact energy function is still unknown and is a big open problem in computational chemistry and condensed matter physics.

Hartree-Fock and its descendants were considered more reliable than DFT, but this has changed recently as DFT techniques have become more refined. Moreover, whereas in Hartree-Fock type calculations, track must be kept of the spatial and spin coordinates of all NN electrons, DFT offers the potential benefit of dealing with only a single function of a single spatial coordinate. For this reason, DFT has been steadily gaining in popularity in recent years."<ref name="hi"/>

The method that was used in this experiment involved, starting from products, optimizing the structure, breaking the bonds that were formed in the transition states, freezing the atoms involved in bond forming, optimising the structure again and then carrying out the transition state analysis at semi-empirical PM6 for exercise 1 and 3 and DFT/B3LYP for exercise 2. Exercise 1 is the reaction between butadiene and ethene. Exercise 2 is the reaction between benzoquinine with cyclopentadiene and exercise 3 is the reaction between xylene with sulfur dioxide.

==Exercise 1:==
The [4+2] cycloaddition reaction between butene and diene is fairly simple for computational analysis. The reactants do not contain any electron withdrawing or electron donating groups, to lower the LUMO of the dienophile or raise the HOMO of the diene. Hence there is a large energy gap and poor orbital overlap between ethene and butadiene and hence poor reactivity. But the approach from any side will produce the same product.

[[File:ssh214_ex1_TS.jpg|thumb|'''Figure 1''': (reaction scheme of exercise 1).]]

'''C-C bondlengths'''
[[File:Ssh214_ts_ex1.jpg|thumb|'''Figure 2''': (carbon numbering).]]

<br>
{| class=”wikitable” border="1" cellpadding="5" cellspacing="0" align="center"
!C-C
!Bond lengths in reactant (Å)
!Type of bond
!Bond lengths in TS (Å)
!Bond length during reaction
!Bond lengths in product (Å)
!Type of bond
|-
|1,2
|1.33345
|sp<sup>2</sup>
|1.37975
|lengthening
|1.50031
|sp<sup>3</sup>
|-
|2,3
|1.47082
|sp<sup>3</sup>
|1.41114
|shortening
|1.33702
|sp<sup>2</sup>
|-
|3,4
|1.33344
|sp<sup>2</sup>
|1.37975
|lengthening
|1.50031
|sp<sup>3</sup>
|-
|4,5
|na
|2 x VdW
|2.11492
|shortening
|1.54008
|sp<sup>3</sup>
|-
|5,6
|1.32755
|sp<sup>2</sup>
|1.38178
|lengthening
|1.54089
|sp<sup>3</sup>
|-
|6,1
|na
|2 x VdW
|2.11435
|shortening
|1.54008
|sp<sup>3</sup>
|}
<br>

The table above summarizes the C-C distances as reactants form product. The C-C double bonds are shorter in length than C-C single bonds. Hence C2-C3 decreases in length as it changes from single to double bond. At the same time, the C1-C2 and C3-C4 length increases as it changes from double bond to single bond. The literature value for the vander waals radii of C is 1.70 A and 2 X VDW of C is 3.40 A. C1-C6 and C4-C5 are shorter than this value in the TS which indicates than there is bond formation. sp3 C-C = 1.57 A and sp2 C-C = 1.33 A.<ref name="yolo"/>

The formation of the two bonds are synchronous as the C1-C6 and C4-C5 have the same length in the TS. Both are forming sp3 bonds. Both sigma bonds are forming at the sane time in this concerted mechanism.

'''MO of ethene and butadiene and transition states:'''

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background:#808000;"|<b>Butadiene</b>
|-
! style="background: #808000;"|HOMO!!style="background: #808000;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo of ex1 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex1 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #808000;"| <b>Ethene</b>
|-
! style="background: #808000;"|HOMO!!style="background: #808000;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo_of_ex1.PNG]] || style="background: white;"|[[File:Ssh214homo of ex1.PNG]]
|}

[[File:Ssh214 mo again 1ex.PNG]]

The MOs of the orbitals have assigned symmetry labels 's' for symmetric and 'as' for antisymmetric. Only 's-s' or 'as-as' interactions are allowed and has a non-zero orbital overlap integral. Hence the orbitals that can interact are the HOMO of the butadiene and the LUMO of the ethane being both antisymmetric and the LUMO of the butadiene and the HOMO of the ethene being both symmetric. The other MOs don’t interact because of difference in symmetry labels or too differences in energy gap. For symmetric-antisymmetric interaction, orbital overlap integral is 0, for symmetric-symmetric interaction the integral is nonzero and for an antisymmetric-antisymmetric interaction it is also nonzero, according to the LCAO principle.

{| class="wikitable"
! MOs of the TS of the cycloaddition between ethene and butadiene
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 8; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
<title>MOs for the Diels Alder reaction</title>

<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}
|
|}

<jmol><jmolApplet>
<title>negative frequency=-948.81 cm-1</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 1</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

<jmol><jmolApplet>
<title>first positive frequency=145.12 cm-1</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 2</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC_ex1.PNG|left|'''IRC of exercise 1'''.]]

The animation shows the transition state scenario. A single negative frequency in results confirms the transition statte, which is further confirmed by the IRC. The IRC also confirmed that there were no intermediates or any other transition state involved. The activation energy is the height difference between the reactant and the TS. This determines whether the reaction is allowed or forbidden. Woodword Hoffman rules are used to determine the possibility of the reaction.

==Exercise 2:==

This exercise is less simpler than the previous exercise as the cycloaddition between benzoquinone and dioxole can form two possible products and hence two possible transition states are available now.The two possibilities are exo and endo. There is a difference in activation energy in both the exo and the endo states, as the approach trajectory is different and this leads to differences in orbital interactions.

'''MOs of reactants and transition states'''

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background: #8ADBF1;"|<b>diene</b>
|-
! style="background: #8ADBF1;"|HOMO!!style="background: #8ADBF1;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo ex2 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #8ADBF1;"| <b>dienophile</b>
|-
! style="background: #8ADBF1;"|HOMO!!style="background: #8ADBF1;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo ex2 dioxole.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 dioxole.PNG]]
|}

[[File:Ssh214ex2,_mos_wed.jpg]]

{| class="wikitable"
|
{| class="wikitable"
!Frontier MOs for the endo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ssh12121212121TSENDO.LOG</uploadedFileContents>
<name>endomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>endomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>endomo</target>
</jmolbutton>
</jmol>
|}
|

{| class="wikitable"
!Frontier MOs for the exo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSh214SUNDAYJMOLEX2_EXOTS.LOG</uploadedFileContents>
<name>exomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exomo</target>
</jmolbutton>
</jmol>
|}

|}

In this exercise, the dienophile has electron donating groups that raises the energy of both the HOMO and the LUMOs. On the other hand, the energy of the cyclohexadiene MOs stays fairly the same as there is no electron donating or accepting groups present. The energy gap between the HOMO of the dionophile and the LUMO of the diene is small enough to interact, resulting in an inverse electron demand Diels alder reaction.

'''Energy'''

{| class="wikitable" style="margin: 1em auto 1em auto;" style="text-align: center;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| +158.42
| -66.51
|-
| Exo
| 0
| +166.89
| -62.71
|}

"At room temperature, kinetic reaction control prevailed and the less stable endo isomer was the main reaction product. At higher temperatures and after long reaction times, the chemical equilibrium can assert itself and the thermodynamically more stable exo isomer can be formed. The exo product is more stable by virtue of a lower degree of steric congestion, while the endo product is favoured by orbital overlap in the transition state."<ref name="cgs"/>

The activation energy was calculated using energy results of reactants and transition states. The Ea of the endo product was found to be 8.47 kJ/mol lower than the exo product due to better orbital interactions in the TS.There is secondary orbital interaction in the endo prodcut that lowers the activation energy of the transition state and hence the endo product is more kinetically favored. The reaction energy of the endo product was more negative compared to the exo product, hence it was the thermodynamically favourable as well.

It can be seen that the HOMOs of the exo TS has mainly primary orbital overlap interactions. On the other hand, the HOMOs of the endo TS has secondary orbital interactions between the diene and the dienophile, that helps to lower the barrier energy.

==Exercise 3:==

In this exercise we examined the reaction between o-xylylene and sulphur dioxide. Three possible products, exo, endo and chelotropic reactions were determined. Presence of one negative frequency confirmed the accuracy of this state. The reaction pathways were concerted but not fully synchronous. The C bonding to the O was seen to be faster than bonding to S since being in period 2, C and O have similar sized orbitals and hence have better overlap. On the other hand, S which is in period 3, is much larger in size and have poorer orbital overlap.<ref name="scho"/>

[[File:Ssh214ex3diagram.PNG| (Reaction scheme for exercise 3).]]
{| class="wikitable" style="margin: 1em auto 1em auto;" style="text-align: left;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| +45.61
| -132.66
|-
| Exo
| 0
| +49.53
| -129.86
|-
| chelotropic
| 0
| +64.43
| -188.67
|}

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #808000;" |Energy path
|-
|style="background: white;" | [[File:Energy diagram ssh214.PNG]]
|}

It can be seen that the endo pathway is favoured as the activation energy involved is the least compared to the exo and chelotropic reactiions. This is for the same reason as better secondary orbital overlap interactions. The chelotropic product is likely to occur at higher temperatures since it has a higher activation energy.

The table below shows the animations of the three reactions and the IRC paths assocated with it.

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #935116;" |Chelotropic IRC path
|-
|style="background: white;" | [[File:SSH214_chelate_anime.gif]] || style="background: white;" | [[File:Ssh214_irc_chelotropic.PNG]]
|-
! colspan="2" style="text-align: center;" style="background: #E67E22;" | Exo IRC path
|-
|style="background: white;" | [[File:Ssh214_ex3_exo.gif]] || style="background: white;" | [[File:Ssh214 irc exo ex3.PNG]]
|-
!colspan="2" style="text-align: center;" style="background: #EDBB99;" | Endo IRC path
|-
|style="background: white;" | [[File:SSH214 ex3 IRC endo.gif]] || style="background: white;" | [[File:Ssh214_irc_endo_ex3.PNG]]
|}

[[File:Xylelene.PNG|thumb|left|: (Dimerisation of xylylene).]]

Xylylene can easily dimerise to form benzocyclobutene as seen in the figure to the left.

Xylylene is highly unstable.The energy of the product drops increasingly as it bonds top the 6 membered ring. This is due to the resonance gained by the delocalisation of the pi system.<ref name="uber"/>

==Conclusion:==

For all the three reactions, the transition states were figured out. The HOMO and the LUMO orbitals were investigated.The IRC confirmed no intermediates present in the reactions. In Exercise 1, the C-C was shorter than the Vander walls radii in the TS, which confirmed the forming of bond. In Exercise 2, the endo product was kinetically and thermodynamically favored over the exo product. In exercise 3, the xylylene can react with SO2 to form 5 different products, three of which were investigated. The chelotropic product was the least likely product to form among the three.

==References:==

<references>
<ref name="hi">www.quora.com/What-is-the-difference-between-density-functional-theory-and-hartree-fock</ref>
<ref name="yolo">https://en.wikipedia.org/wiki/Van_der_Waals_radius</ref>
<ref name="cgs">https://en.wikipedia.org/wiki/Thermodynamic_versus_kinetic_reaction_control</ref>
<ref name="scho">http://sciencenotes.org/periodic-table-chart-element-sizes/</ref>
<ref name="uber">https://en.wikipedia.org/wiki/Xylylene</ref>
<references>

2017-03-23T17:25:44Z

Ssh214:

==Introduction==

[4+2] cycloaddition reactions between diene and dienophile occur via a concerted mechanism. The transition state is cyclic in nature. 2pi bonds are broken to form to new sigma bonds and one new pi bond. Woodward Hoffman rule is applied to check whether the reactions are thermally allowed. Reactions between the HOMO of the diene and the LUMO of the dienophile is known as normal electron demand, whereas when the LUMO of the diene reacts with the HOMO of the dienophile, it is known as inverse electron demand. This experiment shows the effect on orbitals and transition state state energy as electron withdrawing and donationg groups are altered in the reactants, hence effecting the orbital overlaps in the reactions.
The activation energy of the reaction is the energy required to overcome the barrier to form products from reactants. It depends on a number of factors and can be estimated using the gaussview program. Once the transition state is optimised, the Intrinsic reaction Coordinate can be used to determine the activation energy of the reaction. As the reaction is concerted in nature, no intermediates are involved that makes the computational analysis much more simpler.

Transition state is known to be the maximum peak in a reaction coordinate graph. For this point, the second derivative is a negative value and the first derivative of the graph equation is 0. On the other hand, potential energy is the function of energy vs reaction coordinates. It has dimensions of 3N-6. All dimensions are found to be positive in Gaussian except the transition state. Hence there is a negative frequency in the results, which is an imaginary frequency due to the negative value of the secondary derivative.

Two methods used are SEMI EMPIRICAL PM6 and DFT/B3LYP. "Both method describes the quantum states of many electrron systems and solves the electronic degrees of freedom, using the born oppenheimer approximation, The Hartree-Fock method assumes that the many-electron wavefunction takes the form of a determinant of single-electron wavefunctions, called a Slater determinant. The problem associated with this, is that a general many-electron wavefunction cannot be stated as a single determinant. Hence, electronic correlation is not incorporated by Hartree-Fock methods and the follow-on energies tend to be too high. If the complete basis of single-electron wavefunctions is found, then the express exact many-electron wavefunction can be expressed as a linear combination of all possible determinants made of these wavefunctions. This is called Configuration interaction.

In density functional theory (DFT), the many-electron wavefunction is completely bypassed in favor of the electron density. Due to to the the Hohenberg-Kohn Theorems, the ground state energy of the system depends uniquely on the electron density, for example the total energy is a functional of the electron density. Therefore, the variational principle can be applied to reduce the energy with respect to the electron density. The problem with this technique is that the energy functional is not known. At the first level of approximation, the local density approximation (LDA) could be used, where it is assumed that the energy depends locally on the density in the same way it does for a uniform electron gas. Modern methods use generalized gradient approximations (GGAs) where the gradient of the density is taken into account to produce a more accurate functional. However, the exact energy function is still unknown and is a big open problem in computational chemistry and condensed matter physics.

Hartree-Fock and its descendants were considered more reliable than DFT, but this has changed recently as DFT techniques have become more refined. Moreover, whereas in Hartree-Fock type calculations, track must be kept of the spatial and spin coordinates of all NN electrons, DFT offers the potential benefit of dealing with only a single function of a single spatial coordinate. For this reason, DFT has been steadily gaining in popularity in recent years." [1]<ref name="hi"/>

The method that was used in this experiment involved, starting from products, optimizing the structure, breaking the bonds that were formed in the transition states, freezing the atoms involved in bond forming, optimising the structure again and then carrying out the transition state analysis at semi-empirical PM6 for exercise 1 and 3 and DFT/B3LYP for exercise 2. Exercise 1 is the reaction between butadiene and ethene. Exercise 2 is the reaction between benzoquinine with cyclopentadiene and exercise 3 is the reaction between xylene with sulfur dioxide.

==Exercise 1:==
The [4+2] cycloaddition reaction between butene and diene is fairly simple for computational analysis. The reactants do not contain any electron withdrawing or electron donating groups, to lower the LUMO of the dienophile or raise the HOMO of the diene. Hence there is a large energy gap and poor orbital overlap between ethene and butadiene and hence poor reactivity. But the approach from any side will produce the same product.

[[File:ssh214_ex1_TS.jpg|thumb|'''Figure 1''': (reaction scheme of exercise 1).]]

'''C-C bondlengths'''
[[File:Ssh214_ts_ex1.jpg|thumb|'''Figure 2''': (carbon numbering).]]

<br>
{| class=”wikitable” border="1" cellpadding="5" cellspacing="0" align="center"
!C-C
!Bond lengths in reactant (Å)
!Type of bond
!Bond lengths in TS (Å)
!Bond length during reaction
!Bond lengths in product (Å)
!Type of bond
|-
|1,2
|1.33345
|sp<sup>2</sup>
|1.37975
|lengthening
|1.50031
|sp<sup>3</sup>
|-
|2,3
|1.47082
|sp<sup>3</sup>
|1.41114
|shortening
|1.33702
|sp<sup>2</sup>
|-
|3,4
|1.33344
|sp<sup>2</sup>
|1.37975
|lengthening
|1.50031
|sp<sup>3</sup>
|-
|4,5
|na
|2 x VdW
|2.11492
|shortening
|1.54008
|sp<sup>3</sup>
|-
|5,6
|1.32755
|sp<sup>2</sup>
|1.38178
|lengthening
|1.54089
|sp<sup>3</sup>
|-
|6,1
|na
|2 x VdW
|2.11435
|shortening
|1.54008
|sp<sup>3</sup>
|}
<br>

The table above summarizes the C-C distances as reactants form product. The C-C double bonds are shorter in length than C-C single bonds. Hence C2-C3 decreases in length as it changes from single to double bond. At the same time, the C1-C2 and C3-C4 length increases as it changes from double bond to single bond. The literature value for the vander waals radii of C is 1.70 A and 2 X VDW of C is 3.40 A. C1-C6 and C4-C5 are shorter than this value in the TS which indicates than there is bond formation. sp3 C-C = 1.57 A and sp2 C-C = 1.33.<ref name="yolo"/>

The formation of the two bonds are synchronous as the C1-C6 and C4-C5 have the same length in the TS. Both are forming sp3 bonds. Both sigma bonds are forming at the sane time in this concerted mechanism.

'''MO of ethene and butadiene and transition states:'''

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background:#808000;"|<b>Butadiene</b>
|-
! style="background: #808000;"|HOMO!!style="background: #808000;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo of ex1 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex1 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #808000;"| <b>Ethene</b>
|-
! style="background: #808000;"|HOMO!!style="background: #808000;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo_of_ex1.PNG]] || style="background: white;"|[[File:Ssh214homo of ex1.PNG]]
|}

[[File:Ssh214 mo again 1ex.PNG]]

The MOs of the orbitals have assigned symmetry labels 's' for symmetric and 'as' for antisymmetric. Only 's-s' or 'as-as' interactions are allowed and has a non-zero orbital overlap integral. Hence the orbitals that can interact are the HOMO of the butadiene and the LUMO of the ethane being both antisymmetric and the LUMO of the butadiene and the HOMO of the ethene being both symmetric. The other MOs don’t interact because of difference in symmetry labels or too differences in energy gap. For symmetric-antisymmetric interaction, orbital overlap integral is 0, for symmetric-symmetric interaction the integral is nonzero and for an antisymmetric-antisymmetric interaction it is also nonzero, according to the LCAO principle.

{| class="wikitable"
! MOs of the TS of the cycloaddition between ethene and butadiene
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 8; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
<title>MOs for the Diels Alder reaction</title>

<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}
|
|}

<jmol><jmolApplet>
<title>negative frequency</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 1</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

<jmol><jmolApplet>
<title>first positive frequency</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 2</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC_ex1.PNG|left|'''IRC of exercise 1'''.]]

The animation shows the transition state scenario. A single negative frequency in results confirms the transition statte, which is further confirmed by the IRC. The IRC also confirmed that there were no intermediates or any other transition state involved. The activation energy is the height difference between the reactant and the TS. This determines whether the reaction is allowed or forbidden. Woodword Hoffman rules are used to determine the possibility of the reaction.

==Exercise 2:==

This exercise is less simpler than the previous exercise as the cycloaddition between benzoquinone and dioxole can form two possible products and hence two possible transition states are available now.The two possibilities are exo and endo. There is a difference in activation energy in both the exo and the endo states, as the approach trajectory is different and this leads to differences in orbital interactions.

'''MOs of reactants and transition states'''

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background: #8ADBF1;"|<b>diene</b>
|-
! style="background: #8ADBF1;"|HOMO!!style="background: #8ADBF1;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo ex2 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #8ADBF1;"| <b>dienophile</b>
|-
! style="background: #8ADBF1;"|HOMO!!style="background: #8ADBF1;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo ex2 dioxole.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 dioxole.PNG]]
|}

[[File:Ssh214ex2,_mos_wed.jpg]]

{| class="wikitable"
|
{| class="wikitable"
!Frontier MOs for the endo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ssh12121212121TSENDO.LOG</uploadedFileContents>
<name>endomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>endomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>endomo</target>
</jmolbutton>
</jmol>
|}
|

{| class="wikitable"
!Frontier MOs for the exo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSh214SUNDAYJMOLEX2_EXOTS.LOG</uploadedFileContents>
<name>exomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exomo</target>
</jmolbutton>
</jmol>
|}

|}

In this exercise, the dienophile has electron donating groups that raises the energy of both the HOMO and the LUMOs. On the other hand, the energy of the cyclohexadiene MOs stays fairly the same as there is no electron donating or accepting groups present. The energy gap between the HOMO of the dionophile and the LUMO of the diene is small enough to interact, resulting in an inverse electron demand Diels alder reaction.

'''Energy'''

{| class="wikitable" style="margin: 1em auto 1em auto;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| 158.42
| -66.51
|-
| Exo
| 0
| 166.89
| -62.71
|}

"At room temperature, kinetic reaction control prevailed and the less stable endo isomer was the main reaction product. At higher temperatures and after long reaction times, the chemical equilibrium can assert itself and the thermodynamically more stable exo isomer can be formed. The exo product is more stable by virtue of a lower degree of steric congestion, while the endo product is favoured by orbital overlap in the transition state."<ref name="cgs"/>

The activation energy was calculated using energy results of reactants and transition states. The Ea of the endo product was found to be 8.47 kJ/mol lower than the exo product due to better orbital interactions in the TS.There is secondary orbital interaction in the endo prodcut that lowers the activation energy of the transition state and hence the endo product is more kinetically favored. The reaction energy of the endo product was more negative compared to the exo product, hence it was the thermodynamically favourable as well.

It can be seen that the HOMOs of the exo TS has mainly primary orbital overlap interactions. On the other hand, the HOMOs of the endo TS has secondary orbital interactions between the diene and the dienophile, that helps to lower the barrier energy.

==Exercise 3:==

In this exercise we examined the reaction between o-xylylene and sulphur dioxide. Three possible products, exo, endo and chelotropic reactions were determined. Presence of one negative frequency confirmed the accuracy of this state. The reaction pathways were concerted but not fully synchronous. The C bonding to the O was seen to be faster than bonding to S since being in period 2, C and O have similar sized orbitals and hence have better overlap. On the other hand, S which is in period 3, is much larger in size and have poorer orbital overlap.<ref name="scho"/>

[[File:Ssh214ex3diagram.PNG| (Reaction scheme for exercise 3).]]

{| class="wikitable" style="margin: 1em auto 1em auto;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| 45.61
| -132.66
|-
| Exo
| 0
| 49.53
| -129.86
|-
| chelotropic
| 0
| 64.43
| -188.67
|}

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #808000;" |Energy path
|-
|style="background: white;" | [[File:Energy diagram ssh214.PNG]]]
|}

It can be seen that the endo pathway is favoured as the activation energy involved is the least compared to the exo and xhelotropiuc reactiions. This is for the same reason as better secondary orbital overlap interactions. The chelotropic product is likely to occur at higher temperatures since it has higher activation energy.

The table below shows the animations of the three reactions and the IRC paths assocated with it.

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #935116;" |Cheletropic IRC path
|-
|style="background: white;" | [[File:SSH214_chelate_anime.gif]] || style="background: white;" | [[File:Ssh214_irc_chelotropic.PNG]]
|-
! colspan="2" style="text-align: center;" style="background: #E67E22;" | Exo IRC path
|-
|style="background: white;" | [[File:Ssh214_ex3_exo.gif]] || style="background: white;" | [[File:Ssh214 irc exo ex3.PNG]]
|-
!colspan="2" style="text-align: center;" style="background: #EDBB99;" | Endo IRC path
|-
|style="background: white;" | [[File:SSH214 ex3 IRC endo.gif]] || style="background: white;" | [[File:Ssh214_irc_endo_ex3.PNG]]
|}

[[File:Xylelene.PNG|thumb|left|: (Dimerisation of xylylene).]]
Xylene can easily dimerise to form benzocyclobutene as seen in the figure to the left.

Xylylene is highly unstable.The energy of the product drops increasingly as it bonds top the 6 membered ring, due to the resonance gained by the delocalisation of the pi system.<ref name="uber"/>

==Conclusion:==
For all the three reactions, the transition states were figured out. The HOMO and the LUMO orbitals were investigated.The IRC confirmed no intermediates present in the reactions. In Exercise 1, the C-C was shorter than the Vander walls radii in the TS, which confirmed the forming of bond. In Exercise 2, the endo product was kinetically and thermodynamically favored over the exo product. In exercise 3, the xylelene can react with SO2 to form 5 different products, three of which were investigated. The chelotropic product was the least likely product to form among the three.

==References:==

<references>
<ref name="hi">www.quora.com/What-is-the-difference-between-density-functional-theory-and-hartree-fock</ref>
<ref name="yolo">https://en.wikipedia.org/wiki/Van_der_Waals_radius</ref>
<ref name="cgs">https://en.wikipedia.org/wiki/Thermodynamic_versus_kinetic_reaction_control</ref>
<ref name="scho">http://sciencenotes.org/periodic-table-chart-element-sizes/</ref>
<ref name="uber">https://en.wikipedia.org/wiki/Xylylene</ref>
<references>

File:Ssh214 mo again 1ex.PNG

2017-03-23T17:24:48Z

Ssh214:

File:Ssh214mo of ex1.PNG

2017-03-23T17:22:55Z

Ssh214: Ssh214 uploaded a new version of File:Ssh214mo of ex1.PNG

2017-03-22T20:21:59Z

Ssh214:

Rep:Title=Mod:SSH214ts

2017-03-22T19:57:23Z

Ssh214:

File:Ssh214ex2, mos wed.jpg

2017-03-22T19:49:13Z

Ssh214:

File:Ssh214ex2, mos wed.cdx

2017-03-22T19:45:37Z

Ssh214:

Rep:Title=Mod:SSH214ts

2017-03-22T19:40:25Z

Ssh214:

==Introduction==
Transition state is the maximum peak in a reaction coordinate graph. For this point, the second derivative is a negative value and the first derivative of the graph equation is 0. Potential energy is the function of energy vs every coordinates. It has dimensions of 3N-6. All dimensions are found to be positive in Gaussian except the transition state. Hence there is a negative frequency in the results, which is an imaginary frequency due to the negative value of the secondary derivative.

[4+2] cycloaddition reactions between diene and dienophile occur via a concerted mechanism. The transition state is cyclic in nature. 2pi bonds are broken to form to new sigma bonds and one new pi bond. The driving force of the reaction is the pi bonds breaking, as it releases large amounts of energy. Woodward Hoffman rule is applied to check whether the reactions are thermally allowed. Reactions between the HOMO of the diene and the Lumo of the dienophile is known as normal electron demand, whereas when the LUMO of the diene reacts with the HOMO of the dienophile, it is known as inverse electron demand. . This experiment shows the effect on orbitals and ts state energy as electron withdrawing and donationg groups are altered in the reactants, hence effecting the orbital overlaps in the reactions.
The activation energy of the reaction is the energy required to overcome the barrier to form products from reactants. It depends on a number of factors and can be estimated using the gaussview program. Once the transition state is optimised, the Intrinsic reaction Coordinate can be used to determine te activation energy of the reaction. As the reaction is concerted in nature, no intermediates are involved that makes the computational analysis much more simpler.

Two methods used are SEMI EMPIRICAL PM6 and DFT/B3LYP. 'Both method describes the quantum states of many electrron systems and use the born oppenheimer approximation, which solves the electronic degrees of freedom. The Hartree-Fock method assumes that the many-electron wavefunction takes the form of a determinant of single-electron wavefunctions, called a Slater determinant. The problem with this assumption is that a general many-electron wavefunction cannot be expressed as a single determinant. As a result, Hartree-Fock methods do not fully incorporate electronic correlation and the resulting energies tend to be too high. Luckily, if you find a complete basis of single-electron wavefunctions, then you can (in principle) express the exact many-electron wavefunction as a linear combination of all possible determinants made of these wavefunctions. This is called Configuration interaction. There are also many more post-Hartree-Fock techniques which expand on this.

In density functional theory (DFT), the many-electron wavefunction is completely bypassed in favor of the electron density. Thanks to the the Hohenberg-Kohn Theorems, the ground state energy of the system depends uniquely on the electron density, i.e. the total energy is a functional of the electron density. Therefore, one can apply the variational principle to minimize the energy with respect to the electron density. The problem with this technique is that no one knows what the energy functional is. At the first level of approximation, one can use the local density approximation (LDA), where you assume that the energy depends locally on the density in the same way it does for a uniform electron gas. Modern methods use generalized gradient approximations (GGAs) where you take into account the gradient of the density to produce a more accurate functional. However, the exact energy functional is still unknown and is a big open problem in computational chemistry and condensed matter physics.'

Traditionally, Hartree-Fock and its descendants were considered more reliable than DFT, but this has been changing recently as DFT techniques have become more refined. Moreover, whereas in Hartree-Fock type calculations you need to keep track of the spatial and spin coordinates of all NN electrons, DFT offers the potential benefit of dealing with only a single function of a single spatial coordinate. For this reason, DFT has been steadily gaining in popularity.

The method that was used in this experiment involved, starting from products, optimizing the structure, breaking the bonds that were formed in the transition states, freezing the atoms involved in bond forming, optimising the structure again and then carrying out the transition state analysis. Ex1 is the reaction between butadiene and ethene. Ex2 is the reaction between benzoquinine with cyclopentadiene and. ex 3 is the reaction between xylene with sulfur dioxide.

==Exercise 1:==
The [4+2] cycloaddition reaction between butene and diene is fairly simple for computational analysis. The reactants do not contain any electron withdrawing or electron donating groups, to lower the LUMO of the dienophile or raise the HOMO of the diene. Hence there is a large energy gap and poor orbital overlap between ethene and butadiene and hence poor reactivity.

Chemdraw diagram:

[[File:ssh214_ex1_TS.jpg|thumb|'''Figure 1''': (caption).]]

C-C bondlengths
[[File:Ssh214_ts_ex1.jpg|thumb|'''Figure 1''': (caption).]]

<br>
{| class=”wikitable” border="1" cellpadding="5" cellspacing="0" align="center"
!C-C
!Bond lengths in reactant (Å)
!Type of bond
!Bond lengths in TS (Å)
!Bond length during reaction
!Bond lengths in product (Å)
!Type of bond
|-
|1,2
|1.33633
|sp<sup>2</sup>
|1.37881
|lengthening
|1.51201
|sp<sup>3</sup>
|-
|2,3
|1.49571
|sp<sup>3</sup>
|1.34521
|shortening
|1.35421
|sp<sup>2</sup>
|-
|3,4
|1.36789
|sp<sup>2</sup>
|1.38932
|lengthening
|1.505432
|sp<sup>3</sup>
|-
|4,5
|3.41432
|2 x VdW
|2.11462
|shortening
|1.54044
|sp<sup>3</sup>
|-
|5,6
|1.32737
|sp<sup>2</sup>
|1.38179
|lengthening
|1.54094
|sp<sup>3</sup>
|-
|6,1
|3.41427
|2 x VdW
|2.11463
|shortening
|1.54046
|sp<sup>3</sup>
|}
<br>

The table above summarizes the C-C distances as reactants form product. The C-C double bonds are shorter in length than C-C single bonds. Hence C2-C3 decreases iin length as it changes fromk single to double bond. At the same time, the C1-C2 and C3-C4 lenth increases asn it changes from double bomnd to single bond. The literature value VDR of C is 1.70 A and 2 X VDW of C is 3.40 A. C1-C6 and C4-C5 are shorter than this value in the TS which indicates than there is bond formation. sp3 C-C = 1.57 A and sp2 C-C = 1.33.

The formation of the two bonds are synchronous as the C1-C6 and C4-C5 have the same length in the TS. Both are forming sp3 bonds. Both sigma bonds are forming at the sane time in this concerted mechanism.

MO diagram:
The MOs of the orbitals have assigned symmetry labels 'g' or 'u' depending on whether they are symmetrical or unsymmetrical withy respect to inversion. Only 'g-g' or 'u-u' interactions are allowed and has a non-zero orbital overlap integral. Hence the orbitals that can interact are the HOMO of the butadiene and the LUMO of the ethane of ‘u’ symmetry and the LUMO of the butadiene and the HOMO of the ethane of ‘g’ symmetry. The other MOs don’t interact because of large energy gap or difference in symmetry labels.

MO of ethene and butadiene:

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background: #38A5A5;"|<b>Butadiene</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo of ex1 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex1 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #38A5A5;"| <b>Ethene</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo_of_ex1.PNG]] || style="background: white;"|[[File:Ssh214homo of ex1.PNG]]
|}

[[File:Ssh214mo of ex1.PNG]]

{| class="wikitable"
! MOs of the TS of the cycloaddition between ethene and butadiene
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 8; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
<title>MOs for the Diels Alder reaction</title>

<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}
|
|}

<jmol><jmolApplet>
<title>MO18</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 1</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

<jmol><jmolApplet>
<title>MO18</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 2</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC_ex1.PNG|thumb|'''Figure 1''': (caption).]]

The animation shows the transition state scenario. A single negative frequency in results confirms the transition statte, which is further confirmed by the IRC.the IRC also confirmed that there were no intermediates or any other transition state involved. The activation energy is the height difference between the reactant and the TS. This determines whether the reaction is allowed or forbidden. Woodword Hoffman rules are used to determine the possibility of the reaction.

==Exercise 2:==

This exercise is less simpler than the previous exercise as the cycloaddition between benzoquinone and diene can form two possibole products and hence two possible transition states are available now.The two posibilities are exo and endo. There is a difference in activation energy in both the exo and the endo states, as the approach trajectory is different and this leads to differences in orbital interactions.

Reaction mechanism:

MO diagrams:

In this exercise, the dienophile has electron donating groups that raises the energy of both the HOIMO and the LUMOs. On the other hand, the energy of the cyclohexadiene MOs stays fairly the same as there is no electron donating or accepting groups present. The energy gap between the HOMO of the dionophile and the LUMO of the diene is small enough to interact, resulting in an inverse electron demand Diels alder reaction.

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background: #38A5A5;"|<b>diene</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo ex2 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #38A5A5;"| <b>dienophile</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo ex2 dioxole.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 dioxole.PNG]]
|}

SSH214ENDO_FINAL_SUNDAYex2.LOG

{| class="wikitable"
|
{| class="wikitable"
!Frontier MOs for the endo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ssh12121212121TSENDO.LOG</uploadedFileContents>
<name>endomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>endomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>endomo</target>
</jmolbutton>
</jmol>
|}
|

{| class="wikitable"
!Frontier MOs for the exo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSh214SUNDAYJMOLEX2_EXOTS.LOG</uploadedFileContents>
<name>exomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exomo</target>
</jmolbutton>
</jmol>
|}

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| 158.42
| -66.51
|-
| Exo
| 0
| 166.89
| -62.71
|}

At room temperature, kinetic reaction control prevails and the less stable endo isomer is the main reaction product. At higher temperatures and after long reaction times, the chemical equilibrium can assert itself and the thermodynamically more stable exo isomer is formed. The exo product is more stable by virtue of a lower degree of steric congestion, while the endo product is favoured by orbital overlap in the transition state.

The activation energy was calculated using energy results of reactants and transition states. The Ea of he endo product was found to be lower 8.47 kJ/mol lower than the exo product due to better orbital interactions in the TS.There is secondary orbital interaction in the endo prodcut that lowers the ea of the transition state. The endo product is more kinetically favored whereas the exo product is more thermodynamically favoured.

==Exercise 3:==

In this exercise we examined the reaction between o-xylene and sulphur dioxide. Three possible products, exo, endo and chelotropic reactions were determined. Vibrational frequency analysis was carried out using the semi empirical pm6 method. presence of one negative frequency confirmed the accuracy of this state. The reaction pathways were concerted but not fully synchronous. The C bonding to the O was seen to be faster than bonding to S since being in period 2, C and O have similar sized orbitals and hence have better overlap. On the other hand, S which is in period 3, is much larger in size and have poorer orbital overlap. Hence the chelotropic reaction is less likely to occur.

[[File:Ssh214ex3diagram.PNG|thumb|'''Figure 1''': (caption).]]

{| class="wikitable" style="margin: 1em auto 1em auto;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| 45.61
| -132.66
|-
| Exo
| 0
| 49.53
| -129.86
|-
| chelotropic
| 0
| 64.43
| -188.67
|}

It can be seen that the endo pathway is favoured as the activation energy involved is the least compared to the exo and xhelotropiuc reactiions. This is for the same reason as better secondary orbital overlap interactions. The chelotropic product is likely to occur at higher temperatures since it has higher activation energy.

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #808000;" |Energy path
|-
|style="background: white;" | [[File:Energy_2_ssh214.PNG]] || style="background: white;" | [[File:Energy diagram ssh214.PNG]]
|}

IRC

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #F6F33E;" |Cheletropic IRC path
|-
|style="background: white;" | [[File:SSH214_chelate_anime.gif]] || style="background: white;" | [[File:Ssh214_irc_chelotropic.PNG]]
|-
! colspan="2" style="text-align: center;" style="background: #F63EF0;" | Exo IRC path
|-
|style="background: white;" | [[File:Ssh214_ex3_exo.gif]] || style="background: white;" | [[File:Ssh214 irc exo ex3.PNG]]
|-
!colspan="2" style="text-align: center;" style="background: #8ADBF1;" | Endo IRC path
|-
|style="background: white;" | [[File:SSH214 ex3 IRC endo.gif]] || style="background: white;" | [[File:Ssh214_irc_endo_ex3.PNG]]
|}

[[File:Xylelene.PNG|thumb|left|'''Figure 1''': (caption).]]
Xylene can easily dimerise to form benzocyclobutene as seen in the figure to the left.

Xylylene is highly unstable.The energy of the product drops increasinly as it bonds top the 6 membered ring, due to the resonance gained by the delocalisation of the pi system.

File:Ssh214mo of ex1.PNG

2017-03-22T19:35:39Z

Ssh214:

Rep:Title=Mod:SSH214ts

2017-03-22T19:27:04Z

Ssh214:

==Introduction==
Transition state is the maximum peak in a reaction coordinate graph. For this point, the second derivative is a negative value and the first derivative of the graph equation is 0. Potential energy is the function of energy vs every coordinates. It has dimensions of 3N-6. All dimensions are found to be positive in Gaussian except the transition state. Hence there is a negative frequency in the results, which is an imaginary frequency due to the negative value of the secondary derivative.

[4+2] cycloaddition reactions between diene and dienophile occur via a concerted mechanism. The transition state is cyclic in nature. 2pi bonds are broken to form to new sigma bonds and one new pi bond. The driving force of the reaction is the pi bonds breaking, as it releases large amounts of energy. Woodward Hoffman rule is applied to check whether the reactions are thermally allowed. Reactions between the HOMO of the diene and the Lumo of the dienophile is known as normal electron demand, whereas when the LUMO of the diene reacts with the HOMO of the dienophile, it is known as inverse electron demand. . This experiment shows the effect on orbitals and ts state energy as electron withdrawing and donationg groups are altered in the reactants, hence effecting the orbital overlaps in the reactions.
The activation energy of the reaction is the energy required to overcome the barrier to form products from reactants. It depends on a number of factors and can be estimated using the gaussview program. Once the transition state is optimised, the Intrinsic reaction Coordinate can be used to determine te activation energy of the reaction. As the reaction is concerted in nature, no intermediates are involved that makes the computational analysis much more simpler.

Two methods used are SEMI EMPIRICAL PM6 and DFT/B3LYP. 'Both method describes the quantum states of many electrron systems and use the born oppenheimer approximation, which solves the electronic degrees of freedom. The Hartree-Fock method assumes that the many-electron wavefunction takes the form of a determinant of single-electron wavefunctions, called a Slater determinant. The problem with this assumption is that a general many-electron wavefunction cannot be expressed as a single determinant. As a result, Hartree-Fock methods do not fully incorporate electronic correlation and the resulting energies tend to be too high. Luckily, if you find a complete basis of single-electron wavefunctions, then you can (in principle) express the exact many-electron wavefunction as a linear combination of all possible determinants made of these wavefunctions. This is called Configuration interaction. There are also many more post-Hartree-Fock techniques which expand on this.

In density functional theory (DFT), the many-electron wavefunction is completely bypassed in favor of the electron density. Thanks to the the Hohenberg-Kohn Theorems, the ground state energy of the system depends uniquely on the electron density, i.e. the total energy is a functional of the electron density. Therefore, one can apply the variational principle to minimize the energy with respect to the electron density. The problem with this technique is that no one knows what the energy functional is. At the first level of approximation, one can use the local density approximation (LDA), where you assume that the energy depends locally on the density in the same way it does for a uniform electron gas. Modern methods use generalized gradient approximations (GGAs) where you take into account the gradient of the density to produce a more accurate functional. However, the exact energy functional is still unknown and is a big open problem in computational chemistry and condensed matter physics.'

Traditionally, Hartree-Fock and its descendants were considered more reliable than DFT, but this has been changing recently as DFT techniques have become more refined. Moreover, whereas in Hartree-Fock type calculations you need to keep track of the spatial and spin coordinates of all NN electrons, DFT offers the potential benefit of dealing with only a single function of a single spatial coordinate. For this reason, DFT has been steadily gaining in popularity.

The method that was used in this experiment involved, starting from products, optimizing the structure, breaking the bonds that were formed in the transition states, freezing the atoms involved in bond forming, optimising the structure again and then carrying out the transition state analysis. Ex1 is the reaction between butadiene and ethene. Ex2 is the reaction between benzoquinine with cyclopentadiene and. ex 3 is the reaction between xylene with sulfur dioxide.

==Exercise 1:==
The [4+2] cycloaddition reaction between butene and diene is fairly simple for computational analysis. The reactants do not contain any electron withdrawing or electron donating groups, to lower the LUMO of the dienophile or raise the HOMO of the diene. Hence there is a large energy gap and poor orbital overlap between ethene and butadiene and hence poor reactivity.

Chemdraw diagram:

[[File:ssh214_ex1_TS.jpg|thumb|'''Figure 1''': (caption).]]

C-C bondlengths
[[File:Ssh214_ts_ex1.jpg|thumb|'''Figure 1''': (caption).]]

<br>
{| class=”wikitable” border="1" cellpadding="5" cellspacing="0" align="center"
!C-C
!Bond lengths in reactant (Å)
!Type of bond
!Bond lengths in TS (Å)
!Bond length during reaction
!Bond lengths in product (Å)
!Type of bond
|-
|1,2
|1.33633
|sp<sup>2</sup>
|1.37881
|lengthening
|1.51201
|sp<sup>3</sup>
|-
|2,3
|1.49571
|sp<sup>3</sup>
|1.34521
|shortening
|1.35421
|sp<sup>2</sup>
|-
|3,4
|1.36789
|sp<sup>2</sup>
|1.38932
|lengthening
|1.505432
|sp<sup>3</sup>
|-
|4,5
|3.41432
|2 x VdW
|2.11462
|shortening
|1.54044
|sp<sup>3</sup>
|-
|5,6
|1.32737
|sp<sup>2</sup>
|1.38179
|lengthening
|1.54094
|sp<sup>3</sup>
|-
|6,1
|3.41427
|2 x VdW
|2.11463
|shortening
|1.54046
|sp<sup>3</sup>
|}
<br>

The table above summarizes the C-C distances as reactants form product. The C-C double bonds are shorter in length than C-C single bonds. Hence C2-C3 decreases iin length as it changes fromk single to double bond. At the same time, the C1-C2 and C3-C4 lenth increases asn it changes from double bomnd to single bond. The literature value VDR of C is 1.70 A and 2 X VDW of C is 3.40 A. C1-C6 and C4-C5 are shorter than this value in the TS which indicates than there is bond formation. sp3 C-C = 1.57 A and sp2 C-C = 1.33.

The formation of the two bonds are synchronous as the C1-C6 and C4-C5 have the same length in the TS. Both are forming sp3 bonds. Both sigma bonds are forming at the sane time in this concerted mechanism.

MO diagram:
The MOs of the orbitals have assigned symmetry labels 'g' or 'u' depending on whether they are symmetrical or unsymmetrical withy respect to inversion. Only 'g-g' or 'u-u' interactions are allowed and has a non-zero orbital overlap integral. Hence the orbitals that can interact are the HOMO of the butadiene and the LUMO of the ethane of ‘u’ symmetry and the LUMO of the butadiene and the HOMO of the ethane of ‘g’ symmetry. The other MOs don’t interact because of large energy gap or difference in symmetry labels.

MO of ethene and butadiene:

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background: #38A5A5;"|<b>Butadiene</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo of ex1 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex1 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #38A5A5;"| <b>Ethene</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo_of_ex1.PNG]] || style="background: white;"|[[File:Ssh214homo of ex1.PNG]]
|}

{| class="wikitable"
! MOs of the TS of the cycloaddition between ethene and butadiene
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 8; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
<title>MOs for the Diels Alder reaction</title>

<name>TSMOs</name>
</jmolApplet>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 16</script>
<text>HOMO-1</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 17</script>
<text>HOMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 18</script>
<text>LUMO</text>
<target>TSMOs</target>
</jmolbutton>
<jmolbutton>
<script>mo 19</script>
<text>LUMO+1</text>
<target>TSMOs</target>
</jmolbutton>
</jmol>
|}
|
|}

<jmol><jmolApplet>
<title>MO18</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 1</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

<jmol><jmolApplet>
<title>MO18</title>
<color>white</color>
<size>200</size>
<script>frame 9; vibration 2</script>
<uploadedFileContents>SSH214_SATURDAY TS.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC_ex1.PNG|thumb|'''Figure 1''': (caption).]]

The animation shows the transition state scenario. A single negative frequency in results confirms the transition statte, which is further confirmed by the IRC.the IRC also confirmed that there were no intermediates or any other transition state involved. The activation energy is the height difference between the reactant and the TS. This determines whether the reaction is allowed or forbidden. Woodword Hoffman rules are used to determine the possibility of the reaction.

==Exercise 2:==

This exercise is less simpler than the previous exercise as the cycloaddition between benzoquinone and diene can form two possibole products and hence two possible transition states are available now.The two posibilities are exo and endo. There is a difference in activation energy in both the exo and the endo states, as the approach trajectory is different and this leads to differences in orbital interactions.

Reaction mechanism:

MO diagrams:

In this exercise, the dienophile has electron donating groups that raises the energy of both the HOIMO and the LUMOs. On the other hand, the energy of the cyclohexadiene MOs stays fairly the same as there is no electron donating or accepting groups present. The energy gap between the HOMO of the dionophile and the LUMO of the diene is small enough to interact, resulting in an inverse electron demand Diels alder reaction.

{| class="wikitable" border="1"
|colspan="2" style="text-align: center;" style="background: #38A5A5;"|<b>diene</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
| style="background: white;"| [[File:Ssh214lumo ex2 diene.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 diene.PNG]]
|-
|colspan="2" style="text-align: center;" style="background: #38A5A5;"| <b>dienophile</b>
|-
! style="background: #EFECD9;"|HOMO!!style="background: #EFECD9;"| LUMO
|-
|style="background: white;"| [[File:Ssh214lumo ex2 dioxole.PNG]] || style="background: white;"|[[File:Ssh214homo ex2 dioxole.PNG]]
|}

SSH214ENDO_FINAL_SUNDAYex2.LOG

{| class="wikitable"
|
{| class="wikitable"
!Frontier MOs for the endo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Ssh12121212121TSENDO.LOG</uploadedFileContents>
<name>endomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>endomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>endomo</target>
</jmolbutton>
</jmol>
|}
|

{| class="wikitable"
!Frontier MOs for the exo TS
|-
|
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>SSh214SUNDAYJMOLEX2_EXOTS.LOG</uploadedFileContents>
<name>exomo</name>
</jmolApplet>
<jmolbutton>
<script>mo 41</script>
<text>HOMO</text>
<target>exomo</target>
</jmolbutton>
<jmolbutton>
<script>mo 42</script>
<text>LUMO</text>
<target>exomo</target>
</jmolbutton>
</jmol>
|}

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| 158.42
| -66.51
|-
| Exo
| 0
| 166.89
| -62.71
|}

At room temperature, kinetic reaction control prevails and the less stable endo isomer is the main reaction product. At higher temperatures and after long reaction times, the chemical equilibrium can assert itself and the thermodynamically more stable exo isomer is formed. The exo product is more stable by virtue of a lower degree of steric congestion, while the endo product is favoured by orbital overlap in the transition state.

The activation energy was calculated using energy results of reactants and transition states. The Ea of he endo product was found to be lower 8.47 kJ/mol lower than the exo product due to better orbital interactions in the TS.There is secondary orbital interaction in the endo prodcut that lowers the ea of the transition state. The endo product is more kinetically favored whereas the exo product is more thermodynamically favoured.

==Exercise 3:==

In this exercise we examined the reaction between o-xylene and sulphur dioxide. Three possible products, exo, endo and chelotropic reactions were determined. Vibrational frequency analysis was carried out using the semi empirical pm6 method. presence of one negative frequency confirmed the accuracy of this state. The reaction pathways were concerted but not fully synchronous. The C bonding to the O was seen to be faster than bonding to S since being in period 2, C and O have similar sized orbitals and hence have better overlap. On the other hand, S which is in period 3, is much larger in size and have poorer orbital overlap. Hence the chelotropic reaction is less likely to occur.

[[File:Ssh214ex3diagram.PNG|thumb|'''Figure 1''': (caption).]]

{| class="wikitable" style="margin: 1em auto 1em auto;"

! style="font-weight: bold;" | TS
! style="font-weight: bold;" | Energy of reactants (kJ/mol)
! style="font-weight: bold;" | Energy of TS (kJ/mol)
! style="font-weight: bold;" | Energy of the product (kJ/mol)

|-
| Endo
| 0
| 45.61
| -132.66
|-
| Exo
| 0
| 49.53
| -129.86
|-
| chelotropic
| 0
| 64.43
| -188.67
|}

It can be seen that the endo pathway is favoured as the activation energy involved is the least compared to the exo and xhelotropiuc reactiions. This is for the same reason as better secondary orbital overlap interactions. The chelotropic product is likely to occur at higher temperatures since it has higher activation energy.

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #808000;" |Energy path
|-
|style="background: white;" | [[File:Energy_2_ssh214.PNG]] || style="background: white;" | [[File:Energy diagram ssh214.PNG]]
|}

IRC

{| class="wikitable" border="1"
! colspan="2" style="text-align: center;" style="background: #F6F33E;" |Cheletropic IRC path
|-
|style="background: white;" | [[File:SSH214_chelate_anime.gif]] || style="background: white;" | [[File:Ssh214_irc_chelotropic.PNG]]
|-
! colspan="2" style="text-align: center;" style="background: #F63EF0;" | Exo IRC path
|-
|style="background: white;" | [[File:Ssh214_ex3_exo.gif]] || style="background: white;" | [[File:Ssh214 irc exo ex3.PNG]]
|-
!colspan="2" style="text-align: center;" style="background: #8ADBF1;" | Endo IRC path
|-
|style="background: white;" | [[File:SSH214 ex3 IRC endo.gif]] || style="background: white;" | [[File:Ssh214_irc_endo_ex3.PNG]]
|}

[[File:Xylelene.PNG|thumb|left|'''Figure 1''': (caption).]]
Xylene can easily dimerise to form benzocyclobutene as seen in the figure to the left.

Xylylene is highly unstable.The energy of the product drops increasinly as it bonds top the 6 membered ring, due to the resonance gained by the delocalisation of the pi system.